Finite Group Databasebeta

← #30607441

Subgroups — #30607441

Order 15616.

384 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462595C211yesmaximal, characteristic
2D61⋊#365C211yesmaximal, characteristic, complemented
3C2×#16840678C211yesmaximal, characteristic
4#21461936C211yesmaximal, characteristic, complemented
5#21460896C211yesmaximal, characteristic, complemented
6#21460871C211yesmaximal, characteristic, complemented
7#21447565C211yesmaximal, characteristic
8#16840840—21no—
9C2×#14519852C2211yescharacteristic
10#16840809—21no—
11#16840809—21no—
12#16840804—22no—
13D61⋊#108C2211yescharacteristic
14#16840773—21no—
15C2×#14519845C2211yescharacteristic
16#16840760—21no—
17#16840725C2211yescharacteristic
18#16840687—21no—
19#16840686—21no—
20#16840678—22no—
21#16840641—21no—
22C2×#14519796C2211yescharacteristic
23M32×D61C2211yescharacteristic
24#108×D61C2211yescharacteristic
25#16839579C411yescharacteristic, complemented
26#16839577C411yescharacteristic, complemented
27#16839575C411yescharacteristic, complemented
28C61×#361C411yescharacteristic, complemented
29#14519864—22no—
30#14519864—22no—
31#14519864—41no—
32#14519864—41no—
33D61⋊M16—21no—
34D61⋊M16D411yescharacteristic
35C2×#11758217—42no—
36#14519856D411yescharacteristic
37C2×C4⋊#6923—21no—
38#14519852—21no—
39#14519852—21no—
40C2×#11758187—21no—
41#14519848—21no—
42#14519847D411yescharacteristic
43#14519847D411yescharacteristic
44#14519846—41no—
45#14519845—21no—
46#14519845—21no—
47#14519845—41no—
48#14519841—22no—
49#14519841—22no—
50#14519831—21no—
51C8×#6923—21no—
52C2×#11758224—21no—
53#14519796—21no—
54#14519796—21no—
55#14519796D412yes—
56#14519796Q812yes—
57C2×Dic244C2×C411yescharacteristic
58C2×#11758200—21no—
59M16×D61—21no—
60C2×C8×D61C2311yescharacteristic
61#14519717C2×C411yescharacteristic
62#14519716—21no—
63C16×D61—21no—
64#14519713C2×C411yescharacteristic
65#14519712—21no—
66C2×D8×C61C2×C411yescharacteristic
67M32×C61C2×C411yescharacteristic
68#108×C61C2×C411yescharacteristic
69C22×#6923—41no—
70C2×D4×C61—21no—
71C2×C22⋊D61—41no—
72C22×Dic61—41no—
73#11758224—22no—
74#11758224—22no—
75#11758224—41no—
76#11758224—41no—
77C2×C4×D61C2×D411yescharacteristic
78C2×Dic122—21no—
79C22⋊#6923—21no—
80#11758217—42no—
81#11758217—42no—
82#11758217—41no—
83#11758217SD1612yes—
84C2×#92420—42no—
85C2×#92420—42no—
86C4⋊#6923—21no—
87C4⋊#6923—41no—
88C4⋊#6923—41no—
89C4×#6923—21no—
90#11758213—21no—
91#11758213—21no—
92#11758213—21no—
93D61⋊C8—21no—
94D61⋊C8—41no—
95D8×C61—21no—
96D8×C61C4⋊C412yes—
97M16×C61—21no—
98C2×C8×C61C22×C411yescharacteristic
99#11758200—22no—
100#11758200—22no—
101#11758194—21no—
102C2×#92418#4111yescharacteristic
103Dic244—21no—
104Dic244C4⋊C412yes—
105#11758189—41no—
106C8×D61—41no—
107C8×D61C2×D411yescharacteristic
108C8×D61C2×D411yescharacteristic
109C8×D61C2×Q811yescharacteristic
110C8×D61#4111yescharacteristic
111#11758187—41no—
112C16×C61—21no—
113#11758185—21no—
114C23×C61—41no—
115C22×D61#13511yescharacteristic
116C2×#6923—41no—
117C2×#6923—81no—
118C2×#6923—161no—
119D4×C61—22no—
120D4×C61—41no—
121C2×C4×C61C4×D411yescharacteristic
122C22⋊D61—42no—
123C22⋊D61—42no—
124C2×Dic61—41no—
125C2×Dic61—42no—
126C2×Dic61—42no—
127C2×Dic61C2×SD1611yescharacteristic
128C4×D61#12011yescharacteristic
129C4×D61C22⋊Q811yescharacteristic
130C4×D61AGL(1,ℤ/8)11yescharacteristic
131C4×D61AGL(1,ℤ/8)11yescharacteristic
132Dic122—22no—
133Dic122—41no—
134#92420—22no—
135#92420—41no—
136#92420—41no—
137C8×C61—41no—
138C8×C61C2×C4⋊C411yescharacteristic
139C8×C61C4×D411yescharacteristic
140#92418—41no—
141#92418C22⋊Q811yescharacteristic
142#92418#12311yescharacteristic
143#12952—611nomaximal, Sylow
144C22×C61—42no—
145C22×C61—161no—
146C22×C61C4×SD1611yescharacteristic
147C2×D61—41no—
148C2×D61#44911yescharacteristic
149C2×D61#47811yescharacteristic
150#6923—81no—
151#6923—161no—
152C4×C61#38511yescharacteristic
153C4×C61#44211yescharacteristic
154Dic61—42no—
155Dic61#45011yescharacteristic
156Dic61#47611yescharacteristic
157#2957—611no—
158C2×#365—611no—
159#2148—611no—
160C2×#360—611no—
161#1951—611no—
162#1388—611no—
163#1378—611no—
164C2×C61—21no—
165C2×C61—82no—
166C2×C61#186411yescharacteristic
167D61—21no—
168D61—21no—
169C2×#135—611no—
170#568—1221no—
171C2×M32—611no—
172C2×M32—611no—
173#444—1221no—
174#444—1221no—
175#443—1222no—
176C2×#108—611no—
177C2×#108—611no—
178#428—1221no—
179C2×#106—611no—
180#421—1221no—
181#405—611no—
182#365—1221no—
183#365—1221no—
184#362—611no—
185#362—611no—
186#361—611no—
187#361#692311yescharacteristic, complemented
188#360—1222no—
189#343—1221no—
190C61#1295211yescharacteristic, complemented, Sylow
191C2×#41—1221no—
192#135—612no—
193#135—612no—
194#135—1221no—
195#135—1221no—
196C2×Q16—611no—
197C2×SD16—1221no—
198C2×D8C2×#692311yescharacteristic
199#131—1222no—
200#131—1222no—
201#131—2441no—
202#131—2441no—
203C2×M16—611no—
204C2×M16—1221no—
205C2×M16—1221no—
206C2×M16—2442no—
207C22×C8—611no—
208#117—611no—
209C2×C4⋊C4—1221no—
210M32—611no—
211M32—1221no—
212M32—1221no—
213M32—1221no—
214M32C2×#692311yescharacteristic
215C2×C16—1221no—
216C2×C16—1221no—
217#108—611no—
218#108—611no—
219#108—611no—
220#108—1221no—
221#108—1221no—
222#108C2×#692311yescharacteristic
223#107—2441no—
224#106—1221no—
225#106—1221no—
226#106—2441no—
227#104—1222no—
228#104—1222no—
229#97—1221no—
230C4×C8—1221no—
231#41—1222no—
232#41—1222no—
233#41—2441no—
234#41—2441no—
235C2×Q8—1221no—
236C2×D4—21no—
237C2×D4—2441no—
238C22×C4—611no—
239C22×C4—2441no—
240C22×C4—2441no—
241Q16—612no—
242Q16—1221no—
243SD16—1222no—
244SD16—1222no—
245D8—21no—
246D8C4⋊#692312yes—
247M16—21no—
248M16—612no—
249M16—1221no—
250M16—1221no—
251M16—1221no—
252M16—1221no—
253M16—2441no—
254M16—2442no—
255M16—2442no—
256M16—2441no—
257C2×C8—611no—
258C2×C8—611no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8—611no—
262C2×C8—1221no—
263C2×C8—2441no—
264C2×C8—2442no—
265C2×C8—2442no—
266C2×C8—2441no—
267C2×C8C22×#692311yescharacteristic
268C4⋊C4—1221no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C22⋊C4—1221no—
272C42—1221no—
273C16—21no—
274C16—1221no—
275C16—2441no—
276C23—41no—
277C23—611no—
278Q8—1222no—
279Q8—2441no—
280D4—22no—
281D4—41no—
282D4—2442no—
283D4—2442no—
284C2×C4—611no—
285C2×C4—611no—
286C2×C4—611no—
287C2×C4—611no—
288C2×C4—611no—
289C2×C4—9761no—
290C2×C4—4881no—
291C2×C4—2442no—
292C2×C4—2442no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4D4×#692311yescharacteristic
296C8—41no—
297C8—611no—
298C8—611no—
299C8—1222no—
300C8—2441no—
301C8—2441no—
302C8—2441no—
303C8C2×C4⋊#692311yescharacteristic
304C8D4×#692311yescharacteristic
305C22—42no—
306C22—161no—
307C22—611no—
308C22—611no—
309C22—2441no—
310C22SD16×#692311yescharacteristic
311C4—611no—
312C4—611no—
313C4—9761no—
314C4—4881no—
315C4—2442no—
316C4#1684070911yescharacteristic
317C4#1684080311yescharacteristic
318C2—21no—
319C2—82no—
320C2—1221no—
321C2—1221no—
322C2#2146178411yescharacteristic
subgroupG/H
centerC2#21461784
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#361C4
socleC2×C61#1864
prime radicalC2×#14519796C22
cosocleC2×C8×D61C23
hypercenter#361#6923
hypocenterC61#12952
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
2. D61⋊#365C2semidirect
4. #21461936C2semidirect
5. #21460896C2semidirect
6. #21460871C2semidirect
25. #16839579C4semidirect
26. #16839577C4semidirect
27. #16839575C4semidirect
28. C61×#361C4semidirect
187. #361#6923semidirect
190. C61#12952semidirect

Maximal subgroups

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

subgroupindex
#214625952
D61⋊#3652
C2×#168406782
#214619362
#214608962
#214608712
#214475652
#1295261