Finite Group Databasebeta

← #30605402

Subgroups — #30605402

Order 15616.

440 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 74 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#21460804C212yesmaximal, complemented
4#21460801C212yesmaximal
5#21450723C211yesmaximal, characteristic
6#16840778—21no—
7#16840765—21no—
8C2×#14519838—21no—
9#16840642C2212yes—
10#16840608—21no—
11#16840608C2212yes—
12C2×#14519754—21no—
13C2×#14519742C2211yescharacteristic
14C2×D4×Dic61C411yescharacteristic
15#16839694C2211yescharacteristic
16#16839692C411yescharacteristic
17#16839676C2211yescharacteristic
18#16839656—21no—
19#16839655—21no—
20#16839626C411yescharacteristic
21#16839620—21no—
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
31C23×Dic61—21no—
32#14519754—42no—
33#14519754—42no—
34#14519742—41no—
35#14519742—41no—
36D4×Dic61—41no—
37D4×Dic61—41no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196D411yescharacteristic
43C2×#11758196C2311yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
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—
60C2×D4×C61—41no—
61C2×D4×C61—42no—
62C22×C4×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—42no—
69C22×Dic61—42no—
70C22×Dic61—42no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×Dic122D812yes—
78C2×Dic122SD1612yes—
79#11758217—42no—
80#11758217—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—42no—
85C22⋊C4×C61—42no—
86C22⋊Dic61—42no—
87C22⋊Dic61—41no—
88C22⋊Dic61—41no—
89C22⋊Dic61—41no—
90C22⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94#11758196—41no—
95#11758196—41no—
96#11758196—42no—
97#11758196—42no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C23×C61—22no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61C2×C22⋊C411yescharacteristic
112D4×C61—42no—
113D4×C61—42no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61#10212yes—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—84no—
138C2×Dic61#9911yescharacteristic
139C2×Dic61#9911yescharacteristic
140C2×Dic61#10212yes—
141C2×Dic61C2×D811yescharacteristic
142C2×Dic61C2×SD1611yescharacteristic
143Dic122—42no—
144Dic122—42no—
145#92420—82no—
146#92420—82no—
147#11879—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—42no—
151C22×C61—42no—
152C22×C61—42no—
153C22×C61—81no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61C2×#9911yescharacteristic
158C22×C61C2×#10211yescharacteristic
159C22×C61#42111yescharacteristic
160C4×C61—22no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—81no—
164Dic61—21no—
165Dic61—21no—
166Dic61—21no—
167Dic61—22no—
168Dic61—21no—
169Dic61—41no—
170Dic61—81no—
171Dic61—81no—
172#2536—611no—
173#1801—611no—
174#1461—611no—
175#1346—612no—
176#1345—612no—
177C2×C61—21no—
178C2×C61—21no—
179C2×C61—82no—
180C2×C61#151911yescharacteristic
181C2×C61#212011yescharacteristic
182C2×C61#213311yescharacteristic
183C2×C22⋊Q8—1221no—
184C2×C4×Q8—611no—
185C2×C4×D4—611no—
186#431—1221no—
187#423—1221no—
188C2×#101—1221no—
189#398—611no—
190#398—611no—
191#394—611no—
192#394#692311yescharacteristic
193#388—1221no—
194#388—1221no—
195#382—611no—
196#380—1221no—
197#343—612no—
198#324—612no—
199#324—1221no—
200C61#1187911yescharacteristic, complemented, Sylow
201C22×Q8—611no—
202C22×D4C2×#692311yescharacteristic
203C23×C4—1221no—
204C2×M16—1222no—
205C22⋊Q8—2442no—
206C22⋊Q8—2442no—
207C4×Q8—2441no—
208C4×Q8—2441no—
209C4×D4—2441no—
210C4×D4—2441no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4C2×#692311yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—611no—
226C4⋊C8—2441no—
227C4⋊C8—2441no—
228C4⋊C8—2441no—
229#101—2442no—
230C22⋊C8—1222no—
231C4×C8—2441no—
232#95—611no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95C2×#692311yescharacteristic
237C24—21no—
238C2×Q8—612no—
239C2×Q8—612no—
240C2×Q8—2441no—
241C2×Q8—2441no—
242C2×D4—41no—
243C2×D4—42no—
244C22×C4—21no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—2442no—
252C22×C4—2442no—
253C22×C4—2442no—
254C22×C4C22⋊#692311yescharacteristic
255C22×C4C22⋊#692311yescharacteristic
256C22×C4C22×#692311yescharacteristic
257M16—2442no—
258M16—2442no—
259C2×C8—2442no—
260C2×C8—2442no—
261C4⋊C4—41no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2442no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4—2442no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—2441no—
272C22⋊C4—2441no—
273C22⋊C4—2441no—
274C22⋊C4—2441no—
275C22⋊C4—2442no—
276C42—1221no—
277C42—1221no—
278C42—1221no—
279C42—1221no—
280C42—1221no—
281C42—1221no—
282C23—22no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×C22⋊#692311yescharacteristic
290Q8—2442no—
291Q8—2442no—
292D4—42no—
293D4—42no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—612no—
306C2×C4—611no—
307C2×C4—611no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—4884no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4#1451983912yes—
323C8—4882no—
324C8—4882no—
325C22—21no—
326C22—21no—
327C22—42no—
328C22—42no—
329C22—42no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22D61⋊#9911yescharacteristic
335C22C2×#1451983911yescharacteristic
336C22#1684075911yescharacteristic
337C4—22no—
338C4—41no—
339C4—41no—
340C4—81no—
341C4—1221no—
342C4—1222no—
343C4—1221no—
344C4—1221no—
345C4—1221no—
346C4—4881no—
347C4—4881no—
348C4—2441no—
349C2—21no—
350C2—21no—
351C2—82no—
352C2#2146125411yescharacteristic
353C2#2146207111yescharacteristic
354C2#2146211511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#394C4
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×#11758196C23
hypercenter#394#6923
hypocenterC61#11879
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. #21460804C2semidirect
200. C61#11879semidirect

Maximal subgroups

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

subgroupindex
#214616862
#214610632
#214608042
#214608012
#214507232
#1187961