Finite Group Databasebeta

← #29689386

Subgroups — #29689386

Order 15616.

1442 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840325C211yesmaximal, characteristic
2C2×#16839822C211yesmaximal, characteristic, complemented
3#21448424C211yesmaximal, characteristic, complemented
4#21446751C211yesmaximal, characteristic, complemented
5#21446749C211yesmaximal, characteristic, complemented
6#21446747C211yesmaximal, characteristic, complemented
7#21446641C211yesmaximal, characteristic, complemented
8#21446634C211yesmaximal, characteristic, complemented
9#21446629C211yesmaximal, characteristic, complemented
10#21446623C211yesmaximal, characteristic, complemented
11#21445756C211yesmaximal, characteristic, complemented
12#21445756C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445748C211yesmaximal, characteristic, complemented
15C61×#1982C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18#16840325—24no—
19#16840325C418yescomplemented
20C2×#14519773C2211yescharacteristic
21C2×#14519765C2211yescharacteristic
22C2×#14519764C2211yescharacteristic
23C2×#14519749—21no—
24C2×#14519749—21no—
25C2×#14519745—21no—
26C2×#14519745—21no—
27C2×#14519734C2211yescharacteristic
28#16839822—24no—
29C2×C4⋊#92418C2211yescharacteristic, complemented
30C2×#14519702C2211yescharacteristic, complemented
31C2×#14519702C2211yescharacteristic, complemented
32C2×#14519700C2211yescharacteristic, complemented
33C2×#14519700C2211yescharacteristic, complemented
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic, complemented
39C2×#14519698C2211yescharacteristic, complemented
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519687C2211yescharacteristic, complemented
45C2×C8×Dic61C2211yescharacteristic, complemented
46#16839653—21no—
47#16839651—21no—
48#16839646—21no—
49#16839644—21no—
50#16839631C2211yescharacteristic, complemented
51#16839627C2211yescharacteristic, complemented
52#16839619C2211yescharacteristic
53#16839619C2211yescharacteristic
54C4×C4⋊Dic61C2211yescharacteristic, complemented
55C2×#127×C61C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic, complemented
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic, complemented
61C4×C4⋊C4×C61C2211yescharacteristic, complemented
62C24×D61—21no—
63C2×#11758224—22no—
64C2×#11758224—41no—
65C2×#11758224—41no—
66C2×#11758224—41no—
67C2×#11758224—41no—
68C2×#11758224C2×C414yes—
69C22×Dic122C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C2×D4×D61—22no—
76C2×D4×D61—41no—
77C2×D4×D61—41no—
78C2×D4×D61—41no—
79C2×D4×D61—41no—
80C2×D4×D61C2×C414yes—
81C23×Dic61—21no—
82C22×C4×D61C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519773—22no—
86#14519773C2×C414yes—
87#14519765—22no—
88#14519765C2×C414yes—
89#14519764—22no—
90#14519764C2×C414yes—
91#14519749—28no—
92#14519749—28no—
93#14519745—28no—
94#14519745—28no—
95#14519734C2×C414yes—
96#14519734D414yes—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196D411yescharacteristic
102C2×#11758196D411yescharacteristic
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198D411yescharacteristic
110C2×#11758198D411yescharacteristic
111C2×C4×Dic61—21no—
112C2×C4×Dic61C2311yescharacteristic
113C4⋊#92418—22no—
114#14519702—41no—
115#14519702—41no—
116#14519700—41no—
117#14519700—41no—
118#14519699—41no—
119#14519699—41no—
120#14519698—41no—
121#14519698—41no—
122#14519698—41no—
123#14519698—41no—
124#14519697—41no—
125#14519697—41no—
126#14519689—22no—
127#14519689—22no—
128#14519687—22no—
129C8×Dic61—22no—
130#14519684—21no—
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C22×D4×C61—21no—
136C22×D4×C61—21no—
137C22×D4×C61C2311yescharacteristic
138C22×D4×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141#127×C61—22no—
142#127×C61C2×C414yes—
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C42×C61—21no—
146C2×C42×C61C2311yescharacteristic
147C4⋊C8×C61—22no—
148#102×C61—41no—
149#102×C61—41no—
150#102×C61—41no—
151#102×C61—41no—
152#95×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C23×D61—21no—
156C23×D61—24no—
157C23×D61—42no—
158C23×D61—42no—
159C23×D61—81no—
160C23×D61—81no—
161C23×D61—81no—
162C23×D61—81no—
163C23×D61C2×D411yescharacteristic
164C2×D4×C61—24no—
165C2×D4×C61—24no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—81no—
177C2×D4×C61—81no—
178C2×D4×C61—81no—
179C2×D4×C61—81no—
180C2×D4×C61C22×C412yes—
181C2×D4×C61C22×C412yes—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2411yescharacteristic
187C2×C22⋊D61—24no—
188C2×C22⋊D61—24no—
189C2×C22⋊D61—24no—
190C2×C22⋊D61—24no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—81no—
196C2×C22⋊D61—81no—
197C2×C22⋊D61—81no—
198C2×C22⋊D61—81no—
199C22×Dic61—21no—
200C22×Dic61—24no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—42no—
204C22×Dic61—42no—
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208#11758224—44no—
209#11758224—44no—
210#11758224—44no—
211#11758224—44no—
212D4×D61—44no—
213D4×D61—44no—
214D4×D61—44no—
215D4×D61—44no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244C22×C412yes—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61C22×C412yes—
227C2×C4×D61C2×D412yes—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122C22×C412yes—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C42×C61—81no—
245C42×C61C22×C412yes—
246C42×C61C2×D412yes—
247C22⋊Dic61—24no—
248C22⋊Dic61—24no—
249#11758198—24no—
250#11758198—24no—
251#11758198—81no—
252#11758198—81no—
253#11758198C22⋊C414yes—
254#11758198C22⋊C414yes—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259#11758196—81no—
260#11758196—81no—
261#11758196C22⋊C414yes—
262#11758196C22⋊C414yes—
263C4×Dic61—81no—
264C4×Dic61C22×C412yes—
265C4×Dic61C2×D412yes—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61C22×D411yescharacteristic
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—22no—
294C22×D61—48no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—84no—
302C22×D61—84no—
303C22×D61—84no—
304C22×D61—84no—
305C22×D61—84no—
306C22×D61—84no—
307C22×D61C2×C22⋊C412yes—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61—41no—
313D4×C61—41no—
314D4×C61—41no—
315D4×C61—41no—
316D4×C61—84no—
317D4×C61—84no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61C2×C22⋊C412yes—
329C2×C4×C61C2×C22⋊C412yes—
330C2×C4×C61C23×C411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61H(5,𝔽2)11yescharacteristic
333C2×C4×C61H(5,𝔽2)11yescharacteristic
334C2×C4×C61H(5,𝔽2)11yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C22⋊D61—48no—
337C22⋊D61—48no—
338C22⋊D61—84no—
339C22⋊D61—84no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—22no—
347C2×Dic61—48no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61C2×C22⋊C412yes—
357C2×Dic61C2×C22⋊C412yes—
358C2×Dic61C2×C22⋊C412yes—
359D244—22no—
360D244—22no—
361D244—41no—
362D244—41no—
363C4×D61—22no—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—22no—
367Dic122—22no—
368Dic122—22no—
369Dic122—41no—
370Dic122—41no—
371C8×C61—41no—
372C8×C61—41no—
373#92418—41no—
374#92418—41no—
375#21813—611nomaximal, Sylow
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—81no—
383C22×C61—81no—
384C22×C61—81no—
385C22×C61—81no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61C22×C22⋊C411yescharacteristic
391C22×C61#53511yescharacteristic
392C22×C61#53511yescharacteristic
393C22×C61#57611yescharacteristic
394C22×C61#57611yescharacteristic
395C22×C61#57711yescharacteristic
396C22×C61#57711yescharacteristic
397C2×D61—22no—
398C2×D61—22no—
399C2×D61—22no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—816no—
408C2×D61—81no—
409C2×D61—81no—
410C2×D61—81no—
411C2×D61—81no—
412C4×C61—22no—
413C4×C61—22no—
414C4×C61—81no—
415C4×C61—81no—
416C4×C61#51811yescharacteristic
417C4×C61#51811yescharacteristic
418C4×C61#53511yescharacteristic
419C4×C61#53511yescharacteristic
420Dic61—22no—
421Dic61—22no—
422Dic61—22no—
423Dic61—42no—
424Dic61—81no—
425Dic61—81no—
426C2×#535—611no—
427C2×#433—611no—
428#2314—611no—
429#1983—611no—
430#1983—611no—
431#1982—611no—
432#1982D6111yescharacteristic, complemented
433#1961—611no—
434#1959—611no—
435#1958—611no—
436#1957—611no—
437#1788—611no—
438#1788—611no—
439#1786—611no—
440#1786—611no—
441C2×C61—82no—
442C2×C61—82no—
443C2×C61#230911yescharacteristic
444C2×C61#289711yescharacteristic
445C2×C61#289711yescharacteristic
446C2×C61#322011yescharacteristic
447C2×C61#322211yescharacteristic
448C2×C61#322411yescharacteristic
449C2×C61#322411yescharacteristic
450D61—42no—
451D61—82no—
452C22×#41—611no—
453C23×D4—611no—
454#535—618no—
455#535—1224no—
456C2×#127—611no—
457C2×#127C2×D6111yescharacteristic
458C2×#124—611no—
459C2×#124—611no—
460C2×#121—1221no—
461C2×#121—1221no—
462C2×#120—1221no—
463C2×#120—1221no—
464C2×#117—611no—
465#433—1224no—
466C2×C4⋊C8—611no—
467C2×C4⋊C8C2×D6111yescharacteristic, complemented
468C2×#103—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#102—611no—
473C2×#102—611no—
474C2×#102—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102C2×D6111yescharacteristic
481C2×#102C2×D6111yescharacteristic
482C2×#102C2×D6111yescharacteristic, complemented
483C2×#102C2×D6111yescharacteristic, complemented
484C2×C22⋊C8—611no—
485C2×C22⋊C8—611no—
486C2×#97—611no—
487C2×C4×C8—611no—
488#388—1221no—
489#388—1221no—
490#387—1221no—
491#387—1221no—
492#384—611no—
493#382—611no—
494#380—611no—
495#380—611no—
496C4×C4⋊C4—611no—
497C4×C4⋊C4C2×D6111yescharacteristic, complemented
498C61#2181311yescharacteristic, complemented, Sylow
499C25—1221no—
500C2×#41—614no—
501C2×#41—1222no—
502C2×#41—2441no—
503C2×#41—2441no—
504C2×#41—2441no—
505C2×#41—2441no—
506C22×Q8—611no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—614no—
510C22×D4—611no—
511C22×D4—1222no—
512C22×D4—1221no—
513C22×D4—1221no—
514C22×D4—1221no—
515C22×D4—1221no—
516C22×D4—2441no—
517C22×D4—2441no—
518C22×D4—2441no—
519C22×D4—2441no—
520C22×D4C22×D6111yescharacteristic
521C22×D4C22×D6111yescharacteristic
522C23×C4—611no—
523C23×C4—1221no—
524C22×C8—611no—
525C22×C8—611no—
526C22×C8C22×D6111yescharacteristic
527C22×C8C22×D6111yescharacteristic
528#127—22no—
529#127—614no—
530#127—1222no—
531#127C4×D6114yes—
532#124—614no—
533#124—614no—
534#124—1222no—
535#124—1222no—
536#121—1228no—
537#121—1228no—
538#120—1228no—
539#120—1228no—
540#117—614no—
541#117—614no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4C22×D6111yescharacteristic
549C2×C4⋊C4C22×D6111yescharacteristic
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C42—21no—
559C2×C42—611no—
560C2×C42—1221no—
561C2×C42C22×D6111yescharacteristic
562C4⋊C8—22no—
563C4⋊C8—1222no—
564#103—2441no—
565#103—2441no—
566#103—2441no—
567#103—2441no—
568#102—41no—
569#102—41no—
570#102—41no—
571#102—41no—
572#102—2441no—
573#102—2441no—
574#102—2441no—
575#102—2441no—
576#102—2441no—
577#102—2441no—
578#102—2441no—
579#102—2441no—
580C22⋊C8—1222no—
581C22⋊C8—1222no—
582#97—1222no—
583C4×C8—1222no—
584#95—21no—
585#95—1221no—
586#95—1221no—
587#95—1221no—
588#95—1221no—
589#95—1221no—
590C24—21no—
591C24—21no—
592C24—611no—
593C24—1224no—
594C24—1221no—
595C24—4881no—
596C24—4881no—
597C24—4881no—
598C24—4881no—
599C24—2442no—
600C24—2442no—
601#41—2444no—
602#41—2444no—
603#41—2444no—
604#41—2444no—
605C2×Q8—612no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—81no—
624C2×D4—81no—
625C2×D4—81no—
626C2×D4—81no—
627C2×D4—612no—
628C2×D4—1224no—
629C2×D4—1224no—
630C2×D4—1224no—
631C2×D4—1224no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—4881no—
638C2×D4—4881no—
639C2×D4—4881no—
640C2×D4—4881no—
641C2×D4—2444no—
642C2×D4—2444no—
643C2×D4—2444no—
644C2×D4—2444no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4C2×C4×D6112yes—
650C2×D4C2×C4×D6112yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—612no—
657C22×C4—612no—
658C22×C4—1224no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—2442no—
667C22×C4—2442no—
668C22×C4D4×D6111yescharacteristic
669C22×C4D4×D6111yescharacteristic
670C22×C4C23×D6111yescharacteristic
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—614no—
688C4⋊C4—614no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—4881no—
694C4⋊C4—4881no—
695C22⋊C4—614no—
696C22⋊C4—614no—
697C22⋊C4—1224no—
698C22⋊C4—1224no—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—4881no—
702C22⋊C4—4881no—
703C42—81no—
704C42—612no—
705C42—612no—
706C42—4881no—
707C42C2×C4×D6112yes—
708C42D4×D6112yes—
709C23—22no—
710C23—22no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—612no—
724C23—1221no—
725C23—1221no—
726C23—1221no—
727C23—1221no—
728C23—1221no—
729C23—1221no—
730C23—1222no—
731C23—4884no—
732C23—4884no—
733C23—4884no—
734C23—4884no—
735C23—4884no—
736C23—4884no—
737C23—2448no—
738C23—2441no—
739C23—2441no—
740C23—2441no—
741C23—2441no—
742C23—2441no—
743C23—2441no—
744C23C2×D4×D6111yescharacteristic
745Q8—1222no—
746Q8—1222no—
747Q8—2441no—
748Q8—2441no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—84no—
758D4—84no—
759D4—1222no—
760D4—1222no—
761D4—4884no—
762D4—4884no—
763D4—2448no—
764D4—2448no—
765D4—2441no—
766D4—2441no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—612no—
778C2×C4—612no—
779C2×C4—612no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—2448no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4C22⋊C4×D6112yes—
801C2×C4C22⋊C4×D6112yes—
802C2×C4C22×C4×D6111yescharacteristic
803C2×C4C2×D4×D6111yescharacteristic
804C2×C4#1451982211yescharacteristic
805C2×C4#1451982211yescharacteristic
806C2×C4#1451982311yescharacteristic
807C2×C4#1451982311yescharacteristic
808C8—41no—
809C8—41no—
810C8—2441no—
811C8—2441no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—1222no—
827C22—1222no—
828C22—1222no—
829C22—48816no—
830C22—4881no—
831C22—4881no—
832C22—4881no—
833C22—4881no—
834C22—2442no—
835C22—2442no—
836C22—2442no—
837C22—2441no—
838C22—2441no—
839C22—2441no—
840C22—2441no—
841C22C2×C22⋊C4×D6111yescharacteristic
842C22#1684032811yescharacteristic
843C22#1684032811yescharacteristic
844C22#1684056311yescharacteristic
845C22#1684056611yescharacteristic
846C22#1684056811yescharacteristic
847C22#1684057211yescharacteristic
848C4—22no—
849C4—22no—
850C4—81no—
851C4—81no—
852C4—1222no—
853C4—1222no—
854C4—1222no—
855C4—4881no—
856C4—4881no—
857C4—2442no—
858C4#1684023411yescharacteristic
859C4#1684023411yescharacteristic
860C4#1684032511yescharacteristic
861C4#1684033011yescharacteristic
862C2—82no—
863C2—82no—
864C2—4882no—
865C2—2442no—
866C2#2144839811yescharacteristic
867C2#2145434011yescharacteristic
868C2#2145434411yescharacteristic
869C2#2145686811yescharacteristic
870C2#2145689011yescharacteristic
871C2#2145691011yescharacteristic
872C2#2145691811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1982C2
socleC23×C61C22×D4
prime radicalC2×#16840325C2
cosocleC22×C4×C61C24
hypercenter#1982D61
hypocenterC61#21813
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. C2×#16839822C2semidirect
3. #21448424C2semidirect
4. #21446751C2semidirect
5. #21446749C2semidirect
6. #21446747C2semidirect
7. #21446641C2semidirect
8. #21446634C2semidirect
9. #21446629C2semidirect
10. #21446623C2semidirect
11. #21445756C2semidirect
12. #21445756C2semidirect
13. #21445748C2semidirect
14. #21445748C2semidirect
15. C61×#1982C2semidirect
19. #16840325C4semidirect
29. C2×C4⋊#92418C22semidirect
30. C2×#14519702C22semidirect
31. C2×#14519702C22semidirect
32. C2×#14519700C22semidirect
33. C2×#14519700C22semidirect
38. C2×#14519698C22semidirect
39. C2×#14519698C22semidirect
44. C2×#14519687C22semidirect
45. C2×C8×Dic61C22semidirect
50. #16839631C22semidirect
51. #16839627C22semidirect
54. C4×C4⋊Dic61C22semidirect
56. C2×C4⋊C8×C61C22semidirect
59. C2×#102×C61C22semidirect
60. C2×#102×C61C22semidirect
61. C4×C4⋊C4×C61C22semidirect
432. #1982D61semidirect
467. C2×C4⋊C8C2×D61semidirect
482. C2×#102C2×D61semidirect
483. C2×#102C2×D61semidirect
497. C4×C4⋊C4C2×D61semidirect
498. C61#21813semidirect

Maximal subgroups

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

subgroupindex
C2×#168403252
C2×#168398222
#214484242
#214467512
#214467492
#214467472
#214466412
#214466342
#214466292
#214466232
#214457562
#214457482
C61×#19822
#2181361