Finite Group Databasebeta

← #29589603

Subgroups — #29589603

Order 15616.

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

normal subgroups only

This group has 366 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#21450275C211yesmaximal, characteristic
2#21444152C211yesmaximal, characteristic
3#21444132C211yesmaximal, characteristic
4#21443763C211yesmaximal, characteristic, complemented
5#21443752C211yesmaximal, characteristic, complemented
6#21443752C211yesmaximal, characteristic, complemented
7C61×#1324C211yesmaximal, characteristic, complemented
8C2×#14519757C411yescharacteristic
9C2×#14519735C2211yescharacteristic
10#16839816—21no—
11#16839812—21no—
12#16839691—21no—
13#16839691—21no—
14#16839668C411yescharacteristic
15#16839667C2211yescharacteristic
16#16839649—21no—
17#16839649—21no—
18#16839631C411yescharacteristic
19C4×#11758198C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839485—21no—
23#16839485—21no—
24C61×#382C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×C4×D61C2×C411yescharacteristic
29#14519757—41no—
30#14519757—41no—
31#14519735—41no—
32#14519735—41no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198D411yescharacteristic
40C2×#11758198D411yescharacteristic
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44#14519706—41no—
45#14519706—41no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48#14519687—41no—
49C8×Dic61—41no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2311yescharacteristic
57C2×C42×C61C2×C411yescharacteristic
58C22⋊C8×C61—21no—
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62C23×D61C22⋊C411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—41no—
78C2×Dic122—21no—
79C2×Dic122—21no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C42×C61—21no—
87C42×C61—21no—
88#11758198—41no—
89#11758198—41no—
90#11758198—42no—
91#11758198—42no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95#11758196—42no—
96#11758196—42no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—41no—
102C2×#92418—41no—
103C2×#92418—41no—
104C23×C61C2×C22⋊C411yescharacteristic
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—41no—
109C22×D61—41no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
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#13111yescharacteristic
123C2×C4×C61#13111yescharacteristic
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—22no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61#9911yescharacteristic
137C2×Dic61#9911yescharacteristic
138C4×D61—41no—
139C4×D61—41no—
140C4×D61—41no—
141C4×D61—41no—
142Dic122—81no—
143Dic122—81no—
144C8×C61—81no—
145C8×C61—81no—
146#92418—81no—
147#92418—81no—
148#11556—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61#40811yescharacteristic
152C22×C61C2×#9911yescharacteristic
153C22×C61#41311yescharacteristic
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—81no—
158C2×D61—81no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—81no—
164C4×C61—81no—
165Dic61—21no—
166Dic61—21no—
167Dic61—42no—
168Dic61—41no—
169Dic61—41no—
170Dic61—81no—
171#2499—611no—
172#1464—611no—
173#1458—611no—
174#1324—611no—
175#1324D6111yescharacteristic, complemented
176#1319—611no—
177#1319—611no—
178C2×C61—21no—
179C2×C61—21no—
180C2×C61#146811yescharacteristic
181C2×C61#212911yescharacteristic
182C2×C61#213211yescharacteristic
183D61—81no—
184C2×C22⋊Q8—611no—
185C2×#117—611no—
186#432—1221no—
187#431—1221no—
188#397—1221no—
189#397—1221no—
190#391—611no—
191#391—611no—
192#387—1221no—
193#387—1221no—
194#384—611no—
195#382C2×D6111yescharacteristic
196C4×C22⋊C4—611no—
197#324—611no—
198#324—611no—
199#324C2×D6111yescharacteristic
200#324C2×D6111yescharacteristic
201#323—1221no—
202#323—1221no—
203C61#1155611yescharacteristic, complemented, Sylow
204C22×Q8—611no—
205C23×C4—611no—
206C22⋊Q8—2441no—
207C22⋊Q8—2441no—
208#117—2441no—
209#117—2441no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4C4×D6111yescharacteristic
215C2×C4⋊C4C22×D6111yescharacteristic
216C2×C22⋊C4—611no—
217C2×C22⋊C4—611no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42C4×D6111yescharacteristic
224C4⋊C8—2441no—
225C4⋊C8—2441no—
226C22⋊C8—21no—
227C22⋊C8—21no—
228C22⋊C8—1221no—
229C22⋊C8—1221no—
230#97—2441no—
231C4×C8—2441no—
232#95—21no—
233#95—21no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239C24—611no—
240C2×Q8—1221no—
241C2×Q8—1221no—
242C2×Q8—2441no—
243C2×Q8—2441no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—2441no—
256C22×C4C2×C4×D6111yescharacteristic
257C22×C4D4×D6111yescharacteristic
258C22×C4D4×D6111yescharacteristic
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—2441no—
262C2×C8—2441no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4—2442no—
269C4⋊C4—2442no—
270C22⋊C4—2441no—
271C22⋊C4—2441no—
272C22⋊C4—2442no—
273C22⋊C4—2442no—
274C42—21no—
275C42—21no—
276C42—1221no—
277C42—1221no—
278C42—1221no—
279C42—1221no—
280C42—2441no—
281C23—1221no—
282C23—1221no—
283C23—1221no—
284C23—2441no—
285C23—2441no—
286C23C22⋊C4×D6111yescharacteristic
287Q8—4881no—
288Q8—4881no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1222no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4#1451978311yescharacteristic
320C2×C4#1451978511yescharacteristic
321C8—81no—
322C8—81no—
323C8—4881no—
324C8—4881no—
325C22—21no—
326C22—21no—
327C22—4881no—
328C22—4881no—
329C22—2441no—
330C22—2441no—
331C22—2441no—
332C22#1683972711yescharacteristic
333C22#99×D6111yescharacteristic
334C22#1683974511yescharacteristic
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—81no—
341C4—1221no—
342C4—1221no—
343C4—4881no—
344C4—2442no—
345C4—2441no—
346C4—2441no—
347C2—21no—
348C2—21no—
349C2—4881no—
350C2#2144416611yescharacteristic
351C2#2144749211yescharacteristic
352C2#2144750111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1324C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1324D61
hypocenterC61#11556
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
4. #21443763C2semidirect
5. #21443752C2semidirect
6. #21443752C2semidirect
7. C61×#1324C2semidirect
175. #1324D61semidirect
203. C61#11556semidirect

Maximal subgroups

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

subgroupindex
#214502752
#214441522
#214441322
#214437632
#214437522
C61×#13242
#1155661