Finite Group Databasebeta

← #30601610

Subgroups — #30601610

Order 15616.

774 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 166 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#21461752C211yesmaximal, characteristic, complemented
2C42×#92420C211yesmaximal, characteristic, complemented
3C2×#16840610C212yesmaximal, complemented
4C2×D4⋊#92420C212yesmaximal, complemented
5#21448383C211yesmaximal, characteristic
6C2×#14519844—22no—
7C2×C4⋊#92420C2212yes—
8C2×C4×#92420—22no—
9C2×C4×#92420C2212yes—
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—
23#14519844—44no—
24C4⋊#92420—22no—
25C4⋊#92420—22no—
26C4×#92420—28no—
27C4×#92420—22no—
28C4×#92420D414yescomplemented
29C22×D244C2×C411yescharacteristic
30C22×C22⋊D61—22no—
31C23×Dic61—21no—
32C22×C4×D61—21no—
33#14519773—22no—
34#14519773C814yescomplemented
35D4×Dic61—22no—
36D4×Dic61—22no—
37#14519739—22no—
38#14519739—22no—
39#14519737—44no—
40#14519737—44no—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×#11758196—22no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—22no—
45C2×#11758198—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D412yes—
48C2×C4×Dic61D412yes—
49C2×C4×Dic61C2311yescharacteristic
50C22×D4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61—22no—
53C2×C42×C61C2×C411yescharacteristic
54C24×C61—21no—
55C23×D61—21no—
56C2×D4×C61—22no—
57C2×D4×C61—21no—
58C2×D4×C61—22no—
59C2×D4×C61C2×C812yes—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C412yes—
62C22×C4×C61C22×C411yescharacteristic
63C2×C22⋊D61—28no—
64C2×C22⋊D61—44no—
65C2×C22⋊D61—44no—
66C22×Dic61—21no—
67C22×Dic61—41no—
68C22×Dic61—41no—
69C22×Dic61—42no—
70C22×Dic61—42no—
71C22×Dic61C22⋊C412yes—
72C22×Dic61C2×D411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×D244—22no—
75C2×D244—22no—
76C2×D244—21no—
77C2×D244C2×C812yes—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61—42no—
81C2×C4×D61—42no—
82C2×#92420—28no—
83C2×#92420—24no—
84C2×#92420—42no—
85C2×#92420—44no—
86C4⋊C4×C61—22no—
87C22⋊C4×C61—44no—
88C42×C61—22no—
89C22⋊Dic61—42no—
90#11758198—44no—
91#11758198—42no—
92C4⋊Dic61—22no—
93#11758196—44no—
94C4×Dic61—24no—
95C4×Dic61C2×C812yes—
96C4×Dic61M1612yes—
97C4×Dic61D814yes—
98C4×Dic61SD1614yes—
99C4×Dic61C2×D412yes—
100C4×Dic61#4112yes—
101C23×C61—22no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—42no—
105C23×C61—42no—
106C23×C61C2×C22⋊C411yescharacteristic
107C22×D61—22no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—42no—
111C22×D61—42no—
112D4×C61—24no—
113D4×C61—42no—
114C2×C4×C61—22no—
115C2×C4×C61—22no—
116C2×C4×C61—41no—
117C2×C4×C61—42no—
118C2×C4×C61#10214yes—
119C2×C4×C61C4×D412yes—
120C2×C4×C61C22×C811yescharacteristic
121C2×C4×C61C2×M1611yescharacteristic
122C2×C4×C61#13112yes—
123C22⋊D61—416no—
124C2×Dic61—22no—
125C2×Dic61—41no—
126C2×Dic61—42no—
127C2×Dic61—82no—
128C2×Dic61—81no—
129C2×Dic61—81no—
130C2×Dic61C22⋊C814yes—
131C2×Dic61#10214yes—
132C2×Dic61#10414yes—
133C2×Dic61#12112yes—
134C2×Dic61#12411yescharacteristic
135C2×Dic61#12711yescharacteristic
136C2×Dic61C2×D812yes—
137C2×Dic61C2×SD1612yes—
138D244—24no—
139D244—42no—
140C4×D61—82no—
141C4×D61—81no—
142C4×D61—81no—
143#92420—28no—
144#92420—82no—
145#9638—611nomaximal, Sylow
146C22×C61—42no—
147C22×C61—44no—
148C22×C61—81no—
149C22×C61—81no—
150C22×C61—82no—
151C22×C61#39011yescharacteristic
152C22×C61C2×C22⋊C811yescharacteristic
153C22×C61#40811yescharacteristic
154C22×C61C2×#10212yes—
155C22×C61C2×#10412yes—
156C2×D61—42no—
157C2×D61—44no—
158C2×D61—81no—
159C2×D61—81no—
160C2×D61—82no—
161C4×C61—24no—
162C4×C61—81no—
163C4×C61C8×D412yes—
164C4×C61#43612yes—
165Dic61—22no—
166Dic61—81no—
167Dic61D4⋊C818yescomplemented
168Dic61#48612yes—
169Dic61#49211yescharacteristic
170Dic61#49311yescharacteristic
171C4×#127—611no—
172#1842—611no—
173C42×C8—611no—
174C2×D4⋊C8—612no—
175C2×D4⋊C8—612no—
176C2×C61—82no—
177C2×C61C2×D4⋊C812yes—
178C2×C61#149212yes—
179C2×C61#195411yescharacteristic
180C2×C61#195711yescharacteristic
181C2×C61#196211yescharacteristic
182D61—82no—
183C2×#127—611no—
184C2×C4×D4—611no—
185C2×C4×D4—611no—
186C2×C4×D4—1222no—
187C2×C4⋊C8—612no—
188C2×C4⋊C8—1222no—
189C2×C4×C8—612no—
190C2×C4×C8—1222no—
191#390—611no—
192#390—1222no—
193#390#692311yescharacteristic
194#384—611no—
195C43—611no—
196D4⋊C8—1224no—
197D4⋊C8—1224no—
198C61#963811yescharacteristic, complemented, Sylow
199C22×D4—611no—
200C22×D4—1222no—
201C22×D4C2×#692311yescharacteristic
202C23×C4—1221no—
203C23×C4—1221no—
204C22×C8—1222no—
205C22×C8—1222no—
206#127—614no—
207#127—1222no—
208C4×D4—1222no—
209C4×D4—1222no—
210C4×D4—1222no—
211C4×D4—1222no—
212C4×D4—2444no—
213C4×D4—2444no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1222no—
216C2×C4⋊C4C2×#692311yescharacteristic
217C2×C22⋊C4—22no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1222no—
221C2×C42—612no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—612no—
225C2×C42C2×#692311yescharacteristic
226C4⋊C8—1222no—
227C4⋊C8—1222no—
228C4⋊C8—2444no—
229C4×C8—614no—
230C4×C8—1222no—
231C4×C8—1228no—
232C24—21no—
233C24—1221no—
234C2×D4—22no—
235C2×D4—21no—
236C2×D4—22no—
237C2×D4—612no—
238C2×D4—1228no—
239C2×D4—1222no—
240C2×D4—1221no—
241C2×D4—1222no—
242C2×D4—2444no—
243C2×D4—2444no—
244C2×D4D61⋊C812yes—
245C22×C4—21no—
246C22×C4—612no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—2441no—
251C22×C4—2441no—
252C22×C4—2442no—
253C22×C4—2442no—
254C22×C4—2441no—
255C22×C4—2441no—
256C22×C4—2442no—
257C22×C4—2442no—
258C22×C4C22⋊#692312yes—
259C22×C4C22×#692311yescharacteristic
260C2×C8—1224no—
261C2×C8—1228no—
262C2×C8—2442no—
263C2×C8—2444no—
264C4⋊C4—22no—
265C4⋊C4—1222no—
266C4⋊C4—2444no—
267C22⋊C4—44no—
268C22⋊C4—2442no—
269C22⋊C4—2442no—
270C22⋊C4—2444no—
271C42—22no—
272C42—614no—
273C42—614no—
274C42—612no—
275C42—612no—
276C42—612no—
277C42—612no—
278C42—1224no—
279C23—22no—
280C23—41no—
281C23—41no—
282C23—42no—
283C23—42no—
284C23—1222no—
285C23—2441no—
286C23—2441no—
287C23—2442no—
288C23—2442no—
289C23C2×C22⋊#692311yescharacteristic
290D4—24no—
291D4—42no—
292D4—1224no—
293D4—24416no—
294D4—2442no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—614no—
302C2×C4—614no—
303C2×C4—612no—
304C2×C4—612no—
305C2×C4—614no—
306C2×C4—612no—
307C2×C4—1222no—
308C2×C4—4882no—
309C2×C4—4881no—
310C2×C4—4881no—
311C2×C4—4882no—
312C2×C4—4881no—
313C2×C4—4881no—
314C2×C4—2441no—
315C2×C4—2442no—
316C2×C4#1451983914yes—
317C2×C4D4×#692312yes—
318C2×C4C2×D61⋊C811yescharacteristic
319C2×C4D61⋊M1611yescharacteristic
320C2×C4#1451986412yes—
321C8—1228no—
322C8—4882no—
323C22—44no—
324C22—42no—
325C22—82no—
326C22—81no—
327C22—81no—
328C22—4882no—
329C22—4881no—
330C22—4881no—
331C22—2444no—
332C22—2442no—
333C22#1684071411yescharacteristic
334C22D61⋊(C22⋊C8)11yescharacteristic
335C22#1684073511yescharacteristic
336C22C2×#1451983912yes—
337C22D61⋊#10412yes—
338C4—24no—
339C4—81no—
340C4—618no—
341C4—612no—
342C4—611no—
343C4—611no—
344C4—1222no—
345C4—4881no—
346C4#1684078912yes—
347C4#1684079512yes—
348C2—82no—
349C2—4882no—
350C2D61⋊(D4⋊C8)12yes—
351C2#2146116412yes—
352C2#2146194211yescharacteristic
353C2#2146194711yescharacteristic
354C2#2146195411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519773C4
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#9638
LCSG ▷ C2×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. #21461752C2semidirect
2. C42×#92420C2semidirect
3. C2×#16840610C2semidirect
4. C2×D4⋊#92420C2semidirect
28. C4×#92420D4semidirect
34. #14519773C8semidirect
167. Dic61D4⋊C8semidirect
198. C61#9638semidirect

Maximal subgroups

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

subgroupindex
#214617522
C42×#924202
C2×#168406102
C2×D4⋊#924202
#214483832
#963861