Finite Group Databasebeta

← #29700799

Subgroups — #29700799

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839879C211yesmaximal, characteristic, complemented
2#21454546C211yesmaximal, characteristic, complemented
3C2×#16839779C211yesmaximal, characteristic, complemented
4#21454268C211yesmaximal, characteristic, complemented
5#21446713C211yesmaximal, characteristic, complemented
6#21446525C211yesmaximal, characteristic, complemented
7#21446469C211yesmaximal, characteristic, complemented
8#21446268C211yesmaximal, characteristic, complemented
9#21446148C211yesmaximal, characteristic, complemented
10#21446148C211yesmaximal, characteristic, complemented
11#21446096C211yesmaximal, characteristic, complemented
12#21446026C211yesmaximal, characteristic, complemented
13#21445666C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C61×#3002C211yesmaximal, characteristic
16C2×#14519784C2211yescharacteristic
17C2×#14519784C2211yescharacteristic
18C2×#14519784C2211yescharacteristic, complemented
19C22×#11758194C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21#16839879—24no—
22#16839840—21no—
23#16839834—21no—
24#16839834—21no—
25D4×#92418—21no—
26C2×#14519713C2211yescharacteristic, complemented
27C2×#14519713C2211yescharacteristic, complemented
28#16839789C2211yescharacteristic, complemented
29#16839779—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×C8×Dic61C2211yescharacteristic, 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
69#14519784—22no—
70#14519784—22no—
71#14519784—22no—
72#14519784—41no—
73#14519784—41no—
74#14519784—41no—
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C2×#11758194—21no—
79C2×#11758194—22no—
80C2×#11758194—41no—
81C2×#11758194C2311yescharacteristic
82C2×#11758194C2311yescharacteristic
83C2×#11758194C2311yescharacteristic
84C2×#11758194C2311yescharacteristic
85C22×#92418—21no—
86C22×#92418—21no—
87C22×#92418—21no—
88C22×#92418—21no—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91#14519736—22no—
92#14519736—41no—
93C2×C4⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
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—41no—
121C4×#92418—21no—
122C8×Dic61—22no—
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
144C2×Q16×C61C2×C411yescharacteristic
145C2×SD16×C61C2×C411yescharacteristic
146C2×SD16×C61C2×C411yescharacteristic
147C2×SD16×C61C2×C411yescharacteristic
148C2×SD16×C61C2×C411yescharacteristic
149C2×D8×C61C2×C411yescharacteristic
150C2×D8×C61C2×C411yescharacteristic
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
163#103×C61C2×C411yescharacteristic
164#103×C61C2×C411yescharacteristic
165#103×C61C2×C411yescharacteristic
166#102×C61C2×C411yescharacteristic
167#102×C61C2×C411yescharacteristic
168#102×C61C2×C411yescharacteristic
169#102×C61C2×C411yescharacteristic
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—
237Q16×C61—22no—
238Q16×C61—41no—
239SD16×C61—22no—
240SD16×C61—22no—
241SD16×C61—41no—
242SD16×C61—41no—
243D8×C61—22no—
244D8×C61—41no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61C22×C411yescharacteristic
250C2×C8×C61C22×C411yescharacteristic
251C2×C8×C61C22×C411yescharacteristic
252C2×C8×C61C22×C411yescharacteristic
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61C22×C411yescharacteristic
256C4⋊C4×C61C22×C411yescharacteristic
257C22⋊C4×C61—21no—
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C42×C61—21no—
263C22⋊Dic61—42no—
264C4⋊Dic61—42no—
265C4×Dic61—21no—
266C4×Dic61—21no—
267C4×Dic61—21no—
268C4×Dic61C2×D412yes—
269#11758194—21no—
270#11758194—21no—
271#11758194—21no—
272#11758194—21no—
273#11758194—21no—
274#11758194—21no—
275#11758194—21no—
276#11758194—42no—
277#11758194—42no—
278#11758194—42no—
279#11758194—42no—
280#11758194C2×D412yes—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—42no—
290C2×#92418—42no—
291C2×#92418—42no—
292C2×#92418—42no—
293C2×#92418C2×D411yescharacteristic
294C2×#92418C2×D411yescharacteristic
295C2×#92418C2×D411yescharacteristic
296C2×#92418C2×D411yescharacteristic
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—81no—
307C23×C61C4×D411yescharacteristic
308C23×C61C4×D411yescharacteristic
309C23×C61C2×#4111yescharacteristic
310Q8×C61—21no—
311Q8×C61—21no—
312Q8×C61—21no—
313Q8×C61—21no—
314Q8×C61—21no—
315Q8×C61—42no—
316Q8×C61C4×D412yes—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—21no—
320D4×C61—21no—
321D4×C61—21no—
322D4×C61—21no—
323D4×C61—21no—
324D4×C61—42no—
325D4×C61—42no—
326D4×C61—42no—
327D4×C61—42no—
328D4×C61—41no—
329D4×C61—41no—
330D4×C61—41no—
331D4×C61—41no—
332D4×C61—81no—
333D4×C61C4×D412yes—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
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—22no—
343C2×C4×C61—21no—
344C2×C4×C61—22no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—42no—
352C2×C4×C61—42no—
353C2×C4×C61—42no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61C4×D411yescharacteristic
359C2×C4×C61C4×D411yescharacteristic
360C2×C4×C61C23×C411yescharacteristic
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C2×#4111yescharacteristic
364C2×C4×C61H(5,𝔽2)11yescharacteristic
365C2×C4×C61H(5,𝔽2)11yescharacteristic
366C2×Dic61—22no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C8×C61—21no—
373C8×C61—21no—
374C8×C61—21no—
375C8×C61—21no—
376#92418—21no—
377#92418—21no—
378#92418—22no—
379#92418—21no—
380#92418—21no—
381#92418—41no—
382#92418—41no—
383#92418—41no—
384#22889—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—22no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—84no—
405C22×C61C2×C4×D411yescharacteristic
406C22×C61#54611yescharacteristic
407C22×C61#55111yescharacteristic
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—22no—
411C4×C61—41no—
412C4×C61—41no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61C2×C4×D411yescharacteristic
416C4×C61#51811yescharacteristic
417C4×C61D4211yescharacteristic
418C4×C61#54611yescharacteristic
419Dic61—42no—
420Dic61—81no—
421#3002D6111yescharacteristic
422C2×#443—611no—
423#2933—611no—
424C2×#421—611no—
425#2880—611no—
426#1975—611no—
427#1937—611no—
428#1929—611no—
429#1897—611no—
430#1876—611no—
431#1876—611no—
432#1866—611no—
433#1855—611no—
434#1765—611no—
435#1750—611no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—41no—
439C2×C61—41no—
440C2×C61—42no—
441C2×C61—81no—
442C2×C61—81no—
443C2×C61#235811yescharacteristic
444C2×C61#295511yescharacteristic
445C2×C61#295711yescharacteristic
446C22×#41C2×D6111yescharacteristic
447C2×#135C2×D6111yescharacteristic
448C2×#135C2×D6111yescharacteristic
449C2×#131—611no—
450C2×#131—611no—
451C2×#131—611no—
452C22×M16—611no—
453#525C2×D6111yescharacteristic
454C2×#117—611no—
455#452Dic6111yescharacteristic, complemented
456#452Dic6111yescharacteristic, complemented
457#451Dic6111yescharacteristic, complemented
458#450Dic6111yescharacteristic, complemented
459#449Dic6111yescharacteristic, complemented
460#449Dic6111yescharacteristic, complemented
461#448Dic6111yescharacteristic, complemented
462#447Dic6111yescharacteristic, complemented
463#443—1224no—
464#436—1221no—
465#435—1221no—
466#435—1221no—
467C8×D4—1221no—
468C2×#108—611no—
469C2×#108—611no—
470#424—611no—
471#421—1224no—
472C2×#104—611no—
473C2×#104—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104—611no—
478#416C2×D6111yescharacteristic
479#416C2×D6111yescharacteristic
480#408—611no—
481#408—611no—
482#408—611no—
483#408—1221no—
484#408—1221no—
485#407—611no—
486#407—1221no—
487C2×C22⋊C8—611no—
488C2×C22⋊C8—1221no—
489C2×C22⋊C8C2×D6111yescharacteristic
490#405—611no—
491C2×#97—611no—
492C2×C4×C8—611no—
493#341—611no—
494#341—611no—
495#339—611no—
496#339—611no—
497#336—611no—
498#336—611no—
499C61#2288911yescharacteristic, complemented, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×Dic6111yescharacteristic
507C2×#41C2×Dic6111yescharacteristic
508C2×#41C22×D6111yescharacteristic
509C2×#41C22×D6111yescharacteristic
510C2×#41C22×D6111yescharacteristic
511C22×Q8C2×Dic6111yescharacteristic
512C22×D4—21no—
513C22×D4C2×Dic6111yescharacteristic
514C23×C4—21no—
515C23×C4C22×D6111yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×Dic6111yescharacteristic
521C2×Q16C2×Dic6111yescharacteristic
522C2×SD16C2×Dic6111yescharacteristic
523C2×SD16C2×Dic6111yescharacteristic
524C2×SD16C2×Dic6111yescharacteristic
525C2×SD16C2×Dic6111yescharacteristic
526C2×D8C2×Dic6111yescharacteristic
527C2×D8C2×Dic6111yescharacteristic
528#131—1222no—
529#131—1222no—
530#131—1222no—
531#131—2441no—
532#131—2441no—
533#131—2441no—
534C2×M16—611no—
535C2×M16—611no—
536C2×M16—611no—
537C2×M16—611no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16—1222no—
543C2×M16—2441no—
544C22×C8—611no—
545C22×C8—611no—
546C22×C8—1221no—
547C22×C8—1221no—
548C22×C8—1221no—
549C22×C8—1221no—
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552#123—21no—
553C22⋊Q8C2×Dic6111yescharacteristic
554C22⋊Q8C2×Dic6111yescharacteristic
555#121C2×Dic6111yescharacteristic
556#121C2×Dic6111yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—1222no—
561#117—2441no—
562#117C22×D6111yescharacteristic
563C2×C4⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C42—611no—
566C2×C42—611no—
567#108—1222no—
568#108—2441no—
569C4⋊C8—1221no—
570C4⋊C8—1221no—
571#104—614no—
572#104—1222no—
573#104—1222no—
574#104—1222no—
575#104—1222no—
576#104—2441no—
577#103C2×Dic6111yescharacteristic
578#103C2×Dic6111yescharacteristic
579#103C2×Dic6111yescharacteristic
580#103C2×Dic6111yescharacteristic
581#102C2×Dic6111yescharacteristic
582#102C2×Dic6111yescharacteristic
583#102C2×Dic6111yescharacteristic
584#102C2×Dic6111yescharacteristic
585C22⋊C8—611no—
586C22⋊C8—611no—
587C22⋊C8—611no—
588C22⋊C8—611no—
589C22⋊C8—1221no—
590C22⋊C8—1221no—
591C22⋊C8—1221no—
592C22⋊C8—1221no—
593C22⋊C8—1221no—
594C22⋊C8—1221no—
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597C22⋊C8C2×Dic6111yescharacteristic
598C22⋊C8C2×Dic6111yescharacteristic
599C22⋊C8C2×Dic6111yescharacteristic
600C22⋊C8C2×Dic6111yescharacteristic
601#97—1221no—
602#97—2441no—
603C4×C8—1221no—
604C4×C8—1222no—
605C24—21no—
606C24#1175822411yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41D4×D6112yes—
626#41#1175822412yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×Dic6111yescharacteristic
631C2×Q8C22×Dic6111yescharacteristic
632C2×Q8C22×Dic6111yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×Dic6111yescharacteristic
646C2×D4C22×Dic6111yescharacteristic
647C2×D4C22×Dic6111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4D4×D6111yescharacteristic
663C22×C4D4×D6111yescharacteristic
664C22×C4#1175822411yescharacteristic
665C22×C4C22×Dic6111yescharacteristic
666C22×C4C22×Dic6111yescharacteristic
667C22×C4C23×D6111yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—612no—
677M16—1221no—
678M16—1221no—
679M16—1221no—
680M16—1221no—
681M16—1221no—
682M16—1221no—
683M16—1221no—
684M16—2442no—
685M16—2442no—
686M16—2442no—
687M16—2442no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—611no—
693C2×C8—611no—
694C2×C8—611no—
695C2×C8—611no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—1221no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—2442no—
705C2×C8—2442no—
706C2×C8—2442no—
707C2×C8—2442no—
708C2×C8C22×Dic6111yescharacteristic
709C2×C8C22×Dic6111yescharacteristic
710C2×C8C22×Dic6111yescharacteristic
711C2×C8C22×Dic6111yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—2442no—
715C4⋊C4C22×Dic6111yescharacteristic
716C4⋊C4C22×Dic6111yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—2442no—
723C42—21no—
724C42—612no—
725C42—1221no—
726C42—1221no—
727C42—1221no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23D4×Dic6111yescharacteristic
739C23D4×Dic6111yescharacteristic
740C23C2×#1175822411yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8D4×Dic6112yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4D4×Dic6112yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—1222no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4D4×Dic6111yescharacteristic
796C2×C4D4×Dic6111yescharacteristic
797C2×C4C23×Dic6111yescharacteristic
798C2×C4C2×D4×D6111yescharacteristic
799C2×C4C2×D4×D6111yescharacteristic
800C2×C4C2×#1175822411yescharacteristic
801C2×C4#1451982211yescharacteristic
802C2×C4#1451982211yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—1221no—
808C8—1221no—
809C8—1222no—
810C8—1221no—
811C8—1221no—
812C8—2441no—
813C8—2441no—
814C8—2441no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×D4×Dic6111yescharacteristic
836C22#1684039911yescharacteristic
837C22#1684044311yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—4881no—
846C4—2442no—
847C4C2×D4×Dic6111yescharacteristic
848C4#1684023711yescharacteristic
849C4#1684039411yescharacteristic
850C4#1684039911yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2#2144880311yescharacteristic
859C2#2145472211yescharacteristic
860C2#2145473611yescharacteristic
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#22889
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×#16839879C2semidirect
2. #21454546C2semidirect
3. C2×#16839779C2semidirect
4. #21454268C2semidirect
5. #21446713C2semidirect
6. #21446525C2semidirect
7. #21446469C2semidirect
8. #21446268C2semidirect
9. #21446148C2semidirect
10. #21446148C2semidirect
11. #21446096C2semidirect
12. #21446026C2semidirect
13. #21445666C2semidirect
14. #21445587C2semidirect
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×C8×Dic61C22semidirect
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
455. #452Dic61semidirect
456. #452Dic61semidirect
457. #451Dic61semidirect
458. #450Dic61semidirect
459. #449Dic61semidirect
460. #449Dic61semidirect
461. #448Dic61semidirect
462. #447Dic61semidirect
499. C61#22889semidirect

Maximal subgroups

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

subgroupindex
C2×#168398792
#214545462
C2×#168397792
#214542682
#214467132
#214465252
#214464692
#214462682
#214461482
#214460962
#214460262
#214456662
#214455872
C61×#30022
#2288961