Finite Group Databasebeta

← #29583207

Subgroups — #29583207

Order 15616.

352 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 77 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#21446762C211yesmaximal, characteristic
2#21444369C211yesmaximal, characteristic
3#21444330C211yesmaximal, characteristic
4#21443712C211yesmaximal, characteristic
5#21443683C211yesmaximal, characteristic
6#21443675C211yesmaximal, characteristic
7C61×#2606C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16839819C2211yescharacteristic
10#16839819C2211yescharacteristic
11C4×#11758194C2211yescharacteristic
12#16839522—21no—
13#16839522—21no—
14#16839498—21no—
15#16839498—21no—
16#16839498—21no—
17#16839498—21no—
18C61×#398—21no—
19C61×#398—21no—
20C61×#389—21no—
21C61×#389—21no—
22C61×#387—21no—
23C61×#387—21no—
24C61×#383C2211yescharacteristic
25C4×C4⋊C4×C61C2211yescharacteristic
26C61×#376C2211yescharacteristic
27C2×#11758194—21no—
28#14519777Q811yescharacteristic
29#14519777Q811yescharacteristic
30#14519769—21no—
31#14519756—21no—
32#14519756—21no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35#14519736—21no—
36C4⋊#92418—21no—
37C4⋊#92418—21no—
38C22⋊#92418—21no—
39C22⋊#92418—21no—
40#14519688—21no—
41#14519688—21no—
42#14519688—21no—
43C4×#92418—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C42×C61—21no—
52C2×C42×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C2×C42×C61C2311yescharacteristic
55#95×C61—21no—
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61D411yescharacteristic
62#95×C61D411yescharacteristic
63#95×C61D411yescharacteristic
64#95×C61D411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C2×Dic122—21no—
75C2×Dic122—21no—
76C4⋊C4×C61—42no—
77C4⋊C4×C61—42no—
78C4⋊C4×C61—42no—
79C4⋊C4×C61—42no—
80C4⋊C4×C61—42no—
81C4⋊C4×C61—81no—
82C4⋊C4×C61—81no—
83C42×C61—42no—
84C42×C61—41no—
85C42×C61—41no—
86C42×C61C2×Q811yescharacteristic
87C42×C61#4111yescharacteristic
88C42×C61#4111yescharacteristic
89C42×C61#4111yescharacteristic
90C22⋊Dic61—41no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95#11758196—41no—
96#11758196—41no—
97C4×Dic61—41no—
98#11758194—22no—
99#11758194—41no—
100C2×#92418—41no—
101C2×#92418—41no—
102C2×#92418—41no—
103C23×C61#12011yescharacteristic
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—22no—
107C2×C4×C61—22no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61C22⋊Q811yescharacteristic
127C2×C4×C61C22⋊Q811yescharacteristic
128C2×C4×C61C22⋊Q811yescharacteristic
129C2×C4×C61#12411yescharacteristic
130C2×C4×C61#12411yescharacteristic
131C2×C4×C61#12411yescharacteristic
132C2×Dic61—41no—
133C2×Dic61—41no—
134Dic122—81no—
135Dic122—81no—
136#92418—42no—
137#92418—81no—
138#92418—81no—
139#10381—611nomaximal, Sylow
140C22×C61—21no—
141C22×C61—21no—
142C22×C61#39311yescharacteristic
143C22×C61#45511yescharacteristic
144C22×C61#45611yescharacteristic
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—42no—
152C4×C61—42no—
153C4×C61—81no—
154C4×C61—81no—
155C4×C61—81no—
156C4×C61—81no—
157Dic61—81no—
158Dic61—81no—
159#2606D6111yescharacteristic
160#1986—611no—
161#1515—611no—
162#1506—611no—
163#1300—611no—
164#1288—611no—
165#1285—611no—
166C2×C61—21no—
167C2×C61—21no—
168C2×C61#202811yescharacteristic
169C2×C61#203111yescharacteristic
170C2×C61#203111yescharacteristic
171#533—611no—
172#432—611no—
173#432—611no—
174C4×M16—611no—
175#398—21no—
176#398—21no—
177#389—21no—
178#389—21no—
179#387—21no—
180#387—21no—
181#383C2×D6111yescharacteristic
182C4×C4⋊C4C2×D6111yescharacteristic
183#376C2×D6111yescharacteristic
184#339—1221no—
185#339—1221no—
186#328—1221no—
187#328—1221no—
188#328—1221no—
189#328—1221no—
190C61#1038111yescharacteristic, complemented, Sylow
191C2×M16—1221no—
192C4⋊Q8—611no—
193C4⋊Q8—611no—
194#125—1221no—
195C22⋊Q8—1221no—
196C22⋊Q8—1221no—
197C4×Q8—1221no—
198C4×Q8—1221no—
199#117—1221no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C42—21no—
208C2×C42C22⋊D6111yescharacteristic
209C2×C42C22⋊D6111yescharacteristic
210C2×C42C22×D6111yescharacteristic
211C4⋊C8—1221no—
212C4⋊C8—1221no—
213C22⋊C8—1221no—
214C22⋊C8—1221no—
215#97—1221no—
216#97—1221no—
217#97—1221no—
218C4×C8—1221no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95C22⋊D6111yescharacteristic
226#95C22⋊D6111yescharacteristic
227#95C22⋊D6111yescharacteristic
228#95C22⋊D6111yescharacteristic
229C2×Q8—1221no—
230C2×Q8—1221no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4C2×C22⋊D6111yescharacteristic
238C22×C4C2×C22⋊D6111yescharacteristic
239C22×C4C2×C22⋊D6111yescharacteristic
240M16—1222no—
241M16—2441no—
242C2×C8—2441no—
243C2×C8—2441no—
244C2×C8—2441no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—81no—
251C4⋊C4—81no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4—1221no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C22⋊C4—2441no—
259C42—41no—
260C42—41no—
261C42—42no—
262C42—2441no—
263C42Q8×D6111yescharacteristic
264C42#1175822611yescharacteristic
265C42#1175822611yescharacteristic
266C42#1175822611yescharacteristic
267C23#1451974611yescharacteristic
268Q8—4881no—
269Q8—4881no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4#1451975311yescharacteristic
295C2×C4#1451975311yescharacteristic
296C2×C4#1451975311yescharacteristic
297C2×C4#1451976611yescharacteristic
298C2×C4#1451976611yescharacteristic
299C2×C4#1451976611yescharacteristic
300C8—4881no—
301C8—4881no—
302C8—2442no—
303C22—21no—
304C22—21no—
305C22#1683967311yescharacteristic
306C22#1683994011yescharacteristic
307C22#1683994511yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—42no—
315C4—42no—
316C4—81no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—4881no—
321C4—4881no—
322C2—21no—
323C2—21no—
324C2#2144697711yescharacteristic
325C2#2144698811yescharacteristic
326C2#2144698811yescharacteristic
subgroupG/H
centerC22#16839673
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2606C2
socleC22×C61#393
prime radicalC23×C61#120
hypercenter#2606D61
hypocenterC61#10381
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2606

Complements

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

NH ≅ G/Ntype
190. C61#10381semidirect

Maximal subgroups

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

subgroupindex
#214467622
#214443692
#214443302
#214437122
#214436832
#214436752
C61×#26062
#1038161