Finite Group Databasebeta

← #30601860

Subgroups — #30601860

Order 15616.

392 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C4×#14519848C211yesmaximal, characteristic
2#21461277C211yesmaximal, characteristic
3#21461277C211yesmaximal, characteristic
4#21461143C211yesmaximal, characteristic
5#21461142C211yesmaximal, characteristic
6#21461029C211yesmaximal, characteristic
7#21456404C211yesmaximal, characteristic
8#16840781C2211yescharacteristic
9C2×#14519848—21no—
10C4×#11758213C2211yescharacteristic
11C4×#11758213C2211yescharacteristic
12C4×#11758213C2211yescharacteristic
13#16840638—21no—
14#16840619—22no—
15#16840619—22no—
16#16840612—22no—
17Q8⋊#92420—22no—
18#92420⋊C8—21no—
19#16840603—21no—
20#16840317C2211yescharacteristic
21#16840317C2211yescharacteristic
22#16840165C411yescharacteristic
23#16840141C411yescharacteristic
24#16840113C411yescharacteristic
25#16840002—21no—
26#16840002—21no—
27#16839854—21no—
28#16839854—21no—
29C4×C8×D61C2211yescharacteristic
30C61×#487C411yescharacteristic
31C2×#11758213—21no—
32C2×#11758213—21no—
33C2×#11758213—21no—
34#14519848—24no—
35C4⋊#92420D412yes—
36#14519834—21no—
37#14519832—21no—
38#14519832—21no—
39#14519832D412yes—
40C4×#92420—21no—
41C4×#92420—21no—
42C4×#92420—21no—
43C4×#92420—21no—
44C2×#11758202—21no—
45C2×#11758202—21no—
46C2×C8×D61D411yescharacteristic
47C2×C8×D61D411yescharacteristic
48#14519777C2×C411yescharacteristic
49#14519777C2×C411yescharacteristic
50#14519768—21no—
51#14519768—21no—
52#14519757—21no—
53#14519757—21no—
54#14519753—21no—
55#14519753—21no—
56Q8×Dic61—21no—
57Q8×Dic61—21no—
58#14519742—21no—
59#14519742—21no—
60#14519735—21no—
61#14519735—21no—
62C42×D61C2311yescharacteristic
63#14519710—21no—
64#14519710—21no—
65#14519702—21no—
66#14519702—21no—
67C4×#92418C2×C411yescharacteristic
68C8×Dic61D411yescharacteristic
69C8×Dic61D411yescharacteristic
70C4⋊Q8×C61C2×C411yescharacteristic
71C4⋊Q8×C61C2×C411yescharacteristic
72#103×C61—21no—
73#103×C61—21no—
74C4×C8×C61C2×C411yescharacteristic
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C2×C4×D61C2×D411yescharacteristic
78C2×C4×D61#4111yescharacteristic
79C2×C4×D61#4111yescharacteristic
80C2×Dic122—21no—
81C2×Dic122—21no—
82C2×#92420—22no—
83C2×#92420—22no—
84C2×#92420—41no—
85C2×#92420—41no—
86#11758213—22no—
87#11758213—22no—
88#11758213—41no—
89#11758213—41no—
90#11758213—42no—
91C2×C8×C61C22⋊C411yescharacteristic
92C2×C8×C61C22⋊C411yescharacteristic
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C42×C61C22×C411yescharacteristic
98#11758202—42no—
99#11758202—42no—
100#11758198—41no—
101#11758198—41no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—41no—
107C4⋊Dic61—41no—
108#11758196—41no—
109#11758196—41no—
110C4×Dic61—41no—
111C4×Dic61—41no—
112C4×Dic61C2×D411yescharacteristic
113C4×Dic61C2×D411yescharacteristic
114C4×Dic61C2×D411yescharacteristic
115C2×#92418C22⋊C411yescharacteristic
116C2×#92418C22⋊C411yescharacteristic
117C8×D61—22no—
118C8×D61—41no—
119C22×D61#12411yescharacteristic
120Q8×C61—41no—
121Q8×C61—41no—
122Q8×C61—42no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61C2×C22⋊C411yescharacteristic
126C2×C4×C61C4×D411yescharacteristic
127C2×C4×C61C4×D411yescharacteristic
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61#12111yescharacteristic
131C2×Dic61#12111yescharacteristic
132C2×Dic61#12711yescharacteristic
133C4×D61—21no—
134C4×D61—21no—
135C4×D61—22no—
136C4×D61—22no—
137Dic122—41no—
138Dic122—41no—
139Dic122—42no—
140#92420—42no—
141#92420—42no—
142#92420—42no—
143#92420—42no—
144C8×C61—21no—
145C8×C61—21no—
146#92418—21no—
147#92418#10412yes—
148#9727—611nomaximal, Sylow
149C22×C61#39011yescharacteristic
150C2×D61—21no—
151C2×D61—21no—
152C2×D61—21no—
153C4×C61—21no—
154C4×C61—81no—
155C4×C61—81no—
156C4×C61C2×#10411yescharacteristic
157C4×C61#42111yescharacteristic
158C4×C61#44412yes—
159Dic61—21no—
160Dic61—21no—
161Dic61—81no—
162Dic61—81no—
163Dic61#47312yes—
164#3170—611no—
165C4×#108—611no—
166#1526—611no—
167#1526—611no—
168#1485—611no—
169#1485—611no—
170#1451—611no—
171C2×C61#197511yescharacteristic
172C2×C61#197911yescharacteristic
173C2×C61#198011yescharacteristic
174D61—41no—
175#533—611no—
176#533—611no—
177#500—611no—
178#494—611no—
179#487—611no—
180#487#692311yescharacteristic
181#467—1221no—
182#467—1221no—
183C4×Q16—1221no—
184C4×Q16—1221no—
185#431—611no—
186C2×#108—1221no—
187C4×M16—611no—
188C4×M16—611no—
189C4×M16—611no—
190C2×C4×C8—611no—
191#341—1221no—
192#330—1222no—
193#330—1222no—
194Q8⋊C8—1222no—
195Q8⋊C8—1222no—
196#322—1221no—
197#322—1221no—
198C61#972711yescharacteristic, complemented, Sylow
199C2×Q16—1221no—
200C2×Q16—1221no—
201C2×M16—1221no—
202C2×M16—1221no—
203C2×M16—1221no—
204C22×C8—611no—
205C22×C8—611no—
206C4⋊Q8—611no—
207C4⋊Q8—611no—
208C4⋊Q8C2×#692311yescharacteristic
209C4⋊Q8C2×#692311yescharacteristic
210#125—1221no—
211#125—1221no—
212C22⋊Q8—1221no—
213C22⋊Q8—1221no—
214C22⋊Q8—1221no—
215C22⋊Q8—1221no—
216C4×Q8—1221no—
217C4×Q8—1221no—
218C4×Q8—1221no—
219C4×Q8—1221no—
220#117—1221no—
221#117—1221no—
222C2×C42—611no—
223#108—1224no—
224#107—1221no—
225#107—1221no—
226C4⋊C8—612no—
227#103—21no—
228#103—21no—
229#103—1221no—
230#103—1221no—
231C22⋊C8—1221no—
232#97—612no—
233#97—1221no—
234#97—1221no—
235C4×C8—611no—
236C4×C8—611no—
237C4×C8—611no—
238C4×C8—1221no—
239C4×C8—1221no—
240C4×C8—1221no—
241C4×C8—1221no—
242C4×C8C2×#692311yescharacteristic
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—1221no—
246C2×Q8—1221no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250Q16—2442no—
251Q16—2442no—
252M16—1222no—
253M16—1222no—
254M16—2442no—
255M16—2441no—
256M16—2441no—
257C2×C8—611no—
258C2×C8—611no—
259C2×C8—1222no—
260C2×C8—1222no—
261C2×C8—1222no—
262C2×C8—2441no—
263C2×C8—2441no—
264C2×C8—2441no—
265C2×C8C22⋊#692311yescharacteristic
266C2×C8C22⋊#692311yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C22⋊C4—2441no—
280C22⋊C4—2441no—
281C42—611no—
282C42—611no—
283C42—611no—
284C42—2441no—
285C42—2441no—
286C42C22×#692311yescharacteristic
287C23—611no—
288Q8—41no—
289Q8—41no—
290Q8—42no—
291Q8—2441no—
292Q8—2441no—
293Q8—2442no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—611no—
297C2×C4—611no—
298C2×C4—611no—
299C2×C4—1222no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1222no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4C2×C22⋊#692311yescharacteristic
306C2×C4D4×#692311yescharacteristic
307C2×C4D4×#692311yescharacteristic
308C8—21no—
309C8—21no—
310C8—612no—
311C8—1221no—
312C8—2442no—
313C8—2442no—
314C8—2442no—
315C8—2442no—
316C22—1221no—
317C22—1221no—
318C22—1221no—
319C22#1684071411yescharacteristic
320C4—21no—
321C4—81no—
322C4—81no—
323C4—612no—
324C4—1221no—
325C4—1221no—
326C4—4881no—
327C4—4881no—
328C4D61⋊#10411yescharacteristic
329C4#1684075911yescharacteristic
330C4#1684080712yes—
331C2—2441no—
332C2#2146197511yescharacteristic
333C2#2146198111yescharacteristic
334C2#2146198411yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#487C4
socleC22×C61#390
prime radicalC22×D61#124
cosocleC42×D61C23
hypercenter#487#6923
hypocenterC61#9727
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
198. C61#9727semidirect

Maximal subgroups

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

subgroupindex
C4×#145198482
#214612772
#214611432
#214611422
#214610292
#214564042
#972761