Finite Group Databasebeta

← #34058623

Subgroups — #34058623

Order 19072.

1152 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750359C211yesmaximal, characteristic, complemented
2#23750330C211yesmaximal, characteristic, complemented
3#23750323C211yesmaximal, characteristic, complemented
4#23750320C211yesmaximal, characteristic, complemented
5#23750320C211yesmaximal, characteristic, complemented
6#23750312C211yesmaximal, characteristic, complemented
7#23750303C211yesmaximal, characteristic, complemented
8#23750301C211yesmaximal, characteristic, complemented
9#23750301C211yesmaximal, characteristic, complemented
10#23750298C211yesmaximal, characteristic, complemented
11#23750273C211yesmaximal, characteristic, complemented
12#23750269C211yesmaximal, characteristic, complemented
13#23750267C211yesmaximal, characteristic, complemented
14#23750265C211yesmaximal, characteristic, complemented
15#23750265C211yesmaximal, characteristic, complemented
16D4×C22⋊D149C211yesmaximal, characteristic, complemented
17#23750243C211yesmaximal, characteristic, complemented
18#23750227C211yesmaximal, characteristic, complemented
19#23750222C211yesmaximal, characteristic, complemented
20#23750218C211yesmaximal, characteristic, complemented
21#23750213C211yesmaximal, characteristic, complemented
22#23750211C211yesmaximal, characteristic, complemented
23#23750152C211yesmaximal, characteristic, complemented
24#23750152C211yesmaximal, characteristic, complemented
25#23750136C211yesmaximal, characteristic, complemented
26#23750133C211yesmaximal, characteristic, complemented
27#123×D149C211yesmaximal, characteristic, complemented
28#23750106C211yesmaximal, characteristic, complemented
29#23750098C211yesmaximal, characteristic, complemented
30C2×C4×C22⋊D149C211yesmaximal, characteristic, complemented
31C2×#123×C149C211yesmaximal, characteristic, complemented
32C2×#14558736C2211yescharacteristic
33C2×#14558736C2211yescharacteristic, complemented
34C2×#14558735C2211yescharacteristic, complemented
35C22×C22⋊D149C2211yescharacteristic
36C22×C22⋊D149C2211yescharacteristic
37C2×D4×D149C2211yescharacteristic
38C22×C4×D149C2211yescharacteristic, complemented
39#18011910C2211yescharacteristic, complemented
40#18011907C2211yescharacteristic
41#18011906C2211yescharacteristic, complemented
42#18011906C2211yescharacteristic, complemented
43#18011906C2211yescharacteristic, complemented
44#18011906C2211yescharacteristic, complemented
45#18011904C2211yescharacteristic, complemented
46#18011904C2211yescharacteristic, complemented
47#18011904C2211yescharacteristic, complemented
48#18011904C2211yescharacteristic, complemented
49#18011904C2211yescharacteristic, complemented
50#18011904C2211yescharacteristic, complemented
51#18011902C2211yescharacteristic, complemented
52#18011901C2211yescharacteristic, complemented
53#18011901C2211yescharacteristic, complemented
54#18011901C2211yescharacteristic, complemented
55#18011901C2211yescharacteristic, complemented
56#18011898C2211yescharacteristic, complemented
57#18011897C2211yescharacteristic, complemented
58#18011897C2211yescharacteristic, complemented
59#18011897C2211yescharacteristic, complemented
60#18011897C2211yescharacteristic, complemented
61#18011897C2211yescharacteristic, complemented
62#18011897C2211yescharacteristic, complemented
63#18011896C2211yescharacteristic, complemented
64#18011896C2211yescharacteristic, complemented
65#18011896C2211yescharacteristic, complemented
66#18011896C2211yescharacteristic, complemented
67#18011895C2211yescharacteristic, complemented
68#18011895C2211yescharacteristic, complemented
69#18011894C2211yescharacteristic, complemented
70#18011894C2211yescharacteristic, complemented
71#18011894C2211yescharacteristic, complemented
72#18011894C2211yescharacteristic, complemented
73#18011893C2211yescharacteristic, complemented
74#18011893C2211yescharacteristic, complemented
75#18011893C2211yescharacteristic, complemented
76#18011893C2211yescharacteristic, complemented
77#18011893C2211yescharacteristic, complemented
78#18011893C2211yescharacteristic, complemented
79#18011892C2211yescharacteristic
80#18011892C2211yescharacteristic, complemented
81#18011891C2211yescharacteristic, complemented
82#18011890C2211yescharacteristic, complemented
83#18011890C2211yescharacteristic, complemented
84#18011890C2211yescharacteristic, complemented
85#18011890C2211yescharacteristic, complemented
86#18011889C2211yescharacteristic, complemented
87#18011889C2211yescharacteristic, complemented
88#18011889C2211yescharacteristic, complemented
89#18011889C2211yescharacteristic, complemented
90#18011888C2211yescharacteristic, complemented
91#18011888C2211yescharacteristic, complemented
92#18011888C2211yescharacteristic, complemented
93#18011888C2211yescharacteristic, complemented
94#18011886C2211yescharacteristic, complemented
95#18011885C2211yescharacteristic
96#18011885C2211yescharacteristic, complemented
97#18011885C2211yescharacteristic, complemented
98#18011885C2211yescharacteristic, complemented
99#18011884C2211yescharacteristic, complemented
100#18011884C2211yescharacteristic, complemented
101#18011884C2211yescharacteristic, complemented
102#18011884C2211yescharacteristic, complemented
103#18011884C2211yescharacteristic, complemented
104#18011884C2211yescharacteristic, complemented
105#18011883C2211yescharacteristic
106#18011883C2211yescharacteristic
107#18011883C2211yescharacteristic
108#18011883C2211yescharacteristic, complemented
109#18011882C2211yescharacteristic
110#18011882C2211yescharacteristic, complemented
111#18011881C2211yescharacteristic, complemented
112#18011881C2211yescharacteristic, complemented
113#18011880C2211yescharacteristic
114#18011880C2211yescharacteristic
115#18011880C2211yescharacteristic, complemented
116#18011880C2211yescharacteristic, complemented
117#18011879C2211yescharacteristic
118#18011879C2211yescharacteristic
119#18011876C2211yescharacteristic, complemented
120#18011876C2211yescharacteristic, complemented
121#18011876C2211yescharacteristic, complemented
122D4×Dic149C2211yescharacteristic
123D4×Dic149C2211yescharacteristic, complemented
124#18011873C2211yescharacteristic, complemented
125#18011873C2211yescharacteristic, complemented
126#18011873C2211yescharacteristic, complemented
127C4×C22⋊D149C2211yescharacteristic
128C4×C22⋊D149C2211yescharacteristic
129C4×C22⋊D149C2211yescharacteristic
130C4×C22⋊D149C2211yescharacteristic
131C4×C22⋊D149C2211yescharacteristic, complemented
132C4×C22⋊D149C2211yescharacteristic, complemented
133C4×C22⋊D149C2211yescharacteristic, complemented
134C4×C22⋊D149C2211yescharacteristic, complemented
135C4×C22⋊D149C2211yescharacteristic, complemented
136C4×C22⋊D149C2211yescharacteristic, complemented
137C4×C22⋊D149C2211yescharacteristic, complemented
138C4×C22⋊D149C2211yescharacteristic, complemented
139C4×C22⋊D149C2211yescharacteristic, complemented
140C4×C22⋊D149C2211yescharacteristic, complemented
141C4×C22⋊D149C2211yescharacteristic, complemented
142C4×C22⋊D149C2211yescharacteristic, complemented
143#18011871C2211yescharacteristic, complemented
144#18011871C2211yescharacteristic, complemented
145#18011871C2211yescharacteristic, complemented
146#18011871C2211yescharacteristic, complemented
147#18011871C2211yescharacteristic, complemented
148#18011871C2211yescharacteristic, complemented
149#18011871C2211yescharacteristic, complemented
150#18011871C2211yescharacteristic, complemented
151#18011870C2211yescharacteristic, complemented
152#18011870C2211yescharacteristic, complemented
153#18011869C2211yescharacteristic, complemented
154#18011869C2211yescharacteristic, complemented
155#18011869C2211yescharacteristic, complemented
156#18011867C2211yescharacteristic, complemented
157#18011867C2211yescharacteristic, complemented
158#18011867C2211yescharacteristic, complemented
159#18011867C2211yescharacteristic, complemented
160C2×#14558715C2211yescharacteristic, complemented
161C4⋊C4×D149C2211yescharacteristic, complemented
162C4⋊C4×D149C2211yescharacteristic, complemented
163C4⋊C4×D149C2211yescharacteristic, complemented
164C2×C22⋊Dic149C2211yescharacteristic, complemented
165C2×C22⋊Dic149C2211yescharacteristic, complemented
166C2×#14558713C2211yescharacteristic, complemented
167C22⋊C4×D149C2211yescharacteristic, complemented
168C22⋊C4×D149C2211yescharacteristic, complemented
169C22⋊C4×D149C2211yescharacteristic, complemented
170C22⋊C4×D149C2211yescharacteristic, complemented
171C2×C4×Dic149C2211yescharacteristic, complemented
172C22×D4×C149C2211yescharacteristic
173C23×C4×C149C2211yescharacteristic, complemented
174#123×C149C2211yescharacteristic
175#123×C149C2211yescharacteristic
176#123×C149C2211yescharacteristic, complemented
177#123×C149C2211yescharacteristic, complemented
178#123×C149C2211yescharacteristic, complemented
179#123×C149C2211yescharacteristic, complemented
180#123×C149C2211yescharacteristic, complemented
181#123×C149C2211yescharacteristic, complemented
182C2×C4⋊C4×C149C2211yescharacteristic, complemented
183C2×C4⋊C4×C149C2211yescharacteristic, complemented
184C2×C22⋊C4×C149C2211yescharacteristic, complemented
185C2×C22⋊C4×C149C2211yescharacteristic, complemented
186C2×C22⋊C4×C149C2211yescharacteristic, complemented
187C23×D149C2311yescharacteristic
188C23×D149C2311yescharacteristic
189#14558736—24no—
190#14558736—42no—
191#14558735—42no—
192C2×Dic298C2311yescharacteristic
193C2×Dic298C2311yescharacteristic
194C2×Dic298C2311yescharacteristic
195C2×Dic298C2311yescharacteristic
196C2×D596C2311yescharacteristic
197C2×D596C2311yescharacteristic
198C2×D596C2311yescharacteristic
199C2×D596C2311yescharacteristic
200C2×C22⋊D149—24no—
201C2×C22⋊D149—24no—
202C2×C22⋊D149C2311yescharacteristic
203C2×C22⋊D149C2311yescharacteristic
204C2×C22⋊D149C2311yescharacteristic
205C2×C22⋊D149C2311yescharacteristic
206C2×C22⋊D149C2311yescharacteristic
207C2×C22⋊D149C2311yescharacteristic
208C2×C22⋊D149C2311yescharacteristic
209C2×C22⋊D149C2311yescharacteristic
210C2×C22⋊D149C2311yescharacteristic
211C2×C22⋊D149C2311yescharacteristic
212C2×C22⋊D149C2311yescharacteristic
213C2×C22⋊D149C2311yescharacteristic
214C2×C22⋊D149C2311yescharacteristic
215C2×C22⋊D149C2311yescharacteristic
216C2×C22⋊D149C2311yescharacteristic
217C2×C22⋊D149C2311yescharacteristic
218D4×D149—42no—
219C22×Dic149C2311yescharacteristic
220C22×Dic149C2311yescharacteristic
221C22×Dic149C2311yescharacteristic
222C22×Dic149C2311yescharacteristic
223C22×Dic149C2311yescharacteristic
224C22×Dic149C2311yescharacteristic
225C2×C4×D149—42no—
226C2×C4×D149C2311yescharacteristic
227C2×C4×D149C2311yescharacteristic
228C2×C4×D149C2311yescharacteristic
229C2×C4×D149C2311yescharacteristic
230C2×C4×D149C2311yescharacteristic
231C2×C4×D149C2311yescharacteristic
232C2×C4×D149C2311yescharacteristic
233C2×C4×D149C2311yescharacteristic
234C2×C4×D149C2311yescharacteristic
235C2×C4×D149C2311yescharacteristic
236C2×C4×D149C2311yescharacteristic
237C2×C4×D149C2311yescharacteristic
238C4⋊Dic149C2311yescharacteristic
239C4⋊Dic149C2311yescharacteristic
240C4⋊Dic149C2311yescharacteristic
241C4⋊Dic149C2311yescharacteristic
242C4⋊Dic149C2311yescharacteristic
243C4⋊Dic149C2311yescharacteristic
244C4⋊Dic149C2311yescharacteristic
245C4⋊Dic149C2311yescharacteristic
246#14558715C2311yescharacteristic
247#14558715C2311yescharacteristic
248#14558715C2311yescharacteristic
249#14558715C2311yescharacteristic
250#14558715C2311yescharacteristic
251#14558715C2311yescharacteristic
252#14558715C2311yescharacteristic
253#14558715C2311yescharacteristic
254#14558715C2311yescharacteristic
255#14558715C2311yescharacteristic
256#14558715C2311yescharacteristic
257#14558715C2311yescharacteristic
258#14558715C2311yescharacteristic
259#14558715C2311yescharacteristic
260#14558715C2311yescharacteristic
261#14558715C2311yescharacteristic
262#14558715C2311yescharacteristic
263#14558715C2311yescharacteristic
264#14558715C2311yescharacteristic
265#14558715C2311yescharacteristic
266C22⋊Dic149C2311yescharacteristic
267C22⋊Dic149C2311yescharacteristic
268C22⋊Dic149C2311yescharacteristic
269C22⋊Dic149C2311yescharacteristic
270C22⋊Dic149C2311yescharacteristic
271C22⋊Dic149C2311yescharacteristic
272C22⋊Dic149C2311yescharacteristic
273C22⋊Dic149C2311yescharacteristic
274C22⋊Dic149C2311yescharacteristic
275C22⋊Dic149C2311yescharacteristic
276C22⋊Dic149C2311yescharacteristic
277C22⋊Dic149C2311yescharacteristic
278C22⋊Dic149C2311yescharacteristic
279C22⋊Dic149C2311yescharacteristic
280C22⋊Dic149C2311yescharacteristic
281C22⋊Dic149C2311yescharacteristic
282#14558713C2311yescharacteristic
283#14558713C2311yescharacteristic
284#14558713C2311yescharacteristic
285#14558713C2311yescharacteristic
286#14558713C2311yescharacteristic
287#14558713C2311yescharacteristic
288#14558713C2311yescharacteristic
289#14558713C2311yescharacteristic
290#14558713C2311yescharacteristic
291#14558713C2311yescharacteristic
292#14558713C2311yescharacteristic
293#14558713C2311yescharacteristic
294#14558713C2311yescharacteristic
295#14558713C2311yescharacteristic
296#14558713C2311yescharacteristic
297#14558713C2311yescharacteristic
298#14558713C2311yescharacteristic
299#14558713C2311yescharacteristic
300#14558713C2311yescharacteristic
301#14558713C2311yescharacteristic
302C4×Dic149C2311yescharacteristic
303C4×Dic149C2311yescharacteristic
304C4×Dic149C2311yescharacteristic
305C4×Dic149C2311yescharacteristic
306C4×Dic149C2311yescharacteristic
307C4×Dic149C2311yescharacteristic
308C4×Dic149C2311yescharacteristic
309C4×Dic149C2311yescharacteristic
310C4×Dic149C2311yescharacteristic
311C4×Dic149C2311yescharacteristic
312C4×Dic149C2311yescharacteristic
313C4×Dic149C2311yescharacteristic
314C24×C149C2311yescharacteristic
315C24×C149C2311yescharacteristic
316C2×D4×C149—42no—
317C2×D4×C149C2311yescharacteristic
318C2×D4×C149C2311yescharacteristic
319C2×D4×C149C2311yescharacteristic
320C2×D4×C149C2311yescharacteristic
321C22×C4×C149—42no—
322C22×C4×C149C2311yescharacteristic
323C22×C4×C149C2311yescharacteristic
324C22×C4×C149C2311yescharacteristic
325C22×C4×C149C2311yescharacteristic
326C22×C4×C149C2311yescharacteristic
327C22×C4×C149C2311yescharacteristic
328C22×C4×C149C2311yescharacteristic
329C22×C4×C149C2311yescharacteristic
330C22×C4×C149C2311yescharacteristic
331C4⋊C4×C149C2311yescharacteristic
332C4⋊C4×C149C2311yescharacteristic
333C4⋊C4×C149C2311yescharacteristic
334C4⋊C4×C149C2311yescharacteristic
335C4⋊C4×C149C2311yescharacteristic
336C4⋊C4×C149C2311yescharacteristic
337C4⋊C4×C149C2311yescharacteristic
338C4⋊C4×C149C2311yescharacteristic
339C22⋊C4×C149C2311yescharacteristic
340C22⋊C4×C149C2311yescharacteristic
341C22⋊C4×C149C2311yescharacteristic
342C22⋊C4×C149C2311yescharacteristic
343C22⋊C4×C149C2311yescharacteristic
344C22⋊C4×C149C2311yescharacteristic
345C22⋊C4×C149C2311yescharacteristic
346C22⋊C4×C149C2311yescharacteristic
347C22⋊C4×C149C2311yescharacteristic
348C22⋊C4×C149C2311yescharacteristic
349C22⋊C4×C149C2311yescharacteristic
350C22⋊C4×C149C2311yescharacteristic
351C22×D149—22no—
352C22×D149—22no—
353C22×D149—22no—
354C22×D149—41no—
355C22×D149—41no—
356C22×D149—41no—
357C22×D149C2411yescharacteristic
358C22×D149C2411yescharacteristic
359C22×D149C2411yescharacteristic
360C22×D149C2411yescharacteristic
361Dic298—22no—
362Dic298—41no—
363Dic298—41no—
364Dic298—41no—
365D596—22no—
366D596—41no—
367D596—41no—
368D596—41no—
369C22⋊D149—22no—
370C22⋊D149—22no—
371C22⋊D149—22no—
372C22⋊D149—22no—
373C22⋊D149—22no—
374C22⋊D149—22no—
375C22⋊D149—22no—
376C22⋊D149—22no—
377C22⋊D149—22no—
378C22⋊D149—41no—
379C22⋊D149—41no—
380C22⋊D149—41no—
381C22⋊D149—41no—
382C22⋊D149—41no—
383C22⋊D149—41no—
384C22⋊D149#4114yescomplemented
385C2×Dic149—22no—
386C2×Dic149—22no—
387C2×Dic149—22no—
388C2×Dic149—41no—
389C2×Dic149—41no—
390C2×Dic149—41no—
391C2×Dic149C2411yescharacteristic
392C2×Dic149C2411yescharacteristic
393C2×Dic149C2411yescharacteristic
394C2×Dic149C2411yescharacteristic
395C2×Dic149C2411yescharacteristic
396C2×Dic149C2411yescharacteristic
397C2×Dic149C2411yescharacteristic
398C2×Dic149C2411yescharacteristic
399C2×Dic149C2411yescharacteristic
400C2×Dic149C2411yescharacteristic
401C2×Dic149C2411yescharacteristic
402C2×Dic149C2411yescharacteristic
403C4×D149—22no—
404C4×D149—22no—
405C4×D149—41no—
406C4×D149—41no—
407C4×D149—41no—
408C4×D149—41no—
409C4×D149—41no—
410C4×D149—41no—
411C4×D149—41no—
412C4×D149—41no—
413C4×D149—41no—
414C4×D149—41no—
415C23×C149—22no—
416C23×C149—22no—
417C23×C149—22no—
418C23×C149—41no—
419C23×C149—41no—
420C23×C149—41no—
421C23×C149C2411yescharacteristic
422C23×C149C2411yescharacteristic
423C23×C149C2411yescharacteristic
424C23×C149C2411yescharacteristic
425C23×C149C2411yescharacteristic
426D4×C149—22no—
427D4×C149—22no—
428D4×C149—41no—
429D4×C149—41no—
430C2×C4×C149—22no—
431C2×C4×C149—22no—
432C2×C4×C149—22no—
433C2×C4×C149—41no—
434C2×C4×C149—41no—
435C2×C4×C149—41no—
436C2×C4×C149—41no—
437C2×C4×C149—41no—
438C2×C4×C149—41no—
439C2×C4×C149C2411yescharacteristic
440C2×C4×C149C2411yescharacteristic
441C2×C4×C149C2411yescharacteristic
442C2×C4×C149C2411yescharacteristic
443C2×C4×C149C2411yescharacteristic
444C2×C4×C149C2411yescharacteristic
445C2×C4×C149C2411yescharacteristic
446C2×C4×C149C2411yescharacteristic
447C2×C4×C149C2411yescharacteristic
448C2×C4×C149C2411yescharacteristic
449C22×C149—21no—
450C22×C149—21no—
451C22×C149—21no—
452C22×C149—21no—
453C22×C149—21no—
454C22×C149—21no—
455C22×C149—21no—
456C22×C149—21no—
457C22×C149—21no—
458C22×C149—21no—
459C22×C149—21no—
460C22×C149—21no—
461C22×C149—21no—
462C22×C149—44no—
463C22×C149—82no—
464C22×C149C2×#4112yes—
465C22×C149H(5,𝔽2)12yes—
466C22×C149C2511yescharacteristic
467C2×D149—21no—
468C2×D149—21no—
469C2×D149—21no—
470C2×D149—21no—
471C2×D149—21no—
472C2×D149—21no—
473C2×D149—21no—
474C2×D149—21no—
475C2×D149—21no—
476C2×D149—21no—
477C2×D149—21no—
478C2×D149—44no—
479C2×D149—82no—
480C2×D149C2×#4112yes—
481C4×C149—21no—
482C4×C149—21no—
483C4×C149—21no—
484C4×C149—21no—
485C4×C149—21no—
486C4×C149—21no—
487C4×C149—21no—
488C4×C149—21no—
489C4×C149—21no—
490C4×C149—21no—
491Dic149—21no—
492Dic149—21no—
493Dic149—21no—
494Dic149—21no—
495Dic149—21no—
496Dic149—21no—
497Dic149—21no—
498Dic149—21no—
499Dic149—21no—
500Dic149—21no—
501Dic149—21no—
502Dic149C2×#4112yes—
503C2×C149—22no—
504C2×C149—22no—
505C2×C149—41no—
506C2×C149—41no—
507C2×C149—41no—
508C2×C149C22×#4111yescharacteristic
509C2×C149C2×H(5,𝔽2)11yescharacteristic
510C2×C149#58511yescharacteristic
511D149—22no—
512D149—41no—
513D149—41no—
514D149—41no—
515C149#351311yescharacteristic, complemented, Sylow
516#3513—1491nomaximal, Sylow
517#559—1491no—
518#554—1491no—
519#553—1491no—
520#553—1491no—
521#553—1491no—
522#552—1491no—
523#551—1491no—
524#551—1491no—
525#551—1491no—
526#551—1491no—
527#547—1491no—
528#546—1491no—
529#546—1491no—
530#546—1491no—
531#546—1491no—
532D42—1491no—
533#542—1491no—
534#540—1491no—
535#539—1491no—
536#539—1491no—
537#538—1491no—
538#538—1491no—
539#529—1491no—
540#529—1491no—
541#525—1491no—
542#525—1491no—
543C2×#123—1491no—
544C2×#123D14911yescharacteristic, complemented
545#520—1491no—
546#518—1491no—
547C2×C4×D4—1491no—
548C2×#41—1491no—
549C2×#41—1491no—
550C2×#41—1491no—
551C22×D4—1491no—
552C22×D4—1491no—
553C22×D4—1491no—
554C22×D4C2×D14911yescharacteristic
555C23×C4—1491no—
556C23×C4C2×D14911yescharacteristic, complemented
557C4⋊Q8—1491no—
558#127—1491no—
559#126—1491no—
560#126—1491no—
561#126—1491no—
562#126—1491no—
563#126—1491no—
564#126—1491no—
565#126—1491no—
566#126—1491no—
567#126—1491no—
568#126—1491no—
569#125—1491no—
570#125—1491no—
571#125—1491no—
572#125—1491no—
573#125—1491no—
574#124—1491no—
575#124—1491no—
576#124—1491no—
577#124—1491no—
578#124—1491no—
579#124—1491no—
580#124—1491no—
581#123—1491no—
582#123—1491no—
583#123—1491no—
584#123—1491no—
585#123—1491no—
586#123—1491no—
587#123—1491no—
588#123—1491no—
589#123—1491no—
590#123—1491no—
591#123—1491no—
592#123—1491no—
593#123—1491no—
594#123—1491no—
595#123—1491no—
596#123—1491no—
597#123—1491no—
598#123—1491no—
599#123C2×D14911yescharacteristic
600#123C2×D14911yescharacteristic
601#123C2×D14911yescharacteristic, complemented
602#123C2×D14911yescharacteristic, complemented
603#123C2×D14911yescharacteristic, complemented
604#123C2×D14911yescharacteristic, complemented
605#123C2×D14911yescharacteristic, complemented
606#123C2×D14911yescharacteristic, complemented
607C22⋊Q8—1491no—
608C22⋊Q8—1491no—
609C22⋊Q8—1491no—
610C22⋊Q8—1491no—
611C22⋊Q8—1491no—
612C22⋊Q8—1491no—
613C22⋊Q8—1491no—
614C22⋊Q8—1491no—
615C22⋊Q8—1491no—
616C22⋊Q8—1491no—
617C22⋊Q8—1491no—
618C22⋊Q8—1491no—
619C22⋊Q8—1491no—
620#121—1491no—
621#121—1491no—
622#121—1491no—
623#121—1491no—
624#121—1491no—
625#121—1491no—
626#121—1491no—
627#121—1491no—
628#121—1491no—
629#121—1491no—
630#121—1491no—
631#121—1491no—
632#121—1491no—
633#121—1491no—
634#121—1491no—
635#121—1491no—
636#121—1491no—
637#120—1491no—
638#120—1491no—
639#120—1491no—
640#120—1491no—
641#120—1491no—
642#120—1491no—
643#120—1491no—
644#120—1491no—
645C4×Q8—1491no—
646C4×Q8—1491no—
647C4×Q8—1491no—
648C4×D4—1491no—
649C4×D4—1491no—
650C4×D4—1491no—
651C4×D4—1491no—
652C4×D4—1491no—
653C4×D4—1491no—
654C4×D4—1491no—
655C4×D4—1491no—
656C4×D4—1491no—
657C4×D4—1491no—
658C4×D4—1491no—
659C4×D4—1491no—
660C4×D4—1491no—
661C4×D4—1491no—
662C4×D4—1491no—
663C4×D4—1491no—
664C4×D4—1491no—
665C4×D4—1491no—
666C4×D4—1491no—
667C4×D4—1491no—
668C4×D4—1491no—
669C4×D4—1491no—
670C4×D4—1491no—
671C4×D4—1491no—
672C4×D4—1491no—
673C4×D4—1491no—
674C4×D4—1491no—
675C4×D4—1491no—
676C4×D4—1491no—
677#117—1491no—
678#117—1491no—
679#117—1491no—
680#117—1491no—
681#117—1491no—
682#117—1491no—
683#117—1491no—
684#117—1491no—
685#117—1491no—
686C2×C4⋊C4—1491no—
687C2×C4⋊C4—1491no—
688C2×C4⋊C4—1491no—
689C2×C4⋊C4—1491no—
690C2×C4⋊C4C2×D14911yescharacteristic, complemented
691C2×C4⋊C4C2×D14911yescharacteristic, complemented
692C2×C22⋊C4—1491no—
693C2×C22⋊C4—1491no—
694C2×C22⋊C4—1491no—
695C2×C22⋊C4—1491no—
696C2×C22⋊C4—1491no—
697C2×C22⋊C4—1491no—
698C2×C22⋊C4—1491no—
699C2×C22⋊C4C2×D14911yescharacteristic, complemented
700C2×C22⋊C4C2×D14911yescharacteristic, complemented
701C2×C22⋊C4C2×D14911yescharacteristic, complemented
702C2×C42—1491no—
703C24—1491no—
704C24—1491no—
705C24C22×D14911yescharacteristic
706C24C22×D14911yescharacteristic
707#41—2984no—
708#41—5962no—
709#41—5962no—
710C2×Q8—1491no—
711C2×Q8—1491no—
712C2×Q8—1491no—
713C2×Q8—1491no—
714C2×D4—42no—
715C2×D4—2984no—
716C2×D4—2984no—
717C2×D4—5962no—
718C2×D4—1491no—
719C2×D4—1491no—
720C2×D4—1491no—
721C2×D4—1491no—
722C2×D4—1491no—
723C2×D4—1491no—
724C2×D4—1491no—
725C2×D4—1491no—
726C2×D4—1491no—
727C2×D4—1491no—
728C2×D4—1491no—
729C2×D4—1491no—
730C2×D4—1491no—
731C2×D4—1491no—
732C2×D4—1491no—
733C2×D4—1491no—
734C2×D4—1491no—
735C2×D4—1491no—
736C2×D4—1491no—
737C2×D4—1491no—
738C2×D4C22×D14911yescharacteristic
739C2×D4C22×D14911yescharacteristic
740C2×D4C22×D14911yescharacteristic
741C2×D4C22×D14911yescharacteristic
742C22×C4—42no—
743C22×C4—5962no—
744C22×C4—1491no—
745C22×C4—1491no—
746C22×C4—1491no—
747C22×C4—1491no—
748C22×C4—1491no—
749C22×C4—1491no—
750C22×C4—1491no—
751C22×C4—1491no—
752C22×C4—1491no—
753C22×C4—1491no—
754C22×C4—1491no—
755C22×C4—1491no—
756C22×C4—1491no—
757C22×C4—1491no—
758C22×C4—1491no—
759C22×C4—1491no—
760C22×C4—1491no—
761C22×C4—1491no—
762C22×C4C22×D14911yescharacteristic
763C22×C4C22×D14911yescharacteristic
764C22×C4C22×D14911yescharacteristic
765C22×C4C22×D14911yescharacteristic
766C22×C4C22×D14911yescharacteristic
767C22×C4C22×D14911yescharacteristic
768C22×C4C22×D14911yescharacteristic
769C22×C4C22×D14911yescharacteristic
770C22×C4C22×D14911yescharacteristic
771C4⋊C4—1491no—
772C4⋊C4—1491no—
773C4⋊C4—1491no—
774C4⋊C4—1491no—
775C4⋊C4—1491no—
776C4⋊C4—1491no—
777C4⋊C4—1491no—
778C4⋊C4—1491no—
779C4⋊C4—1491no—
780C4⋊C4—1491no—
781C4⋊C4—1491no—
782C4⋊C4—1491no—
783C4⋊C4—1491no—
784C4⋊C4—1491no—
785C4⋊C4—1491no—
786C4⋊C4—1491no—
787C4⋊C4—1491no—
788C4⋊C4—1491no—
789C4⋊C4—1491no—
790C4⋊C4—1491no—
791C4⋊C4—1491no—
792C4⋊C4—1491no—
793C4⋊C4—1491no—
794C4⋊C4—1491no—
795C4⋊C4—1491no—
796C4⋊C4—1491no—
797C4⋊C4—1491no—
798C4⋊C4—1491no—
799C4⋊C4C22×D14911yescharacteristic
800C4⋊C4C22×D14911yescharacteristic
801C4⋊C4C22×D14911yescharacteristic
802C4⋊C4C22×D14911yescharacteristic
803C4⋊C4C22×D14911yescharacteristic
804C4⋊C4C22×D14911yescharacteristic
805C4⋊C4C22×D14911yescharacteristic
806C4⋊C4C22×D14911yescharacteristic
807C22⋊C4—1491no—
808C22⋊C4—1491no—
809C22⋊C4—1491no—
810C22⋊C4—1491no—
811C22⋊C4—1491no—
812C22⋊C4—1491no—
813C22⋊C4—1491no—
814C22⋊C4—1491no—
815C22⋊C4—1491no—
816C22⋊C4—1491no—
817C22⋊C4—1491no—
818C22⋊C4—1491no—
819C22⋊C4—1491no—
820C22⋊C4—1491no—
821C22⋊C4—1491no—
822C22⋊C4—1491no—
823C22⋊C4—1491no—
824C22⋊C4—1491no—
825C22⋊C4—1491no—
826C22⋊C4—1491no—
827C22⋊C4—1491no—
828C22⋊C4—1491no—
829C22⋊C4—1491no—
830C22⋊C4—1491no—
831C22⋊C4—1491no—
832C22⋊C4—1491no—
833C22⋊C4—1491no—
834C22⋊C4—1491no—
835C22⋊C4—1491no—
836C22⋊C4—1491no—
837C22⋊C4—1491no—
838C22⋊C4—1491no—
839C22⋊C4—1491no—
840C22⋊C4—1491no—
841C22⋊C4—1491no—
842C22⋊C4—1491no—
843C22⋊C4C22×D14911yescharacteristic
844C22⋊C4C22×D14911yescharacteristic
845C22⋊C4C22×D14911yescharacteristic
846C22⋊C4C22×D14911yescharacteristic
847C22⋊C4C22×D14911yescharacteristic
848C22⋊C4C22×D14911yescharacteristic
849C22⋊C4C22×D14911yescharacteristic
850C22⋊C4C22×D14911yescharacteristic
851C22⋊C4C22×D14911yescharacteristic
852C22⋊C4C22×D14911yescharacteristic
853C22⋊C4C22×D14911yescharacteristic
854C22⋊C4C22×D14911yescharacteristic
855C42—1491no—
856C42—1491no—
857C42—1491no—
858C42—1491no—
859C42—1491no—
860C42—1491no—
861C42—1491no—
862C42—1491no—
863C42—1491no—
864C42—1491no—
865C42—1491no—
866C42—1491no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—2982no—
874C23—2982no—
875C23—2982no—
876C23—5961no—
877C23—5961no—
878C23—5961no—
879C23—1491no—
880C23—1491no—
881C23—1491no—
882C23—1491no—
883C23C23×D14911yescharacteristic
884C23C23×D14911yescharacteristic
885C23C23×D14911yescharacteristic
886C23C23×D14911yescharacteristic
887C23C23×D14911yescharacteristic
888Q8—2982no—
889Q8—5961no—
890Q8—5961no—
891Q8—5961no—
892D4—22no—
893D4—22no—
894D4—41no—
895D4—41no—
896D4—2982no—
897D4—2982no—
898D4—2982no—
899D4—2982no—
900D4—2982no—
901D4—2982no—
902D4—2982no—
903D4—2982no—
904D4—2982no—
905D4—2982no—
906D4—5961no—
907D4—5961no—
908D4—5961no—
909D4—5961no—
910D4—5961no—
911D4—5961no—
912D4—5961no—
913D4—5961no—
914D4—5961no—
915D4—1494no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—2982no—
926C2×C4—2982no—
927C2×C4—2982no—
928C2×C4—2982no—
929C2×C4—2982no—
930C2×C4—5961no—
931C2×C4—5961no—
932C2×C4—5961no—
933C2×C4—5961no—
934C2×C4—5961no—
935C2×C4—5961no—
936C2×C4—5961no—
937C2×C4—5961no—
938C2×C4—5961no—
939C2×C4—5961no—
940C2×C4—5961no—
941C2×C4—5961no—
942C2×C4—5961no—
943C2×C4—1491no—
944C2×C4—1491no—
945C2×C4—1491no—
946C2×C4—1491no—
947C2×C4—1491no—
948C2×C4—1491no—
949C2×C4—1491no—
950C2×C4—1491no—
951C2×C4—1491no—
952C2×C4—1491no—
953C2×C4—1491no—
954C2×C4—1491no—
955C2×C4C23×D14911yescharacteristic
956C2×C4C23×D14911yescharacteristic
957C2×C4C23×D14911yescharacteristic
958C2×C4C23×D14911yescharacteristic
959C2×C4C23×D14911yescharacteristic
960C2×C4C23×D14911yescharacteristic
961C2×C4C23×D14911yescharacteristic
962C2×C4C23×D14911yescharacteristic
963C2×C4C23×D14911yescharacteristic
964C2×C4C23×D14911yescharacteristic
965C22—21no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—21no—
971C22—21no—
972C22—21no—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—21no—
977C22—21no—
978C22—44no—
979C22—82no—
980C22—2981no—
981C22—2981no—
982C22—2981no—
983C22—2981no—
984C22—2981no—
985C22—2981no—
986C22—2981no—
987C22—2981no—
988C22—2981no—
989C22—2981no—
990C22—2981no—
991C22—5964no—
992C22—1492no—
993C22—11922no—
994C22#41×D14912yes—
995C22#1801195612yes—
996C22C24×D14911yescharacteristic
997C4—21no—
998C4—21no—
999C4—21no—
1000C4—21no—
1001C4—21no—
1002C4—21no—
1003C4—21no—
1004C4—21no—
1005C4—21no—
1006C4—21no—
1007C4—2981no—
1008C4—2981no—
1009C4—2981no—
1010C4—2981no—
1011C4—2981no—
1012C4—2981no—
1013C4—2981no—
1014C4—2981no—
1015C4—2981no—
1016C4—2981no—
1017C4—2981no—
1018C4—1492no—
1019C2—22no—
1020C2—22no—
1021C2—41no—
1022C2—41no—
1023C2—41no—
1024C2—2982no—
1025C2—5961no—
1026C2—5961no—
1027C2—5961no—
1028C2C2×#41×D14911yescharacteristic
1029C2C2×#1801195611yescharacteristic
1030C2#2375046111yescharacteristic
subgroupG/H
center, FrattiniC22C24×D149
commutator, socle, cosocleC22×C149C25
FittingC2×#123×C149C2
hypercenterC2×#123D149
hypocenterC149#3513
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×#123

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23750359C2semidirect
2. #23750330C2semidirect
3. #23750323C2semidirect
4. #23750320C2semidirect
5. #23750320C2semidirect
6. #23750312C2semidirect
7. #23750303C2semidirect
8. #23750301C2semidirect
9. #23750301C2semidirect
10. #23750298C2semidirect
11. #23750273C2semidirect
12. #23750269C2semidirect
13. #23750267C2semidirect
14. #23750265C2semidirect
15. #23750265C2semidirect
16. D4×C22⋊D149C2semidirect
17. #23750243C2semidirect
18. #23750227C2semidirect
19. #23750222C2semidirect
20. #23750218C2semidirect
21. #23750213C2semidirect
22. #23750211C2semidirect
23. #23750152C2semidirect
24. #23750152C2semidirect
25. #23750136C2semidirect
26. #23750133C2semidirect
27. #123×D149C2semidirect
28. #23750106C2semidirect
29. #23750098C2semidirect
30. C2×C4×C22⋊D149C2semidirect
31. C2×#123×C149C2semidirect
33. C2×#14558736C22semidirect
34. C2×#14558735C22semidirect
38. C22×C4×D149C22semidirect
39. #18011910C22semidirect
41. #18011906C22semidirect
42. #18011906C22semidirect
43. #18011906C22semidirect
44. #18011906C22semidirect
45. #18011904C22semidirect
46. #18011904C22semidirect
47. #18011904C22semidirect
48. #18011904C22semidirect
49. #18011904C22semidirect
50. #18011904C22semidirect
51. #18011902C22semidirect
52. #18011901C22semidirect
53. #18011901C22semidirect
54. #18011901C22semidirect
55. #18011901C22semidirect
56. #18011898C22semidirect
57. #18011897C22semidirect
58. #18011897C22semidirect
59. #18011897C22semidirect
60. #18011897C22semidirect
61. #18011897C22semidirect
62. #18011897C22semidirect
63. #18011896C22semidirect
64. #18011896C22semidirect
65. #18011896C22semidirect
66. #18011896C22semidirect
67. #18011895C22semidirect
68. #18011895C22semidirect
69. #18011894C22semidirect
70. #18011894C22semidirect
71. #18011894C22semidirect
72. #18011894C22semidirect
73. #18011893C22semidirect
74. #18011893C22semidirect
75. #18011893C22semidirect
76. #18011893C22semidirect
77. #18011893C22semidirect
78. #18011893C22semidirect
80. #18011892C22semidirect
81. #18011891C22semidirect
82. #18011890C22semidirect
83. #18011890C22semidirect
84. #18011890C22semidirect
85. #18011890C22semidirect
86. #18011889C22semidirect
87. #18011889C22semidirect
88. #18011889C22semidirect
89. #18011889C22semidirect
90. #18011888C22semidirect
91. #18011888C22semidirect
92. #18011888C22semidirect
93. #18011888C22semidirect
94. #18011886C22semidirect
96. #18011885C22semidirect
97. #18011885C22semidirect
98. #18011885C22semidirect
99. #18011884C22semidirect
100. #18011884C22semidirect
101. #18011884C22semidirect
102. #18011884C22semidirect
103. #18011884C22semidirect
104. #18011884C22semidirect
108. #18011883C22semidirect
110. #18011882C22semidirect
111. #18011881C22semidirect
112. #18011881C22semidirect
115. #18011880C22semidirect
116. #18011880C22semidirect
119. #18011876C22semidirect
120. #18011876C22semidirect
121. #18011876C22semidirect
123. D4×Dic149C22semidirect
124. #18011873C22semidirect
125. #18011873C22semidirect
126. #18011873C22semidirect
131. C4×C22⋊D149C22semidirect
132. C4×C22⋊D149C22semidirect
133. C4×C22⋊D149C22semidirect
134. C4×C22⋊D149C22semidirect
135. C4×C22⋊D149C22semidirect
136. C4×C22⋊D149C22semidirect
137. C4×C22⋊D149C22semidirect
138. C4×C22⋊D149C22semidirect
139. C4×C22⋊D149C22semidirect
140. C4×C22⋊D149C22semidirect
141. C4×C22⋊D149C22semidirect
142. C4×C22⋊D149C22semidirect
143. #18011871C22semidirect
144. #18011871C22semidirect
145. #18011871C22semidirect
146. #18011871C22semidirect
147. #18011871C22semidirect
148. #18011871C22semidirect
149. #18011871C22semidirect
150. #18011871C22semidirect
151. #18011870C22semidirect
152. #18011870C22semidirect
153. #18011869C22semidirect
154. #18011869C22semidirect
155. #18011869C22semidirect
156. #18011867C22semidirect
157. #18011867C22semidirect
158. #18011867C22semidirect
159. #18011867C22semidirect
160. C2×#14558715C22semidirect
161. C4⋊C4×D149C22semidirect
162. C4⋊C4×D149C22semidirect
163. C4⋊C4×D149C22semidirect
164. C2×C22⋊Dic149C22semidirect
165. C2×C22⋊Dic149C22semidirect
166. C2×#14558713C22semidirect
167. C22⋊C4×D149C22semidirect
168. C22⋊C4×D149C22semidirect
169. C22⋊C4×D149C22semidirect
170. C22⋊C4×D149C22semidirect
171. C2×C4×Dic149C22semidirect
173. C23×C4×C149C22semidirect
176. #123×C149C22semidirect
177. #123×C149C22semidirect
178. #123×C149C22semidirect
179. #123×C149C22semidirect
180. #123×C149C22semidirect
181. #123×C149C22semidirect
182. C2×C4⋊C4×C149C22semidirect
183. C2×C4⋊C4×C149C22semidirect
184. C2×C22⋊C4×C149C22semidirect
185. C2×C22⋊C4×C149C22semidirect
186. C2×C22⋊C4×C149C22semidirect
384. C22⋊D149#41semidirect
515. C149#3513semidirect
544. C2×#123D149semidirect
556. C23×C4C2×D149semidirect
601. #123C2×D149semidirect
602. #123C2×D149semidirect
603. #123C2×D149semidirect
604. #123C2×D149semidirect
605. #123C2×D149semidirect
606. #123C2×D149semidirect
690. C2×C4⋊C4C2×D149semidirect
691. C2×C4⋊C4C2×D149semidirect
699. C2×C22⋊C4C2×D149semidirect
700. C2×C22⋊C4C2×D149semidirect
701. C2×C22⋊C4C2×D149semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237503592
#237503302
#237503232
#237503202
#237503122
#237503032
#237503012
#237502982
#237502732
#237502692
#237502672
#237502652
D4×C22⋊D1492
#237502432
#237502272
#237502222
#237502182
#237502132
#237502112
#237501522
#237501362
#237501332
#123×D1492
#237501062
#237500982
C2×C4×C22⋊D1492
C2×#123×C1492
#3513149