Finite Group Databasebeta

← #29581330

Subgroups — #29581330

Order 15616.

484 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#16840168C211yesmaximal, characteristic
2C2×#16840130C211yesmaximal, characteristic
3#21453887C211yesmaximal, characteristic
4C2×#16839503C211yesmaximal, characteristic
5C2×#16839503C211yesmaximal, characteristic
6#21443700C211yesmaximal, characteristic
7C61×#1993C211yesmaximal, characteristic
8C2×#14519769C2211yescharacteristic
9C2×#14519769C2211yescharacteristic
10#16840168—22no—
11#16840168—22no—
12#16840130—22no—
13#16840130—22no—
14C2×#14519710—21no—
15C2×#14519708—21no—
16C2×#14519701—21no—
17C2×#14519701—21no—
18C2×#14519688C2211yescharacteristic
19C2×#14519688C2211yescharacteristic
20#16839702—21no—
21#16839702—21no—
22#16839694—21no—
23#16839694—21no—
24#16839692—22no—
25#16839503—22no—
26#16839503—22no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C2×#97×C61C2211yescharacteristic
29C61×#382C2211yescharacteristic
30C61×#340—22no—
31C22×#92418—21no—
32C22×#92418—21no—
33#14519769—21no—
34#14519769—21no—
35#14519769—21no—
36#14519769—21no—
37#14519769—21no—
38#14519769—21no—
39#14519769—21no—
40#14519769—21no—
41C2×C4⋊Dic61—22no—
42C2×C4⋊Dic61D411yescharacteristic
43C2×C4⋊Dic61D411yescharacteristic
44C2×C4⋊Dic61D411yescharacteristic
45C2×C4⋊Dic61D411yescharacteristic
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758196—21no—
50#14519710—24no—
51#14519708—24no—
52#14519701—24no—
53#14519701—24no—
54#14519688—21no—
55#14519688—21no—
56#14519688D412yes—
57#14519688D412yes—
58#14519684—22no—
59#14519684—22no—
60#14519684—22no—
61C22×Q8×C61—21no—
62C22×C8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61D412yes—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61D412yes—
70C2×C42×C61C2311yescharacteristic
71#97×C61—21no—
72#97×C61—21no—
73#95×C61—21no—
74#95×C61—21no—
75C2×Q8×C61—22no—
76C2×Q8×C61—44no—
77C2×Q8×C61—41no—
78C22×C4×C61—22no—
79C22×C4×C61—41no—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C2×C8×C61—22no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C4⋊C4×C61—22no—
91C4⋊C4×C61—22no—
92C4⋊C4×C61—42no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C42×C61C2×D411yescharacteristic
96C42×C61C2×D411yescharacteristic
97C42×C61C2×D411yescharacteristic
98C42×C61#4111yescharacteristic
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—82no—
108#11758196—41no—
109#11758196—41no—
110#11758196—41no—
111#11758196—41no—
112#11758196—41no—
113#11758196—41no—
114#11758196—41no—
115#11758196—41no—
116C2×#92418—24no—
117C2×#92418—22no—
118C2×#92418—22no—
119C2×#92418—42no—
120C23×C61#12011yescharacteristic
121Q8×C61—44no—
122Q8×C61—82no—
123C2×C4×C61—22no—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—21no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61—82no—
132C2×C4×C61#12011yescharacteristic
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12711yescharacteristic
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—42no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C8×C61—42no—
149#92418—24no—
150#92418—42no—
151#10084—611nomaximal, Sylow
152C22×C61#39211yescharacteristic
153C22×C61#45412yes—
154C22×C61#45511yescharacteristic
155C22×C61#45612yes—
156C22×C61#45611yescharacteristic
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—82no—
164C4×C61—82no—
165Dic61—81no—
166Dic61—81no—
167Dic61—81no—
168Dic61—81no—
169C2×#501—611no—
170C2×#491—611no—
171#2822—611no—
172#1993D6111yescharacteristic
173C2×#330—611no—
174C2×#330—611no—
175#1295—611no—
176C2×C61#166312yes—
177C2×C61#166412yes—
178C2×C61#200311yescharacteristic
179C2×C61#200511yescharacteristic
180C2×C61#200711yescharacteristic
181C2×C4⋊Q8C2×D6111yescharacteristic
182C2×#125—611no—
183C2×#125—611no—
184#501—1222no—
185#501—1222no—
186#491—1222no—
187#491—1222no—
188C2×#107—1221no—
189C2×#106—1221no—
190C2×#103—1221no—
191C2×#103—1221no—
192C2×#97—611no—
193C2×#97—611no—
194C2×#97C2×D6111yescharacteristic
195#400—1221no—
196#400—1221no—
197#398—1221no—
198#398—1221no—
199#398—1222no—
200#382C2×D6111yescharacteristic
201#340—22no—
202#330—1222no—
203#330—1222no—
204C61#1008411yescharacteristic, complemented, Sylow
205C22×Q8—21no—
206C22×C8—21no—
207C22×C8—1221no—
208C22×C8—1221no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8D24412yes—
213#125—1221no—
214#125—1221no—
215#125—1221no—
216#125—1221no—
217#125—1221no—
218#125—1221no—
219#125—1221no—
220#125—1221no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—1222no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4C22⋊D6112yes—
233C2×C42C22×D6111yescharacteristic
234#107—1224no—
235#106—1224no—
236#103—1224no—
237#103—1224no—
238#97—21no—
239#97—21no—
240#97—612no—
241#97—612no—
242#97—1221no—
243#97—1221no—
244#95—21no—
245#95—21no—
246#95—1222no—
247#95—1222no—
248#95—1222no—
249C2×Q8—22no—
250C2×Q8—44no—
251C2×Q8—41no—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4D4×D6111yescharacteristic
259C22×C4D4×D6111yescharacteristic
260C22×C4C2×C22⋊D6111yescharacteristic
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—1224no—
265C2×C8—1222no—
266C2×C8—1222no—
267C2×C8—2442no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—42no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—4882no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C42C2×D24411yescharacteristic
291C42#1175822211yescharacteristic
292C42D4×D6111yescharacteristic
293C42D4×D6111yescharacteristic
294C23#1451974511yescharacteristic
295Q8—44no—
296Q8—82no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2442no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2442no—
316C2×C4#1451974711yescharacteristic
317C2×C4#1451974711yescharacteristic
318C2×C4#1451975011yescharacteristic
319C2×C4#1451975011yescharacteristic
320C2×C4#1451975111yescharacteristic
321C2×C4#1451977311yescharacteristic
322C8—42no—
323C8—1224no—
324C8—2442no—
325C22#1683967111yescharacteristic
326C22#1683993312yes—
327C22#1683993911yescharacteristic
328C22#1683994312yes—
329C22#1683994411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—82no—
338C4—4881no—
339C4—4881no—
340C4—4881no—
341C4—4881no—
342C2#2144514612yes—
343C2#2144515212yes—
344C2#2144684211yescharacteristic
345C2#2144685611yescharacteristic
346C2#2144686511yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1993C2
socle, prime radicalC23×C61#120
hypercenter#1993D61
hypocenterC61#10084
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
204. C61#10084semidirect

Maximal subgroups

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

subgroupindex
C2×#168401682
C2×#168401302
#214538872
C2×#168395032
#214437002
C61×#19932
#1008461