Finite Group Databasebeta

← #30602006

Subgroups — #30602006

Order 15616.

418 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 96 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#21462012C211yesmaximal, characteristic
2#21461962C211yesmaximal, characteristic
3#21461376C211yesmaximal, characteristic
4#21461334C211yesmaximal, characteristic
5#21461328C211yesmaximal, characteristic
6#21461028C211yesmaximal, characteristic
7C2×#16840159C211yesmaximal, characteristic
8#16840779C2211yescharacteristic
9#16840765C2211yescharacteristic
10#16840765C2211yescharacteristic
11C2×#14519838—22no—
12C4×#11758217C2211yescharacteristic
13#16840642—22no—
14#16840626—21no—
15#16840625—21no—
16#16840621—22no—
17#16840621—22no—
18#92420⋊C8—21no—
19#16840603—21no—
20C2×#14519776C2211yescharacteristic
21C2×#14519776C2211yescharacteristic
22#16840159—21no—
23#16840159—21no—
24#16840159—21no—
25#16840159—21no—
26C2×#14519709C411yescharacteristic
27C2×#14519708C411yescharacteristic
28C2×#14519708C411yescharacteristic
29C2×C8×Dic61C2211yescharacteristic
30C2×#106×C61C411yescharacteristic
31C2×#11758217—21no—
32C2×#11758217—21no—
33C2×#11758217D412yes—
34#14519844—21no—
35#14519844—21no—
36#14519844D412yes—
37C4⋊#92420—21no—
38C4⋊#92420—21no—
39#14519838—44no—
40C22⋊#92420—21no—
41#14519832—21no—
42C4×#92420—21no—
43C4×#92420—21no—
44C22×Dic122—21no—
45C22×Dic122—21no—
46C22×#92418C2×C411yescharacteristic
47#14519776—21no—
48#14519776—21no—
49#14519776—21no—
50#14519776—21no—
51#14519776—21no—
52#14519776—21no—
53#14519776—21no—
54#14519776—21no—
55C2×C4⋊Dic61C2×C411yescharacteristic
56C2×C4⋊Dic61C2×C411yescharacteristic
57C2×#11758196—21no—
58C2×#11758196—21no—
59C2×C4×Dic61C2311yescharacteristic
60#14519709—21no—
61#14519709—21no—
62#14519708—21no—
63#14519708—21no—
64#14519708—21no—
65#14519708—21no—
66C8×Dic61D411yescharacteristic
67C8×Dic61D411yescharacteristic
68C8×Dic61D411yescharacteristic
69C8×Dic61D411yescharacteristic
70C22×C8×C61C2×C411yescharacteristic
71C2×C4⋊C4×C61C2×C411yescharacteristic
72C2×C4⋊C4×C61C2×C411yescharacteristic
73#106×C61—21no—
74#106×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C22×C411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61#4111yescharacteristic
82C2×Dic122—41no—
83C2×Dic122—41no—
84C2×Dic122—41no—
85C2×Dic122—41no—
86C2×Dic122—42no—
87C2×Dic122—42no—
88C2×Dic122—82no—
89#11758217—22no—
90#11758217—22no—
91#11758217—42no—
92#11758217—42no—
93C2×#92420—22no—
94C2×#92420—22no—
95C2×#92420—41no—
96C2×#92420—41no—
97C2×C8×C61—22no—
98C2×C8×C61C22⋊C411yescharacteristic
99C2×C8×C61C22⋊C411yescharacteristic
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108#11758196—41no—
109#11758196—41no—
110#11758196—41no—
111#11758196—41no—
112C4×Dic61C2×D411yescharacteristic
113C4×Dic61C2×D411yescharacteristic
114C4×Dic61C2×D411yescharacteristic
115C4×Dic61#4111yescharacteristic
116C2×#92418—22no—
117C2×#92418C22⋊C411yescharacteristic
118C2×#92418C22⋊C411yescharacteristic
119C23×C61C4×D411yescharacteristic
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—81no—
126C2×C4×C61C2×C22⋊C411yescharacteristic
127C2×C4×C61C4×D411yescharacteristic
128C2×Dic61—22no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—42no—
132C2×Dic61—81no—
133C2×Dic61#12111yescharacteristic
134C2×Dic61#12111yescharacteristic
135C2×Dic61#12411yescharacteristic
136C2×Dic61#12711yescharacteristic
137C2×Dic61AGL(1,ℤ/8)12yes—
138C2×Dic61#13712yes—
139Dic122—82no—
140Dic122—82no—
141Dic122—82no—
142Dic122—81no—
143Dic122—81no—
144#92420—42no—
145#92420—42no—
146#92420—81no—
147#92420—81no—
148C8×C61—21no—
149C8×C61#10112yescomplemented
150#92418—21no—
151#92418#10112yescomplemented
152#9806—611nomaximal, Sylow
153C22×C61—21no—
154C22×C61—21no—
155C22×C61#39011yescharacteristic
156C22×C61#44012yes—
157C4×C61—21no—
158C4×C61—81no—
159C4×C61—81no—
160C4×C61C2×#10111yescharacteristic
161C4×C61C2×#10111yescharacteristic
162Dic61—21no—
163Dic61—81no—
164Dic61—81no—
165Dic61#46812yes—
166Dic61#47112yes—
167Dic61#49611yescharacteristic
168Dic61#49711yescharacteristic
169C2×#498—611no—
170#1997—611no—
171#1966—611no—
172#1567—611no—
173#1549—611no—
174#1546—611no—
175#1451—611no—
176C2×C61—22no—
177C2×C61#196611yescharacteristic
178C2×C61#197311yescharacteristic
179C2×C61#197711yescharacteristic
180C2×C4⋊Q8—611no—
181C2×C4⋊Q8—611no—
182#498—1221no—
183#498—1221no—
184#498—1221no—
185#498—1221no—
186#431—611no—
187C2×#106—611no—
188C2×#106—611no—
189C2×#106—611no—
190C2×#106#692311yescharacteristic
191#423—611no—
192#423—611no—
193C2×#101—1222no—
194C4×M16—611no—
195C2×C4×C8—611no—
196#343—1222no—
197#335—1221no—
198#335—1221no—
199#332—1222no—
200#332—1222no—
201#322—1221no—
202#322—1221no—
203C61#980611yescharacteristic, complemented, Sylow
204C22×Q8—1221no—
205C22×Q8—1221no—
206C2×M16—612no—
207C2×M16—1221no—
208C2×M16—1221no—
209C22×C8—611no—
210C22×C8C2×#692311yescharacteristic
211C4⋊Q8—1221no—
212C4⋊Q8—1221no—
213C4⋊Q8—1221no—
214C4⋊Q8—1221no—
215C4⋊Q8—1221no—
216C4⋊Q8—1221no—
217C4⋊Q8—1221no—
218C4⋊Q8—1221no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4C2×#692311yescharacteristic
224C2×C4⋊C4C2×#692311yescharacteristic
225C2×C42—611no—
226#106—21no—
227#106—21no—
228#106—1221no—
229#106—1221no—
230#106—1221no—
231#106—1221no—
232#106—1221no—
233#106—1221no—
234C4⋊C8—612no—
235C4⋊C8—1221no—
236C4⋊C8—1221no—
237C4⋊C8—1221no—
238C4⋊C8—1221no—
239#101—2444no—
240C22⋊C8—1221no—
241#97—1221no—
242C4×C8—611no—
243C4×C8—611no—
244C4×C8—611no—
245C4×C8—611no—
246C4×C8—1221no—
247C4×C8—1221no—
248C2×Q8—4882no—
249C2×Q8—2442no—
250C2×Q8—2441no—
251C2×Q8—2441no—
252C2×Q8—2441no—
253C2×Q8—2441no—
254C2×Q8—2442no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4C22×#692311yescharacteristic
262M16—1222no—
263M16—1222no—
264M16—2442no—
265M16—2442no—
266C2×C8—22no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8—1222no—
270C2×C8—1222no—
271C2×C8—1222no—
272C2×C8—2441no—
273C2×C8—2441no—
274C2×C8C22⋊#692311yescharacteristic
275C2×C8C22⋊#692311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C42—611no—
289C42—611no—
290C42—611no—
291C42—611no—
292C23D4×#692311yescharacteristic
293Q8—4882no—
294Q8—4882no—
295Q8—4881no—
296Q8—4881no—
297Q8—4882no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—81no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—612no—
308C2×C4—612no—
309C2×C4—611no—
310C2×C4—1222no—
311C2×C4—4881no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2442no—
315C2×C4C2×C22⋊#692311yescharacteristic
316C2×C4D4×#692311yescharacteristic
317C8—21no—
318C8—612no—
319C8—1221no—
320C8—4881no—
321C8—4881no—
322C8—2442no—
323C8—2442no—
324C8#1451983812yescomplemented
325C22—21no—
326C22—21no—
327C22#1684071411yescharacteristic
328C22#1684080112yes—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—612no—
333C4—611no—
334C4—611no—
335C4—612no—
336C4—1221no—
337C4—4881no—
338C4—4881no—
339C4C2×#1451983811yescharacteristic
340C4D61⋊#10111yescharacteristic
341C2—22no—
342C2#2146196211yescharacteristic
343C2#2146196911yescharacteristic
344C2#2146197911yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#106×C61C4
socleC22×C61#390
prime radicalC23×C61C4×D4
cosocleC2×C4×Dic61C23
hypercenterC2×#106#6923
hypocenterC61#9806
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
149. C8×C61#101semidirect
151. #92418#101semidirect
203. C61#9806semidirect
324. C8#14519838semidirect

Maximal subgroups

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

subgroupindex
#214620122
#214619622
#214613762
#214613342
#214613282
#214610282
C2×#168401592
#980661