Finite Group Databasebeta

← #30600867

Subgroups — #30600867

Order 15616.

360 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 72 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#21462731C211yesmaximal, characteristic
2#21461345C211yesmaximal, characteristic
3#21461301C211yesmaximal, characteristic
4#21461093C211yesmaximal, characteristic
5#21460726C211yesmaximal, characteristic
6#21460677C211yesmaximal, characteristic
7#21457022C211yesmaximal, characteristic
8#16840814—21no—
9#16840814—21no—
10#16840813—21no—
11#16840812—21no—
12#16840786—21no—
13#16840786—21no—
14#16840783C2211yescharacteristic
15#16840782C2211yescharacteristic
16#16840782C2211yescharacteristic
17#16840779C2211yescharacteristic
18#16840622—21no—
19#16840621—21no—
20#16840619—21no—
21#16840619—21no—
22#16840608—21no—
23#16840608—21no—
24#16840314C2211yescharacteristic
25C2×#14519768C2211yescharacteristic
26#16840169—21no—
27#16840129—21no—
28#16840098C411yescharacteristic
29#16840095C411yescharacteristic
30#16840092C411yescharacteristic
31#16840072—21no—
32#16840071—21no—
33#16839816C2211yescharacteristic
34C61×#483C411yescharacteristic
35#14519844—21no—
36#14519844—21no—
37#14519844—21no—
38#14519844—21no—
39#14519844—21no—
40C4⋊#92420—21no—
41C4⋊#92420—21no—
42C4⋊#92420—21no—
43C22⋊#92420—21no—
44C22⋊#92420—21no—
45C22⋊#92420—21no—
46C22⋊#92420D411yescharacteristic
47C22⋊#92420D411yescharacteristic
48#14519832—21no—
49#14519832—21no—
50#14519832—21no—
51#14519832—21no—
52#14519832D411yescharacteristic
53#14519832D411yescharacteristic
54C4×#92420—21no—
55C4×#92420—21no—
56C4×#92420—21no—
57#14519776D411yescharacteristic
58#14519775D411yescharacteristic
59#14519768—21no—
60#14519768—21no—
61#14519768—21no—
62#14519768—21no—
63#14519767—21no—
64#14519756C2×C411yescharacteristic
65#14519754—21no—
66Q8×Dic61D411yescharacteristic
67#14519742—21no—
68#14519742D411yescharacteristic
69#14519733—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61C2×C411yescharacteristic
72C2×#11758196—21no—
73C2×C4×Dic61C2311yescharacteristic
74#14519711—21no—
75#14519710—21no—
76#14519708—21no—
77#14519706—21no—
78#14519702—21no—
79#14519701—21no—
80#14519700—21no—
81C22⋊#92418C2×C411yescharacteristic
82#14519687—21no—
83C22⋊Q8×C61C2×C411yescharacteristic
84C2×C4⋊C4×C61C2×C411yescharacteristic
85#106×C61—21no—
86#103×C61—21no—
87C22⋊C8×C61C2×C411yescharacteristic
88C2×Q8×C61C22⋊C411yescharacteristic
89C22×C4×C61—21no—
90C22×C4×C61C22×C411yescharacteristic
91C22×Dic61—21no—
92C22×Dic61C2×D411yescharacteristic
93C22×Dic61#4111yescharacteristic
94C2×Dic122—21no—
95C2×Dic122C22⋊C411yescharacteristic
96C2×#92420—21no—
97C2×#92420—21no—
98C2×#92420—21no—
99C2×#92420—21no—
100C2×#92420—41no—
101C2×#92420—41no—
102C2×C8×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61C22⋊C411yescharacteristic
107C22⋊C4×C61—21no—
108C22⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—41no—
113C4⋊Dic61—41no—
114C4⋊Dic61C22⋊C411yescharacteristic
115#11758196—21no—
116#11758196—21no—
117#11758196—21no—
118#11758196—21no—
119#11758196—21no—
120#11758196—41no—
121#11758196—41no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124C4×Dic61C2×D411yescharacteristic
125C4×Dic61C2×D411yescharacteristic
126C4×Dic61C2×D411yescharacteristic
127C4×Dic61#4111yescharacteristic
128C2×#92418—21no—
129C23×C61C4×D411yescharacteristic
130Q8×C61—41no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—81no—
136C2×C4×C61C2×C22⋊C411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—42no—
143C2×Dic61—41no—
144C2×Dic61#12011yescharacteristic
145C2×Dic61#12111yescharacteristic
146C2×Dic61#12111yescharacteristic
147C2×Dic61#12311yescharacteristic
148Dic122—41no—
149Dic122—81no—
150#92420—41no—
151#92420—41no—
152#92420—41no—
153#92420—41no—
154#92420—81no—
155#92420—81no—
156C8×C61—41no—
157#92418—41no—
158#9336—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61#38611yescharacteristic
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—81no—
168Dic61—21no—
169Dic61—21no—
170Dic61—21no—
171Dic61—21no—
172Dic61—41no—
173Dic61—41no—
174Dic61—81no—
175#3236—611no—
176#2987—611no—
177#1554—611no—
178#1534—611no—
179#1470—611no—
180#1308—611no—
181#1287—611no—
182C2×C61—41no—
183C2×C61#188111yescharacteristic
184C2×C61#190511yescharacteristic
185C2×C61#191511yescharacteristic
186#533—611no—
187C2×#125—611no—
188#501—1221no—
189#491—1221no—
190#484—611no—
191#484—611no—
192#483—611no—
193#483#692311yescharacteristic
194#479—1221no—
195#479—1221no—
196#446—1221no—
197#446—1221no—
198#446—1221no—
199#446—1221no—
200#433—1221no—
201#433—1221no—
202#432—611no—
203#432—611no—
204#432—611no—
205#432—611no—
206#431—611no—
207#333—1221no—
208#332—1221no—
209#330—1221no—
210#330—1221no—
211#324—1221no—
212#324—1221no—
213C61#933611yescharacteristic, complemented, Sylow
214C4⋊Q8—611no—
215C4⋊Q8—611no—
216#125—1221no—
217#125—1221no—
218#125—1221no—
219#125—1221no—
220#125—1221no—
221C22⋊Q8—611no—
222C22⋊Q8—1221no—
223C22⋊Q8C2×#692311yescharacteristic
224C4×Q8—611no—
225C4×Q8—611no—
226C4×Q8—1221no—
227#117—1221no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4C2×#692311yescharacteristic
232C2×C42—611no—
233#107—1221no—
234#107—1221no—
235#106—21no—
236#106—1221no—
237C4⋊C8—1221no—
238C4⋊C8—1221no—
239C4⋊C8—1221no—
240C4⋊C8—1221no—
241C4⋊C8—1221no—
242C4⋊C8—1221no—
243C4⋊C8—1221no—
244C4⋊C8—1221no—
245C4⋊C8—1221no—
246#103—21no—
247#103—1221no—
248#103—1221no—
249#103—1221no—
250C22⋊C8—611no—
251C22⋊C8—611no—
252C22⋊C8—611no—
253C22⋊C8—1221no—
254C22⋊C8—1221no—
255C22⋊C8—1221no—
256C22⋊C8C2×#692311yescharacteristic
257#97—611no—
258#97—611no—
259#97—1221no—
260#97—1221no—
261#97—1221no—
262#97—1221no—
263#97—1221no—
264C4×C8—1221no—
265C4×C8—1221no—
266C4×C8—1221no—
267C2×Q8—611no—
268C2×Q8—1221no—
269C2×Q8C22⋊#692311yescharacteristic
270C22×C4—21no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—1221no—
274C22×C4C22×#692311yescharacteristic
275C2×C8—21no—
276C2×C8—1221no—
277C2×C8—1221no—
278C2×C8—1221no—
279C2×C8—1221no—
280C2×C8—1221no—
281C2×C8—2441no—
282C2×C8—2441no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—611no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4C22⋊#692311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—1221no—
302C42—611no—
303C42—611no—
304C42—611no—
305C42—611no—
306C42—1221no—
307C42—1221no—
308C23D4×#692311yescharacteristic
309Q8—41no—
310Q8—4881no—
311Q8—2441no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—611no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2442no—
326C2×C4—2441no—
327C2×C4C2×C22⋊#692311yescharacteristic
328C2×C4D4×#692311yescharacteristic
329C8—41no—
330C8—4881no—
331C8—4881no—
332C8—2441no—
333C8—2441no—
334C8—2441no—
335C8—2441no—
336C8—2441no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22#1684071011yescharacteristic
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—81no—
346C4—1221no—
347C4—1221no—
348C4—1221no—
349C4—1221no—
350C4—4881no—
351C4—2441no—
352C4—2441no—
353C2—41no—
354C2#2146181611yescharacteristic
355C2#2146185511yescharacteristic
356C2#2146187111yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#483C4
socleC22×C61#386
prime radicalC23×C61C4×D4
cosocleC2×C4×Dic61C23
hypercenter#483#6923
hypocenterC61#9336
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
213. C61#9336semidirect

Maximal subgroups

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

subgroupindex
#214627312
#214613452
#214613012
#214610932
#214607262
#214606772
#214570222
#933661