Finite Group Databasebeta

← #29647820

Subgroups — #29647820

Order 15616.

1002 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#21459647C211yesmaximal, characteristic
2#21454845C211yesmaximal, characteristic, complemented
3#21448793C211yesmaximal, characteristic, complemented
4#21444376C211yesmaximal, characteristic, complemented
5#21444375C211yesmaximal, characteristic, complemented
6#21444356C211yesmaximal, characteristic, complemented
7#21444354C211yesmaximal, characteristic, complemented
8#21444350C211yesmaximal, characteristic, complemented
9#21444346C211yesmaximal, characteristic, complemented
10#21444343C211yesmaximal, characteristic, complemented
11#21444341C211yesmaximal, characteristic, complemented
12#21444337C211yesmaximal, characteristic, complemented
13#21444333C211yesmaximal, characteristic, complemented
14#21444308C211yesmaximal, characteristic, complemented
15C61×#1501C211yesmaximal, characteristic, complemented
16#16840462—21no—
17#16840459C411yescharacteristic, complemented
18#16840457—21no—
19#16840456C411yescharacteristic, complemented
20#16840451C411yescharacteristic, complemented
21#16840446C411yescharacteristic, complemented
22#16840441—21no—
23#16840440—21no—
24#16840422C411yescharacteristic, complemented
25#16840419C411yescharacteristic, complemented
26#16840409C411yescharacteristic, complemented
27#16840400C411yescharacteristic, complemented
28#16840354—21no—
29#16840347—21no—
30#16840322—21no—
31#16840298C2211yescharacteristic
32#16840293C2211yescharacteristic
33#16840273C2211yescharacteristic
34C22⋊Q8×D61C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840234—21no—
37C2×C4×C22⋊D61C2211yescharacteristic
38#16839833—21no—
39#16839833—21no—
40#16839830—21no—
41#16839830—21no—
42#16839816C2211yescharacteristic, complemented
43#16839816C2211yescharacteristic, complemented
44#16839724C2211yescharacteristic
45#16839724C2211yescharacteristic
46C2×C22⋊#92418C2211yescharacteristic, complemented
47#16839662—21no—
48#16839656—21no—
49#16839653—21no—
50#16839626C2211yescharacteristic, complemented
51#16839625C2211yescharacteristic, complemented
52#16839624C2211yescharacteristic
53C4×#11758196—21no—
54#16839613C2211yescharacteristic, complemented
55#16839609C2211yescharacteristic
56#16839500C2211yescharacteristic, complemented
57#16839500C2211yescharacteristic, complemented
58#16839499C2211yescharacteristic, complemented
59#16839499C2211yescharacteristic, complemented
60#16839498C2211yescharacteristic, complemented
61#16839498C2211yescharacteristic, complemented
62#16839497C2211yescharacteristic
63#16839497C2211yescharacteristic
64#16839496C2211yescharacteristic
65#16839496C2211yescharacteristic
66#16839495C2211yescharacteristic
67#16839495C2211yescharacteristic
68C61×#525C2211yescharacteristic
69C2×C22⋊C8×C61C2211yescharacteristic, complemented
70C4×C22⋊C4×C61C2211yescharacteristic, complemented
71C61×#328C2211yescharacteristic, complemented
72C61×#328C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758222C2×C411yescharacteristic
76C2×Q8×D61C2×C411yescharacteristic
77C22×C22⋊D61D411yescharacteristic
78C2×D4×D61—21no—
79C2×D4×D61C2×C411yescharacteristic
80C22×C4×D61C2311yescharacteristic
81C2×#11758189—21no—
82C2×#11758189—21no—
83C22×#92418—21no—
84#14519772—21no—
85#14519771—21no—
86#14519770—21no—
87#14519770—21no—
88#14519770—21no—
89#14519770—21no—
90#14519769—21no—
91#14519768C2×C411yescharacteristic
92#14519768C2×C411yescharacteristic
93#14519767—21no—
94#14519766C2×C411yescharacteristic
95#14519764—21no—
96#14519764C2×C411yescharacteristic
97#14519763—21no—
98#14519761—21no—
99#14519760—21no—
100#14519760—21no—
101#14519759—21no—
102#14519759—21no—
103#14519759—21no—
104#14519759—21no—
105#14519758—21no—
106#14519758—21no—
107#14519757C2×C411yescharacteristic
108#14519756—21no—
109#14519756C2×C411yescharacteristic
110#14519756C2311yescharacteristic
111#14519755—21no—
112#14519755—21no—
113#14519754—21no—
114#14519753C2×C411yescharacteristic
115#14519752C2×C411yescharacteristic
116#14519751C2×C411yescharacteristic
117#14519751C2311yescharacteristic
118#14519750—21no—
119#14519750—21no—
120#14519750—21no—
121#14519749—21no—
122#14519749—21no—
123#14519748—21no—
124#14519748—21no—
125#14519748—21no—
126#14519748C2×C411yescharacteristic
127#14519746—21no—
128#14519745—21no—
129#14519745—21no—
130Q8×Dic61C2×C411yescharacteristic
131#14519742C2×C411yescharacteristic
132C4×D244—21no—
133D4×Dic61—21no—
134D4×Dic61C2×C411yescharacteristic
135#14519739—21no—
136#14519739C2×C411yescharacteristic
137C4×C22⋊D61—21no—
138C4×C22⋊D61—21no—
139C4×C22⋊D61—21no—
140C4×C22⋊D61C2×C411yescharacteristic
141C4×C22⋊D61C2×C411yescharacteristic
142C4×C22⋊D61C2×C411yescharacteristic
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61D411yescharacteristic
145C4×C22⋊D61D411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148#14519737—21no—
149#14519737—21no—
150#14519736C2×C411yescharacteristic
151#14519735—21no—
152#14519735—21no—
153#14519734—21no—
154#14519733—21no—
155C2×#11758196—21no—
156C2×#11758196—21no—
157C2×#11758196D411yescharacteristic
158C4⋊C4×D61—21no—
159C4⋊C4×D61C2×C411yescharacteristic
160C4⋊C4×D61C2×C411yescharacteristic
161C2×C22⋊Dic61—21no—
162C2×C22⋊Dic61D411yescharacteristic
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198D411yescharacteristic
167C22⋊C4×D61—21no—
168C22⋊C4×D61—21no—
169C22⋊C4×D61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61C2311yescharacteristic
173#14519706—21no—
174#14519706—21no—
175C22⋊#92418—21no—
176C22⋊#92418C2311yescharacteristic
177C22⋊#92418C2311yescharacteristic
178#14519689—21no—
179#14519689—21no—
180#14519687—21no—
181#14519687—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187C2×#41×C61C2×C411yescharacteristic
188C23×C4×C61C2311yescharacteristic
189C22×C8×C61—21no—
190#123×C61—21no—
191C22⋊Q8×C61C2×C411yescharacteristic
192C22⋊Q8×C61C2311yescharacteristic
193#121×C61C2×C411yescharacteristic
194#121×C61C2311yescharacteristic
195#120×C61—21no—
196C4×D4×C61—21no—
197C4×D4×C61—21no—
198#117×C61C2×C411yescharacteristic
199C2×C22⋊C4×C61—21no—
200C2×C42×C61—21no—
201C22⋊C8×C61—21no—
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61C2×D411yescharacteristic
207C23×D61—21no—
208C23×D61C2×D411yescharacteristic
209#41×C61—81no—
210C2×Q8×C61C22×C411yescharacteristic
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61C22×C411yescharacteristic
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—81no—
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2411yescharacteristic
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—41no—
231C2×C22⋊D61—41no—
232C2×C22⋊D61C22⋊C411yescharacteristic
233C2×C22⋊D61C22⋊C411yescharacteristic
234C2×C22⋊D61C22⋊C411yescharacteristic
235C2×C22⋊D61C22⋊C411yescharacteristic
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242Q8×D61—81no—
243D4×D61—42no—
244D4×D61—42no—
245D4×D61—81no—
246#11758222—81no—
247C2×D244—21no—
248C2×D244C22×C411yescharacteristic
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—81no—
255C2×C4×D61C22×C411yescharacteristic
256C2×C4×D61C22×C411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×Dic122—21no—
260C2×Dic122C22×C411yescharacteristic
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—81no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61C22×C411yescharacteristic
267C4⋊C4×C61C22×C411yescharacteristic
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—42no—
274C42×C61—21no—
275C42×C61—81no—
276C22⋊Dic61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—81no—
284C22⋊Dic61C22⋊C411yescharacteristic
285C22⋊Dic61C22⋊C411yescharacteristic
286C22⋊Dic61C22⋊C411yescharacteristic
287C22⋊Dic61C22⋊C411yescharacteristic
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—42no—
297#11758198—81no—
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61C22×C411yescharacteristic
307C4⋊Dic61C22×C411yescharacteristic
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—42no—
317#11758196—42no—
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320#11758196C22⋊C411yescharacteristic
321#11758196C22⋊C411yescharacteristic
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×D61—42no—
350C22×D61—81no—
351C22×D61—81no—
352C22×D61C2×C22⋊C411yescharacteristic
353C22×D61C2×C22⋊C411yescharacteristic
354Q8×C61—41no—
355D4×C61—41no—
356D4×C61—41no—
357D4×C61—41no—
358D4×C61—81no—
359D4×C61—81no—
360C2×C4×C61—22no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
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—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—81no—
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C23×C411yescharacteristic
379C2×C4×C61C22×D411yescharacteristic
380C22⋊D61—41no—
381C22⋊D61—41no—
382C22⋊D61—41no—
383C22⋊D61—41no—
384C22⋊D61—42no—
385C22⋊D61—41no—
386C22⋊D61—41no—
387C22⋊D61—81no—
388C22⋊D61—81no—
389C22⋊D61—81no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
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—42no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—42no—
417C4×D61—81no—
418C4×D61—81no—
419C4×D61—81no—
420C4×D61—81no—
421Dic122—41no—
422Dic122—81no—
423C8×C61—41no—
424C8×C61—41no—
425#92418—41no—
426#92418—41no—
427#17625—611nomaximal, Sylow
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—81no—
440C22×C61—81no—
441C22×C61C22×C22⋊C411yescharacteristic
442C22×C61#57511yescharacteristic
443C22×C61#57511yescharacteristic
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—81no—
454C2×D61—81no—
455C2×D61—162no—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—42no—
461C4×C61—41no—
462C4×C61—41no—
463C4×C61—41no—
464C4×C61—81no—
465Dic61—21no—
466Dic61—21no—
467Dic61—21no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—41no—
472Dic61—41no—
473Dic61—41no—
474Dic61—81no—
475Dic61—81no—
476#3505—611no—
477#2973—611no—
478#2357—611no—
479#1516—611no—
480#1516—611no—
481#1512—611no—
482#1512—611no—
483#1511—611no—
484#1510—611no—
485#1509—611no—
486#1509—611no—
487#1508—611no—
488#1507—611no—
489#1501—611no—
490#1501D6111yescharacteristic, complemented
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#553—611no—
503#553—611no—
504#553—1221no—
505#553—1221no—
506#552—611no—
507#552—611no—
508#551—1221no—
509#551—1221no—
510#548—611no—
511#548—611no—
512#546—611no—
513#546—611no—
514#539—1221no—
515#538—1221no—
516#534—1221no—
517#529—611no—
518#529—611no—
519#525—611no—
520#525C2×D6111yescharacteristic
521C2×C22⋊Q8—611no—
522C2×#121—611no—
523#518—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, complemented
535#390—1221no—
536#388—1221no—
537#388—1221no—
538#382—611no—
539#381—611no—
540#381—611no—
541C4×C4⋊C4—611no—
542C4×C4⋊C4—1221no—
543C4×C22⋊C4—611no—
544C4×C22⋊C4C2×D6111yescharacteristic, complemented
545#328—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328—611no—
551#328C2×D6111yescharacteristic, complemented
552#328C2×D6111yescharacteristic, complemented
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#1762511yescharacteristic, complemented, Sylow
562C2×#41—611no—
563C2×#41C4×D6111yescharacteristic
564C22×Q8—611no—
565C22×D4—611no—
566C22×D4—611no—
567C22×D4—1221no—
568C23×C4—611no—
569C23×C4C22×D6111yescharacteristic
570C2×M16—1221no—
571C2×M16—1221no—
572C22×C8—21no—
573C22×C8—1221no—
574#126—1221no—
575#126—1221no—
576#126—1221no—
577#126—1221no—
578#126—1221no—
579#126—1221no—
580#125—611no—
581#125—611no—
582#125—1221no—
583#125—1221no—
584#124—611no—
585#124—611no—
586#124—1221no—
587#124—1221no—
588#123—21no—
589#123—1221no—
590#123—1221no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598C22⋊Q8—611no—
599C22⋊Q8—611no—
600C22⋊Q8—611no—
601C22⋊Q8—611no—
602C22⋊Q8—1221no—
603C22⋊Q8—1221no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8C4×D6111yescharacteristic
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#121C4×D6111yescharacteristic
621#121C22×D6111yescharacteristic
622#120—21no—
623#120—1221no—
624#120—1221no—
625#120—1221no—
626C4×Q8—611no—
627C4×Q8—611no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—611no—
631C4×D4—611no—
632C4×D4—611no—
633C4×D4—611no—
634C4×D4—611no—
635C4×D4—611no—
636C4×D4—611no—
637C4×D4—611no—
638C4×D4—611no—
639C4×D4—611no—
640C4×D4—1221no—
641C4×D4—1221no—
642C4×D4—1221no—
643C4×D4—1221no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4—1221no—
648#117—611no—
649#117—1221no—
650#117—1221no—
651#117—1221no—
652#117—1221no—
653#117C4×D6111yescharacteristic
654C2×C4⋊C4—611no—
655C2×C4⋊C4—611no—
656C2×C4⋊C4—611no—
657C2×C4⋊C4—1221no—
658C2×C4⋊C4—1221no—
659C2×C4⋊C4—1221no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—611no—
662C2×C22⋊C4—611no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C22⋊C4—1221no—
670C2×C42—21no—
671C2×C42—611no—
672C2×C42—1221no—
673C2×C42—1221no—
674C4⋊C8—1221no—
675C4⋊C8—1221no—
676C22⋊C8—21no—
677C22⋊C8—611no—
678C22⋊C8—611no—
679C22⋊C8—1221no—
680C22⋊C8—1221no—
681C22⋊C8—1221no—
682C22⋊C8C22×D6111yescharacteristic
683C22⋊C8C22×D6111yescharacteristic
684#97—1221no—
685#97—1221no—
686#95—611no—
687#95—611no—
688#95—1221no—
689#95—1221no—
690#95—1221no—
691#95C22×D6111yescharacteristic
692#95C22×D6111yescharacteristic
693C24—611no—
694C24—1221no—
695C24D4×D6111yescharacteristic
696#41—81no—
697#41—4881no—
698C2×Q8—611no—
699C2×Q8—1221no—
700C2×Q8—4881no—
701C2×Q8C2×C4×D6111yescharacteristic
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—611no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—611no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—4881no—
717C2×D4—2441no—
718C2×D4—2441no—
719C2×D4—2442no—
720C2×D4—2442no—
721C2×D4C2×C4×D6111yescharacteristic
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—81no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—4881no—
742C22×C4C2×C4×D6111yescharacteristic
743C22×C4C2×C4×D6111yescharacteristic
744C22×C4D4×D6111yescharacteristic
745C22×C4D4×D6111yescharacteristic
746C22×C4D4×D6111yescharacteristic
747C22×C4C23×D6111yescharacteristic
748M16—4881no—
749M16—4881no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—81no—
753C2×C8—1221no—
754C2×C8—1221no—
755C2×C8—4881no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—611no—
759C4⋊C4—611no—
760C4⋊C4—611no—
761C4⋊C4—611no—
762C4⋊C4—611no—
763C4⋊C4—611no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—2442no—
777C4⋊C4—2442no—
778C4⋊C4C2×C4×D6111yescharacteristic
779C4⋊C4C2×C4×D6111yescharacteristic
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—42no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—611no—
790C22⋊C4—611no—
791C22⋊C4—611no—
792C22⋊C4—611no—
793C22⋊C4—611no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
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—4881no—
810C22⋊C4—4881no—
811C22⋊C4—2442no—
812C42—21no—
813C42—81no—
814C42—611no—
815C42—611no—
816C42—611no—
817C42—611no—
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—4881no—
834C23—4881no—
835C23—2441no—
836C23—2441no—
837C23—2442no—
838C23C22⋊C4×D6111yescharacteristic
839C23C22⋊C4×D6111yescharacteristic
840C23C2×D4×D6111yescharacteristic
841Q8—41no—
842Q8—4881no—
843Q8—2441no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—81no—
848D4—81no—
849D4—4881no—
850D4—4881no—
851D4—4881no—
852D4—2441no—
853D4—2442no—
854D4—2441no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2442no—
859D4—2441no—
860D4—2441no—
861C2×C4—22no—
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—81no—
877C2×C4—611no—
878C2×C4—611no—
879C2×C4—611no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—4881no—
889C2×C4—4881no—
890C2×C4—4881no—
891C2×C4—4881no—
892C2×C4—4881no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2442no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4C22⋊C4×D6111yescharacteristic
907C2×C4C22⋊C4×D6111yescharacteristic
908C2×C4C22×C4×D6111yescharacteristic
909C2×C4C2×D4×D6111yescharacteristic
910C8—41no—
911C8—41no—
912C8—2441no—
913C8—2441no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—81no—
926C22—81no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—9762no—
934C22—4881no—
935C22—4881no—
936C22—2441no—
937C22—2441no—
938C22—2441no—
939C22C2×C22⋊C4×D6111yescharacteristic
940C22#1684055911yescharacteristic
941C22#1684055911yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—81no—
951C4—1221no—
952C4—1221no—
953C4—1221no—
954C4—1221no—
955C4—1221no—
956C4—1221no—
957C4—4881no—
958C4—4881no—
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#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1501C2
socleC22×C61C22×C22⋊C4
prime radical#21459647C2
cosocleC22×C4×C61C24
hypercenter#1501D61
hypocenterC61#17625
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. #21454845C2semidirect
3. #21448793C2semidirect
4. #21444376C2semidirect
5. #21444375C2semidirect
6. #21444356C2semidirect
7. #21444354C2semidirect
8. #21444350C2semidirect
9. #21444346C2semidirect
10. #21444343C2semidirect
11. #21444341C2semidirect
12. #21444337C2semidirect
13. #21444333C2semidirect
14. #21444308C2semidirect
15. C61×#1501C2semidirect
17. #16840459C4semidirect
19. #16840456C4semidirect
20. #16840451C4semidirect
21. #16840446C4semidirect
24. #16840422C4semidirect
25. #16840419C4semidirect
26. #16840409C4semidirect
27. #16840400C4semidirect
42. #16839816C22semidirect
43. #16839816C22semidirect
46. C2×C22⋊#92418C22semidirect
50. #16839626C22semidirect
51. #16839625C22semidirect
54. #16839613C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839499C22semidirect
59. #16839499C22semidirect
60. #16839498C22semidirect
61. #16839498C22semidirect
69. C2×C22⋊C8×C61C22semidirect
70. C4×C22⋊C4×C61C22semidirect
71. C61×#328C22semidirect
72. C61×#328C22semidirect
490. #1501D61semidirect
534. C2×C22⋊C8C2×D61semidirect
544. C4×C22⋊C4C2×D61semidirect
551. #328C2×D61semidirect
552. #328C2×D61semidirect
561. C61#17625semidirect

Maximal subgroups

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

subgroupindex
#214596472
#214548452
#214487932
#214443762
#214443752
#214443562
#214443542
#214443502
#214443462
#214443432
#214443412
#214443372
#214443332
#214443082
C61×#15012
#1762561