Finite Group Databasebeta

← #29590763

Subgroups — #29590763

Order 15616.

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

normal subgroups only

This group has 368 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#21451647C211yesmaximal, characteristic
2#21445901C211yesmaximal, characteristic
3#21444152C211yesmaximal, characteristic
4#21443847C211yesmaximal, characteristic, complemented
5#21443846C211yesmaximal, characteristic, complemented
6#21443845C211yesmaximal, characteristic, complemented
7C61×#1353C211yesmaximal, characteristic, complemented
8C2×#14519776C411yescharacteristic
9C2×#14519735C2211yescharacteristic
10#16839816—21no—
11#16839725—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—
30#14519776—41no—
31#14519776—41no—
32#14519735—41no—
33#14519735—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198C2×C411yescharacteristic
43C2×#11758198D411yescharacteristic
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519706—41no—
47C22⋊#92418—21no—
48#14519689—41no—
49#14519689—41no—
50#14519687—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C2×M16×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2311yescharacteristic
58C22⋊C8×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61C2×C411yescharacteristic
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—42no—
79C2×Dic122—81no—
80C2×Dic122—81no—
81M16×C61—41no—
82M16×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87#11758198—41no—
88#11758198—41no—
89#11758198—81no—
90#11758198—81no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—81no—
94#11758196—42no—
95#11758196—41no—
96#11758196—41no—
97#11758196—81no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102#11758194—41no—
103#11758194—41no—
104C2×#92418—41no—
105C2×#92418—41no—
106C23×C61C2×C22⋊C411yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—41no—
111C22×D61—41no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
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—41no—
124C2×C4×C61#13711yescharacteristic
125C2×C4×C61#13711yescharacteristic
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61#9911yescharacteristic
139C2×Dic61#9911yescharacteristic
140C4×D61—41no—
141C4×D61—41no—
142C4×D61—41no—
143C4×D61—41no—
144Dic122—84no—
145C8×C61—81no—
146C8×C61—81no—
147#92418—81no—
148#92418—81no—
149#11818—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61C2×#9911yescharacteristic
153C22×C61#41911yescharacteristic
154C22×C61#42111yescharacteristic
155C2×D61—42no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—81no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—81no—
165C4×C61—81no—
166Dic61—21no—
167Dic61—21no—
168Dic61—41no—
169Dic61—41no—
170Dic61—81no—
171Dic61—81no—
172#2628—611no—
173#1822—611no—
174#1464—611no—
175#1353—611no—
176#1353—611no—
177#1353—611no—
178#1353D6111yescharacteristic, complemented
179C2×C61—21no—
180C2×C61—21no—
181C2×C61#151111yescharacteristic
182C2×C61#212311yescharacteristic
183C2×C61#213411yescharacteristic
184D61—81no—
185C2×C4⋊Q8—611no—
186C2×#117—611no—
187#432—1221no—
188#407—1221no—
189#400—611no—
190#400C2×D6111yescharacteristic
191#399—611no—
192#399—611no—
193#395—1221no—
194#393—1221no—
195#389—1221no—
196#382—611no—
197#380—1221no—
198#343—611no—
199#343—1221no—
200#343C2×D6111yescharacteristic
201#324—611no—
202#324C2×D6111yescharacteristic
203#323—1221no—
204C61#1181811yescharacteristic, complemented, Sylow
205C22×Q8—1221no—
206C23×C4—611no—
207C2×M16—21no—
208C2×M16—1221no—
209C4⋊Q8—2441no—
210C4⋊Q8—2441no—
211#117—2441no—
212#117—2441no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4C4×D6111yescharacteristic
220C2×C4⋊C4C22×D6111yescharacteristic
221C2×C22⋊C4—611no—
222C2×C22⋊C4—611no—
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C2×C42—611no—
226C2×C42—611no—
227C4⋊C8—2441no—
228C22⋊C8—21no—
229C22⋊C8—1221no—
230C22⋊C8—2441no—
231C22⋊C8—2441no—
232#97—2441no—
233#95—21no—
234#95—21no—
235#95—611no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95C4×D6111yescharacteristic
240C24—611no—
241C2×Q8—4881no—
242C2×Q8—4881no—
243C2×Q8—2442no—
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
259M16—41no—
260M16—41no—
261M16—2441no—
262M16—2441no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—2441no—
266C2×C8—2441no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—4881no—
270C4⋊C4—4881no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2442no—
276C22⋊C4—4881no—
277C22⋊C4—4881no—
278C22⋊C4—2441no—
279C22⋊C4—2441no—
280C42—1221no—
281C42—1221no—
282C42—1221no—
283C42—1221no—
284C23—1221no—
285C23—1221no—
286C23—1221no—
287C23—2441no—
288C23—2441no—
289C23C22⋊C4×D6111yescharacteristic
290Q8—4884no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
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—2441no—
320C2×C4—2441no—
321C2×C4#1451980611yescharacteristic
322C2×C4#1451980911yescharacteristic
323C8—81no—
324C8—81no—
325C8—4881no—
326C8—4881no—
327C22—21no—
328C22—21no—
329C22—4881no—
330C22—2442no—
331C22—2441no—
332C22—2441no—
333C22—2441no—
334C22#99×D6111yescharacteristic
335C22#1683976911yescharacteristic
336C22#1683977711yescharacteristic
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—1221no—
344C4—1221no—
345C4—4881no—
346C4—4881no—
347C4—2441no—
348C4—2441no—
349C2—21no—
350C2—21no—
351C2—4881no—
352C2#2144435011yescharacteristic
353C2#2144747111yescharacteristic
354C2#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#11818
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
178. #1353D61semidirect
204. C61#11818semidirect

Maximal subgroups

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

subgroupindex
#214516472
#214459012
#214441522
#214438472
#214438462
#214438452
C61×#13532
#1181861