Finite Group Databasebeta

← #29695569

Subgroups — #29695569

Order 15616.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840406C211yesmaximal, characteristic
2C2×#16839831C211yesmaximal, characteristic, complemented
3C2×#16839755C211yesmaximal, characteristic, complemented
4#21448769C211yesmaximal, characteristic, complemented
5#21446750C211yesmaximal, characteristic, complemented
6#21446634C211yesmaximal, characteristic, complemented
7#21446252C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic, complemented
9#21446138C211yesmaximal, characteristic, complemented
10#21446131C211yesmaximal, characteristic, complemented
11#21445817C211yesmaximal, characteristic, complemented
12#21445756C211yesmaximal, characteristic, complemented
13#21445750C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C2×C61×#418C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic, complemented
18#16840406—24no—
19#16840406C418yescomplemented
20C2×#14519764C2211yescharacteristic
21C2×#14519758—21no—
22C2×#14519756C2211yescharacteristic
23C2×#14519749—21no—
24C2×#14519748C2211yescharacteristic
25C2×#14519746—21no—
26C2×D4×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519735C2211yescharacteristic, complemented
29C22×C22⋊Dic61—21no—
30#16839831—24no—
31C2×#14519706C2211yescharacteristic, complemented
32#16839755—24no—
33C2×#14519702C2211yescharacteristic, complemented
34C2×#14519702C2211yescharacteristic, complemented
35C2×#14519700C2211yescharacteristic, complemented
36C2×#14519700C2211yescharacteristic, complemented
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519689C2211yescharacteristic, complemented
43C2×#14519687C2211yescharacteristic, complemented
44#16839662—21no—
45#16839653—21no—
46#16839650—21no—
47#16839631C2211yescharacteristic, complemented
48#16839622C2211yescharacteristic
49#16839619C2211yescharacteristic, complemented
50C4⋊C4×Dic61C2211yescharacteristic, complemented
51C4×#11758196—21no—
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C23×D4×C61C2211yescharacteristic
57C22×M16×C61C2211yescharacteristic
58C2×#117×C61C2211yescharacteristic
59C61×#418—24no—
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×#102×C61C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—41no—
68C2×#11758224—41no—
69C2×#11758224C2×C414yes—
70C22×Dic122C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C22⋊D61D411yescharacteristic
74C23×Dic61—21no—
75C23×Dic61—21no—
76C22×C4×D61C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C2×C8×D61—22no—
80C2×C8×D61—22no—
81C2×C8×D61—41no—
82#14519764—22no—
83#14519764C2×C414yes—
84#14519758—28no—
85#14519756—22no—
86#14519756C2×C414yes—
87#14519749—28no—
88#14519748—22no—
89#14519748C2×C414yes—
90#14519746—28no—
91D4×Dic61—22no—
92D4×Dic61C2×C414yes—
93C4×C22⋊D61C2×C414yes—
94C4×C22⋊D61D414yes—
95#14519735—22no—
96#14519735—41no—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196D411yescharacteristic
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—28no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61D411yescharacteristic
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198D411yescharacteristic
115C2×C4×Dic61—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61C2311yescharacteristic
118#14519706—22no—
119#14519702—22no—
120#14519702—41no—
121#14519700—22no—
122#14519700—41no—
123#14519698—22no—
124#14519698—22no—
125#14519698—41no—
126#14519698—41no—
127C22⋊#92418—22no—
128#14519689—22no—
129#14519687—22no—
130#14519684—21no—
131#14519684—21no—
132#14519684—21no—
133C25×C61—21no—
134C22×D4×C61—22no—
135C22×D4×C61—22no—
136C22×D4×C61—21no—
137C22×D4×C61—22no—
138C22×D4×C61—41no—
139C22×D4×C61—41no—
140C22×D4×C61C2×C414yes—
141C22×D4×C61C2311yescharacteristic
142C22×D4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C2×M16×C61—22no—
145C2×M16×C61—22no—
146C2×M16×C61—41no—
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149#117×C61—22no—
150#117×C61—41no—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—21no—
154C2×C42×C61—21no—
155#102×C61—22no—
156#102×C61—22no—
157#102×C61—22no—
158#102×C61D414yescomplemented
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—24no—
162C24×C61—42no—
163C24×C61—42no—
164C24×C61—42no—
165C24×C61—42no—
166C24×C61—81no—
167C24×C61—81no—
168C24×C61C2×D411yescharacteristic
169C23×D61C2×D411yescharacteristic
170C2×D4×C61—28no—
171C2×D4×C61—24no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—44no—
181C2×D4×C61—44no—
182C2×D4×C61—44no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61C22×C412yes—
186C2×D4×C61C22×C412yes—
187C2×D4×C61C2×D412yes—
188C2×D4×C61#4112yes—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61C22×C412yes—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—41no—
202C2×C22⋊D61—41no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—81no—
206C2×C22⋊D61—81no—
207C2×C22⋊D61C22⋊C414yes—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—24no—
211C22×Dic61—24no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—42no—
215C22×Dic61—42no—
216C22×Dic61—81no—
217C22×Dic61—81no—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221#11758224—28no—
222#11758224—44no—
223#11758224—44no—
224#11758224—44no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61C22×C412yes—
230C2×C4×D61C2×D412yes—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122C22×C412yes—
237M16×C61—44no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61C2×D412yes—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61C2×D412yes—
248C22⋊C4×C61—42no—
249C42×C61—42no—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252C22⋊Dic61—24no—
253C22⋊Dic61—24no—
254C22⋊Dic61—24no—
255C22⋊Dic61—81no—
256C22⋊Dic61C22⋊C414yes—
257#11758198—42no—
258#11758198—81no—
259#11758198C22⋊C414yes—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61C22×C412yes—
266#11758196—24no—
267#11758196—42no—
268#11758196—81no—
269#11758196C22⋊C414yes—
270C4×Dic61—42no—
271C4×Dic61—42no—
272C4×Dic61C22×C412yes—
273C4×Dic61C2×D412yes—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C8×D61—44no—
281C23×C61—22no—
282C23×C61—21no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—22no—
291C23×C61—48no—
292C23×C61—48no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—84no—
304C23×C61—84no—
305C23×C61—84no—
306C23×C61—84no—
307C23×C61—84no—
308C23×C61C2×C22⋊C412yes—
309C23×C61C22×D411yescharacteristic
310C22×D61—21no—
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—21no—
315C22×D61—21no—
316C22×D61C2×C22⋊C412yes—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—22no—
322D4×C61—48no—
323D4×C61—41no—
324D4×C61—41no—
325D4×C61C4×D414yes—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61C2×C22⋊C412yes—
339C2×C4×C61C23×C411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C2×#4111yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344C2×C4×C61H(5,𝔽2)11yescharacteristic
345C22⋊D61—44no—
346C22⋊D61—48no—
347C22⋊D61—84no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—48no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—84no—
368C2×Dic61C2×C22⋊C412yes—
369C2×Dic61C2×C22⋊C412yes—
370C2×Dic61C2×C22⋊C412yes—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375Dic122—22no—
376Dic122—22no—
377Dic122—41no—
378Dic122—41no—
379C8×C61—22no—
380C8×C61—41no—
381#92418—41no—
382#92418—41no—
383#22424—611nomaximal, Sylow
384C22×C61—24no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—41no—
391C22×C61—42no—
392C22×C61—41no—
393C22×C61—42no—
394C22×C61—41no—
395C22×C61—42no—
396C22×C61—41no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—816no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61C22×C22⋊C411yescharacteristic
407C22×C61D4211yescharacteristic
408C22×C61#54611yescharacteristic
409C22×C61#57511yescharacteristic
410C22×C61#57511yescharacteristic
411C22×C61#57611yescharacteristic
412C22×C61#57711yescharacteristic
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C4×C61—22no—
421C4×C61—42no—
422C4×C61—81no—
423C4×C61C2×C4×D411yescharacteristic
424C4×C61#51811yescharacteristic
425C4×C61D4211yescharacteristic
426C4×C61#54611yescharacteristic
427Dic61—22no—
428Dic61—22no—
429Dic61—22no—
430Dic61—42no—
431Dic61—42no—
432Dic61—81no—
433Dic61—81no—
434C2×#546—611no—
435C2×#435—611no—
436C2×#418D6111yescharacteristic, complemented
437C2×#416—611no—
438#2354—611no—
439#1983—611no—
440#1959—611no—
441#1894—611no—
442#1893—611no—
443#1875—611no—
444#1873—611no—
445#1802—611no—
446#1788—611no—
447#1786—611no—
448#1762—611no—
449C2×C61—42no—
450C2×C61—44no—
451C2×C61—82no—
452C2×C61D4×C22⋊C411yescharacteristic
453C2×C61#289611yescharacteristic
454C2×C61#289711yescharacteristic
455C2×C61#326711yescharacteristic
456C2×C61#326811yescharacteristic
457C2×C61#331111yescharacteristic
458C2×C61#331911yescharacteristic
459D61—42no—
460C22×#41—611no—
461C23×D4C2×D6111yescharacteristic
462C22×M16C2×D6111yescharacteristic
463C23×C8—611no—
464#546—618no—
465#546—1224no—
466C2×#124—611no—
467C2×#123—1221no—
468C2×C22⋊Q8—611no—
469C2×#121—611no—
470C2×#121—1221no—
471C2×#120—1221no—
472C2×C4×D4—611no—
473C2×C4×D4—611no—
474C2×#117—611no—
475C2×#117C2×D6111yescharacteristic
476C22×C22⋊C4—1221no—
477#435—1224no—
478C2×C4⋊C8—611no—
479#418—24no—
480#416—1224no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102C2×D6111yescharacteristic
490C2×#102C2×D6111yescharacteristic
491C2×#102C2×D6111yescharacteristic
492C2×#102C2×D6111yescharacteristic
493C2×C22⋊C8—611no—
494C2×C22⋊C8—611no—
495C2×#97—611no—
496#390—1221no—
497#388—1221no—
498#388—1221no—
499#384—611no—
500#380—611no—
501#380—611no—
502C4×C4⋊C4—611no—
503C4×C4⋊C4—1221no—
504#340—611no—
505#340—611no—
506#340—611no—
507#340—611no—
508C61#2242411yescharacteristic, complemented, Sylow
509C25—21no—
510C2×#41—614no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—2441no—
515C2×#41—2441no—
516C22×Q8—611no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—611no—
524C22×D4—1221no—
525C22×D4—1221no—
526C22×D4C4×D6114yes—
527C22×D4C22×D6111yescharacteristic
528C22×D4C22×D6111yescharacteristic
529C23×C4—611no—
530C23×C4—1221no—
531C23×C4—1221no—
532C23×C4C22×D6111yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C22×C8—611no—
537C22×C8—611no—
538C22×C8—1222no—
539C22×C8—1222no—
540C22×C8—2441no—
541C22×C8C22×D6111yescharacteristic
542C22×C8C22×D6111yescharacteristic
543#124—614no—
544#124—1222no—
545#123—1228no—
546C22⋊Q8—614no—
547C22⋊Q8—1222no—
548#121—614no—
549#121—1228no—
550#121—1222no—
551#120—1228no—
552C4×D4—614no—
553C4×D4—614no—
554C4×D4—614no—
555C4×D4—1222no—
556#117—22no—
557#117—41no—
558#117—1222no—
559#117—2441no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—611no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—1228no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C42—21no—
582C2×C42—611no—
583C2×C42—1221no—
584C2×C42—1221no—
585C4⋊C8—1222no—
586#103—1222no—
587#103—1222no—
588#103—2441no—
589#103—2441no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—1222no—
594#102—1222no—
595#102—2441no—
596#102—2441no—
597#102C22⋊D6114yescomplemented
598C22⋊C8—1222no—
599C22⋊C8—1222no—
600#97—1222no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24—611no—
614C24D4×D6111yescharacteristic
615#41—1228no—
616#41—2444no—
617#41—2444no—
618#41—2444no—
619C2×Q8—612no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×D4—28no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—24no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—614no—
641C2×D4—1224no—
642C2×D4—1224no—
643C2×D4—4881no—
644C2×D4—4881no—
645C2×D4—2441no—
646C2×D4—2441no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4C2×C4×D6112yes—
650C2×D4C2×C4×D6112yes—
651C2×D4#1175822212yes—
652C2×D4C2×C22⋊D6112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—1224no—
665C22×C4—1224no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—4881no—
675C22×C4—4881no—
676C22×C4—2442no—
677C22×C4—2442no—
678C22×C4C2×C4×D6112yes—
679C22×C4D4×D6112yes—
680C22×C4D4×D6111yescharacteristic
681C22×C4C23×D6111yescharacteristic
682M16—44no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—2444no—
695C2×C8C2×C22⋊D6112yes—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—614no—
700C4⋊C4—612no—
701C4⋊C4—1221no—
702C4⋊C4—1224no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—4881no—
708C4⋊C4—2442no—
709C4⋊C4C2×C22⋊D6112yes—
710C22⋊C4—42no—
711C22⋊C4—614no—
712C22⋊C4—614no—
713C22⋊C4—1224no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—4881no—
719C22⋊C4—4881no—
720C22⋊C4—2442no—
721C42—42no—
722C42—612no—
723C42—612no—
724C42—2442no—
725C42—2442no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—48no—
737C23—48no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—84no—
749C23—84no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—612no—
754C23—1221no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23—1221no—
760C23C22⋊C4×D6112yes—
761C23C2×D4×D6111yescharacteristic
762Q8—1222no—
763Q8—1222no—
764Q8—2441no—
765Q8—2441no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—41no—
773D4—41no—
774D4—4884no—
775D4—2444no—
776D4—2448no—
777D4C4×C22⋊D6114yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—612no—
791C2×C4—612no—
792C2×C4—612no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—4884no—
806C2×C4—2448no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4C22⋊C4×D6112yes—
818C2×C4C22×C4×D6111yescharacteristic
819C2×C4C2×D4×D6111yescharacteristic
820C2×C4C22×C22⋊D6111yescharacteristic
821C2×C4C2×#1175822211yescharacteristic
822C2×C4#1451982211yescharacteristic
823C2×C4#1451982211yescharacteristic
824C8—22no—
825C8—41no—
826C8—2441no—
827C8—2441no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—42no—
833C22—41no—
834C22—42no—
835C22—41no—
836C22—42no—
837C22—41no—
838C22—42no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—816no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—1222no—
851C22—1222no—
852C22—1222no—
853C22—2441no—
854C22—2441no—
855C22—2441no—
856C22—2441no—
857C22C2×C22⋊C4×D6111yescharacteristic
858C22D4×C22⋊D6111yescharacteristic
859C22#1684040211yescharacteristic
860C22#1684055811yescharacteristic
861C22#1684055811yescharacteristic
862C22#1684056611yescharacteristic
863C22#1684057211yescharacteristic
864C4—22no—
865C4—42no—
866C4—81no—
867C4—1222no—
868C4—1222no—
869C4—1222no—
870C4—4881no—
871C4—4881no—
872C4—2442no—
873C4—2442no—
874C4C2×C4×C22⋊D6111yescharacteristic
875C4#1684023511yescharacteristic
876C4D4×C22⋊D6111yescharacteristic
877C4#1684040211yescharacteristic
878C2—42no—
879C2—44no—
880C2—82no—
881C2—2442no—
882C2C22⋊C4×C22⋊D6111yescharacteristic
883C2#2145433311yescharacteristic
884C2#2145434411yescharacteristic
885C2#2145733811yescharacteristic
886C2#2145735311yescharacteristic
887C2#2145785611yescharacteristic
888C2#2145797611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#418C2
socleC23×C61C22×D4
prime radicalC2×#16840406C2
cosocleC22×C4×C61C24
hypercenterC2×#418D61
hypocenterC61#22424
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#16839831C2semidirect
3. C2×#16839755C2semidirect
4. #21448769C2semidirect
5. #21446750C2semidirect
6. #21446634C2semidirect
7. #21446252C2semidirect
8. #21446244C2semidirect
9. #21446138C2semidirect
10. #21446131C2semidirect
11. #21445817C2semidirect
12. #21445756C2semidirect
13. #21445750C2semidirect
14. #21445646C2semidirect
15. C2×C61×#418C2semidirect
17. C22×C8×D61C22semidirect
19. #16840406C4semidirect
28. C2×#14519735C22semidirect
31. C2×#14519706C22semidirect
33. C2×#14519702C22semidirect
34. C2×#14519702C22semidirect
35. C2×#14519700C22semidirect
36. C2×#14519700C22semidirect
42. C2×#14519689C22semidirect
43. C2×#14519687C22semidirect
47. #16839631C22semidirect
49. #16839619C22semidirect
50. C4⋊C4×Dic61C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
158. #102×C61D4semidirect
436. C2×#418D61semidirect
508. C61#22424semidirect
597. #102C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404062
C2×#168398312
C2×#168397552
#214487692
#214467502
#214466342
#214462522
#214462442
#214461382
#214461312
#214458172
#214457562
#214457502
#214456462
C2×C61×#4182
#2242461