Finite Group Databasebeta

← #30598978

Subgroups — #30598978

Order 15616.

462 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461368C211yesmaximal, characteristic, complemented
2C2×#16840624C211yesmaximal, characteristic, complemented
3#21461116C212yesmaximal
4#21460665C212yesmaximal, complemented
5#21454241C211yesmaximal, characteristic
6#16840778C2212yes—
7C2×C4⋊#92420C2212yes—
8#16840626—21no—
9#16840624—21no—
10#16840624—21no—
11#16840624—21no—
12#16840612—22no—
13#16840610—22no—
14C2×#14519785C411yescharacteristic
15C2×#14519783C411yescharacteristic
16#16840230C2211yescharacteristic
17#16839719—21no—
18#16839718C411yescharacteristic
19#16839716—21no—
20#16839714—21no—
21M16×Dic61C2211yescharacteristic
22C2×C8×Dic61C2211yescharacteristic
23C4×C8×D61—21no—
24C61×#405C411yescharacteristic
25C22×#92420—22no—
26C4⋊#92420—22no—
27C4⋊#92420—22no—
28C4⋊#92420—22no—
29C22⋊#92420—22no—
30C4×#92420—22no—
31C2×#11758222C2×C411yescharacteristic
32#14519785—22no—
33#14519785C814yescomplemented
34#14519783—22no—
35#14519783—22no—
36C2×#11758194C2×C411yescharacteristic
37C2×#11758189—21no—
38C2×#11758189—21no—
39C22×#92418C2×C411yescharacteristic
40C2×C8×D61—21no—
41C2×C8×D61—21no—
42#14519742D411yescharacteristic
43#14519742Q811yescharacteristic
44#14519739D411yescharacteristic
45#14519739Q811yescharacteristic
46#14519737—21no—
47#14519737—21no—
48#14519734—21no—
49C2×C4×Dic61C2311yescharacteristic
50C42×D61—21no—
51#14519688—21no—
52#14519687—21no—
53C4×#92418—21no—
54C8×Dic61—21no—
55C8×Dic61D411yescharacteristic
56C8×Dic61D411yescharacteristic
57C8×Dic61D411yescharacteristic
58C8×Dic61D411yescharacteristic
59C2×M16×C61C2×C411yescharacteristic
60C22×C8×C61C2×C411yescharacteristic
61#117×C61C2×C411yescharacteristic
62#97×C61—21no—
63C4×C8×C61—21no—
64C22×C4×C61C22×C411yescharacteristic
65C2×C22⋊D61—21no—
66C22×Dic61#4111yescharacteristic
67C22×Dic61#4111yescharacteristic
68#11758222—21no—
69#11758222—21no—
70#11758222C2×C812yes—
71#11758222M1612yes—
72C2×D244C4⋊C411yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×Dic122C4⋊C411yescharacteristic
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—82no—
80M16×C61—21no—
81M16×C61C2×C812yes—
82C2×C8×C61—21no—
83C2×C8×C61—21no—
84C2×C8×C61—21no—
85C2×C8×C61C22⋊C411yescharacteristic
86C2×C8×C61C22⋊C411yescharacteristic
87C4⋊C4×C61C4⋊C411yescharacteristic
88C4⋊C4×C61C4⋊C411yescharacteristic
89C22⋊C4×C61—21no—
90C42×C61—21no—
91#11758198—21no—
92#11758198—21no—
93#11758196—21no—
94#11758196—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61C2×D411yescharacteristic
98C4×Dic61C2×D411yescharacteristic
99C4×Dic61C2×D411yescharacteristic
100C4×Dic61C2×Q811yescharacteristic
101#11758194—21no—
102#11758194M1612yes—
103C2×#92418—21no—
104C2×#92418C22⋊C411yescharacteristic
105C2×#92418C22⋊C411yescharacteristic
106C2×#92418C2×C812yes—
107C2×#92418M1612yes—
108#11758189—24no—
109#11758189—24no—
110C8×D61—24no—
111C8×D61—24no—
112C23×C61#11711yescharacteristic
113C22×D61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61C2×C22⋊C411yescharacteristic
117C2×C4×C61C2×C4⋊C411yescharacteristic
118C2×C4×C61C22×C811yescharacteristic
119C2×C4×C61C2×M1611yescharacteristic
120C2×C4×C61C2×M1611yescharacteristic
121C2×C4×C61C2×M1611yescharacteristic
122C22⋊D61—22no—
123C22⋊D61—22no—
124C2×Dic61—21no—
125C2×Dic61—22no—
126C2×Dic61—41no—
127C2×Dic61#12111yescharacteristic
128C2×Dic61#12111yescharacteristic
129C2×Dic61C22⋊Q811yescharacteristic
130C2×Dic61C22⋊Q811yescharacteristic
131D244—21no—
132D244C4⋊C812yes—
133C4×D61—22no—
134C4×D61—22no—
135C4×D61—42no—
136C4×D61—42no—
137Dic122—21no—
138Dic122C4⋊C812yes—
139#92420—82no—
140#92420—82no—
141C8×C61—22no—
142C8×C61—21no—
143C8×C61—21no—
144#92418—22no—
145#92418C22⋊C812yes—
146#92418C22⋊C812yes—
147#8604—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61#38011yescharacteristic
151C22×C61#43111yescharacteristic
152C22×C61#43211yescharacteristic
153C2×D61—22no—
154C2×D61—41no—
155C2×D61—41no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61C2×C22⋊C811yescharacteristic
159C4×C61#40711yescharacteristic
160C4×C61C2×C4⋊C811yescharacteristic
161C4×C61#42311yescharacteristic
162Dic61—22no—
163Dic61—21no—
164Dic61—21no—
165Dic61—21no—
166Dic61#47112yes—
167C4×#131—611no—
168#1564—611no—
169C2×#334—611no—
170#1477—612no—
171#1283—612no—
172C2×C61—21no—
173C2×C61—21no—
174C2×C61#179711yescharacteristic
175C2×C61#181411yescharacteristic
176C2×C61#181511yescharacteristic
177D61—42no—
178C2×#131—611no—
179C2×#131—611no—
180C4×#41—611no—
181#431—612no—
182C2×C4⋊C8—612no—
183#405—611no—
184#405—1221no—
185#405—1221no—
186#405#692311yescharacteristic
187C4×M16—611no—
188C4×M16—1221no—
189C2×C4×C8—611no—
190C2×C4×C8—1221no—
191#335—1221no—
192#334—1221no—
193#334—1221no—
194#334—1221no—
195Q8⋊C8—1222no—
196D4⋊C8—1222no—
197C61#860411yescharacteristic, complemented, Sylow
198C2×#41—611no—
199#131—614no—
200#131—1222no—
201#131—1222no—
202#131—1222no—
203C2×M16—611no—
204C2×M16—1221no—
205C2×M16—1221no—
206C2×M16C2×#692311yescharacteristic
207C22×C8—611no—
208C22×C8—1221no—
209C22×C8—1221no—
210C22×C8—1222no—
211C22×C8C2×#692311yescharacteristic
212C4×Q8—611no—
213C4×Q8—611no—
214C4×D4—611no—
215C4×D4—611no—
216C4×D4—1221no—
217C4×D4—1221no—
218#117—1221no—
219#117C2×#692311yescharacteristic
220C2×C42—611no—
221C2×C42—1221no—
222C4⋊C8—1222no—
223C4⋊C8—1222no—
224C4⋊C8—1222no—
225C22⋊C8—1222no—
226#97—21no—
227#97—1221no—
228#97—1221no—
229C4×C8—21no—
230C4×C8—611no—
231C4×C8—611no—
232C4×C8—611no—
233C4×C8—611no—
234C4×C8—1221no—
235C4×C8—1221no—
236C4×C8—1222no—
237#41—612no—
238#41—612no—
239#41—1221no—
240#41—1221no—
241C2×Q8—611no—
242C2×D4—611no—
243C2×D4—1221no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4C22×#692311yescharacteristic
250M16—21no—
251M16—612no—
252M16—1224no—
253M16—1224no—
254M16—1221no—
255M16D61⋊C812yes—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8—612no—
262C2×C8—612no—
263C2×C8—1224no—
264C2×C8—1224no—
265C2×C8—1221no—
266C2×C8—4882no—
267C2×C8—2442no—
268C2×C8—2442no—
269C2×C8C22⋊#692311yescharacteristic
270C2×C8C22⋊#692311yescharacteristic
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4C4⋊#692311yescharacteristic
274C4⋊C4C4⋊#692311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C42—21no—
279C42—611no—
280C42—611no—
281C42—611no—
282C42—611no—
283C42—1221no—
284C42—1221no—
285C23—1221no—
286C23#1451985611yescharacteristic
287Q8—612no—
288Q8—1221no—
289D4—612no—
290D4—1222no—
291D4—1222no—
292D4—1221no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—611no—
296C2×C4—611no—
297C2×C4—611no—
298C2×C4—611no—
299C2×C4—1222no—
300C2×C4—1221no—
301C2×C4—1222no—
302C2×C4—1222no—
303C2×C4—2442no—
304C2×C4—2442no—
305C2×C4—2441no—
306C2×C4C2×C22⋊#692311yescharacteristic
307C2×C4C2×C4⋊#692311yescharacteristic
308C2×C4C2×D61⋊C811yescharacteristic
309C2×C4D61⋊M1611yescharacteristic
310C2×C4D61⋊M1611yescharacteristic
311C2×C4D61⋊M1611yescharacteristic
312C8—22no—
313C8—21no—
314C8—21no—
315C8—612no—
316C8—612no—
317C8—1222no—
318C8—4882no—
319C8—4882no—
320C22—21no—
321C22—21no—
322C22—1222no—
323C22—2441no—
324C22—2441no—
325C22#1684070411yescharacteristic
326C22#1684078011yescharacteristic
327C22#1684078511yescharacteristic
328C4—41no—
329C4—41no—
330C4—612no—
331C4—1222no—
332C4—1221no—
333C4—1221no—
334C4—1221no—
335C4D61⋊(C22⋊C8)11yescharacteristic
336C4#1684073411yescharacteristic
337C4D61⋊(C4⋊C8)11yescharacteristic
338C4#1684076711yescharacteristic
339C2—21no—
340C2—21no—
341C2—2442no—
342C2#2146167611yescharacteristic
343C2#2146170611yescharacteristic
344C2#2146170711yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#405C4
socleC22×C61#380
prime radicalC2×#11758222C2×C4
cosocleC2×C4×Dic61C23
hypercenter#405#6923
hypocenterC61#8604
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #21461368C2semidirect
2. C2×#16840624C2semidirect
4. #21460665C2semidirect
33. #14519785C8semidirect
197. C61#8604semidirect

Maximal subgroups

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

subgroupindex
#214613682
C2×#168406242
#214611162
#214606652
#214542412
#860461