Finite Group Databasebeta

← #29689156

Subgroups — #29689156

Order 15616.

1362 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459149C211yesmaximal, characteristic
2#21454263C211yesmaximal, characteristic, complemented
3#21448305C211yesmaximal, characteristic, complemented
4#21446266C211yesmaximal, characteristic, complemented
5#21446264C211yesmaximal, characteristic, complemented
6#21446261C211yesmaximal, characteristic, complemented
7#21446259C211yesmaximal, characteristic, complemented
8#21446122C211yesmaximal, characteristic, complemented
9#21446121C211yesmaximal, characteristic, complemented
10#21446119C211yesmaximal, characteristic, complemented
11#21445917C211yesmaximal, characteristic, complemented
12#21445917C211yesmaximal, characteristic, complemented
13#21445761C211yesmaximal, characteristic, complemented
14#21445761C211yesmaximal, characteristic, complemented
15C61×#1871C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#41×D61C2211yescharacteristic
18C22×#11758194C2211yescharacteristic, complemented
19#16840342C411yescharacteristic, complemented
20#16840342C411yescharacteristic, complemented
21#16840341C411yescharacteristic, complemented
22#16840341C411yescharacteristic, complemented
23#16840335C411yescharacteristic, complemented
24#16840335C411yescharacteristic, complemented
25#16840334—21no—
26#16840328C411yescharacteristic, complemented
27#16840328C411yescharacteristic, complemented
28#16840327—21no—
29#16840323—21no—
30#16840322—21no—
31#16840309—21no—
32#16840309—21no—
33#16840274C2211yescharacteristic
34#16840273C2211yescharacteristic
35#16840271—21no—
36#16840271—21no—
37#16840269C2211yescharacteristic
38C2×#14519734C2211yescharacteristic, complemented
39#117×D61C2211yescharacteristic
40C2×C42×D61C2211yescharacteristic, complemented
41C2×#14519705C2211yescharacteristic
42C2×#14519705C2211yescharacteristic
43C2×#14519704C2211yescharacteristic
44C2×#14519704C2211yescharacteristic
45C2×#14519703C2211yescharacteristic
46C2×#14519703C2211yescharacteristic
47#16839730—21no—
48#16839730—21no—
49#16839728—21no—
50#16839728—21no—
51#16839725C2211yescharacteristic
52#16839725C2211yescharacteristic
53#16839725C2211yescharacteristic, complemented
54#16839725C2211yescharacteristic, complemented
55#16839666—21no—
56#16839662—21no—
57#16839640—21no—
58#16839638—21no—
59C4×#11758198C2211yescharacteristic
60C4×#11758198C2211yescharacteristic
61C4×C22⋊Dic61C2211yescharacteristic, complemented
62#16839523C2211yescharacteristic, complemented
63#16839523C2211yescharacteristic, complemented
64#16839522C2211yescharacteristic, complemented
65#16839522C2211yescharacteristic, complemented
66#16839521C2211yescharacteristic, complemented
67#16839521C2211yescharacteristic, complemented
68C22×M16×C61C2211yescharacteristic, complemented
69C61×#525C2211yescharacteristic
70C2×#104×C61C2211yescharacteristic
71C2×#104×C61C2211yescharacteristic
72C4×C22⋊C4×C61C2211yescharacteristic, complemented
73C61×#339C2211yescharacteristic, complemented
74C61×#339C2211yescharacteristic, complemented
75C2×#11758226C2×C411yescharacteristic, complemented
76C2×#11758222—21no—
77C2×#11758222—41no—
78C2×#11758222—41no—
79C2×#11758222—41no—
80C2×#11758222—41no—
81C2×#11758222C2×C411yescharacteristic
82C2×#11758222C2×C411yescharacteristic
83C2×#11758222C2×C411yescharacteristic
84C2×#11758222C2×C411yescharacteristic
85C2×#11758222D411yescharacteristic
86C2×#11758222D411yescharacteristic
87C2×#11758222D411yescharacteristic
88C2×#11758222D411yescharacteristic
89C2×#11758222C2311yescharacteristic
90C2×#11758224—21no—
91C2×#11758224C2×C411yescharacteristic, complemented
92#41×D61—41no—
93#41×D61—41no—
94#41×D61—41no—
95#41×D61—41no—
96C22×Dic122D411yescharacteristic
97C2×Q8×D61C2×C411yescharacteristic, complemented
98C22×D244D411yescharacteristic
99C22×C22⋊D61D411yescharacteristic
100C22×C22⋊D61D411yescharacteristic
101C2×D4×D61—21no—
102C2×D4×D61C2×C411yescharacteristic, complemented
103C22×C4×D61—21no—
104C22×C4×D61—21no—
105C22×C4×D61C2311yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C2×#11758194—21no—
108C2×#11758194—41no—
109C2×#11758194—41no—
110C2×#11758194C2311yescharacteristic
111C2×#11758194C2311yescharacteristic
112C22×#92418—21no—
113#14519776—21no—
114#14519776—21no—
115#14519773—21no—
116#14519773—21no—
117#14519763—21no—
118#14519763—21no—
119#14519763—21no—
120#14519763—21no—
121#14519762—21no—
122#14519762—21no—
123#14519761—21no—
124#14519760—21no—
125#14519759—21no—
126#14519759—21no—
127#14519758—21no—
128#14519757C2×C411yescharacteristic
129#14519757C2×C411yescharacteristic
130#14519756C2×C411yescharacteristic, complemented
131#14519756C2×C411yescharacteristic, complemented
132#14519755—21no—
133#14519755—21no—
134#14519754—21no—
135#14519754—21no—
136#14519753C2×C411yescharacteristic
137#14519753C2×C411yescharacteristic
138#14519752—21no—
139#14519752—21no—
140#14519752C2×C411yescharacteristic
141#14519752C2×C411yescharacteristic
142#14519751C2×C411yescharacteristic, complemented
143#14519751C2×C411yescharacteristic, complemented
144#14519750—21no—
145#14519750—21no—
146#14519750—21no—
147#14519750—21no—
148#14519750—21no—
149#14519750—21no—
150#14519749—21no—
151#14519749—21no—
152#14519748—21no—
153#14519748—21no—
154#14519748C2×C411yescharacteristic
155#14519748C2×C411yescharacteristic
156#14519747—21no—
157#14519747—21no—
158#14519747—21no—
159#14519746—21no—
160#14519745—21no—
161#14519745—21no—
162#14519745—21no—
163C4×D244—21no—
164C4×D244—21no—
165C4×C22⋊D61—21no—
166C4×C22⋊D61—21no—
167C4×C22⋊D61—21no—
168C4×C22⋊D61—21no—
169#14519736C2311yescharacteristic
170#14519735C2×C411yescharacteristic, complemented
171#14519735C2×C411yescharacteristic, complemented
172#14519734—21no—
173#14519734—41no—
174#14519734—41no—
175#14519733—21no—
176C2×#11758196—21no—
177C4⋊C4×D61C2×C411yescharacteristic, complemented
178C4⋊C4×D61C2×C411yescharacteristic, complemented
179C2×C22⋊Dic61—21no—
180C2×#11758198—21no—
181C2×#11758198—21no—
182C2×#11758198—21no—
183C22⋊C4×D61—21no—
184C2×C4×Dic61—21no—
185C2×C4×Dic61C2311yescharacteristic
186C2×C4×Dic61C2311yescharacteristic
187C42×D61—21no—
188C42×D61—41no—
189C42×D61—41no—
190#14519705—41no—
191#14519705—41no—
192#14519704—41no—
193#14519704—41no—
194#14519703—41no—
195#14519703—41no—
196#14519689—21no—
197#14519689—21no—
198#14519689—21no—
199#14519689—21no—
200#14519689—21no—
201#14519689—21no—
202#14519689—21no—
203#14519689—21no—
204#14519684—21no—
205#14519684—21no—
206#14519684—21no—
207C2×#41×C61C2311yescharacteristic
208C23×C4×C61C2311yescharacteristic
209C2×M16×C61—21no—
210C2×M16×C61—41no—
211C2×M16×C61—41no—
212C2×M16×C61C2311yescharacteristic
213C2×M16×C61C2311yescharacteristic
214C22×C8×C61—21no—
215#123×C61—21no—
216C22⋊Q8×C61C2×C411yescharacteristic, complemented
217C22⋊Q8×C61C2×C411yescharacteristic, complemented
218#121×C61C2×C411yescharacteristic, complemented
219#121×C61C2×C411yescharacteristic, complemented
220#120×C61—21no—
221C4×D4×C61—21no—
222C4×D4×C61—21no—
223#117×C61C2311yescharacteristic
224C2×C22⋊C4×C61—21no—
225C2×C42×C61C2311yescharacteristic
226C2×C42×C61C2311yescharacteristic
227#104×C61—41no—
228#104×C61—41no—
229#95×C61—21no—
230C24×C61C2×D411yescharacteristic
231C23×D61—21no—
232C23×D61C2×D411yescharacteristic
233C23×D61C2×D411yescharacteristic
234#41×C61—21no—
235#41×C61—21no—
236#41×C61—21no—
237#41×C61—21no—
238C2×Q8×C61C22×C411yescharacteristic
239C2×D4×C61—21no—
240C2×D4×C61—21no—
241C2×D4×C61—21no—
242C2×D4×C61C22×C411yescharacteristic
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61C22×C411yescharacteristic
251C22×C4×C61C22×C411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2411yescharacteristic
256C2×C22⋊D61—21no—
257C2×C22⋊D61—21no—
258C2×C22⋊D61—21no—
259C2×C22⋊D61—21no—
260C2×C22⋊D61—21no—
261C2×C22⋊D61—21no—
262C2×C22⋊D61—21no—
263C2×C22⋊D61—41no—
264C2×C22⋊D61—41no—
265C2×C22⋊D61—41no—
266C2×C22⋊D61—41no—
267C2×C22⋊D61C22⋊C411yescharacteristic
268C2×C22⋊D61C22⋊C411yescharacteristic
269C2×C22⋊D61C22⋊C411yescharacteristic
270C2×C22⋊D61C22⋊C411yescharacteristic
271C2×C22⋊D61C22⋊C411yescharacteristic
272C2×C22⋊D61C22⋊C411yescharacteristic
273C2×C22⋊D61C22⋊C411yescharacteristic
274C2×C22⋊D61C22⋊C411yescharacteristic
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61C2×D411yescharacteristic
279C22×Dic61C2×D411yescharacteristic
280#11758226—41no—
281#11758226—41no—
282Q8×D61—41no—
283Q8×D61—41no—
284#11758224—41no—
285#11758224—41no—
286#11758224—42no—
287#11758224—42no—
288D4×D61—41no—
289D4×D61—41no—
290D4×D61—42no—
291D4×D61—42no—
292#11758222—21no—
293#11758222—21no—
294#11758222—21no—
295#11758222—21no—
296#11758222—41no—
297#11758222—41no—
298#11758222—41no—
299#11758222—41no—
300#11758222—41no—
301#11758222—41no—
302#11758222—41no—
303#11758222—41no—
304#11758222—41no—
305#11758222—41no—
306#11758222—41no—
307#11758222—41no—
308#11758222—41no—
309#11758222—41no—
310#11758222—41no—
311#11758222—41no—
312#11758222—42no—
313#11758222—42no—
314C2×D244—21no—
315C2×D244—21no—
316C2×D244—21no—
317C2×D244—41no—
318C2×D244—41no—
319C2×D244C22⋊C411yescharacteristic
320C2×D244C22⋊C411yescharacteristic
321C2×D244C22⋊C411yescharacteristic
322C2×D244C22⋊C411yescharacteristic
323C2×D244C22×C411yescharacteristic
324C2×C4×D61—21no—
325C2×C4×D61—21no—
326C2×C4×D61—21no—
327C2×C4×D61—21no—
328C2×C4×D61—21no—
329C2×C4×D61—21no—
330C2×C4×D61—21no—
331C2×C4×D61—21no—
332C2×C4×D61—21no—
333C2×C4×D61—21no—
334C2×C4×D61—21no—
335C2×C4×D61—21no—
336C2×C4×D61—21no—
337C2×C4×D61—42no—
338C2×C4×D61—42no—
339C2×C4×D61—42no—
340C2×C4×D61—42no—
341C2×C4×D61—42no—
342C2×C4×D61C22×C411yescharacteristic
343C2×C4×D61C22×C411yescharacteristic
344C2×C4×D61C22×C411yescharacteristic
345C2×C4×D61C22×C411yescharacteristic
346C2×C4×D61C2×D411yescharacteristic
347C2×C4×D61C2×D411yescharacteristic
348C2×C4×D61C2×D411yescharacteristic
349C2×C4×D61C2×D411yescharacteristic
350C2×Dic122—21no—
351C2×Dic122—41no—
352C2×Dic122—41no—
353C2×Dic122C22⋊C411yescharacteristic
354C2×Dic122C22⋊C411yescharacteristic
355C2×Dic122C22⋊C411yescharacteristic
356C2×Dic122C22⋊C411yescharacteristic
357C2×Dic122C22×C411yescharacteristic
358M16×C61—21no—
359M16×C61—21no—
360M16×C61—21no—
361M16×C61—21no—
362M16×C61—42no—
363C2×C8×C61—21no—
364C2×C8×C61—21no—
365C2×C8×C61—42no—
366C4⋊C4×C61—21no—
367C4⋊C4×C61—21no—
368C4⋊C4×C61C22×C411yescharacteristic
369C4⋊C4×C61C22×C411yescharacteristic
370C22⋊C4×C61—21no—
371C22⋊C4×C61—21no—
372C22⋊C4×C61—21no—
373C22⋊C4×C61—21no—
374C22⋊C4×C61—21no—
375C22⋊C4×C61—42no—
376C42×C61—21no—
377C42×C61—21no—
378C42×C61—21no—
379C42×C61—21no—
380C42×C61—21no—
381C22⋊Dic61—21no—
382C22⋊Dic61—21no—
383C22⋊Dic61—21no—
384C22⋊Dic61—21no—
385C22⋊Dic61—21no—
386C22⋊Dic61—42no—
387#11758198—21no—
388#11758198—21no—
389#11758198—21no—
390#11758198—21no—
391#11758198—21no—
392#11758198—21no—
393#11758198—21no—
394#11758198—21no—
395#11758198—21no—
396#11758198—21no—
397#11758198—42no—
398#11758198—42no—
399#11758198—42no—
400C4⋊Dic61—21no—
401C4⋊Dic61—21no—
402C4⋊Dic61C22×C411yescharacteristic
403C4⋊Dic61C22×C411yescharacteristic
404#11758196—21no—
405#11758196—21no—
406#11758196—21no—
407#11758196—21no—
408#11758196—21no—
409#11758196—21no—
410#11758196—42no—
411C4×Dic61—21no—
412C4×Dic61—21no—
413C4×Dic61—21no—
414C4×Dic61—21no—
415C4×Dic61—21no—
416C4×Dic61—21no—
417C4×Dic61—21no—
418C4×Dic61—42no—
419#11758194—21no—
420#11758194—21no—
421#11758194—21no—
422#11758194—21no—
423#11758194—42no—
424C2×#92418—21no—
425C2×#92418—21no—
426C2×#92418—42no—
427C23×C61—21no—
428C23×C61—21no—
429C23×C61—21no—
430C23×C61—41no—
431C23×C61—41no—
432C23×C61C2×C22⋊C411yescharacteristic
433C23×C61C2×C22⋊C411yescharacteristic
434C23×C61C22×D411yescharacteristic
435C22×D61—21no—
436C22×D61—21no—
437C22×D61—21no—
438C22×D61—21no—
439C22×D61—21no—
440C22×D61—41no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—42no—
445C22×D61—81no—
446C22×D61—81no—
447C22×D61C2×C22⋊C411yescharacteristic
448C22×D61C2×C22⋊C411yescharacteristic
449C22×D61C2×C22⋊C411yescharacteristic
450C22×D61C2×C22⋊C411yescharacteristic
451Q8×C61—21no—
452Q8×C61—21no—
453D4×C61—21no—
454D4×C61—21no—
455D4×C61—41no—
456D4×C61—41no—
457D4×C61—81no—
458D4×C61—81no—
459C2×C4×C61—21no—
460C2×C4×C61—21no—
461C2×C4×C61—21no—
462C2×C4×C61—21no—
463C2×C4×C61—21no—
464C2×C4×C61—21no—
465C2×C4×C61—21no—
466C2×C4×C61—21no—
467C2×C4×C61—21no—
468C2×C4×C61—21no—
469C2×C4×C61—22no—
470C2×C4×C61—21no—
471C2×C4×C61—21no—
472C2×C4×C61—21no—
473C2×C4×C61—41no—
474C2×C4×C61—41no—
475C2×C4×C61—41no—
476C2×C4×C61—41no—
477C2×C4×C61—41no—
478C2×C4×C61—41no—
479C2×C4×C61—41no—
480C2×C4×C61C2×C22⋊C411yescharacteristic
481C2×C4×C61C2×C22⋊C411yescharacteristic
482C2×C4×C61C23×C411yescharacteristic
483C2×C4×C61C22×D411yescharacteristic
484C2×C4×C61H(5,𝔽2)11yescharacteristic
485C2×C4×C61H(5,𝔽2)11yescharacteristic
486C2×C4×C61H(5,𝔽2)11yescharacteristic
487C2×C4×C61H(5,𝔽2)11yescharacteristic
488C22⋊D61—41no—
489C22⋊D61—41no—
490C22⋊D61—41no—
491C22⋊D61—41no—
492C22⋊D61—41no—
493C22⋊D61—41no—
494C22⋊D61—41no—
495C22⋊D61—41no—
496C22⋊D61—42no—
497C22⋊D61—42no—
498C22⋊D61—41no—
499C22⋊D61—41no—
500C22⋊D61—81no—
501C22⋊D61—81no—
502C22⋊D61—81no—
503C22⋊D61—81no—
504C2×Dic61—21no—
505C2×Dic61—21no—
506C2×Dic61—21no—
507C2×Dic61—21no—
508C2×Dic61—22no—
509C2×Dic61—21no—
510C2×Dic61—21no—
511C2×Dic61—21no—
512C2×Dic61—42no—
513C2×Dic61—41no—
514C2×Dic61—41no—
515C2×Dic61—41no—
516C2×Dic61—41no—
517C2×Dic61—41no—
518C2×Dic61C2×C22⋊C411yescharacteristic
519C2×Dic61C2×C22⋊C411yescharacteristic
520C2×Dic61C2×C22⋊C411yescharacteristic
521C2×Dic61C2×C22⋊C411yescharacteristic
522D244—21no—
523D244—21no—
524D244—41no—
525D244—41no—
526D244—41no—
527D244—41no—
528D244—42no—
529D244—81no—
530D244—81no—
531C4×D61—21no—
532C4×D61—21no—
533C4×D61—21no—
534C4×D61—21no—
535C4×D61—21no—
536C4×D61—21no—
537C4×D61—21no—
538C4×D61—21no—
539C4×D61—21no—
540C4×D61—21no—
541C4×D61—21no—
542C4×D61—21no—
543C4×D61—21no—
544C4×D61—21no—
545C4×D61—21no—
546C4×D61—21no—
547C4×D61—42no—
548C4×D61—42no—
549C4×D61—48no—
550C4×D61—41no—
551C4×D61—41no—
552C4×D61—81no—
553C4×D61—81no—
554Dic122—21no—
555Dic122—21no—
556Dic122—41no—
557Dic122—41no—
558Dic122—41no—
559Dic122—41no—
560Dic122—42no—
561C8×C61—41no—
562C8×C61—41no—
563#92418—41no—
564#92418—41no—
565#21775—611nomaximal, Sylow
566C22×C61—21no—
567C22×C61—21no—
568C22×C61—21no—
569C22×C61—21no—
570C22×C61—21no—
571C22×C61—21no—
572C22×C61—21no—
573C22×C61—21no—
574C22×C61—41no—
575C22×C61—41no—
576C22×C61—41no—
577C22×C61—81no—
578C22×C61—81no—
579C22×C61C22×C22⋊C411yescharacteristic
580C22×C61#53411yescharacteristic
581C22×C61#53411yescharacteristic
582C2×D61—21no—
583C2×D61—21no—
584C2×D61—21no—
585C2×D61—21no—
586C2×D61—21no—
587C2×D61—21no—
588C2×D61—21no—
589C2×D61—21no—
590C2×D61—21no—
591C2×D61—21no—
592C2×D61—21no—
593C2×D61—21no—
594C2×D61—42no—
595C2×D61—42no—
596C2×D61—41no—
597C2×D61—41no—
598C2×D61—41no—
599C2×D61—81no—
600C2×D61—81no—
601C2×D61—84no—
602C4×C61—21no—
603C4×C61—21no—
604C4×C61—42no—
605C4×C61—41no—
606C4×C61—41no—
607C4×C61—41no—
608C4×C61—81no—
609C4×C61#51811yescharacteristic
610C4×C61#51811yescharacteristic
611C4×C61#53411yescharacteristic
612C4×C61#53411yescharacteristic
613Dic61—21no—
614Dic61—21no—
615Dic61—21no—
616Dic61—21no—
617Dic61—42no—
618Dic61—41no—
619Dic61—41no—
620Dic61—41no—
621Dic61—81no—
622#3449—611no—
623#2879—611no—
624#2297—611no—
625#1897—611no—
626#1897—611no—
627#1896—611no—
628#1896—611no—
629#1871—611no—
630#1871—611no—
631#1871—611no—
632#1871D6111yescharacteristic, complemented
633#1826—611no—
634#1826—611no—
635#1789—611no—
636#1789—611no—
637C2×C61—21no—
638C2×C61—21no—
639C2×C61—41no—
640C2×C61—41no—
641C2×C61—81no—
642C2×C61#230811yescharacteristic
643C2×C61#290111yescharacteristic
644C2×C61#290111yescharacteristic
645D61—41no—
646D61—41no—
647D61—41no—
648D61—41no—
649D61—81no—
650C22×#41—611no—
651C22×#41—611no—
652C22×M16—611no—
653C22×M16C2×D6111yescharacteristic, complemented
654#537—611no—
655#537—611no—
656#537—611no—
657#537—611no—
658#536—611no—
659#536—611no—
660#536—1221no—
661#535—611no—
662#535—611no—
663#535—1221no—
664#534—1221no—
665#534—1221no—
666#532—1221no—
667#532—1221no—
668#525—611no—
669#525—611no—
670#525—611no—
671#525—1221no—
672#525—1221no—
673#525C2×D6111yescharacteristic
674C2×#117—611no—
675C2×#117—611no—
676C22×C42—611no—
677C2×#104—611no—
678C2×#104—611no—
679C2×#104—611no—
680C2×#104—611no—
681C2×#104—611no—
682C2×#104—611no—
683C2×#104C2×D6111yescharacteristic
684C2×#104C2×D6111yescharacteristic
685#408—1221no—
686#408—1221no—
687#408—1221no—
688#408—1221no—
689#407—611no—
690#407—611no—
691#407—611no—
692#407—611no—
693#391—1221no—
694#390—1221no—
695#386—1221no—
696#386—1221no—
697C4×C22⋊C4—611no—
698C4×C22⋊C4—611no—
699C4×C22⋊C4—611no—
700C4×C22⋊C4C2×D6111yescharacteristic, complemented
701#339—611no—
702#339—611no—
703#339—611no—
704#339—611no—
705#339—611no—
706#339—611no—
707#339C2×D6111yescharacteristic, complemented
708#339C2×D6111yescharacteristic, complemented
709C61#2177511yescharacteristic, complemented, Sylow
710C2×#41—611no—
711C2×#41—611no—
712C2×#41—611no—
713C2×#41—611no—
714C2×#41—611no—
715C2×#41—611no—
716C2×#41—611no—
717C2×#41—611no—
718C2×#41—611no—
719C2×#41—611no—
720C2×#41—611no—
721C2×#41—1221no—
722C2×#41—1221no—
723C2×#41—2441no—
724C2×#41—2441no—
725C2×#41—2441no—
726C2×#41—2441no—
727C2×#41—2441no—
728C2×#41—2441no—
729C2×#41—2441no—
730C2×#41—2441no—
731C2×#41C22×D6111yescharacteristic
732C22×Q8—611no—
733C22×Q8—611no—
734C22×D4—611no—
735C22×D4—611no—
736C22×D4—611no—
737C22×D4—611no—
738C22×D4—1221no—
739C23×C4—611no—
740C23×C4—611no—
741C23×C4—1221no—
742C23×C4—1221no—
743C23×C4C22×D6111yescharacteristic
744C2×M16—21no—
745C2×M16—41no—
746C2×M16—41no—
747C2×M16—611no—
748C2×M16—611no—
749C2×M16—1221no—
750C2×M16—2441no—
751C2×M16—2441no—
752C2×M16C22×D6111yescharacteristic
753C2×M16C22×D6111yescharacteristic
754C22×C8—21no—
755C22×C8—1221no—
756C4⋊Q8—1221no—
757C4⋊Q8—1221no—
758#127—1221no—
759#127—1221no—
760#124—1221no—
761#124—1221no—
762#124—1221no—
763#124—1221no—
764#123—21no—
765#123—1221no—
766#123—1221no—
767#123—1221no—
768#123—1221no—
769#123—1221no—
770#123—1221no—
771#123—1221no—
772C22⋊Q8—611no—
773C22⋊Q8—611no—
774C22⋊Q8—611no—
775C22⋊Q8—611no—
776C22⋊Q8—611no—
777C22⋊Q8—611no—
778C22⋊Q8—1221no—
779C22⋊Q8—1221no—
780C22⋊Q8—1221no—
781C22⋊Q8—1221no—
782C22⋊Q8C4×D6111yescharacteristic, complemented
783C22⋊Q8C4×D6111yescharacteristic, complemented
784#121—611no—
785#121—611no—
786#121—611no—
787#121—611no—
788#121—611no—
789#121—611no—
790#121—1221no—
791#121—1221no—
792#121—1221no—
793#121—1221no—
794#121—1221no—
795#121—1221no—
796#121—1221no—
797#121—1221no—
798#121—1221no—
799#121—1221no—
800#121—1221no—
801#121—1221no—
802#121C4×D6111yescharacteristic, complemented
803#121C4×D6111yescharacteristic, complemented
804#120—21no—
805#120—1221no—
806#120—1221no—
807#120—1221no—
808#120—1221no—
809#120—1221no—
810#120—1221no—
811#120—1221no—
812C4×D4—21no—
813C4×D4—21no—
814C4×D4—1221no—
815C4×D4—1221no—
816C4×D4—1221no—
817C4×D4—1221no—
818C4×D4—1221no—
819C4×D4—1221no—
820#117—611no—
821#117—611no—
822#117—611no—
823#117—1221no—
824#117—1221no—
825#117—2441no—
826#117—2441no—
827#117C22×D6111yescharacteristic
828C2×C4⋊C4—611no—
829C2×C4⋊C4—611no—
830C2×C4⋊C4—1221no—
831C2×C22⋊C4—21no—
832C2×C22⋊C4—1221no—
833C2×C22⋊C4—1221no—
834C2×C22⋊C4—1221no—
835C2×C22⋊C4—1221no—
836C2×C22⋊C4—1221no—
837C2×C42—611no—
838C2×C42—611no—
839C2×C42—1221no—
840C2×C42—1221no—
841C2×C42—2441no—
842C2×C42—2441no—
843C2×C42C22×D6111yescharacteristic
844C2×C42C22×D6111yescharacteristic
845#104—41no—
846#104—41no—
847#104—2441no—
848#104—2441no—
849#104—2441no—
850#104—2441no—
851#104—2441no—
852#104—2441no—
853C22⋊C8—1221no—
854C22⋊C8—1221no—
855C22⋊C8—1221no—
856C22⋊C8—1221no—
857C22⋊C8—1221no—
858C22⋊C8—1221no—
859C22⋊C8—1221no—
860C22⋊C8—1221no—
861#95—21no—
862#95—1221no—
863#95—1221no—
864#95—1221no—
865C24—611no—
866C24—611no—
867C24—1221no—
868C24D4×D6111yescharacteristic
869#41—21no—
870#41—21no—
871#41—21no—
872#41—21no—
873#41—1221no—
874#41—1221no—
875#41—1221no—
876#41—1221no—
877#41—2441no—
878#41—2441no—
879#41—2441no—
880#41—2441no—
881#41—2441no—
882#41—2441no—
883#41—2441no—
884#41—2441no—
885#41—2441no—
886#41—2441no—
887#41—2441no—
888#41—2441no—
889#41—2441no—
890#41—2441no—
891#41—2441no—
892#41—2441no—
893#41—2442no—
894#41—2442no—
895#41—2441no—
896#41—2441no—
897#41—2442no—
898#41—2442no—
899#41—2441no—
900#41—2441no—
901C2×Q8—611no—
902C2×Q8—611no—
903C2×Q8—611no—
904C2×Q8—611no—
905C2×Q8—611no—
906C2×Q8—1221no—
907C2×Q8—2441no—
908C2×Q8—2441no—
909C2×Q8—2441no—
910C2×Q8—2441no—
911C2×Q8C2×C4×D6111yescharacteristic
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—611no—
916C2×D4—611no—
917C2×D4—611no—
918C2×D4—611no—
919C2×D4—611no—
920C2×D4—611no—
921C2×D4—611no—
922C2×D4—611no—
923C2×D4—611no—
924C2×D4—611no—
925C2×D4—611no—
926C2×D4—611no—
927C2×D4—611no—
928C2×D4—1221no—
929C2×D4—1221no—
930C2×D4—1221no—
931C2×D4—1221no—
932C2×D4—1221no—
933C2×D4—1221no—
934C2×D4—1221no—
935C2×D4—1221no—
936C2×D4—1221no—
937C2×D4—1221no—
938C2×D4—2441no—
939C2×D4—2441no—
940C2×D4—2441no—
941C2×D4—2441no—
942C2×D4—2441no—
943C2×D4—2441no—
944C2×D4—2441no—
945C2×D4—2441no—
946C2×D4—2442no—
947C2×D4—2442no—
948C2×D4C2×C4×D6111yescharacteristic
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—611no—
957C22×C4—611no—
958C22×C4—611no—
959C22×C4—611no—
960C22×C4—611no—
961C22×C4—611no—
962C22×C4—611no—
963C22×C4—611no—
964C22×C4—611no—
965C22×C4—611no—
966C22×C4—1221no—
967C22×C4—1221no—
968C22×C4—1221no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—1221no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—1221no—
976C22×C4—1221no—
977C22×C4—1221no—
978C22×C4—1221no—
979C22×C4—1221no—
980C22×C4—1221no—
981C22×C4—1221no—
982C22×C4—2442no—
983C22×C4—2442no—
984C22×C4—2442no—
985C22×C4—2442no—
986C22×C4—2442no—
987C22×C4C2×C4×D6111yescharacteristic
988C22×C4C2×C4×D6111yescharacteristic
989C22×C4D4×D6111yescharacteristic
990C22×C4D4×D6111yescharacteristic
991C22×C4D4×D6111yescharacteristic
992C22×C4C23×D6111yescharacteristic
993M16—21no—
994M16—21no—
995M16—21no—
996M16—21no—
997M16—42no—
998M16—1221no—
999M16—1221no—
1000M16—1221no—
1001M16—1221no—
1002M16—2442no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—42no—
1006C2×C8—1221no—
1007C2×C8—1221no—
1008C2×C8—2442no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—611no—
1012C4⋊C4—611no—
1013C4⋊C4—1221no—
1014C4⋊C4—1221no—
1015C4⋊C4—1221no—
1016C4⋊C4—1221no—
1017C4⋊C4—1221no—
1018C4⋊C4—1221no—
1019C4⋊C4—1221no—
1020C4⋊C4—1221no—
1021C4⋊C4—2442no—
1022C4⋊C4C2×C4×D6111yescharacteristic
1023C4⋊C4C2×C4×D6111yescharacteristic
1024C22⋊C4—21no—
1025C22⋊C4—21no—
1026C22⋊C4—21no—
1027C22⋊C4—21no—
1028C22⋊C4—21no—
1029C22⋊C4—42no—
1030C22⋊C4—1221no—
1031C22⋊C4—1221no—
1032C22⋊C4—1221no—
1033C22⋊C4—1221no—
1034C22⋊C4—1221no—
1035C22⋊C4—1221no—
1036C22⋊C4—1221no—
1037C22⋊C4—1221no—
1038C22⋊C4—1221no—
1039C22⋊C4—1221no—
1040C22⋊C4—1221no—
1041C22⋊C4—1221no—
1042C22⋊C4—1221no—
1043C22⋊C4—1221no—
1044C22⋊C4—1221no—
1045C22⋊C4—2442no—
1046C22⋊C4—2442no—
1047C22⋊C4—2442no—
1048C22⋊C4—2442no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—1221no—
1055C42—1221no—
1056C42—1221no—
1057C42—1221no—
1058C42—1221no—
1059C42—1221no—
1060C42—1221no—
1061C42—2442no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—41no—
1066C23—41no—
1067C23—611no—
1068C23—611no—
1069C23—611no—
1070C23—611no—
1071C23—1221no—
1072C23—1221no—
1073C23—1221no—
1074C23—1221no—
1075C23—1221no—
1076C23—4881no—
1077C23—4881no—
1078C23—2441no—
1079C23—2441no—
1080C23—2441no—
1081C23—2441no—
1082C23—2442no—
1083C23C22⋊C4×D6111yescharacteristic
1084C23C22⋊C4×D6111yescharacteristic
1085C23C2×D4×D6111yescharacteristic
1086Q8—21no—
1087Q8—21no—
1088Q8—1221no—
1089Q8—1221no—
1090Q8—2441no—
1091Q8—2441no—
1092Q8—2441no—
1093Q8—2441no—
1094Q8—2442no—
1095D4—21no—
1096D4—21no—
1097D4—41no—
1098D4—41no—
1099D4—81no—
1100D4—81no—
1101D4—1221no—
1102D4—1221no—
1103D4—4881no—
1104D4—4881no—
1105D4—4881no—
1106D4—4881no—
1107D4—4881no—
1108D4—4881no—
1109D4—2441no—
1110D4—2441no—
1111D4—2441no—
1112D4—2441no—
1113D4—2442no—
1114D4—2441no—
1115D4—2441no—
1116D4—2441no—
1117D4—2441no—
1118D4—2441no—
1119D4—2441no—
1120D4—2441no—
1121D4—2441no—
1122D4—2442no—
1123D4—2442no—
1124D4—2441no—
1125D4—2441no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—611no—
1148C2×C4—611no—
1149C2×C4—611no—
1150C2×C4—611no—
1151C2×C4—1221no—
1152C2×C4—1221no—
1153C2×C4—1221no—
1154C2×C4—1221no—
1155C2×C4—1221no—
1156C2×C4—1221no—
1157C2×C4—1221no—
1158C2×C4—1221no—
1159C2×C4—1221no—
1160C2×C4—1221no—
1161C2×C4—1221no—
1162C2×C4—1221no—
1163C2×C4—1221no—
1164C2×C4—1221no—
1165C2×C4—1221no—
1166C2×C4—1221no—
1167C2×C4—1221no—
1168C2×C4—1221no—
1169C2×C4—1221no—
1170C2×C4—1221no—
1171C2×C4—1222no—
1172C2×C4—1221no—
1173C2×C4—1221no—
1174C2×C4—1221no—
1175C2×C4—4881no—
1176C2×C4—4881no—
1177C2×C4—2442no—
1178C2×C4—2442no—
1179C2×C4—2448no—
1180C2×C4—2442no—
1181C2×C4—2441no—
1182C2×C4—2441no—
1183C2×C4—2441no—
1184C2×C4—2441no—
1185C2×C4—2441no—
1186C2×C4—2441no—
1187C2×C4—2441no—
1188C2×C4C22⋊C4×D6111yescharacteristic
1189C2×C4C22⋊C4×D6111yescharacteristic
1190C2×C4C22×C4×D6111yescharacteristic
1191C2×C4C2×D4×D6111yescharacteristic
1192C2×C4#1451982211yescharacteristic
1193C2×C4#1451982211yescharacteristic
1194C2×C4#1451982311yescharacteristic
1195C2×C4#1451982311yescharacteristic
1196C8—41no—
1197C8—41no—
1198C8—2441no—
1199C8—2441no—
1200C22—21no—
1201C22—21no—
1202C22—21no—
1203C22—21no—
1204C22—21no—
1205C22—21no—
1206C22—21no—
1207C22—21no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—81no—
1212C22—81no—
1213C22—1221no—
1214C22—1221no—
1215C22—1221no—
1216C22—1221no—
1217C22—1221no—
1218C22—1221no—
1219C22—1221no—
1220C22—1221no—
1221C22—1221no—
1222C22—1221no—
1223C22—1221no—
1224C22—1221no—
1225C22—4881no—
1226C22—4881no—
1227C22—4884no—
1228C22—2442no—
1229C22—2442no—
1230C22—2441no—
1231C22—2441no—
1232C22—2441no—
1233C22C2×C22⋊C4×D6111yescharacteristic
1234C22#1684032011yescharacteristic
1235C22#1684032011yescharacteristic
1236C4—21no—
1237C4—21no—
1238C4—42no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—81no—
1243C4—1221no—
1244C4—1221no—
1245C4—1221no—
1246C4—1221no—
1247C4—4881no—
1248C4—2442no—
1249C4—2441no—
1250C4—2441no—
1251C4—2441no—
1252C4#1684023411yescharacteristic
1253C4#1684023411yescharacteristic
1254C4#1684032211yescharacteristic
1255C4#1684032311yescharacteristic
1256C2—21no—
1257C2—21no—
1258C2—41no—
1259C2—41no—
1260C2—81no—
1261C2—4881no—
1262C2—2441no—
1263C2—2441no—
1264C2—2441no—
1265C2—2441no—
1266C2#2144839311yescharacteristic
1267C2#2145436311yescharacteristic
1268C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1871C2
socleC22×C61C22×C22⋊C4
prime radical#21459149C2
cosocleC22×C4×C61C24
hypercenter#1871D61
hypocenterC61#21775
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. #21454263C2semidirect
3. #21448305C2semidirect
4. #21446266C2semidirect
5. #21446264C2semidirect
6. #21446261C2semidirect
7. #21446259C2semidirect
8. #21446122C2semidirect
9. #21446121C2semidirect
10. #21446119C2semidirect
11. #21445917C2semidirect
12. #21445917C2semidirect
13. #21445761C2semidirect
14. #21445761C2semidirect
15. C61×#1871C2semidirect
18. C22×#11758194C22semidirect
19. #16840342C4semidirect
20. #16840342C4semidirect
21. #16840341C4semidirect
22. #16840341C4semidirect
23. #16840335C4semidirect
24. #16840335C4semidirect
26. #16840328C4semidirect
27. #16840328C4semidirect
38. C2×#14519734C22semidirect
40. C2×C42×D61C22semidirect
53. #16839725C22semidirect
54. #16839725C22semidirect
61. C4×C22⋊Dic61C22semidirect
62. #16839523C22semidirect
63. #16839523C22semidirect
64. #16839522C22semidirect
65. #16839522C22semidirect
66. #16839521C22semidirect
67. #16839521C22semidirect
68. C22×M16×C61C22semidirect
72. C4×C22⋊C4×C61C22semidirect
73. C61×#339C22semidirect
74. C61×#339C22semidirect
75. C2×#11758226C2×C4semidirect
91. C2×#11758224C2×C4semidirect
97. C2×Q8×D61C2×C4semidirect
102. C2×D4×D61C2×C4semidirect
130. #14519756C2×C4semidirect
131. #14519756C2×C4semidirect
142. #14519751C2×C4semidirect
143. #14519751C2×C4semidirect
170. #14519735C2×C4semidirect
171. #14519735C2×C4semidirect
177. C4⋊C4×D61C2×C4semidirect
178. C4⋊C4×D61C2×C4semidirect
216. C22⋊Q8×C61C2×C4semidirect
217. C22⋊Q8×C61C2×C4semidirect
218. #121×C61C2×C4semidirect
219. #121×C61C2×C4semidirect
632. #1871D61semidirect
653. C22×M16C2×D61semidirect
700. C4×C22⋊C4C2×D61semidirect
707. #339C2×D61semidirect
708. #339C2×D61semidirect
709. C61#21775semidirect
782. C22⋊Q8C4×D61semidirect
783. C22⋊Q8C4×D61semidirect
802. #121C4×D61semidirect
803. #121C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214591492
#214542632
#214483052
#214462662
#214462642
#214462612
#214462592
#214461222
#214461212
#214461192
#214459172
#214457612
C61×#18712
#2177561