Finite Group Databasebeta

← #30599138

Subgroups — #30599138

Order 15616.

386 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C4×#14519847C211yesmaximal, characteristic, complemented
2#21461375C211yesmaximal, characteristic, complemented
3#21461157C212yesmaximal
4#21460705C212yesmaximal, complemented
5#21454784C211yesmaximal, characteristic
6C2×#14519847—21no—
7#16840766C2212yes—
8C4×#11758213C2212yes—
9#16840638—21no—
10#16840624—21no—
11#16840624—21no—
12Q8⋊#92420—22no—
13#16840610—22no—
14C4×#11758226C2211yescharacteristic
15#16839893C411yescharacteristic
16#16839841C411yescharacteristic
17#16839839C411yescharacteristic
18#16839835—21no—
19#16839832—21no—
20#16839814—21no—
21#16839814C2211yescharacteristic
22#16839714—21no—
23C4×C8×D61C2211yescharacteristic
24C61×#446C411yescharacteristic
25C2×#11758213—22no—
26C2×#11758213—22no—
27#14519847—24no—
28C4⋊#92420—22no—
29C4⋊#92420—22no—
30#14519832—22no—
31C4×#92420—22no—
32C2×#11758226Q811yescharacteristic
33C2×#11758189—21no—
34C2×#11758189—21no—
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37Q8×Dic61D411yescharacteristic
38C4×D244—21no—
39C4×D244C2×C411yescharacteristic
40#14519739—21no—
41#14519739D411yescharacteristic
42#14519735—21no—
43#14519735Q811yescharacteristic
44C42×D61—21no—
45C42×D61C2311yescharacteristic
46C4⋊#92418—21no—
47C4⋊#92418C2×C411yescharacteristic
48#14519689—21no—
49#14519689—21no—
50#14519689—21no—
51#14519688—21no—
52C4×#92418C2×C411yescharacteristic
53C8×Dic61—21no—
54C8×Dic61D411yescharacteristic
55C8×Dic61D411yescharacteristic
56C4×Q8×C61C2×C411yescharacteristic
57C4⋊C8×C61—21no—
58C4⋊C8×C61C2×C411yescharacteristic
59#97×C61—21no—
60C4×C8×C61C2×C411yescharacteristic
61C2×Q8×C61C4⋊C411yescharacteristic
62#11758226—42no—
63C2×D244—21no—
64C2×D244C4⋊C411yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61C2×D411yescharacteristic
69C2×C4×D61C2×Q811yescharacteristic
70C2×C4×D61#4111yescharacteristic
71C2×#92420—42no—
72C2×#92420—42no—
73#11758213—24no—
74#11758213—42no—
75#11758213—82no—
76C2×C8×C61—21no—
77C2×C8×C61C22⋊C411yescharacteristic
78C2×C8×C61C22⋊C411yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61C4⋊C411yescharacteristic
81C42×C61—21no—
82C42×C61C22×C411yescharacteristic
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61C4⋊C411yescharacteristic
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61C2×D411yescharacteristic
91C4×Dic61C2×D411yescharacteristic
92C4×Dic61#4111yescharacteristic
93C2×#92418—21no—
94C2×#92418C22⋊C411yescharacteristic
95C2×#92418C22⋊C411yescharacteristic
96#11758189—42no—
97#11758189—42no—
98C8×D61—22no—
99C8×D61—41no—
100C22×D61—21no—
101C22×D61C22⋊Q811yescharacteristic
102Q8×C61—22no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61C2×C22⋊C411yescharacteristic
106C2×C4×C61C2×C4⋊C411yescharacteristic
107C2×C4×C61#11711yescharacteristic
108C2×Dic61—21no—
109C2×Dic61#12111yescharacteristic
110C2×Dic61#12111yescharacteristic
111C2×Dic61C22⋊Q811yescharacteristic
112D244—22no—
113D244—42no—
114C4×D61—21no—
115C4×D61—21no—
116C4×D61—22no—
117C4×D61—22no—
118C4×D61—42no—
119C4×D61—41no—
120C4×D61—41no—
121C4×D61—42no—
122#92420—44no—
123#92420—82no—
124C8×C61—21no—
125C8×C61—21no—
126C8×C61—41no—
127#92418—21no—
128#92418—41no—
129#92418#10412yes—
130#8672—611nomaximal, Sylow
131C22×C61#38011yescharacteristic
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—21no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—41no—
138C4×C61—21no—
139C4×C61—41no—
140C4×C61—41no—
141C4×C61C2×#10411yescharacteristic
142C4×C61#42111yescharacteristic
143C4×C61#43012yes—
144Dic61—21no—
145Dic61—21no—
146Dic61—41no—
147Dic61#47112yes—
148#2965—611no—
149C4×#108—611no—
150#1566—611no—
151#1489—612no—
152#1299—612no—
153C2×C61#180611yescharacteristic
154C2×C61#181111yescharacteristic
155C2×C61#181511yescharacteristic
156D61—41no—
157D61—81no—
158C4×#41—611no—
159#446—611no—
160#446#692311yescharacteristic
161#436—611no—
162#436—611no—
163#435—1221no—
164#435—1221no—
165#431—611no—
166#431—1221no—
167C2×#108—1221no—
168#423—612no—
169C4×M16—612no—
170C4×M16—1221no—
171C2×C4×C8—611no—
172#341—1221no—
173#334—1221no—
174#334—1221no—
175Q8⋊C8—1222no—
176D4⋊C8—1222no—
177C61#867211yescharacteristic, complemented, Sylow
178C2×#41—611no—
179C2×M16—1221no—
180C2×M16—1221no—
181C2×M16—1222no—
182C2×M16—1222no—
183C22×C8—611no—
184C22×C8—611no—
185C4×Q8—611no—
186C4×Q8C2×#692311yescharacteristic
187C4×D4—611no—
188C4×D4—611no—
189C4×D4—1221no—
190C4×D4—1221no—
191#117—611no—
192#117—1221no—
193C2×C42—611no—
194C2×C42—1221no—
195#108—1224no—
196C4⋊C8—21no—
197C4⋊C8—611no—
198C4⋊C8—1221no—
199C4⋊C8—1222no—
200C4⋊C8—1222no—
201C4⋊C8C2×#692311yescharacteristic
202C22⋊C8—1221no—
203C22⋊C8—1221no—
204C22⋊C8—1221no—
205#97—21no—
206#97—1221no—
207#97—1222no—
208C4×C8—611no—
209C4×C8—611no—
210C4×C8—611no—
211C4×C8—1221no—
212C4×C8—1222no—
213C4×C8C2×#692311yescharacteristic
214#41—2442no—
215C2×Q8C4⋊#692311yescharacteristic
216C2×D4—611no—
217C2×D4—1221no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4—1221no—
224M16—1224no—
225M16—4882no—
226M16—2442no—
227M16—2442no—
228M16—2442no—
229C2×C8—21no—
230C2×C8—611no—
231C2×C8—611no—
232C2×C8—1222no—
233C2×C8—1221no—
234C2×C8—2441no—
235C2×C8—2442no—
236C2×C8—2442no—
237C2×C8C22⋊#692311yescharacteristic
238C2×C8C22⋊#692311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—611no—
241C4⋊C4—1221no—
242C4⋊C4C4⋊#692311yescharacteristic
243C22⋊C4—1221no—
244C22⋊C4—1221no—
245C22⋊C4—1221no—
246C42—21no—
247C42—611no—
248C42—611no—
249C42—611no—
250C42—1221no—
251C42—1221no—
252C42C22×#692311yescharacteristic
253C23—611no—
254C23—1221no—
255Q8—22no—
256D4—1222no—
257D4—2442no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—611no—
261C2×C4—611no—
262C2×C4—611no—
263C2×C4—1222no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1222no—
267C2×C4—1221no—
268C2×C4—2442no—
269C2×C4—2442no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4C2×C22⋊#692311yescharacteristic
273C2×C4C2×C4⋊#692311yescharacteristic
274C2×C4#1451985611yescharacteristic
275C8—21no—
276C8—21no—
277C8—41no—
278C8—612no—
279C8—1221no—
280C8—4882no—
281C8—2444no—
282C8—2441no—
283C22—1221no—
284C22—1221no—
285C22—1221no—
286C22—2441no—
287C22—2441no—
288C22—2441no—
289C22#1684070411yescharacteristic
290C4—21no—
291C4—41no—
292C4—41no—
293C4—612no—
294C4—1221no—
295C4—1221no—
296C4—2441no—
297C4D61⋊#10411yescharacteristic
298C4#1684076111yescharacteristic
299C4#1684077712yes—
300C2—4881no—
301C2—2441no—
302C2#2146169411yescharacteristic
303C2#2146170011yescharacteristic
304C2#2146170711yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#446C4
socleC22×C61#380
prime radicalC2×#11758226Q8
cosocleC42×D61C23
hypercenter#446#6923
hypocenterC61#8672
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #446

Complements

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

NH ≅ G/Ntype
1. C4×#14519847C2semidirect
2. #21461375C2semidirect
4. #21460705C2semidirect
177. C61#8672semidirect

Maximal subgroups

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

subgroupindex
C4×#145198472
#214613752
#214611572
#214607052
#214547842
#867261