Finite Group Databasebeta

← #30607869

Subgroups — #30607869

Order 15616.

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

normal subgroups only

This group has 334 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
1C2×#16840674C211yesmaximal, characteristic
2#21462031C211yesmaximal, characteristic, complemented
3#21461980C211yesmaximal, characteristic
4#21461937C211yesmaximal, characteristic, complemented
5#21460894C211yesmaximal, characteristic, complemented
6#21460878C211yesmaximal, characteristic, complemented
7#361×D61C211yesmaximal, characteristic
8C2×D61⋊C16C2211yescharacteristic
9D61⋊#108C2211yescharacteristic
10#16840773—21no—
11C2×#14519846C2211yescharacteristic
12#16840754—21no—
13D61⋊#100—21no—
14#16840725C2211yescharacteristic
15#16840674—21no—
16#16840674—21no—
17#16840649—21no—
18C16×#6923—21no—
19#16840641—21no—
20C2×D8×D61C2211yescharacteristic
21M32×D61C2211yescharacteristic
22#108×D61C2211yescharacteristic
23#16839576C411yescharacteristic, complemented
24#16839575C411yescharacteristic, complemented
25#16839574C411yescharacteristic, complemented
26C61×#361C411yescharacteristic, complemented
27D61⋊M16—21no—
28D61⋊M16D411yescharacteristic
29#14519856D411yescharacteristic
30C2×C4⋊#6923—21no—
31D61⋊C16—21no—
32D61⋊C16D411yescharacteristic
33D61⋊C16D411yescharacteristic
34C2×#11758187—21no—
35#14519848—21no—
36#14519847—21no—
37#14519846—21no—
38#14519846—21no—
39#14519846—41no—
40#14519845—41no—
41#14519839—41no—
42#14519839—41no—
43#14519837—42no—
44#14519831—21no—
45C8×#6923—21no—
46C2×D4×D61—21no—
47C2×D488C2×C411yescharacteristic
48C2×#11758199—21no—
49D8×D61—21no—
50D8×D61—21no—
51D8×D61—21no—
52D8×D61—21no—
53M16×D61—21no—
54C2×C8×D61C2311yescharacteristic
55#14519717C2×C411yescharacteristic
56#14519716—21no—
57C16×D61—21no—
58#14519713C2×C411yescharacteristic
59#14519712—21no—
60C2×D8×C61C2×C411yescharacteristic
61M32×C61C2×C411yescharacteristic
62#108×C61C2×C411yescharacteristic
63C23×D61—41no—
64C22×#6923—41no—
65C2×D4×C61—21no—
66C2×C22⋊D61—41no—
67D4×D61—41no—
68D4×D61—41no—
69D4×D61—41no—
70D4×D61—41no—
71C2×D244—21no—
72C2×C4×D61C2×D411yescharacteristic
73C22⋊#6923—21no—
74#11758217—41no—
75#11758217SD1612yes—
76C4⋊#6923—41no—
77C4⋊#6923—41no—
78C4⋊#6923D811yescharacteristic
79C4⋊#6923D811yescharacteristic
80C4×#6923—21no—
81#11758213—21no—
82#11758213—41no—
83D61⋊C8—21no—
84D61⋊C8—41no—
85D8×C61—21no—
86D8×C61—21no—
87M16×C61—21no—
88C2×C8×C61C22×C411yescharacteristic
89#11758199—41no—
90#11758199—41no—
91#11758194—21no—
92C2×#92418#4111yescharacteristic
93D488—21no—
94D488—21no—
95#11758189—41no—
96C8×D61—41no—
97C8×D61C2×D411yescharacteristic
98C8×D61#4111yescharacteristic
99C8×D61#4111yescharacteristic
100C8×D61#4111yescharacteristic
101#11758187—21no—
102#11758187—21no—
103C16×C61—21no—
104#11758185—21no—
105C23×C61—41no—
106C22×D61—41no—
107C22×D61—81no—
108C22×D61—81no—
109C22×D61—161no—
110C22×D61—161no—
111C22×D61#13511yescharacteristic
112C2×#6923—21no—
113C2×#6923—21no—
114C2×#6923—81no—
115C2×#6923—161no—
116D4×C61—41no—
117D4×C61—41no—
118C2×C4×C61C4×D411yescharacteristic
119C22⋊D61—81no—
120C22⋊D61—81no—
121C2×Dic61C2×SD1611yescharacteristic
122D244—41no—
123D244—41no—
124C4×D61#12111yescharacteristic
125C4×D61#12411yescharacteristic
126C4×D61C2×D811yescharacteristic
127C4×D61#13511yescharacteristic
128#92420—22no—
129#92420—81no—
130C8×C61—41no—
131C8×C61#11711yescharacteristic
132C8×C61C4×D411yescharacteristic
133#92418—41no—
134#92418#12311yescharacteristic
135#92418#12611yescharacteristic
136#13144—611nomaximal, Sylow
137C22×C61—81no—
138C22×C61—161no—
139C22×C61C4×SD1611yescharacteristic
140C2×D61—21no—
141C2×D61—21no—
142C2×D61—81no—
143C2×D61—162no—
144C2×D61—161no—
145C2×D61—161no—
146C2×D61—161no—
147C2×D61#46611yescharacteristic
148C2×D61#48811yescharacteristic
149#6923—41no—
150#6923—41no—
151#6923—161no—
152C4×C61#38811yescharacteristic
153C4×C61C4×D811yescharacteristic
154Dic61#46511yescharacteristic
155Dic61#48611yescharacteristic
156C2×#361—611no—
157C2×#357—611no—
158#2108—611no—
159#1978—611no—
160#1952—611no—
161#1387—611no—
162#1381—611no—
163C2×C61—21no—
164C2×C61—161no—
165C2×C61#193411yescharacteristic
166D61—21no—
167D61—161no—
168D61#222111yescharacteristic
169D61#222311yescharacteristic
170C22×D8—611no—
171C2×M32—611no—
172C22×C16—611no—
173C2×#108—611no—
174C2×#108—611no—
175#428—1221no—
176C2×#107—611no—
177#418—1221no—
178C2×#100—1221no—
179#405—611no—
180#361—611no—
181#361—611no—
182#361—611no—
183#361#692311yescharacteristic, complemented
184#357—1221no—
185#357—1221no—
186#346—1221no—
187C4×C16—1221no—
188#343—1221no—
189C61#1314411yescharacteristic, complemented, Sylow
190C22×D4—1221no—
191C2×D8—611no—
192C2×D8—1221no—
193C2×D8—1221no—
194C2×D8—1221no—
195C2×D8—1221no—
196C2×D8—1221no—
197C2×D8C2×#692311yescharacteristic
198C2×M16—611no—
199C2×M16—1221no—
200C2×M16—1221no—
201C22×C8—611no—
202#117—611no—
203C2×C4⋊C4—1221no—
204M32—611no—
205M32—1221no—
206M32C2×#692311yescharacteristic
207C2×C16—611no—
208C2×C16—611no—
209C2×C16—1221no—
210C2×C16—1221no—
211C2×C16—1221no—
212#108—611no—
213#108—1221no—
214#108—1221no—
215#108—1221no—
216#108C2×#692311yescharacteristic
217#107—1221no—
218#107—1221no—
219#107—2441no—
220#106—2441no—
221#102—2441no—
222#102—2441no—
223#100—2442no—
224#97—1221no—
225C4×C8—1221no—
226C24—2441no—
227C2×D4—21no—
228C2×D4—1221no—
229C2×D4—2441no—
230C2×D4—2441no—
231C2×D4—2441no—
232C2×D4—2441no—
233C2×D4—2441no—
234C22×C4—611no—
235C22×C4—2441no—
236D8—21no—
237D8—21no—
238D8—1221no—
239D8—1221no—
240D8—2441no—
241D8—2441no—
242M16—21no—
243M16—612no—
244M16—1221no—
245M16—1221no—
246M16—2441no—
247M16—2441no—
248M16—2441no—
249C2×C8—611no—
250C2×C8—611no—
251C2×C8—611no—
252C2×C8—611no—
253C2×C8—611no—
254C2×C8—1221no—
255C2×C8—2441no—
256C2×C8—2441no—
257C2×C8C22×#692311yescharacteristic
258C4⋊C4—611no—
259C4⋊C4—611no—
260C4⋊C4—2441no—
261C4⋊C4—2441no—
262C22⋊C4—1221no—
263C42—1221no—
264C16—21no—
265C16—1221no—
266C16—1221no—
267C16—1221no—
268C23—41no—
269C23—611no—
270C23—9761no—
271C23—9761no—
272C23—4881no—
273C23—4881no—
274C23—2441no—
275D4—41no—
276D4—41no—
277D4—4881no—
278D4—4881no—
279D4—2441no—
280D4—2441no—
281C2×C4—611no—
282C2×C4—611no—
283C2×C4—611no—
284C2×C4—611no—
285C2×C4—611no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—9761no—
289C2×C4—4881no—
290C2×C4D4×#692311yescharacteristic
291C8—41no—
292C8—611no—
293C8—611no—
294C8—1222no—
295C8—4881no—
296C8—2441no—
297C8#1451985611yescharacteristic
298C8D4×#692311yescharacteristic
299C22—81no—
300C22—161no—
301C22—611no—
302C22—611no—
303C22—1221no—
304C22—1221no—
305C22—9761no—
306C22—9761no—
307C22—9761no—
308C22—9762no—
309C22—4881no—
310C22SD16×#692311yescharacteristic
311C4—611no—
312C4—611no—
313C4—9761no—
314C4—2441no—
315C4—2441no—
316C4#1684071211yescharacteristic
317C4D8×#692311yescharacteristic
318C2—21no—
319C2—161no—
320C2—611no—
321C2—611no—
322C2—1221no—
323C2—9761no—
324C2#2146190911yescharacteristic
subgroupG/H
centerC2#21461909
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#361C4
socleC2×C61#1934
prime radicalC2×D8×D61C22
cosocleC2×C8×D61C23
hypercenter#361#6923
hypocenterC61#13144
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. #21462031C2semidirect
4. #21461937C2semidirect
5. #21460894C2semidirect
6. #21460878C2semidirect
23. #16839576C4semidirect
24. #16839575C4semidirect
25. #16839574C4semidirect
26. C61×#361C4semidirect
183. #361#6923semidirect
189. C61#13144semidirect

Maximal subgroups

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

subgroupindex
C2×#168406742
#214620312
#214619802
#214619372
#214608942
#214608782
#361×D612
#1314461