Finite Group Databasebeta

← #29700754

Subgroups — #29700754

Order 15616.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839884C211yesmaximal, characteristic, complemented
2#21454546C211yesmaximal, characteristic, complemented
3C22×#14519704C211yesmaximal, characteristic, complemented
4#21454268C211yesmaximal, characteristic, complemented
5#21446713C211yesmaximal, characteristic, complemented
6#21446532C211yesmaximal, characteristic, complemented
7#21446469C211yesmaximal, characteristic, complemented
8#21446263C211yesmaximal, characteristic, complemented
9#21446148C211yesmaximal, characteristic, complemented
10#21446148C211yesmaximal, characteristic, complemented
11#21446096C211yesmaximal, characteristic, complemented
12#21446026C211yesmaximal, characteristic, complemented
13#21445666C211yesmaximal, characteristic, complemented
14#21445583C211yesmaximal, characteristic, complemented
15C61×#3002C211yesmaximal, characteristic
16C2×#14519784C2211yescharacteristic
17C2×#14519784C2211yescharacteristic
18C2×#14519784C2211yescharacteristic, complemented
19C22×#11758194C2211yescharacteristic
20C22×C4×Dic61C2211yescharacteristic
21#16839884—24no—
22#16839840—21no—
23#16839834—21no—
24#16839834—21no—
25D4×#92418—21no—
26C2×#14519713C2211yescharacteristic, complemented
27C2×#14519713C2211yescharacteristic, complemented
28#16839789C2211yescharacteristic, complemented
29C2×#14519704—24no—
30C2×#14519704C2211yescharacteristic
31C2×#14519704C2211yescharacteristic
32C2×#14519704C2211yescharacteristic
33C2×#14519704C2211yescharacteristic
34C2×#14519704C2211yescharacteristic, complemented
35C2×#14519704C2211yescharacteristic, complemented
36#16839729—21no—
37#16839729—21no—
38#16839729C2211yescharacteristic
39#16839729C2211yescharacteristic
40#16839729C2211yescharacteristic, complemented
41#16839726—21no—
42#16839726C2211yescharacteristic
43C2×C22⋊#92418—21no—
44C2×C22⋊#92418C2211yescharacteristic
45#16839718C2211yescharacteristic, complemented
46C2×#14519687C2211yescharacteristic, complemented
47C2×#14519687C2211yescharacteristic, complemented
48#16839527C2211yescharacteristic, complemented
49#16839527C2211yescharacteristic, complemented
50#16839521C2211yescharacteristic, complemented
51#16839521C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C22×#41×C61C2211yescharacteristic
55C2×#135×C61C2211yescharacteristic
56C2×#135×C61C2211yescharacteristic
57C61×#525C2211yescharacteristic
58C61×#452C411yescharacteristic, complemented
59C61×#452C411yescharacteristic, complemented
60C61×#451C411yescharacteristic, complemented
61C61×#450C411yescharacteristic, complemented
62C61×#449C411yescharacteristic, complemented
63C61×#449C411yescharacteristic, complemented
64C61×#448C411yescharacteristic, complemented
65C61×#447C411yescharacteristic, complemented
66C61×#416C2211yescharacteristic
67C61×#416C2211yescharacteristic
68C2×C22⋊C8×C61C2211yescharacteristic
69C23×Dic61—21no—
70#14519784—22no—
71#14519784—22no—
72#14519784—22no—
73#14519784—41no—
74#14519784—41no—
75#14519784—41no—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C2×#11758194—21no—
79C2×#11758194—21no—
80C2×#11758194—22no—
81C2×#11758194—41no—
82C2×#11758194C2311yescharacteristic
83C2×#11758194C2311yescharacteristic
84C2×#11758194C2311yescharacteristic
85C2×#11758194C2311yescharacteristic
86C22×#92418—21no—
87C22×#92418—21no—
88C22×#92418—21no—
89C22×#92418—21no—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C2×C4×Dic61—22no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61—41no—
95C2×C4×Dic61C2311yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97#14519713—22no—
98#14519713—41no—
99C4⋊#92418—21no—
100C4⋊#92418—21no—
101#14519704—22no—
102#14519704—22no—
103#14519704—22no—
104#14519704—22no—
105#14519704—41no—
106#14519704D414yescomplemented
107C22⋊#92418—21no—
108C22⋊#92418—21no—
109C22⋊#92418—21no—
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113C22⋊#92418—21no—
114C22⋊#92418—21no—
115C22⋊#92418D411yescharacteristic
116C22⋊#92418D411yescharacteristic
117C22⋊#92418D411yescharacteristic
118C22⋊#92418D411yescharacteristic
119#14519688—21no—
120#14519687—22no—
121#14519687—41no—
122C4×#92418—21no—
123C2×#41×C61—21no—
124C2×#41×C61—21no—
125C2×#41×C61—22no—
126C2×#41×C61—22no—
127C2×#41×C61—41no—
128C2×#41×C61—41no—
129C2×#41×C61C2×C411yescharacteristic
130C2×#41×C61C2×C411yescharacteristic
131C2×#41×C61C2311yescharacteristic
132C2×#41×C61C2311yescharacteristic
133C2×#41×C61C2311yescharacteristic
134C22×Q8×C61C2×C411yescharacteristic
135C22×D4×C61—21no—
136C22×D4×C61C2×C411yescharacteristic
137C23×C4×C61—21no—
138C23×C4×C61C2311yescharacteristic
139#135×C61—22no—
140#135×C61—22no—
141#135×C61—41no—
142#135×C61—41no—
143C2×Q16×C61C2×C411yescharacteristic, complemented
144C2×Q16×C61C2×C411yescharacteristic, complemented
145C2×SD16×C61C2×C411yescharacteristic, complemented
146C2×SD16×C61C2×C411yescharacteristic, complemented
147C2×SD16×C61C2×C411yescharacteristic, complemented
148C2×SD16×C61C2×C411yescharacteristic, complemented
149C2×D8×C61C2×C411yescharacteristic, complemented
150C2×D8×C61C2×C411yescharacteristic, complemented
151C22×C8×C61C2311yescharacteristic
152C22×C8×C61C2311yescharacteristic
153#123×C61—21no—
154C22⋊Q8×C61C2×C411yescharacteristic
155C22⋊Q8×C61C2×C411yescharacteristic
156#121×C61C2×C411yescharacteristic
157#121×C61C2×C411yescharacteristic
158#120×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61—21no—
161#117×C61C2311yescharacteristic
162#103×C61C2×C411yescharacteristic, complemented
163#103×C61C2×C411yescharacteristic, complemented
164#103×C61C2×C411yescharacteristic, complemented
165#103×C61C2×C411yescharacteristic, complemented
166#102×C61C2×C411yescharacteristic, complemented
167#102×C61C2×C411yescharacteristic, complemented
168#102×C61C2×C411yescharacteristic, complemented
169#102×C61C2×C411yescharacteristic, complemented
170C22⋊C8×C61C2×C411yescharacteristic
171C22⋊C8×C61C2×C411yescharacteristic
172C22⋊C8×C61C2×C411yescharacteristic
173C22⋊C8×C61C2×C411yescharacteristic
174C24×C61—21no—
175C24×C61#4111yescharacteristic
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—22no—
179#41×C61—22no—
180#41×C61—21no—
181#41×C61—21no—
182#41×C61—21no—
183#41×C61—21no—
184#41×C61—21no—
185#41×C61—21no—
186#41×C61—21no—
187#41×C61—21no—
188#41×C61—42no—
189#41×C61—42no—
190#41×C61—41no—
191#41×C61—41no—
192#41×C61—42no—
193#41×C61—42no—
194#41×C61C2×D412yes—
195#41×C61#4112yes—
196C2×Q8×C61—21no—
197C2×Q8×C61—22no—
198C2×Q8×C61—41no—
199C2×Q8×C61C22×C411yescharacteristic
200C2×Q8×C61C22×C411yescharacteristic
201C2×Q8×C61C22×C411yescharacteristic
202C2×D4×C61—21no—
203C2×D4×C61—22no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—41no—
212C2×D4×C61—42no—
213C2×D4×C61—42no—
214C2×D4×C61C22×C411yescharacteristic
215C2×D4×C61C22×C411yescharacteristic
216C2×D4×C61C22×C411yescharacteristic
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—42no—
228C22×C4×C61—42no—
229C22×C4×C61C22×C411yescharacteristic
230C22×C4×C61C22×C411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61#4111yescharacteristic
234C22×C4×C61C2411yescharacteristic
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—42no—
238C22×Dic61—42no—
239C22×Dic61—42no—
240Q16×C61—22no—
241Q16×C61—41no—
242SD16×C61—22no—
243SD16×C61—22no—
244SD16×C61—41no—
245SD16×C61—41no—
246D8×C61—22no—
247D8×C61—41no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61C22×C411yescharacteristic
253C2×C8×C61C22×C411yescharacteristic
254C2×C8×C61C22×C411yescharacteristic
255C2×C8×C61C22×C411yescharacteristic
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61C22×C411yescharacteristic
259C4⋊C4×C61C22×C411yescharacteristic
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C42×C61—21no—
266C4×Dic61—21no—
267C4×Dic61—21no—
268C4×Dic61—21no—
269C4×Dic61—42no—
270C4×Dic61C2×D412yes—
271#11758194—21no—
272#11758194—21no—
273#11758194—21no—
274#11758194—21no—
275#11758194—21no—
276#11758194—21no—
277#11758194—21no—
278#11758194—42no—
279#11758194—42no—
280#11758194—42no—
281#11758194—42no—
282#11758194C2×D412yes—
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—42no—
292C2×#92418—42no—
293C2×#92418—42no—
294C2×#92418—42no—
295C2×#92418C2×D411yescharacteristic
296C2×#92418C2×D411yescharacteristic
297C2×#92418C2×D411yescharacteristic
298C2×#92418C2×D411yescharacteristic
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—22no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—41no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61—81no—
309C23×C61C4×D411yescharacteristic
310C23×C61C4×D411yescharacteristic
311C23×C61C2×#4111yescharacteristic
312Q8×C61—21no—
313Q8×C61—21no—
314Q8×C61—21no—
315Q8×C61—21no—
316Q8×C61—21no—
317Q8×C61—42no—
318Q8×C61C4×D412yes—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—21no—
322D4×C61—21no—
323D4×C61—21no—
324D4×C61—21no—
325D4×C61—21no—
326D4×C61—42no—
327D4×C61—42no—
328D4×C61—42no—
329D4×C61—41no—
330D4×C61—41no—
331D4×C61—41no—
332D4×C61—41no—
333D4×C61—42no—
334D4×C61—81no—
335D4×C61C4×D412yes—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—22no—
345C2×C4×C61—21no—
346C2×C4×C61—22no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—42no—
354C2×C4×C61—42no—
355C2×C4×C61—42no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61C4×D411yescharacteristic
361C2×C4×C61C4×D411yescharacteristic
362C2×C4×C61C23×C411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C2×#4111yescharacteristic
366C2×C4×C61H(5,𝔽2)11yescharacteristic
367C2×C4×C61H(5,𝔽2)11yescharacteristic
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—48no—
374C2×Dic61—41no—
375C8×C61—21no—
376C8×C61—21no—
377C8×C61—21no—
378C8×C61—21no—
379#92418—21no—
380#92418—21no—
381#92418—22no—
382#92418—21no—
383#92418—21no—
384#92418—41no—
385#92418—41no—
386#92418—41no—
387#22886—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—22no—
394C22×C61—21no—
395C22×C61—21no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61—84no—
407C22×C61#44412yescomplemented
408C22×C61C2×C4×D411yescharacteristic
409C22×C61#54611yescharacteristic
410C22×C61#55111yescharacteristic
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—22no—
414C4×C61—41no—
415C4×C61—41no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61C2×C4×D411yescharacteristic
419C4×C61#51811yescharacteristic
420C4×C61D4211yescharacteristic
421C4×C61#54611yescharacteristic
422Dic61—42no—
423Dic61—42no—
424#3002D6111yescharacteristic
425C2×#444—611no—
426#2933—611no—
427C22×#104—611no—
428#2880—611no—
429#1975—611no—
430#1938—611no—
431#1929—611no—
432#1896—611no—
433#1876—611no—
434#1876—611no—
435#1866—611no—
436#1855—611no—
437#1765—611no—
438#1749—611no—
439C2×C61—21no—
440C2×C61—22no—
441C2×C61—21no—
442C2×C61—41no—
443C2×C61—42no—
444C2×C61—81no—
445C2×C61—81no—
446C2×C61#235811yescharacteristic
447C2×C61C2×#44411yescharacteristic
448C2×C61#295611yescharacteristic
449C22×#41C2×D6111yescharacteristic
450C2×#135C2×D6111yescharacteristic
451C2×#135C2×D6111yescharacteristic
452C2×#131—611no—
453C2×#131—611no—
454C2×#131—611no—
455C22×M16—611no—
456#525C2×D6111yescharacteristic
457C22×C42—611no—
458#452Dic6111yescharacteristic, complemented
459#452Dic6111yescharacteristic, complemented
460#451Dic6111yescharacteristic, complemented
461#450Dic6111yescharacteristic, complemented
462#449Dic6111yescharacteristic, complemented
463#449Dic6111yescharacteristic, complemented
464#448Dic6111yescharacteristic, complemented
465#447Dic6111yescharacteristic, complemented
466#444—1224no—
467#436—1221no—
468#435—1221no—
469#435—1221no—
470C8×D4—1221no—
471C2×#108—611no—
472C2×#108—611no—
473#424—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104—611no—
478C2×#104—611no—
479C2×#104—611no—
480C2×#104—1224no—
481#416C2×D6111yescharacteristic
482#416C2×D6111yescharacteristic
483#408—611no—
484#408—611no—
485#408—611no—
486#408—1221no—
487#408—1221no—
488#407—611no—
489#407—1221no—
490C2×C22⋊C8—611no—
491C2×C22⋊C8—1221no—
492C2×C22⋊C8C2×D6111yescharacteristic
493#405—611no—
494C2×#97—611no—
495C2×#97—611no—
496#341—611no—
497#341—611no—
498#339—611no—
499#339—611no—
500#336—611no—
501#336—611no—
502C61#2288611yescharacteristic, complemented, Sylow
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×Dic6111yescharacteristic
510C2×#41C2×Dic6111yescharacteristic
511C2×#41C22×D6111yescharacteristic
512C2×#41C22×D6111yescharacteristic
513C2×#41C22×D6111yescharacteristic
514C22×Q8C2×Dic6111yescharacteristic
515C22×D4—21no—
516C22×D4C2×Dic6111yescharacteristic
517C23×C4—21no—
518C23×C4—1221no—
519C23×C4C22×D6111yescharacteristic
520#135—22no—
521#135—22no—
522#135—41no—
523#135—41no—
524C2×Q16C2×Dic6111yescharacteristic, complemented
525C2×Q16C2×Dic6111yescharacteristic, complemented
526C2×SD16C2×Dic6111yescharacteristic, complemented
527C2×SD16C2×Dic6111yescharacteristic, complemented
528C2×SD16C2×Dic6111yescharacteristic, complemented
529C2×SD16C2×Dic6111yescharacteristic, complemented
530C2×D8C2×Dic6111yescharacteristic, complemented
531C2×D8C2×Dic6111yescharacteristic, complemented
532#131—1222no—
533#131—1222no—
534#131—1222no—
535#131—2441no—
536#131—2441no—
537#131—2441no—
538C2×M16—611no—
539C2×M16—611no—
540C2×M16—611no—
541C2×M16—611no—
542C2×M16—1221no—
543C2×M16—1221no—
544C2×M16—1221no—
545C2×M16—1221no—
546C2×M16—1222no—
547C2×M16—2441no—
548C22×C8—611no—
549C22×C8—611no—
550C22×C8—1221no—
551C22×C8—1221no—
552C22×C8—1221no—
553C22×C8—1221no—
554C22×C8C22×D6111yescharacteristic
555C22×C8C22×D6111yescharacteristic
556#123—21no—
557C22⋊Q8C2×Dic6111yescharacteristic
558C22⋊Q8C2×Dic6111yescharacteristic
559#121C2×Dic6111yescharacteristic
560#121C2×Dic6111yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D6111yescharacteristic
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—1222no—
568C2×C42—1221no—
569C2×C42—2441no—
570#108—1222no—
571#108—2441no—
572C4⋊C8—1221no—
573C4⋊C8—1221no—
574#104—614no—
575#104—1222no—
576#104—1222no—
577#104—1222no—
578#104—1222no—
579#104—2441no—
580#103C2×Dic6111yescharacteristic, complemented
581#103C2×Dic6111yescharacteristic, complemented
582#103C2×Dic6111yescharacteristic, complemented
583#103C2×Dic6111yescharacteristic, complemented
584#102C2×Dic6111yescharacteristic, complemented
585#102C2×Dic6111yescharacteristic, complemented
586#102C2×Dic6111yescharacteristic, complemented
587#102C2×Dic6111yescharacteristic, complemented
588C22⋊C8—611no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—1221no—
593C22⋊C8—1221no—
594C22⋊C8—1221no—
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8C2×Dic6111yescharacteristic
601C22⋊C8C2×Dic6111yescharacteristic
602C22⋊C8C2×Dic6111yescharacteristic
603C22⋊C8C2×Dic6111yescharacteristic
604#97—1221no—
605#97—1222no—
606#97—2441no—
607C4×C8—1221no—
608C24—21no—
609C24#1175822411yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—42no—
623#41—42no—
624#41—41no—
625#41—41no—
626#41—42no—
627#41—42no—
628#41D4×D6112yes—
629#41#1175822412yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8C22×Dic6111yescharacteristic
634C2×Q8C22×Dic6111yescharacteristic
635C2×Q8C22×Dic6111yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C22×Dic6111yescharacteristic
649C2×D4C22×Dic6111yescharacteristic
650C2×D4C22×Dic6111yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—2442no—
666C22×C4—2442no—
667C22×C4—2442no—
668C22×C4D4×D6111yescharacteristic
669C22×C4D4×D6111yescharacteristic
670C22×C4#1175822411yescharacteristic
671C22×C4C22×Dic6111yescharacteristic
672C22×C4C22×Dic6111yescharacteristic
673C22×C4C23×D6111yescharacteristic
674Q16—22no—
675Q16—41no—
676SD16—22no—
677SD16—22no—
678SD16—41no—
679SD16—41no—
680D8—22no—
681D8—41no—
682M16—612no—
683M16—1221no—
684M16—1221no—
685M16—1221no—
686M16—1221no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—2442no—
691M16—2442no—
692M16—2442no—
693M16—2442no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—611no—
699C2×C8—611no—
700C2×C8—611no—
701C2×C8—611no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—2442no—
711C2×C8—2442no—
712C2×C8—2442no—
713C2×C8—2442no—
714C2×C8C22×Dic6111yescharacteristic
715C2×C8C22×Dic6111yescharacteristic
716C2×C8C22×Dic6111yescharacteristic
717C2×C8C22×Dic6111yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C22×Dic6111yescharacteristic
721C4⋊C4C22×Dic6111yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—612no—
729C42—1221no—
730C42—1221no—
731C42—1221no—
732C42—2442no—
733C23—21no—
734C23—22no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23D4×Dic6111yescharacteristic
744C23D4×Dic6111yescharacteristic
745C23C2×#1175822411yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8D4×Dic6112yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—81no—
769D4D4×Dic6112yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2448no—
800C2×C4—2441no—
801C2×C4D4×Dic6111yescharacteristic
802C2×C4D4×Dic6111yescharacteristic
803C2×C4C23×Dic6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C2×D4×D6111yescharacteristic
806C2×C4C2×#1175822411yescharacteristic
807C2×C4#1451982211yescharacteristic
808C2×C4#1451982211yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—1221no—
814C8—1221no—
815C8—1222no—
816C8—1221no—
817C8—1221no—
818C8—2441no—
819C8—2441no—
820C8—2441no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22#1683988412yescomplemented
841C22C2×D4×Dic6111yescharacteristic
842C22#1684039911yescharacteristic
843C22#1684044311yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—2442no—
852C4—2442no—
853C4C2×D4×Dic6111yescharacteristic
854C4#1684023711yescharacteristic
855C4#1684039411yescharacteristic
856C4#1684039911yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2#2144880311yescharacteristic
865C2C2×#1683988411yescharacteristic
866C2#2145472911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#3002C2
socleC22×C61C2×C4×D4
cosocleC22×C4×C61C24
hypercenter#3002D61
hypocenterC61#22886
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. C2×#16839884C2semidirect
2. #21454546C2semidirect
3. C22×#14519704C2semidirect
4. #21454268C2semidirect
5. #21446713C2semidirect
6. #21446532C2semidirect
7. #21446469C2semidirect
8. #21446263C2semidirect
9. #21446148C2semidirect
10. #21446148C2semidirect
11. #21446096C2semidirect
12. #21446026C2semidirect
13. #21445666C2semidirect
14. #21445583C2semidirect
18. C2×#14519784C22semidirect
26. C2×#14519713C22semidirect
27. C2×#14519713C22semidirect
28. #16839789C22semidirect
34. C2×#14519704C22semidirect
35. C2×#14519704C22semidirect
40. #16839729C22semidirect
45. #16839718C22semidirect
46. C2×#14519687C22semidirect
47. C2×#14519687C22semidirect
48. #16839527C22semidirect
49. #16839527C22semidirect
50. #16839521C22semidirect
51. #16839521C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
58. C61×#452C4semidirect
59. C61×#452C4semidirect
60. C61×#451C4semidirect
61. C61×#450C4semidirect
62. C61×#449C4semidirect
63. C61×#449C4semidirect
64. C61×#448C4semidirect
65. C61×#447C4semidirect
106. #14519704D4semidirect
143. C2×Q16×C61C2×C4semidirect
144. C2×Q16×C61C2×C4semidirect
145. C2×SD16×C61C2×C4semidirect
146. C2×SD16×C61C2×C4semidirect
147. C2×SD16×C61C2×C4semidirect
148. C2×SD16×C61C2×C4semidirect
149. C2×D8×C61C2×C4semidirect
150. C2×D8×C61C2×C4semidirect
162. #103×C61C2×C4semidirect
163. #103×C61C2×C4semidirect
164. #103×C61C2×C4semidirect
165. #103×C61C2×C4semidirect
166. #102×C61C2×C4semidirect
167. #102×C61C2×C4semidirect
168. #102×C61C2×C4semidirect
169. #102×C61C2×C4semidirect
407. C22×C61#444semidirect
458. #452Dic61semidirect
459. #452Dic61semidirect
460. #451Dic61semidirect
461. #450Dic61semidirect
462. #449Dic61semidirect
463. #449Dic61semidirect
464. #448Dic61semidirect
465. #447Dic61semidirect
502. C61#22886semidirect
524. C2×Q16C2×Dic61semidirect
525. C2×Q16C2×Dic61semidirect
526. C2×SD16C2×Dic61semidirect
527. C2×SD16C2×Dic61semidirect
528. C2×SD16C2×Dic61semidirect
529. C2×SD16C2×Dic61semidirect
530. C2×D8C2×Dic61semidirect
531. C2×D8C2×Dic61semidirect
580. #103C2×Dic61semidirect
581. #103C2×Dic61semidirect
582. #103C2×Dic61semidirect
583. #103C2×Dic61semidirect
584. #102C2×Dic61semidirect
585. #102C2×Dic61semidirect
586. #102C2×Dic61semidirect
587. #102C2×Dic61semidirect
840. C22#16839884semidirect

Maximal subgroups

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

subgroupindex
C2×#168398842
#214545462
C22×#145197042
#214542682
#214467132
#214465322
#214464692
#214462632
#214461482
#214460962
#214460262
#214456662
#214455832
C61×#30022
#2288661