Finite Group Databasebeta

← #29695347

Subgroups — #29695347

Order 15616.

1668 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840400C211yesmaximal, characteristic
2C2×#99×D61C211yesmaximal, characteristic, complemented
3#21448669C212yesmaximal, complemented
4#21446653C212yesmaximal, complemented
5#21446277C212yesmaximal, complemented
6#21446269C212yesmaximal, complemented
7#21445805C211yesmaximal, characteristic, complemented
8#21445737C211yesmaximal, characteristic, complemented
9#21445732C211yesmaximal, characteristic, complemented
10#99×Dic61C211yesmaximal, characteristic, complemented
11C2×C61×#410C211yesmaximal, characteristic, complemented
12C22×D4×D61C2211yescharacteristic
13#16840400—22no—
14#16840400—22no—
15#16840400—22no—
16#16840400—22no—
17C2×#14519766C411yescharacteristic, complemented
18C2×#14519760C411yescharacteristic, complemented
19C2×#14519760C2211yescharacteristic
20C2×#14519753C411yescharacteristic, complemented
21C2×#14519751C411yescharacteristic, complemented
22C2×#14519749C411yescharacteristic, complemented
23C2×#14519749C2211yescharacteristic
24C2×#14519745C411yescharacteristic, complemented
25C2×#14519745C2211yescharacteristic
26C2×D4×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61C411yescharacteristic, complemented
28C22×#11758198C411yescharacteristic, complemented
29C22×#11758198C2211yescharacteristic
30C2×C22⋊C4×D61C2212yes—
31C2×#14519692C2211yescharacteristic
32C2×#14519692C2211yescharacteristic
33C2×#14519692C2212yescomplemented
34C2×#14519691C2212yes—
35C2×#14519691C2212yes—
36#99×D61—24no—
37#16839653—22no—
38#16839652—22no—
39#16839633—22no—
40#16839625C2212yescomplemented
41#16839620C2212yescomplemented
42#16839617C2212yes—
43C22⋊C4×Dic61C2212yescomplemented
44C4×#11758198—22no—
45#16839528C2212yescomplemented
46#16839528C2212yescomplemented
47C22×#41×C61C2211yescharacteristic
48C2×#117×C61C2212yescomplemented
49C61×#410—24no—
50C2×#99×C61C2211yescharacteristic
51C2×#99×C61C2211yescharacteristic
52C2×#99×C61C2212yescomplemented
53C24×D61C2×C411yescharacteristic
54C24×D61C2311yescharacteristic
55C22×D244C2×C411yescharacteristic
56C22×C22⋊D61C2×C411yescharacteristic
57C22×C22⋊D61C2×C411yescharacteristic
58C22×C22⋊D61C2×C411yescharacteristic
59C22×C22⋊D61C2×C411yescharacteristic, complemented
60C22×C22⋊D61C2311yescharacteristic
61C2×D4×D61—22no—
62C2×D4×D61—22no—
63C2×D4×D61—22no—
64C2×D4×D61—22no—
65C2×D4×D61—42no—
66C23×Dic61C2×C411yescharacteristic, complemented
67C23×Dic61C2311yescharacteristic
68C22×C4×D61—22no—
69C22×C4×D61C2×C411yescharacteristic
70#14519766—22no—
71#14519766—22no—
72#14519760—22no—
73#14519760—22no—
74#14519760—22no—
75#14519760—22no—
76#14519753—22no—
77#14519753—22no—
78#14519751—22no—
79#14519751—22no—
80#14519749—22no—
81#14519749—22no—
82#14519749—22no—
83#14519749—22no—
84#14519745—22no—
85#14519745—22no—
86#14519745—22no—
87#14519745—22no—
88D4×Dic61—22no—
89D4×Dic61—22no—
90C4×C22⋊D61—21no—
91C4×C22⋊D61—21no—
92C4×C22⋊D61—21no—
93C4×C22⋊D61—21no—
94C2×C4⋊Dic61C2×C411yescharacteristic, complemented
95C2×#11758196—22no—
96C2×#11758196C2×C411yescharacteristic, complemented
97C2×#11758196C2×C411yescharacteristic, complemented
98C2×#11758196C2×C411yescharacteristic, complemented
99C2×C22⋊Dic61C2×C411yescharacteristic, complemented
100C2×C22⋊Dic61C2×C411yescharacteristic, complemented
101C2×C22⋊Dic61C2312yes—
102C2×C22⋊Dic61C2312yes—
103C2×C22⋊Dic61C2311yescharacteristic
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic, complemented
118C2×#11758198C2×C411yescharacteristic, complemented
119C2×#11758198C2×C411yescharacteristic, complemented
120C2×#11758198D412yes—
121C2×#11758198D412yes—
122C2×#11758198D412yes—
123C2×#11758198D412yes—
124C22⋊C4×D61—24no—
125C22⋊C4×D61—42no—
126C2×C4×Dic61—22no—
127C2×C4×Dic61C2×C411yescharacteristic, complemented
128#14519692—22no—
129#14519692—22no—
130#14519692—42no—
131#14519691—24no—
132#14519691—42no—
133#14519684—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137C2×#41×C61—22no—
138C2×#41×C61—22no—
139C2×#41×C61—22no—
140C2×#41×C61—22no—
141C2×#41×C61—42no—
142C22×Q8×C61C2×C411yescharacteristic, complemented
143C22×D4×C61C2×C411yescharacteristic, complemented
144C22×D4×C61C2311yescharacteristic
145C22×D4×C61C2311yescharacteristic
146C23×C4×C61C2×C411yescharacteristic, complemented
147C23×C4×C61C2×C411yescharacteristic, complemented
148C23×C4×C61C2311yescharacteristic
149#117×C61—24no—
150#117×C61—42no—
151C2×C4⋊C4×C61—22no—
152C2×C22⋊C4×C61C2312yes—
153C2×C22⋊C4×C61C2312yes—
154C2×C42×C61—22no—
155#99×C61—22no—
156#99×C61—24no—
157#99×C61D414yescomplemented
158C24×C61C22×C411yescharacteristic
159C24×C61C22×C411yescharacteristic
160C24×C61C2411yescharacteristic
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—42no—
168C23×D61—41no—
169C23×D61—42no—
170C23×D61—81no—
171C23×D61—81no—
172C23×D61C22×C411yescharacteristic
173C23×D61C22×C411yescharacteristic
174C23×D61C22×C411yescharacteristic
175C23×D61C2×D412yes—
176C23×D61C2×D412yes—
177#41×C61—44no—
178#41×C61—44no—
179#41×C61—44no—
180#41×C61—44no—
181C2×Q8×C61—22no—
182C2×Q8×C61—22no—
183C2×Q8×C61—41no—
184C2×D4×C61—22no—
185C2×D4×C61—22no—
186C2×D4×C61—22no—
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61—21no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—41no—
193C2×D4×C61C2×D412yes—
194C2×D4×C61#4112yes—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—41no—
207C22×C4×C61—41no—
208C22×C4×C61C22×C411yescharacteristic
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C2×D412yes—
213C22×C4×C61C2×D412yes—
214C2×C22⋊D61—22no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—22no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—22no—
219C2×C22⋊D61—22no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—22no—
223C2×C22⋊D61—22no—
224C2×C22⋊D61—41no—
225C2×C22⋊D61—42no—
226C2×C22⋊D61—81no—
227C2×C22⋊D61—81no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—22no—
231C22×Dic61—22no—
232C22×Dic61—81no—
233C22×Dic61—81no—
234C22×Dic61C22×C411yescharacteristic
235C22×Dic61C22×C411yescharacteristic
236C22×Dic61C22×C411yescharacteristic
237C22×Dic61C22×C411yescharacteristic
238C22×Dic61C22×C411yescharacteristic
239C22×Dic61C2×D412yes—
240C22×Dic61C2×D412yes—
241D4×D61—44no—
242D4×D61—44no—
243D4×D61—44no—
244D4×D61—44no—
245C2×D244—22no—
246C2×D244—22no—
247C2×D244—41no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—22no—
251C2×C4×D61—41no—
252C2×C4×D61—44no—
253C2×C4×D61—44no—
254C2×C4×D61—82no—
255C4⋊C4×C61—44no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—22no—
259C22⋊C4×C61C2×D414yes—
260C42×C61—44no—
261C22⋊Dic61—22no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—22no—
265C22⋊Dic61—22no—
266C22⋊Dic61—22no—
267C22⋊Dic61—22no—
268C22⋊Dic61—22no—
269#11758198—21no—
270#11758198—21no—
271#11758198—22no—
272#11758198—21no—
273#11758198—21no—
274#11758198—22no—
275#11758198—21no—
276#11758198—21no—
277#11758198—44no—
278#11758198—44no—
279#11758198—82no—
280#11758198C22⋊C411yescharacteristic
281#11758198C22⋊C411yescharacteristic
282#11758198C22⋊C411yescharacteristic
283#11758198C22⋊C411yescharacteristic
284#11758198C22⋊C412yes—
285#11758198C22⋊C412yes—
286#11758198C22⋊C412yes—
287#11758198C22⋊C412yes—
288#11758198C22⋊C412yes—
289#11758198C22⋊C412yes—
290C4⋊Dic61—22no—
291#11758196—21no—
292#11758196—21no—
293#11758196—22no—
294#11758196—22no—
295#11758196—82no—
296C4×Dic61—21no—
297C4×Dic61—21no—
298C4×Dic61—82no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61C4×D412yes—
311C23×C61C23×C411yescharacteristic
312C23×C61C22×D412yes—
313C23×C61C22×D411yescharacteristic
314C23×C61C2×#4111yescharacteristic
315C23×C61H(5,𝔽2)12yes—
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—24no—
325C22×D61—22no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—42no—
330C22×D61—41no—
331C22×D61—42no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—41no—
340C22×D61—41no—
341C22×D61—81no—
342C22×D61—81no—
343C22×D61—82no—
344C22×D61—84no—
345C22×D61—82no—
346C22×D61—84no—
347C22×D61—84no—
348C22×D61C2×C22⋊C411yescharacteristic
349C22×D61C2×C22⋊C412yes—
350C22×D61C2×C22⋊C411yescharacteristic
351Q8×C61—44no—
352D4×C61—24no—
353D4×C61—24no—
354D4×C61—44no—
355D4×C61—42no—
356D4×C61—42no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—24no—
371C2×C4×C61—42no—
372C2×C4×C61—42no—
373C2×C4×C61—42no—
374C2×C4×C61—42no—
375C2×C4×C61—42no—
376C2×C4×C61—42no—
377C2×C4×C61—42no—
378C2×C4×C61—42no—
379C2×C4×C61—42no—
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C2×C22⋊C412yes—
383C2×C4×C61C4×D412yes—
384C22⋊D61—44no—
385C22⋊D61—42no—
386C22⋊D61—42no—
387C22⋊D61—42no—
388C22⋊D61—42no—
389C22⋊D61—82no—
390C22⋊D61—82no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—42no—
397C2×Dic61—42no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—42no—
403C2×Dic61—42no—
404C2×Dic61—42no—
405C2×Dic61—42no—
406C2×Dic61—42no—
407C2×Dic61—42no—
408C2×Dic61—81no—
409C2×Dic61—81no—
410C2×Dic61C2×C22⋊C411yescharacteristic
411C2×Dic61C2×C22⋊C411yescharacteristic
412C2×Dic61C2×C22⋊C412yes—
413D244—44no—
414C4×D61—42no—
415C4×D61—42no—
416C4×D61—88no—
417#22405—611nomaximal, Sylow
418C22×C61—22no—
419C22×C61—21no—
420C22×C61—22no—
421C22×C61—21no—
422C22×C61—22no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—81no—
434C22×C61—81no—
435C22×C61C22×C22⋊C411yescharacteristic
436C22×C61C2×C4×D411yescharacteristic
437C22×C61#51811yescharacteristic
438C22×C61D4212yes—
439C22×C61#54612yes—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—22no—
444C2×D61—21no—
445C2×D61—22no—
446C2×D61—22no—
447C2×D61—21no—
448C2×D61—44no—
449C2×D61—44no—
450C2×D61—42no—
451C2×D61—42no—
452C2×D61—41no—
453C2×D61—41no—
454C2×D61—41no—
455C2×D61—84no—
456C2×D61—81no—
457C2×D61—81no—
458C2×D61—82no—
459C2×D61—82no—
460C2×D61—84no—
461C2×D61—81no—
462C2×D61—81no—
463C2×D61#41012yescomplemented
464C4×C61—22no—
465C4×C61—21no—
466C4×C61—21no—
467C4×C61—22no—
468C4×C61—44no—
469C4×C61—41no—
470C4×C61—82no—
471Dic61—21no—
472Dic61—21no—
473Dic61—22no—
474Dic61—41no—
475Dic61—41no—
476Dic61—41no—
477Dic61—82no—
478Dic61—82no—
479C2×#546—611no—
480C2×#410D6111yescharacteristic, complemented
481C22×#99—611no—
482#2342—612no—
483#1964—612no—
484#1899—612no—
485#1898—612no—
486#1799—611no—
487#1782—611no—
488#1781—611no—
489C4×#99—611no—
490C2×C61—22no—
491C2×C61—22no—
492C2×C61—21no—
493C2×C61—21no—
494C2×C61—42no—
495C2×C61—81no—
496C2×C61D4×C22⋊C411yescharacteristic
497C2×C61C2×#41011yescharacteristic
498C2×C61#288311yescharacteristic
499D61—22no—
500D61—42no—
501D61—41no—
502D61—81no—
503C22×#41C2×D6111yescharacteristic
504C23×D4—611no—
505#546—1222no—
506#546—1222no—
507#546—1222no—
508#546—1222no—
509C2×#124—611no—
510C2×#123—611no—
511C2×#123—611no—
512C2×C22⋊Q8—611no—
513C2×#121—611no—
514C2×#121—611no—
515C2×#121—611no—
516C2×#120—611no—
517C2×#120—611no—
518C2×C4×D4—611no—
519C2×C4×D4—611no—
520C2×#117C2×D6112yescomplemented
521C22×C22⋊C4—611no—
522C22×C22⋊C4—611no—
523C22×C22⋊C4—612no—
524#410—24no—
525C2×#99—611no—
526C2×#99—611no—
527C2×#99—612no—
528C2×#99—612no—
529C2×#99—612no—
530C2×#99—1224no—
531C2×#99C2×D6111yescharacteristic
532C2×#99C2×D6111yescharacteristic
533C2×#99C2×D6112yescomplemented
534#388—1222no—
535#388—1222no—
536#385—1222no—
537#381—612no—
538#380—612no—
539#379—612no—
540C4×C22⋊C4—612no—
541C4×C22⋊C4—1222no—
542#342—612no—
543#342—612no—
544C61#2240511yescharacteristic, complemented, Sylow
545C25—611no—
546C25—611no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—42no—
552C22×Q8C4×D6111yescharacteristic, complemented
553C22×D4—611no—
554C22×D4—611no—
555C22×D4—611no—
556C22×D4—611no—
557C22×D4—611no—
558C22×D4—611no—
559C22×D4—1222no—
560C22×D4—1222no—
561C22×D4—1222no—
562C22×D4—1222no—
563C22×D4—2442no—
564C22×D4C4×D6111yescharacteristic, complemented
565C22×D4C22×D6111yescharacteristic
566C22×D4C22×D6111yescharacteristic
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—1222no—
571C23×C4C4×D6111yescharacteristic, complemented
572C23×C4C4×D6111yescharacteristic, complemented
573C23×C4C22×D6111yescharacteristic
574#124—1222no—
575#124—1222no—
576#123—1222no—
577#123—1222no—
578#123—1222no—
579#123—1222no—
580C22⋊Q8—1222no—
581C22⋊Q8—1222no—
582#121—1222no—
583#121—1222no—
584#121—1222no—
585#121—1222no—
586#121—1222no—
587#121—1222no—
588#120—1222no—
589#120—1222no—
590#120—1222no—
591#120—1222no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1222no—
597C4×D4—1222no—
598#117—24no—
599#117—42no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—1222no—
606C2×C22⋊C4—611no—
607C2×C22⋊C4—611no—
608C2×C22⋊C4—611no—
609C2×C22⋊C4—611no—
610C2×C22⋊C4—612no—
611C2×C22⋊C4—612no—
612C2×C22⋊C4—612no—
613C2×C22⋊C4—612no—
614C2×C22⋊C4—611no—
615C2×C22⋊C4—611no—
616C2×C22⋊C4—611no—
617C2×C22⋊C4—611no—
618C2×C22⋊C4—611no—
619C2×C22⋊C4—611no—
620C2×C22⋊C4—611no—
621C2×C22⋊C4—611no—
622C2×C22⋊C4—612no—
623C2×C22⋊C4—612no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1224no—
629C2×C22⋊C4—1222no—
630C2×C22⋊C4—1222no—
631C2×C22⋊C4—1222no—
632C2×C22⋊C4—2442no—
633C2×C22⋊C4C22×D6112yes—
634C2×C22⋊C4C22×D6112yes—
635C2×C42—22no—
636C2×C42—611no—
637C2×C42—1222no—
638#99—22no—
639#99—24no—
640#99—1222no—
641#99—1222no—
642#99—1224no—
643#99—2442no—
644#99—2442no—
645#99C22⋊D6114yescomplemented
646#95—1222no—
647#95—1222no—
648#95—1222no—
649#95—1222no—
650C24—611no—
651C24—612no—
652C24—611no—
653C24—612no—
654C24—611no—
655C24—1221no—
656C24—1221no—
657C24—1221no—
658C24—1221no—
659C24—1222no—
660C24—1222no—
661C24—4881no—
662C24—4881no—
663C24—2441no—
664C24—2442no—
665C24—2442no—
666C24C2×C4×D6111yescharacteristic
667C24C2×C4×D6111yescharacteristic
668C24C23×D6111yescharacteristic
669#41—44no—
670#41—44no—
671#41—44no—
672#41—44no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—41no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—41no—
685C2×D4—1222no—
686C2×D4—1222no—
687C2×D4—1222no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4—1222no—
691C2×D4—1222no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1222no—
695C2×D4—1222no—
696C2×D4—1222no—
697C2×D4—4881no—
698C2×D4—4881no—
699C2×D4—2441no—
700C2×D4—2441no—
701C2×D4—2444no—
702C2×D4—2444no—
703C2×D4—2444no—
704C2×D4—2444no—
705C2×D4—2442no—
706C2×D4#1175822212yes—
707C2×D4C2×C22⋊D6112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—612no—
724C22×C4—612no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1222no—
733C22×C4—1222no—
734C22×C4—1222no—
735C22×C4—4882no—
736C22×C4—4881no—
737C22×C4—4881no—
738C22×C4—2441no—
739C22×C4—2444no—
740C22×C4—2444no—
741C22×C4C2×C4×D6111yescharacteristic
742C22×C4C2×C4×D6111yescharacteristic
743C22×C4C2×C4×D6111yescharacteristic
744C22×C4C2×C4×D6111yescharacteristic
745C22×C4D4×D6112yes—
746C22×C4D4×D6112yes—
747C4⋊C4—44no—
748C4⋊C4—1222no—
749C4⋊C4—1222no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1222no—
753C4⋊C4—4882no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—611no—
758C22⋊C4—611no—
759C22⋊C4—611no—
760C22⋊C4—611no—
761C22⋊C4—612no—
762C22⋊C4—612no—
763C22⋊C4—612no—
764C22⋊C4—612no—
765C22⋊C4—612no—
766C22⋊C4—612no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1222no—
772C22⋊C4—1222no—
773C22⋊C4—1221no—
774C22⋊C4—1221no—
775C22⋊C4—1222no—
776C22⋊C4—1221no—
777C22⋊C4—1221no—
778C22⋊C4—1222no—
779C22⋊C4—1222no—
780C22⋊C4—1222no—
781C22⋊C4—1222no—
782C22⋊C4—1222no—
783C22⋊C4—4882no—
784C22⋊C4—2444no—
785C22⋊C4—2444no—
786C22⋊C4C2×C22⋊D6114yes—
787C42—44no—
788C42—1221no—
789C42—1221no—
790C42—4882no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—611no—
803C23—611no—
804C23—612no—
805C23—1224no—
806C23—1222no—
807C23—1221no—
808C23—1221no—
809C23—1222no—
810C23—1222no—
811C23—1221no—
812C23—1221no—
813C23—1222no—
814C23—1222no—
815C23—1221no—
816C23—1221no—
817C23—1221no—
818C23—4881no—
819C23—4881no—
820C23—4884no—
821C23—4884no—
822C23—4882no—
823C23—4882no—
824C23—4884no—
825C23—2442no—
826C23—2441no—
827C23—2442no—
828C23—2441no—
829C23—2442no—
830C23—2441no—
831C23—2442no—
832C23—2442no—
833C23—2441no—
834C23—2441no—
835C23—2442no—
836C23—2442no—
837C23C4×C22⋊D6112yes—
838C23C22×C4×D6111yescharacteristic
839C23C2×D4×D6112yes—
840C23C22×C22⋊D6111yescharacteristic
841C23C2×#1175822211yescharacteristic
842C23#1451982212yes—
843Q8—44no—
844D4—24no—
845D4—24no—
846D4—44no—
847D4—42no—
848D4—42no—
849D4—4882no—
850D4—4882no—
851D4—2444no—
852D4—2444no—
853D4—2442no—
854D4—2442no—
855D4—2442no—
856D4—2442no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—24no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—612no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—4888no—
889C2×C4—4881no—
890C2×C4—4881no—
891C2×C4—2442no—
892C2×C4—2442no—
893C2×C4—2442no—
894C2×C4—2442no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2442no—
898C2×C4—2442no—
899C2×C4—2442no—
900C2×C4—2442no—
901C2×C4—2442no—
902C2×C4—2442no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4C22⋊C4×D6111yescharacteristic
906C2×C4C22⋊C4×D6111yescharacteristic
907C2×C4C22⋊C4×D6112yes—
908C2×C4C4×C22⋊D6112yes—
909C22—22no—
910C22—21no—
911C22—22no—
912C22—21no—
913C22—22no—
914C22—41no—
915C22—41no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—81no—
925C22—81no—
926C22—612no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1222no—
931C22—1221no—
932C22—1222no—
933C22—1222no—
934C22—1221no—
935C22—4881no—
936C22—4881no—
937C22—4882no—
938C22—4882no—
939C22—4881no—
940C22—4881no—
941C22—4884no—
942C22—4884no—
943C22—2444no—
944C22—2442no—
945C22—2442no—
946C22—2444no—
947C22—2441no—
948C22—2441no—
949C22—2441no—
950C22C2×C22⋊C4×D6111yescharacteristic
951C22C2×C4×C22⋊D6111yescharacteristic
952C22#1684023511yescharacteristic
953C22D4×C22⋊D6112yes—
954C22#1684040212yes—
955C4—21no—
956C4—21no—
957C4—22no—
958C4—22no—
959C4—44no—
960C4—41no—
961C4—82no—
962C4—1221no—
963C4—1221no—
964C4—1222no—
965C4—4882no—
966C4—4882no—
967C4—2441no—
968C4—2441no—
969C4—2441no—
970C2—22no—
971C2—22no—
972C2—21no—
973C2—21no—
974C2—42no—
975C2—81no—
976C2—1222no—
977C2—4881no—
978C2—2441no—
979C2—2442no—
980C2C22⋊C4×C22⋊D6111yescharacteristic
981C2#410×D6111yescharacteristic
982C2#2145427811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C61×#410C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840400C2
cosocleC24×C61C24
hypercenterC2×#410D61
hypocenterC61#22405
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#99×D61C2semidirect
3. #21448669C2semidirect
4. #21446653C2semidirect
5. #21446277C2semidirect
6. #21446269C2semidirect
7. #21445805C2semidirect
8. #21445737C2semidirect
9. #21445732C2semidirect
10. #99×Dic61C2semidirect
11. C2×C61×#410C2semidirect
17. C2×#14519766C4semidirect
18. C2×#14519760C4semidirect
20. C2×#14519753C4semidirect
21. C2×#14519751C4semidirect
22. C2×#14519749C4semidirect
24. C2×#14519745C4semidirect
27. C2×C4×C22⋊D61C4semidirect
28. C22×#11758198C4semidirect
33. C2×#14519692C22semidirect
40. #16839625C22semidirect
41. #16839620C22semidirect
43. C22⋊C4×Dic61C22semidirect
45. #16839528C22semidirect
46. #16839528C22semidirect
48. C2×#117×C61C22semidirect
52. C2×#99×C61C22semidirect
59. C22×C22⋊D61C2×C4semidirect
66. C23×Dic61C2×C4semidirect
94. C2×C4⋊Dic61C2×C4semidirect
96. C2×#11758196C2×C4semidirect
97. C2×#11758196C2×C4semidirect
98. C2×#11758196C2×C4semidirect
99. C2×C22⋊Dic61C2×C4semidirect
100. C2×C22⋊Dic61C2×C4semidirect
117. C2×#11758198C2×C4semidirect
118. C2×#11758198C2×C4semidirect
119. C2×#11758198C2×C4semidirect
127. C2×C4×Dic61C2×C4semidirect
142. C22×Q8×C61C2×C4semidirect
143. C22×D4×C61C2×C4semidirect
146. C23×C4×C61C2×C4semidirect
147. C23×C4×C61C2×C4semidirect
157. #99×C61D4semidirect
463. C2×D61#410semidirect
480. C2×#410D61semidirect
520. C2×#117C2×D61semidirect
533. C2×#99C2×D61semidirect
544. C61#22405semidirect
552. C22×Q8C4×D61semidirect
564. C22×D4C4×D61semidirect
571. C23×C4C4×D61semidirect
572. C23×C4C4×D61semidirect
645. #99C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404002
C2×#99×D612
#214486692
#214466532
#214462772
#214462692
#214458052
#214457372
#214457322
#99×Dic612
C2×C61×#4102
#2240561