Finite Group Databasebeta

← #30606503

Subgroups — #30606503

Order 15616.

576 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C2×#16840665C212yesmaximal
2#21461569C211yesmaximal, characteristic
3#21461566C211yesmaximal, characteristic
4#21460903C212yesmaximal
5#21448338C211yesmaximal, characteristic
6C2×#14519837C2212yes—
7C2×#14519835C2212yes—
8C4×#11758217—21no—
9C4×C22⋊#6923—21no—
10#16840665C418yescomplemented
11#16840642—21no—
12#16840640—21no—
13C2×#14519761C2211yescharacteristic
14C2×#14519737C2211yescharacteristic
15C22×C4×Dic61C411yescharacteristic, complemented
16#16839652—21no—
17#16839645—21no—
18#16839641C2211yescharacteristic
19#16839623C411yescharacteristic, complemented
20C4⋊C4×Dic61—21no—
21C22⋊C4×Dic61C411yescharacteristic, complemented
22#16839609—21no—
23C61×#385C411yescharacteristic, complemented
24C2×#11758217—22no—
25C2×C22⋊#6923—22no—
26C2×C4×#6923—41no—
27#14519837—22no—
28#14519837C2×C414yes—
29#14519835—22no—
30#14519835C2×C414yes—
31#14519832—41no—
32C4×#92420—41no—
33(C2×#6923)⋊C4—41no—
34C22×C22⋊D61C2311yescharacteristic
35C23×Dic61C2×C411yescharacteristic
36C23×Dic61C2×C411yescharacteristic
37C22×C4×D61D411yescharacteristic
38#14519761—22no—
39#14519761C2×C414yes—
40#14519737—41no—
41#14519737—41no—
42C2×C4⋊Dic61—21no—
43C2×#11758196D411yescharacteristic
44C2×C22⋊Dic61C2×C411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198D411yescharacteristic
48C2×C4×Dic61—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—21no—
51C2×C4×Dic61—41no—
52C2×C4×Dic61—41no—
53C2×C4×Dic61D411yescharacteristic
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58C23×C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61—21no—
60C2×C22⋊C4×C61C2×C411yescharacteristic
61C2×C22⋊C4×C61C2×C411yescharacteristic
62#95×C61—21no—
63C24×C61C22×C411yescharacteristic
64C23×D61C2×D411yescharacteristic
65C22×#6923—42no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—42no—
69C22×C4×C61—41no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61C22×C412yes—
75C2×C22⋊D61#4112yes—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—42no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61C4212yescomplemented
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C2×D411yescharacteristic
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—42no—
91C22⋊#6923—24no—
92C22⋊#6923—42no—
93#11758217—24no—
94#11758217—42no—
95C2×#92420—42no—
96C4×#6923—82no—
97C4⋊C4×C61—42no—
98C22⋊C4×C61—21no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61C4212yescomplemented
101C22⋊Dic61—41no—
102#11758198—24no—
103#11758198—41no—
104#11758198—42no—
105C4⋊Dic61—24no—
106#11758196—41no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—42no—
110C4×Dic61—42no—
111C4×Dic61—41no—
112C4×Dic61—41no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61C2×C4211yescharacteristic
118C23×C61C2×C22⋊C411yescharacteristic
119C23×C61#11711yescharacteristic
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61C4×D412yes—
125C2×#6923—44no—
126C2×#6923—82no—
127C2×#6923—82no—
128C2×C4×C61—22no—
129C2×C4×C61—22no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—42no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C22⋊D61—42no—
141C22⋊D61—42no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—21no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—42no—
152C2×Dic61—42no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61#9911yescharacteristic
158C2×Dic61#9911yescharacteristic
159C2×Dic61C4×D412yes—
160C4×D61—42no—
161C4×D61—81no—
162#92420—44no—
163C4×#352—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—42no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61C4×C22⋊C411yescharacteristic
174C22×C61C2×#9911yescharacteristic
175C22×C61#41011yescharacteristic
176C2×D61—22no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—42no—
180C2×D61—81no—
181#6923—84no—
182C4×C61—42no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—42no—
186Dic61—21no—
187Dic61—22no—
188Dic61—41no—
189Dic61—42no—
190Dic61—81no—
191Dic61#35212yescomplemented
192C4×#123—611no—
193C2×#352—612no—
194C4×#100—611no—
195C4×#99—611no—
196#1390—612no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61—41no—
200C2×C61—41no—
201C2×C61C4×#9911yescharacteristic
202C2×C61C2×#35211yescharacteristic
203C2×C61#212011yescharacteristic
204D61—42no—
205C2×#123—611no—
206C2×C4×D4—611no—
207C22×C42—611no—
208C2×#100—612no—
209C2×#99—612no—
210C4×M16—1221no—
211#388—1221no—
212#387—1221no—
213#386—611no—
214#385#692311yescharacteristic, complemented
215#381—611no—
216C4×C4⋊C4—1221no—
217C4×C22⋊C4—611no—
218C4×C22⋊C4—1221no—
219C4×C22⋊C4—1221no—
220#352—618no—
221#343—1221no—
222#342—1221no—
223C61C4×#35211yescharacteristic, complemented, Sylow
224C22×D4—611no—
225C23×C4—611no—
226C23×C4—611no—
227C23×C4—611no—
228C23×C4C2×#692311yescharacteristic
229C2×M16—1222no—
230#123—614no—
231#123—1222no—
232C4×D4—2441no—
233C4×D4—2441no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1221no—
237C2×C22⋊C4—611no—
238C2×C22⋊C4—611no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1222no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4C2×#692311yescharacteristic
243C2×C22⋊C4C2×#692311yescharacteristic
244C2×C42—611no—
245C2×C42—1221no—
246C2×C42—1221no—
247C2×C42—1221no—
248C2×C42—2441no—
249C2×C42—2441no—
250C2×C42—2441no—
251#100—614no—
252#100—1222no—
253#99—614no—
254#99—1222no—
255#97—2441no—
256C4×C8—2441no—
257#95—21no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95—2441no—
263C24—611no—
264C24C22×#692311yescharacteristic
265C2×D4—612no—
266C2×D4—612no—
267C2×D4—2441no—
268C2×D4—2441no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—42no—
272C22×C4—41no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—612no—
276C22×C4—611no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—2442no—
285C22×C4—2442no—
286C22×C4—2442no—
287C22×C4—2441no—
288C22×C4—2441no—
289C22×C4C22⋊#692311yescharacteristic
290C22×C4C22⋊#692311yescharacteristic
291M16—1224no—
292M16—2442no—
293C2×C8—2442no—
294C4⋊C4—42no—
295C4⋊C4—1224no—
296C4⋊C4—2441no—
297C22⋊C4—21no—
298C22⋊C4—41no—
299C22⋊C4—1224no—
300C22⋊C4—1224no—
301C22⋊C4—2441no—
302C22⋊C4—2442no—
303C22⋊C4—2442no—
304C22⋊C4—2441no—
305C22⋊C4C4×#692312yescomplemented
306C42—1221no—
307C42—1221no—
308C42—4882no—
309C42—2441no—
310C42—2441no—
311C42—2442no—
312C42—2442no—
313C23—21no—
314C23—21no—
315C23—41no—
316C23—41no—
317C23—612no—
318C23—1221no—
319C23—1221no—
320C23—2441no—
321C23—2441no—
322C23C2×C4×#692311yescharacteristic
323C23C2×C22⋊#692311yescharacteristic
324C23#1451985611yescharacteristic
325D4—2442no—
326D4—2442no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—611no—
340C2×C4—611no—
341C2×C4—612no—
342C2×C4—1222no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1222no—
347C2×C4—4881no—
348C2×C4—4882no—
349C2×C4—4882no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2444no—
356C2×C4—2441no—
357C2×C4—2442no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2442no—
362C8—2444no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—42no—
370C22—41no—
371C22—41no—
372C22—1222no—
373C22—4881no—
374C22—2442no—
375C22—2441no—
376C22—2441no—
377C22C4×C22⋊#692311yescharacteristic
378C22D61⋊#9911yescharacteristic
379C22#1684074311yescharacteristic
380C4—42no—
381C4—41no—
382C4—41no—
383C4—42no—
384C4—612no—
385C4—1221no—
386C4—1222no—
387C4—4881no—
388C4—4884no—
389C4—2441no—
390C4—2442no—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—2442no—
396C2#2146156411yescharacteristic
397C2D61⋊#35211yescharacteristic
398C2#2146207111yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#385C4
socleC22×C61C2×#99
prime radical, cosocleC22×C22⋊D61C23
hypercenter#385#6923
hypocenterC61C4×#352
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #385

Complements

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

NH ≅ G/Ntype
10. #16840665C4semidirect
15. C22×C4×Dic61C4semidirect
19. #16839623C4semidirect
21. C22⋊C4×Dic61C4semidirect
23. C61×#385C4semidirect
84. C22×Dic61C42semidirect
100. C22⋊C4×C61C42semidirect
191. Dic61#352semidirect
214. #385#6923semidirect
223. C61C4×#352semidirect
305. C22⋊C4C4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168406652
#214615692
#214615662
#214609032
#214483382
C4×#35261