Finite Group Databasebeta

← #30599140

Subgroups — #30599140

Order 15616.

386 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 92 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#21461377C211yesmaximal, characteristic, complemented
3#21461157C212yesmaximal
4#21460705C212yesmaximal, complemented
5#21454784C211yesmaximal, characteristic
6C2×#14519847—21no—
7#16840766C2212yes—
8C4×#11758213C2212yes—
9#16840638—21no—
10#16840625—21no—
11#16840625—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—21no—
118C4×D61—21no—
119C4×D61—42no—
120C4×D61—41no—
121C4×D61—41no—
122C4×D61—41no—
123C4×D61—41no—
124#92420—44no—
125#92420—82no—
126C8×C61—21no—
127C8×C61—41no—
128C8×C61#10412yes—
129#92418—21no—
130#92418—21no—
131#92418—41no—
132#8673—611nomaximal, Sylow
133C22×C61#38011yescharacteristic
134C2×D61—21no—
135C2×D61—21no—
136C2×D61—21no—
137C2×D61—41no—
138C2×D61—41no—
139C2×D61—41no—
140C4×C61—21no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61C2×#10411yescharacteristic
144C4×C61#42111yescharacteristic
145C4×C61#43012yes—
146Dic61—21no—
147Dic61—21no—
148Dic61—41no—
149Dic61#47211yescharacteristic
150Dic61#47311yescharacteristic
151#2965—611no—
152C4×#108—611no—
153#1567—611no—
154#1489—612no—
155#1299—612no—
156C2×C61#180611yescharacteristic
157C2×C61#181111yescharacteristic
158C2×C61#181611yescharacteristic
159D61—41no—
160D61—81no—
161C4×#41—611no—
162#446—611no—
163#446#692311yescharacteristic
164#436—611no—
165#436—611no—
166#435—1221no—
167#435—1221no—
168#431—611no—
169#431—1221no—
170C2×#108—1221no—
171#423—612no—
172C4×M16—612no—
173C4×M16—1221no—
174C2×C4×C8—611no—
175#341—1221no—
176#335—1221no—
177#335—1221no—
178Q8⋊C8—1222no—
179D4⋊C8—1222no—
180C61#867311yescharacteristic, complemented, Sylow
181C2×#41—611no—
182C2×M16—1221no—
183C2×M16—1221no—
184C2×M16—1222no—
185C2×M16—1222no—
186C22×C8—611no—
187C22×C8—611no—
188C4×Q8—611no—
189C4×Q8C2×#692311yescharacteristic
190C4×D4—611no—
191C4×D4—611no—
192C4×D4—1221no—
193C4×D4—1221no—
194#117—611no—
195#117—1221no—
196C2×C42—611no—
197C2×C42—1221no—
198#108—1224no—
199C4⋊C8—21no—
200C4⋊C8—611no—
201C4⋊C8—1221no—
202C4⋊C8—1222no—
203C4⋊C8—1222no—
204C4⋊C8C2×#692311yescharacteristic
205C22⋊C8—1221no—
206C22⋊C8—1221no—
207C22⋊C8—1221no—
208#97—21no—
209#97—1221no—
210#97—1222no—
211C4×C8—611no—
212C4×C8—611no—
213C4×C8—611no—
214C4×C8—1221no—
215C4×C8—1222no—
216C4×C8C2×#692311yescharacteristic
217#41—2442no—
218C2×Q8C4⋊#692311yescharacteristic
219C2×D4—611no—
220C2×D4—1221no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4—1221no—
227M16—1224no—
228M16—4882no—
229M16—2442no—
230M16—2442no—
231M16—2442no—
232C2×C8—21no—
233C2×C8—611no—
234C2×C8—611no—
235C2×C8—1222no—
236C2×C8—1221no—
237C2×C8—2441no—
238C2×C8—2442no—
239C2×C8—2442no—
240C2×C8C22⋊#692311yescharacteristic
241C2×C8C22⋊#692311yescharacteristic
242C4⋊C4—21no—
243C4⋊C4—611no—
244C4⋊C4—1221no—
245C4⋊C4C4⋊#692311yescharacteristic
246C22⋊C4—1221no—
247C22⋊C4—1221no—
248C22⋊C4—1221no—
249C42—21no—
250C42—611no—
251C42—611no—
252C42—611no—
253C42—1221no—
254C42—1221no—
255C42C22×#692311yescharacteristic
256C23—611no—
257C23—1221no—
258Q8—22no—
259D4—1222no—
260D4—2442no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—611no—
264C2×C4—611no—
265C2×C4—611no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1222no—
271C2×C4—1221no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2442no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4C2×C22⋊#692311yescharacteristic
278C2×C4C2×C4⋊#692311yescharacteristic
279C2×C4#1451985611yescharacteristic
280C8—21no—
281C8—41no—
282C8—1221no—
283C8—1221no—
284C8—4882no—
285C8—2444no—
286C8—2441no—
287C8#1451984212yes—
288C22—1221no—
289C22—1221no—
290C22—1221no—
291C22—2441no—
292C22—2441no—
293C22—2441no—
294C22#1684070411yescharacteristic
295C4—21no—
296C4—41no—
297C4—41no—
298C4—611no—
299C4—611no—
300C4—1221no—
301C4—1221no—
302C4—2441no—
303C4C2×#1451984211yescharacteristic
304C4#1684075911yescharacteristic
305C4#1684077712yes—
306C2—4881no—
307C2—2441no—
308C2#2146169211yescharacteristic
309C2#2146170011yescharacteristic
310C2#2146170811yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#446C4
socleC22×C61#380
prime radicalC2×#11758226Q8
cosocleC42×D61C23
hypercenter#446#6923
hypocenterC61#8673
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. #21461377C2semidirect
4. #21460705C2semidirect
180. C61#8673semidirect

Maximal subgroups

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

subgroupindex
C4×#145198472
#214613772
#214611572
#214607052
#214547842
#867361