Finite Group Databasebeta

← #29590326

Subgroups — #29590326

Order 15616.

432 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 83 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#21451647C211yesmaximal, characteristic
2#21445556C211yesmaximal, characteristic
3#21444132C211yesmaximal, characteristic
4#21443847C211yesmaximal, characteristic, complemented
5#21443846C211yesmaximal, characteristic, complemented
6#21443845C211yesmaximal, characteristic, complemented
7C61×#1353C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519776C411yescharacteristic
10C2×#14519735C2211yescharacteristic
11#16839812—21no—
12#16839701C2211yescharacteristic
13#16839699C411yescharacteristic
14#16839697C411yescharacteristic
15#16839683—21no—
16#16839675—21no—
17#16839659—21no—
18#16839626C411yescharacteristic
19#16839621—21no—
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#400C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122—21no—
28C22×C4×D61D411yescharacteristic
29C2×#11758194—21no—
30C2×#11758189—41no—
31M16×D61—24no—
32M16×D61—42no—
33C2×C8×D61—41no—
34#14519776—41no—
35#14519776—41no—
36#14519735—41no—
37#14519735—41no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198C2×C411yescharacteristic
47C2×#11758198D411yescharacteristic
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519706—41no—
51C22⋊#92418—21no—
52C8×Dic61—41no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
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
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—22no—
78C2×C4×D61SD1612yes—
79C2×C4×D61Q1612yes—
80C2×Dic122—42no—
81C2×Dic122—81no—
82C2×Dic122—81no—
83M16×C61—22no—
84M16×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89#11758198—41no—
90#11758198—41no—
91#11758198—81no—
92#11758198—81no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—81no—
96#11758196—41no—
97#11758196—41no—
98#11758196—42no—
99#11758196—81no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104#11758194—22no—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418—41no—
108#11758189—44no—
109C8×D61—44no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61#10312yes—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—41no—
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—41no—
128C2×C4×C61C2×SD1611yescharacteristic
129C2×C4×C61C2×Q1611yescharacteristic
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—41no—
139C2×Dic61—41no—
140C2×Dic61#9911yescharacteristic
141C2×Dic61#9911yescharacteristic
142C2×Dic61#10312yes—
143C2×Dic61#10412yes—
144C4×D61—22no—
145C4×D61—22no—
146C4×D61—22no—
147C4×D61—22no—
148Dic122—84no—
149C8×C61—42no—
150C8×C61—81no—
151#92418—42no—
152#92418—81no—
153#11723—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61C2×#9911yescharacteristic
157C22×C61C2×#10311yescharacteristic
158C22×C61C2×#10411yescharacteristic
159C2×D61—22no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—42no—
163C2×D61—81no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—81no—
169C4×C61—81no—
170Dic61—41no—
171Dic61—41no—
172Dic61—81no—
173Dic61—81no—
174Dic61#32812yes—
175Dic61#32812yes—
176#2628—611no—
177#1742—611no—
178#1458—611no—
179#1353—611no—
180#1353—611no—
181#1353—611no—
182#1353D6111yescharacteristic, complemented
183C2×C61—21no—
184C2×C61—21no—
185C2×C61C2×#32811yescharacteristic
186C2×C61#212311yescharacteristic
187C2×C61#213411yescharacteristic
188D61—42no—
189C22×M16—1221no—
190C2×C4⋊Q8—611no—
191C2×#117—611no—
192#431—1221no—
193#400—611no—
194#400C2×D6111yescharacteristic
195#399—611no—
196#399—611no—
197#395—1221no—
198#393—1221no—
199#389—1221no—
200#382—611no—
201#380—1221no—
202#343—611no—
203#343—1221no—
204#343C2×D6111yescharacteristic
205#324—611no—
206#324C2×D6111yescharacteristic
207#323—1221no—
208C61#1172311yescharacteristic, complemented, Sylow
209C22×Q8—1221no—
210C23×C4—611no—
211C2×M16—21no—
212C2×M16—1224no—
213C2×M16—1221no—
214C2×M16—2441no—
215C2×M16—2442no—
216C22×C8—2441no—
217C4⋊Q8—2441no—
218C4⋊Q8—2441no—
219#117—2441no—
220#117—2441no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4C4×D6111yescharacteristic
228C2×C4⋊C4C22×D6111yescharacteristic
229C2×C22⋊C4—611no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C42—611no—
234C2×C42—611no—
235C4⋊C8—2441no—
236C22⋊C8—21no—
237C22⋊C8—1221no—
238C4×C8—2441no—
239#95—21no—
240#95—21no—
241#95—611no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95C4×D6111yescharacteristic
246C24—611no—
247C2×Q8—4881no—
248C2×Q8—4881no—
249C2×Q8—2442no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—611no—
253C22×C4—612no—
254C22×C4—612no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1222no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4C2×C4×D6111yescharacteristic
263C22×C4D4×D6111yescharacteristic
264C22×C4D4×D6111yescharacteristic
265M16—22no—
266M16—41no—
267M16—1222no—
268M16—2444no—
269M16—2441no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—2444no—
273C2×C8—2441no—
274C2×C8—2441no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—4881no—
278C4⋊C4—4881no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2442no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C22⋊C4—4881no—
285C22⋊C4—4881no—
286C22⋊C4—2441no—
287C22⋊C4—2441no—
288C42—1221no—
289C42—1221no—
290C42—1221no—
291C42—1221no—
292C23—612no—
293C23—1221no—
294C23—1221no—
295C23—2441no—
296C23—2441no—
297C23C22⋊C4×D6111yescharacteristic
298Q8—4884no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—612no—
314C2×C4—612no—
315C2×C4—1222no—
316C2×C4—1222no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4SD16×D6111yescharacteristic
330C2×C4Q16×D6111yescharacteristic
331C8—42no—
332C8—81no—
333C8—4881no—
334C8—2442no—
335C22—21no—
336C22—21no—
337C22—1222no—
338C22—4881no—
339C22—2442no—
340C22—2441no—
341C22—2441no—
342C22#99×D6111yescharacteristic
343C22#103×D6111yescharacteristic
344C22#104×D6111yescharacteristic
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—612no—
352C4—612no—
353C4—4881no—
354C4—4881no—
355C4—2441no—
356C4—2441no—
357C2—21no—
358C2—21no—
359C2—2442no—
360C2#328×D6111yescharacteristic
361C2#2144747111yescharacteristic
362C2#2144750911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1353C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1353D61
hypocenterC61#11723
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
4. #21443847C2semidirect
5. #21443846C2semidirect
6. #21443845C2semidirect
7. C61×#1353C2semidirect
182. #1353D61semidirect
208. C61#11723semidirect

Maximal subgroups

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

subgroupindex
#214516472
#214455562
#214441322
#214438472
#214438462
#214438452
C61×#13532
#1172361