Finite Group Databasebeta

← #30608448

Subgroups — #30608448

Order 15616.

308 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 54 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#21462117C211yesmaximal, characteristic
2#21462102C211yesmaximal, characteristic
3#21460967C211yesmaximal, characteristic, complemented
4#21460966C211yesmaximal, characteristic, complemented
5#21460948C211yesmaximal, characteristic, complemented
6#21460948C211yesmaximal, characteristic, complemented
7#21456895C211yesmaximal, characteristic
8D61⋊#101—21no—
9#16840743—21no—
10#16840672—21no—
11#16840671C2211yescharacteristic
12#16840671C2211yescharacteristic
13#16840669C2211yescharacteristic
14#16840669C2211yescharacteristic
15#16840668—21no—
16#16840373C411yescharacteristic, complemented
17#16840337C2211yescharacteristic
18#16840154C2211yescharacteristic
19#16840130C411yescharacteristic, complemented
20#16840117C2211yescharacteristic
21#16839986—21no—
22#16839970—21no—
23#16839923—21no—
24#16839916—21no—
25#16839821C411yescharacteristic, complemented
26C61×#494C411yescharacteristic, complemented
27D61⋊M16—41no—
28#14519856—41no—
29#14519838—21no—
30#14519838—21no—
31#14519838—41no—
32#14519836—21no—
33#14519836—21no—
34#14519836—41no—
35C2×#11758226D411yescharacteristic
36C2×Q8×D61D411yescharacteristic
37C2×#11758202—21no—
38C2×#11758201—21no—
39#14519775D411yescharacteristic
40#14519772—41no—
41#14519769C2×C411yescharacteristic
42#14519767—41no—
43#14519766D411yescharacteristic
44#14519765C2311yescharacteristic
45#14519762—41no—
46#14519755—41no—
47#14519753—21no—
48Q8×Dic61—21no—
49#14519734C2×C411yescharacteristic
50#14519706—21no—
51#14519702—21no—
52#14519701—21no—
53#14519701—21no—
54#14519699—21no—
55#14519689—21no—
56#14519688C2×C411yescharacteristic
57C2×Q16×C61—21no—
58C2×Q16×C61—21no—
59C4⋊Q8×C61C2×C411yescharacteristic
60C4⋊Q8×C61C2×C411yescharacteristic
61C4×C8×C61C2×C411yescharacteristic
62C2×Q8×C61—21no—
63C2×Q8×C61C22⋊C411yescharacteristic
64C2×Q8×C61C22⋊C411yescharacteristic
65#11758226—81no—
66Q8×D61—81no—
67C2×D244—21no—
68C2×D244C2×D411yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61C22⋊C411yescharacteristic
72C2×Dic122—21no—
73C2×Dic122C2×D411yescharacteristic
74C22⋊#6923—41no—
75C22⋊#6923—41no—
76#11758217—41no—
77#11758217—41no—
78C4⋊#6923—81no—
79C4×#6923—81no—
80#11758213—81no—
81D61⋊C8—81no—
82Q16×C61—81no—
83Q16×C61—81no—
84C2×C8×C61—21no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C42×C61C22×C411yescharacteristic
88#11758202—81no—
89#11758201—81no—
90#11758198—21no—
91#11758198—41no—
92#11758198—41no—
93#11758198—41no—
94C4⋊Dic61—21no—
95C4⋊Dic61—41no—
96#11758196—21no—
97#11758196—41no—
98#11758196—41no—
99#11758196—41no—
100C4×Dic61—41no—
101C4×Dic61C22⋊C411yescharacteristic
102C2×#92418—21no—
103C22×D61—21no—
104C22×D61#9911yescharacteristic
105C2×#6923—81no—
106C2×#6923—81no—
107Q8×C61—41no—
108Q8×C61—41no—
109Q8×C61—41no—
110Q8×C61—41no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—41no—
115C2×C4×C61C2×C22⋊C411yescharacteristic
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—41no—
119C2×Dic61#9911yescharacteristic
120D244—41no—
121D244—81no—
122C4×D61—41no—
123C4×D61—41no—
124C4×D61—41no—
125C4×D61—41no—
126C4×D61—41no—
127Dic122—41no—
128Dic122—81no—
129#92420—81no—
130#92420—81no—
131C8×C61—41no—
132#92418—41no—
133#13608—611nomaximal, Sylow
134C22×C61C2×#9911yescharacteristic
135C2×D61—21no—
136C2×D61—41no—
137C2×D61—41no—
138C2×D61—81no—
139#6923—161no—
140#6923—161no—
141C4×C61—21no—
142C4×C61—41no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61—81no—
146Dic61—21no—
147Dic61—41no—
148Dic61—41no—
149Dic61—81no—
150#3223—611no—
151#2133—611no—
152#2129—611no—
153#1414—611no—
154#1414—611no—
155#1407—611no—
156#1407—611no—
157C2×C61—21no—
158C2×C61#212711yescharacteristic
159D61—41no—
160D61—81no—
161#541—611no—
162#536—611no—
163#497—611no—
164#494#692311yescharacteristic, complemented
165#491—611no—
166#488—611no—
167#464—1221no—
168#462—1221no—
169#452—1221no—
170#451—1221no—
171#433—611no—
172C2×#101—1221no—
173#410—1221no—
174#356—1221no—
175#355—611no—
176#355—611no—
177#354—611no—
178#354—611no—
179#354—1221no—
180C61#1360811yescharacteristic, complemented, Sylow
181C2×#41—611no—
182C22×Q8—611no—
183C2×Q16—21no—
184C2×Q16—21no—
185C2×Q16—1221no—
186C2×SD16—1221no—
187C2×M16—2441no—
188C4⋊Q8—611no—
189C4⋊Q8C2×#692311yescharacteristic
190C4⋊Q8C2×#692311yescharacteristic
191#126—2441no—
192#125—611no—
193#125—2441no—
194#124—611no—
195#124—611no—
196#123—2441no—
197C22⋊Q8—1221no—
198C22⋊Q8—2441no—
199C4×Q8—1221no—
200#117—611no—
201#117—2441no—
202C4⋊C8—1221no—
203#103—1221no—
204#103—1221no—
205#103—1221no—
206#102—1221no—
207#101—1221no—
208#101—1221no—
209#101—2441no—
210#99—1221no—
211#99—1221no—
212#99—2441no—
213C22⋊C8—1221no—
214#97—611no—
215C4×C8C2×#692311yescharacteristic
216#41—4881no—
217C2×Q8—21no—
218C2×Q8—611no—
219C2×Q8—1221no—
220C2×Q8—4881no—
221C2×Q8C22⋊#692311yescharacteristic
222C2×Q8C22⋊#692311yescharacteristic
223C2×D4—611no—
224C2×D4—1221no—
225C22×C4—611no—
226C22×C4—1221no—
227C22×C4—1221no—
228Q16—81no—
229Q16—81no—
230Q16—4881no—
231SD16—4881no—
232M16—4881no—
233M16—2441no—
234M16—2441no—
235C2×C8—21no—
236C2×C8—1221no—
237C2×C8—4881no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—1221no—
241C4⋊C4—1221no—
242C4⋊C4—4881no—
243C4⋊C4—2441no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C22⋊C4—1221no—
248C22⋊C4—2441no—
249C22⋊C4—2441no—
250C22⋊C4—2441no—
251C22⋊C4—2441no—
252C22⋊C4—2441no—
253C42—611no—
254C42—4881no—
255C42—2441no—
256C42C22×#692311yescharacteristic
257C23—611no—
258C23—1221no—
259Q8—41no—
260Q8—41no—
261Q8—41no—
262Q8—41no—
263Q8—4881no—
264Q8—2441no—
265D4—4881no—
266D4—2441no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—611no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—4881no—
275C2×C4—4881no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4C2×C22⋊#692311yescharacteristic
283C8—41no—
284C8—4881no—
285C8—4881no—
286C8—2441no—
287C22—1221no—
288C22—4881no—
289C22—2441no—
290C22—2441no—
291C22D61⋊#9911yescharacteristic
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—81no—
297C4—1221no—
298C4—9761no—
299C4—9761no—
300C4—4881no—
301C4—2441no—
302C4—2441no—
303C2—21no—
304C2—4881no—
305C2—2441no—
306C2#2146209511yescharacteristic
subgroupG/H
centerC2#21462095
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#494C4
socleC2×C61#2127
prime radicalC2×#11758226D4
cosocle#14519765C23
hypercenter#494#6923
hypocenterC61#13608
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #21460967C2semidirect
4. #21460966C2semidirect
5. #21460948C2semidirect
6. #21460948C2semidirect
16. #16840373C4semidirect
19. #16840130C4semidirect
25. #16839821C4semidirect
26. C61×#494C4semidirect
164. #494#6923semidirect
180. C61#13608semidirect

Maximal subgroups

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

subgroupindex
#214621172
#214621022
#214609672
#214609662
#214609482
#214568952
#1360861