Finite Group Databasebeta

← #29647729

Subgroups — #29647729

Order 15616.

1038 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459654C211yesmaximal, characteristic
2#21454842C211yesmaximal, characteristic, complemented
3#21448760C211yesmaximal, characteristic, complemented
4#21444397C211yesmaximal, characteristic, complemented
5#21444396C211yesmaximal, characteristic, complemented
6#21444389C211yesmaximal, characteristic, complemented
7#21444385C211yesmaximal, characteristic, complemented
8#21444374C211yesmaximal, characteristic, complemented
9#21444372C211yesmaximal, characteristic, complemented
10#21444309C211yesmaximal, characteristic, complemented
11#21444307C211yesmaximal, characteristic, complemented
12#21444303C211yesmaximal, characteristic, complemented
13#328×D61C211yesmaximal, characteristic, complemented
14#327×D61C211yesmaximal, characteristic, complemented
15C61×#1500C211yesmaximal, characteristic, complemented
16#16840465C411yescharacteristic, complemented
17#16840463—21no—
18#16840462C411yescharacteristic, complemented
19#16840456—21no—
20#16840453C411yescharacteristic, complemented
21#16840450C411yescharacteristic, complemented
22#16840437—21no—
23#16840436—21no—
24#16840424C411yescharacteristic, complemented
25#16840420C411yescharacteristic, complemented
26#16840407C411yescharacteristic, complemented
27#16840405C411yescharacteristic, complemented
28#16840356—21no—
29#16840345—21no—
30#16840323—21no—
31#16840296C2211yescharacteristic
32#16840275C2211yescharacteristic
33#16840272C2211yescharacteristic
34C22⋊Q8×D61C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840234—21no—
37C2×C4×D244C2211yescharacteristic
38C8×D244—21no—
39C8×D244—21no—
40#16839827—21no—
41#16839827—21no—
42#16839815C2211yescharacteristic, complemented
43C22⋊C8×D61C2211yescharacteristic
44C22⋊C8×D61C2211yescharacteristic
45C22⋊C8×D61C2211yescharacteristic, complemented
46C22⋊C8×D61C2211yescharacteristic, complemented
47#16839653—21no—
48#16839645—21no—
49#16839640—21no—
50#16839630C2211yescharacteristic, complemented
51#16839624C2211yescharacteristic, complemented
52#16839621C2211yescharacteristic
53C4×#11758198—21no—
54#16839609C2211yescharacteristic, complemented
55#95×D61C2211yescharacteristic
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×#529C2211yescharacteristic
69C61×#431C2211yescharacteristic, complemented
70C61×#376C2211yescharacteristic, complemented
71C61×#328C2211yescharacteristic, complemented
72C61×#328C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758226C2×C411yescharacteristic, complemented
76C2×#11758224C2×C411yescharacteristic, complemented
77C2×Q8×D61C2×C411yescharacteristic
78C22×D244D411yescharacteristic
79C2×D4×D61—21no—
80C2×D4×D61C2×C411yescharacteristic
81C22×C4×D61—21no—
82C22×C4×D61C2311yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87C2×C8×D61—21no—
88#14519772—21no—
89#14519772—21no—
90#14519771—21no—
91#14519771—21no—
92#14519770—21no—
93#14519769C2×C411yescharacteristic, complemented
94#14519768—21no—
95#14519767—21no—
96#14519765—21no—
97#14519765C2×C411yescharacteristic, complemented
98#14519763—21no—
99#14519762—21no—
100#14519762—21no—
101#14519762—21no—
102#14519762—21no—
103#14519761—21no—
104#14519760—21no—
105#14519760—21no—
106#14519759—21no—
107#14519759—21no—
108#14519757—21no—
109#14519757C2×C411yescharacteristic
110#14519757C2×C411yescharacteristic, complemented
111#14519756C2311yescharacteristic
112#14519755—21no—
113#14519754—21no—
114#14519754—21no—
115#14519753C2×C411yescharacteristic
116#14519753C2×C411yescharacteristic, complemented
117#14519752—21no—
118#14519752—21no—
119#14519752C2×C411yescharacteristic
120#14519752C2×C411yescharacteristic, complemented
121#14519751—21no—
122#14519751C2311yescharacteristic
123#14519750—21no—
124#14519750—21no—
125#14519750—21no—
126#14519750—21no—
127#14519749—21no—
128#14519748C2×C411yescharacteristic
129#14519748C2×C411yescharacteristic, complemented
130#14519747—21no—
131#14519747—21no—
132#14519747—21no—
133#14519745—21no—
134C4×Dic122C2×C411yescharacteristic, complemented
135C4×D244—21no—
136C4×D244C2×C411yescharacteristic
137C4×D244C2×C411yescharacteristic
138C4×D244C2×C411yescharacteristic
139C4×D244C2×C411yescharacteristic
140C4×D244C2×C411yescharacteristic, complemented
141C4×D244D411yescharacteristic
142C4×D244D411yescharacteristic
143C4×D244D411yescharacteristic
144C4×D244D411yescharacteristic
145D4×Dic61—21no—
146#14519739—21no—
147#14519739—21no—
148C4×C22⋊D61—21no—
149C4×C22⋊D61—21no—
150#14519737—21no—
151#14519737—21no—
152#14519737—21no—
153#14519735—21no—
154#14519735C2×C411yescharacteristic, complemented
155#14519735C2×C411yescharacteristic, complemented
156#14519734—21no—
157#14519734—21no—
158C2×C4⋊Dic61D411yescharacteristic
159C2×#11758196—21no—
160C4⋊C4×D61—21no—
161C4⋊C4×D61C2×C411yescharacteristic
162C4⋊C4×D61C2×C411yescharacteristic
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198D411yescharacteristic
168C2×#11758198D411yescharacteristic
169C22⋊C4×D61—21no—
170C22⋊C4×D61—21no—
171C22⋊C4×D61—21no—
172C2×C4×Dic61—21no—
173C4⋊#92418—21no—
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180C4×#92418—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187#126×C61—21no—
188#125×C61C2×C411yescharacteristic, complemented
189#124×C61C2×C411yescharacteristic, complemented
190#123×C61—21no—
191C22⋊Q8×C61C2311yescharacteristic
192#121×C61C2311yescharacteristic
193C4×Q8×C61C2×C411yescharacteristic, complemented
194C4×D4×C61—21no—
195C4×D4×C61C2×C411yescharacteristic, complemented
196#117×C61—21no—
197C2×C42×C61—21no—
198C2×C42×C61C2311yescharacteristic
199C4⋊C8×C61—21no—
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202C4×C8×C61—21no—
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C23×D61—21no—
207C23×D61C2×D411yescharacteristic
208C23×D61C2×D411yescharacteristic
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61C22×C411yescharacteristic
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2411yescharacteristic
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228#11758226—81no—
229Q8×D61—81no—
230#11758224—81no—
231D4×D61—42no—
232D4×D61—42no—
233D4×D61—81no—
234C2×D244—22no—
235C2×D244—22no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244C22⋊C411yescharacteristic
240C2×D244C22⋊C411yescharacteristic
241C2×D244C22⋊C411yescharacteristic
242C2×D244C22⋊C411yescharacteristic
243C2×D244C22×C411yescharacteristic
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—42no—
250C2×C4×D61—42no—
251C2×C4×D61—81no—
252C2×C4×D61—81no—
253C2×C4×D61—81no—
254C2×C4×D61C22×C411yescharacteristic
255C2×C4×D61C22×C411yescharacteristic
256C2×C4×D61C22×C411yescharacteristic
257C2×C4×D61C22×C411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×Dic122—21no—
263C2×Dic122C22×C411yescharacteristic
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61C22×C411yescharacteristic
271C4⋊C4×C61C22×C411yescharacteristic
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C42×C61—21no—
278C42×C61—42no—
279C42×C61C22×C411yescharacteristic
280C42×C61C22×C411yescharacteristic
281C42×C61C2×D411yescharacteristic
282C42×C61C2×D411yescharacteristic
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286#11758198—21no—
287#11758198—21no—
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—21no—
297#11758198—21no—
298#11758198—42no—
299#11758198—42no—
300#11758198—81no—
301#11758198C22⋊C411yescharacteristic
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304#11758198C22⋊C411yescharacteristic
305#11758198C22⋊C411yescharacteristic
306#11758198C22⋊C411yescharacteristic
307#11758198C22⋊C411yescharacteristic
308#11758198C22⋊C411yescharacteristic
309C4⋊Dic61—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61C22⋊C411yescharacteristic
312C4⋊Dic61C22⋊C411yescharacteristic
313C4⋊Dic61C22⋊C411yescharacteristic
314C4⋊Dic61C22⋊C411yescharacteristic
315C4⋊Dic61C22×C411yescharacteristic
316C4⋊Dic61C22×C411yescharacteristic
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—81no—
326C4×Dic61—21no—
327C4×Dic61—21no—
328C4×Dic61—21no—
329C4×Dic61—81no—
330C2×#92418—21no—
331C2×#92418—21no—
332C8×D61—81no—
333C8×D61—81no—
334C8×D61—81no—
335C8×D61—81no—
336C23×C61—21no—
337C23×C61C22×D411yescharacteristic
338C22×D61—21no—
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—42no—
346C22×D61—81no—
347C22×D61—81no—
348C22×D61C2×C22⋊C411yescharacteristic
349C22×D61C2×C22⋊C411yescharacteristic
350C22×D61C2×C22⋊C411yescharacteristic
351C22×D61C2×C22⋊C411yescharacteristic
352C22×D61#13512yes—
353C22×D61#13512yes—
354Q8×C61—41no—
355D4×C61—41no—
356D4×C61—41no—
357D4×C61—41no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
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—81no—
372C2×C4×C61C2×C22⋊C411yescharacteristic
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C23×C411yescharacteristic
377C2×C4×C61C22×D411yescharacteristic
378C22⋊D61—41no—
379C22⋊D61—41no—
380C22⋊D61—42no—
381C22⋊D61—81no—
382C22⋊D61—81no—
383C22⋊D61—81no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—81no—
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400D244—22no—
401D244—22no—
402D244—22no—
403D244—22no—
404D244—41no—
405D244—42no—
406D244—81no—
407D244—81no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
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—
421C4×D61—84no—
422Dic122—41no—
423Dic122—81no—
424C8×C61—41no—
425C8×C61—41no—
426#92418—41no—
427#92418—41no—
428#17615—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61C22×C22⋊C411yescharacteristic
435C22×C61C2×#13511yescharacteristic
436C22×C61C2×#13511yescharacteristic
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61—162no—
455C2×D61#41612yes—
456C2×D61#41612yes—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—21no—
463C4×C61—42no—
464C4×C61—41no—
465C4×C61—41no—
466C4×C61—41no—
467C4×C61—81no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—41no—
473Dic61—41no—
474Dic61—41no—
475Dic61—81no—
476Dic61—81no—
477#3505—611no—
478#2972—611no—
479#2353—611no—
480#1521—611no—
481#1521—611no—
482#1520—611no—
483#1519—611no—
484#1516—611no—
485#1516—611no—
486#1501—611no—
487#1501—611no—
488#1500—611no—
489#1500D6111yescharacteristic, complemented
490C2×#328—611no—
491C2×#327—611no—
492C2×C61—21no—
493C2×C61—21no—
494C2×C61—81no—
495C2×C61#288311yescharacteristic
496C2×C61C2×#41611yescharacteristic
497C2×C61#290111yescharacteristic
498D61—22no—
499D61—22no—
500D61—41no—
501D61—41no—
502D61—81no—
503#553—611no—
504#553—611no—
505#553—1221no—
506#553—1221no—
507#552—611no—
508#552—611no—
509#551—1221no—
510#551—1221no—
511#548—611no—
512#548—611no—
513#546—611no—
514#546—611no—
515#539—1221no—
516#538—1221no—
517#534—1221no—
518#529—611no—
519#529C2×D6111yescharacteristic
520#525—611no—
521#525—611no—
522C2×C22⋊Q8—611no—
523C2×#121—611no—
524#518—1221no—
525C2×C4×D4—611no—
526C8×D4—1221no—
527C8×D4—1221no—
528C8×D4—1221no—
529C8×D4—1221no—
530#431—611no—
531#431C2×D6111yescharacteristic, complemented
532C2×C22⋊C8—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535C2×C22⋊C8—611no—
536#388—1221no—
537#387—1221no—
538#386—1221no—
539#383—611no—
540#381—611no—
541#380—611no—
542C4×C22⋊C4—611no—
543C4×C22⋊C4—1221no—
544#376C2×D6111yescharacteristic, complemented
545C2×#95—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328—611no—
551#328—611no—
552#328C2×D6111yescharacteristic, complemented
553#328C2×D6111yescharacteristic, complemented
554#327—611no—
555#327—611no—
556#327—611no—
557#327—611no—
558#327—611no—
559#327—611no—
560#327C2×D6111yescharacteristic
561#327C2×D6111yescharacteristic
562C61#1761511yescharacteristic, complemented, Sylow
563C2×#41—611no—
564C2×#41—611no—
565C22×Q8—611no—
566C22×D4—611no—
567C22×D4—611no—
568C22×D4—1221no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—1221no—
572C22×C8—1221no—
573C22×C8—1221no—
574C22×C8—1221no—
575C22×C8—1221no—
576#126—21no—
577#126—1221no—
578#126—1221no—
579#126—1221no—
580#126—1221no—
581#126—1221no—
582#125—611no—
583#125—1221no—
584#125—1221no—
585#125C4×D6111yescharacteristic, complemented
586#124—611no—
587#124—1221no—
588#124—1221no—
589#124C4×D6111yescharacteristic, complemented
590#123—21no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600C22⋊Q8—611no—
601C22⋊Q8—611no—
602C22⋊Q8—611no—
603C22⋊Q8—611no—
604C22⋊Q8—611no—
605C22⋊Q8—1221no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8C22×D6111yescharacteristic
610#121—611no—
611#121—611no—
612#121—611no—
613#121—611no—
614#121—611no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121—1221no—
622#121—1221no—
623#121C22×D6111yescharacteristic
624#120—1221no—
625#120—1221no—
626#120—1221no—
627#120—1221no—
628C4×Q8—611no—
629C4×Q8C4×D6111yescharacteristic, complemented
630C4×D4—21no—
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—
648C4×D4—1221no—
649C4×D4C4×D6111yescharacteristic, complemented
650#117—21no—
651#117—611no—
652#117—611no—
653#117—1221no—
654#117—1221no—
655#117—1221no—
656C2×C4⋊C4—611no—
657C2×C4⋊C4—611no—
658C2×C4⋊C4—611no—
659C2×C4⋊C4—1221no—
660C2×C4⋊C4—1221no—
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—1221no—
672C2×C42C22×D6111yescharacteristic
673C4⋊C8—21no—
674C4⋊C8—1221no—
675C22⋊C8—611no—
676C22⋊C8—611no—
677C22⋊C8—1221no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680C22⋊C8—1221no—
681C22⋊C8C22×D6111yescharacteristic
682C22⋊C8C22×D6111yescharacteristic
683C4×C8—21no—
684C4×C8—1221no—
685#95—21no—
686#95—611no—
687#95—611no—
688#95—1221no—
689#95—1221no—
690#95—1221no—
691#95—1221no—
692#95C22×D6111yescharacteristic
693#95C22×D6111yescharacteristic
694C24—611no—
695C24—611no—
696C24—1221no—
697#41—4881no—
698#41—4881no—
699C2×Q8—611no—
700C2×Q8—1221no—
701C2×Q8—4881no—
702C2×Q8C2×C4×D6111yescharacteristic
703C2×D4—21no—
704C2×D4—611no—
705C2×D4—611no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—1222no—
710C2×D4—1222no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—4881no—
720C2×D4—2442no—
721C2×D4—2442no—
722C2×D4C2×C4×D6111yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
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—1221no—
744C22×C4—4881no—
745C22×C4—4881no—
746C22×C4—4881no—
747C22×C4—2442no—
748C22×C4—2442no—
749C22×C4D4×D6111yescharacteristic
750C22×C4D4×D6111yescharacteristic
751C22×C4C23×D6111yescharacteristic
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—4881no—
757C2×C8—4881no—
758C2×C8—4881no—
759C2×C8—4881no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—611no—
765C4⋊C4—611no—
766C4⋊C4—611no—
767C4⋊C4—611no—
768C4⋊C4—611no—
769C4⋊C4—611no—
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—1221no—
780C4⋊C4—4881no—
781C4⋊C4C2×C4×D6111yescharacteristic
782C4⋊C4C2×C4×D6111yescharacteristic
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
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—1221no—
810C22⋊C4—1221no—
811C22⋊C4—4881no—
812C22⋊C4—2442no—
813C22⋊C4—2442no—
814C42—21no—
815C42—42no—
816C42—1221no—
817C42—1221no—
818C42—1221no—
819C42—4881no—
820C42C2×C4×D6111yescharacteristic
821C42C2×C4×D6111yescharacteristic
822C42D4×D6111yescharacteristic
823C42D4×D6111yescharacteristic
824C23—21no—
825C23—611no—
826C23—611no—
827C23—612no—
828C23—612no—
829C23—611no—
830C23—611no—
831C23—1221no—
832C23—1221no—
833C23—1221no—
834C23—4881no—
835C23—4881no—
836C23—2441no—
837C23—2441no—
838C23—2441no—
839C23—2441no—
840C23—2442no—
841C23C2×D4×D6111yescharacteristic
842Q8—41no—
843Q8—4881no—
844Q8—2441no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—1222no—
849D4—1222no—
850D4—1222no—
851D4—1222no—
852D4—4881no—
853D4—4881no—
854D4—4881no—
855D4—4881no—
856D4—4881no—
857D4—2441no—
858D4—2442no—
859D4—2442no—
860D4—2441no—
861D4—2441no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—81no—
876C2×C4—611no—
877C2×C4—611no—
878C2×C4—611no—
879C2×C4—611no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—4881no—
884C2×C4—4881no—
885C2×C4—4884no—
886C2×C4—4881no—
887C2×C4—4881no—
888C2×C4—4881no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
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×C4C22⋊C4×D6111yescharacteristic
910C2×C4C22×C4×D6111yescharacteristic
911C2×C4C2×D4×D6111yescharacteristic
912C8—41no—
913C8—41no—
914C8—2441no—
915C8—2441no—
916C22—21no—
917C22—21no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—612no—
922C22—612no—
923C22—1221no—
924C22—1221no—
925C22—1221no—
926C22—1221no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—9762no—
934C22—4881no—
935C22—4881no—
936C22—2442no—
937C22—2442no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22C2×C22⋊C4×D6111yescharacteristic
942C22#135×D6111yescharacteristic
943C22#135×D6111yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—21no—
949C4—21no—
950C4—42no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—1221no—
956C4—1221no—
957C4—1221no—
958C4—1221no—
959C4—4881no—
960C4—4881no—
961C4—2441no—
962C4—2441no—
963C4—2441no—
964C2—21no—
965C2—21no—
966C2—81no—
967C2—1222no—
968C2—1222no—
969C2—4881no—
970C2—2441no—
971C2—2441no—
972C2#2145427811yescharacteristic
973C2#416×D6111yescharacteristic
974C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1500C2
socleC22×C61C22×C22⋊C4
prime radical#21459654C2
cosocleC22×C4×C61C24
hypercenter#1500D61
hypocenterC61#17615
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1500

Complements

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

NH ≅ G/Ntype
2. #21454842C2semidirect
3. #21448760C2semidirect
4. #21444397C2semidirect
5. #21444396C2semidirect
6. #21444389C2semidirect
7. #21444385C2semidirect
8. #21444374C2semidirect
9. #21444372C2semidirect
10. #21444309C2semidirect
11. #21444307C2semidirect
12. #21444303C2semidirect
13. #328×D61C2semidirect
14. #327×D61C2semidirect
15. C61×#1500C2semidirect
16. #16840465C4semidirect
18. #16840462C4semidirect
20. #16840453C4semidirect
21. #16840450C4semidirect
24. #16840424C4semidirect
25. #16840420C4semidirect
26. #16840407C4semidirect
27. #16840405C4semidirect
42. #16839815C22semidirect
45. C22⋊C8×D61C22semidirect
46. C22⋊C8×D61C22semidirect
50. #16839630C22semidirect
51. #16839624C22semidirect
54. #16839609C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839499C22semidirect
59. #16839499C22semidirect
60. #16839498C22semidirect
61. #16839498C22semidirect
69. C61×#431C22semidirect
70. C61×#376C22semidirect
71. C61×#328C22semidirect
72. C61×#328C22semidirect
75. C2×#11758226C2×C4semidirect
76. C2×#11758224C2×C4semidirect
93. #14519769C2×C4semidirect
97. #14519765C2×C4semidirect
110. #14519757C2×C4semidirect
116. #14519753C2×C4semidirect
120. #14519752C2×C4semidirect
129. #14519748C2×C4semidirect
134. C4×Dic122C2×C4semidirect
140. C4×D244C2×C4semidirect
154. #14519735C2×C4semidirect
155. #14519735C2×C4semidirect
188. #125×C61C2×C4semidirect
189. #124×C61C2×C4semidirect
193. C4×Q8×C61C2×C4semidirect
195. C4×D4×C61C2×C4semidirect
489. #1500D61semidirect
531. #431C2×D61semidirect
544. #376C2×D61semidirect
552. #328C2×D61semidirect
553. #328C2×D61semidirect
562. C61#17615semidirect
585. #125C4×D61semidirect
589. #124C4×D61semidirect
629. C4×Q8C4×D61semidirect
649. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214596542
#214548422
#214487602
#214443972
#214443962
#214443892
#214443852
#214443742
#214443722
#214443092
#214443072
#214443032
#328×D612
#327×D612
C61×#15002
#1761561