Finite Group Databasebeta

← #30595705

Subgroups — #30595705

Order 15616.

438 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 98 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#21461736C211yesmaximal, characteristic, complemented
2#21461534C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460636C212yesmaximal
5#21454187C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C4×#92420—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519772—21no—
13#16839664C411yescharacteristic
14#16839663C411yescharacteristic
15#16839663C2211yescharacteristic
16#16839661C411yescharacteristic
17#16839658C2211yescharacteristic
18#16839654—21no—
19#16839652—21no—
20#16839651—21no—
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26C4×#92420—24no—
27C22×D244C2×C411yescharacteristic
28#14519772—42no—
29#14519772—42no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—21no—
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45#14519684—21no—
46#14519684—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C42×C61C2×C411yescharacteristic
51#95×C61—21no—
52C23×D61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22×C411yescharacteristic
58C22×Dic61—21no—
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C22⋊C411yescharacteristic
61C22×Dic61C2×D411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C2×D244—22no—
64C2×D244—41no—
65C2×D244—41no—
66C2×#92420—24no—
67C2×#92420—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—42no—
75C42×C61—41no—
76#11758198—42no—
77#11758198—42no—
78#11758198—42no—
79#11758198—42no—
80#11758198—41no—
81#11758198—41no—
82#11758198—42no—
83C4⋊Dic61—22no—
84C4⋊Dic61—42no—
85#11758196—41no—
86#11758196—41no—
87C4×Dic61—22no—
88C4×Dic61—22no—
89C4×Dic61—22no—
90C4×Dic61—41no—
91C4×Dic61—41no—
92C4×Dic61D812yes—
93C4×Dic61SD1612yes—
94C23×C61C2×C22⋊C411yescharacteristic
95C22×D61—41no—
96C22×D61—41no—
97C22×D61—41no—
98C22×D61—41no—
99C22×D61—41no—
100C22×D61—41no—
101C22×D61—41no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61#10212yes—
115C2×C4×C61#10412yes—
116C2×C4×C61#13112yes—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61#10212yes—
130C2×Dic61C2×D811yescharacteristic
131C2×Dic61C2×SD1611yescharacteristic
132C2×Dic61#13512yes—
133D244—82no—
134#92420—44no—
135#92420—82no—
136#7666—611nomaximal, Sylow
137C22×C61#40811yescharacteristic
138C22×C61#41011yescharacteristic
139C22×C61#41311yescharacteristic
140C22×C61C2×#10211yescharacteristic
141C22×C61#41611yescharacteristic
142C22×C61C2×#10411yescharacteristic
143C22×C61#42111yescharacteristic
144C2×D61—81no—
145C2×D61—81no—
146C2×D61—81no—
147C2×D61—81no—
148C2×D61—81no—
149C2×D61—81no—
150C2×D61—81no—
151C4×C61—22no—
152C4×C61—22no—
153C4×C61—22no—
154C4×C61—81no—
155C4×C61—81no—
156Dic61—22no—
157Dic61—22no—
158Dic61—21no—
159Dic61—21no—
160Dic61—41no—
161Dic61—81no—
162#2860—611no—
163#1831—611no—
164#1744—611no—
165#1271—612no—
166#1270—612no—
167C2×C61#147311yescharacteristic
168C2×C61#148211yescharacteristic
169C2×C61#149211yescharacteristic
170C2×C61#150011yescharacteristic
171C2×C61#151711yescharacteristic
172C2×C61#153211yescharacteristic
173C2×C61#154011yescharacteristic
174D61—161no—
175C2×#126—1221no—
176C2×C4⋊C8—1221no—
177C2×C4×C8—1221no—
178#390—611no—
179#390—611no—
180#390—611no—
181#389—611no—
182#389—611no—
183#389#692311yescharacteristic
184#388—1221no—
185#388—1221no—
186#388—1221no—
187C43—611no—
188#336—612no—
189#336—612no—
190#336—1221no—
191#336—1221no—
192C61#766611yescharacteristic, complemented, Sylow
193C22×D4—611no—
194C22×C8—1222no—
195C22×C8—1222no—
196#126—2442no—
197#126—2442no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4C2×#692311yescharacteristic
203C2×C4⋊C4C2×#692311yescharacteristic
204C2×C22⋊C4—1221no—
205C2×C22⋊C4—1221no—
206C2×C22⋊C4—1221no—
207C2×C22⋊C4—1221no—
208C2×C22⋊C4—1221no—
209C2×C22⋊C4—1221no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—611no—
214C2×C42—611no—
215C2×C42—611no—
216C2×C42C2×#692311yescharacteristic
217C4⋊C8—2442no—
218C4×C8—1224no—
219#95—21no—
220#95—1221no—
221#95—1221no—
222C24—1221no—
223C2×D4—1222no—
224C2×D4—2441no—
225C2×D4—2441no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—1221no—
233C22×C4C22⋊#692311yescharacteristic
234C22×C4C22⋊#692311yescharacteristic
235C22×C4C22×#692311yescharacteristic
236C2×C8—1224no—
237C2×C8—2442no—
238C2×C8—2442no—
239C2×C8—2442no—
240C2×C8—2442no—
241C2×C8—2442no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—42no—
245C4⋊C4—1222no—
246C4⋊C4—2441no—
247C4⋊C4—2441no—
248C4⋊C4—2442no—
249C22⋊C4—2442no—
250C22⋊C4—2442no—
251C22⋊C4—2441no—
252C22⋊C4—2441no—
253C22⋊C4—2442no—
254C22⋊C4—2442no—
255C22⋊C4—2442no—
256C42—41no—
257C42—612no—
258C42—612no—
259C42—1222no—
260C42—1222no—
261C42—1222no—
262C42—2441no—
263C42—2441no—
264C23—2441no—
265C23—2441no—
266C23—2441no—
267C23—2441no—
268C23—2441no—
269C23—2441no—
270C23—2441no—
271C23C2×C22⋊#692311yescharacteristic
272D4—4882no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—612no—
286C2×C4—611no—
287C2×C4—611no—
288C2×C4—612no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4#1451983912yes—
302C2×C4#1451984212yes—
303C2×C4#1451986512yes—
304C8—4882no—
305C8—2444no—
306C22—4881no—
307C22—4881no—
308C22—4881no—
309C22—4881no—
310C22—4881no—
311C22—4881no—
312C22—4881no—
313C22#1684073711yescharacteristic
314C22#1684074111yescharacteristic
315C22#1684074911yescharacteristic
316C22C2×#1451983911yescharacteristic
317C22#1684075211yescharacteristic
318C22C2×#1451984211yescharacteristic
319C22#1684075911yescharacteristic
320C4—22no—
321C4—22no—
322C4—22no—
323C4—81no—
324C4—81no—
325C4—1221no—
326C4—1221no—
327C4—1222no—
328C4—1222no—
329C4—4881no—
330C4—2441no—
331C2—9761no—
332C2#2146110211yescharacteristic
333C2#2146113311yescharacteristic
334C2#2146116611yescharacteristic
335C2#2146119211yescharacteristic
336C2#2146124911yescharacteristic
337C2#2146129711yescharacteristic
338C2#2146131711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#7666
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
1. #21461736C2semidirect
2. #21461534C2semidirect
3. #21460638C2semidirect
192. C61#7666semidirect

Maximal subgroups

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

subgroupindex
#214617362
#214615342
#214606382
#214606362
#214541872
#766661