Finite Group Databasebeta

← #29590501

Subgroups — #29590501

Order 15616.

436 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 71 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#21451518C211yesmaximal, characteristic
2#21445550C211yesmaximal, characteristic
3#21444150C211yesmaximal, characteristic
4#21443844C211yesmaximal, characteristic
5#21443842C211yesmaximal, characteristic
6#21443819C211yesmaximal, characteristic
7C61×#1344C211yesmaximal, characteristic
8C2×#14519768C411yescharacteristic, complemented
9C2×#14519733—21no—
10C2×#14519733C2211yescharacteristic
11#16839816—21no—
12#16839702C411yescharacteristic, complemented
13#16839698C2211yescharacteristic
14#16839693C411yescharacteristic, complemented
15#16839659—21no—
16#16839655—21no—
17#16839644—21no—
18#16839634—21no—
19#16839607C411yescharacteristic, complemented
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#397C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C23×Dic61D411yescharacteristic
28#14519768—41no—
29#14519768—41no—
30#14519733—24no—
31#14519733—41no—
32#14519733—41no—
33#14519733—42no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—41no—
40C2×#11758196C2×C411yescharacteristic
41C2×#11758196D411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61D411yescharacteristic
45C2×C4×Dic61—21no—
46C2×C4×Dic61—41no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519706—41no—
50C22⋊#92418—21no—
51#14519687—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C24×C61C2×D411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—22no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—41no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C2×C8×C61—41no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—22no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊Dic61—22no—
90C22⋊Dic61—41no—
91C22⋊Dic61—42no—
92C22⋊Dic61—41no—
93C4⋊Dic61—42no—
94C4⋊Dic61—41no—
95#11758196—41no—
96#11758196—41no—
97#11758196—42no—
98#11758196—44no—
99#11758196—41no—
100#11758196—41no—
101#11758196—42no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—42no—
107C4×Dic61—44no—
108C2×#92418—41no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61C2×C22⋊C411yescharacteristic
114C23×C61AGL(1,ℤ/8)11yescharacteristic
115C23×C61#13711yescharacteristic
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—42no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—22no—
132C2×Dic61—22no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—22no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—42no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150C2×Dic61#9911yescharacteristic
151C2×Dic61#9911yescharacteristic
152C2×Dic61#10412yes—
153C8×C61—81no—
154#92418—81no—
155#11760—611nomaximal, Sylow
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—81no—
165C22×C61C2×#9911yescharacteristic
166C22×C61#41711yescharacteristic
167C22×C61C2×#10411yescharacteristic
168C4×C61—41no—
169C4×C61—41no—
170C4×C61—81no—
171C4×C61—82no—
172C4×C61—81no—
173Dic61—21no—
174Dic61—21no—
175Dic61—22no—
176Dic61—42no—
177Dic61—41no—
178Dic61—41no—
179Dic61—82no—
180Dic61—81no—
181#2611—611no—
182#1740—611no—
183#1464—611no—
184#1352—611no—
185#1352—611no—
186#1344—611no—
187#1344D6111yescharacteristic
188C2×C61—21no—
189C2×C61—21no—
190C2×C61—41no—
191C2×C61—41no—
192C2×C61#150411yescharacteristic
193C2×C61#212311yescharacteristic
194C2×C61#212611yescharacteristic
195C2×#125—611no—
196C2×#117—611no—
197C2×#117—1221no—
198#432—1221no—
199#400—611no—
200#399—611no—
201#398—611no—
202#397C2×D6111yescharacteristic
203#389—1221no—
204#388—1221no—
205#387—1221no—
206#385—1221no—
207#376—611no—
208#342—611no—
209#342—1221no—
210#342C2×D6111yescharacteristic
211#324—1221no—
212#323—611no—
213#323C2×D6111yescharacteristic
214C61#1176011yescharacteristic, complemented, Sylow
215C23×C4—611no—
216#125—2441no—
217#125—2441no—
218#117—1224no—
219#117—2441no—
220#117—2441no—
221#117—2442no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—2441no—
230C2×C4⋊C4C4×D6111yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4C22×D6111yescharacteristic
237C2×C42—611no—
238C2×C42—611no—
239C2×C42—1221no—
240C2×C42—2441no—
241C4⋊C8—2441no—
242C22⋊C8—21no—
243C22⋊C8—1221no—
244#97—2441no—
245#95—21no—
246#95—611no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251#95C4×D6111yescharacteristic
252C24D4×D6111yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1222no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—2441no—
268C22×C4C2×C4×D6111yescharacteristic
269C22×C4D4×D6111yescharacteristic
270C2×C8—41no—
271C2×C8—2441no—
272C4⋊C4—41no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2442no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2442no—
280C4⋊C4—2442no—
281C4⋊C4—2444no—
282C22⋊C4—22no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—1222no—
288C22⋊C4—2441no—
289C22⋊C4—2442no—
290C22⋊C4—2441no—
291C42—1221no—
292C42—1221no—
293C42—1221no—
294C42—1221no—
295C42—2442no—
296C42—2444no—
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23C22⋊C4×D6111yescharacteristic
302C23#1451980111yescharacteristic
303C23#1451980611yescharacteristic
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—611no—
318C2×C4—611no—
319C2×C4—612no—
320C2×C4—1222no—
321C2×C4—1222no—
322C2×C4—1222no—
323C2×C4—1222no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1222no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4—2442no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C8—81no—
342C8—4881no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—81no—
352C22#99×D6111yescharacteristic
353C22#1683976011yescharacteristic
354C22#104×D6111yescharacteristic
355C4—41no—
356C4—41no—
357C4—81no—
358C4—82no—
359C4—81no—
360C4—1221no—
361C4—1221no—
362C4—1222no—
363C4—4882no—
364C4—4881no—
365C4—2442no—
366C4—2441no—
367C4—2441no—
368C2—21no—
369C2—21no—
370C2—41no—
371C2—41no—
372C2#2144432011yescharacteristic
373C2#2144747111yescharacteristic
374C2#2144748311yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1344C2
socleC22×C61C2×#99
prime radicalC24×C61C2×D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1344D61
hypocenterC61#11760
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
8. C2×#14519768C4semidirect
12. #16839702C4semidirect
14. #16839693C4semidirect
19. #16839607C4semidirect
214. C61#11760semidirect

Maximal subgroups

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

subgroupindex
#214515182
#214455502
#214441502
#214438442
#214438422
#214438192
C61×#13442
#1176061