Finite Group Databasebeta

← #30602009

Subgroups — #30602009

Order 15616.

418 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 90 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#21462011C211yesmaximal, characteristic
2#21461962C211yesmaximal, characteristic
3#21461376C211yesmaximal, characteristic
4#21461332C211yesmaximal, characteristic
5#21461328C211yesmaximal, characteristic
6#21461028C211yesmaximal, characteristic
7C2×#16840111C211yesmaximal, characteristic
8#16840779C2211yescharacteristic
9#16840765C2211yescharacteristic
10#16840765C2211yescharacteristic
11C2×#14519838—22no—
12C4×#11758217C2211yescharacteristic
13#16840642—22no—
14#16840626—21no—
15#16840625—21no—
16#16840622—22no—
17#16840621—22no—
18#92420⋊C8—21no—
19#16840603—21no—
20C2×#14519776C2211yescharacteristic
21C2×#14519775C2211yescharacteristic
22#16840111—21no—
23#16840111—21no—
24#16840111—21no—
25#16840111—21no—
26C2×#14519702C411yescharacteristic
27C2×#14519701C411yescharacteristic
28C2×#14519700C411yescharacteristic
29C2×C8×Dic61C2211yescharacteristic
30C2×#103×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×Dic122C2×C411yescharacteristic
46C22×#92418C2×C411yescharacteristic
47#14519776—21no—
48#14519776—21no—
49#14519776—21no—
50#14519776—21no—
51#14519775—21no—
52#14519775—21no—
53#14519775—21no—
54#14519775—21no—
55C2×C4⋊Dic61C2×C411yescharacteristic
56C2×#11758196—21no—
57C2×#11758196—21no—
58C2×#11758196—21no—
59C2×C4×Dic61C2311yescharacteristic
60#14519702—21no—
61#14519702—21no—
62#14519701—21no—
63#14519701—21no—
64#14519700—21no—
65#14519700—21no—
66C8×Dic61D411yescharacteristic
67C8×Dic61D411yescharacteristic
68C8×Dic61D411yescharacteristic
69C8×Dic61D411yescharacteristic
70C22×Q8×C61C2×C411yescharacteristic
71C22×C8×C61C2×C411yescharacteristic
72C2×C4⋊C4×C61C2×C411yescharacteristic
73#103×C61—21no—
74#103×C61—21no—
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61—41no—
78C2×Q8×C61—41no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61C22×C411yescharacteristic
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61C2×D411yescharacteristic
85C22×Dic61#4111yescharacteristic
86C2×Dic122—21no—
87C2×Dic122—21no—
88C2×Dic122—41no—
89C2×Dic122—41no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×Dic122—42no—
93C2×Dic122—42no—
94#11758217—22no—
95#11758217—22no—
96#11758217—42no—
97#11758217—42no—
98C2×#92420—22no—
99C2×#92420—22no—
100C2×#92420—41no—
101C2×#92420—41no—
102C2×C8×C61—41no—
103C2×C8×C61C22⋊C411yescharacteristic
104C2×C8×C61C22⋊C411yescharacteristic
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109#11758196—41no—
110#11758196—41no—
111#11758196—41no—
112#11758196—41no—
113#11758196—41no—
114#11758196—41no—
115C4×Dic61C2×D411yescharacteristic
116C4×Dic61C2×D411yescharacteristic
117C4×Dic61C2×D411yescharacteristic
118C4×Dic61#4111yescharacteristic
119C2×#92418—41no—
120C2×#92418C22⋊C411yescharacteristic
121C2×#92418C22⋊C411yescharacteristic
122C23×C61C4×D411yescharacteristic
123Q8×C61—41no—
124Q8×C61—41no—
125Q8×C61—81no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—42no—
131C2×C4×C61—81no—
132C2×C4×C61C2×C22⋊C411yescharacteristic
133C2×C4×C61C4×D411yescharacteristic
134C2×Dic61—22no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—42no—
138C2×Dic61—81no—
139C2×Dic61#12111yescharacteristic
140C2×Dic61#12111yescharacteristic
141C2×Dic61#12411yescharacteristic
142C2×Dic61#12711yescharacteristic
143C2×Dic61AGL(1,ℤ/8)12yes—
144C2×Dic61#13712yes—
145Dic122—41no—
146Dic122—41no—
147Dic122—82no—
148Dic122—81no—
149Dic122—81no—
150Dic122—81no—
151#92420—42no—
152#92420—42no—
153#92420—81no—
154#92420—81no—
155C8×C61—21no—
156C8×C61—21no—
157#92418—21no—
158#92418—21no—
159#9809—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61#39011yescharacteristic
163C22×C61#44012yes—
164C4×C61—21no—
165C4×C61—81no—
166C4×C61—81no—
167C4×C61#41311yescharacteristic
168C4×C61#41311yescharacteristic
169Dic61—21no—
170Dic61—81no—
171Dic61—81no—
172Dic61#46812yes—
173Dic61#47312yes—
174Dic61#49611yescharacteristic
175Dic61#49711yescharacteristic
176C2×#487—611no—
177#1997—611no—
178#1966—611no—
179#1567—611no—
180#1548—611no—
181#1546—611no—
182#1451—611no—
183C2×C61—22no—
184C2×C61#196711yescharacteristic
185C2×C61#197311yescharacteristic
186C2×C61#197911yescharacteristic
187C2×C4⋊Q8—611no—
188C2×C4⋊Q8—611no—
189#487—1221no—
190#487—1221no—
191#487—1221no—
192#487—1221no—
193#431—611no—
194#423—611no—
195#423—611no—
196C2×#103—611no—
197C2×#103—611no—
198C2×#103—611no—
199C2×#103#692311yescharacteristic
200C2×#101—1222no—
201C4×M16—611no—
202C2×C4×C8—611no—
203#343—1222no—
204#335—1221no—
205#335—1221no—
206#333—1222no—
207#332—1222no—
208#322—1221no—
209#322—1221no—
210C61#980911yescharacteristic, complemented, Sylow
211C22×Q8—611no—
212C22×Q8—1221no—
213C22×Q8C2×#692311yescharacteristic
214C2×M16—612no—
215C2×M16—1221no—
216C2×M16—1221no—
217C22×C8—611no—
218C22×C8C2×#692311yescharacteristic
219C4⋊Q8—1221no—
220C4⋊Q8—1221no—
221C4⋊Q8—1221no—
222C4⋊Q8—1221no—
223C4⋊Q8—1221no—
224C4⋊Q8—1221no—
225C4⋊Q8—1221no—
226C4⋊Q8—1221no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4C2×#692311yescharacteristic
232C2×C42—611no—
233C4⋊C8—612no—
234C4⋊C8—1221no—
235C4⋊C8—1221no—
236C4⋊C8—1221no—
237C4⋊C8—1221no—
238#103—21no—
239#103—21no—
240#103—1221no—
241#103—1221no—
242#103—1221no—
243#103—1221no—
244#103—1221no—
245#103—1221no—
246#101—2444no—
247C22⋊C8—1221no—
248#97—1221no—
249C4×C8—611no—
250C4×C8—611no—
251C4×C8—611no—
252C4×C8—611no—
253C4×C8—1221no—
254C4×C8—1221no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—1221no—
260C2×Q8—1221no—
261C2×Q8—2441no—
262C2×Q8—2441no—
263C2×Q8—2442no—
264C2×Q8—2441no—
265C2×Q8—2441no—
266C2×Q8—2442no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4C22×#692311yescharacteristic
274M16—1222no—
275M16—1222no—
276M16—2442no—
277M16—2442no—
278C2×C8—41no—
279C2×C8—611no—
280C2×C8—611no—
281C2×C8—1222no—
282C2×C8—1222no—
283C2×C8—2441no—
284C2×C8—2441no—
285C2×C8—2441no—
286C2×C8C22⋊#692311yescharacteristic
287C2×C8C22⋊#692311yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C42—611no—
299C42—611no—
300C42—611no—
301C42—611no—
302C23D4×#692311yescharacteristic
303Q8—41no—
304Q8—41no—
305Q8—81no—
306Q8—4881no—
307Q8—4882no—
308Q8—4881no—
309Q8—4881no—
310Q8—2441no—
311Q8—2441no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—81no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—612no—
322C2×C4—612no—
323C2×C4—611no—
324C2×C4—1222no—
325C2×C4—4881no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2442no—
329C2×C4C2×C22⋊#692311yescharacteristic
330C2×C4D4×#692311yescharacteristic
331C8—21no—
332C8—21no—
333C8—1221no—
334C8—1221no—
335C8—4881no—
336C8—4881no—
337C8—2442no—
338C8—2442no—
339C22—21no—
340C22—21no—
341C22#1684071411yescharacteristic
342C22#1684080112yes—
343C4—21no—
344C4—81no—
345C4—81no—
346C4—612no—
347C4—611no—
348C4—611no—
349C4—612no—
350C4—1221no—
351C4—4881no—
352C4—4881no—
353C4#1684074811yescharacteristic
354C4#1684074911yescharacteristic
355C2—22no—
356C2#2146196311yescharacteristic
357C2#2146196911yescharacteristic
358C2#2146198111yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#103×C61C4
socleC22×C61#390
prime radicalC23×C61C4×D4
cosocleC2×C4×Dic61C23
hypercenterC2×#103#6923
hypocenterC61#9809
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
210. C61#9809semidirect

Maximal subgroups

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

subgroupindex
#214620112
#214619622
#214613762
#214613322
#214613282
#214610282
C2×#168401112
#980961