Finite Group Databasebeta

← #30598982

Subgroups — #30598982

Order 15616.

462 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461368C211yesmaximal, characteristic, complemented
2C2×#16840626C211yesmaximal, characteristic, complemented
3#21461116C212yesmaximal
4#21460665C212yesmaximal, complemented
5#21454241C211yesmaximal, characteristic
6#16840778C2212yes—
7C2×C4⋊#92420C2212yes—
8#16840626—21no—
9#16840626—21no—
10#16840626—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—21no—
126C2×Dic61—21no—
127C2×Dic61—41no—
128C2×Dic61#12111yescharacteristic
129C2×Dic61#12111yescharacteristic
130C2×Dic61C22⋊Q811yescharacteristic
131C2×Dic61C22⋊Q811yescharacteristic
132D244—21no—
133D244C4⋊C812yes—
134C4×D61—22no—
135C4×D61—22no—
136C4×D61—42no—
137C4×D61—41no—
138C4×D61—41no—
139Dic122—21no—
140Dic122C4⋊C812yes—
141#92420—82no—
142#92420—82no—
143C8×C61—22no—
144C8×C61—21no—
145C8×C61—21no—
146#92418—22no—
147#92418C22⋊C812yes—
148#92418C22⋊C812yes—
149#8605—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61#38011yescharacteristic
153C22×C61#43111yescharacteristic
154C22×C61#43211yescharacteristic
155C2×D61—22no—
156C2×D61—41no—
157C2×D61—41no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61C2×C22⋊C811yescharacteristic
161C4×C61#40711yescharacteristic
162C4×C61C2×C4⋊C811yescharacteristic
163C4×C61#42311yescharacteristic
164Dic61—22no—
165Dic61—21no—
166Dic61—21no—
167Dic61—21no—
168Dic61#47211yescharacteristic
169Dic61#47311yescharacteristic
170C4×#131—611no—
171#1564—611no—
172C2×#335—611no—
173#1477—612no—
174#1283—612no—
175C2×C61—21no—
176C2×C61—21no—
177C2×C61#179711yescharacteristic
178C2×C61#181411yescharacteristic
179C2×C61#181611yescharacteristic
180D61—42no—
181C2×#131—611no—
182C2×#131—611no—
183C4×#41—611no—
184#431—612no—
185C2×C4⋊C8—612no—
186#405—611no—
187#405—1221no—
188#405—1221no—
189#405#692311yescharacteristic
190C4×M16—611no—
191C4×M16—1221no—
192C2×C4×C8—611no—
193C2×C4×C8—1221no—
194#335—1221no—
195#335—1221no—
196#335—1221no—
197#334—1221no—
198Q8⋊C8—1222no—
199D4⋊C8—1222no—
200C61#860511yescharacteristic, complemented, Sylow
201C2×#41—611no—
202#131—614no—
203#131—1222no—
204#131—1222no—
205#131—1222no—
206C2×M16—611no—
207C2×M16—1221no—
208C2×M16—1221no—
209C2×M16C2×#692311yescharacteristic
210C22×C8—611no—
211C22×C8—1221no—
212C22×C8—1221no—
213C22×C8—1222no—
214C22×C8C2×#692311yescharacteristic
215C4×Q8—611no—
216C4×Q8—611no—
217C4×D4—611no—
218C4×D4—611no—
219C4×D4—1221no—
220C4×D4—1221no—
221#117—1221no—
222#117C2×#692311yescharacteristic
223C2×C42—611no—
224C2×C42—1221no—
225C4⋊C8—1222no—
226C4⋊C8—1222no—
227C4⋊C8—1222no—
228C22⋊C8—1222no—
229#97—21no—
230#97—1221no—
231#97—1221no—
232C4×C8—21no—
233C4×C8—611no—
234C4×C8—611no—
235C4×C8—611no—
236C4×C8—611no—
237C4×C8—1221no—
238C4×C8—1221no—
239C4×C8—1222no—
240#41—612no—
241#41—612no—
242#41—1221no—
243#41—1221no—
244C2×Q8—611no—
245C2×D4—611no—
246C2×D4—1221no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4C22×#692311yescharacteristic
253M16—21no—
254M16—612no—
255M16—1224no—
256M16—1224no—
257M16—1221no—
258M16D61⋊C812yes—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8—612no—
265C2×C8—612no—
266C2×C8—1224no—
267C2×C8—1224no—
268C2×C8—1221no—
269C2×C8—4882no—
270C2×C8—2442no—
271C2×C8—2442no—
272C2×C8C22⋊#692311yescharacteristic
273C2×C8C22⋊#692311yescharacteristic
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4C4⋊#692311yescharacteristic
277C4⋊C4C4⋊#692311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C42—21no—
282C42—611no—
283C42—611no—
284C42—611no—
285C42—611no—
286C42—1221no—
287C42—1221no—
288C23—1221no—
289C23#1451985611yescharacteristic
290Q8—612no—
291Q8—1221no—
292D4—612no—
293D4—1222no—
294D4—1222no—
295D4—1221no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—611no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—611no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1222no—
306C2×C4—1222no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2442no—
310C2×C4—2441no—
311C2×C4C2×C22⋊#692311yescharacteristic
312C2×C4C2×C4⋊#692311yescharacteristic
313C2×C4C2×D61⋊C811yescharacteristic
314C2×C4D61⋊M1611yescharacteristic
315C2×C4D61⋊M1611yescharacteristic
316C2×C4D61⋊M1611yescharacteristic
317C8—22no—
318C8—21no—
319C8—21no—
320C8—612no—
321C8—612no—
322C8—1222no—
323C8—4882no—
324C8—4882no—
325C22—21no—
326C22—21no—
327C22—1222no—
328C22—2441no—
329C22—2441no—
330C22#1684070411yescharacteristic
331C22#1684078011yescharacteristic
332C22#1684078511yescharacteristic
333C4—41no—
334C4—41no—
335C4—611no—
336C4—611no—
337C4—1222no—
338C4—1221no—
339C4—1221no—
340C4—1221no—
341C4D61⋊(C22⋊C8)11yescharacteristic
342C4#1684073411yescharacteristic
343C4D61⋊(C4⋊C8)11yescharacteristic
344C4#1684076711yescharacteristic
345C2—21no—
346C2—21no—
347C2—2442no—
348C2#2146167611yescharacteristic
349C2#2146170511yescharacteristic
350C2#2146170811yescharacteristic
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#8605
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×#16840626C2semidirect
4. #21460665C2semidirect
33. #14519785C8semidirect
200. C61#8605semidirect

Maximal subgroups

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

subgroupindex
#214613682
C2×#168406262
#214611162
#214606652
#214542412
#860561