Finite Group Databasebeta

← #30601629

Subgroups — #30601629

Order 15616.

714 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 142 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#21461751C211yesmaximal, characteristic, complemented
2#21461534C211yesmaximal, characteristic, complemented
3C2×#16840610C212yesmaximal, complemented
4C2×D4⋊#92420C212yesmaximal, complemented
5#21448383C211yesmaximal, characteristic
6C2×C4⋊#92420—22no—
7C2×C4⋊#92420C2212yes—
8C2×C4×#92420C2212yes—
9#16840628—22no—
10#16840610—24no—
11D4⋊#92420—24no—
12C2×#14519773C411yescharacteristic
13C2×D4×Dic61C2211yescharacteristic
14C2×#14519739C2211yescharacteristic
15C2×#14519737—22no—
16#16839664C411yescharacteristic
17#16839662—22no—
18#16839631C411yescharacteristic
19C42×Dic61C2211yescharacteristic
20C61×#390C411yescharacteristic
21C22×#92420—22no—
22C22×#92420—22no—
23C4⋊#92420—22no—
24C4⋊#92420—22no—
25C4⋊#92420—44no—
26C4×#92420—22no—
27C4×#92420D414yescomplemented
28C22×D244C2×C411yescharacteristic
29C22×C22⋊D61—22no—
30C23×Dic61—21no—
31C22×C4×D61—21no—
32#14519773—22no—
33#14519773—22no—
34D4×Dic61—22no—
35D4×Dic61—22no—
36#14519739—22no—
37#14519739—22no—
38#14519737—44no—
39#14519737—44no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—22no—
42C2×C22⋊Dic61—21no—
43C2×#11758198—22no—
44C2×#11758198—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D412yes—
47C2×C4×Dic61D412yes—
48C2×C4×Dic61C2311yescharacteristic
49C22×D4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61—22no—
52C2×C42×C61C2×C411yescharacteristic
53C24×C61—21no—
54C23×D61—21no—
55C2×D4×C61—22no—
56C2×D4×C61—21no—
57C2×D4×C61—22no—
58C2×D4×C61M1612yes—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C412yes—
61C22×C4×C61C22×C411yescharacteristic
62C2×C22⋊D61—28no—
63C2×C22⋊D61—44no—
64C2×C22⋊D61—44no—
65C22×Dic61—21no—
66C22×Dic61—41no—
67C22×Dic61—41no—
68C22×Dic61—42no—
69C22×Dic61—42no—
70C22×Dic61C22⋊C412yes—
71C22×Dic61C2×D411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C2×D244—22no—
74C2×D244—22no—
75C2×D244—21no—
76C2×D244M1612yes—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×#92420—24no—
82C2×#92420—44no—
83C2×#92420—42no—
84C2×#92420—44no—
85C4⋊C4×C61—22no—
86C22⋊C4×C61—44no—
87C42×C61—22no—
88C22⋊Dic61—42no—
89#11758198—44no—
90#11758198—42no—
91C4⋊Dic61—22no—
92#11758196—44no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—42no—
96C4×Dic61D814yes—
97C4×Dic61SD1614yes—
98C4×Dic61C2×D412yes—
99C4×Dic61#4112yes—
100C23×C61—22no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61—42no—
104C23×C61—42no—
105C23×C61C2×C22⋊C411yescharacteristic
106C22×D61—22no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—42no—
110C22×D61—42no—
111D4×C61—24no—
112D4×C61—42no—
113C2×C4×C61—22no—
114C2×C4×C61—22no—
115C2×C4×C61—41no—
116C2×C4×C61—42no—
117C2×C4×C61#10214yes—
118C2×C4×C61C4×D412yes—
119C2×C4×C61C2×M1611yescharacteristic
120C2×C4×C61C2×M1611yescharacteristic
121C2×C4×C61#13112yes—
122C22⋊D61—416no—
123C2×Dic61—22no—
124C2×Dic61—22no—
125C2×Dic61—22no—
126C2×Dic61—41no—
127C2×Dic61—42no—
128C2×Dic61—82no—
129C2×Dic61—81no—
130C2×Dic61—81no—
131C2×Dic61#10214yes—
132C2×Dic61#12112yes—
133C2×Dic61#12411yescharacteristic
134C2×Dic61#12711yescharacteristic
135C2×Dic61C2×D812yes—
136C2×Dic61C2×SD1612yes—
137D244—24no—
138D244—42no—
139C4×D61—82no—
140C4×D61—81no—
141C4×D61—81no—
142#92420—44no—
143#92420—82no—
144#9644—611nomaximal, Sylow
145C22×C61—42no—
146C22×C61—44no—
147C22×C61—81no—
148C22×C61—81no—
149C22×C61—82no—
150C22×C61#39011yescharacteristic
151C22×C61#40711yescharacteristic
152C22×C61#40811yescharacteristic
153C22×C61C2×#10212yes—
154C22×C61#42112yes—
155C2×D61—42no—
156C2×D61—44no—
157C2×D61—81no—
158C2×D61—81no—
159C2×D61—82no—
160C4×C61—24no—
161C4×C61—81no—
162C4×C61#43512yes—
163C4×C61#43512yes—
164Dic61—22no—
165Dic61—24no—
166Dic61—81no—
167Dic61#48612yes—
168Dic61#49211yescharacteristic
169Dic61#49311yescharacteristic
170C4×#127—611no—
171#1842—611no—
172#1744—611no—
173C2×D4⋊C8—612no—
174C2×D4⋊C8—612no—
175C2×C61—82no—
176C2×C61#148012yes—
177C2×C61#148612yes—
178C2×C61#195511yescharacteristic
179C2×C61#195711yescharacteristic
180C2×C61#196311yescharacteristic
181D61—82no—
182C2×#127—611no—
183C2×C4×D4—611no—
184C2×C4×D4—611no—
185C2×C4×D4—1222no—
186C2×C4⋊C8—612no—
187C2×C4⋊C8—1222no—
188C2×C4×C8—612no—
189#390—611no—
190#390—1222no—
191#390#692311yescharacteristic
192#384—611no—
193C43—611no—
194#336—1222no—
195D4⋊C8—1224no—
196D4⋊C8—1224no—
197C61#964411yescharacteristic, complemented, Sylow
198C22×D4—611no—
199C22×D4—1222no—
200C22×D4C2×#692311yescharacteristic
201C23×C4—1221no—
202C23×C4—1221no—
203C22×C8—1222no—
204C22×C8—1222no—
205#127—1222no—
206#127—1222no—
207C4×D4—1222no—
208C4×D4—1222no—
209C4×D4—1222no—
210C4×D4—1222no—
211C4×D4—2444no—
212C4×D4—2444no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1222no—
215C2×C4⋊C4C2×#692311yescharacteristic
216C2×C22⋊C4—22no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1222no—
220C2×C42—612no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—612no—
224C2×C42C2×#692311yescharacteristic
225C4⋊C8—1222no—
226C4⋊C8—1222no—
227C4⋊C8—2444no—
228C4×C8—614no—
229C4×C8—1222no—
230C24—21no—
231C24—1221no—
232C2×D4—22no—
233C2×D4—21no—
234C2×D4—22no—
235C2×D4—612no—
236C2×D4—1228no—
237C2×D4—1222no—
238C2×D4—1221no—
239C2×D4—1222no—
240C2×D4—2444no—
241C2×D4—2444no—
242C2×D4#1175821312yes—
243C22×C4—21no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—612no—
247C22×C4—1221no—
248C22×C4—2441no—
249C22×C4—2441no—
250C22×C4—2442no—
251C22×C4—2442no—
252C22×C4—2441no—
253C22×C4—2441no—
254C22×C4—2442no—
255C22×C4—2442no—
256C22×C4C22⋊#692312yes—
257C22×C4C22×#692311yescharacteristic
258C2×C8—1224no—
259C2×C8—2442no—
260C2×C8—2444no—
261C2×C8—2444no—
262C4⋊C4—22no—
263C4⋊C4—1222no—
264C4⋊C4—2444no—
265C22⋊C4—44no—
266C22⋊C4—2442no—
267C22⋊C4—2442no—
268C22⋊C4—2444no—
269C42—22no—
270C42—614no—
271C42—614no—
272C42—612no—
273C42—612no—
274C42—1221no—
275C42—1221no—
276C42—2442no—
277C23—22no—
278C23—41no—
279C23—41no—
280C23—42no—
281C23—42no—
282C23—1222no—
283C23—2441no—
284C23—2441no—
285C23—2442no—
286C23—2442no—
287C23C2×C22⋊#692311yescharacteristic
288D4—24no—
289D4—42no—
290D4—1224no—
291D4—24416no—
292D4—2442no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—611no—
298C2×C4—611no—
299C2×C4—612no—
300C2×C4—612no—
301C2×C4—612no—
302C2×C4—614no—
303C2×C4—1222no—
304C2×C4—1222no—
305C2×C4—1222no—
306C2×C4—4882no—
307C2×C4—4881no—
308C2×C4—4881no—
309C2×C4—4882no—
310C2×C4—4881no—
311C2×C4—4881no—
312C2×C4—2441no—
313C2×C4—2442no—
314C2×C4#1451983914yes—
315C2×C4D4×#692312yes—
316C2×C4D61⋊M1611yescharacteristic
317C2×C4C2×#1175821311yescharacteristic
318C2×C4#1451986412yes—
319C8—4882no—
320C8—2444no—
321C22—44no—
322C22—42no—
323C22—82no—
324C22—81no—
325C22—81no—
326C22—4882no—
327C22—4881no—
328C22—4881no—
329C22—2444no—
330C22—2442no—
331C22#1684071411yescharacteristic
332C22#1684073311yescharacteristic
333C22#1684073511yescharacteristic
334C22C2×#1451983912yes—
335C22#1684075912yes—
336C4—24no—
337C4—81no—
338C4—612no—
339C4—611no—
340C4—611no—
341C4—1224no—
342C4—1222no—
343C4—4881no—
344C4#1684079112yes—
345C4#1684079412yes—
346C2—82no—
347C2—4882no—
348C2#2146112412yes—
349C2#2146114512yes—
350C2#2146194411yescharacteristic
351C2#2146194711yescharacteristic
352C2#2146195611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519773C4
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#9644
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #21461751C2semidirect
2. #21461534C2semidirect
3. C2×#16840610C2semidirect
4. C2×D4⋊#92420C2semidirect
27. C4×#92420D4semidirect
197. C61#9644semidirect

Maximal subgroups

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

subgroupindex
#214617512
#214615342
C2×#168406102
C2×D4⋊#924202
#214483832
#964461