Finite Group Databasebeta

← #30605369

Subgroups — #30605369

Order 15616.

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

normal subgroups only

This group has 364 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#21462057C211yesmaximal, characteristic
2#21461702C211yesmaximal, characteristic
3#21460792C212yesmaximal, complemented
4#21460791C212yesmaximal, complemented
5#21455472C211yesmaximal, characteristic
6C2×#14519851—21no—
7#16840772—21no—
8#16840741—21no—
9#16840659—21no—
10#16840659C2212yes—
11#16840630C2212yes—
12C2×Q16×D61C411yescharacteristic, complemented
13C2×#14519785C2211yescharacteristic
14#16840335—21no—
15#16840021C2211yescharacteristic
16#16840020C411yescharacteristic, complemented
17#16840017C2211yescharacteristic
18#16840002—21no—
19#16840001—21no—
20#16839797C411yescharacteristic, complemented
21#16839769—21no—
22C61×#470C411yescharacteristic, complemented
23#14519856—22no—
24#14519851—22no—
25#14519851—41no—
26C2×#11758187—41no—
27#14519846—41no—
28#14519845—41no—
29#14519836—41no—
30#14519835—41no—
31C2×#11758222D411yescharacteristic
32C2×Q8×D61—21no—
33C2×Dic244C2×C411yescharacteristic
34C2×#11758202—21no—
35Q16×D61—41no—
36Q16×D61—41no—
37#14519785—41no—
38#14519785—41no—
39C2×#11758189D411yescharacteristic
40C2×#11758189C2311yescharacteristic
41C22×#92418D411yescharacteristic
42C2×C8×D61C2×C411yescharacteristic
43C2×C8×D61D411yescharacteristic
44#14519776—41no—
45#14519763—41no—
46#14519762—41no—
47#14519759—41no—
48#14519757—21no—
49#14519756—21no—
50#14519753—21no—
51#14519735—21no—
52#14519710—21no—
53#14519709C2×C411yescharacteristic
54#14519702—21no—
55#14519701—21no—
56#14519700—21no—
57C2×Q16×C61C2×C411yescharacteristic
58C2×M16×C61C2×C411yescharacteristic
59C22⋊Q8×C61—21no—
60#106×C61C2×C411yescharacteristic
61#103×C61—21no—
62C2×Q8×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C2×C22⋊D61D811yescharacteristic
65C2×C22⋊D61SD1611yescharacteristic
66Q8×D61—42no—
67Q8×D61—42no—
68#11758222—41no—
69#11758222—41no—
70C2×D244D811yescharacteristic
71C2×C4×D61—41no—
72C2×C4×D61C22⋊C411yescharacteristic
73C2×C4×D61C2×D411yescharacteristic
74C2×Dic122—21no—
75C2×Dic122—41no—
76C2×Dic122SD1611yescharacteristic
77C22⋊#6923—42no—
78C4⋊#6923—42no—
79C4×#6923—42no—
80Q16×C61—41no—
81M16×C61—41no—
82C2×C8×C61C22⋊C411yescharacteristic
83C2×C8×C61C22×C411yescharacteristic
84C4⋊C4×C61—21no—
85C4⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊Dic61—41no—
88#11758202—41no—
89#11758202—41no—
90#11758198—41no—
91#11758198—41no—
92#11758198—41no—
93C4⋊Dic61—21no—
94C4⋊Dic61—41no—
95#11758196—41no—
96#11758196—41no—
97C4×Dic61—41no—
98C2×#92418—21no—
99C2×#92418—21no—
100C2×#92418C22⋊C411yescharacteristic
101C2×#92418C2×D411yescharacteristic
102Dic244—41no—
103#11758189—41no—
104#11758189—41no—
105C8×D61—21no—
106C8×D61—21no—
107C8×D61—21no—
108C8×D61—21no—
109#11758187—42no—
110C23×C61#10211yescharacteristic
111C22×D61#10211yescharacteristic
112C22×D61C2×D811yescharacteristic
113C2×#6923—82no—
114Q8×C61—41no—
115Q8×C61—41no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61#10211yescharacteristic
121C2×C4×C61C2×C22⋊C411yescharacteristic
122C22⋊D61—41no—
123C22⋊D61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61#10211yescharacteristic
127C2×Dic61C2×SD1611yescharacteristic
128D244—41no—
129C4×D61—21no—
130C4×D61—21no—
131C4×D61—21no—
132C4×D61—21no—
133C4×D61—82no—
134Dic122—41no—
135Dic122—41no—
136Dic122—41no—
137Dic122—82no—
138C8×C61—21no—
139C8×C61—21no—
140#92418—21no—
141#92418#9911yescharacteristic
142#92418#9911yescharacteristic
143#11869—611nomaximal, Sylow
144C22×C61—21no—
145C22×C61—41no—
146C22×C61C2×#10211yescharacteristic
147C2×D61—21no—
148C2×D61—21no—
149C2×D61—41no—
150C2×D61—41no—
151#6923—162no—
152C4×C61—21no—
153C4×C61—81no—
154C4×C61—81no—
155C4×C61C2×#9911yescharacteristic
156C4×C61#42111yescharacteristic
157Dic61—21no—
158Dic61—21no—
159Dic61—81no—
160Dic61—81no—
161#3059—611no—
162#2115—611no—
163#1812—611no—
164#1340—612no—
165#1340—612no—
166C2×C61—21no—
167C2×C61—41no—
168C2×C61#151911yescharacteristic
169D61—41no—
170D61—41no—
171C22×Q16—611no—
172C2×#131—611no—
173#536—1221no—
174C2×M32—1221no—
175#470—611no—
176#470—611no—
177#470—611no—
178#470#692311yescharacteristic, complemented
179#467—1221no—
180#467—1221no—
181#427—611no—
182#427—1221no—
183#419—1221no—
184#410—1221no—
185#349—612no—
186#349—1221no—
187H(3,ℤ/4)—612no—
188C61#1186911yescharacteristic, complemented, Sylow
189C2×#41—611no—
190C22×Q8—1221no—
191C2×Q16—611no—
192C2×Q16—1221no—
193C2×Q16—2441no—
194C2×Q16—2441no—
195C2×Q16C2×#692311yescharacteristic
196#131—2441no—
197#131—2441no—
198C2×M16—611no—
199C2×M16—611no—
200C2×M16C2×#692311yescharacteristic
201C22×C8—611no—
202C22×C8—611no—
203C22×C8—611no—
204C4⋊Q8—2441no—
205#124—2441no—
206#123—2441no—
207#123—2441no—
208C22⋊Q8—21no—
209C22⋊Q8—1221no—
210C22⋊Q8—1221no—
211C22⋊Q8—1221no—
212#117—1221no—
213#117—1222no—
214M32—1222no—
215M32—2441no—
216C2×C16—2441no—
217#107—1221no—
218#107—2441no—
219#106—611no—
220#106—2441no—
221#106C2×#692311yescharacteristic
222#103—21no—
223#103—1221no—
224#103—1221no—
225#103—1221no—
226#99—2441no—
227#99—2441no—
228#41—2441no—
229#41—2441no—
230C2×Q8—21no—
231C2×Q8—611no—
232C2×Q8—1221no—
233C2×Q8—2441no—
234C2×Q8—2442no—
235C2×Q8—2442no—
236C2×D4—611no—
237C2×D4—611no—
238C2×D4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—2441no—
242C22×C4C22⋊#692311yescharacteristic
243Q16—41no—
244Q16—2441no—
245Q16—2441no—
246Q16—2441no—
247M16—41no—
248M16—2441no—
249M16—2441no—
250C2×C8—611no—
251C2×C8—611no—
252C2×C8—1221no—
253C2×C8—1221no—
254C2×C8—1221no—
255C2×C8—1221no—
256C2×C8—1221no—
257C2×C8—1221no—
258C2×C8C22⋊#692311yescharacteristic
259C2×C8C22×#692311yescharacteristic
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—1221no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2442no—
266C4⋊C4—2441no—
267C22⋊C4—41no—
268C22⋊C4—2441no—
269C22⋊C4—2441no—
270C22⋊C4—2441no—
271C22⋊C4—2442no—
272C22⋊C4—2441no—
273C42—2441no—
274C42—2442no—
275C16—2442no—
276C23—611no—
277C23—611no—
278C23#1451983911yescharacteristic
279Q8—41no—
280Q8—41no—
281Q8—4882no—
282Q8—2441no—
283Q8—2441no—
284Q8—2441no—
285D4—2441no—
286D4—2441no—
287D4—2441no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—4882no—
299C2×C4—4882no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4#1451983911yescharacteristic
303C2×C4C2×C22⋊#692311yescharacteristic
304C8—21no—
305C8—21no—
306C8—611no—
307C8—611no—
308C8—1221no—
309C22—21no—
310C22—41no—
311C22—1221no—
312C22—1221no—
313C22—2441no—
314C22—2441no—
315C22C2×#1451983911yescharacteristic
316C4—21no—
317C4—81no—
318C4—81no—
319C4—1221no—
320C4—1221no—
321C4—9762no—
322C4—4881no—
323C4—4881no—
324C4D61⋊#9911yescharacteristic
325C4#1684075911yescharacteristic
326C2—21no—
327C2—41no—
328C2—2441no—
329C2—2441no—
330C2#2146125411yescharacteristic
subgroupG/H
centerC2#21461254
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#470C4
socleC2×C61#1519
prime radicalC2×#11758222D4
cosocleC2×#11758189C23
hypercenter#470#6923
hypocenterC61#11869
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #470

Complements

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

NH ≅ G/Ntype
3. #21460792C2semidirect
4. #21460791C2semidirect
12. C2×Q16×D61C4semidirect
16. #16840020C4semidirect
20. #16839797C4semidirect
22. C61×#470C4semidirect
178. #470#6923semidirect
188. C61#11869semidirect

Maximal subgroups

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

subgroupindex
#214620572
#214617022
#214607922
#214607912
#214554722
#1186961