Finite Group Databasebeta

← #29569092

Subgroups — #29569092

Order 15616.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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#21452851C211yesmaximal, characteristic
2#21447378C211yesmaximal, characteristic
3#21447292C211yesmaximal, characteristic
4#21447227C211yesmaximal, characteristic
5#21443641C211yesmaximal, characteristic
6#21443641C211yesmaximal, characteristic
7C61×#1272C211yesmaximal, characteristic
8C2×#14519775—21no—
9C2×#14519711—21no—
10C2×#14519701—21no—
11#16839692—21no—
12#16839683—21no—
13#16839683—21no—
14#16839660C2211yescharacteristic
15#16839660C2211yescharacteristic
16#16839647—21no—
17#16839647—21no—
18#16839632C2211yescharacteristic
19#16839525—21no—
20#16839525—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×#92418—21no—
29#14519775—42no—
30#14519775—42no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×C4×Dic61—21no—
44#14519711—42no—
45#14519701—42no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61D411yescharacteristic
52C22×C8×C61—21no—
53C22×C8×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56#95×C61—21no—
57#95×C61—21no—
58C2×Q8×C61—21no—
59C2×Q8×C61—41no—
60C2×Q8×C61—41no—
61C2×Q8×C61D812yes—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—41no—
72C2×Dic122—42no—
73C2×Dic122—81no—
74C2×Dic122—81no—
75C2×C8×C61—22no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C4⋊C4×C61—41no—
82C42×C61—41no—
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87C4⋊Dic61—42no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—81no—
93C4⋊Dic61SD1612yes—
94C4⋊Dic61Q1612yes—
95#11758196—42no—
96#11758196—42no—
97#11758196—41no—
98#11758196—41no—
99#11758196—41no—
100#11758196—41no—
101C4×Dic61—42no—
102C2×#92418—41no—
103C2×#92418—41no—
104C2×#92418—41no—
105C23×C61#12011yescharacteristic
106Q8×C61—42no—
107Q8×C61—81no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—22no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61C2×D811yescharacteristic
121C2×C4×C61C2×SD1611yescharacteristic
122C2×C4×C61C2×Q1611yescharacteristic
123C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C61#13711yescharacteristic
125C2×C4×C61#13711yescharacteristic
126C2×Dic61—22no—
127C2×Dic61—22no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—81no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141Dic122—84no—
142C8×C61—42no—
143C8×C61—81no—
144#92418—81no—
145#7794—611nomaximal, Sylow
146C22×C61#44711yescharacteristic
147C22×C61#44811yescharacteristic
148C22×C61#45111yescharacteristic
149C22×C61#45411yescharacteristic
150C22×C61#45511yescharacteristic
151C22×C61#45611yescharacteristic
152C22×C61#45811yescharacteristic
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—42no—
160C4×C61—81no—
161Dic61—42no—
162Dic61—42no—
163Dic61—81no—
164Dic61—81no—
165Dic61—161no—
166#2734—611no—
167#2099—611no—
168#2083—611no—
169#2072—611no—
170#1272D6111yescharacteristic
171#1271—611no—
172#1271—611no—
173C2×C61#160711yescharacteristic
174C2×C61#161111yescharacteristic
175C2×C61#161711yescharacteristic
176C2×C61#162711yescharacteristic
177C2×C61#164511yescharacteristic
178C2×C61#164911yescharacteristic
179C2×C61#166411yescharacteristic
180C2×C4⋊Q8—1221no—
181C2×#107—1221no—
182C2×#103—1221no—
183#398—1221no—
184#395—1221no—
185#395—1221no—
186#391C2×D6111yescharacteristic
187#389—611no—
188#389—611no—
189#387—1221no—
190#387—1221no—
191#384—611no—
192#340—1221no—
193#340—1221no—
194#340—1221no—
195#340—1221no—
196#336—611no—
197#336C2×D6111yescharacteristic
198#336C2×D6111yescharacteristic
199C61#779411yescharacteristic, complemented, Sylow
200C22×Q8—1221no—
201C22×Q8D24411yescharacteristic
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—1221no—
205C4⋊Q8—2442no—
206C4⋊Q8—2442no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4D24411yescharacteristic
220C2×C42—1221no—
221C2×C42C22×D6111yescharacteristic
222#107—2442no—
223#103—2442no—
224#95—21no—
225#95—21no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231C2×Q8—21no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—4881no—
235C2×Q8—4881no—
236C2×Q8—2442no—
237C2×Q8D48812yes—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—2441no—
245C22×C4C2×D24411yescharacteristic
246C22×C4D4×D6111yescharacteristic
247C22×C4D4×D6111yescharacteristic
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—2441no—
255C2×C8—2441no—
256C2×C8—2441no—
257C4⋊C4—41no—
258C4⋊C4—612no—
259C4⋊C4—612no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—4881no—
263C4⋊C4—2442no—
264C4⋊C4—2441no—
265C4⋊C4—2441no—
266C4⋊C4—2442no—
267C4⋊C4—2442no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C42—41no—
277C42—2442no—
278C23#1451974711yescharacteristic
279Q8—42no—
280Q8—81no—
281Q8—4884no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—1222no—
295C2×C4—1222no—
296C2×C4—4881no—
297C2×C4—4881no—
298C2×C4—4881no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4C2×D48811yescharacteristic
310C2×C4SD16×D6111yescharacteristic
311C2×C4Q16×D6111yescharacteristic
312C2×C4#1451980511yescharacteristic
313C2×C4#1451980611yescharacteristic
314C2×C4#1451980911yescharacteristic
315C8—42no—
316C8—81no—
317C8—4881no—
318C22#1683989811yescharacteristic
319C22#1683990211yescharacteristic
320C22#1683991911yescharacteristic
321C22#1683993611yescharacteristic
322C22#1683994211yescharacteristic
323C22#1683994611yescharacteristic
324C22#1683995311yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—81no—
333C4—9761no—
334C4—4881no—
335C4—4881no—
336C4—2442no—
337C4—2442no—
338C2#2144480711yescharacteristic
339C2#2144482811yescharacteristic
340C2#2144486211yescharacteristic
341C2#2144492411yescharacteristic
342C2#2144504111yescharacteristic
343C2#2144507011yescharacteristic
344C2#2144515611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61#120
hypercenter#1272D61
hypocenterC61#7794
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
199. C61#7794semidirect

Maximal subgroups

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

subgroupindex
#214528512
#214473782
#214472922
#214472272
#214436412
C61×#12722
#779461