Finite Group Databasebeta

← #29590729

Subgroups — #29590729

Order 15616.

402 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 69 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#21449088C211yesmaximal, characteristic
2#21445895C211yesmaximal, characteristic
3#21444150C211yesmaximal, characteristic
4#21443843C211yesmaximal, characteristic
5#21443841C211yesmaximal, characteristic
6#21443839C211yesmaximal, characteristic
7C61×#1352C211yesmaximal, characteristic
8C2×#14519742C411yescharacteristic, complemented
9C2×#14519733C2211yescharacteristic
10#16839816—21no—
11#16839700C411yescharacteristic, complemented
12#16839693—21no—
13#16839685—21no—
14#16839683C411yescharacteristic, complemented
15#16839674C2211yescharacteristic
16#16839623—21no—
17C4⋊C4×Dic61—21no—
18#16839613C411yescharacteristic, complemented
19C22⋊C4×Dic61—21no—
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#399C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C23×Dic61D411yescharacteristic
29#14519742—41no—
30#14519742—41no—
31#14519733—41no—
32#14519733—41no—
33C2×C4⋊Dic61—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196C2×C411yescharacteristic
37C2×#11758196D411yescharacteristic
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61D411yescharacteristic
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519706—41no—
46C22⋊#92418—21no—
47#14519687—41no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—41no—
53#14519684—41no—
54#14519684C2×C411yescharacteristic
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61C2×C411yescharacteristic
62C24×C61C2×D411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—41no—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C2×Dic122—41no—
81C2×Dic122—42no—
82C2×C8×C61—41no—
83C4⋊C4×C61—42no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—42no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊Dic61—41no—
90C22⋊Dic61—42no—
91C22⋊Dic61—41no—
92C22⋊Dic61—41no—
93C4⋊Dic61—42no—
94#11758196—41no—
95#11758196—41no—
96#11758196—42no—
97#11758196—42no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—42no—
103C4×Dic61—41no—
104C4×Dic61—41no—
105C2×#92418—41no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61C2×C22⋊C411yescharacteristic
111C23×C61#13711yescharacteristic
112C23×C61#13711yescharacteristic
113C2×C4×C61—22no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
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—81no—
124C2×C4×C61—81no—
125C2×C4×C61—81no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—22no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61#9911yescharacteristic
149C2×Dic61#9911yescharacteristic
150Dic122—42no—
151Dic122—42no—
152C8×C61—81no—
153#92418—81no—
154#11810—611nomaximal, Sylow
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—81no—
164C22×C61C2×#9911yescharacteristic
165C22×C61#41911yescharacteristic
166C22×C61#42111yescharacteristic
167C4×C61—42no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61—81no—
171C4×C61—161no—
172Dic61—21no—
173Dic61—21no—
174Dic61—42no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178Dic61—81no—
179Dic61—161no—
180#2396—611no—
181#1820—611no—
182#1464—611no—
183#1352—611no—
184#1352D6111yescharacteristic
185#1351—611no—
186#1351—611no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61—41no—
190C2×C61—41no—
191C2×C61#151111yescharacteristic
192C2×C61#212011yescharacteristic
193C2×C61#212611yescharacteristic
194C2×C4×Q8—611no—
195C2×#117—611no—
196#432—1221no—
197#400—611no—
198#399C2×D6111yescharacteristic
199#398—1221no—
200#396—1221no—
201#395—611no—
202#393—611no—
203#381—1221no—
204C4×C4⋊C4—611no—
205C4×C4⋊C4—1221no—
206C4×C22⋊C4—1221no—
207#342—611no—
208#342—1221no—
209#342C2×D6111yescharacteristic
210#324—1221no—
211#323—611no—
212#323C2×D6111yescharacteristic
213C61#1181011yescharacteristic, complemented, Sylow
214C22×Q8—611no—
215C23×C4—611no—
216C4×Q8—2441no—
217C4×Q8—2441no—
218#117—2441no—
219#117—2441no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4C4×D6111yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—611no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4C22×D6111yescharacteristic
233C2×C42—611no—
234C2×C42—611no—
235C2×C42—1221no—
236C2×C42—1221no—
237C4⋊C8—2441no—
238C22⋊C8—21no—
239C22⋊C8—1221no—
240#97—2441no—
241#95—611no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95—2441no—
247#95—2441no—
248#95C4×D6111yescharacteristic
249C24D4×D6111yescharacteristic
250C2×Q8—2441no—
251C2×Q8—2442no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—2441no—
266C22×C4—2441no—
267C22×C4C2×C4×D6111yescharacteristic
268C22×C4D4×D6111yescharacteristic
269C2×C8—41no—
270C2×C8—2441no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2442no—
276C4⋊C4—2442no—
277C4⋊C4—2442no—
278C22⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—2441no—
283C22⋊C4—2442no—
284C22⋊C4—2441no—
285C22⋊C4—2441no—
286C42—1221no—
287C42—1221no—
288C42—1221no—
289C42—1221no—
290C42—2441no—
291C42—2441no—
292C42—2442no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23C22⋊C4×D6111yescharacteristic
298C23#1451980611yescharacteristic
299C23#1451980911yescharacteristic
300Q8—2442no—
301Q8—2442no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1222no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C8—81no—
340C8—4881no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22#99×D6111yescharacteristic
351C22#1683976911yescharacteristic
352C22#1683977711yescharacteristic
353C4—42no—
354C4—41no—
355C4—41no—
356C4—81no—
357C4—161no—
358C4—1221no—
359C4—1221no—
360C4—9761no—
361C4—4881no—
362C4—2441no—
363C4—2442no—
364C4—2441no—
365C4—2441no—
366C2—21no—
367C2—21no—
368C2—41no—
369C2—41no—
370C2#2144435011yescharacteristic
371C2#2144745911yescharacteristic
372C2#2144748111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1352C2
socleC22×C61C2×#99
prime radicalC24×C61C2×D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1352D61
hypocenterC61#11810
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
8. C2×#14519742C4semidirect
11. #16839700C4semidirect
14. #16839683C4semidirect
18. #16839613C4semidirect
213. C61#11810semidirect

Maximal subgroups

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

subgroupindex
#214490882
#214458952
#214441502
#214438432
#214438412
#214438392
C61×#13522
#1181061