Finite Group Databasebeta

← #30604889

Subgroups — #30604889

Order 15616.

440 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461569C211yesmaximal, characteristic
2#21461057C211yesmaximal, characteristic
3#21460818C212yesmaximal, complemented
4#21460804C212yesmaximal, complemented
5#21449084C211yesmaximal, characteristic
6C2×#14519837—21no—
7C2×C22⋊#92420—21no—
8C4×#11758217—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840606—21no—
12C2×#14519737C2211yescharacteristic
13C2×#14519735C411yescharacteristic
14#16839700C2211yescharacteristic
15#16839694C2211yescharacteristic
16#16839688—21no—
17#16839687C411yescharacteristic
18#16839678—21no—
19C4⋊C4×Dic61—21no—
20C22⋊C4×Dic61—21no—
21#16839609C411yescharacteristic
22C61×#399C411yescharacteristic
23C2×#11758217—22no—
24C22×#92420—41no—
25#14519837—24no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28#14519832—41no—
29C4×#92420—41no—
30C22×C22⋊D61D411yescharacteristic
31C23×Dic61D411yescharacteristic
32C22×C4×D61C2×C411yescharacteristic
33#14519737—41no—
34#14519737—41no—
35#14519735—41no—
36#14519735—41no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196C2311yescharacteristic
40C2×C22⋊Dic61—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198D411yescharacteristic
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61D411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61C2×C411yescharacteristic
56#95×C61C2×C411yescharacteristic
57C24×C61C22⋊C411yescharacteristic
58C23×D61C22⋊C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C2×C22⋊D61—22no—
64C2×C22⋊D61—22no—
65C2×C22⋊D61—41no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—42no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—42no—
77#11758217—24no—
78#11758217—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—82no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—42no—
86C22⋊Dic61—42no—
87#11758198—41no—
88#11758198—42no—
89#11758198—42no—
90C4⋊Dic61—42no—
91C4⋊Dic61—41no—
92#11758196—41no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—42no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61#10412yes—
103C23×C61C2×C22⋊C411yescharacteristic
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—41no—
108C22×D61—41no—
109C2×C4×C61—22no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C22⋊D61—44no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—22no—
123C2×Dic61—21no—
124C2×Dic61—42no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—81no—
133C2×Dic61#9911yescharacteristic
134C2×Dic61#9911yescharacteristic
135C2×Dic61#13512yes—
136C4×D61—42no—
137C4×D61—42no—
138#92420—44no—
139#92420—82no—
140#11735—611nomaximal, Sylow
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—22no—
144C22×C61—42no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61—81no—
148C22×C61C2×#9911yescharacteristic
149C22×C61#41611yescharacteristic
150C22×C61C2×#10411yescharacteristic
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—81no—
155C2×D61—81no—
156C4×C61—42no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—81no—
160Dic61—21no—
161Dic61—22no—
162Dic61—41no—
163Dic61—81no—
164Dic61—81no—
165Dic61#35212yes—
166#2395—611no—
167C4×#100—611no—
168#1459—611no—
169#1353—612no—
170#1346—612no—
171C2×C61—21no—
172C2×C61—21no—
173C2×C61—42no—
174C2×C61#150111yescharacteristic
175C2×C61C2×#35211yescharacteristic
176C2×C61#213211yescharacteristic
177D61—81no—
178C2×C4×D4—611no—
179C2×#117—611no—
180C2×#100—1221no—
181C2×C22⋊C8—1221no—
182C4×M16—1221no—
183#400—611no—
184#399#692311yescharacteristic
185#398—611no—
186#397—611no—
187#397—1221no—
188#394—1221no—
189C4×C4⋊C4—1221no—
190C4×C22⋊C4—611no—
191C4×C22⋊C4—1221no—
192#343—612no—
193#324—612no—
194#323—1221no—
195C61#1173511yescharacteristic, complemented, Sylow
196C22×D4—611no—
197C23×C4—611no—
198C23×C4—611no—
199C2×M16—1222no—
200C22×C8—2441no—
201C4×D4—2441no—
202C4×D4—2441no—
203#117—2441no—
204#117—2441no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4C2×#692311yescharacteristic
210C2×C22⋊C4—21no—
211C2×C22⋊C4—611no—
212C2×C22⋊C4—1221no—
213C2×C22⋊C4—1221no—
214C2×C22⋊C4—1221no—
215C2×C22⋊C4C2×#692311yescharacteristic
216C2×C42—611no—
217C2×C42—1221no—
218C2×C42—1221no—
219#100—1224no—
220C22⋊C8—1222no—
221C22⋊C8—2441no—
222#97—2441no—
223C4×C8—2441no—
224#95—611no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95C2×#692311yescharacteristic
230C24—611no—
231C24C22⋊#692311yescharacteristic
232C2×D4—1222no—
233C2×D4—1222no—
234C2×D4—2441no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—2442no—
247C22×C4—2442no—
248C22×C4C22⋊#692311yescharacteristic
249C22×C4C22×#692311yescharacteristic
250M16—1224no—
251M16—2442no—
252C2×C8—4882no—
253C2×C8—2442no—
254C2×C8—2442no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C4⋊C4—2442no—
260C22⋊C4—41no—
261C22⋊C4—42no—
262C22⋊C4—2441no—
263C22⋊C4—2442no—
264C22⋊C4—2442no—
265C22⋊C4—2442no—
266C42—1221no—
267C42—1221no—
268C42—2441no—
269C42—2441no—
270C42—2442no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23—1221no—
276C23—1221no—
277C23—1221no—
278C23—2441no—
279C23—2441no—
280C23#1451984212yes—
281C23C2×C22⋊#692311yescharacteristic
282D4—2444no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—611no—
294C2×C4—611no—
295C2×C4—612no—
296C2×C4—1222no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—4881no—
301C2×C4—2442no—
302C2×C4—2442no—
303C2×C4—2442no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C8—4882no—
312C8—2444no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—81no—
320C22—4881no—
321C22—4881no—
322C22—2441no—
323C22—2441no—
324C22—2441no—
325C22D61⋊#9911yescharacteristic
326C22#1684075211yescharacteristic
327C22C2×#1451984211yescharacteristic
328C4—42no—
329C4—41no—
330C4—41no—
331C4—81no—
332C4—612no—
333C4—1221no—
334C4—1222no—
335C4—4881no—
336C4—4881no—
337C4—2441no—
338C2—21no—
339C2—21no—
340C2—42no—
341C2—4881no—
342C2#2146119711yescharacteristic
343C2D61⋊#35211yescharacteristic
344C2#2146211111yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#399C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×#11758196C23
hypercenter#399#6923
hypocenterC61#11735
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #399

Complements

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

NH ≅ G/Ntype
3. #21460818C2semidirect
4. #21460804C2semidirect
195. C61#11735semidirect

Maximal subgroups

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

subgroupindex
#214615692
#214610572
#214608182
#214608042
#214490842
#1173561