Finite Group Databasebeta

← #30605412

Subgroups — #30605412

Order 15616.

476 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461686C211yesmaximal, characteristic, complemented
2#21461063C211yesmaximal, characteristic, complemented
3#21460802C212yesmaximal, complemented
4#21460801C212yesmaximal, complemented
5#21450817C211yesmaximal, characteristic
6#16840778—21no—
7#16840765—21no—
8C2×#14519838—21no—
9#16840642C2212yes—
10#16840608—21no—
11#16840608C2212yes—
12C2×#14519773C411yescharacteristic
13C2×#14519763—21no—
14C2×#14519742C2211yescharacteristic
15#16839680C2211yescharacteristic
16#16839679C411yescharacteristic
17#16839676C2211yescharacteristic
18#16839662—21no—
19#16839662—21no—
20#16839662—21no—
21#16839613C411yescharacteristic
22C61×#394C411yescharacteristic
23C2×#11758217—22no—
24#14519844—41no—
25C4⋊#92420—41no—
26C4⋊#92420—41no—
27#14519838—42no—
28C22⋊#92420—22no—
29C4×#92420—41no—
30C22×Dic122D411yescharacteristic
31C22×D244C2×C411yescharacteristic
32C22×C22⋊D61—21no—
33C22×C22⋊D61—21no—
34#14519773—41no—
35#14519773—41no—
36#14519763—42no—
37#14519763—42no—
38#14519742—41no—
39#14519742—41no—
40C2×#11758196—21no—
41C2×#11758196D411yescharacteristic
42C2×#11758196C2311yescharacteristic
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53#14519684C2×C411yescharacteristic
54C22×D4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58#95×C61C2×C411yescharacteristic
59C24×C61—21no—
60C23×D61—21no—
61C2×D4×C61—41no—
62C2×D4×C61—81no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C2×C22⋊D61—42no—
68C2×C22⋊D61—42no—
69C2×C22⋊D61—42no—
70C2×C22⋊D61—42no—
71C2×C22⋊D61—41no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61—42no—
74C22×Dic61—21no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C22×Dic61C2×D411yescharacteristic
79C2×D244—41no—
80C2×D244—81no—
81C2×Dic122—41no—
82C2×Dic122—41no—
83C2×Dic122D812yes—
84C2×Dic122SD1612yes—
85#11758217—42no—
86#11758217—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C4⋊C4×C61—41no—
90C22⋊C4×C61—42no—
91C22⋊C4×C61—81no—
92C22⋊Dic61—41no—
93C22⋊Dic61—41no—
94C22⋊Dic61—81no—
95#11758198—42no—
96#11758198—41no—
97#11758198—41no—
98#11758198—81no—
99#11758198—81no—
100#11758196—41no—
101#11758196—41no—
102#11758196—42no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—42no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125D4×C61—82no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
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—
135C2×C4×C61#10212yes—
136C22⋊D61—82no—
137C22⋊D61—84no—
138C22⋊D61—82no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—22no—
144C2×Dic61—21no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61#9911yescharacteristic
150C2×Dic61#9911yescharacteristic
151C2×Dic61#10212yes—
152C2×Dic61C2×D811yescharacteristic
153C2×Dic61C2×SD1611yescharacteristic
154D244—82no—
155Dic122—42no—
156Dic122—42no—
157#92420—82no—
158#92420—82no—
159#11882—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61C2×#9911yescharacteristic
170C22×C61C2×#10211yescharacteristic
171C22×C61#42111yescharacteristic
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C4×C61—22no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—81no—
183Dic61—21no—
184Dic61—21no—
185Dic61—22no—
186Dic61—21no—
187Dic61—41no—
188Dic61—81no—
189Dic61#35512yes—
190#2548—611no—
191#1801—611no—
192#1461—611no—
193#1345—612no—
194#1345—612no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—161no—
198C2×C61#151911yescharacteristic
199C2×C61#212211yescharacteristic
200C2×C61C2×#35511yescharacteristic
201D61—161no—
202C2×#127—611no—
203C2×#124—1221no—
204C2×C4×Q8—611no—
205#431—1221no—
206#423—1221no—
207C2×#101—1221no—
208#394—611no—
209#394—611no—
210#394—611no—
211#394#692311yescharacteristic
212#390—1221no—
213#390—1221no—
214#390—1221no—
215C4×C4⋊C4—611no—
216#343—612no—
217#324—612no—
218#324—1221no—
219C61#1188211yescharacteristic, complemented, Sylow
220C22×Q8—611no—
221C22×D4—611no—
222C22×D4—1221no—
223C22×D4—1221no—
224C22×D4C2×#692311yescharacteristic
225C2×M16—1222no—
226#127—2441no—
227#127—2441no—
228#124—2442no—
229#124—2442no—
230C4×Q8—2441no—
231C4×Q8—2441no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4C2×#692311yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—1221no—
248C4⋊C8—2441no—
249C4⋊C8—2441no—
250C4⋊C8—2441no—
251#101—2442no—
252C22⋊C8—1222no—
253C4×C8—2441no—
254#95—611no—
255#95C2×#692311yescharacteristic
256C24—21no—
257C24—1221no—
258C2×Q8—612no—
259C2×Q8—612no—
260C2×Q8—2441no—
261C2×Q8—2441no—
262C2×D4—41no—
263C2×D4—81no—
264C2×D4—4881no—
265C2×D4—2441no—
266C2×D4—2442no—
267C2×D4—2441no—
268C2×D4—2441no—
269C2×D4—2442no—
270C2×D4—2442no—
271C2×D4—2442no—
272C2×D4—2442no—
273C22×C4—21no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4C22⋊#692311yescharacteristic
280C22×C4C22⋊#692311yescharacteristic
281C22×C4C22×#692311yescharacteristic
282M16—2442no—
283M16—2442no—
284C2×C8—2442no—
285C2×C8—2442no—
286C4⋊C4—41no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2442no—
290C22⋊C4—42no—
291C22⋊C4—81no—
292C22⋊C4—4881no—
293C22⋊C4—4881no—
294C22⋊C4—4881no—
295C22⋊C4—2441no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C22⋊C4—2442no—
300C42—1221no—
301C42—1221no—
302C42—1221no—
303C42—1221no—
304C42—1221no—
305C42—1221no—
306C42—2442no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23C2×C22⋊#692311yescharacteristic
322Q8—2442no—
323Q8—2442no—
324D4—82no—
325D4—4882no—
326D4—4882no—
327D4—4884no—
328D4—4882no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—612no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—1222no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4#1451983912yes—
354C8—4882no—
355C8—4882no—
356C22—21no—
357C22—21no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—4881no—
366C22—4881no—
367C22—4881no—
368C22—4881no—
369C22—4881no—
370C22—4881no—
371C22—4881no—
372C22D61⋊#9911yescharacteristic
373C22C2×#1451983911yescharacteristic
374C22#1684075911yescharacteristic
375C4—22no—
376C4—41no—
377C4—41no—
378C4—81no—
379C4—612no—
380C4—1221no—
381C4—1222no—
382C4—1221no—
383C4—1221no—
384C4—4881no—
385C4—2441no—
386C2—21no—
387C2—21no—
388C2—161no—
389C2—9761no—
390C2#2146125411yescharacteristic
391C2#2146207911yescharacteristic
392C2D61⋊#35511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#394C4
socleC22×C61C2×#99
prime radicalC2×#14519773C4
cosocleC2×#11758196C23
hypercenter#394#6923
hypocenterC61#11882
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #21461686C2semidirect
2. #21461063C2semidirect
3. #21460802C2semidirect
4. #21460801C2semidirect
219. C61#11882semidirect

Maximal subgroups

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

subgroupindex
#214616862
#214610632
#214608022
#214608012
#214508172
#1188261