Finite Group Databasebeta

← #29695572

Subgroups — #29695572

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×#16840400C211yesmaximal, characteristic
2C2×#16839830C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4C2×#16839758C211yesmaximal, characteristic, complemented
5#21448763C211yesmaximal, characteristic, complemented
6#21446748C211yesmaximal, characteristic, complemented
7#21446632C211yesmaximal, characteristic, complemented
8#21446249C211yesmaximal, characteristic, complemented
9#21446245C211yesmaximal, characteristic, complemented
10#21446139C211yesmaximal, characteristic, complemented
11#21446128C211yesmaximal, characteristic, complemented
12#21445817C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C23×#92418C2211yescharacteristic, complemented
19#16840400—24no—
20#16840400C418yescomplemented
21C2×#14519766C2211yescharacteristic
22C2×#14519760—21no—
23C2×#14519753C2211yescharacteristic
24C2×#14519751C2211yescharacteristic
25C2×#14519749—21no—
26C2×#14519745—21no—
27C2×D4×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519736C2211yescharacteristic, complemented
30C2×#14519735C2211yescharacteristic
31C22×#11758198—21no—
32#16839830—24no—
33C2×#14519706C2211yescharacteristic, complemented
34#16839765—24no—
35#16839758—24no—
36C2×#14519701C2211yescharacteristic, complemented
37C2×#14519701C2211yescharacteristic, complemented
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519687C2211yescharacteristic, complemented
46#16839662—21no—
47#16839656—21no—
48#16839651—21no—
49#16839631C2211yescharacteristic, complemented
50#16839619C2211yescharacteristic
51C4⋊C4×Dic61C2211yescharacteristic, complemented
52#16839613—21no—
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C22×#41×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic, complemented
59C2×#103×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic, complemented
63C61×#380C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C22⋊D61D411yescharacteristic
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61—22no—
72C2×D4×D61—41no—
73C2×D4×D61—41no—
74C2×D4×D61C2×C414yes—
75C23×Dic61—21no—
76C22×C4×D61C2311yescharacteristic
77C2×#11758189—22no—
78C2×#11758189—22no—
79C2×#11758189—41no—
80C22×#92418—22no—
81C22×#92418—22no—
82C22×#92418—41no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519766—22no—
86#14519766C2×C414yes—
87#14519760—28no—
88#14519753—22no—
89#14519753C2×C414yes—
90#14519751—22no—
91#14519751C2×C414yes—
92#14519749—28no—
93#14519745—28no—
94D4×Dic61—22no—
95D4×Dic61C2×C414yes—
96C4×C22⋊D61C2×C414yes—
97C4×C22⋊D61D414yes—
98#14519736—22no—
99#14519736—41no—
100#14519735—22no—
101#14519735—41no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196D411yescharacteristic
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61D411yescharacteristic
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—28no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198D411yescharacteristic
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519706—22no—
125#14519701—22no—
126#14519701—22no—
127#14519699—22no—
128#14519699—41no—
129#14519698—22no—
130#14519698D414yescomplemented
131#14519697—22no—
132#14519697—41no—
133#14519689—22no—
134#14519687—22no—
135#14519684—21no—
136#14519684—21no—
137C2×#41×C61—22no—
138C2×#41×C61—22no—
139C2×#41×C61—22no—
140C2×#41×C61—41no—
141C2×#41×C61—41no—
142C2×#41×C61C2×C414yes—
143C22×Q8×C61C2311yescharacteristic
144C22×D4×C61—21no—
145C22×D4×C61C2311yescharacteristic
146C23×C4×C61—21no—
147C23×C4×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153#103×C61—41no—
154#103×C61—41no—
155#102×C61—22no—
156#102×C61—22no—
157C22⋊C8×C61—22no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C23×D61—24no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—81no—
168C23×D61—81no—
169C23×D61C2×D411yescharacteristic
170#41×C61—28no—
171#41×C61—44no—
172#41×C61—44no—
173#41×C61—44no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61C22×C412yes—
180C2×D4×C61—24no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
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—24no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—42no—
198C22×C4×C61—42no—
199C22×C4×C61C22×C412yes—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D412yes—
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—41no—
206C2×C22⋊D61—41no—
207C2×C22⋊D61—42no—
208C2×C22⋊D61—42no—
209C2×C22⋊D61—81no—
210C2×C22⋊D61—81no—
211C2×C22⋊D61C22⋊C414yes—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—21no—
216C22×Dic61—81no—
217C22×Dic61—81no—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221D4×D61—28no—
222D4×D61—44no—
223D4×D61—44no—
224D4×D61—44no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244C22×C412yes—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61C22×C412yes—
236C2×C4×D61C2×D412yes—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C22⋊C4×C61—81no—
248C22⋊Dic61—24no—
249C22⋊Dic61—42no—
250C22⋊Dic61C22⋊C414yes—
251#11758198—24no—
252#11758198—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—42no—
256#11758198—81no—
257#11758198C22⋊C414yes—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61C22×C412yes—
263C4⋊Dic61C2×D412yes—
264#11758196—24no—
265#11758196—42no—
266#11758196—81no—
267#11758196C22⋊C414yes—
268C4×Dic61—42no—
269C4×Dic61—42no—
270C4×Dic61—42no—
271C4×Dic61C22×C412yes—
272C4×Dic61C2×D412yes—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—44no—
279C2×#92418C2×D412yes—
280#11758189—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—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61C2×C22⋊C412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—22no—
303C22×D61—48no—
304C22×D61—48no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—84no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61C2×C22⋊C412yes—
317Q8×C61—22no—
318Q8×C61—22no—
319Q8×C61—41no—
320Q8×C61—41no—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—48no—
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—48no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61C2×C22⋊C412yes—
343C2×C4×C61C23×C411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C2×#4111yescharacteristic
347C2×C4×C61H(5,𝔽2)11yescharacteristic
348C2×C4×C61H(5,𝔽2)11yescharacteristic
349C22⋊D61—44no—
350C22⋊D61—48no—
351C22⋊D61—84no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—22no—
359C2×Dic61—22no—
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—
371D244—22no—
372D244—22no—
373D244—41no—
374D244—41no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—22no—
379C8×C61—41no—
380C8×C61—41no—
381#92418—22no—
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—42no—
391C22×C61—41no—
392C22×C61—42no—
393C22×C61—41no—
394C22×C61—42no—
395C22×C61—41no—
396C22×C61—42no—
397C22×C61—41no—
398C22×C61C22×C22⋊C411yescharacteristic
399C22×C61D4211yescharacteristic
400C22×C61#54611yescharacteristic
401C22×C61#57511yescharacteristic
402C22×C61#57511yescharacteristic
403C22×C61#57611yescharacteristic
404C22×C61#57711yescharacteristic
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—816no—
416C2×D61—81no—
417C2×D61—81no—
418C2×D61—81no—
419C2×D61—81no—
420C4×C61—22no—
421C4×C61—42no—
422C4×C61—81no—
423C4×C61—81no—
424C4×C61C2×C4×D411yescharacteristic
425C4×C61#51811yescharacteristic
426C4×C61D4211yescharacteristic
427C4×C61#54611yescharacteristic
428Dic61—22no—
429Dic61—22no—
430Dic61—22no—
431Dic61—42no—
432Dic61—42no—
433Dic61—81no—
434C2×#546—611no—
435C2×#435—611no—
436C2×#418—611no—
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#1788D6111yescharacteristic, complemented
447#1786—611no—
448#1762—611no—
449C2×C61—44no—
450C2×C61—42no—
451C2×C61D4×C22⋊C411yescharacteristic
452C2×C61#289611yescharacteristic
453C2×C61#289711yescharacteristic
454C2×C61#326711yescharacteristic
455C2×C61#326811yescharacteristic
456C2×C61#331111yescharacteristic
457C2×C61#331911yescharacteristic
458D61—42no—
459D61—82no—
460C22×#41C2×D6111yescharacteristic
461C23×D4—611no—
462C22×M16—611no—
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×#117—611no—
476C22×C22⋊C4—1221no—
477#435—1224no—
478C2×C4⋊C8—611no—
479#418—1224no—
480#416—1224no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103C2×D6111yescharacteristic, complemented
484C2×#103C2×D6111yescharacteristic, complemented
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102C2×D6111yescharacteristic
492C2×#102C2×D6111yescharacteristic
493C2×C22⋊C8—611no—
494C2×C22⋊C8C2×D6111yescharacteristic, complemented
495C2×#97—611no—
496#390—1221no—
497#388—1221no—
498#388—1221no—
499#384—611no—
500#380—611no—
501#380C2×D6111yescharacteristic, complemented
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—1221no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C4×D6114yes—
516C22×Q8C22×D6111yescharacteristic
517C22×D4—21no—
518C22×D4—611no—
519C22×D4—614no—
520C22×D4—611no—
521C22×D4—1222no—
522C22×D4—1221no—
523C22×D4—1222no—
524C22×D4—1222no—
525C22×D4—1221no—
526C22×D4—2441no—
527C22×D4—2441no—
528C22×D4C22×D6111yescharacteristic
529C23×C4—21no—
530C23×C4—611no—
531C23×C4—1221no—
532C23×C4C22×D6111yescharacteristic
533C2×M16—1222no—
534C2×M16—1222no—
535C2×M16—2441no—
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—1222no—
557#117—1222no—
558#117—2441no—
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—611no—
582C2×C42—1221no—
583C2×C42—1221no—
584C2×C42—1221no—
585C4⋊C8—1222no—
586#103—41no—
587#103—41no—
588#103—1222no—
589#103—1222no—
590#102—22no—
591#102—22no—
592#102—614no—
593#102—1222no—
594#102—1222no—
595#102—1222no—
596#102—2441no—
597#102—2441no—
598C22⋊C8—22no—
599C22⋊C8—1222no—
600#97—1222no—
601#95—21no—
602#95—1221no—
603#95—1221no—
604C24—21no—
605C24—611no—
606C24—1224no—
607C24—1221no—
608C24—4881no—
609C24—4881no—
610C24—2442no—
611C24—2442no—
612C24—2442no—
613C24—2442no—
614C24D4×D6111yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C2×C4×D6112yes—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—614no—
632C2×D4—612no—
633C2×D4—1224no—
634C2×D4—1228no—
635C2×D4—1224no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—4881no—
642C2×D4—4881no—
643C2×D4—2444no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2441no—
647C2×D4—2441no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4C2×C4×D6112yes—
651C2×D4D4×D6112yes—
652C2×D4#1175822412yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—24no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—612no—
667C22×C4—612no—
668C22×C4—1224no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—4881no—
677C22×C4—4881no—
678C22×C4C2×C4×D6112yes—
679C22×C4D4×D6112yes—
680C22×C4D4×D6111yescharacteristic
681C22×C4C23×D6111yescharacteristic
682M16—2444no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—612no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—2444no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—614no—
701C4⋊C4—612no—
702C4⋊C4—612no—
703C4⋊C4—1224no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—4881no—
709C4⋊C4—2442no—
710C22⋊C4—81no—
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—2442no—
720C22⋊C4—2442no—
721C42—612no—
722C42—612no—
723C42—2442no—
724C42—2442no—
725C42—2442no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—22no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—612no—
740C23—1221no—
741C23—1221no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—1222no—
747C23—4884no—
748C23—4884no—
749C23—4884no—
750C23—4884no—
751C23—4884no—
752C23—2448no—
753C23—2448no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23C22⋊C4×D6112yes—
761C23C2×D4×D6111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—48no—
770D4—1222no—
771D4—1222no—
772D4—4884no—
773D4—2444no—
774D4—2448no—
775D4—2441no—
776D4—2441no—
777D4#1451973714yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—48no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—612no—
795C2×C4—612no—
796C2×C4—612no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—4884no—
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×C4C2×D4×D6111yescharacteristic
821C2×C4C2×#1175822411yescharacteristic
822C2×C4#1451982211yescharacteristic
823C2×C4#1451982211yescharacteristic
824C8—41no—
825C8—41no—
826C8—1222no—
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—1222no—
843C22—1222no—
844C22—1222no—
845C22—48816no—
846C22—4881no—
847C22—4881no—
848C22—4881no—
849C22—4881no—
850C22—2442no—
851C22—2442no—
852C22—2442no—
853C22—2441no—
854C22—2441no—
855C22—2441no—
856C22—2441no—
857C22C2×C22⋊C4×D6111yescharacteristic
858C22#1684039411yescharacteristic
859C22#1684039911yescharacteristic
860C22#1684055911yescharacteristic
861C22#1684055911yescharacteristic
862C22#1684056611yescharacteristic
863C22#1684057111yescharacteristic
864C4—22no—
865C4—42no—
866C4—81no—
867C4—81no—
868C4—1222no—
869C4—1222no—
870C4—1222no—
871C4—4881no—
872C4—2442no—
873C4—2442no—
874C4C2×#1451973711yescharacteristic
875C4#1684023511yescharacteristic
876C4#1684039411yescharacteristic
877C4#1684039911yescharacteristic
878C2—42no—
879C2—44no—
880C2—4882no—
881C2—2442no—
882C2#2144863511yescharacteristic
883C2#2145433411yescharacteristic
884C2#2145434311yescharacteristic
885C2#2145734811yescharacteristic
886C2#2145736311yescharacteristic
887C2#2145785911yescharacteristic
888C2#2145797911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1788C2
socleC23×C61C22×D4
prime radicalC2×#16840400C2
cosocleC22×C4×C61C24
hypercenter#1788D61
hypocenterC61#22424
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#16839830C2semidirect
3. C2×#16839765C2semidirect
4. C2×#16839758C2semidirect
5. #21448763C2semidirect
6. #21446748C2semidirect
7. #21446632C2semidirect
8. #21446249C2semidirect
9. #21446245C2semidirect
10. #21446139C2semidirect
11. #21446128C2semidirect
12. #21445817C2semidirect
13. #21445748C2semidirect
14. #21445646C2semidirect
15. C61×#1788C2semidirect
18. C23×#92418C22semidirect
20. #16840400C4semidirect
29. C2×#14519736C22semidirect
33. C2×#14519706C22semidirect
36. C2×#14519701C22semidirect
37. C2×#14519701C22semidirect
45. C2×#14519687C22semidirect
49. #16839631C22semidirect
51. C4⋊C4×Dic61C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
58. C2×#103×C61C22semidirect
59. C2×#103×C61C22semidirect
62. C2×C22⋊C8×C61C22semidirect
63. C61×#380C22semidirect
130. #14519698D4semidirect
446. #1788D61semidirect
483. C2×#103C2×D61semidirect
484. C2×#103C2×D61semidirect
494. C2×C22⋊C8C2×D61semidirect
501. #380C2×D61semidirect
508. C61#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#168404002
C2×#168398302
C2×#168397652
C2×#168397582
#214487632
#214467482
#214466322
#214462492
#214462452
#214461392
#214461282
#214458172
#214457482
#214456462
C61×#17882
#2242461