Finite Group Databasebeta

← #30597514

Subgroups — #30597514

Order 15616.

542 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C4×#14519837C211yesmaximal, characteristic
2#21461058C211yesmaximal, characteristic
3C8×#11758217C212yesmaximal, complemented
4#21460664C212yesmaximal, complemented
5C2×#16839825C211yesmaximal, characteristic
6#16840779C2212yes—
7C2×#14519837C412yes—
8C4×#11758217C2212yes—
9#16840642C412yes—
10#16840606C412yes—
11#16840605C412yes—
12#92420⋊C8—22no—
13C8×#92420—22no—
14C23×#92418C411yescharacteristic
15C22×C8×D61C411yescharacteristic
16C2×C4×C22⋊D61C2211yescharacteristic
17#16839825—22no—
18#16839825—22no—
19C2×#14519706C2211yescharacteristic
20C2×#14519689C411yescharacteristic
21C2×C8×Dic61C2211yescharacteristic
22C2×C22⋊C8×C61C411yescharacteristic
23C2×#11758217C2×C414yes—
24#14519844—22no—
25#14519837C818yescomplemented
26C22⋊#92420C2×C414yes—
27#14519832—22no—
28C4×#92420—22no—
29C4×#92420—22no—
30C22×C22⋊D61C2×C411yescharacteristic
31C22×C4×D61C2×C411yescharacteristic
32C22×#92418—21no—
33C22×#92418—21no—
34C22×#92418—42no—
35C22×#92418C2×C411yescharacteristic
36C22×#92418C2×C411yescharacteristic
37C2×C8×D61—21no—
38C2×C8×D61—21no—
39C2×C8×D61—42no—
40C4×C22⋊D61—22no—
41C4×C22⋊D61—22no—
42C2×#11758196C2×C411yescharacteristic
43C2×C22⋊Dic61C2×C411yescharacteristic
44C2×#11758198C2×C411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46#14519706—22no—
47#14519689—22no—
48C8×Dic61D412yes—
49C8×Dic61D412yes—
50C23×C4×C61C2×C411yescharacteristic
51C22×C8×C61C2×C411yescharacteristic
52C22×C8×C61C2×C411yescharacteristic
53C22⋊C8×C61—22no—
54C24×C61C4211yescharacteristic
55C23×D61C4211yescharacteristic
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—41no—
59C22×C4×C61—41no—
60C22×C4×C61C4211yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C2×C22⋊D61—22no—
63C2×C22⋊D61—22no—
64C2×C22⋊D61C2×C814yes—
65C22×Dic61C4211yescharacteristic
66C22×Dic61C22×C411yescharacteristic
67C22×Dic61C22×C411yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—41no—
71C2×C4×D61—41no—
72#11758217—24no—
73#11758217C2×C818yescomplemented
74C2×#92420—24no—
75C2×#92420—24no—
76C2×C8×C61—21no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61C22⋊C412yes—
80C22⋊Dic61—22no—
81#11758198—22no—
82#11758196—22no—
83C4×Dic61C2×D412yes—
84C4×Dic61#4112yes—
85C2×#92418—22no—
86C2×#92418—21no—
87C2×#92418—42no—
88C2×#92418—42no—
89C2×#92418—41no—
90C2×#92418C22⋊C411yescharacteristic
91C2×#92418C22⋊C411yescharacteristic
92C8×D61—42no—
93C8×D61—42no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—41no—
97C23×C61—41no—
98C23×C61C4×C812yes—
99C23×C61C2×C4211yescharacteristic
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—41no—
103C22×D61—41no—
104C22×D61C4×C812yes—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—42no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61C2×C22⋊C411yescharacteristic
113C2×C4×C61#11711yescharacteristic
114C22⋊D61—28no—
115C2×Dic61—21no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61C4×D412yes—
119C2×Dic61C4×D412yes—
120C2×Dic61C22×C812yes—
121C2×Dic61#13112yes—
122C4×D61—42no—
123C4×D61—41no—
124C4×D61—41no—
125#92420—28no—
126#92420—44no—
127C8×C61—22no—
128C8×C61—41no—
129#92418—21no—
130#92418—41no—
131#92418#10012yescomplemented
132C8×#100—611nomaximal, Sylow
133C22×C61—21no—
134C22×C61—21no—
135C22×C61—22no—
136C22×C61—42no—
137C22×C61—42no—
138C22×C61—41no—
139C22×C61—41no—
140C22×C61C4×C22⋊C411yescharacteristic
141C22×C61C2×C4×C811yescharacteristic
142C22×C61#40511yescharacteristic
143C2×D61—22no—
144C2×D61—42no—
145C2×D61—41no—
146C2×D61—41no—
147C2×D61—42no—
148C4×C61—21no—
149C4×C61—41no—
150C4×C61C2×#10011yescharacteristic
151C4×C61#41311yescharacteristic
152Dic61—22no—
153Dic61—41no—
154Dic61C8×D414yes—
155C2×C8×D4—611no—
156C4×#100—611no—
157#1460—611no—
158C8×M16—612no—
159#1283—612no—
160C2×C61—21no—
161C2×C61—21no—
162C2×C61—42no—
163C2×C61C8×C22⋊C411yescharacteristic
164C2×C61C4×#10011yescharacteristic
165C2×C61#175711yescharacteristic
166D61—42no—
167C23×C8—611no—
168C23×C8—611no—
169C2×C4×D4—611no—
170C8×D4—1222no—
171C8×D4—1222no—
172#431—612no—
173C2×C4⋊C8—611no—
174C2×#100—612no—
175C2×C22⋊C8—611no—
176C2×C22⋊C8#692311yescharacteristic
177C4×M16—612no—
178C2×C4×C8—611no—
179#343—612no—
180#323—612no—
181#323—612no—
182#322—1222no—
183C82—1222no—
184C61C8×#10011yescharacteristic, complemented, Sylow
185C22×D4—611no—
186C23×C4—611no—
187C23×C4C2×#692311yescharacteristic
188C2×M16—614no—
189C22×C8—611no—
190C22×C8—611no—
191C22×C8—1221no—
192C22×C8—1221no—
193C22×C8—1221no—
194C22×C8—1221no—
195C22×C8—2442no—
196C22×C8—2442no—
197C22×C8C2×#692311yescharacteristic
198C22×C8C2×#692311yescharacteristic
199C4×D4—1222no—
200C4×D4—1222no—
201C2×C4⋊C4—611no—
202C2×C22⋊C4—611no—
203C2×C22⋊C4—611no—
204C2×C42—611no—
205C4⋊C8—1222no—
206C4⋊C8—1222no—
207#100—618no—
208C22⋊C8—22no—
209C22⋊C8—614no—
210C22⋊C8—1222no—
211#97—1222no—
212C4×C8—612no—
213C4×C8—612no—
214C4×C8—1222no—
215C4×C8—1222no—
216C24—611no—
217C24C4×#692311yescharacteristic
218C2×D4—614no—
219C2×D4—1222no—
220C2×D4—1222no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4—2441no—
231C22×C4—2441no—
232C22×C4C4×#692311yescharacteristic
233C22×C4C22×#692311yescharacteristic
234M16—618no—
235M16—1224no—
236C2×C8—21no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—611no—
240C2×C8—611no—
241C2×C8—1222no—
242C2×C8—1224no—
243C2×C8—1224no—
244C2×C8—1221no—
245C2×C8—2442no—
246C2×C8—2442no—
247C2×C8—2442no—
248C2×C8—2442no—
249C2×C8—2441no—
250C2×C8C22⋊#692312yes—
251C4⋊C4—1222no—
252C22⋊C4—1222no—
253C22⋊C4—1222no—
254C42—612no—
255C42—612no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—612no—
261C23—1221no—
262C23—1221no—
263C23—2441no—
264C23—2441no—
265C23C8×#692312yes—
266C23C2×C4×#692311yescharacteristic
267D4—1228no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—612no—
276C2×C4—612no—
277C2×C4—612no—
278C2×C4—612no—
279C2×C4—1221no—
280C2×C4—2442no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4C2×C22⋊#692311yescharacteristic
286C2×C4#1451985611yescharacteristic
287C8—22no—
288C8—41no—
289C8—612no—
290C8—1228no—
291C8—1221no—
292C8—2444no—
293C8—2441no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—1222no—
302C22—2442no—
303C22—2442no—
304C22—2441no—
305C22—2441no—
306C22C4×C22⋊#692311yescharacteristic
307C22C2×C8×#692311yescharacteristic
308C22#1684072511yescharacteristic
309C4—21no—
310C4—41no—
311C4—614no—
312C4—1222no—
313C4—2441no—
314C4D61⋊#10011yescharacteristic
315C4#1684074911yescharacteristic
316C2—21no—
317C2—21no—
318C2—42no—
319C2—2442no—
320C2C8×C22⋊#692311yescharacteristic
321C2#2146156911yescharacteristic
322C2#2146157511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC22×C61C2×C4×C8
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61C4×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61C8×#100
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C8×#11758217C2semidirect
4. #21460664C2semidirect
25. #14519837C8semidirect
73. #11758217C2×C8semidirect
131. #92418#100semidirect
184. C61C8×#100semidirect

Maximal subgroups

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

subgroupindex
C4×#145198372
#214610582
C8×#117582172
#214606642
C2×#168398252
C8×#10061