Finite Group Databasebeta

← #30593996

Subgroups — #30593996

Order 15616.

402 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 96 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#21461674C211yesmaximal, characteristic
2#21461483C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic
4C22×#11758213—21no—
5C2×C4⋊#92420—21no—
6C2×#14519834C412yes—
7#16840628—21no—
8#16840628—21no—
9#16840628C412yes—
10C2×C42×D61C2211yescharacteristic
11C2×C4⋊#92418C411yescharacteristic
12C2×#14519689—21no—
13#16839516—21no—
14C2×C4⋊C8×C61C411yescharacteristic
15C2×#11758213—22no—
16C2×#11758213—22no—
17C2×#11758213—41no—
18C2×#11758213—41no—
19C2×#11758213—41no—
20C2×#11758213—41no—
21C22×#92420—22no—
22C22×#92420—22no—
23C4⋊#92420—41no—
24C4⋊#92420—41no—
25#14519834—42no—
26C22×C4×D61C2×C411yescharacteristic
27C22×C4×D61D411yescharacteristic
28C22×C4×D61Q811yescharacteristic
29C22×#92418—21no—
30C2×C4×Dic61C2×C411yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32C2×C4×Dic61D411yescharacteristic
33C42×D61—41no—
34C42×D61—41no—
35C4⋊#92418—41no—
36#14519689—41no—
37#14519689—41no—
38C22×C8×C61—21no—
39C2×C42×C61C2×C411yescharacteristic
40C4⋊C8×C61—41no—
41C23×D61C4⋊C411yescharacteristic
42C22×C4×C61C4211yescharacteristic
43C22×C4×C61C22⋊C411yescharacteristic
44C22×C4×C61C4⋊C411yescharacteristic
45C22×Dic61C22⋊C411yescharacteristic
46C22×Dic61C22⋊C411yescharacteristic
47C22×Dic61C4⋊C411yescharacteristic
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61—41no—
57C2×C4×D61—41no—
58C2×C4×D61—41no—
59C2×C4×D61—41no—
60C2×C4×D61D811yescharacteristic
61C2×C4×D61SD1611yescharacteristic
62C2×C4×D61SD1611yescharacteristic
63C2×C4×D61Q1611yescharacteristic
64C2×#92420—24no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70#11758213—42no—
71#11758213—42no—
72#11758213—42no—
73#11758213—42no—
74C2×C8×C61—41no—
75C2×C8×C61—41no—
76C2×C8×C61—41no—
77C42×C61—21no—
78C42×C61—21no—
79C4×Dic61—21no—
80C4×Dic61—21no—
81C4×Dic61—41no—
82C4×Dic61—41no—
83C2×#92418—41no—
84C2×#92418—41no—
85C2×#92418—41no—
86C23×C61#9511yescharacteristic
87C22×D61—21no—
88C22×D61—21no—
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—21no—
92C22×D61—21no—
93C22×D61#10611yescharacteristic
94C22×D61#10711yescharacteristic
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61#9911yescharacteristic
101C2×C4×C61#9911yescharacteristic
102C2×C4×C61#10211yescharacteristic
103C2×C4×C61#10311yescharacteristic
104C2×C4×C61#10411yescharacteristic
105C2×C4×C61#10411yescharacteristic
106C2×C4×C61#10811yescharacteristic
107C2×C4×C61#10811yescharacteristic
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61#10011yescharacteristic
116C2×Dic61#10111yescharacteristic
117C2×Dic61#10211yescharacteristic
118C2×Dic61#10311yescharacteristic
119C4×D61—21no—
120C4×D61—21no—
121C4×D61—21no—
122C4×D61—21no—
123C4×D61—21no—
124C4×D61—21no—
125C4×D61—21no—
126C4×D61—21no—
127C4×D61—42no—
128C4×D61—42no—
129C4×D61—42no—
130C4×D61—42no—
131#92420—44no—
132#92420—82no—
133C8×C61—81no—
134#92418—81no—
135#7045—611nomaximal, Sylow
136C22×C61#33811yescharacteristic
137C22×C61#33911yescharacteristic
138C22×C61#34011yescharacteristic
139C22×C61#34111yescharacteristic
140C22×C61#34211yescharacteristic
141C22×C61#34311yescharacteristic
142C22×C61#34411yescharacteristic
143C2×D61—21no—
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—21no—
148C2×D61—21no—
149C2×D61—41no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61#32711yescharacteristic
157C4×C61#32711yescharacteristic
158C4×C61#32811yescharacteristic
159C4×C61#32811yescharacteristic
160Dic61—21no—
161Dic61—21no—
162Dic61—21no—
163Dic61—21no—
164Dic61—41no—
165#1797—611no—
166#1797—611no—
167#1728—611no—
168C2×C61#129111yescharacteristic
169C2×C61#129211yescharacteristic
170C2×C61#129311yescharacteristic
171C2×C61#129411yescharacteristic
172C2×C61#129911yescharacteristic
173C2×C61#130111yescharacteristic
174C2×C61#130511yescharacteristic
175D61—41no—
176D61—41no—
177C22×M16—1221no—
178C22×C42—611no—
179C2×C4⋊C8—611no—
180C2×C4⋊C8—1221no—
181C2×C4⋊C8#692311yescharacteristic
182C2×C22⋊C8—612no—
183C2×C22⋊C8—1221no—
184#336—612no—
185#336—1221no—
186#336—1221no—
187#336—1221no—
188C61#704511yescharacteristic, complemented, Sylow
189C23×C4—611no—
190C23×C4—611no—
191C23×C4—611no—
192C2×M16—1222no—
193C2×M16—1222no—
194C2×M16—2441no—
195C2×M16—2441no—
196C2×M16—2441no—
197C2×M16—2441no—
198C22×C8—21no—
199C22×C8—1222no—
200C22×C8—1222no—
201C22×C8—1221no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—2441no—
206C2×C42—2441no—
207C2×C42C2×#692311yescharacteristic
208C4⋊C8—41no—
209C4⋊C8—2441no—
210C4⋊C8—2441no—
211C4⋊C8—2441no—
212C22⋊C8—2441no—
213C22⋊C8—2441no—
214C22⋊C8—2442no—
215C24—611no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4—1221no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4—2441no—
232C22×C4—2441no—
233C22×C4—2441no—
234C22×C4—2441no—
235C22×C4C4×#692311yescharacteristic
236C22×C4C4⋊#692311yescharacteristic
237C22×C4C22⋊#692311yescharacteristic
238M16—2442no—
239M16—2442no—
240M16—2442no—
241M16—2442no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—1224no—
246C2×C8—2442no—
247C2×C8—2442no—
248C2×C8—2442no—
249C2×C8—2441no—
250C2×C8—2441no—
251C2×C8—2441no—
252C2×C8—2442no—
253C2×C8—2442no—
254C42—21no—
255C42—21no—
256C42—1221no—
257C42—1221no—
258C42—2441no—
259C42—2441no—
260C23—611no—
261C23—611no—
262C23—1221no—
263C23—1221no—
264C23—1221no—
265C23—1221no—
266C23—1221no—
267C23—1221no—
268C23(C2×#6923)⋊C411yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—611no—
275C2×C4—611no—
276C2×C4—611no—
277C2×C4—611no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—2442no—
294C2×C4—2442no—
295C2×C4—2442no—
296C2×C4—2442no—
297C2×C4#1451983511yescharacteristic
298C2×C4#1451983611yescharacteristic
299C2×C4#1451983911yescharacteristic
300C2×C4#1451984011yescharacteristic
301C2×C4#1451984111yescharacteristic
302C2×C4#1451984211yescharacteristic
303C2×C4#1451984711yescharacteristic
304C2×C4#1451984811yescharacteristic
305C8—81no—
306C8—4882no—
307C8—4881no—
308C8—2444no—
309C22—1221no—
310C22—1221no—
311C22—1221no—
312C22—1221no—
313C22—1221no—
314C22—1221no—
315C22—2441no—
316C22—2441no—
317C22—2441no—
318C22—2441no—
319C22#1684063111yescharacteristic
320C22#1684063211yescharacteristic
321C22#1684063511yescharacteristic
322C22#1684063811yescharacteristic
323C22#1684064011yescharacteristic
324C22#1684064111yescharacteristic
325C22#1684064511yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—1221no—
330C4—1221no—
331C4—1221no—
332C4—1221no—
333C4—2441no—
334C4#1684061311yescharacteristic
335C4#1684061411yescharacteristic
336C4#1684061511yescharacteristic
337C4#1684061611yescharacteristic
338C2—2441no—
339C2—2441no—
340C2#2146068511yescharacteristic
341C2#2146068811yescharacteristic
342C2#2146069111yescharacteristic
343C2#2146069211yescharacteristic
344C2#2146070511yescharacteristic
345C2#2146071111yescharacteristic
346C2#2146071911yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC22×C4×C61C42
FrattiniC2×C42C2×#6923
FittingC2×C4⋊C8×C61C4
socleC23×C61#95
prime radicalC23×D61C4⋊C4
cosocleC2×C42×D61C22
hypercenterC2×C4⋊C8#6923
hypocenterC61#7045
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
188. C61#7045semidirect

Maximal subgroups

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

subgroupindex
#214616742
#214614832
#214457962
#704561