Finite Group Databasebeta

← #30604867

Subgroups — #30604867

Order 15616.

500 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461566C211yesmaximal, characteristic, complemented
2#21461057C211yesmaximal, characteristic, complemented
3#21460813C212yesmaximal, complemented
4#21460797C212yesmaximal, complemented
5#21451676C211yesmaximal, characteristic
6C2×#14519835—21no—
7C2×C22⋊#92420—21no—
8C4×C22⋊#6923—21no—
9#16840640C2212yes—
10#16840608—21no—
11#16840606C2212yes—
12C2×#14519764C411yescharacteristic, complemented
13C2×#14519737C2211yescharacteristic
14#16839690—21no—
15#16839675C2211yescharacteristic
16#16839674C411yescharacteristic, complemented
17#16839670—21no—
18#16839670C2211yescharacteristic
19#16839642—21no—
20#16839638—21no—
21#16839629C411yescharacteristic, complemented
22C61×#392C411yescharacteristic, complemented
23C22×#92420—41no—
24C2×C22⋊#6923—22no—
25C2×C4×#6923—41no—
26#14519835—24no—
27C22⋊#92420—22no—
28C22⋊#92420—41no—
29(C2×#6923)⋊C4—41no—
30C22×Dic122C2×C411yescharacteristic
31C22×C22⋊D61—21no—
32C22×C22⋊D61D411yescharacteristic
33C23×Dic61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35#14519764—41no—
36#14519764—41no—
37#14519737—41no—
38#14519737—41no—
39C2×#11758196D411yescharacteristic
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198C2311yescharacteristic
46C2×C4×Dic61C2×C411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C22×D4×C61—21no—
53C22×D4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61C2×C411yescharacteristic
56#95×C61C2×C411yescharacteristic
57C24×C61—21no—
58C24×C61C22⋊C411yescharacteristic
59C23×D61C2×D411yescharacteristic
60C22×#6923—42no—
61C2×D4×C61—41no—
62C2×D4×C61—42no—
63C2×D4×C61—81no—
64C2×D4×C61—81no—
65C2×D4×C61—81no—
66C22×C4×C61—21no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C2×C22⋊D61—22no—
70C2×C22⋊D61—22no—
71C2×C22⋊D61—41no—
72C2×C22⋊D61—42no—
73C2×C22⋊D61—81no—
74C2×C22⋊D61—81no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—81no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C2×D411yescharacteristic
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—81no—
86C2×Dic122—41no—
87C2×Dic122—81no—
88C22⋊#6923—24no—
89C22⋊#6923—42no—
90C2×#92420—42no—
91C2×#92420—82no—
92C4×#6923—82no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—81no—
95C22⋊Dic61—42no—
96C22⋊Dic61—41no—
97C22⋊Dic61—41no—
98C22⋊Dic61—81no—
99C22⋊Dic61—81no—
100#11758198—41no—
101#11758198—81no—
102#11758196—41no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61#10412yes—
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61#13512yes—
123C2×#6923—44no—
124C2×#6923—82no—
125C2×#6923—82no—
126D4×C61—82no—
127D4×C61—84no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C22⋊D61—44no—
136C22⋊D61—84no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—42no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—81no—
151C2×Dic61#9911yescharacteristic
152C2×Dic61#9911yescharacteristic
153C4×D61—42no—
154C4×D61—81no—
155Dic122—82no—
156#92420—82no—
157#11730—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—22no—
161C22×C61—42no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61C2×#9911yescharacteristic
173C22×C61#41611yescharacteristic
174C22×C61C2×#10411yescharacteristic
175C2×D61—22no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—42no—
179C2×D61—81no—
180#6923—84no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—81no—
184Dic61—21no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61—81no—
189Dic61—81no—
190#2631—611no—
191C4×#99—611no—
192#1459—611no—
193#1351—612no—
194#1343—612no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—42no—
198C2×C61—161no—
199C2×C61#150111yescharacteristic
200C2×C61#212211yescharacteristic
201C2×C61#212711yescharacteristic
202D61—42no—
203C2×#124—611no—
204C2×C4×D4—611no—
205C2×#99—1221no—
206C2×C22⋊C8—1221no—
207#397—1221no—
208#393—611no—
209#393—611no—
210#392—611no—
211#392—1221no—
212#392#692311yescharacteristic, complemented
213#386—1221no—
214#386—1221no—
215#383—611no—
216C4×C22⋊C4—1221no—
217#342—612no—
218#324—1221no—
219#323—612no—
220C61#1173011yescharacteristic, complemented, Sylow
221C22×Q8—611no—
222C22×D4—21no—
223C22×D4—611no—
224C22×D4—1221no—
225C22×D4C2×#692311yescharacteristic
226C23×C4—611no—
227C23×C4—611no—
228C22×C8—2441no—
229#124—2441no—
230#124—2441no—
231C4×D4—2441no—
232C4×D4—2441no—
233C2×C4⋊C4—611no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—611no—
236C2×C22⋊C4—1222no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4C2×#692311yescharacteristic
243C2×C42—611no—
244C2×C42—2441no—
245#99—1224no—
246C22⋊C8—1222no—
247C22⋊C8—2441no—
248#95—611no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252#95—1221no—
253#95—2441no—
254#95C2×#692311yescharacteristic
255C24—21no—
256C24—611no—
257C24C22⋊#692311yescharacteristic
258C2×Q8—4881no—
259C2×Q8—2441no—
260C2×D4—41no—
261C2×D4—42no—
262C2×D4—81no—
263C2×D4—81no—
264C2×D4—81no—
265C2×D4—1222no—
266C2×D4—1222no—
267C2×D4—4881no—
268C2×D4—4881no—
269C2×D4—2441no—
270C2×D4—2442no—
271C22×C4—21no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—4881no—
282C22×C4—4881no—
283C22×C4—2442no—
284C22×C4C22⋊#692311yescharacteristic
285C22×C4C22×#692311yescharacteristic
286C2×C8—4882no—
287C2×C8—2442no—
288C4⋊C4—2441no—
289C22⋊C4—41no—
290C22⋊C4—81no—
291C22⋊C4—1224no—
292C22⋊C4—4881no—
293C22⋊C4—4881no—
294C22⋊C4—4881no—
295C22⋊C4—2441no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C22⋊C4—2442no—
299C22⋊C4—2442no—
300C42—1221no—
301C42—1221no—
302C42—4882no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—612no—
315C23—1221no—
316C23—1221no—
317C23—2441no—
318C23—2441no—
319C23#1451984112yes—
320C23C2×C22⋊#692311yescharacteristic
321Q8—4882no—
322D4—82no—
323D4—84no—
324D4—4884no—
325D4—2444no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—4881no—
340C2×C4—4881no—
341C2×C4—4882no—
342C2×C4—4882no—
343C2×C4—2442no—
344C2×C4—2441no—
345C2×C4—2442no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2444no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C8—4882no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—42no—
359C22—41no—
360C22—41no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—1222no—
370C22—4881no—
371C22—2442no—
372C22—2441no—
373C22—2441no—
374C22D61⋊#9911yescharacteristic
375C22#1684075211yescharacteristic
376C22C2×#1451984111yescharacteristic
377C4—41no—
378C4—41no—
379C4—81no—
380C4—1221no—
381C4—1221no—
382C4—4881no—
383C4—4884no—
384C4—4881no—
385C4—2441no—
386C4—2441no—
387C2—21no—
388C2—21no—
389C2—42no—
390C2—161no—
391C2—2442no—
392C2#2146119511yescharacteristic
393C2#2146207911yescharacteristic
394C2#2146209511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#392C4
socleC22×C61C2×#99
prime radical#21451676C2
cosocleC2×#11758198C23
hypercenter#392#6923
hypocenterC61#11730
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. #21461566C2semidirect
2. #21461057C2semidirect
3. #21460813C2semidirect
4. #21460797C2semidirect
12. C2×#14519764C4semidirect
16. #16839674C4semidirect
21. #16839629C4semidirect
22. C61×#392C4semidirect
212. #392#6923semidirect
220. C61#11730semidirect

Maximal subgroups

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

subgroupindex
#214615662
#214610572
#214608132
#214607972
#214516762
#1173061