Finite Group Databasebeta

← #26232413

Subgroups — #26232413

Order 12032.

1294 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689799C211yesmaximal, characteristic
2#20246237C211yesmaximal, characteristic, complemented
3#20244373C211yesmaximal, characteristic, complemented
4#20244372C211yesmaximal, characteristic, complemented
5#20243846C211yesmaximal, characteristic, complemented
6#20243844C211yesmaximal, characteristic, complemented
7#20243841C211yesmaximal, characteristic
8#20243839C211yesmaximal, characteristic
9#20243463C211yesmaximal, characteristic, complemented
10#20243460C211yesmaximal, characteristic, complemented
11#20243373C211yesmaximal, characteristic, complemented
12C4×#13093938C211yesmaximal, characteristic, complemented
13#20243120C211yesmaximal, characteristic, complemented
14C2×#15688889C211yesmaximal, characteristic, complemented
15C47×#2342C211yesmaximal, characteristic, complemented
16#15689799—21no—
17#15689799—21no—
18#15689799—21no—
19#15689799—21no—
20#15689799—21no—
21#15689799—21no—
22#15689799—21no—
23#15689799—21no—
24C2×#13094017C411yescharacteristic, complemented
25C2×#13094017C411yescharacteristic, complemented
26C2×#13094010C411yescharacteristic, complemented
27C2×#13094008C411yescharacteristic, complemented
28C2×#13094007C2211yescharacteristic
29C2×#13094006C411yescharacteristic, complemented
30C2×#13094003C2211yescharacteristic
31C2×#13094001C411yescharacteristic, complemented
32C2×#13093993C2211yescharacteristic
33C2×C4×C22⋊D47C2211yescharacteristic
34C2×(C22⋊D47)⋊C4C411yescharacteristic, complemented
35C2×#13093983C2211yescharacteristic
36C2×#13093983C2211yescharacteristic
37C2×#13093980C411yescharacteristic, complemented
38C22×C22⋊Dic47C2211yescharacteristic
39C22×C22⋊Dic47C2211yescharacteristic
40C2×#13093938C2211yescharacteristic
41C2×#13093938C2211yescharacteristic
42C2×#13093938C2211yescharacteristic
43C2×#13093938C2211yescharacteristic
44#15689016—21no—
45#15689016—21no—
46#15688998—21no—
47#15688986C2211yescharacteristic
48#15688983C2211yescharacteristic
49#15688979C2211yescharacteristic
50C22⋊C4×Dic47—21no—
51C4×C22⋊Dic47C2211yescharacteristic
52#15688889C2211yescharacteristic
53#15688889C2211yescharacteristic
54#15688889C2211yescharacteristic
55#15688889C2211yescharacteristic
56#15688889C2211yescharacteristic
57#15688889C2211yescharacteristic
58#15688889C2211yescharacteristic
59#15688889C2211yescharacteristic
60#15688889C2211yescharacteristic
61#15688889C2211yescharacteristic
62#15688889C2211yescharacteristic
63#15688889C2211yescharacteristic
64C2×#117×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C47×#388—21no—
68C47×#388—21no—
69C47×#385—21no—
70C47×#381C2211yescharacteristic
71C47×#380C2211yescharacteristic
72C47×#379C2211yescharacteristic
73C4×C22⋊C4×C47—21no—
74C4×C22⋊C4×C47C2211yescharacteristic
75C22×Dic94C2×C411yescharacteristic, complemented
76C22×C22⋊D47C2×C411yescharacteristic
77C22×C22⋊D47C2×C411yescharacteristic
78C22×C22⋊D47C2311yescharacteristic
79C23×Dic47—21no—
80C23×Dic47C2×C411yescharacteristic
81C23×Dic47C2×C411yescharacteristic
82C22×C4×D47C2×C411yescharacteristic, complemented
83#13094017—21no—
84#13094017—21no—
85#13094017—21no—
86#13094017—21no—
87#13094017—21no—
88#13094017—21no—
89#13094017—21no—
90#13094017—21no—
91#13094010—21no—
92#13094010—21no—
93#13094010—21no—
94#13094010—21no—
95#13094008—21no—
96#13094008—21no—
97#13094008—21no—
98#13094008—21no—
99#13094007—21no—
100#13094007—21no—
101#13094007—21no—
102#13094007—21no—
103#13094006—21no—
104#13094006—21no—
105#13094006—21no—
106#13094006—21no—
107#13094003—21no—
108#13094003—21no—
109#13094003—21no—
110#13094003—21no—
111#13094001—21no—
112#13094001—21no—
113#13094001—21no—
114#13094001—21no—
115#13093993—21no—
116#13093993—21no—
117#13093993—21no—
118#13093993—21no—
119C4×C22⋊D47—21no—
120C4×C22⋊D47—21no—
121C4×C22⋊D47—21no—
122C4×C22⋊D47—21no—
123(C22⋊D47)⋊C4—21no—
124(C22⋊D47)⋊C4—21no—
125(C22⋊D47)⋊C4—21no—
126(C22⋊D47)⋊C4—21no—
127#13093983—21no—
128#13093983—21no—
129#13093983—21no—
130#13093983—21no—
131#13093983—22no—
132#13093983—41no—
133#13093980—21no—
134#13093980—21no—
135#13093980—21no—
136#13093980—21no—
137C2×C4⋊Dic47—21no—
138C2×C4⋊Dic47—21no—
139C2×C4⋊Dic47C2×C411yescharacteristic, complemented
140C2×C4⋊Dic47C2×C411yescharacteristic, complemented
141C2×C4⋊Dic47C2×C411yescharacteristic, complemented
142C2×Dic47⋊C4C2×C411yescharacteristic, complemented
143C2×Dic47⋊C4C2×C411yescharacteristic, complemented
144C2×Dic47⋊C4C2×C411yescharacteristic, complemented
145C2×Dic47⋊C4C2×C411yescharacteristic, complemented
146C2×Dic47⋊C4C2×C411yescharacteristic, complemented
147C2×C22⋊Dic47—21no—
148C2×C22⋊Dic47—21no—
149C2×C22⋊Dic47—21no—
150C2×C22⋊Dic47—21no—
151C2×C22⋊Dic47—22no—
152C2×C22⋊Dic47—21no—
153C2×C22⋊Dic47—21no—
154C2×C22⋊Dic47—21no—
155C2×C22⋊Dic47—41no—
156C2×C22⋊Dic47C2×C411yescharacteristic
157C2×C22⋊Dic47C2×C411yescharacteristic
158C2×C22⋊Dic47C2×C411yescharacteristic
159C2×C22⋊Dic47C2×C411yescharacteristic
160C2×C22⋊Dic47C2311yescharacteristic
161C2×C22⋊Dic47C2311yescharacteristic
162C2×C22⋊Dic47C2311yescharacteristic
163C2×C22⋊Dic47C2311yescharacteristic
164C2×C22⋊Dic47C2311yescharacteristic
165C2×C22⋊Dic47C2311yescharacteristic
166C2×C22⋊Dic47C2311yescharacteristic
167C2×(C2×D47)⋊C4C2×C411yescharacteristic, complemented
168C2×(C2×D47)⋊C4C2×C411yescharacteristic, complemented
169C2×(C2×D47)⋊C4C2×C411yescharacteristic, complemented
170C2×C4×Dic47—21no—
171C2×C4×Dic47—21no—
172C2×C4×Dic47C2×C411yescharacteristic, complemented
173C2×C4×Dic47C2×C411yescharacteristic, complemented
174C2×C4×Dic47C2×C411yescharacteristic, complemented
175#13093938—22no—
176#13093938—22no—
177#13093938—41no—
178#13093938—41no—
179C47⋊#95—21no—
180C47⋊#95—21no—
181C47⋊#95—21no—
182C47⋊#95—21no—
183C25×C47C2311yescharacteristic
184C23×C4×C47—21no—
185C23×C4×C47C2311yescharacteristic
186C23×C4×C47C2311yescharacteristic
187#117×C47—22no—
188#117×C47—41no—
189C2×C4⋊C4×C47—21no—
190C2×C4⋊C4×C47—21no—
191C2×C22⋊C4×C47—22no—
192C2×C22⋊C4×C47—21no—
193C2×C22⋊C4×C47—21no—
194C2×C22⋊C4×C47—21no—
195C2×C22⋊C4×C47—41no—
196C2×C22⋊C4×C47C2×C411yescharacteristic
197C2×C22⋊C4×C47C2×C411yescharacteristic
198C2×C22⋊C4×C47C2×C411yescharacteristic
199C2×C22⋊C4×C47C2×C411yescharacteristic
200C2×C22⋊C4×C47D411yescharacteristic
201C2×C22⋊C4×C47D411yescharacteristic
202C2×C22⋊C4×C47D411yescharacteristic
203C2×C22⋊C4×C47D411yescharacteristic
204C2×C22⋊C4×C47D411yescharacteristic
205C2×C22⋊C4×C47D411yescharacteristic
206C2×C22⋊C4×C47D411yescharacteristic
207C2×C22⋊C4×C47D411yescharacteristic
208C2×C22⋊C4×C47C2311yescharacteristic
209C2×C22⋊C4×C47C2311yescharacteristic
210C2×C22⋊C4×C47C2311yescharacteristic
211C2×C22⋊C4×C47C2311yescharacteristic
212C2×C42×C47—21no—
213C2×C42×C47—21no—
214#95×C47—21no—
215#95×C47—21no—
216#95×C47—21no—
217#95×C47—21no—
218C24×C47—21no—
219C24×C47—21no—
220C24×C47—21no—
221C24×C47—21no—
222C24×C47—42no—
223C24×C47—81no—
224C24×C47C22×C411yescharacteristic
225C24×C47C22×C411yescharacteristic
226C24×C47C2×D411yescharacteristic
227C24×C47C2×D411yescharacteristic
228C24×C47C2×D411yescharacteristic
229C24×C47C2×D411yescharacteristic
230C24×C47C2411yescharacteristic
231C23×D47C22×C411yescharacteristic
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—21no—
240C22×C4×C47—42no—
241C22×C4×C47—42no—
242C22×C4×C47—81no—
243C22×C4×C47—81no—
244C22×C4×C47C22×C411yescharacteristic
245C22×C4×C47C22×C411yescharacteristic
246C22×C4×C47C22×C411yescharacteristic
247C22×C4×C47C22×C411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2×D411yescharacteristic
252C22×C4×C47C2×D411yescharacteristic
253C22×C4×C47C2×D411yescharacteristic
254C22×C4×C47C2×D411yescharacteristic
255C22×C4×C47C2×D411yescharacteristic
256C2×C22⋊D47—21no—
257C2×C22⋊D47—21no—
258C2×C22⋊D47—21no—
259C2×C22⋊D47—21no—
260C2×C22⋊D47—21no—
261C2×C22⋊D47—21no—
262C2×C22⋊D47—21no—
263C2×C22⋊D47—21no—
264C2×C22⋊D47—21no—
265C2×C22⋊D47—21no—
266C2×C22⋊D47—42no—
267C2×C22⋊D47—81no—
268C22×Dic47—21no—
269C22×Dic47—21no—
270C22×Dic47—21no—
271C22×Dic47—21no—
272C22×Dic47—21no—
273C22×Dic47—21no—
274C22×Dic47—21no—
275C22×Dic47—21no—
276C22×Dic47—42no—
277C22×Dic47—42no—
278C22×Dic47—42no—
279C22×Dic47—81no—
280C22×Dic47—81no—
281C22×Dic47C22×C411yescharacteristic
282C22×Dic47C22×C411yescharacteristic
283C22×Dic47C22×C411yescharacteristic
284C22×Dic47C22×C411yescharacteristic
285C22×Dic47C22×C411yescharacteristic
286C22×Dic47C22×C411yescharacteristic
287C22×Dic47C22×C411yescharacteristic
288C2×C4×D47—21no—
289C2×C4×D47—21no—
290C2×C4×D47—81no—
291C2×Dic94—21no—
292C2×Dic94—21no—
293C2×Dic94—81no—
294C4⋊C4×C47—42no—
295C4⋊C4×C47—81no—
296C22⋊C4×C47—21no—
297C22⋊C4×C47—21no—
298C22⋊C4×C47—21no—
299C22⋊C4×C47—21no—
300C22⋊C4×C47—21no—
301C22⋊C4×C47—21no—
302C22⋊C4×C47—21no—
303C22⋊C4×C47—42no—
304C22⋊C4×C47—42no—
305C22⋊C4×C47—81no—
306C22⋊C4×C47C22⋊C411yescharacteristic
307C22⋊C4×C47C22⋊C411yescharacteristic
308C22⋊C4×C47C22⋊C411yescharacteristic
309C22⋊C4×C47C22⋊C411yescharacteristic
310C22⋊C4×C47C22⋊C411yescharacteristic
311C22⋊C4×C47C22⋊C411yescharacteristic
312C22⋊C4×C47C22⋊C411yescharacteristic
313C22⋊C4×C47C22⋊C411yescharacteristic
314C22⋊C4×C47C22⋊C411yescharacteristic
315C22⋊C4×C47C22⋊C411yescharacteristic
316C22⋊C4×C47C22⋊C411yescharacteristic
317C22⋊C4×C47C22⋊C411yescharacteristic
318C22⋊C4×C47C22⋊C411yescharacteristic
319C22⋊C4×C47C22⋊C411yescharacteristic
320C22⋊C4×C47C22⋊C411yescharacteristic
321C22⋊C4×C47C22⋊C411yescharacteristic
322C22⋊C4×C47#4112yes—
323C42×C47—42no—
324C42×C47—81no—
325C22⋊Dic47—21no—
326C22⋊Dic47—21no—
327C22⋊Dic47—21no—
328C22⋊Dic47—21no—
329C22⋊Dic47—21no—
330C22⋊Dic47—21no—
331C22⋊Dic47—21no—
332C22⋊Dic47—21no—
333C22⋊Dic47—21no—
334C22⋊Dic47—21no—
335C22⋊Dic47—21no—
336C22⋊Dic47—21no—
337C22⋊Dic47—21no—
338C22⋊Dic47—21no—
339C22⋊Dic47—21no—
340C22⋊Dic47—21no—
341C22⋊Dic47—21no—
342C22⋊Dic47—21no—
343C22⋊Dic47—21no—
344C22⋊Dic47—21no—
345C22⋊Dic47—21no—
346C22⋊Dic47—42no—
347C22⋊Dic47—42no—
348C22⋊Dic47—81no—
349C22⋊Dic47#4112yes—
350(C2×D47)⋊C4—21no—
351(C2×D47)⋊C4—21no—
352(C2×D47)⋊C4—21no—
353(C2×D47)⋊C4—21no—
354(C2×D47)⋊C4—21no—
355(C2×D47)⋊C4—21no—
356C4⋊Dic47—21no—
357C4⋊Dic47—21no—
358C4⋊Dic47—21no—
359C4⋊Dic47—21no—
360C4⋊Dic47—21no—
361C4⋊Dic47—21no—
362C4⋊Dic47—42no—
363C4⋊Dic47—81no—
364Dic47⋊C4—21no—
365Dic47⋊C4—21no—
366Dic47⋊C4—21no—
367Dic47⋊C4—21no—
368Dic47⋊C4—21no—
369Dic47⋊C4—21no—
370Dic47⋊C4—21no—
371Dic47⋊C4—21no—
372Dic47⋊C4—21no—
373Dic47⋊C4—21no—
374C4×Dic47—21no—
375C4×Dic47—21no—
376C4×Dic47—21no—
377C4×Dic47—21no—
378C4×Dic47—21no—
379C4×Dic47—21no—
380C4×Dic47—42no—
381C4×Dic47—81no—
382C23×C47—21no—
383C23×C47—21no—
384C23×C47—21no—
385C23×C47—21no—
386C23×C47—21no—
387C23×C47—21no—
388C23×C47—22no—
389C23×C47—22no—
390C23×C47—22no—
391C23×C47—21no—
392C23×C47—21no—
393C23×C47—21no—
394C23×C47—21no—
395C23×C47—21no—
396C23×C47—21no—
397C23×C47—41no—
398C23×C47—41no—
399C23×C47—41no—
400C23×C47—41no—
401C23×C47—41no—
402C23×C47—41no—
403C23×C47—41no—
404C23×C47—41no—
405C23×C47—41no—
406C23×C47—41no—
407C23×C47—41no—
408C23×C47—82no—
409C23×C47—82no—
410C23×C47—82no—
411C23×C47—82no—
412C23×C47C2×C22⋊C411yescharacteristic
413C23×C47C2×C22⋊C411yescharacteristic
414C23×C47C2×C22⋊C411yescharacteristic
415C23×C47C2×C22⋊C411yescharacteristic
416C23×C47C23×C411yescharacteristic
417C23×C47C22×D411yescharacteristic
418C23×C47C22×D411yescharacteristic
419C23×C47C2×#4111yescharacteristic
420C23×C47C2×#4111yescharacteristic
421C23×C47H(5,𝔽2)11yescharacteristic
422C23×C472−1+411yescharacteristic
423C22×D47—21no—
424C22×D47—21no—
425C22×D47—21no—
426C22×D47—41no—
427C22×D47—41no—
428C2×C4×C47—21no—
429C2×C4×C47—21no—
430C2×C4×C47—21no—
431C2×C4×C47—21no—
432C2×C4×C47—21no—
433C2×C4×C47—21no—
434C2×C4×C47—21no—
435C2×C4×C47—21no—
436C2×C4×C47—21no—
437C2×C4×C47—21no—
438C2×C4×C47—21no—
439C2×C4×C47—21no—
440C2×C4×C47—22no—
441C2×C4×C47—41no—
442C2×C4×C47—41no—
443C2×C4×C47—41no—
444C2×C4×C47—41no—
445C2×C4×C47—41no—
446C2×C4×C47—41no—
447C2×C4×C47—41no—
448C2×C4×C47—41no—
449C2×C4×C47—41no—
450C2×C4×C47—41no—
451C2×C4×C47—41no—
452C2×C4×C47—41no—
453C2×C4×C47—41no—
454C2×C4×C47—41no—
455C2×C4×C47—41no—
456C2×C4×C47—41no—
457C2×C4×C47—41no—
458C2×C4×C47—84no—
459C2×C4×C47C2×C22⋊C411yescharacteristic
460C2×C4×C47C2×C22⋊C411yescharacteristic
461C2×C4×C47C2×C22⋊C411yescharacteristic
462C2×C4×C47C2×C22⋊C411yescharacteristic
463C2×C4×C47C2×C22⋊C411yescharacteristic
464C2×C4×C47C2×C22⋊C411yescharacteristic
465C2×C4×C47C2×C22⋊C411yescharacteristic
466C2×C4×C47C2×C22⋊C411yescharacteristic
467C22⋊D47—42no—
468C22⋊D47—41no—
469C22⋊D47—41no—
470C22⋊D47—41no—
471C22⋊D47—41no—
472C22⋊D47—42no—
473C22⋊D47—81no—
474C22⋊D47—81no—
475C2×Dic47—21no—
476C2×Dic47—21no—
477C2×Dic47—21no—
478C2×Dic47—21no—
479C2×Dic47—21no—
480C2×Dic47—21no—
481C2×Dic47—21no—
482C2×Dic47—21no—
483C2×Dic47—21no—
484C2×Dic47—22no—
485C2×Dic47—41no—
486C2×Dic47—41no—
487C2×Dic47—42no—
488C2×Dic47—42no—
489C2×Dic47—41no—
490C2×Dic47—41no—
491C2×Dic47—41no—
492C2×Dic47—41no—
493C2×Dic47—41no—
494C2×Dic47—41no—
495C2×Dic47—41no—
496C2×Dic47—41no—
497C2×Dic47—41no—
498C2×Dic47—41no—
499C2×Dic47—41no—
500C2×Dic47—41no—
501C2×Dic47—41no—
502C2×Dic47—41no—
503C2×Dic47—41no—
504C2×Dic47—81no—
505C2×Dic47—81no—
506C2×Dic47—84no—
507C4×D47—81no—
508C4×D47—81no—
509Dic94—81no—
510Dic94—81no—
511#22477—471nomaximal, Sylow
512C22×C47—21no—
513C22×C47—21no—
514C22×C47—21no—
515C22×C47—21no—
516C22×C47—21no—
517C22×C47—21no—
518C22×C47—21no—
519C22×C47—21no—
520C22×C47—21no—
521C22×C47—21no—
522C22×C47—21no—
523C22×C47—21no—
524C22×C47—21no—
525C22×C47—21no—
526C22×C47—21no—
527C22×C47—21no—
528C22×C47—21no—
529C22×C47—41no—
530C22×C47—41no—
531C22×C47—41no—
532C22×C47—41no—
533C22×C47—42no—
534C22×C47—42no—
535C22×C47—42no—
536C22×C47—42no—
537C22×C47—42no—
538C22×C47—42no—
539C22×C47—81no—
540C22×C47—81no—
541C22×C47—81no—
542C22×C47—81no—
543C22×C47—81no—
544C22×C47—81no—
545C22×C47#41012yes—
546C22×C47C22×C22⋊C411yescharacteristic
547C22×C47C4×#4111yescharacteristic
548C22×C47#52011yescharacteristic
549C22×C47#54611yescharacteristic
550C22×C47#54611yescharacteristic
551C22×C47#54711yescharacteristic
552C22×C47#54711yescharacteristic
553C2×D47—41no—
554C2×D47—41no—
555C2×D47—41no—
556C2×D47—81no—
557C2×D47—81no—
558C4×C47—21no—
559C4×C47—21no—
560C4×C47—21no—
561C4×C47—21no—
562C4×C47—21no—
563C4×C47—21no—
564C4×C47—21no—
565C4×C47—21no—
566C4×C47—42no—
567C4×C47—81no—
568C4×C47—81no—
569C4×C47—81no—
570Dic47—42no—
571Dic47—41no—
572Dic47—41no—
573Dic47—41no—
574Dic47—41no—
575Dic47—41no—
576Dic47—41no—
577Dic47—41no—
578Dic47—81no—
579Dic47—81no—
580Dic47—81no—
581C2×#551—471no—
582#2342—471no—
583#2342D4711yescharacteristic, complemented
584#1996—471no—
585#1996—471no—
586#1899—471no—
587#1899—471no—
588#1898—471no—
589#1898—471no—
590#1820—471no—
591#1819—471no—
592#1799—471no—
593C4×#99—471no—
594#1740—471no—
595C2×#342—471no—
596C2×C47—21no—
597C2×C47—21no—
598C2×C47—21no—
599C2×C47—21no—
600C2×C47—21no—
601C2×C47—21no—
602C2×C47—22no—
603C2×C47—41no—
604C2×C47—41no—
605C2×C47—41no—
606C2×C47#233911yescharacteristic
607C2×C47C2×#41011yescharacteristic
608C2×C47#288311yescharacteristic
609D47—81no—
610#551—941no—
611#551—941no—
612#551—941no—
613#551—941no—
614#551—941no—
615#551—941no—
616#551—941no—
617#551—941no—
618C2×#126—471no—
619C2×#126—471no—
620C2×#124—471no—
621C2×#123—471no—
622C2×#123—471no—
623C2×#123—471no—
624C2×C22⋊Q8—471no—
625C2×C22⋊Q8—471no—
626C2×#120—471no—
627C2×C4×D4—471no—
628C2×C4×D4—471no—
629C2×#117—471no—
630C2×#117—471no—
631C2×#117—471no—
632C2×#117C2×D4711yescharacteristic
633C22×C22⋊C4—471no—
634C22×C22⋊C4—471no—
635C22×C22⋊C4C2×D4711yescharacteristic
636C22×C22⋊C4C2×D4711yescharacteristic
637C2×#99—471no—
638C2×#99—471no—
639C2×#99—471no—
640C2×#99—471no—
641#388—21no—
642#388—21no—
643#388—941no—
644#388—941no—
645#385—21no—
646#385—941no—
647#381—471no—
648#381C2×D4711yescharacteristic
649#380—471no—
650#380C2×D4711yescharacteristic
651#379—471no—
652#379C2×D4711yescharacteristic
653C4×C22⋊C4—21no—
654C4×C22⋊C4—471no—
655C4×C22⋊C4—941no—
656C4×C22⋊C4C2×D4711yescharacteristic
657#342—471no—
658#342—471no—
659#342—471no—
660#342—471no—
661#342—471no—
662#342—471no—
663#342—471no—
664#342—471no—
665#342—471no—
666#342—471no—
667#342—471no—
668#342—471no—
669C47#2247711yescharacteristic, complemented, Sylow
670C25C22×D4711yescharacteristic
671C22×Q8—471no—
672C22×D4—471no—
673C22×D4—471no—
674C22×D4—471no—
675C23×C4—21no—
676C23×C4—471no—
677C23×C4—471no—
678C23×C4—471no—
679C23×C4—941no—
680C23×C4C22×D4711yescharacteristic
681C23×C4C22×D4711yescharacteristic
682#126—941no—
683#126—941no—
684#126—941no—
685#126—941no—
686#126—941no—
687#126—941no—
688#126—941no—
689#126—941no—
690#124—941no—
691#124—941no—
692#124—941no—
693#124—941no—
694#123—941no—
695#123—941no—
696#123—941no—
697#123—941no—
698#123—941no—
699#123—941no—
700#123—941no—
701#123—941no—
702#123—941no—
703#123—941no—
704#123—941no—
705#123—941no—
706C22⋊Q8—941no—
707C22⋊Q8—941no—
708C22⋊Q8—941no—
709C22⋊Q8—941no—
710C22⋊Q8—941no—
711C22⋊Q8—941no—
712C22⋊Q8—941no—
713C22⋊Q8—941no—
714#120—941no—
715#120—941no—
716#120—941no—
717#120—941no—
718C4×D4—941no—
719C4×D4—941no—
720C4×D4—941no—
721C4×D4—941no—
722C4×D4—941no—
723C4×D4—941no—
724C4×D4—941no—
725C4×D4—941no—
726#117—22no—
727#117—41no—
728#117—941no—
729#117—941no—
730#117—941no—
731#117—941no—
732#117—941no—
733#117—941no—
734#117—941no—
735#117—941no—
736#117—942no—
737#117—1881no—
738C2×C4⋊C4—21no—
739C2×C4⋊C4—21no—
740C2×C4⋊C4—471no—
741C2×C4⋊C4—471no—
742C2×C4⋊C4—471no—
743C2×C4⋊C4—471no—
744C2×C4⋊C4—471no—
745C2×C4⋊C4—471no—
746C2×C4⋊C4—471no—
747C2×C4⋊C4—471no—
748C2×C4⋊C4—941no—
749C2×C4⋊C4—941no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—21no—
754C2×C22⋊C4—41no—
755C2×C22⋊C4—471no—
756C2×C22⋊C4—471no—
757C2×C22⋊C4—471no—
758C2×C22⋊C4—471no—
759C2×C22⋊C4—471no—
760C2×C22⋊C4—471no—
761C2×C22⋊C4—471no—
762C2×C22⋊C4—471no—
763C2×C22⋊C4—471no—
764C2×C22⋊C4—471no—
765C2×C22⋊C4—471no—
766C2×C22⋊C4—471no—
767C2×C22⋊C4—471no—
768C2×C22⋊C4—471no—
769C2×C22⋊C4—942no—
770C2×C22⋊C4—941no—
771C2×C22⋊C4—941no—
772C2×C22⋊C4—941no—
773C2×C22⋊C4—941no—
774C2×C22⋊C4—941no—
775C2×C22⋊C4—941no—
776C2×C22⋊C4—941no—
777C2×C22⋊C4—1881no—
778C2×C22⋊C4C4×D4711yescharacteristic
779C2×C22⋊C4C4×D4711yescharacteristic
780C2×C22⋊C4C4×D4711yescharacteristic
781C2×C22⋊C4C4×D4711yescharacteristic
782C2×C22⋊C4D18811yescharacteristic
783C2×C22⋊C4D18811yescharacteristic
784C2×C22⋊C4D18811yescharacteristic
785C2×C22⋊C4D18811yescharacteristic
786C2×C22⋊C4C22⋊D4711yescharacteristic
787C2×C22⋊C4C22⋊D4711yescharacteristic
788C2×C22⋊C4C22⋊D4711yescharacteristic
789C2×C22⋊C4C22⋊D4711yescharacteristic
790C2×C22⋊C4C22×D4711yescharacteristic
791C2×C22⋊C4C22×D4711yescharacteristic
792C2×C22⋊C4C22×D4711yescharacteristic
793C2×C22⋊C4C22×D4711yescharacteristic
794C2×C42—21no—
795C2×C42—21no—
796C2×C42—471no—
797C2×C42—471no—
798C2×C42—471no—
799C2×C42—941no—
800C2×C42—941no—
801#99—942no—
802#99—942no—
803#99—1881no—
804#99—1881no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—941no—
810#95—941no—
811#95—941no—
812#95—941no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—42no—
818C24—81no—
819C24—471no—
820C24C2×C4×D4711yescharacteristic
821C24C2×C4×D4711yescharacteristic
822C24C2×D18811yescharacteristic
823C24C2×D18811yescharacteristic
824C24C2×C22⋊D4711yescharacteristic
825C24C2×C22⋊D4711yescharacteristic
826C24C23×D4711yescharacteristic
827C2×Q8—941no—
828C2×Q8—941no—
829C2×Q8—3761no—
830C2×D4—941no—
831C2×D4—941no—
832C2×D4—941no—
833C2×D4—941no—
834C2×D4—941no—
835C2×D4—941no—
836C2×D4—941no—
837C2×D4—941no—
838C2×D4—941no—
839C2×D4—941no—
840C2×D4—3761no—
841C2×D4—1882no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—471no—
855C22×C4—471no—
856C22×C4—471no—
857C22×C4—471no—
858C22×C4—471no—
859C22×C4—471no—
860C22×C4—471no—
861C22×C4—941no—
862C22×C4—941no—
863C22×C4—941no—
864C22×C4—941no—
865C22×C4—941no—
866C22×C4—941no—
867C22×C4—941no—
868C22×C4—941no—
869C22×C4—941no—
870C22×C4—941no—
871C22×C4—3761no—
872C22×C4—3761no—
873C22×C4—3761no—
874C22×C4—1882no—
875C22×C4—1882no—
876C22×C4—1882no—
877C22×C4C2×C4×D4711yescharacteristic
878C22×C4C2×C4×D4711yescharacteristic
879C22×C4C2×C4×D4711yescharacteristic
880C22×C4C2×C4×D4711yescharacteristic
881C22×C4C2×D18811yescharacteristic
882C22×C4C2×D18811yescharacteristic
883C22×C4C2×D18811yescharacteristic
884C22×C4C2×D18811yescharacteristic
885C22×C4C2×C22⋊D4711yescharacteristic
886C22×C4C2×C22⋊D4711yescharacteristic
887C22×C4C2×C22⋊D4711yescharacteristic
888C22×C4C2×C22⋊D4711yescharacteristic
889C4⋊C4—42no—
890C4⋊C4—81no—
891C4⋊C4—941no—
892C4⋊C4—941no—
893C4⋊C4—941no—
894C4⋊C4—941no—
895C4⋊C4—941no—
896C4⋊C4—941no—
897C4⋊C4—941no—
898C4⋊C4—941no—
899C4⋊C4—941no—
900C4⋊C4—941no—
901C4⋊C4—941no—
902C4⋊C4—941no—
903C4⋊C4—941no—
904C4⋊C4—941no—
905C4⋊C4—941no—
906C4⋊C4—941no—
907C4⋊C4—3761no—
908C4⋊C4—1882no—
909C22⋊C4—21no—
910C22⋊C4—21no—
911C22⋊C4—21no—
912C22⋊C4—21no—
913C22⋊C4—21no—
914C22⋊C4—21no—
915C22⋊C4—21no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—81no—
919C22⋊C4—472no—
920C22⋊C4—941no—
921C22⋊C4—941no—
922C22⋊C4—941no—
923C22⋊C4—941no—
924C22⋊C4—941no—
925C22⋊C4—941no—
926C22⋊C4—941no—
927C22⋊C4—941no—
928C22⋊C4—941no—
929C22⋊C4—941no—
930C22⋊C4—941no—
931C22⋊C4—941no—
932C22⋊C4—941no—
933C22⋊C4—941no—
934C22⋊C4—941no—
935C22⋊C4—941no—
936C22⋊C4—941no—
937C22⋊C4—941no—
938C22⋊C4—941no—
939C22⋊C4—941no—
940C22⋊C4—941no—
941C22⋊C4—941no—
942C22⋊C4—941no—
943C22⋊C4—941no—
944C22⋊C4—941no—
945C22⋊C4—941no—
946C22⋊C4—941no—
947C22⋊C4—3761no—
948C22⋊C4—1882no—
949C22⋊C4—1882no—
950C22⋊C4(C2×D47)⋊C411yescharacteristic
951C22⋊C4(C2×D47)⋊C411yescharacteristic
952C22⋊C4(C2×D47)⋊C411yescharacteristic
953C22⋊C4(C2×D47)⋊C411yescharacteristic
954C22⋊C4(C2×D47)⋊C411yescharacteristic
955C22⋊C4(C2×D47)⋊C411yescharacteristic
956C22⋊C4(C2×D47)⋊C411yescharacteristic
957C22⋊C4(C2×D47)⋊C411yescharacteristic
958C22⋊C4(C2×D47)⋊C411yescharacteristic
959C22⋊C4(C2×D47)⋊C411yescharacteristic
960C22⋊C4(C2×D47)⋊C411yescharacteristic
961C22⋊C4(C2×D47)⋊C411yescharacteristic
962C22⋊C4(C2×D47)⋊C411yescharacteristic
963C22⋊C4(C2×D47)⋊C411yescharacteristic
964C22⋊C4(C2×D47)⋊C411yescharacteristic
965C22⋊C4(C2×D47)⋊C411yescharacteristic
966C22⋊C4#1062535212yes—
967C42—42no—
968C42—81no—
969C42—941no—
970C42—941no—
971C42—941no—
972C42—941no—
973C42—941no—
974C42—941no—
975C42—3761no—
976C42—1882no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—82no—
1004C23—82no—
1005C23—82no—
1006C23—82no—
1007C23—941no—
1008C23—941no—
1009C23—941no—
1010C23—1881no—
1011C23—1881no—
1012C23C2×(C2×D47)⋊C411yescharacteristic
1013C23C2×(C2×D47)⋊C411yescharacteristic
1014C23C2×(C2×D47)⋊C411yescharacteristic
1015C23C2×(C2×D47)⋊C411yescharacteristic
1016C23C22×C4×D4711yescharacteristic
1017C23C22×C22⋊D4711yescharacteristic
1018C23C22×D18811yescharacteristic
1019C23#41×D4711yescharacteristic
1020C23C2×#1062535211yescharacteristic
1021C23#1309406911yescharacteristic
1022C23#1309407111yescharacteristic
1023Q8—3761no—
1024Q8—3761no—
1025D4—3761no—
1026D4—3761no—
1027D4—1882no—
1028D4—1881no—
1029D4—1881no—
1030D4—1881no—
1031D4—1881no—
1032D4—1882no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—84no—
1064C2×C4—942no—
1065C2×C4—941no—
1066C2×C4—941no—
1067C2×C4—941no—
1068C2×C4—941no—
1069C2×C4—941no—
1070C2×C4—941no—
1071C2×C4—941no—
1072C2×C4—941no—
1073C2×C4—941no—
1074C2×C4—3761no—
1075C2×C4—3761no—
1076C2×C4—3764no—
1077C2×C4—3761no—
1078C2×C4—3761no—
1079C2×C4—1881no—
1080C2×C4—1881no—
1081C2×C4—1881no—
1082C2×C4—1881no—
1083C2×C4—1881no—
1084C2×C4—1881no—
1085C2×C4—1881no—
1086C2×C4—1881no—
1087C2×C4—1881no—
1088C2×C4—1881no—
1089C2×C4—1881no—
1090C2×C4—1882no—
1091C2×C4—1882no—
1092C2×C4—1881no—
1093C2×C4—1881no—
1094C2×C4—1881no—
1095C2×C4—1881no—
1096C2×C4—1881no—
1097C2×C4—1881no—
1098C2×C4C2×(C2×D47)⋊C411yescharacteristic
1099C2×C4C2×(C2×D47)⋊C411yescharacteristic
1100C2×C4C2×(C2×D47)⋊C411yescharacteristic
1101C2×C4C2×(C2×D47)⋊C411yescharacteristic
1102C2×C4C2×(C2×D47)⋊C411yescharacteristic
1103C2×C4C2×(C2×D47)⋊C411yescharacteristic
1104C2×C4C2×(C2×D47)⋊C411yescharacteristic
1105C2×C4C2×(C2×D47)⋊C411yescharacteristic
1106C22—21no—
1107C22—21no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—3761no—
1140C22—3761no—
1141C22—1881no—
1142C22—1881no—
1143C22—1881no—
1144C22#1568909612yes—
1145C22C22×(C2×D47)⋊C411yescharacteristic
1146C22C4×#1062535211yescharacteristic
1147C22#1568960211yescharacteristic
1148C22#1568976711yescharacteristic
1149C22#1568976811yescharacteristic
1150C22#1568977211yescharacteristic
1151C22#1568977711yescharacteristic
1152C4—21no—
1153C4—21no—
1154C4—21no—
1155C4—21no—
1156C4—21no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—42no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—3761no—
1165C4—3761no—
1166C4—3761no—
1167C4—1882no—
1168C4—1881no—
1169C4—1881no—
1170C4—1881no—
1171C4—1881no—
1172C4—1881no—
1173C4—1881no—
1174C4—1881no—
1175C2—21no—
1176C2—21no—
1177C2—21no—
1178C2—21no—
1179C2—22no—
1180C2—21no—
1181C2—21no—
1182C2—41no—
1183C2—41no—
1184C2—41no—
1185C2—3761no—
1186C2#2024621311yescharacteristic
1187C2C2×#1568909611yescharacteristic
1188C2#2025184811yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#2342C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#13093993C22
cosocleC24×C47C24
hypercenter#2342D47
hypocenterC47#22477
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. #20246237C2semidirect
3. #20244373C2semidirect
4. #20244372C2semidirect
5. #20243846C2semidirect
6. #20243844C2semidirect
9. #20243463C2semidirect
10. #20243460C2semidirect
11. #20243373C2semidirect
12. C4×#13093938C2semidirect
13. #20243120C2semidirect
14. C2×#15688889C2semidirect
15. C47×#2342C2semidirect
24. C2×#13094017C4semidirect
25. C2×#13094017C4semidirect
26. C2×#13094010C4semidirect
27. C2×#13094008C4semidirect
29. C2×#13094006C4semidirect
31. C2×#13094001C4semidirect
34. C2×(C22⋊D47)⋊C4C4semidirect
37. C2×#13093980C4semidirect
75. C22×Dic94C2×C4semidirect
82. C22×C4×D47C2×C4semidirect
139. C2×C4⋊Dic47C2×C4semidirect
140. C2×C4⋊Dic47C2×C4semidirect
141. C2×C4⋊Dic47C2×C4semidirect
142. C2×Dic47⋊C4C2×C4semidirect
143. C2×Dic47⋊C4C2×C4semidirect
144. C2×Dic47⋊C4C2×C4semidirect
145. C2×Dic47⋊C4C2×C4semidirect
146. C2×Dic47⋊C4C2×C4semidirect
167. C2×(C2×D47)⋊C4C2×C4semidirect
168. C2×(C2×D47)⋊C4C2×C4semidirect
169. C2×(C2×D47)⋊C4C2×C4semidirect
172. C2×C4×Dic47C2×C4semidirect
173. C2×C4×Dic47C2×C4semidirect
174. C2×C4×Dic47C2×C4semidirect
583. #2342D47semidirect
669. C47#22477semidirect

Maximal subgroups

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

subgroupindex
C2×#156897992
#202462372
#202443732
#202443722
#202438462
#202438442
#202438412
#202438392
#202434632
#202434602
#202433732
C4×#130939382
#202431202
C2×#156888892
C47×#23422
#2247747