Finite Group Databasebeta

← #30607428

Subgroups — #30607428

Order 15616.

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

normal subgroups only

This group has 380 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#21462599C211yesmaximal, characteristic
2#21462175C211yesmaximal, characteristic, complemented
3C2×#16840677C211yesmaximal, characteristic
4#21461939C211yesmaximal, characteristic, complemented
5#21460878C211yesmaximal, characteristic, complemented
6#21460875C211yesmaximal, characteristic, complemented
7#21447567C211yesmaximal, characteristic
8#16840842—21no—
9C2×D61⋊C16C2211yescharacteristic
10#16840808—22no—
11#16840806—21no—
12#16840806—21no—
13#16840777—21no—
14C2×#14519848C2211yescharacteristic
15D61⋊#108C2211yescharacteristic
16#16840761—21no—
17#16840725C2211yescharacteristic
18#16840691—21no—
19#16840690—21no—
20#16840677—22no—
21#16840645—21no—
22C2×#14519800C2211yescharacteristic
23M32×D61C2211yescharacteristic
24#108×D61C2211yescharacteristic
25#16839578C411yescharacteristic, complemented
26#16839576C411yescharacteristic, complemented
27#16839574C411yescharacteristic, complemented
28C61×#362C411yescharacteristic, complemented
29#14519865—22no—
30#14519865—22no—
31#14519865—41no—
32#14519865—41no—
33C2×#11758213—21no—
34D61⋊M16—21no—
35D61⋊M16—42no—
36D61⋊M16D411yescharacteristic
37#14519856D411yescharacteristic
38D61⋊C16—21no—
39D61⋊C16—21no—
40C2×#11758187—21no—
41#14519848—21no—
42#14519848—21no—
43#14519848—41no—
44#14519848D411yescharacteristic
45#14519848D411yescharacteristic
46#14519847—21no—
47#14519847—41no—
48#14519842—22no—
49#14519842—22no—
50#14519831—21no—
51C8×#6923—21no—
52C2×#11758226—21no—
53#14519800—21no—
54#14519800—21no—
55#14519800D412yes—
56#14519800Q812yes—
57C2×#11758201—21no—
58C2×D488C2×C411yescharacteristic
59M16×D61—21no—
60C2×C8×D61C2311yescharacteristic
61#14519717C2×C411yescharacteristic
62#14519716—21no—
63C16×D61—21no—
64#14519713C2×C411yescharacteristic
65#14519712—21no—
66C2×Q16×C61C2×C411yescharacteristic
67M32×C61C2×C411yescharacteristic
68#108×C61C2×C411yescharacteristic
69C2×Q8×C61—21no—
70#11758226—22no—
71#11758226—22no—
72#11758226—41no—
73#11758226—41no—
74C2×D244—21no—
75C2×D244—41no—
76C2×C4×D61—41no—
77C2×C4×D61C2×D411yescharacteristic
78C22⋊#6923—21no—
79#11758217—21no—
80#11758217—41no—
81C2×#92420—41no—
82C4⋊#6923—21no—
83C4×#6923—21no—
84#11758213—21no—
85#11758213—21no—
86#11758213—42no—
87#11758213—42no—
88#11758213—41no—
89#11758213—41no—
90#11758213D811yescharacteristic
91#11758213D811yescharacteristic
92D61⋊C8—21no—
93D61⋊C8—42no—
94D61⋊C8—42no—
95D61⋊C8—41no—
96Q16×C61—21no—
97Q16×C61C4⋊C412yes—
98M16×C61—21no—
99C2×C8×C61C22×C411yescharacteristic
100#11758201—22no—
101#11758201—22no—
102#11758194—21no—
103C2×#92418#4111yescharacteristic
104D488—21no—
105D488C4⋊C412yes—
106#11758189—41no—
107C8×D61—41no—
108C8×D61C2×D411yescharacteristic
109C8×D61C2×D411yescharacteristic
110C8×D61C2×Q811yescharacteristic
111C8×D61#4111yescharacteristic
112#11758187—41no—
113C16×C61—21no—
114#11758185—21no—
115C22×D61—41no—
116C22×D61#13711yescharacteristic
117C2×#6923—41no—
118Q8×C61—22no—
119Q8×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61C4×D411yescharacteristic
122C2×Dic61AGL(1,ℤ/8)11yescharacteristic
123D244—22no—
124D244—42no—
125D244—42no—
126D244—41no—
127C4×D61—42no—
128C4×D61—42no—
129C4×D61#12011yescharacteristic
130C4×D61C22⋊Q811yescharacteristic
131C4×D61C2×D811yescharacteristic
132C4×D61#13511yescharacteristic
133#92420—21no—
134#92420—21no—
135#92420—41no—
136#92420—41no—
137#92420—81no—
138C8×C61—41no—
139C8×C61C2×C4⋊C411yescharacteristic
140C8×C61C4×D411yescharacteristic
141#92418—41no—
142#92418C22⋊Q811yescharacteristic
143#92418#12311yescharacteristic
144#12942—611nomaximal, Sylow
145C22×C61#44011yescharacteristic
146C2×D61—41no—
147C2×D61—42no—
148C2×D61—161no—
149C2×D61#45211yescharacteristic
150C2×D61#47411yescharacteristic
151#6923—81no—
152C4×C61—42no—
153C4×C61#38511yescharacteristic
154C4×C61C4×D811yescharacteristic
155Dic61#44711yescharacteristic
156Dic61#47811yescharacteristic
157#2957—611no—
158#2161—611no—
159#2148—611no—
160C2×#359—611no—
161#1953—611no—
162#1381—611no—
163#1379—611no—
164C2×C61—21no—
165C2×C61#186211yescharacteristic
166D61—21no—
167D61—21no—
168D61—82no—
169C2×#135—611no—
170#568—1221no—
171C2×M32—611no—
172C22×C16—611no—
173#444—1222no—
174#443—1221no—
175#443—1221no—
176#430—1221no—
177C2×#108—611no—
178C2×#108—611no—
179C2×#108—611no—
180#421—1221no—
181#405—611no—
182#368—1221no—
183#368—1221no—
184#362—611no—
185#362#692311yescharacteristic, complemented
186#361—611no—
187#361—611no—
188#359—1222no—
189#344—1221no—
190C61#1294211yescharacteristic, complemented, Sylow
191C2×#41—1221no—
192#135—612no—
193#135—612no—
194#135—1221no—
195#135—1221no—
196C2×Q16C2×#692311yescharacteristic
197C2×SD16—1221no—
198C2×D8—611no—
199#131—1222no—
200#131—1222no—
201#131—2441no—
202#131—2441no—
203C2×M16—611no—
204C2×M16—1221no—
205C2×M16—1221no—
206C2×M16—1221no—
207C2×M16—2442no—
208C22×C8—611no—
209#117—611no—
210M32—611no—
211M32—1221no—
212M32C2×#692311yescharacteristic
213C2×C16—1221no—
214C2×C16—1221no—
215C2×C16—1221no—
216C2×C16—1221no—
217#108—611no—
218#108—611no—
219#108—611no—
220#108—1221no—
221#108—1221no—
222#108—1221no—
223#108—1221no—
224#108—2441no—
225#108—2441no—
226#108C2×#692311yescharacteristic
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—21no—
236C2×D4—1221no—
237C2×D4—2441no—
238C22×C4—611no—
239C22×C4—2441no—
240Q16—21no—
241Q16C4⋊#692312yes—
242SD16—1222no—
243SD16—1222no—
244D8—612no—
245D8—1221no—
246M16—21no—
247M16—611no—
248M16—611no—
249M16—1221no—
250M16—1221no—
251M16—1221no—
252M16—1221no—
253M16—2441no—
254M16—2442no—
255M16—2442no—
256M16—2441no—
257M16—2441no—
258M16—2441no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8—611no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8—1221no—
265C2×C8—2441no—
266C2×C8—2442no—
267C2×C8—2442no—
268C2×C8—2441no—
269C2×C8—2441no—
270C2×C8C22×#692311yescharacteristic
271C4⋊C4—1221no—
272C22⋊C4—1221no—
273C42—1221no—
274C16—21no—
275C16—1221no—
276C16—2441no—
277C23—611no—
278C23—2441no—
279Q8—22no—
280Q8—41no—
281D4—1222no—
282D4—2442no—
283D4—2442no—
284D4—2441no—
285C2×C4—41no—
286C2×C4—611no—
287C2×C4—611no—
288C2×C4—611no—
289C2×C4—611no—
290C2×C4—611no—
291C2×C4—2442no—
292C2×C4—2442no—
293C2×C4—2441no—
294C2×C4D4×#692311yescharacteristic
295C8—41no—
296C8—611no—
297C8—611no—
298C8—1221no—
299C8—1221no—
300C8—4881no—
301C8—2441no—
302C8—2441no—
303C8—2441no—
304C8C2×C4⋊#692311yescharacteristic
305C8D4×#692311yescharacteristic
306C22—611no—
307C22—611no—
308C22—9761no—
309C22—2441no—
310C22—2442no—
311C22#1684080111yescharacteristic
312C4—42no—
313C4—611no—
314C4—611no—
315C4—4881no—
316C4#1684070911yescharacteristic
317C4D8×#692311yescharacteristic
318C2—21no—
319C2—1221no—
320C2—1221no—
321C2—4882no—
322C2#2146178211yescharacteristic
subgroupG/H
centerC2#21461782
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#362C4
socleC2×C61#1862
prime radicalC2×#14519800C22
cosocleC2×C8×D61C23
hypercenter#362#6923
hypocenterC61#12942
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
2. #21462175C2semidirect
4. #21461939C2semidirect
5. #21460878C2semidirect
6. #21460875C2semidirect
25. #16839578C4semidirect
26. #16839576C4semidirect
27. #16839574C4semidirect
28. C61×#362C4semidirect
185. #362#6923semidirect
190. C61#12942semidirect

Maximal subgroups

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

subgroupindex
#214625992
#214621752
C2×#168406772
#214619392
#214608782
#214608752
#214475672
#1294261