Finite Group Databasebeta

← #34083329

Subgroups — #34083329

Order 19328.

1134 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752959C211yesmaximal, characteristic, complemented
2#23752958C211yesmaximal, characteristic, complemented
3#23752957C211yesmaximal, characteristic, complemented
4#23752918C211yesmaximal, characteristic, complemented
5#23752916C211yesmaximal, characteristic, complemented
6#23752872C211yesmaximal, characteristic, complemented
7#23752870C211yesmaximal, characteristic, complemented
8#23752864C211yesmaximal, characteristic, complemented
9#23752860C211yesmaximal, characteristic, complemented
10#23752859C211yesmaximal, characteristic, complemented
11#23752855C211yesmaximal, characteristic, complemented
12#23752854C211yesmaximal, characteristic, complemented
13#23752854C211yesmaximal, characteristic, complemented
14#23752851C211yesmaximal, characteristic, complemented
15#23752851C211yesmaximal, characteristic, complemented
16#23752837C211yesmaximal, characteristic, complemented
17#23752837C211yesmaximal, characteristic, complemented
18#23752830C211yesmaximal, characteristic, complemented
19#23752826C211yesmaximal, characteristic, complemented
20#23752810C211yesmaximal, characteristic, complemented
21#23752805C211yesmaximal, characteristic, complemented
22#23752798C211yesmaximal, characteristic, complemented
23#23752796C211yesmaximal, characteristic, complemented
24#23752792C211yesmaximal, characteristic, complemented
25#23752791C211yesmaximal, characteristic, complemented
26#23752791C211yesmaximal, characteristic, complemented
27#23752789C211yesmaximal, characteristic, complemented
28#23752720C211yesmaximal, characteristic, complemented
29C22⋊Q8×D151C211yesmaximal, characteristic, complemented
30#121×D151C211yesmaximal, characteristic, complemented
31#562×C151C211yesmaximal, characteristic, complemented
32C2×#14559005C2211yescharacteristic, complemented
33C2×#14559004C2211yescharacteristic, complemented
34C2×#14559004C2211yescharacteristic, complemented
35C2×#14559004C2211yescharacteristic, complemented
36C2×#14559003C2211yescharacteristic, complemented
37C2×#14559003C2211yescharacteristic, complemented
38C2×#14559003C2211yescharacteristic, complemented
39C2×Q8×D151C2211yescharacteristic, complemented
40C2×D4×D151C2211yescharacteristic
41C2×D4×D151C2211yescharacteristic
42C2×D4×D151C2211yescharacteristic
43C22×C4×D151C2211yescharacteristic
44#18012738C2211yescharacteristic, complemented
45#18012737C2211yescharacteristic, complemented
46#18012734C2211yescharacteristic, complemented
47#18012733C2211yescharacteristic, complemented
48#18012732C2211yescharacteristic, complemented
49#18012732C2211yescharacteristic, complemented
50#18012730C2211yescharacteristic, complemented
51#18012729C2211yescharacteristic, complemented
52#18012729C2211yescharacteristic, complemented
53#18012728C2211yescharacteristic, complemented
54#18012726C2211yescharacteristic, complemented
55#18012725C2211yescharacteristic, complemented
56#18012725C2211yescharacteristic, complemented
57#18012725C2211yescharacteristic, complemented
58#18012725C2211yescharacteristic, complemented
59#18012725C2211yescharacteristic, complemented
60#18012725C2211yescharacteristic, complemented
61#18012724C2211yescharacteristic, complemented
62#18012724C2211yescharacteristic, complemented
63#18012724C2211yescharacteristic, complemented
64#18012724C2211yescharacteristic, complemented
65#18012724C2211yescharacteristic, complemented
66#18012723C2211yescharacteristic, complemented
67#18012722C2211yescharacteristic, complemented
68#18012721C2211yescharacteristic, complemented
69#18012721C2211yescharacteristic, complemented
70#18012721C2211yescharacteristic, complemented
71#18012721C2211yescharacteristic, complemented
72#18012721C2211yescharacteristic, complemented
73#18012720C2211yescharacteristic, complemented
74#18012720C2211yescharacteristic, complemented
75#18012719C2211yescharacteristic
76#18012719C2211yescharacteristic
77#18012719C2211yescharacteristic, complemented
78#18012719C2211yescharacteristic, complemented
79#18012719C2211yescharacteristic, complemented
80#18012718C2211yescharacteristic, complemented
81#18012718C2211yescharacteristic, complemented
82#18012718C2211yescharacteristic, complemented
83#18012717C2211yescharacteristic
84#18012717C2211yescharacteristic
85#18012717C2211yescharacteristic
86#18012717C2211yescharacteristic
87#18012717C2211yescharacteristic
88#18012717C2211yescharacteristic, complemented
89#18012717C2211yescharacteristic, complemented
90#18012717C2211yescharacteristic, complemented
91#18012717C2211yescharacteristic, complemented
92#18012717C2211yescharacteristic, complemented
93#18012717C2211yescharacteristic, complemented
94#18012717C2211yescharacteristic, complemented
95#18012716C2211yescharacteristic, complemented
96#18012716C2211yescharacteristic, complemented
97#18012716C2211yescharacteristic, complemented
98#18012716C2211yescharacteristic, complemented
99#18012716C2211yescharacteristic, complemented
100#18012716C2211yescharacteristic, complemented
101#18012716C2211yescharacteristic, complemented
102#18012716C2211yescharacteristic, complemented
103#18012715C2211yescharacteristic
104#18012715C2211yescharacteristic
105#18012715C2211yescharacteristic, complemented
106#18012715C2211yescharacteristic, complemented
107#18012714C2211yescharacteristic
108#18012714C2211yescharacteristic, complemented
109#18012714C2211yescharacteristic, complemented
110#18012713C2211yescharacteristic
111#18012713C2211yescharacteristic, complemented
112#18012712C2211yescharacteristic
113#18012712C2211yescharacteristic
114#18012712C2211yescharacteristic
115#18012712C2211yescharacteristic, complemented
116#18012712C2211yescharacteristic, complemented
117#18012712C2211yescharacteristic, complemented
118#18012712C2211yescharacteristic, complemented
119#18012712C2211yescharacteristic, complemented
120#18012712C2211yescharacteristic, complemented
121#18012712C2211yescharacteristic, complemented
122#18012712C2211yescharacteristic, complemented
123#18012711C2211yescharacteristic
124#18012711C2211yescharacteristic
125#18012711C2211yescharacteristic, complemented
126#18012711C2211yescharacteristic, complemented
127#18012711C2211yescharacteristic, complemented
128#18012711C2211yescharacteristic, complemented
129#18012711C2211yescharacteristic, complemented
130#18012710C2211yescharacteristic
131#18012710C2211yescharacteristic, complemented
132#18012710C2211yescharacteristic, complemented
133#18012710C2211yescharacteristic, complemented
134#18012710C2211yescharacteristic, complemented
135#18012709C2211yescharacteristic
136#18012709C2211yescharacteristic
137#18012709C2211yescharacteristic
138#18012707C2211yescharacteristic
139#18012707C2211yescharacteristic
140#18012707C2211yescharacteristic
141C4×Dic302C2211yescharacteristic, complemented
142#18012704C2211yescharacteristic, complemented
143C4×D604C2211yescharacteristic
144C4×D604C2211yescharacteristic, complemented
145#18012701C2211yescharacteristic
146#18012701C2211yescharacteristic
147#18012701C2211yescharacteristic, complemented
148#18012701C2211yescharacteristic, complemented
149C4×C22⋊D151C2211yescharacteristic
150C4×C22⋊D151C2211yescharacteristic, complemented
151C4×C22⋊D151C2211yescharacteristic, complemented
152(C22⋊D151)⋊C4C2211yescharacteristic
153(C22⋊D151)⋊C4C2211yescharacteristic
154(C22⋊D151)⋊C4C2211yescharacteristic, complemented
155(C22⋊D151)⋊C4C2211yescharacteristic, complemented
156(C22⋊D151)⋊C4C2211yescharacteristic, complemented
157#18012695C2211yescharacteristic, complemented
158C2×Dic151⋊C4C2211yescharacteristic, complemented
159C4⋊C4×D151C2211yescharacteristic
160C4⋊C4×D151C2211yescharacteristic, complemented
161C4⋊C4×D151C2211yescharacteristic, complemented
162C4⋊C4×D151C2211yescharacteristic, complemented
163C4⋊C4×D151C2211yescharacteristic, complemented
164C2×(C2×D151)⋊C4C2211yescharacteristic
165C2×(C2×D151)⋊C4C2211yescharacteristic
166C22⋊C4×D151C2211yescharacteristic
167C22⋊C4×D151C2211yescharacteristic
168C22⋊C4×D151C2211yescharacteristic
169C22⋊C4×D151C2211yescharacteristic
170C22⋊C4×D151C2211yescharacteristic
171C22⋊C4×D151C2211yescharacteristic
172#125×C151C2211yescharacteristic, complemented
173#124×C151C2211yescharacteristic, complemented
174#124×C151C2211yescharacteristic, complemented
175#123×C151C2211yescharacteristic, complemented
176#123×C151C2211yescharacteristic, complemented
177#123×C151C2211yescharacteristic, complemented
178#123×C151C2211yescharacteristic, complemented
179C22⋊Q8×C151C2211yescharacteristic, complemented
180C22⋊Q8×C151C2211yescharacteristic, complemented
181C22⋊Q8×C151C2211yescharacteristic, complemented
182C22⋊Q8×C151C2211yescharacteristic, complemented
183#121×C151C2211yescharacteristic
184#121×C151C2211yescharacteristic, complemented
185#121×C151C2211yescharacteristic, complemented
186#121×C151C2211yescharacteristic, complemented
187C23×D151C2311yescharacteristic
188C23×D151C2311yescharacteristic
189C23×D151C2311yescharacteristic
190#14559005—42no—
191#14559004—42no—
192#14559004—42no—
193#14559004—42no—
194#14559003—42no—
195#14559003—42no—
196#14559003—42no—
197C2×Dic302C2311yescharacteristic
198C2×Dic302C2311yescharacteristic
199C2×Dic302C2311yescharacteristic
200C2×Dic302C2311yescharacteristic
201C2×Dic302C2311yescharacteristic
202C2×Dic302C2311yescharacteristic
203C2×Dic302C2311yescharacteristic
204Q8×D151—42no—
205C2×D604C2311yescharacteristic
206C2×D604C2311yescharacteristic
207C2×D604C2311yescharacteristic
208C2×D604C2311yescharacteristic
209C2×D604C2311yescharacteristic
210C2×D604C2311yescharacteristic
211C2×D604C2311yescharacteristic
212C2×C22⋊D151C2311yescharacteristic
213C2×C22⋊D151C2311yescharacteristic
214C2×C22⋊D151C2311yescharacteristic
215C2×C22⋊D151C2311yescharacteristic
216C2×C22⋊D151C2311yescharacteristic
217C2×C22⋊D151C2311yescharacteristic
218C2×C22⋊D151C2311yescharacteristic
219C2×C22⋊D151C2311yescharacteristic
220C2×C22⋊D151C2311yescharacteristic
221C2×C22⋊D151C2311yescharacteristic
222C2×C22⋊D151C2311yescharacteristic
223C2×C22⋊D151C2311yescharacteristic
224C2×C22⋊D151C2311yescharacteristic
225C2×C22⋊D151C2311yescharacteristic
226D4×D151—42no—
227D4×D151—42no—
228D4×D151—42no—
229C22×Dic151C2311yescharacteristic
230C22×Dic151C2311yescharacteristic
231C22×Dic151C2311yescharacteristic
232C22×Dic151C2311yescharacteristic
233C22×Dic151C2311yescharacteristic
234C2×C4×D151—42no—
235C2×C4×D151C2311yescharacteristic
236C2×C4×D151C2311yescharacteristic
237C2×C4×D151C2311yescharacteristic
238C2×C4×D151C2311yescharacteristic
239C2×C4×D151C2311yescharacteristic
240C2×C4×D151C2311yescharacteristic
241C2×C4×D151C2311yescharacteristic
242C2×C4×D151C2311yescharacteristic
243C2×C4×D151C2311yescharacteristic
244C2×C4×D151C2311yescharacteristic
245C2×C4×D151C2311yescharacteristic
246C2×C4×D151C2311yescharacteristic
247C2×C4×D151C2311yescharacteristic
248C2×C4×D151C2311yescharacteristic
249C2×C4×D151C2311yescharacteristic
250C2×C4×D151C2311yescharacteristic
251C2×C4×D151C2311yescharacteristic
252C4⋊Dic151C2311yescharacteristic
253C4⋊Dic151C2311yescharacteristic
254C4⋊Dic151C2311yescharacteristic
255C4⋊Dic151C2311yescharacteristic
256C4⋊Dic151C2311yescharacteristic
257C4⋊Dic151C2311yescharacteristic
258C4⋊Dic151C2311yescharacteristic
259C4⋊Dic151C2311yescharacteristic
260Dic151⋊C4C2311yescharacteristic
261Dic151⋊C4C2311yescharacteristic
262Dic151⋊C4C2311yescharacteristic
263Dic151⋊C4C2311yescharacteristic
264Dic151⋊C4C2311yescharacteristic
265Dic151⋊C4C2311yescharacteristic
266Dic151⋊C4C2311yescharacteristic
267Dic151⋊C4C2311yescharacteristic
268Dic151⋊C4C2311yescharacteristic
269Dic151⋊C4C2311yescharacteristic
270Dic151⋊C4C2311yescharacteristic
271Dic151⋊C4C2311yescharacteristic
272Dic151⋊C4C2311yescharacteristic
273Dic151⋊C4C2311yescharacteristic
274Dic151⋊C4C2311yescharacteristic
275Dic151⋊C4C2311yescharacteristic
276Dic151⋊C4C2311yescharacteristic
277Dic151⋊C4C2311yescharacteristic
278Dic151⋊C4C2311yescharacteristic
279Dic151⋊C4C2311yescharacteristic
280C22⋊Dic151C2311yescharacteristic
281C22⋊Dic151C2311yescharacteristic
282C22⋊Dic151C2311yescharacteristic
283C22⋊Dic151C2311yescharacteristic
284C22⋊Dic151C2311yescharacteristic
285C22⋊Dic151C2311yescharacteristic
286C22⋊Dic151C2311yescharacteristic
287C22⋊Dic151C2311yescharacteristic
288C22⋊Dic151C2311yescharacteristic
289C22⋊Dic151C2311yescharacteristic
290(C2×D151)⋊C4C2311yescharacteristic
291(C2×D151)⋊C4C2311yescharacteristic
292(C2×D151)⋊C4C2311yescharacteristic
293(C2×D151)⋊C4C2311yescharacteristic
294(C2×D151)⋊C4C2311yescharacteristic
295(C2×D151)⋊C4C2311yescharacteristic
296(C2×D151)⋊C4C2311yescharacteristic
297(C2×D151)⋊C4C2311yescharacteristic
298(C2×D151)⋊C4C2311yescharacteristic
299(C2×D151)⋊C4C2311yescharacteristic
300(C2×D151)⋊C4C2311yescharacteristic
301(C2×D151)⋊C4C2311yescharacteristic
302(C2×D151)⋊C4C2311yescharacteristic
303(C2×D151)⋊C4C2311yescharacteristic
304(C2×D151)⋊C4C2311yescharacteristic
305(C2×D151)⋊C4C2311yescharacteristic
306(C2×D151)⋊C4C2311yescharacteristic
307(C2×D151)⋊C4C2311yescharacteristic
308(C2×D151)⋊C4C2311yescharacteristic
309(C2×D151)⋊C4C2311yescharacteristic
310(C2×D151)⋊C4C2311yescharacteristic
311(C2×D151)⋊C4C2311yescharacteristic
312(C2×D151)⋊C4C2311yescharacteristic
313(C2×D151)⋊C4C2311yescharacteristic
314C4×Dic151C2311yescharacteristic
315C4×Dic151C2311yescharacteristic
316C4×Dic151C2311yescharacteristic
317C4×Dic151C2311yescharacteristic
318C4×Dic151C2311yescharacteristic
319C2×Q8×C151C2311yescharacteristic
320C2×Q8×C151C2311yescharacteristic
321C2×D4×C151C2311yescharacteristic
322C2×D4×C151C2311yescharacteristic
323C2×D4×C151C2311yescharacteristic
324C2×D4×C151C2311yescharacteristic
325C2×D4×C151C2311yescharacteristic
326C2×D4×C151C2311yescharacteristic
327C22×C4×C151C2311yescharacteristic
328C22×C4×C151C2311yescharacteristic
329C22×C4×C151C2311yescharacteristic
330C22×C4×C151C2311yescharacteristic
331C4⋊C4×C151C2311yescharacteristic
332C4⋊C4×C151C2311yescharacteristic
333C4⋊C4×C151C2311yescharacteristic
334C4⋊C4×C151C2311yescharacteristic
335C4⋊C4×C151C2311yescharacteristic
336C4⋊C4×C151C2311yescharacteristic
337C4⋊C4×C151C2311yescharacteristic
338C4⋊C4×C151C2311yescharacteristic
339C4⋊C4×C151C2311yescharacteristic
340C4⋊C4×C151C2311yescharacteristic
341C22⋊C4×C151C2311yescharacteristic
342C22⋊C4×C151C2311yescharacteristic
343C22⋊C4×C151C2311yescharacteristic
344C22⋊C4×C151C2311yescharacteristic
345C22⋊C4×C151C2311yescharacteristic
346C22⋊C4×C151C2311yescharacteristic
347C22⋊C4×C151C2311yescharacteristic
348C22⋊C4×C151C2311yescharacteristic
349C22⋊C4×C151C2311yescharacteristic
350C22⋊C4×C151C2311yescharacteristic
351C22⋊C4×C151C2311yescharacteristic
352C22⋊C4×C151C2311yescharacteristic
353C42×C151C2311yescharacteristic
354C22×D151—22no—
355C22×D151—22no—
356C22×D151—22no—
357C22×D151—22no—
358C22×D151—41no—
359C22×D151—41no—
360C22×D151—41no—
361C22×D151—41no—
362C22×D151—41no—
363C22×D151C2411yescharacteristic
364C22×D151C2411yescharacteristic
365C22×D151C2411yescharacteristic
366C22×D151C2411yescharacteristic
367C22×D151C2411yescharacteristic
368Dic302—22no—
369Dic302—22no—
370Dic302—41no—
371Dic302—41no—
372Dic302—41no—
373Dic302—41no—
374Dic302—41no—
375D604—22no—
376D604—22no—
377D604—22no—
378D604—22no—
379D604—41no—
380D604—41no—
381D604—41no—
382C22⋊D151—22no—
383C22⋊D151—22no—
384C22⋊D151—22no—
385C22⋊D151—22no—
386C22⋊D151—22no—
387C22⋊D151—22no—
388C22⋊D151—41no—
389C22⋊D151—41no—
390C22⋊D151—41no—
391C22⋊D151—41no—
392C22⋊D151—41no—
393C22⋊D151—41no—
394C22⋊D151—41no—
395C22⋊D151—41no—
396C2×Dic151—22no—
397C2×Dic151—22no—
398C2×Dic151—41no—
399C2×Dic151—41no—
400C2×Dic151—41no—
401C2×Dic151C2411yescharacteristic
402C2×Dic151C2411yescharacteristic
403C2×Dic151C2411yescharacteristic
404C2×Dic151C2411yescharacteristic
405C2×Dic151C2411yescharacteristic
406C2×Dic151C2411yescharacteristic
407C2×Dic151C2411yescharacteristic
408C2×Dic151C2411yescharacteristic
409C2×Dic151C2411yescharacteristic
410C2×Dic151C2411yescharacteristic
411C2×Dic151C2411yescharacteristic
412C4×D151—22no—
413C4×D151—22no—
414C4×D151—22no—
415C4×D151—22no—
416C4×D151—22no—
417C4×D151—41no—
418C4×D151—41no—
419C4×D151—41no—
420C4×D151—41no—
421C4×D151—41no—
422C4×D151—41no—
423C4×D151—41no—
424C4×D151—41no—
425C4×D151—41no—
426C4×D151—41no—
427C4×D151—41no—
428C4×D151—41no—
429C23×C151C2411yescharacteristic
430C23×C151C2411yescharacteristic
431C23×C151C2411yescharacteristic
432C23×C151C2411yescharacteristic
433Q8×C151—41no—
434Q8×C151—41no—
435D4×C151—41no—
436D4×C151—41no—
437D4×C151—41no—
438D4×C151—41no—
439D4×C151—41no—
440D4×C151—41no—
441C2×C4×C151—41no—
442C2×C4×C151—41no—
443C2×C4×C151—41no—
444C2×C4×C151—41no—
445C2×C4×C151C2411yescharacteristic
446C2×C4×C151C2411yescharacteristic
447C2×C4×C151C2411yescharacteristic
448C2×C4×C151C2411yescharacteristic
449C2×C4×C151C2411yescharacteristic
450C2×C4×C151C2411yescharacteristic
451C2×C4×C151C2411yescharacteristic
452C2×C4×C151C2411yescharacteristic
453C2×C4×C151C2411yescharacteristic
454C2×C4×C151C2411yescharacteristic
455C2×C4×C151C2411yescharacteristic
456C22×C151—21no—
457C22×C151—21no—
458C22×C151—21no—
459C22×C151—21no—
460C22×C151—21no—
461C22×C151—21no—
462C22×C151—21no—
463C22×C151—21no—
464C22×C151—21no—
465C22×C151—21no—
466C22×C151—21no—
467C22×C151—21no—
468C22×C151C2511yescharacteristic
469C2×D151—21no—
470C2×D151—21no—
471C2×D151—21no—
472C2×D151—21no—
473C2×D151—21no—
474C2×D151—21no—
475C2×D151—21no—
476C2×D151—21no—
477C2×D151—21no—
478C2×D151—21no—
479C2×D151—21no—
480C2×D151—21no—
481C2×D151—21no—
482C2×D151—44no—
483C2×D151—82no—
484C2×D151—82no—
485C2×D151H(5,𝔽2)12yes—
486C2×D1512−1+412yes—
487C4×C151—21no—
488C4×C151—21no—
489C4×C151—21no—
490C4×C151—21no—
491C4×C151—21no—
492C4×C151—21no—
493C4×C151—21no—
494C4×C151—21no—
495C4×C151—21no—
496C4×C151—21no—
497C4×C151—21no—
498Dic151—21no—
499Dic151—21no—
500Dic151—21no—
501Dic151—21no—
502Dic151—21no—
503Dic151—21no—
504Dic151—21no—
505Dic151—21no—
506Dic151—21no—
507Dic151—21no—
508Dic151H(5,𝔽2)12yes—
509C2×C151—41no—
510C2×C151—41no—
511C2×C151—41no—
512C2×C151—41no—
513C2×C151C2×H(5,𝔽2)11yescharacteristic
514C2×C151C2×H(5,𝔽2)11yescharacteristic
515C2×C151C2×2−1+411yescharacteristic
516D151—22no—
517D151—22no—
518D151—41no—
519D151—41no—
520D151—41no—
521C151#353611yescharacteristic, complemented, Sylow
522#3536—1511nomaximal, Sylow
523#562—1511no—
524#562—1511no—
525#562—1511no—
526#562D15111yescharacteristic, complemented
527#554—1511no—
528#554—1511no—
529#548—1511no—
530#548—1511no—
531#547—1511no—
532#547—1511no—
533#546—1511no—
534#546—1511no—
535#546—1511no—
536#546—1511no—
537#546—1511no—
538#546—1511no—
539#543—1511no—
540#543—1511no—
541#542—1511no—
542#542—1511no—
543#539—1511no—
544#539—1511no—
545#538—1511no—
546#538—1511no—
547#537—1511no—
548#537—1511no—
549#537—1511no—
550#537—1511no—
551#525—1511no—
552C2×C22⋊Q8—1511no—
553C2×#121—1511no—
554C2×#41—1511no—
555C2×#41—1511no—
556C2×#41—1511no—
557C2×#41—1511no—
558C2×#41—1511no—
559C2×#41—1511no—
560C2×#41—1511no—
561C22×Q8—1511no—
562C22×D4—1511no—
563C22×D4—1511no—
564C22×D4—1511no—
565C23×C4—1511no—
566C4⋊Q8—1511no—
567C4⋊Q8—1511no—
568#126—1511no—
569#126—1511no—
570#126—1511no—
571#126—1511no—
572#125—1511no—
573#125—1511no—
574#125—1511no—
575#125C2×D15111yescharacteristic, complemented
576#124—1511no—
577#124—1511no—
578#124—1511no—
579#124—1511no—
580#124—1511no—
581#124—1511no—
582#124—1511no—
583#124—1511no—
584#124C2×D15111yescharacteristic, complemented
585#124C2×D15111yescharacteristic, complemented
586#123—1511no—
587#123—1511no—
588#123—1511no—
589#123—1511no—
590#123—1511no—
591#123—1511no—
592#123—1511no—
593#123—1511no—
594#123—1511no—
595#123—1511no—
596#123—1511no—
597#123—1511no—
598#123—1511no—
599#123—1511no—
600#123C2×D15111yescharacteristic, complemented
601#123C2×D15111yescharacteristic, complemented
602#123C2×D15111yescharacteristic, complemented
603#123C2×D15111yescharacteristic, complemented
604C22⋊Q8—1511no—
605C22⋊Q8—1511no—
606C22⋊Q8—1511no—
607C22⋊Q8—1511no—
608C22⋊Q8—1511no—
609C22⋊Q8—1511no—
610C22⋊Q8—1511no—
611C22⋊Q8—1511no—
612C22⋊Q8—1511no—
613C22⋊Q8—1511no—
614C22⋊Q8—1511no—
615C22⋊Q8—1511no—
616C22⋊Q8—1511no—
617C22⋊Q8—1511no—
618C22⋊Q8—1511no—
619C22⋊Q8—1511no—
620C22⋊Q8—1511no—
621C22⋊Q8—1511no—
622C22⋊Q8—1511no—
623C22⋊Q8—1511no—
624C22⋊Q8—1511no—
625C22⋊Q8—1511no—
626C22⋊Q8—1511no—
627C22⋊Q8—1511no—
628C22⋊Q8—1511no—
629C22⋊Q8—1511no—
630C22⋊Q8—1511no—
631C22⋊Q8—1511no—
632C22⋊Q8—1511no—
633C22⋊Q8—1511no—
634C22⋊Q8—1511no—
635C22⋊Q8—1511no—
636C22⋊Q8C2×D15111yescharacteristic, complemented
637C22⋊Q8C2×D15111yescharacteristic, complemented
638C22⋊Q8C2×D15111yescharacteristic, complemented
639C22⋊Q8C2×D15111yescharacteristic, complemented
640#121—1511no—
641#121—1511no—
642#121—1511no—
643#121—1511no—
644#121—1511no—
645#121—1511no—
646#121—1511no—
647#121—1511no—
648#121—1511no—
649#121—1511no—
650#121—1511no—
651#121—1511no—
652#121—1511no—
653#121—1511no—
654#121—1511no—
655#121—1511no—
656#121—1511no—
657#121—1511no—
658#121—1511no—
659#121—1511no—
660#121—1511no—
661#121—1511no—
662#121—1511no—
663#121—1511no—
664#121—1511no—
665#121—1511no—
666#121—1511no—
667#121—1511no—
668#121C2×D15111yescharacteristic
669#121C2×D15111yescharacteristic, complemented
670#121C2×D15111yescharacteristic, complemented
671#121C2×D15111yescharacteristic, complemented
672#120—1511no—
673#120—1511no—
674#120—1511no—
675#120—1511no—
676#120—1511no—
677#120—1511no—
678C4×Q8—1511no—
679C4×Q8—1511no—
680C4×D4—1511no—
681C4×D4—1511no—
682C4×D4—1511no—
683C4×D4—1511no—
684C4×D4—1511no—
685C4×D4—1511no—
686C4×D4—1511no—
687C4×D4—1511no—
688C4×D4—1511no—
689C4×D4—1511no—
690C4×D4—1511no—
691C4×D4—1511no—
692C4×D4—1511no—
693C4×D4—1511no—
694#117—1511no—
695C2×C4⋊C4—1511no—
696C2×C4⋊C4—1511no—
697C2×C4⋊C4—1511no—
698C2×C4⋊C4—1511no—
699C2×C4⋊C4—1511no—
700C2×C4⋊C4—1511no—
701C2×C22⋊C4—1511no—
702C2×C22⋊C4—1511no—
703C2×C22⋊C4—1511no—
704C2×C22⋊C4—1511no—
705C2×C22⋊C4—1511no—
706C2×C22⋊C4—1511no—
707C2×C22⋊C4—1511no—
708C2×C22⋊C4—1511no—
709C24—1511no—
710C24—1511no—
711C24—1511no—
712#41—6042no—
713#41—6042no—
714#41—6042no—
715#41—6042no—
716#41—6042no—
717#41—6042no—
718#41—6042no—
719C2×Q8—6042no—
720C2×Q8—1511no—
721C2×Q8—1511no—
722C2×Q8—1511no—
723C2×Q8—1511no—
724C2×Q8—1511no—
725C2×Q8—1511no—
726C2×Q8—1511no—
727C2×Q8C22×D15111yescharacteristic
728C2×Q8C22×D15111yescharacteristic
729C2×D4—6042no—
730C2×D4—6042no—
731C2×D4—6042no—
732C2×D4—1511no—
733C2×D4—1511no—
734C2×D4—1511no—
735C2×D4—1511no—
736C2×D4—1511no—
737C2×D4—1511no—
738C2×D4—1511no—
739C2×D4—1511no—
740C2×D4—1511no—
741C2×D4—1511no—
742C2×D4—1511no—
743C2×D4—1511no—
744C2×D4—1511no—
745C2×D4—1511no—
746C2×D4—1511no—
747C2×D4—1511no—
748C2×D4—1511no—
749C2×D4—1511no—
750C2×D4—1511no—
751C2×D4—1511no—
752C2×D4—1511no—
753C2×D4C22×D15111yescharacteristic
754C2×D4C22×D15111yescharacteristic
755C2×D4C22×D15111yescharacteristic
756C2×D4C22×D15111yescharacteristic
757C2×D4C22×D15111yescharacteristic
758C2×D4C22×D15111yescharacteristic
759C22×C4—6042no—
760C22×C4—1511no—
761C22×C4—1511no—
762C22×C4—1511no—
763C22×C4—1511no—
764C22×C4—1511no—
765C22×C4—1511no—
766C22×C4—1511no—
767C22×C4—1511no—
768C22×C4—1511no—
769C22×C4—1511no—
770C22×C4—1511no—
771C22×C4—1511no—
772C22×C4—1511no—
773C22×C4—1511no—
774C22×C4—1511no—
775C22×C4—1511no—
776C22×C4—1511no—
777C22×C4—1511no—
778C22×C4—1511no—
779C22×C4—1511no—
780C22×C4—1511no—
781C22×C4—1511no—
782C22×C4C22×D15111yescharacteristic
783C22×C4C22×D15111yescharacteristic
784C22×C4C22×D15111yescharacteristic
785C22×C4C22×D15111yescharacteristic
786C4⋊C4—1511no—
787C4⋊C4—1511no—
788C4⋊C4—1511no—
789C4⋊C4—1511no—
790C4⋊C4—1511no—
791C4⋊C4—1511no—
792C4⋊C4—1511no—
793C4⋊C4—1511no—
794C4⋊C4—1511no—
795C4⋊C4—1511no—
796C4⋊C4—1511no—
797C4⋊C4—1511no—
798C4⋊C4—1511no—
799C4⋊C4—1511no—
800C4⋊C4—1511no—
801C4⋊C4—1511no—
802C4⋊C4—1511no—
803C4⋊C4—1511no—
804C4⋊C4—1511no—
805C4⋊C4—1511no—
806C4⋊C4—1511no—
807C4⋊C4—1511no—
808C4⋊C4—1511no—
809C4⋊C4—1511no—
810C4⋊C4—1511no—
811C4⋊C4—1511no—
812C4⋊C4—1511no—
813C4⋊C4—1511no—
814C4⋊C4C22×D15111yescharacteristic
815C4⋊C4C22×D15111yescharacteristic
816C4⋊C4C22×D15111yescharacteristic
817C4⋊C4C22×D15111yescharacteristic
818C4⋊C4C22×D15111yescharacteristic
819C4⋊C4C22×D15111yescharacteristic
820C4⋊C4C22×D15111yescharacteristic
821C4⋊C4C22×D15111yescharacteristic
822C4⋊C4C22×D15111yescharacteristic
823C4⋊C4C22×D15111yescharacteristic
824C22⋊C4—1511no—
825C22⋊C4—1511no—
826C22⋊C4—1511no—
827C22⋊C4—1511no—
828C22⋊C4—1511no—
829C22⋊C4—1511no—
830C22⋊C4—1511no—
831C22⋊C4—1511no—
832C22⋊C4—1511no—
833C22⋊C4—1511no—
834C22⋊C4—1511no—
835C22⋊C4—1511no—
836C22⋊C4—1511no—
837C22⋊C4—1511no—
838C22⋊C4—1511no—
839C22⋊C4—1511no—
840C22⋊C4—1511no—
841C22⋊C4—1511no—
842C22⋊C4—1511no—
843C22⋊C4—1511no—
844C22⋊C4—1511no—
845C22⋊C4—1511no—
846C22⋊C4—1511no—
847C22⋊C4—1511no—
848C22⋊C4—1511no—
849C22⋊C4—1511no—
850C22⋊C4—1511no—
851C22⋊C4—1511no—
852C22⋊C4—1511no—
853C22⋊C4—1511no—
854C22⋊C4—1511no—
855C22⋊C4—1511no—
856C22⋊C4—1511no—
857C22⋊C4—1511no—
858C22⋊C4C22×D15111yescharacteristic
859C22⋊C4C22×D15111yescharacteristic
860C22⋊C4C22×D15111yescharacteristic
861C22⋊C4C22×D15111yescharacteristic
862C22⋊C4C22×D15111yescharacteristic
863C22⋊C4C22×D15111yescharacteristic
864C22⋊C4C22×D15111yescharacteristic
865C22⋊C4C22×D15111yescharacteristic
866C22⋊C4C22×D15111yescharacteristic
867C22⋊C4C22×D15111yescharacteristic
868C22⋊C4C22×D15111yescharacteristic
869C22⋊C4C22×D15111yescharacteristic
870C42—1511no—
871C42—1511no—
872C42—1511no—
873C42—1511no—
874C42—1511no—
875C42C22×D15111yescharacteristic
876C23—3022no—
877C23—3022no—
878C23—3022no—
879C23—3022no—
880C23—6041no—
881C23—6041no—
882C23—6041no—
883C23—6041no—
884C23—6041no—
885C23—1511no—
886C23—1511no—
887C23—1511no—
888C23—1511no—
889C23—1511no—
890C23C23×D15111yescharacteristic
891C23C23×D15111yescharacteristic
892C23C23×D15111yescharacteristic
893C23C23×D15111yescharacteristic
894Q8—41no—
895Q8—41no—
896Q8—3022no—
897Q8—3022no—
898Q8—6041no—
899Q8—6041no—
900Q8—6041no—
901Q8—6041no—
902Q8—6041no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—3022no—
910D4—3022no—
911D4—3022no—
912D4—3022no—
913D4—3022no—
914D4—3022no—
915D4—3022no—
916D4—3022no—
917D4—3022no—
918D4—3022no—
919D4—6041no—
920D4—6041no—
921D4—6041no—
922D4—6041no—
923D4—6041no—
924D4—6041no—
925D4—6041no—
926D4—6041no—
927D4—6041no—
928D4—6041no—
929D4—6041no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—3022no—
935C2×C4—3022no—
936C2×C4—3022no—
937C2×C4—3022no—
938C2×C4—3022no—
939C2×C4—3022no—
940C2×C4—3022no—
941C2×C4—6041no—
942C2×C4—6041no—
943C2×C4—6041no—
944C2×C4—6041no—
945C2×C4—6041no—
946C2×C4—6041no—
947C2×C4—6041no—
948C2×C4—6041no—
949C2×C4—6041no—
950C2×C4—6041no—
951C2×C4—6041no—
952C2×C4—6041no—
953C2×C4—6041no—
954C2×C4—6041no—
955C2×C4—6041no—
956C2×C4—1511no—
957C2×C4—1511no—
958C2×C4—1511no—
959C2×C4—1511no—
960C2×C4—1511no—
961C2×C4—1511no—
962C2×C4—1511no—
963C2×C4—1511no—
964C2×C4—1511no—
965C2×C4—1511no—
966C2×C4—1511no—
967C2×C4C23×D15111yescharacteristic
968C2×C4C23×D15111yescharacteristic
969C2×C4C23×D15111yescharacteristic
970C2×C4C23×D15111yescharacteristic
971C2×C4C23×D15111yescharacteristic
972C2×C4C23×D15111yescharacteristic
973C2×C4C23×D15111yescharacteristic
974C2×C4C23×D15111yescharacteristic
975C2×C4C23×D15111yescharacteristic
976C2×C4C23×D15111yescharacteristic
977C2×C4C23×D15111yescharacteristic
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—21no—
984C22—21no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—3021no—
991C22—3021no—
992C22—3021no—
993C22—3021no—
994C22—3021no—
995C22—3021no—
996C22—3021no—
997C22—3021no—
998C22—3021no—
999C22—3021no—
1000C22—3021no—
1001C22—3021no—
1002C22—3021no—
1003C22—6044no—
1004C22—1512no—
1005C22—1512no—
1006C22—12082no—
1007C22—12082no—
1008C22C24×D15111yescharacteristic
1009C4—21no—
1010C4—21no—
1011C4—21no—
1012C4—21no—
1013C4—21no—
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—3021no—
1021C4—3021no—
1022C4—3021no—
1023C4—3021no—
1024C4—3021no—
1025C4—3021no—
1026C4—3021no—
1027C4—3021no—
1028C4—3021no—
1029C4—3021no—
1030C4—1512no—
1031C2—41no—
1032C2—41no—
1033C2—41no—
1034C2—41no—
1035C2—3022no—
1036C2—3022no—
1037C2—6041no—
1038C2—6041no—
1039C2—6041no—
1040C2H(5,𝔽2)×D15111yescharacteristic
1041C2H(5,𝔽2)×D15111yescharacteristic
1042C22−1+4×D15111yescharacteristic
subgroupG/H
center, FrattiniC22C24×D151
commutator, socle, cosocleC22×C151C25
Fitting#562×C151C2
hypercenter#562D151
hypocenterC151#3536
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #23752959C2semidirect
2. #23752958C2semidirect
3. #23752957C2semidirect
4. #23752918C2semidirect
5. #23752916C2semidirect
6. #23752872C2semidirect
7. #23752870C2semidirect
8. #23752864C2semidirect
9. #23752860C2semidirect
10. #23752859C2semidirect
11. #23752855C2semidirect
12. #23752854C2semidirect
13. #23752854C2semidirect
14. #23752851C2semidirect
15. #23752851C2semidirect
16. #23752837C2semidirect
17. #23752837C2semidirect
18. #23752830C2semidirect
19. #23752826C2semidirect
20. #23752810C2semidirect
21. #23752805C2semidirect
22. #23752798C2semidirect
23. #23752796C2semidirect
24. #23752792C2semidirect
25. #23752791C2semidirect
26. #23752791C2semidirect
27. #23752789C2semidirect
28. #23752720C2semidirect
29. C22⋊Q8×D151C2semidirect
30. #121×D151C2semidirect
31. #562×C151C2semidirect
32. C2×#14559005C22semidirect
33. C2×#14559004C22semidirect
34. C2×#14559004C22semidirect
35. C2×#14559004C22semidirect
36. C2×#14559003C22semidirect
37. C2×#14559003C22semidirect
38. C2×#14559003C22semidirect
39. C2×Q8×D151C22semidirect
44. #18012738C22semidirect
45. #18012737C22semidirect
46. #18012734C22semidirect
47. #18012733C22semidirect
48. #18012732C22semidirect
49. #18012732C22semidirect
50. #18012730C22semidirect
51. #18012729C22semidirect
52. #18012729C22semidirect
53. #18012728C22semidirect
54. #18012726C22semidirect
55. #18012725C22semidirect
56. #18012725C22semidirect
57. #18012725C22semidirect
58. #18012725C22semidirect
59. #18012725C22semidirect
60. #18012725C22semidirect
61. #18012724C22semidirect
62. #18012724C22semidirect
63. #18012724C22semidirect
64. #18012724C22semidirect
65. #18012724C22semidirect
66. #18012723C22semidirect
67. #18012722C22semidirect
68. #18012721C22semidirect
69. #18012721C22semidirect
70. #18012721C22semidirect
71. #18012721C22semidirect
72. #18012721C22semidirect
73. #18012720C22semidirect
74. #18012720C22semidirect
77. #18012719C22semidirect
78. #18012719C22semidirect
79. #18012719C22semidirect
80. #18012718C22semidirect
81. #18012718C22semidirect
82. #18012718C22semidirect
88. #18012717C22semidirect
89. #18012717C22semidirect
90. #18012717C22semidirect
91. #18012717C22semidirect
92. #18012717C22semidirect
93. #18012717C22semidirect
94. #18012717C22semidirect
95. #18012716C22semidirect
96. #18012716C22semidirect
97. #18012716C22semidirect
98. #18012716C22semidirect
99. #18012716C22semidirect
100. #18012716C22semidirect
101. #18012716C22semidirect
102. #18012716C22semidirect
105. #18012715C22semidirect
106. #18012715C22semidirect
108. #18012714C22semidirect
109. #18012714C22semidirect
111. #18012713C22semidirect
115. #18012712C22semidirect
116. #18012712C22semidirect
117. #18012712C22semidirect
118. #18012712C22semidirect
119. #18012712C22semidirect
120. #18012712C22semidirect
121. #18012712C22semidirect
122. #18012712C22semidirect
125. #18012711C22semidirect
126. #18012711C22semidirect
127. #18012711C22semidirect
128. #18012711C22semidirect
129. #18012711C22semidirect
131. #18012710C22semidirect
132. #18012710C22semidirect
133. #18012710C22semidirect
134. #18012710C22semidirect
141. C4×Dic302C22semidirect
142. #18012704C22semidirect
144. C4×D604C22semidirect
147. #18012701C22semidirect
148. #18012701C22semidirect
150. C4×C22⋊D151C22semidirect
151. C4×C22⋊D151C22semidirect
154. (C22⋊D151)⋊C4C22semidirect
155. (C22⋊D151)⋊C4C22semidirect
156. (C22⋊D151)⋊C4C22semidirect
157. #18012695C22semidirect
158. C2×Dic151⋊C4C22semidirect
160. C4⋊C4×D151C22semidirect
161. C4⋊C4×D151C22semidirect
162. C4⋊C4×D151C22semidirect
163. C4⋊C4×D151C22semidirect
172. #125×C151C22semidirect
173. #124×C151C22semidirect
174. #124×C151C22semidirect
175. #123×C151C22semidirect
176. #123×C151C22semidirect
177. #123×C151C22semidirect
178. #123×C151C22semidirect
179. C22⋊Q8×C151C22semidirect
180. C22⋊Q8×C151C22semidirect
181. C22⋊Q8×C151C22semidirect
182. C22⋊Q8×C151C22semidirect
184. #121×C151C22semidirect
185. #121×C151C22semidirect
186. #121×C151C22semidirect
521. C151#3536semidirect
526. #562D151semidirect
575. #125C2×D151semidirect
584. #124C2×D151semidirect
585. #124C2×D151semidirect
600. #123C2×D151semidirect
601. #123C2×D151semidirect
602. #123C2×D151semidirect
603. #123C2×D151semidirect
636. C22⋊Q8C2×D151semidirect
637. C22⋊Q8C2×D151semidirect
638. C22⋊Q8C2×D151semidirect
639. C22⋊Q8C2×D151semidirect
669. #121C2×D151semidirect
670. #121C2×D151semidirect
671. #121C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237529592
#237529582
#237529572
#237529182
#237529162
#237528722
#237528702
#237528642
#237528602
#237528592
#237528552
#237528542
#237528512
#237528372
#237528302
#237528262
#237528102
#237528052
#237527982
#237527962
#237527922
#237527912
#237527892
#237527202
C22⋊Q8×D1512
#121×D1512
#562×C1512
#3536151