Finite Group Databasebeta

← #30604753

Subgroups — #30604753

Order 15616.

536 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461525C211yesmaximal, characteristic, complemented
2#21461051C211yesmaximal, characteristic, complemented
3#21460804C212yesmaximal, complemented
4#21460801C212yesmaximal, complemented
5#21449054C211yesmaximal, characteristic
6C22×#11758217—21no—
7#16840779—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840605—21no—
12C2×D4×Dic61—21no—
13C2×D4×Dic61C411yescharacteristic
14C2×#14519733C2211yescharacteristic
15#16839694C2211yescharacteristic
16#16839687C411yescharacteristic
17#16839685—21no—
18#16839676—21no—
19#16839676C2211yescharacteristic
20#16839613C411yescharacteristic
21C22⋊C4×Dic61—21no—
22C61×#392C411yescharacteristic
23C2×#11758217—24no—
24C2×#11758217—22no—
25C2×#11758217—41no—
26C2×#11758217—42no—
27C22×#92420—41no—
28#14519844—41no—
29C22⋊#92420—22no—
30C4×#92420—41no—
31C23×Dic61—21no—
32C23×Dic61D411yescharacteristic
33D4×Dic61—41no—
34D4×Dic61—41no—
35D4×Dic61—42no—
36D4×Dic61—42no—
37#14519733—41no—
38#14519733—41no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196D411yescharacteristic
43C2×#11758196C2311yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61D411yescharacteristic
49C2×C4×Dic61—21no—
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C22×D4×C61—21no—
56C22×D4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61C2×C411yescharacteristic
59#95×C61C2×C411yescharacteristic
60C24×C61—21no—
61C24×C61C22⋊C411yescharacteristic
62C2×D4×C61—42no—
63C2×D4×C61—41no—
64C2×D4×C61—42no—
65C2×D4×C61—42no—
66C2×D4×C61—42no—
67C22×C4×C61—21no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—22no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61—42no—
78C22×Dic61—42no—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61D812yes—
82C22×Dic61SD1612yes—
83C22×Dic61C2×D411yescharacteristic
84C22×Dic61C2×D411yescharacteristic
85#11758217—24no—
86#11758217—44no—
87#11758217—42no—
88C2×#92420—42no—
89C2×#92420—44no—
90C2×#92420—42no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—42no—
93C22⋊Dic61—41no—
94C22⋊Dic61—42no—
95C22⋊Dic61—42no—
96C22⋊Dic61—42no—
97C22⋊Dic61—41no—
98C22⋊Dic61—41no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102#11758196—41no—
103#11758196—41no—
104#11758196—42no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—42no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—22no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61#10212yes—
122C23×C61C2×C22⋊C411yescharacteristic
123D4×C61—42no—
124D4×C61—48no—
125D4×C61—42no—
126C2×C4×C61—22no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—22no—
136C2×Dic61—22no—
137C2×Dic61—22no—
138C2×Dic61—22no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—82no—
150C2×Dic61—82no—
151C2×Dic61#9911yescharacteristic
152C2×Dic61#9911yescharacteristic
153C2×Dic61#10212yes—
154C2×Dic61#10412yes—
155C2×Dic61C2×D811yescharacteristic
156C2×Dic61C2×SD1611yescharacteristic
157#92420—44no—
158#92420—82no—
159#11697—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—22no—
163C22×C61—42no—
164C22×C61—42no—
165C22×C61—42no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—42no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61C2×#9911yescharacteristic
175C22×C61C2×#10211yescharacteristic
176C22×C61C2×#10411yescharacteristic
177C4×C61—42no—
178C4×C61—41no—
179C4×C61—41no—
180Dic61—21no—
181Dic61—21no—
182Dic61—41no—
183Dic61—41no—
184Dic61—81no—
185Dic61—81no—
186Dic61#32712yes—
187Dic61#32712yes—
188#2392—611no—
189#1742—611no—
190#1458—611no—
191#1346—612no—
192#1345—612no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—42no—
196C2×C61—82no—
197C2×C61C2×#32711yescharacteristic
198C2×C61#212011yescharacteristic
199C2×C61#213211yescharacteristic
200C22×M16—1221no—
201C2×C4×D4—611no—
202C2×C4×D4—1221no—
203C2×#117—611no—
204#431—1221no—
205#398—611no—
206#397—611no—
207#396—1221no—
208#394—611no—
209#394—1221no—
210#392#692311yescharacteristic
211C4×C4⋊C4—611no—
212C4×C22⋊C4—1221no—
213#343—612no—
214#343—1221no—
215#324—612no—
216#323—1221no—
217C61#1169711yescharacteristic, complemented, Sylow
218C22×D4—21no—
219C22×D4C2×#692311yescharacteristic
220C23×C4—611no—
221C23×C4—1221no—
222C2×M16—1222no—
223C2×M16—1224no—
224C2×M16—2442no—
225C2×M16—2441no—
226C22×C8—2441no—
227C4×D4—2441no—
228C4×D4—2441no—
229C4×D4—2442no—
230C4×D4—2442no—
231#117—2441no—
232#117—2441no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—611no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4C2×#692311yescharacteristic
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—1221no—
248C4⋊C8—2441no—
249C22⋊C8—1222no—
250C4×C8—2441no—
251#95—611no—
252#95—1221no—
253#95—1221no—
254#95C2×#692311yescharacteristic
255C24—21no—
256C24C22⋊#692311yescharacteristic
257C2×D4—41no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—42no—
262C22×C4—21no—
263C22×C4—611no—
264C22×C4—612no—
265C22×C4—612no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1222no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—2442no—
275C22×C4—2441no—
276C22×C4—2441no—
277C22×C4—2442no—
278C22×C4C22⋊#692311yescharacteristic
279C22×C4C22×#692311yescharacteristic
280M16—1224no—
281M16—2442no—
282M16—2444no—
283C2×C8—2442no—
284C2×C8—2444no—
285C2×C8—2442no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2442no—
290C4⋊C4—2441no—
291C4⋊C4—2441no—
292C22⋊C4—41no—
293C22⋊C4—42no—
294C22⋊C4—2441no—
295C22⋊C4—2441no—
296C22⋊C4—2441no—
297C22⋊C4—2442no—
298C22⋊C4—2442no—
299C22⋊C4—2442no—
300C42—1221no—
301C42—1221no—
302C42—1221no—
303C42—1221no—
304C42—2442no—
305C23—21no—
306C23—21no—
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23#1451983912yes—
317C23C2×C22⋊#692311yescharacteristic
318D4—42no—
319D4—48no—
320D4—42no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—611no—
329C2×C4—611no—
330C2×C4—612no—
331C2×C4—612no—
332C2×C4—611no—
333C2×C4—611no—
334C2×C4—1222no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—4882no—
343C2×C4—4882no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C8—4882no—
353C8—2444no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—42no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22D61⋊#9911yescharacteristic
369C22C2×#1451983911yescharacteristic
370C22D61⋊#10411yescharacteristic
371C4—42no—
372C4—41no—
373C4—41no—
374C4—612no—
375C4—612no—
376C4—1221no—
377C4—1221no—
378C4—4881no—
379C4—4881no—
380C4—2441no—
381C4—2441no—
382C2—21no—
383C2—21no—
384C2—42no—
385C2—82no—
386C2D61⋊#32711yescharacteristic
387C2#2146207111yescharacteristic
388C2#2146211111yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
Fitting, prime radicalC61×#392C4
socleC22×C61C2×#99
cosocleC2×#11758196C23
hypercenter#392#6923
hypocenterC61#11697
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #21461525C2semidirect
2. #21461051C2semidirect
3. #21460804C2semidirect
4. #21460801C2semidirect
217. C61#11697semidirect

Maximal subgroups

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

subgroupindex
#214615252
#214610512
#214608042
#214608012
#214490542
#1169761