Finite Group Databasebeta

← #29689140

Subgroups — #29689140

Order 15616.

1622 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840269C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#21446259C214yesmaximal, complemented
5#21446118C214yesmaximal, complemented
6#21445919C211yesmaximal, characteristic, complemented
7#21445916C211yesmaximal, characteristic, complemented
8#21445763C211yesmaximal, characteristic, complemented
9C61×#1789C211yesmaximal, characteristic, complemented
10C23×C4×D61C2211yescharacteristic
11C2×M16×D61C2212yescomplemented
12#16840269—21no—
13#16840269—21no—
14#16840269—21no—
15#16840269—21no—
16#16840269C412yescomplemented
17#16840269C412yescomplemented
18#16840269C2212yes—
19#16840269C2212yes—
20C2×#14519758—21no—
21C2×#14519753C411yescharacteristic, complemented
22C2×#14519753C411yescharacteristic, complemented
23C2×#14519748C411yescharacteristic, complemented
24C2×#14519748C411yescharacteristic, complemented
25C2×#14519745—21no—
26C2×C4×C22⋊D61—21no—
27C2×C4×C22⋊D61—21no—
28C2×#14519736C2211yescharacteristic
29C2×C22⋊C4×D61—21no—
30C2×C42×D61C2212yescomplemented
31C2×#14519704C2214yescomplemented
32#16839726C2211yescharacteristic
33#16839725C2212yescomplemented
34#16839724—21no—
35#16839724—21no—
36C22⋊C8×D61—21no—
37C22⋊C8×D61—21no—
38C22⋊C4×Dic61—21no—
39C4×#11758198C2212yescomplemented
40C4×C22⋊Dic61C2211yescharacteristic
41#16839609—21no—
42#95×D61—21no—
43#16839523C2214yescomplemented
44#16839522C2214yescomplemented
45C22×#41×C61C2211yescharacteristic
46C2×#104×C61C2214yescomplemented
47C61×#407C2211yescharacteristic
48C4×C22⋊C4×C61C2211yescharacteristic
49C24×D61D411yescharacteristic
50C22×C22⋊D61—21no—
51C22×C22⋊D61—21no—
52C23×Dic61D411yescharacteristic
53C22×C4×D61—22no—
54C22×C4×D61—44no—
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×#11758194C2312yes—
68C2×#11758189—22no—
69M16×D61—44no—
70C2×C8×D61—22no—
71#14519758—22no—
72#14519758—22no—
73#14519758—22no—
74#14519758—22no—
75#14519753—21no—
76#14519753—21no—
77#14519753—21no—
78#14519753—21no—
79#14519753C2×C412yes—
80#14519753C2×C412yes—
81#14519753C2×C412yescomplemented
82#14519753C2×C412yescomplemented
83#14519748—21no—
84#14519748—21no—
85#14519748—21no—
86#14519748—21no—
87#14519748C2×C412yes—
88#14519748C2×C412yes—
89#14519748C2×C412yescomplemented
90#14519748C2×C412yescomplemented
91#14519745—22no—
92#14519745—22no—
93#14519745—22no—
94#14519745—22no—
95C4×C22⋊D61—22no—
96C4×C22⋊D61—22no—
97C4×C22⋊D61—22no—
98C4×C22⋊D61—22no—
99C4×C22⋊D61—22no—
100C4×C22⋊D61—22no—
101C4×C22⋊D61—22no—
102C4×C22⋊D61—22no—
103#14519736—21no—
104#14519736—21no—
105#14519736C2×C412yescomplemented
106#14519736C2312yes—
107C2×C4⋊Dic61C2×C411yescharacteristic, complemented
108C2×C4⋊Dic61C2×C411yescharacteristic, complemented
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—22no—
118C22⋊C4×D61—28no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—22no—
121C2×C4×Dic61C2312yes—
122C42×D61—44no—
123#14519704—44no—
124C22⋊#92418—21no—
125C22⋊#92418—21no—
126#14519689—22no—
127#14519689—22no—
128#14519684—21no—
129#14519684—22no—
130C2×#41×C61—21no—
131C2×#41×C61—21no—
132C2×#41×C61—44no—
133C2×#41×C61C2×C412yescomplemented
134C2×#41×C61C2312yes—
135C22×Q8×C61C2×C411yescharacteristic, complemented
136C22×D4×C61—21no—
137C22×D4×C61C2×C411yescharacteristic, complemented
138C23×C4×C61—21no—
139C23×C4×C61C2311yescharacteristic
140C2×M16×C61C2312yes—
141C2×C22⋊C4×C61—21no—
142C2×C42×C61C2312yes—
143#104×C61—44no—
144C22⋊C8×C61—21no—
145C22⋊C8×C61—21no—
146#95×C61—21no—
147C24×C61—21no—
148C24×C61C2×D411yescharacteristic
149C23×D61—24no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61C22⋊C411yescharacteristic
153C23×D61C22⋊C411yescharacteristic
154C23×D61C22⋊C411yescharacteristic
155C23×D61C22⋊C411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C23×D61C2×D411yescharacteristic
158#41×C61—24no—
159#41×C61—24no—
160#41×C61—42no—
161#41×C61—42no—
162#41×C61—44no—
163#41×C61—44no—
164C2×Q8×C61—21no—
165C2×Q8×C61—42no—
166C2×Q8×C61C22×C412yes—
167C2×D4×C61—22no—
168C2×D4×C61—22no—
169C2×D4×C61—21no—
170C2×D4×C61—42no—
171C2×D4×C61—44no—
172C2×D4×C61C22×C412yes—
173C22×C4×C61—24no—
174C22×C4×C61—21no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—44no—
179C22×C4×C61C22×C411yescharacteristic
180C22×C4×C61C22×C411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2411yescharacteristic
185C2×C22⋊D61—22no—
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—44no—
190C2×C22⋊D61—44no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—22no—
194C22×Dic61—42no—
195C22×Dic61C22⋊C411yescharacteristic
196C22×Dic61C22⋊C411yescharacteristic
197C22×Dic61C22⋊C411yescharacteristic
198C22×Dic61C22⋊C411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201C2×C4×D61—24no—
202C2×C4×D61—24no—
203C2×C4×D61—28no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61—42no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61—44no—
215C2×C4×D61—44no—
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22⋊C411yescharacteristic
220C2×C4×D61C22⋊C411yescharacteristic
221C2×C4×D61C22⋊C411yescharacteristic
222C2×C4×D61C22⋊C411yescharacteristic
223C2×C4×D61C22⋊C411yescharacteristic
224C2×C4×D61C22×C411yescharacteristic
225C2×C4×D61C22×C411yescharacteristic
226C2×C4×D61C22×C411yescharacteristic
227C2×C4×D61C22×C411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232M16×C61—24no—
233C2×C8×C61—22no—
234C22⋊C4×C61—24no—
235C42×C61—24no—
236C22⋊Dic61—24no—
237C22⋊Dic61—22no—
238C22⋊Dic61—22no—
239C22⋊Dic61—22no—
240C22⋊Dic61—22no—
241C22⋊Dic61—22no—
242C22⋊Dic61—22no—
243#11758198—28no—
244#11758198—22no—
245#11758198—22no—
246#11758198—22no—
247#11758198—22no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61C22×C412yes—
251C4⋊Dic61C22×C412yes—
252#11758196—22no—
253#11758196—22no—
254#11758196—22no—
255#11758196—22no—
256C4×Dic61—22no—
257C4×Dic61—22no—
258C4×Dic61—24no—
259C4×Dic61—44no—
260#11758194—24no—
261C2×#92418—22no—
262#11758189—44no—
263C8×D61—44no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—41no—
268C23×C61—42no—
269C23×C61—42no—
270C23×C61—42no—
271C23×C61C2×C22⋊C411yescharacteristic
272C23×C61C2×C22⋊C411yescharacteristic
273C23×C61C22×D411yescharacteristic
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—416no—
292C22×D61#10414yescomplemented
293C22×D61C2×C22⋊C411yescharacteristic
294C22×D61C2×C22⋊C411yescharacteristic
295C22×D61C2×C22⋊C411yescharacteristic
296C22×D61C2×C22⋊C411yescharacteristic
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—42no—
300D4×C61—22no—
301D4×C61—22no—
302D4×C61—42no—
303D4×C61—44no—
304D4×C61—44no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—24no—
311C2×C4×C61—22no—
312C2×C4×C61—44no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—44no—
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C23×C411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61H(5,𝔽2)14yes—
322C22⋊D61—44no—
323C22⋊D61—44no—
324C22⋊D61—44no—
325C22⋊D61—44no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—24no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—416no—
360C8×C61—42no—
361#92418—42no—
362#21773—611nomaximal, Sylow
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—44no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—84no—
375C22×C61C2×#10412yes—
376C22×C61C22×C22⋊C411yescharacteristic
377C22×C61#53412yes—
378C2×D61—28no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—44no—
389C2×D61—44no—
390C2×D61—44no—
391C2×D61—44no—
392C2×D61—44no—
393C2×D61C2×#10412yes—
394C2×D61C2×#10412yes—
395C2×D61#42112yes—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—44no—
399C4×C61—42no—
400C4×C61#51812yes—
401C4×C61#53412yes—
402Dic61—21no—
403Dic61—21no—
404Dic61—21no—
405Dic61—21no—
406Dic61—44no—
407Dic61—42no—
408Dic61—42no—
409C2×#525—611no—
410C2×#407—611no—
411C2×C4×C22⋊C4—611no—
412#1896—614no—
413#1871—614no—
414#1826—611no—
415#1826—611no—
416#1789—611no—
417#1789D6111yescharacteristic, complemented
418C2×C61—22no—
419C2×C61—22no—
420C2×C61—41no—
421C2×C61—82no—
422C2×C61#230811yescharacteristic
423C2×C61C22×#10411yescharacteristic
424C2×C61C2×#42111yescharacteristic
425D61—22no—
426D61—22no—
427D61—22no—
428D61—41no—
429C22×#41C2×D6111yescharacteristic
430C24×C4—611no—
431C22×M16—612no—
432#525—612no—
433#525—612no—
434#525—612no—
435#525—612no—
436#525—1221no—
437#525—1221no—
438#525—1221no—
439#525—1221no—
440C2×#123—1221no—
441C2×C22⋊Q8—611no—
442C2×C22⋊Q8—611no—
443C2×#121—611no—
444C2×#121—611no—
445C2×#120—1221no—
446C2×C4×D4—1221no—
447C2×C4×D4—1221no—
448C2×#117—611no—
449C22×C22⋊C4—1221no—
450C22×C42—612no—
451C2×#104—614no—
452C2×#104C2×D6114yescomplemented
453#407—611no—
454#407—612no—
455#407—1221no—
456#407—1221no—
457#407C2×D6111yescharacteristic
458C2×C22⋊C8—1221no—
459C2×C22⋊C8—1221no—
460C4×C22⋊C4—611no—
461C4×C22⋊C4—612no—
462C4×C22⋊C4—1221no—
463C4×C22⋊C4—1221no—
464C4×C22⋊C4C2×D6111yescharacteristic
465C2×#95—1221no—
466#339—614no—
467#339—614no—
468C61#2177311yescharacteristic, complemented, Sylow
469C25—611no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—44no—
473C2×#41C4×D6112yescomplemented
474C2×#41C22×D6112yes—
475C22×Q8C4×D6111yescharacteristic, complemented
476C22×D4—21no—
477C22×D4—1221no—
478C22×D4—1221no—
479C22×D4C4×D6111yescharacteristic, complemented
480C23×C4—21no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—1222no—
495C23×C4—2444no—
496C23×C4C22×D6111yescharacteristic
497C2×M16—612no—
498C2×M16—1222no—
499C2×M16—2444no—
500C2×M16C22×D6112yes—
501C22×C8—1222no—
502#123—1222no—
503#123—1222no—
504#123—1222no—
505#123—1222no—
506C22⋊Q8—612no—
507C22⋊Q8—612no—
508C22⋊Q8—612no—
509C22⋊Q8—612no—
510C22⋊Q8—1221no—
511C22⋊Q8—1221no—
512C22⋊Q8—1221no—
513C22⋊Q8—1221no—
514#121—612no—
515#121—612no—
516#121—612no—
517#121—612no—
518#121—1221no—
519#121—1221no—
520#121—1221no—
521#121—1221no—
522#120—1222no—
523#120—1222no—
524#120—1222no—
525#120—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1222no—
530C4×D4—1222no—
531C4×D4—1222no—
532C4×D4—1222no—
533C4×D4—1222no—
534#117—612no—
535#117—612no—
536#117—1221no—
537#117—1221no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—1228no—
544C2×C22⋊C4—1222no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C42—612no—
552C2×C42—1221no—
553C2×C42—1222no—
554C2×C42—2444no—
555C2×C42C22×D6112yes—
556#104—44no—
557#104—2444no—
558C22⋊C8—21no—
559C22⋊C8—21no—
560C22⋊C8—1222no—
561C22⋊C8—1222no—
562C22⋊C8—1221no—
563C22⋊C8—1221no—
564#95—21no—
565#95—1222no—
566#95—1221no—
567C24—21no—
568C24—611no—
569C24—611no—
570C24—611no—
571C24—611no—
572C24—611no—
573C24—611no—
574C24—1224no—
575C24—2442no—
576C24—2442no—
577C24D4×D6111yescharacteristic
578#41—24no—
579#41—24no—
580#41—42no—
581#41—42no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—42no—
586C2×Q8C2×C4×D6112yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—42no—
591C2×D4—44no—
592C2×D4—1222no—
593C2×D4—1222no—
594C2×D4—1222no—
595C2×D4—1222no—
596C2×D4—2444no—
597C2×D4—2444no—
598C2×D4C2×C4×D6112yes—
599C22×C4—24no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—44no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—1228no—
628C22×C4—1224no—
629C22×C4—1224no—
630C22×C4—1222no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—2442no—
634C22×C4—2442no—
635C22×C4—2442no—
636C22×C4—2442no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4—2442no—
642C22×C4—2442no—
643C22×C4—2444no—
644C22×C4—2444no—
645C22×C4—2442no—
646C22×C4C2×C4×D6111yescharacteristic
647C22×C4C2×C4×D6111yescharacteristic
648C22×C4D4×D6111yescharacteristic
649C22×C4D4×D6111yescharacteristic
650C22×C4D4×D6111yescharacteristic
651C22×C4C23×D6111yescharacteristic
652M16—24no—
653M16—1224no—
654M16—2444no—
655C2×C8—22no—
656C2×C8—1222no—
657C2×C8—2444no—
658C4⋊C4—612no—
659C4⋊C4—612no—
660C4⋊C4—1222no—
661C4⋊C4—1222no—
662C4⋊C4—1222no—
663C4⋊C4—1222no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C22⋊C4—24no—
667C22⋊C4—1222no—
668C22⋊C4—1222no—
669C22⋊C4—1222no—
670C22⋊C4—1222no—
671C22⋊C4—1228no—
672C22⋊C4—1222no—
673C22⋊C4—1222no—
674C22⋊C4—1222no—
675C22⋊C4—1222no—
676C22⋊C4—1224no—
677C22⋊C4—1222no—
678C22⋊C4—1222no—
679C42—24no—
680C42—1222no—
681C42—1222no—
682C42—1224no—
683C42—2444no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—611no—
692C23—611no—
693C23—611no—
694C23—614no—
695C23—611no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—1222no—
701C23—1222no—
702C23—1222no—
703C23—1222no—
704C23—1222no—
705C23—1222no—
706C23—2441no—
707C23—2441no—
708C23—2441no—
709C23—2441no—
710C23—2441no—
711C23—2441no—
712C23—2441no—
713C23—24416no—
714C23C22⋊C4×D6111yescharacteristic
715C23C22⋊C4×D6111yescharacteristic
716C23C2×D4×D6111yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—42no—
720D4—22no—
721D4—22no—
722D4—42no—
723D4—44no—
724D4—44no—
725D4—2444no—
726D4—2444no—
727D4—2444no—
728D4—2444no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—611no—
742C2×C4—611no—
743C2×C4—611no—
744C2×C4—611no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1224no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—24416no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4—2442no—
774C2×C4—2442no—
775C2×C4C22⋊C4×D6111yescharacteristic
776C2×C4C22⋊C4×D6111yescharacteristic
777C2×C4C22×C4×D6111yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C2×C4#1451982214yes—
780C8—42no—
781C8—2442no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—44no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—84no—
794C22—612no—
795C22—612no—
796C22—612no—
797C22—1228no—
798C22—1221no—
799C22—1221no—
800C22—1221no—
801C22—1221no—
802C22—1221no—
803C22—1221no—
804C22—1221no—
805C22—1221no—
806C22—1221no—
807C22—2444no—
808C22—2444no—
809C22—2444no—
810C22—2444no—
811C22—2444no—
812C22#104×D6112yes—
813C22C2×C22⋊C4×D6111yescharacteristic
814C22#1684032212yes—
815C4—21no—
816C4—21no—
817C4—44no—
818C4—42no—
819C4—1221no—
820C4—1221no—
821C4—1221no—
822C4—1221no—
823C4—2444no—
824C4—2442no—
825C4—2442no—
826C4#1684023512yes—
827C4#1684032212yes—
828C2—22no—
829C2—22no—
830C2—41no—
831C2—82no—
832C2—1222no—
833C2—1222no—
834C2—1222no—
835C2—2441no—
836C2#2144839511yescharacteristic
837C2C2×#104×D6111yescharacteristic
838C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1789C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840269C2
cosocleC22×C4×C61C24
hypercenter#1789D61
hypocenterC61#21773
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. C4×C22⋊C4×D61C2semidirect
4. #21446259C2semidirect
5. #21446118C2semidirect
6. #21445919C2semidirect
7. #21445916C2semidirect
8. #21445763C2semidirect
9. C61×#1789C2semidirect
11. C2×M16×D61C22semidirect
16. #16840269C4semidirect
17. #16840269C4semidirect
21. C2×#14519753C4semidirect
22. C2×#14519753C4semidirect
23. C2×#14519748C4semidirect
24. C2×#14519748C4semidirect
30. C2×C42×D61C22semidirect
31. C2×#14519704C22semidirect
33. #16839725C22semidirect
39. C4×#11758198C22semidirect
43. #16839523C22semidirect
44. #16839522C22semidirect
46. C2×#104×C61C22semidirect
81. #14519753C2×C4semidirect
82. #14519753C2×C4semidirect
89. #14519748C2×C4semidirect
90. #14519748C2×C4semidirect
105. #14519736C2×C4semidirect
107. C2×C4⋊Dic61C2×C4semidirect
108. C2×C4⋊Dic61C2×C4semidirect
133. C2×#41×C61C2×C4semidirect
135. C22×Q8×C61C2×C4semidirect
137. C22×D4×C61C2×C4semidirect
292. C22×D61#104semidirect
417. #1789D61semidirect
452. C2×#104C2×D61semidirect
468. C61#21773semidirect
473. C2×#41C4×D61semidirect
475. C22×Q8C4×D61semidirect
479. C22×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402692
#407×D612
C4×C22⋊C4×D612
#214462592
#214461182
#214459192
#214459162
#214457632
C61×#17892
#2177361