Finite Group Databasebeta

← #30595378

Subgroups — #30595378

Order 15616.

604 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 146 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#21461673C211yesmaximal, characteristic
2C4×C22⋊#92420C211yesmaximal, characteristic
3#21460638C214yesmaximal, complemented
4C2×#16839658C211yesmaximal, characteristic
5C2×C4⋊#92420—21no—
6C2×C22⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C4×#92420—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C22×C4⋊Dic61C411yescharacteristic
12C22×#11758196—21no—
13C22×C4×Dic61C2211yescharacteristic
14#16839658—21no—
15#16839658—21no—
16#16839658C412yes—
17#16839658C2212yes—
18C2×#14519684—21no—
19C22×C4⋊C4×C61C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22C4⋊#92420—42no—
23C22⋊#92420—24no—
24C22⋊#92420—42no—
25C4×#92420—42no—
26C23×Dic61—21no—
27C23×Dic61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—22no—
31C2×C4⋊Dic61C814yescomplemented
32C2×C4⋊Dic61C2×C412yes—
33C2×#11758196—22no—
34C2×#11758196—22no—
35C2×#11758196—42no—
36C2×#11758196—42no—
37C2×C4×Dic61—42no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61C2311yescharacteristic
42#14519684—22no—
43#14519684—22no—
44C23×C4×C61—21no—
45C23×C4×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—42no—
48C2×C4⋊C4×C61C2×C412yes—
49C24×C61C22⋊C411yescharacteristic
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—42no—
54C22×C4×C61—42no—
55C22×C4×C61—42no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C2×C812yes—
58C22×C4×C61M1612yes—
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—24no—
61C22×Dic61—22no—
62C22×Dic61—22no—
63C22×Dic61—22no—
64C22×Dic61—41no—
65C22×Dic61—41no—
66C22×Dic61—41no—
67C22×Dic61—42no—
68C22×Dic61—42no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61D812yes—
72C22×Dic61SD1612yes—
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×#92420—24no—
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C4⋊C4×C61—42no—
82C4⋊C4×C61—42no—
83C4⋊Dic61—24no—
84C4⋊Dic61—22no—
85C4⋊Dic61C2×C814yes—
86#11758196—44no—
87#11758196—42no—
88#11758196—42no—
89C4×Dic61—22no—
90C4×Dic61—22no—
91C4×Dic61—41no—
92C4×Dic61—41no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61C22⋊C812yes—
98C23×C61#10212yes—
99C23×C61#10412yes—
100C23×C61C2×C22⋊C411yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—24no—
104C2×C4×C61—24no—
105C2×C4×C61—42no—
106C2×C4×C61—42no—
107C2×C4×C61—42no—
108C2×C4×C61—84no—
109C2×C4×C61C22⋊C812yes—
110C2×C4×C61#9912yes—
111C2×C4×C61#10112yes—
112C2×C4×C61C22×C811yescharacteristic
113C2×C4×C61C2×M1611yescharacteristic
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—24no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—42no—
125C2×Dic61—42no—
126C2×Dic61—44no—
127C2×Dic61—48no—
128C2×Dic61—42no—
129C2×Dic61—42no—
130C2×Dic61#10212yes—
131C2×Dic61C2×D811yescharacteristic
132C2×Dic61C2×SD1611yescharacteristic
133C2×Dic61#13712yes—
134#92420—44no—
135#92420—82no—
136#7573—611nomaximal, Sylow
137C22×C61—22no—
138C22×C61—22no—
139C22×C61—22no—
140C22×C61—22no—
141C22×C61—22no—
142C22×C61—22no—
143C22×C61D4⋊C814yes—
144C22×C61C2×C22⋊C811yescharacteristic
145C22×C61C2×#9911yescharacteristic
146C22×C61C2×#10111yescharacteristic
147C22×C61C2×#10211yescharacteristic
148C22×C61#41911yescharacteristic
149C22×C61C2×#10411yescharacteristic
150C22×C61#42111yescharacteristic
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—82no—
154C4×C61#32414yes—
155Dic61—22no—
156Dic61—21no—
157Dic61—22no—
158Dic61—21no—
159Dic61—44no—
160Dic61—41no—
161C2×#389—611no—
162#1797—611no—
163C4×C22⋊C8—611no—
164#1271—614no—
165C2×C61—24no—
166C2×C61C2×#32411yescharacteristic
167C2×C61C2×D4⋊C811yescharacteristic
168C2×C61#147911yescharacteristic
169C2×C61#150811yescharacteristic
170C2×C61#151911yescharacteristic
171C2×C61#152811yescharacteristic
172C2×C61#154611yescharacteristic
173C22×C4⋊C4—611no—
174C22×C4⋊C4—1221no—
175C22×C4⋊C4#692311yescharacteristic
176C22×C42—611no—
177C2×C4⋊C8—1221no—
178C2×C22⋊C8—1221no—
179C2×C22⋊C8—1221no—
180C2×C4×C8—1221no—
181#389—612no—
182#389—612no—
183#389—1221no—
184#389—1221no—
185C2×#95—1221no—
186#336—612no—
187#336—612no—
188C61#757311yescharacteristic, complemented, Sylow
189C23×C4—21no—
190C23×C4—611no—
191C23×C4—611no—
192C23×C4—1221no—
193C23×C4C2×#692311yescharacteristic
194C22×C8—1222no—
195C22×C8—1222no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—614no—
199C2×C4⋊C4—612no—
200C2×C4⋊C4—1222no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1222no—
203C2×C4⋊C4—1222no—
204C2×C4⋊C4—2442no—
205C2×C4⋊C4—2442no—
206C2×C4⋊C4C2×#692312yes—
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—611no—
211C2×C42—2442no—
212C4⋊C8—2442no—
213C22⋊C8—1224no—
214C22⋊C8—2442no—
215C4×C8—2442no—
216#95—1222no—
217#95—1222no—
218C24C22⋊#692311yescharacteristic
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—612no—
229C22×C4—612no—
230C22×C4—611no—
231C22×C4—1222no—
232C22×C4—1224no—
233C22×C4—1222no—
234C22×C4—1222no—
235C22×C4—2441no—
236C22×C4—2441no—
237C22×C4—2441no—
238C22×C4—2442no—
239C22×C4—2442no—
240C22×C4D61⋊C812yes—
241C22×C4#1175821312yes—
242C22×C4C22⋊#692311yescharacteristic
243C22×C4C22×#692311yescharacteristic
244C2×C8—1224no—
245C2×C8—2442no—
246C2×C8—2442no—
247C2×C8—2442no—
248C2×C8—2442no—
249C2×C8—2442no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—614no—
253C4⋊C4—1224no—
254C4⋊C4—1222no—
255C4⋊C4—2444no—
256C4⋊C4—2442no—
257C4⋊C4—2442no—
258C42—1222no—
259C42—1222no—
260C42—2441no—
261C42—2441no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23#1451983412yes—
267C23#1451983912yes—
268C23#1451984212yes—
269C23C2×C22⋊#692311yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—84no—
278C2×C4—612no—
279C2×C4—611no—
280C2×C4—611no—
281C2×C4—612no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1224no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—2442no—
293C2×C4—2442no—
294C2×C4—2444no—
295C2×C4—2442no—
296C2×C4—2442no—
297C2×C4—2448no—
298C2×C4#1451983412yes—
299C2×C4#1451983512yes—
300C2×C4#1451983812yes—
301C2×C4C2×D61⋊C811yescharacteristic
302C2×C4C2×#1175821311yescharacteristic
303C8—4882no—
304C8—2444no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22#1684061014yes—
312C22C2×#1451983411yescharacteristic
313C22C2×#1451983511yescharacteristic
314C22C2×#1451983811yescharacteristic
315C22C2×#1451983911yescharacteristic
316C22#1684075511yescharacteristic
317C22C2×#1451984211yescharacteristic
318C22#1684076011yescharacteristic
319C4—21no—
320C4—21no—
321C4—82no—
322C4—1221no—
323C4—1222no—
324C4—1221no—
325C4—1222no—
326C4—2444no—
327C4—2441no—
328C4#1684060814yes—
329C2—24no—
330C2C2×#1684060811yescharacteristic
331C2C2×#1684061011yescharacteristic
332C2#2146112311yescharacteristic
333C2#2146121911yescharacteristic
334C2#2146125511yescharacteristic
335C2#2146128311yescharacteristic
336C2#2146132811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#7573
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460638C2semidirect
31. C2×C4⋊Dic61C8semidirect
188. C61#7573semidirect

Maximal subgroups

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

subgroupindex
#214616732
C4×C22⋊#924202
#214606382
C2×#168396582
#757361