Finite Group Databasebeta

← #29590391

Subgroups — #29590391

Order 15616.

402 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 73 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#21449109C211yesmaximal, characteristic
2#21445614C211yesmaximal, characteristic
3#21444141C211yesmaximal, characteristic
4#21443849C211yesmaximal, characteristic
5#21443826C211yesmaximal, characteristic
6#21443824C211yesmaximal, characteristic
7C61×#1354C211yesmaximal, characteristic
8C2×Q8×Dic61C411yescharacteristic
9C2×#14519742C2211yescharacteristic
10#16839812—21no—
11C2×#14519695—21no—
12M16×Dic61—21no—
13#16839695—21no—
14#16839694C411yescharacteristic
15#16839692C2211yescharacteristic
16#16839683—21no—
17#16839681C411yescharacteristic
18C4⋊C4×Dic61—21no—
19#16839613—21no—
20#16839607C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#395C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C2×#11758194—21no—
29Q8×Dic61—41no—
30Q8×Dic61—41no—
31#14519742—41no—
32#14519742—41no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196C2×C411yescharacteristic
39C2×#11758196D411yescharacteristic
40C2×C4×Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519706—41no—
46#14519695—24no—
47C22⋊#92418—21no—
48#14519687—41no—
49C8×Dic61—41no—
50C8×Dic61—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C22×Q8×C61C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C2×Q8×C61—42no—
64C2×Q8×C61—41no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C2×Dic122—21no—
77C2×Dic122—21no—
78C2×Dic122—22no—
79C2×Dic122—41no—
80M16×C61—22no—
81M16×C61—41no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—42no—
86C4⋊Dic61—42no—
87C4⋊Dic61—42no—
88C4⋊Dic61—41no—
89#11758196—41no—
90#11758196—41no—
91#11758196—42no—
92#11758196—41no—
93#11758196—41no—
94C4×Dic61—24no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—41no—
102C4×Dic61—41no—
103#11758194—22no—
104#11758194—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107C23×C61C2×C22⋊C411yescharacteristic
108Q8×C61—42no—
109Q8×C61—42no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—22no—
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#13511yescharacteristic
123C2×C4×C61#13511yescharacteristic
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—22no—
127C2×Dic61—22no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61#9911yescharacteristic
139C2×Dic61#9911yescharacteristic
140C2×Dic61#10412yes—
141Dic122—42no—
142Dic122—42no—
143C8×C61—42no—
144C8×C61—81no—
145#92418—42no—
146#92418—81no—
147#11736—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61C2×#9911yescharacteristic
151C22×C61#41611yescharacteristic
152C22×C61C2×#10411yescharacteristic
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—42no—
156C4×C61—41no—
157C4×C61—42no—
158C4×C61—41no—
159Dic61—21no—
160Dic61—22no—
161Dic61—42no—
162Dic61—41no—
163Dic61—41no—
164Dic61—81no—
165Dic61#35612yes—
166#2399—611no—
167C4×#101—611no—
168#1461—611no—
169#1354—611no—
170#1354D6111yescharacteristic
171#1346—611no—
172#1346—611no—
173C2×C61—21no—
174C2×C61—21no—
175C2×C61#150111yescharacteristic
176C2×C61#212011yescharacteristic
177C2×C61C2×#35611yescharacteristic
178C2×C4×Q8—611no—
179C2×C4×Q8—611no—
180#431—1221no—
181C2×#101—1221no—
182C4×M16—1221no—
183#398—611no—
184#398—611no—
185#398—1221no—
186#395—611no—
187#395—1221no—
188#395C2×D6111yescharacteristic
189C4×C4⋊C4—1221no—
190C4×C4⋊C4—1221no—
191#376—611no—
192#343—611no—
193#343C2×D6111yescharacteristic
194#324—611no—
195#324—1221no—
196#324C2×D6111yescharacteristic
197C61#1173611yescharacteristic, complemented, Sylow
198C22×Q8—611no—
199C22×Q8C4×D6111yescharacteristic
200C2×M16—21no—
201C2×M16—1221no—
202C4×Q8—2441no—
203C4×Q8—2441no—
204C4×Q8—2441no—
205C4×Q8—2441no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4C22×D6111yescharacteristic
215C2×C42—611no—
216C2×C42—611no—
217C2×C42—611no—
218C2×C42—1221no—
219C2×C42—1221no—
220C4⋊C8—2441no—
221#101—1224no—
222C22⋊C8—21no—
223C22⋊C8—1221no—
224#97—2441no—
225C4×C8—2441no—
226C4×C8—2441no—
227#95—21no—
228#95—611no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95C4×D6111yescharacteristic
234C2×Q8—42no—
235C2×Q8—41no—
236C2×Q8—1222no—
237C2×Q8—1221no—
238C2×Q8—1221no—
239C2×Q8—2441no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4C2×C4×D6111yescharacteristic
249C22×C4D4×D6111yescharacteristic
250C22×C4D4×D6111yescharacteristic
251M16—22no—
252M16—41no—
253M16—1222no—
254M16—2441no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—2441no—
258C2×C8—2441no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C4⋊C4—2442no—
265C4⋊C4—2442no—
266C4⋊C4—2442no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C42—1221no—
270C42—1221no—
271C42—1221no—
272C42—1221no—
273C42—1221no—
274C42—1221no—
275C42—1224no—
276C42—2441no—
277C42—2441no—
278C23C22⋊C4×D6111yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—2442no—
282Q8—2442no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—611no—
296C2×C4—611no—
297C2×C4—612no—
298C2×C4—1222no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1222no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4#1451979811yescharacteristic
313C2×C4#1451980011yescharacteristic
314C8—42no—
315C8—81no—
316C8—4881no—
317C8—2442no—
318C22—21no—
319C22—21no—
320C22#99×D6111yescharacteristic
321C22#1683975711yescharacteristic
322C22#104×D6111yescharacteristic
323C4—21no—
324C4—21no—
325C4—42no—
326C4—41no—
327C4—42no—
328C4—41no—
329C4—612no—
330C4—1221no—
331C4—1222no—
332C4—4881no—
333C4—2442no—
334C4—2441no—
335C4—2441no—
336C2—21no—
337C2—21no—
338C2#2144430911yescharacteristic
339C2#2144745711yescharacteristic
340C2#356×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1354C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1354D61
hypocenterC61#11736
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
197. C61#11736semidirect

Maximal subgroups

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

subgroupindex
#214491092
#214456142
#214441412
#214438492
#214438262
#214438242
C61×#13542
#1173661