Finite Group Databasebeta

← #30608436

Subgroups — #30608436

Order 15616.

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

normal subgroups only

This group has 320 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, complemented
2#21462102C211yesmaximal, characteristic, complemented
3#21460967C211yesmaximal, characteristic, complemented
4#21460966C211yesmaximal, characteristic, complemented
5#21460946C211yesmaximal, characteristic, complemented
6#21460946C211yesmaximal, characteristic, complemented
7#21456873C211yesmaximal, characteristic
8D61⋊#101—21no—
9#16840743—21no—
10#16840672—21no—
11#16840671C2211yescharacteristic
12#16840671C2211yescharacteristic
13#16840669C2211yescharacteristic
14#16840669C2211yescharacteristic
15#16840668—21no—
16#16840366C411yescharacteristic, complemented
17#16840337C2211yescharacteristic
18#16840149C2211yescharacteristic
19#16840130C411yescharacteristic, complemented
20#16840117C2211yescharacteristic
21#16839979—21no—
22#16839965—21no—
23#16839906—21no—
24#16839899—21no—
25#16839821C411yescharacteristic, complemented
26C61×#492C411yescharacteristic, 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×#11758200—21no—
38C2×#11758199—21no—
39#14519775D411yescharacteristic
40#14519769C2×C411yescharacteristic
41#14519766D411yescharacteristic
42#14519765C2311yescharacteristic
43#14519762—41no—
44#14519758—41no—
45#14519755—41no—
46#14519749—41no—
47#14519748—21no—
48D4×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×SD16×C61—21no—
58C2×SD16×C61—21no—
59C4⋊Q8×C61C2×C411yescharacteristic
60#127×C61C2×C411yescharacteristic
61C4×C8×C61C2×C411yescharacteristic
62C2×Q8×C61C22⋊C411yescharacteristic
63C2×Q8×C61C22⋊C411yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61—41no—
66C2×C22⋊D61—41no—
67C22×Dic61—41no—
68#11758226—81no—
69Q8×D61—81no—
70C2×D244—21no—
71C2×D244C2×D411yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61C22⋊C411yescharacteristic
75C2×Dic122—21no—
76C2×Dic122C2×D411yescharacteristic
77C22⋊#6923—41no—
78C22⋊#6923—41no—
79#11758217—41no—
80#11758217—41no—
81C4⋊#6923—81no—
82C4×#6923—81no—
83#11758213—81no—
84D61⋊C8—81no—
85SD16×C61—81no—
86SD16×C61—81no—
87C2×C8×C61—21no—
88C4⋊C4×C61—41no—
89C42×C61C22×C411yescharacteristic
90C22⋊Dic61—41no—
91C22⋊Dic61—41no—
92#11758200—81no—
93#11758199—81no—
94#11758198—21no—
95#11758198—41no—
96#11758198—41no—
97C4⋊Dic61—21no—
98#11758196—21no—
99#11758196—41no—
100#11758196—41no—
101C4×Dic61C22⋊C411yescharacteristic
102C2×#92418—21no—
103C23×C61—41no—
104C22×D61—21no—
105C22×D61#9911yescharacteristic
106C2×#6923—81no—
107C2×#6923—81no—
108Q8×C61—41no—
109Q8×C61—41no—
110D4×C61—41no—
111D4×C61—41no—
112D4×C61—161no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61C2×C22⋊C411yescharacteristic
117C22⋊D61—161no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—41no—
121C2×Dic61—161no—
122C2×Dic61#9911yescharacteristic
123D244—41no—
124D244—81no—
125C4×D61—41no—
126C4×D61—41no—
127C4×D61—41no—
128C4×D61—41no—
129C4×D61—41no—
130Dic122—41no—
131Dic122—81no—
132#92420—81no—
133#92420—81no—
134C8×C61—41no—
135#92418—41no—
136#13606—611nomaximal, Sylow
137C22×C61—81no—
138C22×C61—81no—
139C22×C61—81no—
140C22×C61C2×#9911yescharacteristic
141C2×D61—21no—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61—81no—
145#6923—161no—
146#6923—161no—
147C4×C61—21no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61—41no—
151Dic61—21no—
152Dic61—41no—
153Dic61—41no—
154Dic61—81no—
155#3221—611no—
156#2133—611no—
157#2129—611no—
158#1414—611no—
159#1414—611no—
160#1406—611no—
161#1406—611no—
162C2×C61—21no—
163C2×C61—161no—
164C2×C61#212711yescharacteristic
165D61—41no—
166D61—81no—
167#540—611no—
168#536—611no—
169#496—611no—
170#492#692311yescharacteristic, complemented
171#491—611no—
172#488—611no—
173#463—1221no—
174#461—1221no—
175#449—1221no—
176#448—1221no—
177#433—611no—
178C2×#101—1221no—
179#410—1221no—
180#356—1221no—
181#355—611no—
182#355—611no—
183#354—611no—
184#354—611no—
185#354—1221no—
186C61#1360611yescharacteristic, complemented, Sylow
187C2×#41—611no—
188C22×Q8—611no—
189C2×SD16—21no—
190C2×SD16—21no—
191C2×SD16—1221no—
192C2×D8—1221no—
193C2×M16—2441no—
194C4⋊Q8—611no—
195C4⋊Q8C2×#692311yescharacteristic
196#127C2×#692311yescharacteristic
197#125—611no—
198#124—611no—
199#124—611no—
200#123—2441no—
201#123—2441no—
202C22⋊Q8—2441no—
203#121—1221no—
204#121—2441no—
205C4×D4—1221no—
206#117—611no—
207#117—2441no—
208C4⋊C8—1221no—
209#103—1221no—
210#103—1221no—
211#103—1221no—
212#102—1221no—
213#101—1221no—
214#101—1221no—
215#101—2441no—
216#99—1221no—
217#99—1221no—
218#99—2441no—
219C22⋊C8—1221no—
220#97—611no—
221C4×C8C2×#692311yescharacteristic
222#41—4881no—
223C2×Q8—611no—
224C2×Q8—1221no—
225C2×Q8—4881no—
226C2×Q8C22⋊#692311yescharacteristic
227C2×Q8C22⋊#692311yescharacteristic
228C2×D4—21no—
229C2×D4—41no—
230C2×D4—611no—
231C2×D4—1221no—
232C2×D4—2441no—
233C22×C4—611no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—2441no—
237SD16—81no—
238SD16—81no—
239SD16—4881no—
240D8—4881no—
241M16—4881no—
242M16—2441no—
243M16—2441no—
244C2×C8—21no—
245C2×C8—1221no—
246C2×C8—4881no—
247C4⋊C4—41no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—4881no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C22⋊C4—1221no—
254C22⋊C4—2441no—
255C22⋊C4—2441no—
256C22⋊C4—2441no—
257C22⋊C4—2441no—
258C22⋊C4—2441no—
259C22⋊C4—2441no—
260C42—611no—
261C42—4881no—
262C42C22×#692311yescharacteristic
263C23—41no—
264C23—611no—
265C23—1221no—
266Q8—41no—
267Q8—41no—
268Q8—4881no—
269Q8—2441no—
270D4—41no—
271D4—41no—
272D4—161no—
273D4—9761no—
274D4—4881no—
275D4—2441no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—611no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—9761no—
283C2×C4—4881no—
284C2×C4—4881no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4C2×C22⋊#692311yescharacteristic
292C8—41no—
293C8—4881no—
294C8—4881no—
295C8—2441no—
296C22—81no—
297C22—81no—
298C22—81no—
299C22—1221no—
300C22—4881no—
301C22—2441no—
302C22—2441no—
303C22D61⋊#9911yescharacteristic
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—1221no—
309C4—9761no—
310C4—9761no—
311C4—4881no—
312C4—2441no—
313C4—2441no—
314C2—21no—
315C2—161no—
316C2—4881no—
317C2—2441no—
318C2#2146209511yescharacteristic
subgroupG/H
centerC2#21462095
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#492C4
socleC2×C61#2127
prime radical#21456873C2
cosocle#14519765C23
hypercenter#492#6923
hypocenterC61#13606
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #21462117C2semidirect
2. #21462102C2semidirect
3. #21460967C2semidirect
4. #21460966C2semidirect
5. #21460946C2semidirect
6. #21460946C2semidirect
16. #16840366C4semidirect
19. #16840130C4semidirect
25. #16839821C4semidirect
26. C61×#492C4semidirect
170. #492#6923semidirect
186. C61#13606semidirect

Maximal subgroups

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

subgroupindex
#214621172
#214621022
#214609672
#214609662
#214609462
#214568732
#1360661