Finite Group Databasebeta

← #30594508

Subgroups — #30594508

Order 15616.

376 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 62 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#21461942C211yesmaximal, characteristic
2#21461681C211yesmaximal, characteristic
3#21445806C211yesmaximal, characteristic
4C2×#14519844C411yescharacteristic, complemented
5C2×#14519835—21no—
6C2×#14519834—21no—
7C2×C22⋊#92420—21no—
8C2×C4×#92420C411yescharacteristic, complemented
9#16840704—21no—
10#16840640C412yescomplemented
11C2×#14519737C2211yescharacteristic
12C2×#14519691—21no—
13#16839620—21no—
14#16839529C411yescharacteristic, complemented
15C61×#342C411yescharacteristic, complemented
16C22×#92420—21no—
17C22×#92420—21no—
18C2×C4⋊#6923—41no—
19C2×C22⋊#6923—22no—
20#14519844—41no—
21#14519835—41no—
22#14519835—41no—
23#14519834—42no—
24C22⋊#92420—42no—
25C4×#92420—41no—
26(C2×#6923)⋊C4—41no—
27C22×C22⋊D61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30#14519737—41no—
31#14519737—41no—
32C2×#11758196—41no—
33C2×#11758196Q811yescharacteristic
34C2×C22⋊Dic61—21no—
35C2×#11758198C2×C411yescharacteristic
36C2×C4×Dic61C2×C411yescharacteristic
37#14519691—41no—
38#14519691—41no—
39#14519684—41no—
40C2×C22⋊C4×C61—21no—
41C2×C22⋊C4×C61C2×C411yescharacteristic
42C24×C61C22⋊C411yescharacteristic
43C23×D61C22⋊C411yescharacteristic
44C22×#6923—42no—
45C22×C4×C61—41no—
46C22×C4×C61C4211yescharacteristic
47C22×C4×C61C4⋊C411yescharacteristic
48C2×C22⋊D61—41no—
49C2×C22⋊D61—41no—
50C2×C22⋊D61D811yescharacteristic
51C2×C22⋊D61SD1611yescharacteristic
52C2×C22⋊D61SD1611yescharacteristic
53C2×C22⋊D61Q1611yescharacteristic
54C22×Dic61—21no—
55C22×Dic61—21no—
56C22×Dic61—41no—
57C22×Dic61—41no—
58C22×Dic61—41no—
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C4⋊C411yescharacteristic
61C22×Dic61C4⋊C411yescharacteristic
62C2×C4×D61—21no—
63C2×C4×D61—21no—
64C2×C4×D61—41no—
65C2×C4×D61—41no—
66C22⋊#6923—42no—
67C22⋊#6923—42no—
68C2×#92420—22no—
69C2×#92420—41no—
70C2×#92420—41no—
71C2×#92420—41no—
72C2×#92420—41no—
73C2×#92420—41no—
74C4⋊#6923—81no—
75C4⋊#6923—81no—
76C22⋊C4×C61—41no—
77C22⋊C4×C61—41no—
78C22⋊C4×C61—41no—
79C22⋊Dic61—41no—
80C22⋊Dic61—41no—
81#11758198—41no—
82#11758196—41no—
83#11758196—81no—
84#11758196—81no—
85C4×Dic61—21no—
86C4×Dic61—21no—
87C23×C61—21no—
88C23×C61—21no—
89C23×C61—41no—
90C23×C61—41no—
91C23×C61#9511yescharacteristic
92C23×C61#10211yescharacteristic
93C23×C61#10311yescharacteristic
94C22×D61—21no—
95C22×D61—21no—
96C22×D61—41no—
97C22×D61—41no—
98C22×D61#10211yescharacteristic
99C22×D61#10311yescharacteristic
100C2×#6923—82no—
101C2×#6923—82no—
102C2×#6923—82no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—81no—
108C2×C4×C61—81no—
109C2×C4×C61—81no—
110C22⋊D61—41no—
111C22⋊D61—41no—
112C22⋊D61—41no—
113C22⋊D61—41no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—81no—
123C2×Dic61—81no—
124C2×Dic61—81no—
125C2×Dic61—81no—
126C2×Dic61#9911yescharacteristic
127C2×Dic61#9911yescharacteristic
128C2×Dic61#10611yescharacteristic
129C2×Dic61#10711yescharacteristic
130C4×D61—41no—
131C4×D61—41no—
132C4×D61—81no—
133#92420—42no—
134#92420—81no—
135#7237—611nomaximal, Sylow
136C22×C61—21no—
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—41no—
141C22×C61—41no—
142C22×C61—41no—
143C22×C61—41no—
144C22×C61—81no—
145C22×C61H(3,ℤ/4)11yescharacteristic
146C22×C61#34011yescharacteristic
147C22×C61#34211yescharacteristic
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—81no—
155#6923—162no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—161no—
159Dic61—21no—
160Dic61—21no—
161Dic61—21no—
162Dic61—41no—
163Dic61—161no—
164Dic61#35311yescharacteristic
165Dic61#35411yescharacteristic
166#1954—611no—
167#1799—611no—
168#1799—611no—
169C2×C61—21no—
170C2×C61—21no—
171C2×C61—41no—
172C2×C61—41no—
173C2×C61#128911yescharacteristic
174C2×C61#139111yescharacteristic
175C2×C61#139311yescharacteristic
176D61—41no—
177D61—41no—
178C2×C4×D4—611no—
179C2×C4⋊C8—611no—
180C2×#99—1221no—
181C2×#99—1221no—
182C2×C22⋊C8—1221no—
183C2×C22⋊C8—1221no—
184C2×C4×C8—611no—
185#380—1221no—
186#380—1221no—
187#342—612no—
188#342—611no—
189#342#692311yescharacteristic, complemented
190C61#723711yescharacteristic, complemented, Sylow
191C22×D4—611no—
192C23×C4—611no—
193C23×C4—611no—
194C22×C8—1221no—
195C22×C8—1221no—
196C4×D4—2441no—
197C4×D4—2441no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—2441no—
200C2×C4⋊C4—2441no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4—611no—
203C2×C22⋊C4—1222no—
204C2×C22⋊C4—1221no—
205C2×C22⋊C4C2×#692311yescharacteristic
206C2×C42—611no—
207C4⋊C8—2441no—
208#99—2441no—
209#99—2441no—
210#99—2441no—
211#99—2441no—
212C22⋊C8—2442no—
213C22⋊C8—2442no—
214C4×C8—2441no—
215#95—2441no—
216#95—2441no—
217C24—611no—
218C24C22⋊#692311yescharacteristic
219C2×D4—611no—
220C2×D4—611no—
221C2×D4—611no—
222C2×D4—611no—
223C2×D4—2441no—
224C2×D4—2441no—
225C22×C4—41no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4—2441no—
234C22×C4—2441no—
235C22×C4—2441no—
236C22×C4—2441no—
237C22×C4—2441no—
238C22×C4—2442no—
239C22×C4C4×#692311yescharacteristic
240C22×C4C4⋊#692311yescharacteristic
241C2×C8—1222no—
242C2×C8—2441no—
243C2×C8—2441no—
244C2×C8—2441no—
245C2×C8—2441no—
246C2×C8—2441no—
247C4⋊C4—4881no—
248C4⋊C4—4881no—
249C4⋊C4—4881no—
250C4⋊C4—4881no—
251C4⋊C4—2441no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—2441no—
256C22⋊C4—2441no—
257C22⋊C4—2442no—
258C22⋊C4—2442no—
259C22⋊C4—2441no—
260C42—1221no—
261C42—1221no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23—611no—
267C23—611no—
268C23—1221no—
269C23—1221no—
270C23—2441no—
271C23—2441no—
272C23(C2×#6923)⋊C411yescharacteristic
273C23#1451983911yescharacteristic
274C23#1451984011yescharacteristic
275D4—2441no—
276D4—2441no—
277D4—2441no—
278D4—2441no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—611no—
287C2×C4—611no—
288C2×C4—611no—
289C2×C4—611no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—4881no—
296C2×C4—4881no—
297C2×C4—4881no—
298C2×C4—4881no—
299C2×C4—4881no—
300C2×C4—4882no—
301C2×C4—4882no—
302C2×C4—4882no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C8—4881no—
309C8—2442no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—81no—
319C22—1221no—
320C22—1221no—
321C22—4881no—
322C22—2441no—
323C22—2441no—
324C22—2441no—
325C22—2441no—
326C22#1684062911yescharacteristic
327C22#1684063511yescharacteristic
328C22#1684063911yescharacteristic
329C4—41no—
330C4—41no—
331C4—161no—
332C4—611no—
333C4—611no—
334C4—1221no—
335C4—1221no—
336C4—1221no—
337C4—9761no—
338C4—9762no—
339C4—2441no—
340C2—21no—
341C2—21no—
342C2—41no—
343C2—41no—
344C2—2441no—
345C2—2441no—
346C2#2146068111yescharacteristic
347C2#2146090611yescharacteristic
348C2#2146091211yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C22⋊C4C2×#6923
FittingC61×#342C4
socleC22×C61#342
prime radicalC22×C22⋊D61D4
cosocleC2×#14519737C22
hypercenter#342#6923
hypocenterC61#7237
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #342

Complements

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

NH ≅ G/Ntype
4. C2×#14519844C4semidirect
8. C2×C4×#92420C4semidirect
10. #16840640C4semidirect
14. #16839529C4semidirect
15. C61×#342C4semidirect
189. #342#6923semidirect
190. C61#7237semidirect

Maximal subgroups

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

subgroupindex
#214619422
#214616812
#214458062
#723761