Finite Group Databasebeta

← #30605365

Subgroups — #30605365

Order 15616.

376 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 72 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#21462056C211yesmaximal, characteristic, complemented
2#21461701C211yesmaximal, characteristic, complemented
3#21460792C212yesmaximal, complemented
4#21460790C212yesmaximal, complemented
5#21455482C211yesmaximal, characteristic
6D61⋊M32—21no—
7#16840772—21no—
8#16840741—21no—
9#16840659C2212yes—
10#16840658—21no—
11#16840630C2212yes—
12C2×#14519799C411yescharacteristic, complemented
13C2×#14519783C2211yescharacteristic
14#16840343—21no—
15#16840021C411yescharacteristic, complemented
16#16840021C2211yescharacteristic
17#16840016C411yescharacteristic, complemented
18#16840016C2211yescharacteristic
19#16839992—21no—
20#16839992—21no—
21#16839761—21no—
22C2×#106×C61C411yescharacteristic, complemented
23#14519856—22no—
24#14519852—41no—
25#14519851—22no—
26D61⋊C16—41no—
27#14519846—41no—
28#14519845—41no—
29#14519836—41no—
30#14519835—41no—
31C2×#11758222—21no—
32C2×#11758222D411yescharacteristic
33#14519799—41no—
34#14519799—41no—
35C2×Dic244C2×C411yescharacteristic
36C2×#11758190—21no—
37C2×D488C2×C411yescharacteristic
38#14519783—41no—
39#14519783—41no—
40C2×#11758194D411yescharacteristic
41C2×#11758189C2×C411yescharacteristic
42C2×#11758189C2311yescharacteristic
43C2×C8×D61D411yescharacteristic
44C2×C8×D61D411yescharacteristic
45#14519757—21no—
46#14519757—21no—
47#14519757—41no—
48#14519752—21no—
49#14519752—21no—
50#14519752—41no—
51#14519751—41no—
52#14519751—41no—
53#14519700—21no—
54#14519700—21no—
55#14519697—21no—
56#14519697—21no—
57C22×C8×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61—21no—
59#106×C61—21no—
60#106×C61C2×C411yescharacteristic
61#106×C61C2×C411yescharacteristic
62C22×C4×C61—41no—
63C22×C4×C61C22⋊C411yescharacteristic
64C2×C22⋊D61—41no—
65C2×C22⋊D61D811yescharacteristic
66C2×C22⋊D61SD1611yescharacteristic
67#11758222—41no—
68#11758222—41no—
69#11758222—42no—
70#11758222—42no—
71C2×D244—21no—
72C2×D244—41no—
73C2×D244—41no—
74C2×D244D811yescharacteristic
75C2×C4×D61—41no—
76C2×C4×D61C22⋊C411yescharacteristic
77C2×C4×D61C2×D411yescharacteristic
78C2×Dic122—21no—
79C2×Dic122SD1611yescharacteristic
80C22⋊#6923—42no—
81C4⋊#6923—42no—
82C4×#6923—42no—
83C2×C8×C61—21no—
84C2×C8×C61—21no—
85C2×C8×C61C22⋊C411yescharacteristic
86C2×C8×C61C22×C411yescharacteristic
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—41no—
90#11758198—41no—
91#11758198—41no—
92#11758198—41no—
93#11758198—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96#11758194—41no—
97C2×#92418C22⋊C411yescharacteristic
98C2×#92418C2×D411yescharacteristic
99Dic244—41no—
100D488—41no—
101#11758190—41no—
102#11758190—41no—
103#11758189—41no—
104#11758189—41no—
105C8×D61—21no—
106C8×D61—21no—
107C8×D61—21no—
108C8×D61—21no—
109#11758187—42no—
110C23×C61#10211yescharacteristic
111C22×D61—41no—
112C22×D61#10211yescharacteristic
113C22×D61C2×D811yescharacteristic
114C2×#6923—82no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—161no—
120C2×C4×C61#10211yescharacteristic
121C2×C4×C61C2×C22⋊C411yescharacteristic
122C22⋊D61—41no—
123C22⋊D61—41no—
124C22⋊D61—82no—
125C2×Dic61—41no—
126C2×Dic61#10211yescharacteristic
127C2×Dic61C2×SD1611yescharacteristic
128D244—41no—
129D244—41no—
130D244—41no—
131D244—161no—
132D244—161no—
133C4×D61—21no—
134C4×D61—21no—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—82no—
138Dic122—41no—
139Dic122—41no—
140Dic122—41no—
141C8×C61—21no—
142C8×C61#9911yescharacteristic
143C8×C61#9911yescharacteristic
144#92418—21no—
145#92418—21no—
146#11867—611nomaximal, Sylow
147C22×C61—21no—
148C22×C61—41no—
149C22×C61C2×#10211yescharacteristic
150C2×D61—21no—
151C2×D61—21no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—81no—
155C2×D61—81no—
156C2×D61—81no—
157#6923—162no—
158C4×C61—21no—
159C4×C61—81no—
160C4×C61—81no—
161C4×C61C2×#9911yescharacteristic
162C4×C61#42111yescharacteristic
163Dic61—21no—
164Dic61—21no—
165Dic61—81no—
166#3060—611no—
167#2115—611no—
168#1812—611no—
169#1340—612no—
170#1339—612no—
171C2×C61—21no—
172C2×C61—41no—
173C2×C61#151911yescharacteristic
174D61—41no—
175D61—41no—
176D61—161no—
177C2×#135—611no—
178C2×#131—611no—
179#537—1221no—
180C2×M32—1221no—
181#470—611no—
182#470—611no—
183#469—611no—
184#469—611no—
185#465—1221no—
186#465—1221no—
187#427—1221no—
188C2×#106#692311yescharacteristic, complemented
189#417—1221no—
190#410—1221no—
191#349—612no—
192#349—1221no—
193H(3,ℤ/4)—612no—
194C61#1186711yescharacteristic, complemented, Sylow
195C2×#41—611no—
196C2×#41—1221no—
197#135—2441no—
198#135—2441no—
199C2×Q16—611no—
200C2×SD16—1221no—
201C2×D8—611no—
202#131—2441no—
203#131—2441no—
204C2×M16—611no—
205C2×M16—611no—
206C2×M16—611no—
207C22×C8—611no—
208C22×C8—611no—
209C22×C8C2×#692311yescharacteristic
210C22⋊Q8—1221no—
211C22⋊Q8—1221no—
212C22⋊Q8—2441no—
213#121—1221no—
214#121—1221no—
215#121—2441no—
216#121—2441no—
217#121—2441no—
218#117—1222no—
219C2×C4⋊C4—21no—
220M32—1222no—
221M32—2441no—
222C2×C16—2441no—
223#107—2441no—
224#106—21no—
225#106—2441no—
226#106C2×#692311yescharacteristic
227#106C2×#692311yescharacteristic
228#103—1221no—
229#103—1221no—
230#102—1221no—
231#102—1221no—
232#99—2441no—
233#99—2441no—
234#41—2441no—
235#41—2441no—
236#41—2442no—
237#41—2442no—
238C2×Q8—611no—
239C2×Q8—1221no—
240C2×D4—611no—
241C2×D4—611no—
242C2×D4—611no—
243C2×D4—1221no—
244C2×D4—2441no—
245C2×D4—2441no—
246C2×D4—2441no—
247C22×C4—41no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—2441no—
251C22×C4C22⋊#692311yescharacteristic
252Q16—2441no—
253SD16—2441no—
254SD16—2441no—
255D8—2441no—
256M16—2441no—
257M16—2441no—
258M16—2441no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—611no—
262C2×C8—611no—
263C2×C8—1221no—
264C2×C8—1221no—
265C2×C8—1221no—
266C2×C8—1221no—
267C2×C8C22⋊#692311yescharacteristic
268C2×C8C22×#692311yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2442no—
275C22⋊C4—2441no—
276C22⋊C4—2441no—
277C22⋊C4—2441no—
278C22⋊C4—2441no—
279C22⋊C4—2442no—
280C42—2442no—
281C16—2442no—
282C23—611no—
283C23—611no—
284C23—2441no—
285C23#1451983911yescharacteristic
286Q8—2441no—
287Q8—2441no—
288Q8—2441no—
289D4—9761no—
290D4—9761no—
291D4—4882no—
292D4—2441no—
293D4—2441no—
294D4—2441no—
295D4—2441no—
296D4—2441no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—161no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—4882no—
309C2×C4—4882no—
310C2×C4—2441no—
311C2×C4#1451983911yescharacteristic
312C2×C4C2×C22⋊#692311yescharacteristic
313C8—21no—
314C8—1221no—
315C8—1221no—
316C8#1451983611yescharacteristic
317C8#1451983611yescharacteristic
318C22—21no—
319C22—41no—
320C22—1221no—
321C22—1221no—
322C22—4881no—
323C22—4881no—
324C22—4881no—
325C22—2441no—
326C22—2441no—
327C22C2×#1451983911yescharacteristic
328C4—21no—
329C4—81no—
330C4—81no—
331C4—1221no—
332C4—1221no—
333C4—9762no—
334C4—4881no—
335C4C2×#1451983611yescharacteristic
336C4#1684076111yescharacteristic
337C2—21no—
338C2—41no—
339C2—9761no—
340C2—2441no—
341C2—2441no—
342C2#2146125611yescharacteristic
subgroupG/H
centerC2#21461256
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×#106×C61C4
socleC2×C61#1519
prime radical#21455482C2
cosocleC2×#11758189C23
hypercenterC2×#106#6923
hypocenterC61#11867
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. #21462056C2semidirect
2. #21461701C2semidirect
3. #21460792C2semidirect
4. #21460790C2semidirect
12. C2×#14519799C4semidirect
15. #16840021C4semidirect
17. #16840016C4semidirect
22. C2×#106×C61C4semidirect
188. C2×#106#6923semidirect
194. C61#11867semidirect

Maximal subgroups

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

subgroupindex
#214620562
#214617012
#214607922
#214607902
#214554822
#1186761