Finite Group Databasebeta

← #29647860

Subgroups — #29647860

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459662C211yesmaximal, characteristic
2#21454845C211yesmaximal, characteristic, complemented
3#21448756C211yesmaximal, characteristic, complemented
4#21444373C211yesmaximal, characteristic, complemented
5#21444368C211yesmaximal, characteristic, complemented
6#21444364C211yesmaximal, characteristic, complemented
7#21444361C211yesmaximal, characteristic, complemented
8#21444359C211yesmaximal, characteristic, complemented
9#21444329C211yesmaximal, characteristic, complemented
10#21444325C211yesmaximal, characteristic, complemented
11#21444322C211yesmaximal, characteristic, complemented
12#21444320C211yesmaximal, characteristic, complemented
13#21444311C211yesmaximal, characteristic, complemented
14#21444310C211yesmaximal, characteristic, complemented
15C61×#1516C211yesmaximal, characteristic, complemented
16#16840496—21no—
17#16840495—21no—
18#16840483C411yescharacteristic, complemented
19#16840480C411yescharacteristic, complemented
20#16840476C411yescharacteristic, complemented
21#16840475C411yescharacteristic, complemented
22#16840461—21no—
23#16840457—21no—
24#16840431C411yescharacteristic, complemented
25#16840430C411yescharacteristic, complemented
26#16840414C411yescharacteristic, complemented
27#16840411C411yescharacteristic, complemented
28#16840347—21no—
29#16840345—21no—
30#16840327—21no—
31#16840314C2211yescharacteristic
32#16840307C2211yescharacteristic
33#16840275C2211yescharacteristic
34#16840273C2211yescharacteristic
35#16840272C2211yescharacteristic
36#16840241—21no—
37C2×C4×C22⋊D61C2211yescharacteristic
38#16839833—21no—
39#16839833—21no—
40#16839830—21no—
41#16839830—21no—
42#16839816C2211yescharacteristic
43#16839816C2211yescharacteristic
44#16839724C2211yescharacteristic
45#16839724C2211yescharacteristic
46C2×C22⋊#92418C2211yescharacteristic
47#16839656—21no—
48#16839644—21no—
49#16839638—21no—
50#16839629C2211yescharacteristic
51#16839621C2211yescharacteristic
52C4×C22⋊Dic61C2211yescharacteristic
53#16839609—21no—
54#16839607C2211yescharacteristic
55#95×D61C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839499C2211yescharacteristic
59#16839499C2211yescharacteristic
60#16839498C2211yescharacteristic
61#16839498C2211yescharacteristic
62#16839497C2211yescharacteristic
63#16839497C2211yescharacteristic
64#16839496C2211yescharacteristic
65#16839496C2211yescharacteristic
66#16839495C2211yescharacteristic
67#16839495C2211yescharacteristic
68C61×#525C2211yescharacteristic
69C2×C22⋊C8×C61C2211yescharacteristic
70C61×#381C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758226C2×C411yescharacteristic
76C2×#11758222C2×C411yescharacteristic, complemented
77C2×#11758224—21no—
78C2×#11758224C2×C411yescharacteristic
79C22×C22⋊D61D411yescharacteristic
80C22×C4×D61—21no—
81C22×C4×D61C2311yescharacteristic
82C2×#11758189—21no—
83C2×#11758189—21no—
84C22×#92418—21no—
85#14519776C2×C411yescharacteristic, complemented
86#14519776C2×C411yescharacteristic, complemented
87#14519775C2×C411yescharacteristic, complemented
88#14519773—21no—
89#14519773—21no—
90#14519773C2×C411yescharacteristic, complemented
91#14519772—21no—
92#14519771—21no—
93#14519770—21no—
94#14519770—21no—
95#14519767—21no—
96#14519765—21no—
97#14519764—21no—
98#14519763—21no—
99#14519763—21no—
100#14519763—21no—
101#14519763—21no—
102#14519763—21no—
103#14519762—21no—
104#14519762—21no—
105#14519760—21no—
106#14519760—21no—
107#14519759—21no—
108#14519759—21no—
109#14519758—21no—
110#14519757C2×C411yescharacteristic
111#14519756C2×C411yescharacteristic, complemented
112#14519756C2311yescharacteristic
113#14519754—21no—
114#14519753C2×C411yescharacteristic
115#14519752C2×C411yescharacteristic
116#14519751—21no—
117#14519751C2×C411yescharacteristic, complemented
118#14519751C2311yescharacteristic
119#14519750—21no—
120#14519750—21no—
121#14519750—21no—
122#14519749—21no—
123#14519749—21no—
124#14519749—21no—
125#14519749—21no—
126#14519748—21no—
127#14519748C2×C411yescharacteristic
128#14519747—21no—
129#14519746—21no—
130#14519745—21no—
131Q8×Dic61C2×C411yescharacteristic, complemented
132C4×Dic122—21no—
133#14519742—21no—
134#14519742—21no—
135#14519742C2×C411yescharacteristic, complemented
136D4×Dic61—21no—
137D4×Dic61C2×C411yescharacteristic, complemented
138#14519739—21no—
139#14519739C2×C411yescharacteristic, complemented
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61—21no—
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61C2×C411yescharacteristic
146C4×C22⋊D61C2×C411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150C4×C22⋊D61D411yescharacteristic
151#14519737—21no—
152#14519737—21no—
153#14519737—21no—
154#14519737—21no—
155#14519736C2×C411yescharacteristic, complemented
156#14519735C2×C411yescharacteristic
157#14519735C2×C411yescharacteristic
158#14519734—21no—
159#14519733—21no—
160#14519733—21no—
161C2×#11758196—21no—
162C2×#11758196—21no—
163C2×#11758196D411yescharacteristic
164C4⋊C4×D61—21no—
165C2×C22⋊Dic61—21no—
166C2×C22⋊Dic61D411yescharacteristic
167C2×#11758198—21no—
168C2×#11758198D411yescharacteristic
169C2×C4×Dic61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61C2311yescharacteristic
172#14519706—21no—
173#14519706—21no—
174C22⋊#92418—21no—
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177#14519689—21no—
178#14519689—21no—
179#14519687—21no—
180#14519687—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187C2×#41×C61C2×C411yescharacteristic, complemented
188C23×C4×C61C2311yescharacteristic
189C22×C8×C61—21no—
190#123×C61—21no—
191C22⋊Q8×C61C2×C411yescharacteristic, complemented
192C22⋊Q8×C61C2311yescharacteristic
193#121×C61C2×C411yescharacteristic, complemented
194#121×C61C2311yescharacteristic
195#120×C61—21no—
196C4×D4×C61—21no—
197C4×D4×C61—21no—
198#117×C61C2×C411yescharacteristic, complemented
199C2×C22⋊C4×C61—21no—
200C22⋊C8×C61—21no—
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61C2×D411yescharacteristic
207C23×D61C2×D411yescharacteristic
208#41×C61—81no—
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61C22×C411yescharacteristic
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—81no—
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2411yescharacteristic
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—41no—
232C2×C22⋊D61—41no—
233C2×C22⋊D61C22⋊C411yescharacteristic
234C2×C22⋊D61C22⋊C411yescharacteristic
235C2×C22⋊D61C22⋊C411yescharacteristic
236C2×C22⋊D61C22⋊C411yescharacteristic
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244#11758226—81no—
245#11758224—42no—
246#11758224—42no—
247#11758224—81no—
248#11758222—81no—
249C2×D244—21no—
250C2×D244—21no—
251C2×D244C22×C411yescharacteristic
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—42no—
256C2×C4×D61—42no—
257C2×C4×D61—81no—
258C2×C4×D61—81no—
259C2×C4×D61C22×C411yescharacteristic
260C2×C4×D61C22×C411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×Dic122—21no—
264C2×Dic122—21no—
265C2×Dic122C22×C411yescharacteristic
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—81no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61C22×C411yescharacteristic
272C4⋊C4×C61C22×C411yescharacteristic
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊C4×C61—81no—
279C42×C61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—42no—
286C22⋊Dic61C22⋊C411yescharacteristic
287C22⋊Dic61C22⋊C411yescharacteristic
288C22⋊Dic61C22⋊C411yescharacteristic
289C22⋊Dic61C22⋊C411yescharacteristic
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—42no—
299#11758198C22⋊C411yescharacteristic
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302#11758198C22⋊C411yescharacteristic
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61C22×C411yescharacteristic
306C4⋊Dic61C22×C411yescharacteristic
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—81no—
316#11758196C22⋊C411yescharacteristic
317#11758196C22⋊C411yescharacteristic
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61—42no—
326C4×Dic61—81no—
327C4×Dic61C22×C411yescharacteristic
328C4×Dic61C22×C411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C2×#92418—21no—
332C2×#92418—21no—
333C2×#92418—81no—
334#11758189—81no—
335#11758189—81no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61C2×C22⋊C411yescharacteristic
342C23×C61C2×C22⋊C411yescharacteristic
343C23×C61C22×D411yescharacteristic
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61C2×C22⋊C411yescharacteristic
350C22×D61C2×C22⋊C411yescharacteristic
351Q8×C61—41no—
352D4×C61—41no—
353D4×C61—41no—
354D4×C61—41no—
355D4×C61—81no—
356D4×C61—81no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—81no—
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C2×C4×C61C23×C411yescharacteristic
376C2×C4×C61C22×D411yescharacteristic
377C22⋊D61—41no—
378C22⋊D61—41no—
379C22⋊D61—41no—
380C22⋊D61—41no—
381C22⋊D61—42no—
382C22⋊D61—41no—
383C22⋊D61—41no—
384C22⋊D61—81no—
385C22⋊D61—81no—
386C22⋊D61—81no—
387C22⋊D61—81no—
388C22⋊D61—81no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—22no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—42no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—81no—
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C2×C22⋊C411yescharacteristic
409C2×Dic61C2×C22⋊C411yescharacteristic
410D244—41no—
411D244—81no—
412D244—81no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—42no—
418C4×D61—81no—
419C4×D61—81no—
420C4×D61—84no—
421Dic122—42no—
422Dic122—41no—
423Dic122—81no—
424C8×C61—41no—
425C8×C61—41no—
426#92418—41no—
427#92418—41no—
428#17629—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—81no—
441C22×C61—81no—
442C22×C61C22×C22⋊C411yescharacteristic
443C22×C61#57511yescharacteristic
444C22×C61#57511yescharacteristic
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—42no—
452C2×D61—42no—
453C2×D61—41no—
454C2×D61—41no—
455C2×D61—41no—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—41no—
461C4×C61—41no—
462C4×C61—41no—
463C4×C61—81no—
464C4×C61—81no—
465Dic61—21no—
466Dic61—21no—
467Dic61—21no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—42no—
472Dic61—41no—
473Dic61—41no—
474Dic61—41no—
475Dic61—81no—
476#3506—611no—
477#2973—611no—
478#2353—611no—
479#1516—611no—
480#1516D6111yescharacteristic, complemented
481#1515—611no—
482#1514—611no—
483#1513—611no—
484#1513—611no—
485#1506—611no—
486#1505—611no—
487#1504—611no—
488#1504—611no—
489#1501—611no—
490#1501—611no—
491C2×C61—21no—
492C2×C61—21no—
493C2×C61—41no—
494C2×C61—41no—
495C2×C61—81no—
496C2×C61#288311yescharacteristic
497C2×C61#289611yescharacteristic
498C2×C61#290111yescharacteristic
499D61—41no—
500D61—41no—
501D61—81no—
502#559—1221no—
503#559—1221no—
504#556—611no—
505#556—611no—
506#555—611no—
507#555—611no—
508#553—1221no—
509#553—1221no—
510#550—611no—
511#550—611no—
512#547—611no—
513#547—611no—
514#538—1221no—
515#538—1221no—
516#535—1221no—
517#533—611no—
518#532—611no—
519#525—611no—
520#525—611no—
521#525—611no—
522#525C2×D6111yescharacteristic
523#520—1221no—
524C2×C4×D4—611no—
525#435—1221no—
526#435—1221no—
527#435—1221no—
528#435—1221no—
529#432—611no—
530#432—611no—
531#407—611no—
532#407—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8C2×D6111yescharacteristic
535#388—1221no—
536#387—1221no—
537#386—1221no—
538#383—611no—
539#381C2×D6111yescharacteristic
540#380—611no—
541C4×C22⋊C4—611no—
542C4×C22⋊C4—1221no—
543#376—611no—
544C2×#95—611no—
545#328—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328—611no—
551#328C2×D6111yescharacteristic
552#328C2×D6111yescharacteristic
553#327—611no—
554#327—611no—
555#327—611no—
556#327—611no—
557#327—611no—
558#327—611no—
559#327C2×D6111yescharacteristic
560#327C2×D6111yescharacteristic
561C61#1762911yescharacteristic, complemented, Sylow
562C2×#41—611no—
563C2×#41—611no—
564C2×#41—611no—
565C2×#41—1221no—
566C2×#41C4×D6111yescharacteristic, complemented
567C22×D4—611no—
568C23×C4—611no—
569C23×C4—1221no—
570C23×C4C22×D6111yescharacteristic
571C2×M16—1221no—
572C2×M16—1221no—
573C22×C8—21no—
574C22×C8—1221no—
575C4⋊Q8—611no—
576C4⋊Q8—611no—
577C4⋊Q8—611no—
578#127—611no—
579#127—1221no—
580#127—1221no—
581#126—1221no—
582#126—1221no—
583#126—1221no—
584#126—1221no—
585#125—1221no—
586#124—1221no—
587#124—1221no—
588#124—1221no—
589#124—1221no—
590#124—1221no—
591#124—1221no—
592#124—1221no—
593#123—21no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600#123—1221no—
601C22⋊Q8—611no—
602C22⋊Q8—611no—
603C22⋊Q8—611no—
604C22⋊Q8—611no—
605C22⋊Q8—1221no—
606C22⋊Q8C4×D6111yescharacteristic, complemented
607C22⋊Q8C22×D6111yescharacteristic
608#121—611no—
609#121—611no—
610#121—611no—
611#121—611no—
612#121—1221no—
613#121—1221no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121C4×D6111yescharacteristic, complemented
622#121C22×D6111yescharacteristic
623#120—21no—
624#120—1221no—
625#120—1221no—
626#120—1221no—
627C4×Q8—611no—
628C4×Q8—611no—
629C4×Q8—1221no—
630C4×Q8—1221no—
631C4×Q8—1221no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—611no—
635C4×D4—611no—
636C4×D4—611no—
637C4×D4—611no—
638C4×D4—611no—
639C4×D4—611no—
640C4×D4—611no—
641C4×D4—611no—
642C4×D4—611no—
643C4×D4—611no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4—1221no—
648C4×D4—1221no—
649C4×D4—1221no—
650C4×D4—1221no—
651C4×D4—1221no—
652C4×D4—1221no—
653#117—611no—
654#117—611no—
655#117—611no—
656#117—1221no—
657#117—1221no—
658#117—1221no—
659#117C4×D6111yescharacteristic, complemented
660C2×C4⋊C4—611no—
661C2×C4⋊C4—1221no—
662C2×C4⋊C4—1221no—
663C2×C4⋊C4—1221no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—611no—
666C2×C22⋊C4—611no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C42—611no—
670C2×C42—1221no—
671C2×C42—1221no—
672C4⋊C8—1221no—
673C4⋊C8—1221no—
674C22⋊C8—21no—
675C22⋊C8—611no—
676C22⋊C8—611no—
677C22⋊C8—1221no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680C22⋊C8C22×D6111yescharacteristic
681C22⋊C8C22×D6111yescharacteristic
682#97—1221no—
683#97—1221no—
684#95—21no—
685#95—611no—
686#95—611no—
687#95—1221no—
688#95—1221no—
689#95—1221no—
690#95—1221no—
691#95C22×D6111yescharacteristic
692#95C22×D6111yescharacteristic
693C24—611no—
694C24D4×D6111yescharacteristic
695#41—81no—
696#41—4881no—
697#41—4881no—
698#41—4881no—
699#41—2442no—
700#41—2442no—
701C2×Q8—611no—
702C2×Q8—1221no—
703C2×Q8—1221no—
704C2×Q8C2×C4×D6111yescharacteristic
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—611no—
709C2×D4—611no—
710C2×D4—611no—
711C2×D4—611no—
712C2×D4—611no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—2441no—
723C2×D4—2441no—
724C2×D4C2×C4×D6111yescharacteristic
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—81no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—4881no—
744C22×C4—4881no—
745C22×C4—2442no—
746C22×C4—2442no—
747C22×C4C2×C4×D6111yescharacteristic
748C22×C4C2×C4×D6111yescharacteristic
749C22×C4D4×D6111yescharacteristic
750C22×C4D4×D6111yescharacteristic
751C22×C4D4×D6111yescharacteristic
752C22×C4C23×D6111yescharacteristic
753M16—4881no—
754M16—4881no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—81no—
758C2×C8—1221no—
759C2×C8—1221no—
760C2×C8—4881no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—611no—
764C4⋊C4—611no—
765C4⋊C4—611no—
766C4⋊C4—611no—
767C4⋊C4—611no—
768C4⋊C4—611no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—1221no—
778C4⋊C4—1221no—
779C4⋊C4—4881no—
780C4⋊C4C2×C4×D6111yescharacteristic
781C4⋊C4C2×C4×D6111yescharacteristic
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—81no—
788C22⋊C4—611no—
789C22⋊C4—611no—
790C22⋊C4—611no—
791C22⋊C4—611no—
792C22⋊C4—611no—
793C22⋊C4—611no—
794C22⋊C4—611no—
795C22⋊C4—611no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C22⋊C4—1221no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—2442no—
810C22⋊C4—2442no—
811C42—21no—
812C42—611no—
813C42—611no—
814C42—611no—
815C42—611no—
816C42—1221no—
817C42—1221no—
818C42—1221no—
819C42—1221no—
820C42—1221no—
821C42—4881no—
822C42—2442no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—611no—
829C23—611no—
830C23—1221no—
831C23—1221no—
832C23—1221no—
833C23—2441no—
834C23—2441no—
835C23C22⋊C4×D6111yescharacteristic
836C23C22⋊C4×D6111yescharacteristic
837C23C2×D4×D6111yescharacteristic
838Q8—41no—
839Q8—4881no—
840Q8—2441no—
841Q8—2442no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—81no—
846D4—81no—
847D4—4881no—
848D4—4881no—
849D4—4881no—
850D4—4881no—
851D4—4881no—
852D4—4881no—
853D4—4881no—
854D4—2441no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2442no—
860D4—2441no—
861D4—2441no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—81no—
878C2×C4—611no—
879C2×C4—611no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1222no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—4881no—
891C2×C4—4881no—
892C2×C4—4884no—
893C2×C4—4881no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2442no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2442no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4C22⋊C4×D6111yescharacteristic
908C2×C4C22⋊C4×D6111yescharacteristic
909C2×C4C22×C4×D6111yescharacteristic
910C2×C4C2×D4×D6111yescharacteristic
911C8—41no—
912C8—41no—
913C8—2441no—
914C8—2441no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—81no—
927C22—81no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—1221no—
934C22—2442no—
935C22—2442no—
936C22—2441no—
937C22—2441no—
938C22—2441no—
939C22C2×C22⋊C4×D6111yescharacteristic
940C22#1684055911yescharacteristic
941C22#1684055911yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—81no—
950C4—81no—
951C4—1221no—
952C4—1221no—
953C4—1221no—
954C4—1221no—
955C4—1221no—
956C4—1221no—
957C4—4881no—
958C4—2442no—
959C4—2441no—
960C4—2441no—
961C4—2441no—
962C2—21no—
963C2—21no—
964C2—41no—
965C2—41no—
966C2—81no—
967C2—4881no—
968C2—2441no—
969C2—2441no—
970C2#2145427711yescharacteristic
971C2#2145433411yescharacteristic
972C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1516C2
socleC22×C61C22×C22⋊C4
prime radical#21459662C2
cosocleC22×C4×C61C24
hypercenter#1516D61
hypocenterC61#17629
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. #21454845C2semidirect
3. #21448756C2semidirect
4. #21444373C2semidirect
5. #21444368C2semidirect
6. #21444364C2semidirect
7. #21444361C2semidirect
8. #21444359C2semidirect
9. #21444329C2semidirect
10. #21444325C2semidirect
11. #21444322C2semidirect
12. #21444320C2semidirect
13. #21444311C2semidirect
14. #21444310C2semidirect
15. C61×#1516C2semidirect
18. #16840483C4semidirect
19. #16840480C4semidirect
20. #16840476C4semidirect
21. #16840475C4semidirect
24. #16840431C4semidirect
25. #16840430C4semidirect
26. #16840414C4semidirect
27. #16840411C4semidirect
76. C2×#11758222C2×C4semidirect
85. #14519776C2×C4semidirect
86. #14519776C2×C4semidirect
87. #14519775C2×C4semidirect
90. #14519773C2×C4semidirect
111. #14519756C2×C4semidirect
117. #14519751C2×C4semidirect
131. Q8×Dic61C2×C4semidirect
135. #14519742C2×C4semidirect
137. D4×Dic61C2×C4semidirect
139. #14519739C2×C4semidirect
155. #14519736C2×C4semidirect
187. C2×#41×C61C2×C4semidirect
191. C22⋊Q8×C61C2×C4semidirect
193. #121×C61C2×C4semidirect
198. #117×C61C2×C4semidirect
480. #1516D61semidirect
561. C61#17629semidirect
566. C2×#41C4×D61semidirect
606. C22⋊Q8C4×D61semidirect
621. #121C4×D61semidirect
659. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214596622
#214548452
#214487562
#214443732
#214443682
#214443642
#214443612
#214443592
#214443292
#214443252
#214443222
#214443202
#214443112
#214443102
C61×#15162
#1762961