Finite Group Databasebeta

← #30600096

Subgroups — #30600096

Order 15616.

594 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462312C211yesmaximal, characteristic
2#21461723C211yesmaximal, characteristic
3D61⋊#328C211yesmaximal, characteristic
4#21461008C211yesmaximal, characteristic
5#21460694C211yesmaximal, characteristic
6#21460656C211yesmaximal, characteristic
7#484×D61C211yesmaximal, characteristic
8D61⋊(C22⋊C8)C2211yescharacteristic
9(C2×#6923)⋊Q8—21no—
10#16840713—21no—
11#16840711—21no—
12#16840711—21no—
13#16840709—21no—
14#16840704C2211yescharacteristic
15C22⋊C4×#6923—21no—
16C2×(C2×#6923)⋊C4—21no—
17C2×(C2×#6923)⋊C4—21no—
18C2×(C2×#6923)⋊C4C2211yescharacteristic
19C2×(C2×#6923)⋊C4C2211yescharacteristic
20#16840635—21no—
21#16840635—21no—
22#16840616—21no—
23#16840615—21no—
24C22⋊Q8×D61C2211yescharacteristic
25C2×C4⋊C4×D61C2211yescharacteristic
26#16840099—21no—
27#16840098C411yescharacteristic, complemented
28#16840097C411yescharacteristic, complemented
29#16840096—21no—
30#16840095C411yescharacteristic, complemented
31#107×D61—21no—
32#103×D61—21no—
33C22⋊C8×D61C2211yescharacteristic
34C61×#484C411yescharacteristic, complemented
35C23×#6923—21no—
36C23×#6923D411yescharacteristic
37C23×#6923D411yescharacteristic
38C2×D61⋊C8—21no—
39C2×C4⋊#6923—21no—
40C2×C4⋊#6923—21no—
41C2×C4⋊#6923D411yescharacteristic
42C2×C4⋊#6923D411yescharacteristic
43C2×C22⋊#6923—21no—
44C2×C4×#6923—21no—
45C2×C4×#6923—21no—
46#14519834—21no—
47C22⋊#92420—21no—
48(C2×#6923)⋊C4—21no—
49(C2×#6923)⋊C4—21no—
50(C2×#6923)⋊C4—21no—
51(C2×#6923)⋊C4—21no—
52(C2×#6923)⋊C4—21no—
53(C2×#6923)⋊C4—21no—
54(C2×#6923)⋊C4—21no—
55(C2×#6923)⋊C4—21no—
56(C2×#6923)⋊C4—21no—
57(C2×#6923)⋊C4—42no—
58(C2×#6923)⋊C4—42no—
59C2×Q8×D61D411yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61C2311yescharacteristic
62C2×C8×D61—21no—
63#14519757D411yescharacteristic
64#14519756C2×C411yescharacteristic
65#14519755—21no—
66#14519754—21no—
67#14519753D411yescharacteristic
68C2×C4⋊Dic61C2×C411yescharacteristic
69C2×#11758196—21no—
70C4⋊C4×D61—21no—
71C4⋊C4×D61—21no—
72C4⋊C4×D61—21no—
73C4⋊C4×D61—21no—
74C4⋊C4×D61—21no—
75C4⋊C4×D61D411yescharacteristic
76C22⋊C4×D61—21no—
77#14519711—21no—
78#14519710—21no—
79#14519710—21no—
80#14519702—21no—
81#14519701—21no—
82#14519700—21no—
83C22⋊#92418C2×C411yescharacteristic
84#14519689—21no—
85C22⋊Q8×C61C2×C411yescharacteristic
86C2×C4⋊C4×C61C2×C411yescharacteristic
87#107×C61—21no—
88#103×C61—21no—
89C22⋊C8×C61C2×C411yescharacteristic
90C23×D61C2×D411yescharacteristic
91C22×#6923—21no—
92C22×#6923—21no—
93C22×#6923—22no—
94C22×#6923—21no—
95C22×#6923—21no—
96C22×#6923—21no—
97C22×#6923—21no—
98C22×#6923—21no—
99C22×#6923—41no—
100C22×#6923—41no—
101C22×#6923—41no—
102C22×#6923—41no—
103C22×#6923—41no—
104C22×#6923—41no—
105C22×#6923—41no—
106C22×#6923—41no—
107C22×#6923—41no—
108C22×#6923—41no—
109C22×#6923Q1612yes—
110C2×Q8×C61C22⋊C411yescharacteristic
111C22×C4×C61—21no—
112C22×C4×C61C22×C411yescharacteristic
113C22×Dic61—21no—
114C22×Dic61#4111yescharacteristic
115Q8×D61—41no—
116Q8×D61—41no—
117C2×C4×D61—21no—
118C2×C4×D61—21no—
119C2×C4×D61—41no—
120C2×C4×D61—41no—
121C2×C4×D61—41no—
122C2×C4×D61—41no—
123C2×C4×D61—41no—
124C2×C4×D61—41no—
125C2×C4×D61—41no—
126C2×C4×D61—41no—
127C2×C4×D61C2×D411yescharacteristic
128C2×C4×D61C2×D411yescharacteristic
129C2×C4×D61C2×D411yescharacteristic
130C2×C4×D61#4111yescharacteristic
131C2×Dic122—21no—
132C2×Dic122C22⋊C411yescharacteristic
133C22⋊#6923—41no—
134C22⋊#6923—41no—
135C2×#92420—41no—
136C4⋊#6923—41no—
137C4⋊#6923—41no—
138C4⋊#6923—81no—
139C4⋊#6923—81no—
140C4×#6923—81no—
141C4×#6923—81no—
142D61⋊C8—41no—
143D61⋊C8—41no—
144C2×C8×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61C22⋊C411yescharacteristic
149C22⋊C4×C61—21no—
150C22⋊Dic61—21no—
151#11758198—21no—
152#11758198—21no—
153C4⋊Dic61—21no—
154C4⋊Dic61—21no—
155C4⋊Dic61—21no—
156C4⋊Dic61C22⋊C411yescharacteristic
157#11758196—21no—
158#11758196—21no—
159#11758196—21no—
160#11758196—41no—
161#11758196—41no—
162C2×#92418—21no—
163C8×D61—41no—
164C8×D61—41no—
165C23×C61C4×D411yescharacteristic
166C22×D61—21no—
167C22×D61—21no—
168C22×D61—21no—
169C22×D61—21no—
170C22×D61#12011yescharacteristic
171C22×D61#12111yescharacteristic
172C22×D61C2×Q1611yescharacteristic
173C22×D61#13511yescharacteristic
174C22×D61#13711yescharacteristic
175C22×D61#13711yescharacteristic
176C2×#6923—22no—
177C2×#6923—41no—
178C2×#6923—41no—
179C2×#6923—42no—
180C2×#6923—42no—
181C2×#6923—42no—
182C2×#6923—42no—
183C2×#6923—42no—
184C2×#6923—41no—
185C2×#6923—41no—
186C2×#6923—41no—
187C2×#6923—41no—
188C2×#6923—41no—
189C2×#6923—41no—
190C2×#6923—41no—
191C2×#6923—41no—
192C2×#6923—41no—
193C2×#6923—81no—
194C2×#6923—81no—
195C2×#6923—81no—
196C2×#6923—81no—
197C2×#6923—81no—
198C2×#6923—81no—
199Q8×C61—41no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61C2×C22⋊C411yescharacteristic
207C2×C4×C61C4×D411yescharacteristic
208C2×Dic61—21no—
209C2×Dic61—21no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61#12111yescharacteristic
215C2×Dic61#12311yescharacteristic
216C4×D61—21no—
217C4×D61—21no—
218C4×D61—21no—
219C4×D61—21no—
220C4×D61—41no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—41no—
224C4×D61—41no—
225C4×D61—41no—
226C4×D61—81no—
227C4×D61—81no—
228C4×D61—81no—
229C4×D61—81no—
230Dic122—41no—
231Dic122—81no—
232#92420—81no—
233C8×C61—41no—
234#92418—41no—
235#9046—611nomaximal, Sylow
236C22×C61—21no—
237C22×C61—21no—
238C22×C61#38611yescharacteristic
239C22×C61C4×Q1611yescharacteristic
240C22×C61#44111yescharacteristic
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—21no—
247C2×D61—21no—
248C2×D61—21no—
249C2×D61—21no—
250C2×D61—21no—
251C2×D61#45111yescharacteristic
252C2×D61#45211yescharacteristic
253C2×D61#45311yescharacteristic
254C2×D61#45411yescharacteristic
255C2×D61#45811yescharacteristic
256C2×D61#45811yescharacteristic
257C2×D61#46211yescharacteristic
258C2×D61#46411yescharacteristic
259#6923—42no—
260#6923—82no—
261#6923—81no—
262#6923—81no—
263#6923—81no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—81no—
269Dic61—21no—
270Dic61—21no—
271Dic61—41no—
272Dic61—41no—
273Dic61—81no—
274C2×#484—611no—
275#2329—611no—
276#1824—611no—
277C2×#328—611no—
278#1445—611no—
279#1294—611no—
280#1280—611no—
281C2×C61—21no—
282C2×C61—21no—
283C2×C61#187811yescharacteristic
284C2×C61#188311yescharacteristic
285C2×C61#189011yescharacteristic
286D61—21no—
287D61—21no—
288D61#161411yescharacteristic
289D61#161511yescharacteristic
290D61#161711yescharacteristic
291D61#161811yescharacteristic
292C2×C22⋊Q8—611no—
293C22×C4⋊C4—611no—
294#484—611no—
295#484—611no—
296#484—611no—
297#484—1221no—
298#484—1221no—
299#484#692311yescharacteristic, complemented
300C2×#107—1221no—
301C2×#103—1221no—
302C2×C22⋊C8—611no—
303C2×C22⋊C8—611no—
304#391—1221no—
305#389—1221no—
306#387—1221no—
307#387—1221no—
308#385—1221no—
309#380—611no—
310C4×C22⋊C4—1221no—
311C2×#95—611no—
312C2×#95—611no—
313C2×#95—1221no—
314C2×#95—1221no—
315#340—1221no—
316#340—1221no—
317#328—1221no—
318#328—1221no—
319C61#904611yescharacteristic, complemented, Sylow
320C22×Q8—611no—
321C23×C4—611no—
322C23×C4—611no—
323C23×C4—611no—
324C23×C4—1221no—
325C23×C4—1221no—
326C22×C8—1221no—
327C22×C8—1221no—
328C22⋊Q8—611no—
329C22⋊Q8—611no—
330C22⋊Q8—611no—
331C22⋊Q8—1221no—
332C22⋊Q8—1221no—
333C22⋊Q8C2×#692311yescharacteristic
334C2×C4⋊C4—611no—
335C2×C4⋊C4—611no—
336C2×C4⋊C4—611no—
337C2×C4⋊C4—611no—
338C2×C4⋊C4—1221no—
339C2×C4⋊C4—1221no—
340C2×C4⋊C4—1221no—
341C2×C4⋊C4—1221no—
342C2×C4⋊C4—1221no—
343C2×C4⋊C4—1221no—
344C2×C4⋊C4—1221no—
345C2×C4⋊C4—1221no—
346C2×C4⋊C4C2×#692311yescharacteristic
347C2×C22⋊C4—1221no—
348C2×C22⋊C4—1221no—
349C2×C42—1221no—
350C2×C42—1221no—
351#107—21no—
352#107—1221no—
353#107—1221no—
354#107—1221no—
355#103—21no—
356#103—1221no—
357#103—1221no—
358#103—1221no—
359C22⋊C8—611no—
360C22⋊C8—1221no—
361C22⋊C8—1221no—
362C22⋊C8—1221no—
363C22⋊C8C2×#692311yescharacteristic
364#95—1221no—
365#95—1221no—
366#95—1221no—
367#95—1221no—
368#95—1221no—
369#95—1221no—
370#95—1221no—
371#95—1221no—
372#95—1221no—
373#95—2442no—
374#95—2442no—
375C24—611no—
376C2×Q8—611no—
377C2×Q8—1221no—
378C2×Q8—2441no—
379C2×Q8—2441no—
380C2×Q8C22⋊#692311yescharacteristic
381C22×C4—21no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—612no—
388C22×C4—1221no—
389C22×C4—1221no—
390C22×C4—1221no—
391C22×C4—1221no—
392C22×C4—1221no—
393C22×C4—1221no—
394C22×C4—1221no—
395C22×C4—1221no—
396C22×C4—1221no—
397C22×C4—1222no—
398C22×C4—1221no—
399C22×C4—2441no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4—2441no—
405C22×C4—2441no—
406C22×C4—2441no—
407C22×C4—2441no—
408C22×C4—2441no—
409C22×C4—2441no—
410C22×C4—2441no—
411C22×C4—2441no—
412C22×C4—2441no—
413C22×C4—2441no—
414C22×C4—2441no—
415C22×C4—2441no—
416C22×C4—2441no—
417C22×C4C22×#692311yescharacteristic
418C2×C8—21no—
419C2×C8—1221no—
420C2×C8—2441no—
421C2×C8—2441no—
422C2×C8—2441no—
423C2×C8—2441no—
424C2×C8—2441no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—611no—
429C4⋊C4—1221no—
430C4⋊C4—1221no—
431C4⋊C4—1221no—
432C4⋊C4—1221no—
433C4⋊C4—1221no—
434C4⋊C4—1221no—
435C4⋊C4—4881no—
436C4⋊C4—4881no—
437C4⋊C4—2441no—
438C4⋊C4—2441no—
439C4⋊C4—2441no—
440C4⋊C4—2441no—
441C4⋊C4C22⋊#692311yescharacteristic
442C22⋊C4—21no—
443C22⋊C4—1221no—
444C22⋊C4—1221no—
445C22⋊C4—1221no—
446C22⋊C4—2441no—
447C22⋊C4—2441no—
448C42—4881no—
449C42—4881no—
450C23—611no—
451C23—611no—
452C23—611no—
453C23—611no—
454C23—611no—
455C23—611no—
456C23—1221no—
457C23—1221no—
458C23—1221no—
459C23—1221no—
460C23D4×#692311yescharacteristic
461Q8—41no—
462Q8—4881no—
463Q8—2441no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—611no—
471C2×C4—611no—
472C2×C4—1221no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—1222no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—4881no—
480C2×C4—4881no—
481C2×C4—4881no—
482C2×C4—4881no—
483C2×C4—4881no—
484C2×C4—4881no—
485C2×C4—4881no—
486C2×C4—4881no—
487C2×C4—4881no—
488C2×C4—4881no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4—2441no—
498C2×C4—2441no—
499C2×C4—2441no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4—2441no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4—2442no—
508C2×C4—2442no—
509C2×C4—2442no—
510C2×C4—2442no—
511C2×C4—2441no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4—2442no—
515C2×C4C2×C22⋊#692311yescharacteristic
516C2×C4D4×#692311yescharacteristic
517C8—41no—
518C8—4881no—
519C8—2441no—
520C22—21no—
521C22—21no—
522C22—611no—
523C22—611no—
524C22—611no—
525C22—611no—
526C22—611no—
527C22—611no—
528C22—611no—
529C22—611no—
530C22—1221no—
531C22—1221no—
532C22—1221no—
533C22—1221no—
534C22—1221no—
535C22—1221no—
536C22—1221no—
537C22—1221no—
538C22—1221no—
539C22—1221no—
540C22#1684071011yescharacteristic
541C22Q16×#692311yescharacteristic
542C22#1684080211yescharacteristic
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—81no—
548C4—1221no—
549C4—1221no—
550C4—4881no—
551C4—4881no—
552C4—4881no—
553C4—4882no—
554C4—4881no—
555C4—2442no—
556C4—2441no—
557C4—2441no—
558C2—21no—
559C2—21no—
560C2—611no—
561C2—611no—
562C2—611no—
563C2—611no—
564C2—1221no—
565C2—1221no—
566C2#2146181311yescharacteristic
567C2#2146181911yescharacteristic
568C2#2146182911yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#484C4
socleC22×C61#386
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#484#6923
hypocenterC61#9046
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
27. #16840098C4semidirect
28. #16840097C4semidirect
30. #16840095C4semidirect
34. C61×#484C4semidirect
299. #484#6923semidirect
319. C61#9046semidirect

Maximal subgroups

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

subgroupindex
#214623122
#214617232
D61⋊#3282
#214610082
#214606942
#214606562
#484×D612
#904661