Finite Group Databasebeta

← #29696716

Subgroups — #29696716

Order 15616.

1004 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459397C211yesmaximal, characteristic
2#21454770C211yesmaximal, characteristic, complemented
3#21448291C211yesmaximal, characteristic, complemented
4#21446798C211yesmaximal, characteristic, complemented
5#21446794C211yesmaximal, characteristic, complemented
6#21446764C211yesmaximal, characteristic, complemented
7#21446761C211yesmaximal, characteristic, complemented
8#21446761C211yesmaximal, characteristic, complemented
9#21445838C211yesmaximal, characteristic
10#21445838C211yesmaximal, characteristic
11#21445836C211yesmaximal, characteristic
12#21445630C211yesmaximal, characteristic
13#21445628C211yesmaximal, characteristic
14#21445623C211yesmaximal, characteristic
15C61×#1995C211yesmaximal, characteristic, complemented
16#16840492C411yescharacteristic, complemented
17#16840489C411yescharacteristic, complemented
18#16840489C411yescharacteristic, complemented
19#16840487C411yescharacteristic, complemented
20#16840473C411yescharacteristic, complemented
21#16840470—21no—
22#16840468C411yescharacteristic, complemented
23#16840468C411yescharacteristic, complemented
24#16840466—21no—
25#16840466—21no—
26#16840427C411yescharacteristic, complemented
27#16840425—21no—
28#16840316—21no—
29#16840316—21no—
30#16840316—21no—
31#16840315C2211yescharacteristic
32#16840315C2211yescharacteristic
33C4×#11758222C2211yescharacteristic
34#16840230C2211yescharacteristic
35#16840230C2211yescharacteristic
36C2×C4×Dic122C2211yescharacteristic
37C4×Q8×D61—21no—
38#16839891—21no—
39#16839891—21no—
40#16839889—21no—
41#16839886—21no—
42#16839785C2211yescharacteristic
43#16839785C2211yescharacteristic
44C2×#14519705C2211yescharacteristic
45C2×#14519705C2211yescharacteristic
46C2×#14519703C2211yescharacteristic
47C2×#14519703C2211yescharacteristic
48C4×#11758194C2211yescharacteristic
49M16×Dic61C2211yescharacteristic
50M16×Dic61C2211yescharacteristic
51#16839666—21no—
52#16839659—21no—
53#16839649—21no—
54#16839645—21no—
55C4×#11758196C2211yescharacteristic
56C4×#11758196C2211yescharacteristic
57C4×C4⋊Dic61C2211yescharacteristic
58#16839608C2211yescharacteristic
59C42×Dic61C2211yescharacteristic
60#16839523C2211yescharacteristic
61#16839523C2211yescharacteristic
62#16839522C2211yescharacteristic
63#16839522C2211yescharacteristic
64#16839521C2211yescharacteristic
65#16839521C2211yescharacteristic
66#16839521C2211yescharacteristic
67#16839521C2211yescharacteristic
68C61×#533C2211yescharacteristic
69C61×#423C2211yescharacteristic
70C61×#376C2211yescharacteristic
71C61×#339C2211yescharacteristic
72C61×#339C2211yescharacteristic
73C61×#339C2211yescharacteristic
74C61×#339C2211yescharacteristic
75C2×#11758222C2311yescharacteristic
76C22×Dic122D411yescharacteristic
77C2×Q8×D61—21no—
78C2×#11758194C2311yescharacteristic
79C2×#11758194C2311yescharacteristic
80#14519776—21no—
81#14519776—21no—
82#14519776—21no—
83#14519776C2×C411yescharacteristic
84#14519776C2×C411yescharacteristic
85#14519776C2×C411yescharacteristic
86#14519776C2×C411yescharacteristic
87#14519775—21no—
88#14519775—21no—
89#14519775—21no—
90#14519768C2×C411yescharacteristic
91#14519768C2×C411yescharacteristic
92#14519768C2×C411yescharacteristic
93#14519768C2×C411yescharacteristic
94#14519767—21no—
95#14519767—21no—
96#14519767—21no—
97#14519767—21no—
98#14519767—21no—
99#14519767—21no—
100#14519757—21no—
101#14519757—21no—
102#14519757—21no—
103#14519755—21no—
104#14519755—21no—
105#14519755—21no—
106#14519755—21no—
107#14519755—21no—
108#14519755—21no—
109#14519754—21no—
110#14519754—21no—
111#14519754—21no—
112#14519754—21no—
113#14519753—21no—
114#14519753—21no—
115#14519753—21no—
116Q8×Dic61—21no—
117C4×Dic122—21no—
118C4×Dic122—21no—
119C4×Dic122—21no—
120C4×Dic122—21no—
121C4×Dic122C2×C411yescharacteristic
122C4×Dic122C2×C411yescharacteristic
123C4×Dic122C2×C411yescharacteristic
124C4×Dic122C2×C411yescharacteristic
125C4×Dic122C2×C411yescharacteristic
126C4×Dic122C2×C411yescharacteristic
127C4×Dic122D411yescharacteristic
128C4×Dic122D411yescharacteristic
129C4×Dic122D411yescharacteristic
130C4×Dic122D411yescharacteristic
131#14519742—21no—
132#14519742—21no—
133#14519742—21no—
134#14519742C2×C411yescharacteristic
135#14519742C2×C411yescharacteristic
136#14519742C2×C411yescharacteristic
137#14519742C2×C411yescharacteristic
138C4×D244C2×C411yescharacteristic
139C4×D244C2×C411yescharacteristic
140#14519739C2×C411yescharacteristic
141#14519739C2×C411yescharacteristic
142#14519739C2×C411yescharacteristic
143#14519739C2×C411yescharacteristic
144C4×C22⋊D61—21no—
145C4×C22⋊D61—21no—
146#14519737—21no—
147#14519737—21no—
148#14519737—21no—
149#14519737—21no—
150#14519736C2311yescharacteristic
151#14519734—21no—
152#14519734—21no—
153#14519734—21no—
154C2×C4⋊Dic61—21no—
155C2×C4⋊Dic61D411yescharacteristic
156C2×#11758196—21no—
157C2×#11758196—21no—
158C2×#11758196D411yescharacteristic
159C2×#11758196D411yescharacteristic
160C4⋊C4×D61—21no—
161C4⋊C4×D61—21no—
162C4⋊C4×D61—21no—
163C2×C4×Dic61—21no—
164C2×C4×Dic61—21no—
165C2×C4×Dic61C2311yescharacteristic
166C2×C4×Dic61C2311yescharacteristic
167C2×C4×Dic61C2311yescharacteristic
168C2×C4×Dic61C2311yescharacteristic
169C42×D61—21no—
170C42×D61—21no—
171C42×D61—21no—
172#14519706—21no—
173#14519706—21no—
174#14519706—21no—
175#14519706—21no—
176#14519705—22no—
177#14519705Q814yescomplemented
178#14519703—22no—
179#14519703—22no—
180#14519688—21no—
181#14519687—21no—
182#14519687—21no—
183C4×#92418—21no—
184C8×Dic61—21no—
185C8×Dic61—21no—
186#14519684—21no—
187#14519684—21no—
188#14519684—21no—
189#14519684—21no—
190#14519684—21no—
191C2×M16×C61C2311yescharacteristic
192C2×M16×C61C2311yescharacteristic
193C4⋊Q8×C61C2×C411yescharacteristic
194C4⋊Q8×C61C2×C411yescharacteristic
195#125×C61C2×C411yescharacteristic
196#125×C61C2×C411yescharacteristic
197C22⋊Q8×C61—21no—
198C22⋊Q8×C61—21no—
199C4×Q8×C61—21no—
200C4×Q8×C61—21no—
201#117×C61C2311yescharacteristic
202#117×C61C2311yescharacteristic
203C2×C42×C61C2311yescharacteristic
204C2×C42×C61C2311yescharacteristic
205C2×C42×C61C2311yescharacteristic
206C4⋊C8×C61—21no—
207C4⋊C8×C61—21no—
208#95×C61—21no—
209#95×C61—21no—
210C2×Q8×C61—21no—
211C2×Q8×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2411yescharacteristic
217C2×C22⋊D61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224Q8×D61—44no—
225#11758222—21no—
226#11758222—21no—
227#11758222C2×Q812yes—
228#11758222#4112yes—
229C2×D244C22×C411yescharacteristic
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—42no—
242C2×Dic122C22⋊C411yescharacteristic
243C2×Dic122C22⋊C411yescharacteristic
244C2×Dic122C22⋊C411yescharacteristic
245C2×Dic122C22⋊C411yescharacteristic
246C2×Dic122C22×C411yescharacteristic
247M16×C61—21no—
248M16×C61—21no—
249M16×C61—21no—
250M16×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C22×C411yescharacteristic
260C4⋊C4×C61C22×C411yescharacteristic
261C4⋊C4×C61C22×C411yescharacteristic
262C4⋊C4×C61C22×C411yescharacteristic
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C42×C61—21no—
266C42×C61—21no—
267C42×C61—21no—
268C42×C61—21no—
269C42×C61—21no—
270C42×C61C22×C411yescharacteristic
271C42×C61C22×C411yescharacteristic
272C42×C61C2×D411yescharacteristic
273C42×C61C2×D411yescharacteristic
274C42×C61C2×Q812yescomplemented
275C22⋊Dic61—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—42no—
287C4⋊Dic61C22⋊C411yescharacteristic
288C4⋊Dic61C22⋊C411yescharacteristic
289C4⋊Dic61C22⋊C411yescharacteristic
290C4⋊Dic61C22⋊C411yescharacteristic
291C4⋊Dic61C22×C411yescharacteristic
292C4⋊Dic61C22×C411yescharacteristic
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—42no—
308#11758196—42no—
309#11758196C22⋊C411yescharacteristic
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313#11758196C22⋊C411yescharacteristic
314#11758196C22⋊C411yescharacteristic
315#11758196C22⋊C411yescharacteristic
316#11758196C22⋊C411yescharacteristic
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61—21no—
326C4×Dic61—21no—
327C4×Dic61—21no—
328C4×Dic61—42no—
329C4×Dic61—42no—
330C4×Dic61C22×C411yescharacteristic
331C4×Dic61C22×C411yescharacteristic
332C4×Dic61C22×C411yescharacteristic
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C4×Dic61C2×D411yescharacteristic
337C4×Dic61C2×D411yescharacteristic
338#11758194—21no—
339#11758194—21no—
340#11758194—21no—
341#11758194C2×Q812yescomplemented
342C2×#92418—21no—
343C2×#92418—21no—
344C23×C61C22×D411yescharacteristic
345C22×D61—21no—
346Q8×C61—42no—
347Q8×C61—81no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—22no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61C2×C22⋊C411yescharacteristic
361C2×C4×C61C2×C22⋊C411yescharacteristic
362C2×C4×C61C2×C22⋊C411yescharacteristic
363C2×C4×C61C2×C22⋊C411yescharacteristic
364C2×C4×C61C23×C411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×Q811yescharacteristic
367C2×C4×C61C2×#4111yescharacteristic
368C2×C4×C612−1+411yescharacteristic
369C2×C4×C612−1+411yescharacteristic
370C22⋊D61—22no—
371C22⋊D61—22no—
372C2×Dic61—21no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61C2×C22⋊C411yescharacteristic
386C2×Dic61C2×C22⋊C411yescharacteristic
387C2×Dic61C2×C22⋊C411yescharacteristic
388C2×Dic61C2×C22⋊C411yescharacteristic
389C2×Dic61C2×C22⋊C411yescharacteristic
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C2×C22⋊C411yescharacteristic
393D244—21no—
394D244C4×Q812yes—
395C4×D61—22no—
396C4×D61—22no—
397C4×D61—42no—
398C4×D61—42no—
399C4×D61—42no—
400C4×D61—81no—
401C4×D61—81no—
402C4×D61—81no—
403Dic122—21no—
404Dic122—22no—
405Dic122—22no—
406Dic122—41no—
407Dic122—41no—
408Dic122—42no—
409Dic122—42no—
410Dic122—81no—
411Dic122—81no—
412Dic122C4×Q812yes—
413C8×C61—41no—
414C8×C61—41no—
415#92418—22no—
416#92418—41no—
417#22529—611nomaximal, Sylow
418C22×C61—21no—
419C22×C61—21no—
420C22×C61C22×C22⋊C411yescharacteristic
421C22×C61#54811yescharacteristic
422C22×C61D4×Q811yescharacteristic
423C2×D61—22no—
424C2×D61—41no—
425C2×D61—41no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—42no—
431C4×C61—41no—
432C4×C61—41no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61—81no—
436C4×C61C2×C4×Q811yescharacteristic
437C4×C61#51911yescharacteristic
438C4×C61#54811yescharacteristic
439C4×C61D4×Q811yescharacteristic
440Dic61—22no—
441Dic61—21no—
442Dic61—21no—
443Dic61—21no—
444Dic61—21no—
445Dic61—21no—
446Dic61—21no—
447Dic61—21no—
448Dic61—42no—
449Dic61—41no—
450Dic61—41no—
451Dic61—81no—
452Dic61#42112yes—
453Q8×#41—611no—
454Q8×M16—611no—
455#2295—611no—
456#1995—611no—
457#1995D6111yescharacteristic, complemented
458#1994—611no—
459#1986—611no—
460#1986—611no—
461#1986—611no—
462#1806—611no—
463#1806—611no—
464#1806—611no—
465#1759—611no—
466#1759—611no—
467C4×#104—611no—
468C2×C61—21no—
469C2×C61—21no—
470C2×C61Q8×C22⋊C411yescharacteristic
471C2×C61C2×#42111yescharacteristic
472C2×C61#290111yescharacteristic
473D61—42no—
474Q82—611no—
475#557—611no—
476#557—611no—
477#557—611no—
478#554—611no—
479#554—611no—
480#554—611no—
481#554—1221no—
482#554—1221no—
483#554—1221no—
484D4×Q8—611no—
485D4×Q8—1221no—
486#533—611no—
487#533—611no—
488#533—1221no—
489#533—1221no—
490#533—1221no—
491#533C2×D6111yescharacteristic
492C4×#41—611no—
493C4×#41—611no—
494C4×#41—611no—
495C2×C4×Q8—611no—
496C2×C4×Q8—1221no—
497#446—1221no—
498#446—1221no—
499#446—1221no—
500C8×Q8—1221no—
501#423—611no—
502#423—611no—
503#423C2×D6111yescharacteristic
504C2×#104—611no—
505C2×#104—611no—
506C2×#104—611no—
507C2×#104—611no—
508C4×M16—611no—
509C4×M16—611no—
510C4×M16—611no—
511#391—1221no—
512#389—1221no—
513#387—1221no—
514#387—1221no—
515C4×C4⋊C4—611no—
516C4×C4⋊C4—611no—
517C4×C4⋊C4—611no—
518#376—611no—
519#376C2×D6111yescharacteristic
520C43—611no—
521#339—611no—
522#339—611no—
523#339—611no—
524#339—611no—
525#339—611no—
526#339—611no—
527#339—611no—
528#339—611no—
529#339C2×D6111yescharacteristic
530#339C2×D6111yescharacteristic
531#339C2×D6111yescharacteristic
532#339C2×D6111yescharacteristic
533C61#2252911yescharacteristic, complemented, Sylow
534C2×#41—611no—
535C22×Q8—611no—
536C22×Q8—1221no—
537C2×M16—611no—
538C2×M16—611no—
539C2×M16C22×D6111yescharacteristic
540C2×M16C22×D6111yescharacteristic
541C4⋊Q8—611no—
542C4⋊Q8—611no—
543C4⋊Q8—611no—
544C4⋊Q8—611no—
545C4⋊Q8—1221no—
546C4⋊Q8—1221no—
547C4⋊Q8—1221no—
548C4⋊Q8—1221no—
549C4⋊Q8—1221no—
550C4⋊Q8—1221no—
551C4⋊Q8C4×D6111yescharacteristic
552C4⋊Q8C4×D6111yescharacteristic
553#125—611no—
554#125—611no—
555#125—611no—
556#125—611no—
557#125—1221no—
558#125—1221no—
559#125—1221no—
560#125—1221no—
561#125—1221no—
562#125—1221no—
563#125C4×D6111yescharacteristic
564#125C4×D6111yescharacteristic
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8—1221no—
574C22⋊Q8—1221no—
575C22⋊Q8—1221no—
576C22⋊Q8—1221no—
577C22⋊Q8—1221no—
578C22⋊Q8—1221no—
579C22⋊Q8—1221no—
580C22⋊Q8—1221no—
581C22⋊Q8—1221no—
582C22⋊Q8—1221no—
583C4×Q8—21no—
584C4×Q8—21no—
585C4×Q8—611no—
586C4×Q8—611no—
587C4×Q8—611no—
588C4×Q8—611no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—611no—
592C4×Q8—611no—
593C4×Q8—611no—
594C4×Q8—611no—
595C4×Q8—611no—
596C4×Q8—611no—
597C4×Q8—611no—
598C4×Q8—611no—
599C4×Q8—1221no—
600C4×Q8—1221no—
601C4×Q8—1221no—
602C4×Q8—1221no—
603C4×Q8—1221no—
604C4×Q8—1221no—
605C4×Q8—1221no—
606C4×Q8—1221no—
607C4×D4—611no—
608C4×D4—611no—
609C4×D4—611no—
610C4×D4—611no—
611C4×D4—611no—
612C4×D4—611no—
613C4×D4—1221no—
614C4×D4—1221no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619#117—611no—
620#117—1221no—
621#117—1221no—
622#117—1221no—
623#117C22×D6111yescharacteristic
624#117C22×D6111yescharacteristic
625C2×C4⋊C4—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4—1221no—
631C2×C4⋊C4—1221no—
632C2×C4⋊C4—1221no—
633C2×C4⋊C4—1221no—
634C2×C42—611no—
635C2×C42—611no—
636C2×C42—611no—
637C2×C42—611no—
638C2×C42—1221no—
639C2×C42—1221no—
640C2×C42—1221no—
641C2×C42—1221no—
642C2×C42—1221no—
643C2×C42C22×D6111yescharacteristic
644C2×C42C22×D6111yescharacteristic
645C2×C42C22×D6111yescharacteristic
646C4⋊C8—21no—
647C4⋊C8—21no—
648C4⋊C8—1221no—
649C4⋊C8—1221no—
650C4⋊C8—1221no—
651C4⋊C8—1221no—
652#104—614no—
653#104—1222no—
654#104—1222no—
655#104—1222no—
656#97—1221no—
657#97—1221no—
658#97—1221no—
659C4×C8—1221no—
660C4×C8—1221no—
661C4×C8—1221no—
662#95—21no—
663#95—21no—
664#95—1221no—
665#95—1221no—
666#95—1221no—
667#95—1221no—
668#95—1221no—
669#41—612no—
670#41—612no—
671#41—1221no—
672#41—1221no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—611no—
676C2×Q8—611no—
677C2×Q8—611no—
678C2×Q8—611no—
679C2×Q8—611no—
680C2×Q8—1221no—
681C2×Q8—1221no—
682C2×Q8—1221no—
683C2×Q8—1221no—
684C2×Q8—2442no—
685C2×Q8—2444no—
686C2×D4—611no—
687C2×D4—1221no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4D4×D6111yescharacteristic
704C22×C4D4×D6111yescharacteristic
705C22×C4C23×D6111yescharacteristic
706M16—21no—
707M16—21no—
708M16—21no—
709M16—21no—
710M16—612no—
711M16—1221no—
712M16—1221no—
713M16—1221no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—1221no—
717C2×C8—1221no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—611no—
725C4⋊C4—611no—
726C4⋊C4—611no—
727C4⋊C4—611no—
728C4⋊C4—611no—
729C4⋊C4—611no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—611no—
734C4⋊C4—611no—
735C4⋊C4—611no—
736C4⋊C4—611no—
737C4⋊C4—611no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—2442no—
757C4⋊C4—2442no—
758C4⋊C4—2442no—
759C4⋊C4C2×C4×D6111yescharacteristic
760C4⋊C4C2×C4×D6111yescharacteristic
761C4⋊C4C2×C4×D6111yescharacteristic
762C4⋊C4C2×C4×D6111yescharacteristic
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C42—21no—
773C42—21no—
774C42—21no—
775C42—21no—
776C42—21no—
777C42—611no—
778C42—611no—
779C42—611no—
780C42—611no—
781C42—611no—
782C42—611no—
783C42—611no—
784C42—611no—
785C42—1221no—
786C42—1221no—
787C42—1221no—
788C42—1221no—
789C42—1221no—
790C42—1221no—
791C42—1221no—
792C42—1221no—
793C42—1221no—
794C42—1221no—
795C42—1221no—
796C42—2442no—
797C42—2442no—
798C42C2×C4×D6111yescharacteristic
799C42C2×C4×D6111yescharacteristic
800C42D4×D6111yescharacteristic
801C42D4×D6111yescharacteristic
802C42Q8×D6112yescomplemented
803C23—1221no—
804C23C2×D4×D6111yescharacteristic
805Q8—42no—
806Q8—81no—
807Q8—612no—
808Q8—1222no—
809Q8—1222no—
810Q8—1221no—
811Q8—4881no—
812Q8—4881no—
813Q8—2441no—
814Q8—2441no—
815Q8—2442no—
816Q8—2442no—
817D4—612no—
818D4—1222no—
819D4—1222no—
820D4—1221no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—611no—
834C2×C4—611no—
835C2×C4—611no—
836C2×C4—611no—
837C2×C4—611no—
838C2×C4—611no—
839C2×C4—611no—
840C2×C4—611no—
841C2×C4—1222no—
842C2×C4—1221no—
843C2×C4—1222no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1221no—
847C2×C4—1221no—
848C2×C4—4881no—
849C2×C4—4881no—
850C2×C4—4881no—
851C2×C4—2442no—
852C2×C4—2442no—
853C2×C4—2442no—
854C2×C4—2441no—
855C2×C4—2441no—
856C2×C4—2441no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4C22⋊C4×D6111yescharacteristic
863C2×C4C22⋊C4×D6111yescharacteristic
864C2×C4C22⋊C4×D6111yescharacteristic
865C2×C4C22⋊C4×D6111yescharacteristic
866C2×C4C22×C4×D6111yescharacteristic
867C2×C4C2×D4×D6111yescharacteristic
868C2×C4C2×Q8×D6111yescharacteristic
869C2×C4#41×D6111yescharacteristic
870C2×C4#1451982411yescharacteristic
871C2×C4#1451982511yescharacteristic
872C8—41no—
873C8—41no—
874C8—1222no—
875C8—2441no—
876C22—21no—
877C22—21no—
878C22—1222no—
879C22—2441no—
880C22—2441no—
881C22C2×C22⋊C4×D6111yescharacteristic
882C22#1684042211yescharacteristic
883C22#1684042511yescharacteristic
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—42no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—81no—
894C4—612no—
895C4—1221no—
896C4—1221no—
897C4—1221no—
898C4—1221no—
899C4—1221no—
900C4—1221no—
901C4—1221no—
902C4—1222no—
903C4—4881no—
904C4—2442no—
905C4—2441no—
906C4—2441no—
907C4C4×Q8×D6111yescharacteristic
908C4#1684023811yescharacteristic
909C4#1684042011yescharacteristic
910C4#1684042711yescharacteristic
911C2—21no—
912C2—21no—
913C2—2442no—
914C2#2144865311yescharacteristic
915C2#421×D6111yescharacteristic
916C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1995C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758222C23
cosocleC22×C4×C61C24
hypercenter#1995D61
hypocenterC61#22529
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
2. #21454770C2semidirect
3. #21448291C2semidirect
4. #21446798C2semidirect
5. #21446794C2semidirect
6. #21446764C2semidirect
7. #21446761C2semidirect
8. #21446761C2semidirect
15. C61×#1995C2semidirect
16. #16840492C4semidirect
17. #16840489C4semidirect
18. #16840489C4semidirect
19. #16840487C4semidirect
20. #16840473C4semidirect
22. #16840468C4semidirect
23. #16840468C4semidirect
26. #16840427C4semidirect
177. #14519705Q8semidirect
274. C42×C61C2×Q8semidirect
341. #11758194C2×Q8semidirect
457. #1995D61semidirect
533. C61#22529semidirect
802. C42Q8×D61semidirect

Maximal subgroups

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

subgroupindex
#214593972
#214547702
#214482912
#214467982
#214467942
#214467642
#214467612
#214458382
#214458362
#214456302
#214456282
#214456232
C61×#19952
#2252961