Finite Group Databasebeta

← #30598934

Subgroups — #30598934

Order 15616.

496 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461752C211yesmaximal, characteristic
2#21461735C211yesmaximal, characteristic
3C2×#16840622C212yesmaximal
4#21460697C212yesmaximal
5#21448388C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519844C2212yes—
8C2×#14519844C2212yes—
9C2×C4⋊#92420—21no—
10#16840628—21no—
11#16840628—21no—
12#16840622—24no—
13C2×#14519775C2211yescharacteristic
14C2×Q8×Dic61C411yescharacteristic
15C2×#14519742C411yescharacteristic
16#16839668C411yescharacteristic
17#16839659—21no—
18#16839659—21no—
19#16839631C2211yescharacteristic
20#16839613—21no—
21#16839613—21no—
22C42×Dic61C2211yescharacteristic
23C61×#391C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519844—22no—
27#14519844—22no—
28#14519844—22no—
29#14519844—22no—
30#14519844—42no—
31C4⋊#92420—42no—
32C22×Dic122C2×C411yescharacteristic
33#14519775—21no—
34#14519775—21no—
35#14519775D412yes—
36#14519775Q812yes—
37Q8×Dic61—42no—
38#14519742—42no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61C2311yescharacteristic
54#14519684—21no—
55#14519684—21no—
56C22×Q8×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C42×C61C2×C411yescharacteristic
59#95×C61—21no—
60#95×C61—21no—
61C2×Q8×C61—21no—
62C2×Q8×C61—41no—
63C2×Q8×C61—41no—
64C2×Q8×C61C4⋊C412yes—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×Dic122—21no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122C4⋊C412yes—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C4⋊C4×C61—41no—
87C42×C61—41no—
88C4⋊Dic61—42no—
89C4⋊Dic61—41no—
90#11758196—22no—
91#11758196—22no—
92#11758196—22no—
93#11758196—22no—
94#11758196—42no—
95#11758196—42no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—22no—
99C4×Dic61—22no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—22no—
103C4×Dic61—42no—
104C4×Dic61—42no—
105C4×Dic61SD1612yes—
106C4×Dic61Q1612yes—
107C4×Dic61C2×D411yescharacteristic
108C4×Dic61C2×Q811yescharacteristic
109C4×Dic61#4111yescharacteristic
110C4×Dic61#4111yescharacteristic
111C23×C61C2×C22⋊C411yescharacteristic
112Q8×C61—42no—
113Q8×C61—42no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
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—41no—
127C2×C4×C61#10312yes—
128C2×C4×C61C2×C4⋊C411yescharacteristic
129C2×C4×C61#11711yescharacteristic
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—22no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61#10012yes—
141C2×Dic61#10312yes—
142C2×Dic61#12111yescharacteristic
143C2×Dic61#12111yescharacteristic
144C2×Dic61C22⋊Q811yescharacteristic
145C2×Dic61C22⋊Q811yescharacteristic
146C2×Dic61C2×SD1611yescharacteristic
147C2×Dic61C2×Q1611yescharacteristic
148C2×Dic61#13512yes—
149C2×Dic61AGL(1,ℤ/8)11yescharacteristic
150C2×Dic61#13711yescharacteristic
151C2×Dic61#13712yes—
152Dic122—42no—
153Dic122—42no—
154#92420—82no—
155#92420—82no—
156#8590—611nomaximal, Sylow
157C22×C61#38011yescharacteristic
158C22×C61C2×#10011yescharacteristic
159C22×C61#41311yescharacteristic
160C22×C61C2×#10311yescharacteristic
161C22×C61#41611yescharacteristic
162C22×C61#41711yescharacteristic
163C22×C61#41911yescharacteristic
164C4×C61—22no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—42no—
168C4×C61—41no—
169C4×C61—81no—
170Dic61—22no—
171Dic61—22no—
172Dic61—42no—
173Dic61—81no—
174Dic61#46011yescharacteristic
175Dic61#46211yescharacteristic
176Dic61#46412yes—
177Dic61#47511yescharacteristic
178Dic61#47711yescharacteristic
179Dic61#47912yes—
180C4×C4⋊Q8—611no—
181#1842—611no—
182#1831—611no—
183C2×#333—612no—
184#1296—612no—
185C2×C61#154211yescharacteristic
186C2×C61#154811yescharacteristic
187C2×C61#155111yescharacteristic
188C2×C61#155911yescharacteristic
189C2×C61#180011yescharacteristic
190C2×C61#180311yescharacteristic
191C2×C61#180511yescharacteristic
192C2×C4⋊Q8—611no—
193C2×C4×Q8—611no—
194C2×C4×Q8—611no—
195C2×C4⋊C8—612no—
196C2×C4⋊C8—612no—
197C2×C4⋊C8—1221no—
198C2×C4⋊C8—1221no—
199#391—611no—
200#391#692311yescharacteristic
201#389—1221no—
202#389—1221no—
203#384—611no—
204C4×C4⋊C4—1221no—
205C4×C4⋊C4—1221no—
206C43—611no—
207#336—1221no—
208#336—1221no—
209#333—1224no—
210C61#859011yescharacteristic, complemented, Sylow
211C22×Q8—611no—
212C22×Q8C2×#692311yescharacteristic
213C22×C8—1222no—
214C22×C8—1222no—
215C4⋊Q8—612no—
216C4⋊Q8—612no—
217C4⋊Q8—1221no—
218C4⋊Q8—1221no—
219C4×Q8—2442no—
220C4×Q8—2442no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4C2×#692311yescharacteristic
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—611no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—611no—
235C2×C42—1221no—
236C2×C42—1221no—
237C2×C42C2×#692311yescharacteristic
238C4⋊C8—1222no—
239C4⋊C8—1222no—
240C4⋊C8—1222no—
241C4⋊C8—1222no—
242C4⋊C8—2442no—
243C4⋊C8—2442no—
244#95—21no—
245#95—21no—
246#95—1221no—
247#95—1221no—
248C2×Q8—21no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—612no—
252C2×Q8—1221no—
253C2×Q8—2441no—
254C2×Q8—2441no—
255C2×Q8C4⋊#692312yes—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4C22⋊#692311yescharacteristic
265C22×C4C22⋊#692311yescharacteristic
266C22×C4C22×#692311yescharacteristic
267C2×C8—2442no—
268C2×C8—2442no—
269C2×C8—2442no—
270C2×C8—2442no—
271C2×C8—2442no—
272C2×C8—2442no—
273C4⋊C4—41no—
274C4⋊C4—1222no—
275C4⋊C4—1222no—
276C4⋊C4—1222no—
277C4⋊C4—1222no—
278C4⋊C4—2441no—
279C4⋊C4—2442no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2442no—
283C4⋊C4—2442no—
284C42—41no—
285C42—612no—
286C42—612no—
287C42—611no—
288C42—611no—
289C42—611no—
290C42—611no—
291C42—1221no—
292C42—1222no—
293C42—1221no—
294C42—1222no—
295C42—1222no—
296C42—2442no—
297C42—2442no—
298C23C2×C22⋊#692311yescharacteristic
299Q8—42no—
300Q8—42no—
301Q8—2442no—
302Q8—2442no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—612no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—612no—
326C2×C4—612no—
327C2×C4—612no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1222no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4#1451984012yes—
339C2×C4C2×C4⋊#692311yescharacteristic
340C2×C4#1451985611yescharacteristic
341C8—4882no—
342C8—4882no—
343C22#1684070411yescharacteristic
344C22D61⋊#10011yescharacteristic
345C22#1684074911yescharacteristic
346C22C2×#1451984011yescharacteristic
347C22#1684075211yescharacteristic
348C22#1684075311yescharacteristic
349C22#1684075511yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—42no—
355C4—81no—
356C4—611no—
357C4—611no—
358C4—611no—
359C4—611no—
360C4—612no—
361C4—612no—
362C4—1222no—
363C4—1222no—
364C4—4881no—
365C4—2442no—
366C2#2146132111yescharacteristic
367C2#2146133311yescharacteristic
368C2#2146133911yescharacteristic
369C2#2146135511yescharacteristic
370C2#2146168411yescharacteristic
371C2#2146168811yescharacteristic
372C2#2146169011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#8590
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
210. C61#8590semidirect

Maximal subgroups

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

subgroupindex
#214617522
#214617352
C2×#168406222
#214606972
#214483882
#859061