Finite Group Databasebeta

← #29717601

Subgroups — #29717601

Order 15616.

1604 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840408C211yesmaximal, characteristic
2C2×#16840001C211yesmaximal, characteristic, complemented
3C2×#16839922C211yesmaximal, characteristic, complemented
4C2×#16839912C211yesmaximal, characteristic, complemented
5C22×#14519697C211yesmaximal, characteristic, complemented
6#21447060C211yesmaximal, characteristic, complemented
7#21447001C211yesmaximal, characteristic, complemented
8#21446912C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446156C211yesmaximal, characteristic, complemented
11#21446126C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446065C211yesmaximal, characteristic, complemented
14#21445757C211yesmaximal, characteristic, complemented
15C61×#2417C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C22×#11758202C2211yescharacteristic, complemented
19C22×#11758201C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22#16840408—24no—
23#16840408—24no—
24C2×#14519765C2211yescharacteristic
25C2×#14519762—21no—
26C2×#14519756C2211yescharacteristic
27C2×#14519751C2211yescharacteristic
28C2×#14519750—21no—
29C2×#14519745—21no—
30C2×C4×D244C2211yescharacteristic
31C2×C22⋊C4×D61—21no—
32#16840001—24no—
33#16839922—24no—
34#16839912—24no—
35C2×#14519710C2211yescharacteristic, complemented
36C2×#14519701C2211yescharacteristic, complemented
37C2×#14519700C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519700C2211yescharacteristic, complemented
40C2×#14519697—24no—
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×#14519697C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic
48C2×C22⋊#92418C2211yescharacteristic, complemented
49C2×C22⋊#92418C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53#16839517C2211yescharacteristic, complemented
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic, complemented
56C2×C4×D4×C61C2211yescharacteristic
57C22×C4⋊C4×C61C2211yescharacteristic
58C61×#398—21no—
59C61×#396—21no—
60C61×#391C2211yescharacteristic, complemented
61C61×#389C2211yescharacteristic, complemented
62C61×#386—21no—
63C61×#380—21no—
64C61×#380C2211yescharacteristic, complemented
65C24×D61—21no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—22no—
70C2×#11758222—41no—
71C2×#11758222—41no—
72C22×Dic122C2311yescharacteristic
73C22×D244—22no—
74C22×D244—22no—
75C22×D244—21no—
76C22×D244—22no—
77C22×D244—41no—
78C22×D244—41no—
79C22×D244D414yes—
80C22×D244C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C2×#11758202—22no—
87C2×#11758202—22no—
88C2×#11758202—41no—
89C2×#11758201—22no—
90C2×#11758201—22no—
91C2×#11758201—22no—
92C2×#11758201—22no—
93C2×#11758201—41no—
94C2×#11758201—41no—
95C22×#92418—22no—
96C22×#92418—22no—
97C22×#92418—41no—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102#14519765—22no—
103#14519765—22no—
104#14519762—28no—
105#14519756—22no—
106#14519756D414yes—
107#14519751—22no—
108#14519751—22no—
109#14519750—28no—
110#14519745—28no—
111C4×D244—22no—
112C4×D244—22no—
113C2×C4⋊Dic61C2311yescharacteristic
114C2×#11758196—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C22⋊C4×D61—28no—
121#14519710—22no—
122#14519701—22no—
123#14519700—22no—
124#14519700—22no—
125#14519700—41no—
126#14519697—22no—
127#14519697—22no—
128#14519697—22no—
129#14519697—22no—
130#14519697—22no—
131#14519697D414yescomplemented
132C22⋊#92418—22no—
133C22⋊#92418—22no—
134C22⋊#92418—41no—
135C22×Q8×C61C2311yescharacteristic
136C22×D4×C61D411yescharacteristic
137C23×C4×C61—21no—
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C22⋊Q8×C61—22no—
141C22⋊Q8×C61—22no—
142C22⋊Q8×C61—22no—
143C22⋊Q8×C61—41no—
144C4×D4×C61—22no—
145C4×D4×C61—22no—
146C2×C4⋊C4×C61—22no—
147C2×C4⋊C4×C61—21no—
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61—21no—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61—41no—
152C2×C4⋊C4×C61D411yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C22⋊C4×C61—21no—
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61D411yescharacteristic
160C2×C22⋊C4×C61D411yescharacteristic
161C2×C42×C61C2311yescharacteristic
162#95×C61—21no—
163#95×C61—21no—
164#95×C61—21no—
165#95×C61—21no—
166C24×C61C2×D411yescharacteristic
167C24×C61C2×D411yescharacteristic
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—24no—
171C23×D61—42no—
172C23×D61—42no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—81no—
176C23×D61—81no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×D4×C61—22no—
184C2×D4×C61—22no—
185C2×D4×C61—22no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
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×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—42no—
201C22×C4×C61—42no—
202C22×C4×C61—81no—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D412yes—
208C22×C4×C61C2×D412yes—
209C22×C4×C61C2411yescharacteristic
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—42no—
213C2×C22⋊D61—42no—
214C2×C22⋊D61—81no—
215C2×C22⋊D61—81no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218#11758222—44no—
219#11758222—44no—
220#11758222—44no—
221#11758222—44no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—28no—
230C2×D244—24no—
231C2×D244—21no—
232C2×D244—44no—
233C2×D244—44no—
234C2×D244—44no—
235C2×D244—42no—
236C2×D244—42no—
237C2×D244C2×D412yes—
238C2×D244C2×D412yes—
239C2×D244C2×D412yes—
240C2×D244#4112yes—
241C2×C4×D61—24no—
242C2×C4×D61—24no—
243C2×C4×D61—42no—
244C2×C4×D61—42no—
245C2×C4×D61—81no—
246C2×C4×D61—81no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122—21no—
252C2×Dic122C2×D412yes—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—42no—
260C4⋊C4×C61—42no—
261C4⋊C4×C61—42no—
262C4⋊C4×C61—81no—
263C4⋊C4×C61C2×D412yes—
264C22⋊C4×C61—22no—
265C22⋊C4×C61—22no—
266C22⋊C4×C61—42no—
267C22⋊C4×C61—42no—
268C22⋊C4×C61—81no—
269C42×C61—21no—
270C42×C61—21no—
271C22⋊Dic61—24no—
272#11758202—44no—
273#11758201—44no—
274#11758201—44no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279C4⋊Dic61—21no—
280C4⋊Dic61C2×D412yes—
281#11758196—24no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—44no—
294C2×#92418C2×D412yes—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61#12012yes—
307C23×C61#13512yes—
308C23×C61#13712yes—
309C23×C61C22×D411yescharacteristic
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—48no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—41no—
325C22×D61—48no—
326C22×D61—84no—
327C22×D61—84no—
328C22×D61—84no—
329C22×D61—84no—
330C22×D61—84no—
331Q8×C61—41no—
332Q8×C61—41no—
333Q8×C61—41no—
334Q8×C61—41no—
335D4×C61—44no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—22no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—84no—
368C2×C4×C61#12012yes—
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C22×D411yescharacteristic
372C2×C4×C61C2×#4111yescharacteristic
373C2×C4×C61H(5,𝔽2)11yescharacteristic
374C2×C4×C61H(5,𝔽2)11yescharacteristic
375C22⋊D61—48no—
376C22⋊D61—84no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383D244—22no—
384D244—22no—
385D244—22no—
386D244—22no—
387D244—22no—
388D244—48no—
389D244—41no—
390D244—41no—
391D244#12114yes—
392C4×D61—48no—
393C4×D61—84no—
394Dic122—22no—
395Dic122—22no—
396Dic122—41no—
397Dic122—41no—
398#92418—22no—
399#92418—41no—
400#92418—41no—
401#92418—41no—
402#24426—611nomaximal, Sylow
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—22no—
406C22×C61—22no—
407C22×C61—22no—
408C22×C61—22no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61#45214yescomplemented
417C22×C61C2×#12011yescharacteristic
418C22×C61D4211yescharacteristic
419C22×C61#54611yescharacteristic
420C22×C61C2×#13511yescharacteristic
421C22×C61C2×#13711yescharacteristic
422C22×C61#57611yescharacteristic
423C22×C61#57711yescharacteristic
424C2×D61—24no—
425C2×D61—42no—
426C2×D61—42no—
427C2×D61—42no—
428C2×D61—42no—
429C2×D61—42no—
430C2×D61—42no—
431C2×D61—42no—
432C2×D61—42no—
433C2×D61—42no—
434C2×D61—816no—
435C2×D61—81no—
436C2×D61—81no—
437C2×D61—81no—
438C2×D61—81no—
439C4×C61—22no—
440C4×C61—41no—
441C4×C61—41no—
442C4×C61—41no—
443C4×C61—42no—
444C4×C61—81no—
445C4×C61—81no—
446C4×C61—81no—
447C4×C61C2×#12111yescharacteristic
448C4×C61#53411yescharacteristic
449C4×C61D4211yescharacteristic
450C4×C61#54611yescharacteristic
451Dic61—42no—
452Dic61—42no—
453C2×#546—611no—
454C2×#467—611no—
455C2×#452—611no—
456C2×#450—611no—
457C22×#102—611no—
458#2417D6111yescharacteristic, complemented
459#2042—611no—
460#2033—611no—
461#2015—611no—
462#2000—611no—
463#1877—611no—
464#1872—611no—
465#1869—611no—
466#1862—611no—
467#1788—611no—
468C2×C61—24no—
469C2×C61—81no—
470C2×C61#241011yescharacteristic
471C2×C61C2×#45211yescharacteristic
472C2×C61#301211yescharacteristic
473C2×C61#326611yescharacteristic
474C2×C61#328011yescharacteristic
475C2×C61#329611yescharacteristic
476C2×C61#331411yescharacteristic
477D61—44no—
478D61—82no—
479C22×#41—611no—
480C23×D4—611no—
481C22×Q16—611no—
482C22×SD16—611no—
483C22×SD16—611no—
484C23×C8—611no—
485#546—1224no—
486#546—1224no—
487C2×#124—611no—
488C2×#123—1221no—
489C2×C22⋊Q8—611no—
490C2×C22⋊Q8C2×D6111yescharacteristic
491C2×C22⋊Q8C2×D6111yescharacteristic, complemented
492C2×#121—611no—
493C2×#121—1221no—
494C2×#120—1221no—
495C2×C4×D4—611no—
496C2×C4×D4C2×D6111yescharacteristic
497C22×C4⋊C4C2×D6111yescharacteristic
498C22×C22⋊C4—1221no—
499#467—1224no—
500#452—1224no—
501#450—1224no—
502C2×#107—611no—
503C2×#103—611no—
504C2×#103—611no—
505C2×#103—611no—
506C2×#103—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—1224no—
514C2×C22⋊C8—611no—
515C2×C22⋊C8—611no—
516C2×C22⋊C8—611no—
517#398—21no—
518#396—21no—
519#391C2×D6111yescharacteristic, complemented
520#389C2×D6111yescharacteristic, complemented
521#386—21no—
522#380—21no—
523#380C2×D6111yescharacteristic, complemented
524#340—611no—
525#340—611no—
526#336—611no—
527#336—611no—
528C61#2442611yescharacteristic, complemented, Sylow
529C25—1221no—
530C2×#41—1222no—
531C2×#41—1222no—
532C2×#41—1222no—
533C2×#41—1222no—
534C2×#41—2441no—
535C2×#41—2441no—
536C22×Q8—611no—
537C22×Q8C22×D6111yescharacteristic
538C22×D4—614no—
539C22×D4—611no—
540C22×D4—611no—
541C22×D4—1222no—
542C22×D4—1222no—
543C22×D4—1221no—
544C22×D4—1221no—
545C22×D4—1222no—
546C22×D4—1221no—
547C22×D4—2441no—
548C22×D4—2441no—
549C22×D4C22⋊D6111yescharacteristic
550C23×C4—21no—
551C23×C4—1221no—
552C23×C4—1221no—
553C23×C4C22×D6111yescharacteristic
554C23×C4C22×D6111yescharacteristic
555C2×Q16—1222no—
556C2×Q16—1222no—
557C2×Q16—2441no—
558C2×SD16—1222no—
559C2×SD16—1222no—
560C2×SD16—1222no—
561C2×SD16—1222no—
562C2×SD16—2441no—
563C2×SD16—2441no—
564C22×C8—611no—
565C22×C8—611no—
566C22×C8—611no—
567C22×C8—611no—
568C22×C8—1222no—
569C22×C8—1222no—
570C22×C8—2441no—
571#124—1222no—
572#124—1222no—
573#123—1228no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—41no—
578C22⋊Q8—614no—
579C22⋊Q8—1222no—
580#121—1228no—
581#121—1222no—
582#121—1222no—
583#120—1228no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—1222no—
587C4×D4—1222no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—611no—
595C2×C4⋊C4—1221no—
596C2×C4⋊C4C22⋊D6111yescharacteristic
597C2×C4⋊C4C22×D6111yescharacteristic
598C2×C4⋊C4C22×D6111yescharacteristic
599C2×C4⋊C4C22×D6111yescharacteristic
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—1228no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C22⋊C4—1221no—
607C2×C22⋊C4—1221no—
608C2×C22⋊C4—1221no—
609C2×C22⋊C4C22⋊D6111yescharacteristic
610C2×C22⋊C4C22⋊D6111yescharacteristic
611C2×C42C22×D6111yescharacteristic
612#107—1222no—
613#103—1222no—
614#103—1222no—
615#103—1222no—
616#103—2441no—
617#102—614no—
618#102—1222no—
619#102—1222no—
620#102—1222no—
621#102—1222no—
622#102—1222no—
623C22⋊C8—1222no—
624C22⋊C8—1222no—
625C22⋊C8—2441no—
626#95—21no—
627#95—21no—
628#95—21no—
629#95—21no—
630C24—1221no—
631C24—1224no—
632C24—1221no—
633C24—4881no—
634C24—4881no—
635C24—2442no—
636C24—2442no—
637C24—2442no—
638C24—2442no—
639C24C2×C22⋊D6111yescharacteristic
640C24C2×C22⋊D6111yescharacteristic
641#41—2444no—
642#41—2444no—
643#41—2444no—
644#41—2444no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—612no—
652C2×Q8—1221no—
653C2×Q8—1221no—
654C2×Q8—1221no—
655C2×Q8—1221no—
656C2×Q8—1221no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—612no—
661C2×D4—612no—
662C2×D4—612no—
663C2×D4—612no—
664C2×D4—1228no—
665C2×D4—1224no—
666C2×D4—1224no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—1221no—
674C2×D4—1221no—
675C2×D4—1224no—
676C2×D4—4881no—
677C2×D4—4881no—
678C2×D4—2444no—
679C2×D4—2444no—
680C2×D4—2444no—
681C2×D4—2442no—
682C2×D4—2442no—
683C2×D4—2442no—
684C2×D4—2442no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—81no—
702C22×C4—1224no—
703C22×C4—1224no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—4881no—
707C22×C4—4881no—
708C22×C4—2442no—
709C22×C4—2442no—
710C22×C4D4×D6112yes—
711C22×C4D4×D6112yes—
712C22×C4C2×C22⋊D6111yescharacteristic
713C22×C4C2×C22⋊D6111yescharacteristic
714C22×C4C2×C22⋊D6111yescharacteristic
715C22×C4C2×C22⋊D6111yescharacteristic
716C22×C4C23×D6111yescharacteristic
717Q16—2444no—
718SD16—2444no—
719SD16—2444no—
720C2×C8—612no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—1221no—
724C2×C8—1221no—
725C2×C8—1221no—
726C2×C8—1221no—
727C2×C8—1221no—
728C2×C8—1221no—
729C2×C8—1221no—
730C2×C8—1221no—
731C2×C8—1221no—
732C2×C8—2444no—
733C4⋊C4—21no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4—42no—
742C4⋊C4—81no—
743C4⋊C4—612no—
744C4⋊C4—1221no—
745C4⋊C4—1224no—
746C4⋊C4D4×D6112yes—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—81no—
752C22⋊C4—1224no—
753C22⋊C4—1224no—
754C22⋊C4—1224no—
755C22⋊C4—1224no—
756C22⋊C4—1224no—
757C42—21no—
758C42—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—1222no—
771C23—1222no—
772C23—1222no—
773C23—1222no—
774C23—4884no—
775C23—4884no—
776C23—4884no—
777C23—4884no—
778C23—4884no—
779C23—2448no—
780C23—2441no—
781C23—2441no—
782C23—2441no—
783C23—2441no—
784C23—2441no—
785C23—2441no—
786C23—2448no—
787C23—2441no—
788C23—2441no—
789C23—2441no—
790C23—2441no—
791C23#1451974512yes—
792C23#1451979712yes—
793C23#1451980812yes—
794C23C22×C22⋊D6111yescharacteristic
795Q8—41no—
796Q8—41no—
797Q8—41no—
798Q8—41no—
799Q8—1222no—
800Q8—1222no—
801Q8—2441no—
802Q8—2441no—
803D4—44no—
804D4—614no—
805D4—1222no—
806D4—1222no—
807D4—1222no—
808D4—1222no—
809D4—1222no—
810D4—4884no—
811D4—2448no—
812D4—2448no—
813D4—2441no—
814D4—2441no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—84no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—4884no—
850C2×C4—2448no—
851C2×C4—2441no—
852C2×C4—2441no—
853C2×C4—2441no—
854C2×C4—2441no—
855C2×C4#1451974512yes—
856C2×C4C2×D4×D6111yescharacteristic
857C2×C4C2×D4×D6111yescharacteristic
858C2×C4C2×D4×D6111yescharacteristic
859C2×C4#41×D6111yescharacteristic
860C2×C4#1451982211yescharacteristic
861C2×C4#1451982311yescharacteristic
862C8—1222no—
863C8—2441no—
864C8—2441no—
865C8—2441no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—1224no—
880C22—48816no—
881C22—4881no—
882C22—4881no—
883C22—4881no—
884C22—4881no—
885C22—2442no—
886C22—2442no—
887C22—2442no—
888C22—2442no—
889C22—2442no—
890C22—2442no—
891C22—2442no—
892C22—2442no—
893C22—2442no—
894C22#1683992214yescomplemented
895C22C2×#1451974511yescharacteristic
896C22D4×C22⋊D6111yescharacteristic
897C22#1684040011yescharacteristic
898C22C2×#1451979711yescharacteristic
899C22C2×#1451980811yescharacteristic
900C22#1684056511yescharacteristic
901C22#1684057011yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—81no—
908C4—81no—
909C4—81no—
910C4—2442no—
911C4—2442no—
912C4#121×D6111yescharacteristic
913C4#1684032011yescharacteristic
914C4#1684039611yescharacteristic
915C4#1684040111yescharacteristic
916C2—24no—
917C2—81no—
918C2—4882no—
919C2—2444no—
920C2#2144919011yescharacteristic
921C2C2×#1683992211yescharacteristic
922C2#2145512011yescharacteristic
923C2#2145733011yescharacteristic
924C2#2145750011yescharacteristic
925C2#2145764811yescharacteristic
926C2#2145789411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2417C2
socleC23×C61C22×D4
prime radicalC2×#16840408C2
hypercenter#2417D61
hypocenterC61#24426
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2417

Complements

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

NH ≅ G/Ntype
2. C2×#16840001C2semidirect
3. C2×#16839922C2semidirect
4. C2×#16839912C2semidirect
5. C22×#14519697C2semidirect
6. #21447060C2semidirect
7. #21447001C2semidirect
8. #21446912C2semidirect
9. #21446820C2semidirect
10. #21446156C2semidirect
11. #21446126C2semidirect
12. #21446112C2semidirect
13. #21446065C2semidirect
14. #21445757C2semidirect
15. C61×#2417C2semidirect
18. C22×#11758202C22semidirect
35. C2×#14519710C22semidirect
36. C2×#14519701C22semidirect
37. C2×#14519700C22semidirect
38. C2×#14519700C22semidirect
39. C2×#14519700C22semidirect
48. C2×C22⋊#92418C22semidirect
49. C2×C22⋊#92418C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839517C22semidirect
53. #16839517C22semidirect
55. C2×C22⋊Q8×C61C22semidirect
60. C61×#391C22semidirect
61. C61×#389C22semidirect
64. C61×#380C22semidirect
131. #14519697D4semidirect
416. C22×C61#452semidirect
458. #2417D61semidirect
491. C2×C22⋊Q8C2×D61semidirect
519. #391C2×D61semidirect
520. #389C2×D61semidirect
523. #380C2×D61semidirect
528. C61#24426semidirect
894. C22#16839922semidirect

Maximal subgroups

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

subgroupindex
C2×#168404082
C2×#168400012
C2×#168399222
C2×#168399122
C22×#145196972
#214470602
#214470012
#214469122
#214468202
#214461562
#214461262
#214461122
#214460652
#214457572
C61×#24172
#2442661