Finite Group Databasebeta

← #30593970

Subgroups — #30593970

Order 15616.

844 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461642C211yesmaximal, characteristic
2#21460993C211yesmaximal, characteristic
3#21444040C211yesmaximal, characteristic
4C22×C22⋊#6923—21no—
5C2×#14519834—21no—
6C2×#14519834C412yescomplemented
7C2×C22⋊#92420—21no—
8C2×(C2×#6923)⋊C4—21no—
9C2×(C2×#6923)⋊C4C412yescomplemented
10C23×C4×D61C2211yescharacteristic
11C22×#11758198—21no—
12C2×#14519684—21no—
13C2×#14519684C411yescharacteristic, complemented
14C2×#95×C61C411yescharacteristic, complemented
15C23×#6923—22no—
16C22×#92420—22no—
17C2×C22⋊#6923—22no—
18C2×C22⋊#6923—22no—
19C2×C22⋊#6923—41no—
20C2×C22⋊#6923—41no—
21C2×C22⋊#6923—41no—
22C2×C22⋊#6923—41no—
23#14519834—42no—
24#14519834—42no—
25C22⋊#92420—41no—
26C22⋊#92420—41no—
27(C2×#6923)⋊C4—42no—
28(C2×#6923)⋊C4—42no—
29C24×D61D411yescharacteristic
30C23×Dic61—21no—
31C23×Dic61D411yescharacteristic
32C22×C4×D61—42no—
33C22×C4×D61—42no—
34C22×C4×D61—41no—
35C22×C4×D61—41no—
36C22×C4×D61C2×C411yescharacteristic
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61Q811yescharacteristic
40C2×#11758198—24no—
41C2×#11758198—42no—
42C2×#11758198—41no—
43C2×#11758198—41no—
44#14519684—42no—
45#14519684—41no—
46C23×C4×C61—21no—
47C23×C4×C61C2×C411yescharacteristic
48#95×C61—41no—
49C24×C61C22⋊C411yescharacteristic
50C23×D61—21no—
51C23×D61—21no—
52C23×D61—21no—
53C23×D61—21no—
54C23×D61—22no—
55C23×D61—22no—
56C23×D61—41no—
57C23×D61—41no—
58C23×D61C22⋊C411yescharacteristic
59C23×D61C4⋊C411yescharacteristic
60C23×D61D811yescharacteristic
61C23×D61SD1611yescharacteristic
62C23×D61SD1611yescharacteristic
63C23×D61Q1611yescharacteristic
64C22×#6923—24no—
65C22×#6923—42no—
66C22×#6923—42no—
67C22×#6923—42no—
68C22×#6923—42no—
69C22×#6923—42no—
70C22×#6923—42no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—22no—
74C22×C4×C61—41no—
75C22×C4×C61—41no—
76C22×C4×C61—41no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61C4211yescharacteristic
83C22×C4×C61C4⋊C411yescharacteristic
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—22no—
87C22×Dic61—22no—
88C22×Dic61—41no—
89C22×Dic61—41no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94C22×Dic61—41no—
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C4⋊C411yescharacteristic
97C2×C4×D61—22no—
98C2×C4×D61—22no—
99C2×C4×D61—22no—
100C2×C4×D61—22no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C4×D61—41no—
107C2×C4×D61—41no—
108C2×C4×D61—41no—
109C2×C4×D61—48no—
110C2×C4×D61—48no—
111C22⋊#6923—42no—
112C22⋊#6923—42no—
113C22⋊#6923—42no—
114C22⋊#6923—42no—
115C2×#92420—42no—
116C2×#92420—42no—
117C2×#92420—42no—
118#11758198—44no—
119#11758198—44no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61#9511yescharacteristic
125C23×C61#9911yescharacteristic
126C23×C61#9911yescharacteristic
127C23×C61#10211yescharacteristic
128C23×C61#10311yescharacteristic
129C23×C61#10411yescharacteristic
130C23×C61#10411yescharacteristic
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—42no—
158C22×D61—42no—
159C22×D61—42no—
160C22×D61—42no—
161C22×D61—42no—
162C22×D61—42no—
163C22×D61—42no—
164C22×D61—42no—
165C22×D61#9912yes—
166C22×D61#10211yescharacteristic
167C22×D61#10311yescharacteristic
168C22×D61#10412yes—
169C22×D61#10611yescharacteristic
170C22×D61#10711yescharacteristic
171C2×#6923—44no—
172C2×#6923—44no—
173C2×#6923—44no—
174C2×#6923—82no—
175C2×#6923—82no—
176C2×#6923—82no—
177C2×#6923—82no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61—81no—
190C2×C4×C61—81no—
191C2×C4×C61—81no—
192C2×C4×C61—81no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61—42no—
203C2×Dic61—81no—
204C2×Dic61—81no—
205C2×Dic61—81no—
206C2×Dic61—81no—
207C2×Dic61#9912yes—
208C4×D61—44no—
209C4×D61—44no—
210C4×D61—44no—
211C4×D61—44no—
212#92420—82no—
213#7035—611nomaximal, Sylow
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61#32711yescharacteristic
227C22×C61#32711yescharacteristic
228C22×C61#32811yescharacteristic
229C22×C61#32811yescharacteristic
230C22×C61H(3,ℤ/4)11yescharacteristic
231C22×C61#33911yescharacteristic
232C22×C61#33911yescharacteristic
233C22×C61#34011yescharacteristic
234C22×C61#34211yescharacteristic
235C22×C61#34211yescharacteristic
236C22×C61#34211yescharacteristic
237C2×D61—22no—
238C2×D61—22no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—22no—
244C2×D61—22no—
245C2×D61—21no—
246C2×D61—21no—
247C2×D61—21no—
248C2×D61—21no—
249C2×D61—21no—
250C2×D61—21no—
251C2×D61—42no—
252C2×D61—42no—
253C2×D61—42no—
254C2×D61—42no—
255C2×D61—42no—
256C2×D61—42no—
257C2×D61—42no—
258C2×D61—42no—
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C2×D61—41no—
263C2×D61#32712yes—
264C2×D61#32812yes—
265#6923—84no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—82no—
269Dic61—22no—
270Dic61—41no—
271Dic61—82no—
272#1779—611no—
273C22⋊#95—611no—
274C22⋊#95—611no—
275C2×C61—21no—
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—21no—
279C2×C61#128411yescharacteristic
280C2×C61#128411yescharacteristic
281C2×C61#128911yescharacteristic
282C2×C61#129411yescharacteristic
283C2×C61#129411yescharacteristic
284C2×C61#129711yescharacteristic
285C2×C61#130411yescharacteristic
286D61—22no—
287D61—22no—
288D61—41no—
289D61—41no—
290C24×C4—611no—
291C22×C22⋊C4—1221no—
292C22×C22⋊C4—1221no—
293C2×C22⋊C8—612no—
294C2×C22⋊C8—1221no—
295C2×C22⋊C8—1221no—
296C2×#95—612no—
297C2×#95—611no—
298C2×#95—1221no—
299C2×#95—1221no—
300C2×#95#692311yescharacteristic, complemented
301C61#703511yescharacteristic, complemented, Sylow
302C25—611no—
303C23×C4—21no—
304C23×C4—611no—
305C23×C4—611no—
306C23×C4—611no—
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—1222no—
310C23×C4—1221no—
311C23×C4—2441no—
312C23×C4—2441no—
313C23×C4—2442no—
314C23×C4—2442no—
315C23×C4C2×#692311yescharacteristic
316C22×C8—1222no—
317C2×C22⋊C4—1224no—
318C2×C22⋊C4—1222no—
319C2×C22⋊C4—1222no—
320C2×C22⋊C4—2441no—
321C2×C22⋊C4—2441no—
322C2×C22⋊C4—2442no—
323C2×C22⋊C4—2441no—
324C2×C22⋊C4—2441no—
325C2×C22⋊C4—2441no—
326C2×C22⋊C4—2441no—
327C22⋊C8—2441no—
328C22⋊C8—2441no—
329C22⋊C8—2442no—
330C22⋊C8—2442no—
331#95—41no—
332#95—2441no—
333#95—2442no—
334#95—2442no—
335#95—2442no—
336C24—611no—
337C24—611no—
338C24—611no—
339C24—611no—
340C24—611no—
341C24—611no—
342C24—1222no—
343C24—1222no—
344C24—1221no—
345C24—1221no—
346C24—1221no—
347C24—1221no—
348C24—2441no—
349C24—2441no—
350C24C22⋊#692311yescharacteristic
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—1222no—
365C22×C4—1222no—
366C22×C4—1222no—
367C22×C4—1222no—
368C22×C4—1222no—
369C22×C4—1221no—
370C22×C4—1221no—
371C22×C4—1222no—
372C22×C4—1224no—
373C22×C4—2441no—
374C22×C4—2441no—
375C22×C4—2441no—
376C22×C4—2441no—
377C22×C4—2441no—
378C22×C4—2441no—
379C22×C4—2441no—
380C22×C4—2441no—
381C22×C4—2448no—
382C22×C4—2448no—
383C22×C4—2441no—
384C22×C4—2441no—
385C22×C4—2441no—
386C22×C4—2441no—
387C22×C4—2442no—
388C22×C4—2442no—
389C22×C4—2442no—
390C22×C4—2442no—
391C22×C4—2442no—
392C22×C4—2442no—
393C22×C4—2441no—
394C22×C4—2441no—
395C22×C4—2441no—
396C22×C4C4×#692311yescharacteristic
397C22×C4C4⋊#692311yescharacteristic
398C2×C8—2442no—
399C2×C8—2442no—
400C2×C8—2442no—
401C22⋊C4—2444no—
402C22⋊C4—2444no—
403C22⋊C4—2442no—
404C22⋊C4—2442no—
405C22⋊C4—2442no—
406C22⋊C4—2442no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—612no—
412C23—611no—
413C23—611no—
414C23—612no—
415C23—611no—
416C23—611no—
417C23—1222no—
418C23—1222no—
419C23—1222no—
420C23—1222no—
421C23—1221no—
422C23—1221no—
423C23—1221no—
424C23—1221no—
425C23—1221no—
426C23—1221no—
427C23—1221no—
428C23—1221no—
429C23—1221no—
430C23—1221no—
431C23—1221no—
432C23—1221no—
433C23—1221no—
434C23—1221no—
435C23—1221no—
436C23—1221no—
437C23—1221no—
438C23—1221no—
439C23—2441no—
440C23—2441no—
441C23—2441no—
442C23—2441no—
443C23—2442no—
444C23—2442no—
445C23—2442no—
446C23—2442no—
447C23—2442no—
448C23—2442no—
449C23—2442no—
450C23—2442no—
451C23(C2×#6923)⋊C411yescharacteristic
452C23#1451983511yescharacteristic
453C23#1451983611yescharacteristic
454C23#1451983911yescharacteristic
455C23#1451984011yescharacteristic
456C23#1451984111yescharacteristic
457C23#1451984211yescharacteristic
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—612no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—1221no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—4881no—
480C2×C4—4881no—
481C2×C4—4881no—
482C2×C4—4882no—
483C2×C4—4882no—
484C2×C4—4882no—
485C2×C4—4882no—
486C2×C4—4881no—
487C2×C4—2444no—
488C2×C4—2444no—
489C2×C4—2444no—
490C2×C4—2444no—
491C2×C4—2442no—
492C2×C4—2442no—
493C2×C4—2442no—
494C2×C4—2442no—
495C2×C4—2442no—
496C2×C4—2444no—
497C2×C4—2444no—
498C2×C4—2444no—
499C8—4882no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—612no—
513C22—612no—
514C22—1222no—
515C22—1222no—
516C22—1221no—
517C22—1221no—
518C22—1221no—
519C22—1221no—
520C22—1222no—
521C22—1222no—
522C22—1221no—
523C22—1221no—
524C22—1221no—
525C22—1221no—
526C22—1221no—
527C22—1221no—
528C22—2442no—
529C22—2442no—
530C22—2442no—
531C22—2442no—
532C22—2442no—
533C22—2442no—
534C22—2442no—
535C22—2442no—
536C22—2441no—
537C22—2441no—
538C22—2441no—
539C22—2441no—
540C22#1684061311yescharacteristic
541C22#1684061411yescharacteristic
542C22#1684061511yescharacteristic
543C22#1684061611yescharacteristic
544C22#1684062911yescharacteristic
545C22#1684063211yescharacteristic
546C22#1684063311yescharacteristic
547C22#1684063511yescharacteristic
548C22#1684063911yescharacteristic
549C22#1684063911yescharacteristic
550C22#1684064011yescharacteristic
551C4—41no—
552C4—41no—
553C4—82no—
554C4—1222no—
555C4—4882no—
556C4—4884no—
557C4—2441no—
558C2—21no—
559C2—21no—
560C2—21no—
561C2—21no—
562C2—1222no—
563C2—1222no—
564C2—2441no—
565C2—2441no—
566C2#2146066611yescharacteristic
567C2#2146066711yescharacteristic
568C2#2146068111yescharacteristic
569C2#2146069211yescharacteristic
570C2#2146069311yescharacteristic
571C2#2146070011yescharacteristic
572C2#2146071811yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC22×C4×C61C42
FrattiniC23×C4C2×#6923
FittingC2×#95×C61C4
socleC23×C61#95
prime radicalC24×D61D4
cosocleC23×C4×D61C22
hypercenterC2×#95#6923
hypocenterC61#7035
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
6. C2×#14519834C4semidirect
9. C2×(C2×#6923)⋊C4C4semidirect
13. C2×#14519684C4semidirect
14. C2×#95×C61C4semidirect
300. C2×#95#6923semidirect
301. C61#7035semidirect

Maximal subgroups

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

subgroupindex
#214616422
#214609932
#214440402
#703561