Finite Group Databasebeta

← #30598854

Subgroups — #30598854

Order 15616.

568 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461736C211yesmaximal, characteristic
2C4×#14519844C211yesmaximal, characteristic
3C2×#16840612C212yesmaximal
4#21460655C212yesmaximal
5C4×#14519742C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C4⋊#92420C2212yes—
8C2×C4×#92420C2212yes—
9#16840628—21no—
10#16840628—21no—
11#16840628—21no—
12#16840612—24no—
13C2×C4×Dic122C411yescharacteristic
14C2×#14519742C411yescharacteristic
15C2×#14519742C2211yescharacteristic
16C4⋊C4×Dic61C411yescharacteristic
17C4⋊C4×Dic61C2211yescharacteristic
18C4×#11758196—21no—
19#16839613—21no—
20#16839613—21no—
21C42×Dic61—21no—
22C42×Dic61C2211yescharacteristic
23C4×C4⋊C4×C61C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519844—24no—
27C4⋊#92420—22no—
28C4⋊#92420—22no—
29C4×#92420—22no—
30C4×#92420—22no—
31C22×Dic122C2×C411yescharacteristic
32C4×Dic122—22no—
33C4×Dic122—22no—
34#14519742—22no—
35#14519742—21no—
36#14519742—21no—
37#14519742C814yescomplemented
38#14519742D412yes—
39#14519742Q812yes—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61C2311yescharacteristic
55#14519684—21no—
56#14519684—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C42×C61—21no—
60C2×C42×C61C2×C411yescharacteristic
61#95×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C2×Dic122—21no—
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×Dic122C4⋊C412yes—
77C2×Dic122C2×C812yes—
78C2×Dic122M1612yes—
79C2×#92420—24no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61C4⋊C412yes—
88C4⋊C4×C61C2×C812yes—
89C42×C61—21no—
90C42×C61—21no—
91C42×C61—42no—
92C4⋊Dic61—21no—
93C4⋊Dic61M1612yes—
94#11758196—24no—
95#11758196—24no—
96#11758196—22no—
97#11758196—22no—
98C4×Dic61—24no—
99C4×Dic61—22no—
100C4×Dic61—24no—
101C4×Dic61—22no—
102C4×Dic61—22no—
103C4×Dic61—22no—
104C4×Dic61—22no—
105C4×Dic61—41no—
106C4×Dic61—42no—
107C4×Dic61—42no—
108C4×Dic61C2×C812yes—
109C4×Dic61M1612yes—
110C4×Dic61C2×D411yescharacteristic
111C4×Dic61C2×Q811yescharacteristic
112C4×Dic61#4111yescharacteristic
113C4×Dic61#4111yescharacteristic
114C23×C61C2×C22⋊C411yescharacteristic
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—22no—
118C2×C4×C61—22no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61#10412yes—
127C2×C4×C61C2×C4⋊C411yescharacteristic
128C2×C4×C61#11711yescharacteristic
129C2×C4×C61C22×C811yescharacteristic
130C2×C4×C61C2×M1611yescharacteristic
131C2×C4×C61C2×M1611yescharacteristic
132C2×C4×C61C2×M1611yescharacteristic
133C2×Dic61—22no—
134C2×Dic61—22no—
135C2×Dic61—22no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—22no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61C22⋊C812yes—
146C2×Dic61C22⋊C812yes—
147C2×Dic61#12111yescharacteristic
148C2×Dic61#12111yescharacteristic
149C2×Dic61C22⋊Q811yescharacteristic
150C2×Dic61C22⋊Q811yescharacteristic
151C2×Dic61#13512yes—
152C2×Dic61#13712yes—
153Dic122—22no—
154Dic122—22no—
155Dic122—22no—
156Dic122C4⋊C814yescomplemented
157#92420—44no—
158#92420—82no—
159#8566—611nomaximal, Sylow
160C22×C61#38011yescharacteristic
161C22×C61C2×C22⋊C811yescharacteristic
162C22×C61#40711yescharacteristic
163C22×C61#41611yescharacteristic
164C22×C61#41911yescharacteristic
165C22×C61C2×#10411yescharacteristic
166C22×C61#42111yescharacteristic
167C4×C61—22no—
168C4×C61—42no—
169C4×C61—42no—
170C4×C61—41no—
171C4×C61C2×C4⋊C811yescharacteristic
172C4×C61#42311yescharacteristic
173C4×C61#43111yescharacteristic
174C4×C61#43211yescharacteristic
175Dic61—24no—
176Dic61—21no—
177Dic61—21no—
178Dic61—22no—
179Dic61—22no—
180Dic61—42no—
181Dic61#46412yes—
182Dic61#47912yes—
183C42×Q8—611no—
184#1831—611no—
185C4×C4⋊C8—611no—
186C2×Q8⋊C8—612no—
187#1279—612no—
188C2×C61#147611yescharacteristic
189C2×C61#147911yescharacteristic
190C2×C61#148811yescharacteristic
191C2×C61#149111yescharacteristic
192C2×C61#179711yescharacteristic
193C2×C61#180511yescharacteristic
194C2×C61#180611yescharacteristic
195C2×C4×Q8—611no—
196C2×C4×Q8—611no—
197C2×C4×Q8—611no—
198C2×C4⋊C8—612no—
199C2×C4⋊C8—1221no—
200C2×C4×C8—612no—
201C4×C4⋊C4—611no—
202C4×C4⋊C4—611no—
203C4×C4⋊C4—1221no—
204C4×C4⋊C4—1221no—
205C4×C4⋊C4—1221no—
206C4×C4⋊C4#692311yescharacteristic
207C43—611no—
208C43—1221no—
209#336—1221no—
210#336—1221no—
211#336—1221no—
212Q8⋊C8—1224no—
213C61#856611yescharacteristic, complemented, Sylow
214C22×Q8—611no—
215C22×C8—1222no—
216C22×C8—1222no—
217C4×Q8—614no—
218C4×Q8—612no—
219C4×Q8—612no—
220C4×Q8—1222no—
221C4×Q8—1222no—
222C4×Q8—1221no—
223C4×Q8—1221no—
224C4×Q8—1222no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4C2×#692311yescharacteristic
230C2×C4⋊C4C2×#692311yescharacteristic
231C2×C42—21no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—611no—
235C2×C42—611no—
236C2×C42—611no—
237C2×C42—611no—
238C2×C42—1221no—
239C2×C42—1221no—
240C2×C42—1221no—
241C2×C42—1221no—
242C2×C42—1221no—
243C2×C42C2×#692311yescharacteristic
244C4⋊C8—1222no—
245C4⋊C8—1222no—
246C4⋊C8—1224no—
247C4×C8—1222no—
248C4×C8—1222no—
249#95—21no—
250#95—1221no—
251#95—1221no—
252C2×Q8—612no—
253C2×Q8—612no—
254C2×Q8—612no—
255C2×Q8—1221no—
256C2×Q8—1221no—
257C2×Q8—1221no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4C22⋊#692311yescharacteristic
267C22×C4C22⋊#692311yescharacteristic
268C22×C4C22×#692311yescharacteristic
269C2×C8—1224no—
270C2×C8—2442no—
271C2×C8—2442no—
272C2×C8—2442no—
273C2×C8—2442no—
274C2×C8—2442no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—612no—
278C4⋊C4—1222no—
279C4⋊C4—1222no—
280C4⋊C4—1224no—
281C4⋊C4—1224no—
282C4⋊C4—1221no—
283C4⋊C4D61⋊C812yes—
284C4⋊C4C4⋊#692312yes—
285C42—21no—
286C42—21no—
287C42—42no—
288C42—611no—
289C42—611no—
290C42—611no—
291C42—611no—
292C42—612no—
293C42—612no—
294C42—1222no—
295C42—1222no—
296C42—1222no—
297C42—1222no—
298C42—1224no—
299C42—1224no—
300C42—1222no—
301C42—2441no—
302C42—2442no—
303C42—2442no—
304C23C2×C22⋊#692311yescharacteristic
305Q8—614no—
306Q8—1222no—
307Q8—1222no—
308Q8—1222no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—612no—
323C2×C4—612no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—612no—
327C2×C4—612no—
328C2×C4—1222no—
329C2×C4—1222no—
330C2×C4—1222no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1222no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4#1451984112yes—
341C2×C4C2×C4⋊#692311yescharacteristic
342C2×C4#1451985611yescharacteristic
343C2×C4C2×D61⋊C811yescharacteristic
344C2×C4D61⋊M1611yescharacteristic
345C2×C4D61⋊M1611yescharacteristic
346C2×C4D61⋊M1611yescharacteristic
347C8—4882no—
348C8—2444no—
349C22#1684070411yescharacteristic
350C22D61⋊(C22⋊C8)11yescharacteristic
351C22#1684073411yescharacteristic
352C22#1684075211yescharacteristic
353C22#1684075511yescharacteristic
354C22C2×#1451984111yescharacteristic
355C22#1684075911yescharacteristic
356C4—22no—
357C4—42no—
358C4—41no—
359C4—42no—
360C4—612no—
361C4—612no—
362C4—1222no—
363C4—1222no—
364C4—1224no—
365C4—1221no—
366C4—1221no—
367C4—2442no—
368C4D61⋊(C4⋊C8)11yescharacteristic
369C4#1684076711yescharacteristic
370C4#1684078011yescharacteristic
371C4#1684078511yescharacteristic
372C2#2146111111yescharacteristic
373C2#2146112211yescharacteristic
374C2#2146115211yescharacteristic
375C2#2146116311yescharacteristic
376C2#2146167611yescharacteristic
377C2#2146169011yescharacteristic
378C2#2146169111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8566
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
37. #14519742C8semidirect
156. Dic122C4⋊C8semidirect
213. C61#8566semidirect

Maximal subgroups

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

subgroupindex
#214617362
C4×#145198442
C2×#168406122
#214606552
C4×#145197422
#856661