Finite Group Databasebeta

← #30602149

Subgroups — #30602149

Order 15616.

458 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461752C211yesmaximal, characteristic
2#21461533C211yesmaximal, characteristic
3#21460655C212yesmaximal
4#21460655C212yesmaximal
5#21448378C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519844—21no—
8C2×C4⋊#92420C2212yes—
9C2×C4×#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12C2×#14519768C411yescharacteristic
13#16839660C411yescharacteristic
14#16839647—21no—
15#16839643—21no—
16#16839627C411yescharacteristic
17C4⋊C4×Dic61—21no—
18C4⋊C4×Dic61C2211yescharacteristic
19C4⋊C4×Dic61C2211yescharacteristic
20#16839613—21no—
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26#14519844—42no—
27C4⋊#92420—24no—
28C4×#92420—22no—
29C4×#92420Q814yes—
30#14519768—22no—
31#14519768C814yescomplemented
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61—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—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C42×C61C2×C411yescharacteristic
54#95×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×#92420—24no—
67C2×#92420—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—22no—
74C4⋊C4×C61—42no—
75C4⋊C4×C61C2×C812yes—
76C42×C61—22no—
77C4⋊Dic61—21no—
78C4⋊Dic61—24no—
79C4⋊Dic61—22no—
80C4⋊Dic61C2×C812yes—
81#11758196—24no—
82#11758196—42no—
83C4×Dic61—21no—
84C4×Dic61—21no—
85C4×Dic61—21no—
86C4×Dic61—21no—
87C4×Dic61—41no—
88C4×Dic61—41no—
89C4×Dic61—41no—
90C4×Dic61—41no—
91C4×Dic61—41no—
92C4×Dic61—41no—
93C4×Dic61C2×C812yes—
94C4×Dic61M1612yes—
95C4×Dic61C2×Q812yes—
96C4×Dic61#4112yes—
97C23×C61C2×C22⋊C411yescharacteristic
98C2×C4×C61—22no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61C4×Q812yes—
111C2×C4×C61C22×C811yescharacteristic
112C2×C4×C61C2×M1611yescharacteristic
113C2×C4×C61#13112yes—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—22no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61C22⋊C812yes—
127C2×Dic61C22⋊C812yes—
128C2×Dic61C22⋊Q812yes—
129C2×Dic61#12411yescharacteristic
130C2×Dic61C4⋊Q811yescharacteristic
131C2×Dic61AGL(1,ℤ/8)11yescharacteristic
132C2×Dic61AGL(1,ℤ/8)11yescharacteristic
133C2×Dic61#13711yescharacteristic
134C2×Dic61#13711yescharacteristic
135#92420—44no—
136#92420—82no—
137#9872—611nomaximal, Sylow
138C22×C61#39111yescharacteristic
139C22×C61C2×C22⋊C811yescharacteristic
140C22×C61#40811yescharacteristic
141C22×C61#41711yescharacteristic
142C22×C61#41711yescharacteristic
143C22×C61#42111yescharacteristic
144C22×C61#42111yescharacteristic
145C4×C61—42no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61—81no—
149C4×C61C8×Q812yes—
150C4×C61#44612yes—
151Dic61—22no—
152Dic61—22no—
153Dic61—22no—
154Dic61—42no—
155Dic61—81no—
156Dic61#49011yescharacteristic
157Dic61#49111yescharacteristic
158Dic61#50111yescharacteristic
159Dic61#50111yescharacteristic
160C4×#125—611no—
161#1842—611no—
162#1744—611no—
163#1279—612no—
164#1279—612no—
165C2×C61#147711yescharacteristic
166C2×C61#147711yescharacteristic
167C2×C61#149511yescharacteristic
168C2×C61#149511yescharacteristic
169C2×C61#198411yescharacteristic
170C2×C61#199211yescharacteristic
171C2×C61#199511yescharacteristic
172C2×#125—611no—
173C2×C4⋊C8—612no—
174C2×C4⋊C8—1221no—
175C2×C4⋊C8—1221no—
176C2×C4×C8—612no—
177#389—611no—
178#389#692311yescharacteristic
179#387—1221no—
180#387—1221no—
181#382—611no—
182C4×C4⋊C4—611no—
183C4×C4⋊C4—611no—
184C4×C4⋊C4—1221no—
185C4×C4⋊C4—1221no—
186C43—611no—
187#336—1221no—
188#336—1221no—
189C61#987211yescharacteristic, complemented, Sylow
190C22×C8—1222no—
191C22×C8—1222no—
192#125—614no—
193#125—1222no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—611no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4C2×#692311yescharacteristic
201C2×C4⋊C4C2×#692311yescharacteristic
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42—611no—
208C2×C42—1221no—
209C2×C42—1221no—
210C2×C42C2×#692311yescharacteristic
211C4⋊C8—1224no—
212C4⋊C8—2442no—
213C4⋊C8—2442no—
214C4×C8—614no—
215C4×C8—1222no—
216#95—21no—
217#95—1221no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4C22⋊#692311yescharacteristic
231C22×C4C22⋊#692311yescharacteristic
232C22×C4C22×#692311yescharacteristic
233C2×C8—1224no—
234C2×C8—2442no—
235C2×C8—2442no—
236C2×C8—2442no—
237C2×C8—2442no—
238C2×C8—2442no—
239C4⋊C4—21no—
240C4⋊C4—22no—
241C4⋊C4—42no—
242C4⋊C4—612no—
243C4⋊C4—1224no—
244C4⋊C4—1224no—
245C4⋊C4—1221no—
246C4⋊C4—1222no—
247C4⋊C4—2442no—
248C4⋊C4D61⋊C812yes—
249C42—22no—
250C42—612no—
251C42—612no—
252C42—612no—
253C42—612no—
254C42—1221no—
255C42—1221no—
256C42—1221no—
257C42—1221no—
258C42—2441no—
259C42—2441no—
260C42—2441no—
261C42—2441no—
262C42—2441no—
263C42—2441no—
264C23C2×C22⋊#692311yescharacteristic
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—611no—
278C2×C4—611no—
279C2×C4—611no—
280C2×C4—611no—
281C2×C4—611no—
282C2×C4—611no—
283C2×C4—612no—
284C2×C4—612no—
285C2×C4—612no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1222no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4Q8×#692312yes—
299C2×C4C2×D61⋊C811yescharacteristic
300C2×C4D61⋊M1611yescharacteristic
301C2×C4#1451986412yes—
302C8—4882no—
303C8—2444no—
304C22(C2×#6923)⋊Q811yescharacteristic
305C22D61⋊(C22⋊C8)11yescharacteristic
306C22#1684073511yescharacteristic
307C22#1684075311yescharacteristic
308C22#1684075311yescharacteristic
309C22#1684076011yescharacteristic
310C22#1684076111yescharacteristic
311C4—42no—
312C4—41no—
313C4—41no—
314C4—81no—
315C4—611no—
316C4—611no—
317C4—611no—
318C4—611no—
319C4—1222no—
320C4—1222no—
321C4—1222no—
322C4—4881no—
323C4—2442no—
324C4#1684081112yes—
325C4#1684081412yes—
326C2#2146111511yescharacteristic
327C2#2146111711yescharacteristic
328C2#2146117411yescharacteristic
329C2#2146117611yescharacteristic
330C2#2146199011yescharacteristic
331C2#2146200211yescharacteristic
332C2#2146200711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#9872
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
31. #14519768C8semidirect
189. C61#9872semidirect

Maximal subgroups

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

subgroupindex
#214617522
#214615332
#214606552
#214483782
#987261