Finite Group Databasebeta

← #29695353

Subgroups — #29695353

Order 15616.

1474 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840411C211yesmaximal, characteristic
2C2×#16839734C211yesmaximal, characteristic, complemented
3#21448689C212yesmaximal, complemented
4#21446653C212yesmaximal, complemented
5#21446277C212yesmaximal, complemented
6#21446274C212yesmaximal, complemented
7#21445805C211yesmaximal, characteristic, complemented
8#21445737C211yesmaximal, characteristic, complemented
9#21445735C211yesmaximal, characteristic, complemented
10#99×Dic61C211yesmaximal, characteristic, complemented
11C2×C61×#410C211yesmaximal, characteristic, complemented
12C22×#11758224C2211yescharacteristic
13#16840411—22no—
14#16840411—22no—
15#16840411—22no—
16#16840411—22no—
17C2×#14519775C411yescharacteristic, complemented
18C2×#14519760C411yescharacteristic, complemented
19C2×#14519760C2211yescharacteristic
20C2×#14519758C411yescharacteristic, complemented
21C2×#14519758C2211yescharacteristic
22C2×#14519756C411yescharacteristic, complemented
23C2×#14519753C411yescharacteristic, complemented
24C2×#14519749C411yescharacteristic, complemented
25C2×#14519749C2211yescharacteristic
26C2×D4×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61C411yescharacteristic, complemented
28C2×#14519733C2212yes—
29C22×#11758196C411yescharacteristic, complemented
30C22×#11758196C2211yescharacteristic
31#16839734—24no—
32C2×#14519692C2211yescharacteristic
33C2×#14519692C2211yescharacteristic
34C2×#14519692C2212yes—
35C2×#14519691C2212yes—
36C2×#14519691C2212yes—
37#16839657—22no—
38#16839646—22no—
39#16839643—22no—
40#16839625C2212yes—
41#16839623C2212yes—
42#16839620C2212yes—
43C4×#11758196—22no—
44C22⋊C4×Dic61C2212yes—
45#16839528C2212yes—
46#16839528C2212yes—
47C22×#41×C61C2211yescharacteristic
48C2×#117×C61C2212yes—
49C61×#410—24no—
50C2×#99×C61C2211yescharacteristic
51C2×#99×C61C2212yes—
52C2×#99×C61C2211yescharacteristic
53C2×#11758224—22no—
54C2×#11758224—22no—
55C2×#11758224—22no—
56C2×#11758224—22no—
57C2×#11758224—42no—
58C22×Dic122C2×C411yescharacteristic
59C22×C22⋊D61C2×C411yescharacteristic
60C22×C22⋊D61C2×C411yescharacteristic
61C22×C22⋊D61C2311yescharacteristic
62C23×Dic61C2×C411yescharacteristic
63C23×Dic61C2×C411yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67#14519775—22no—
68#14519775—22no—
69#14519760—22no—
70#14519760—22no—
71#14519760—22no—
72#14519760—22no—
73#14519758—22no—
74#14519758—22no—
75#14519758—22no—
76#14519758—22no—
77#14519756—22no—
78#14519756—22no—
79#14519753—22no—
80#14519753—22no—
81#14519749—22no—
82#14519749—22no—
83#14519749—22no—
84#14519749—22no—
85D4×Dic61—22no—
86D4×Dic61—22no—
87C4×C22⋊D61—21no—
88C4×C22⋊D61—21no—
89C4×C22⋊D61—21no—
90C4×C22⋊D61—21no—
91#14519733—24no—
92#14519733—42no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—22no—
99C2×#11758196—22no—
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2×C411yescharacteristic
105C2×#11758196C2×C411yescharacteristic
106C2×#11758196C2×C411yescharacteristic
107C2×#11758196C2×C411yescharacteristic
108C2×#11758196C2×C411yescharacteristic
109C2×#11758196D412yes—
110C2×#11758196D412yes—
111C2×#11758196D412yes—
112C2×#11758196D412yes—
113C2×C22⋊Dic61C2×C411yescharacteristic
114C2×C22⋊Dic61C2×C411yescharacteristic
115C2×C22⋊Dic61C2×C411yescharacteristic
116C2×C22⋊Dic61C2×C411yescharacteristic
117C2×C22⋊Dic61C2312yes—
118C2×C22⋊Dic61C2312yes—
119C2×C22⋊Dic61C2311yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61C2×C411yescharacteristic
126#14519692—22no—
127#14519692—22no—
128#14519692—42no—
129#14519691—24no—
130#14519691—42no—
131#14519684—22no—
132#14519684—22no—
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
143C22×D4×C61C2×C411yescharacteristic
144C22×D4×C61C2311yescharacteristic
145C22×D4×C61C2311yescharacteristic
146C23×C4×C61C2×C411yescharacteristic
147C23×C4×C61C2×C411yescharacteristic
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×D61C22×C411yescharacteristic
162#41×C61—44no—
163#41×C61—44no—
164#41×C61—44no—
165#41×C61—44no—
166C2×Q8×C61—22no—
167C2×Q8×C61—22no—
168C2×Q8×C61—41no—
169C2×D4×C61—22no—
170C2×D4×C61—22no—
171C2×D4×C61—22no—
172C2×D4×C61—21no—
173C2×D4×C61—22no—
174C2×D4×C61—21no—
175C2×D4×C61—22no—
176C2×D4×C61—22no—
177C2×D4×C61—41no—
178C2×D4×C61C2×D412yes—
179C2×D4×C61#4112yes—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—41no—
192C22×C4×C61—41no—
193C22×C4×C61C22×C411yescharacteristic
194C22×C4×C61C22×C411yescharacteristic
195C22×C4×C61C22×C411yescharacteristic
196C22×C4×C61C22×C411yescharacteristic
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2×D412yes—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—22no—
204C2×C22⋊D61—22no—
205C2×C22⋊D61—21no—
206C2×C22⋊D61—21no—
207C2×C22⋊D61—41no—
208C2×C22⋊D61—42no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—42no—
220C22×Dic61—41no—
221C22×Dic61—42no—
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
229C22×Dic61C2×D412yes—
230C22×Dic61C2×D412yes—
231C22×Dic61C2×D412yes—
232C22×Dic61C2×D412yes—
233#11758224—44no—
234#11758224—44no—
235#11758224—44no—
236#11758224—44no—
237C2×C4×D61—22no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—41no—
241C2×Dic122—22no—
242C2×Dic122—22no—
243C2×Dic122—41no—
244C4⋊C4×C61—44no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—22no—
248C22⋊C4×C61C2×D414yes—
249C42×C61—44no—
250C22⋊Dic61—22no—
251C22⋊Dic61—21no—
252C22⋊Dic61—21no—
253C22⋊Dic61—22no—
254C22⋊Dic61—22no—
255C22⋊Dic61—22no—
256C22⋊Dic61—22no—
257C22⋊Dic61—22no—
258C22⋊Dic61—22no—
259C22⋊Dic61—22no—
260#11758198—21no—
261#11758198—21no—
262#11758198—22no—
263#11758198—22no—
264C4⋊Dic61—22no—
265#11758196—21no—
266#11758196—21no—
267#11758196—22no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—22no—
273#11758196—44no—
274#11758196—44no—
275#11758196C22⋊C411yescharacteristic
276#11758196C22⋊C411yescharacteristic
277#11758196C22⋊C411yescharacteristic
278#11758196C22⋊C411yescharacteristic
279#11758196C22⋊C412yes—
280#11758196C22⋊C412yes—
281#11758196C22⋊C412yes—
282#11758196C22⋊C412yes—
283#11758196C22⋊C412yes—
284#11758196C22⋊C412yes—
285C4×Dic61—21no—
286C4×Dic61—21no—
287C4×Dic61—44no—
288C4×Dic61—44no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61C4×D412yes—
301C23×C61C23×C411yescharacteristic
302C23×C61C22×D412yes—
303C23×C61C22×D411yescharacteristic
304C23×C61C2×#4111yescharacteristic
305C23×C61H(5,𝔽2)12yes—
306C22×D61—21no—
307C22×D61—21no—
308C22×D61—21no—
309C22×D61—41no—
310C22×D61—41no—
311Q8×C61—44no—
312D4×C61—24no—
313D4×C61—24no—
314D4×C61—44no—
315D4×C61—42no—
316D4×C61—42no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—24no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61—42no—
334C2×C4×C61—42no—
335C2×C4×C61—42no—
336C2×C4×C61—42no—
337C2×C4×C61—42no—
338C2×C4×C61—42no—
339C2×C4×C61—42no—
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C2×C22⋊C411yescharacteristic
342C2×C4×C61C2×C22⋊C412yes—
343C2×C4×C61C4×D412yes—
344C22⋊D61—44no—
345C22⋊D61—42no—
346C22⋊D61—42no—
347C22⋊D61—42no—
348C22⋊D61—42no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—24no—
358C2×Dic61—22no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—41no—
365C2×Dic61—42no—
366C2×Dic61—42no—
367C2×Dic61—42no—
368C2×Dic61—42no—
369C2×Dic61—42no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61—42no—
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C412yes—
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C2×C22⋊C411yescharacteristic
382C2×Dic61C2×C22⋊C412yes—
383C2×Dic61C2×C22⋊C411yescharacteristic
384C4×D61—42no—
385C4×D61—42no—
386Dic122—44no—
387#22406—611nomaximal, Sylow
388C22×C61—22no—
389C22×C61—21no—
390C22×C61—22no—
391C22×C61—21no—
392C22×C61—22no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61C22×C22⋊C411yescharacteristic
406C22×C61C2×C4×D411yescharacteristic
407C22×C61#51811yescharacteristic
408C22×C61D4212yes—
409C22×C61#54612yes—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61—81no—
414C2×D61—81no—
415C4×C61—22no—
416C4×C61—21no—
417C4×C61—21no—
418C4×C61—22no—
419C4×C61—44no—
420C4×C61—41no—
421C4×C61—82no—
422Dic61—22no—
423Dic61—21no—
424Dic61—21no—
425Dic61—21no—
426Dic61—22no—
427Dic61—41no—
428Dic61—41no—
429Dic61—41no—
430Dic61—82no—
431Dic61—82no—
432Dic61#41012yescomplemented
433C2×#547—611no—
434C2×#410—611no—
435C2×#410D6111yescharacteristic, complemented
436#2344—612no—
437#1964—612no—
438#1899—612no—
439#1899—612no—
440#1799—611no—
441#1782—611no—
442#1782—611no—
443C4×#99—611no—
444C2×C61—22no—
445C2×C61—22no—
446C2×C61—21no—
447C2×C61—21no—
448C2×C61—42no—
449C2×C61—81no—
450C2×C61D4×C22⋊C411yescharacteristic
451C2×C61C2×#41011yescharacteristic
452C2×C61#288411yescharacteristic
453D61—81no—
454C22×#41—611no—
455C22×#41C2×D6111yescharacteristic
456#547—1222no—
457#547—1222no—
458#547—1222no—
459#547—1222no—
460C2×C4⋊Q8—611no—
461C2×#123—611no—
462C2×#123—611no—
463C2×#123—611no—
464C2×#123—611no—
465C2×C22⋊Q8—611no—
466C2×C22⋊Q8—611no—
467C2×#121—611no—
468C2×#121—611no—
469C2×C4×D4—611no—
470C2×C4×D4—611no—
471C2×#117—612no—
472C2×#117C2×D6112yes—
473C22×C4⋊C4—611no—
474C22×C4⋊C4—611no—
475#410—24no—
476#410—1224no—
477C2×#99—611no—
478C2×#99—611no—
479C2×#99—612no—
480C2×#99—612no—
481C2×#99—612no—
482C2×#99C2×D6111yescharacteristic
483C2×#99C2×D6112yes—
484C2×#99C2×D6111yescharacteristic
485#389—1222no—
486#387—1222no—
487#387—1222no—
488#381—612no—
489#381—612no—
490#380—612no—
491C4×C4⋊C4—1222no—
492C4×C22⋊C4—612no—
493#342—612no—
494#342—612no—
495C61#2240611yescharacteristic, complemented, Sylow
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—42no—
501C2×#41—1222no—
502C2×#41—1222no—
503C2×#41—1222no—
504C2×#41—1222no—
505C2×#41—2442no—
506C22×Q8—611no—
507C22×Q8C4×D6111yescharacteristic
508C22×D4—611no—
509C22×D4—611no—
510C22×D4—611no—
511C22×D4C4×D6111yescharacteristic
512C22×D4C22×D6111yescharacteristic
513C22×D4C22×D6111yescharacteristic
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—611no—
517C23×C4—611no—
518C23×C4—611no—
519C23×C4C4×D6111yescharacteristic
520C23×C4C4×D6111yescharacteristic
521C23×C4C22×D6111yescharacteristic
522C4⋊Q8—1222no—
523C4⋊Q8—1222no—
524#123—1222no—
525#123—1222no—
526#123—1222no—
527#123—1222no—
528#123—1222no—
529#123—1222no—
530#123—1222no—
531#123—1222no—
532C22⋊Q8—1222no—
533C22⋊Q8—1222no—
534C22⋊Q8—1222no—
535C22⋊Q8—1222no—
536#121—1222no—
537#121—1222no—
538#121—1222no—
539#121—1222no—
540C4×D4—1221no—
541C4×D4—1221no—
542C4×D4—1221no—
543C4×D4—1221no—
544C4×D4—1222no—
545C4×D4—1222no—
546#117—24no—
547#117—42no—
548#117—1224no—
549#117—2442no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—612no—
556C2×C4⋊C4—612no—
557C2×C4⋊C4—612no—
558C2×C4⋊C4—612no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1222no—
570C2×C4⋊C4—1222no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—611no—
574C2×C22⋊C4—611no—
575C2×C22⋊C4—611no—
576C2×C22⋊C4—611no—
577C2×C22⋊C4—611no—
578C2×C22⋊C4—611no—
579C2×C22⋊C4—612no—
580C2×C22⋊C4—612no—
581C2×C22⋊C4C22×D6112yes—
582C2×C22⋊C4C22×D6112yes—
583C2×C42—22no—
584C2×C42—611no—
585C2×C42—1222no—
586C2×C42—1222no—
587#99—22no—
588#99—24no—
589#99—1222no—
590#99—1222no—
591#99—1224no—
592#99—2442no—
593#99—2442no—
594#99C22⋊D6114yescomplemented
595#95—1222no—
596#95—1222no—
597#95—1222no—
598#95—1222no—
599#95—1222no—
600#95—1222no—
601C24—611no—
602C24C2×C4×D6111yescharacteristic
603C24C2×C4×D6111yescharacteristic
604C24C23×D6111yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—2444no—
610#41—2444no—
611#41—2444no—
612#41—2444no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—41no—
616C2×Q8—1222no—
617C2×Q8—1222no—
618C2×Q8—2441no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—41no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1222no—
631C2×D4—1222no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1222no—
635C2×D4—1222no—
636C2×D4—2441no—
637C2×D4—2442no—
638C2×D4#1175822212yes—
639C2×D4C2×C22⋊D6112yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—612no—
657C22×C4—612no—
658C22×C4—612no—
659C22×C4—611no—
660C22×C4—612no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4—2441no—
678C22×C4—2442no—
679C22×C4—2441no—
680C22×C4—2442no—
681C22×C4C2×C4×D6111yescharacteristic
682C22×C4C2×C4×D6111yescharacteristic
683C22×C4C2×C4×D6111yescharacteristic
684C22×C4C2×C4×D6111yescharacteristic
685C22×C4D4×D6112yes—
686C22×C4D4×D6112yes—
687C4⋊C4—44no—
688C4⋊C4—611no—
689C4⋊C4—611no—
690C4⋊C4—611no—
691C4⋊C4—611no—
692C4⋊C4—612no—
693C4⋊C4—612no—
694C4⋊C4—612no—
695C4⋊C4—612no—
696C4⋊C4—612no—
697C4⋊C4—612no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1222no—
703C4⋊C4—1222no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1222no—
707C4⋊C4—2444no—
708C4⋊C4—2444no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—1222no—
713C22⋊C4—1222no—
714C22⋊C4—1221no—
715C22⋊C4—1221no—
716C22⋊C4—1222no—
717C22⋊C4—1222no—
718C22⋊C4—1222no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1222no—
722C22⋊C4—1222no—
723C22⋊C4—1222no—
724C22⋊C4—1222no—
725C22⋊C4—1222no—
726C22⋊C4C2×C22⋊D6114yes—
727C42—44no—
728C42—1221no—
729C42—1221no—
730C42—2444no—
731C42—2444no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—2441no—
747C23—2441no—
748C23C4×C22⋊D6112yes—
749C23C22×C4×D6111yescharacteristic
750C23C2×D4×D6112yes—
751C23C22×C22⋊D6111yescharacteristic
752C23C2×#1175822211yescharacteristic
753C23#1451982212yes—
754Q8—44no—
755Q8—2444no—
756D4—24no—
757D4—24no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—2442no—
762D4—2444no—
763D4—2442no—
764D4—2442no—
765D4—2442no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—24no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—611no—
790C2×C4—611no—
791C2×C4—612no—
792C2×C4—611no—
793C2×C4—611no—
794C2×C4—612no—
795C2×C4—1224no—
796C2×C4—1222no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—2442no—
811C2×C4—2442no—
812C2×C4—2442no—
813C2×C4—2441no—
814C2×C4—2442no—
815C2×C4—2442no—
816C2×C4—2442no—
817C2×C4—2442no—
818C2×C4—2442no—
819C2×C4—2442no—
820C2×C4—2442no—
821C2×C4—2442no—
822C2×C4—2442no—
823C2×C4—2442no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4C22⋊C4×D6111yescharacteristic
827C2×C4C22⋊C4×D6111yescharacteristic
828C2×C4C22⋊C4×D6112yes—
829C2×C4C4×C22⋊D6112yes—
830C22—22no—
831C22—21no—
832C22—22no—
833C22—21no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—81no—
846C22—81no—
847C22—4881no—
848C22—4881no—
849C22—2441no—
850C22—2441no—
851C22—2441no—
852C22C2×C22⋊C4×D6111yescharacteristic
853C22C2×C4×C22⋊D6111yescharacteristic
854C22#1684023511yescharacteristic
855C22D4×C22⋊D6112yes—
856C22#1684040212yes—
857C4—21no—
858C4—21no—
859C4—22no—
860C4—22no—
861C4—44no—
862C4—41no—
863C4—82no—
864C4—612no—
865C4—1221no—
866C4—1221no—
867C4—1222no—
868C4—1222no—
869C4—1221no—
870C4—4882no—
871C4—4882no—
872C4—2441no—
873C4—2441no—
874C4—2441no—
875C2—22no—
876C2—22no—
877C2—21no—
878C2—21no—
879C2—42no—
880C2—81no—
881C2—4881no—
882C2C22⋊C4×C22⋊D6111yescharacteristic
883C2#410×D6111yescharacteristic
884C2#2145428111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C61×#410C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840411C2
cosocleC24×C61C24
hypercenterC2×#410D61
hypocenterC61#22406
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×#16839734C2semidirect
3. #21448689C2semidirect
4. #21446653C2semidirect
5. #21446277C2semidirect
6. #21446274C2semidirect
7. #21445805C2semidirect
8. #21445737C2semidirect
9. #21445735C2semidirect
10. #99×Dic61C2semidirect
11. C2×C61×#410C2semidirect
17. C2×#14519775C4semidirect
18. C2×#14519760C4semidirect
20. C2×#14519758C4semidirect
22. C2×#14519756C4semidirect
23. C2×#14519753C4semidirect
24. C2×#14519749C4semidirect
27. C2×C4×C22⋊D61C4semidirect
29. C22×#11758196C4semidirect
157. #99×C61D4semidirect
432. Dic61#410semidirect
435. C2×#410D61semidirect
495. C61#22406semidirect
594. #99C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404112
C2×#168397342
#214486892
#214466532
#214462772
#214462742
#214458052
#214457372
#214457352
#99×Dic612
C2×C61×#4102
#2240661