Finite Group Databasebeta

← #29583680

Subgroups — #29583680

Order 15616.

376 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16840058C211yesmaximal, characteristic
2#21445812C211yesmaximal, characteristic
3#21444589C211yesmaximal, characteristic
4#21444503C211yesmaximal, characteristic
5#21444501C211yesmaximal, characteristic
6#21444215C211yesmaximal, characteristic
7C61×#1301C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16840058—22no—
11#16840058—22no—
12#16839815C2211yescharacteristic
13C2×#14519711—21no—
14#16839786C2211yescharacteristic
15C2×#14519702—21no—
16C2×#14519695—21no—
17#16839530—21no—
18#16839512—22no—
19#16839510—22no—
20#16839509—22no—
21#16839494—22no—
22C61×#431C2211yescharacteristic
23C61×#423C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C22×Dic122—21no—
26C22×Dic122D411yescharacteristic
27C2×#11758194—21no—
28#14519777—21no—
29#14519777—21no—
30#14519777—21no—
31#14519777D412yes—
32C4×Dic122—21no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35C4×Dic122—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61D411yescharacteristic
39C2×#11758196—21no—
40C2×C4×Dic61—21no—
41#14519711—24no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418D412yes—
45#14519702—24no—
46#14519695—42no—
47C22⋊#92418—21no—
48C4×#92418—21no—
49C2×M16×C61—21no—
50C22×C8×C61—21no—
51C2×C42×C61C2311yescharacteristic
52C4⋊C8×C61—21no—
53C4⋊C8×C61—21no—
54C4⋊C8×C61—21no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61D412yes—
57C22⋊C8×C61—21no—
58C4×C8×C61—21no—
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61#4111yescharacteristic
61C22×C4×C61#4111yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—41no—
65C2×Dic122—21no—
66C2×Dic122—21no—
67C2×Dic122—21no—
68C2×Dic122—21no—
69C2×Dic122—21no—
70C2×Dic122—22no—
71C2×Dic122—41no—
72C2×Dic122—82no—
73C2×Dic122SD1612yes—
74M16×C61—41no—
75M16×C61—41no—
76C2×C8×C61—22no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C42×C61C2×D411yescharacteristic
82C42×C61C2×D411yescharacteristic
83C42×C61C2×D411yescharacteristic
84C42×C61#4111yescharacteristic
85C4⋊Dic61—22no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61—22no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91#11758196—41no—
92#11758196—41no—
93C4×Dic61—41no—
94C4×Dic61—41no—
95#11758194—41no—
96#11758194—41no—
97C2×#92418—22no—
98C2×#92418—41no—
99C23×C61#12311yescharacteristic
100C2×C4×C61—22no—
101C2×C4×C61—41no—
102C2×C4×C61#12011yescharacteristic
103C2×C4×C61#12111yescharacteristic
104C2×C4×C61#12111yescharacteristic
105C2×C4×C61#12111yescharacteristic
106C2×C4×C61#12311yescharacteristic
107C2×C4×C61#12411yescharacteristic
108C2×C4×C61C2×SD1611yescharacteristic
109C2×C4×C61#13511yescharacteristic
110C2×C4×C61#13711yescharacteristic
111C2×C4×C61#13711yescharacteristic
112C2×Dic61—22no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—42no—
117C2×Dic61—82no—
118C2×Dic61—81no—
119Dic122—22no—
120Dic122—22no—
121Dic122—41no—
122Dic122—41no—
123Dic122—82no—
124Dic122—82no—
125C8×C61—42no—
126C8×C61—81no—
127C8×C61—81no—
128#92418—42no—
129#92418—81no—
130#10454—611nomaximal, Sylow
131C22×C61—21no—
132C22×C61—21no—
133C22×C61#39411yescharacteristic
134C22×C61#48311yescharacteristic
135C22×C61#48511yescharacteristic
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—21no—
139C4×C61#44811yescharacteristic
140C4×C61#45211yescharacteristic
141C4×C61#46511yescharacteristic
142C4×C61#47011yescharacteristic
143C4×C61#47312yes—
144Dic61—42no—
145Dic61—82no—
146Dic61—81no—
147C2×#477—611no—
148#1801—611no—
149#1570—611no—
150#1549—611no—
151#1548—611no—
152#1479—611no—
153#1301D6111yescharacteristic
154C2×C61—21no—
155C2×C61—21no—
156C2×C61#203511yescharacteristic
157C2×C61#204711yescharacteristic
158C2×C61#204811yescharacteristic
159C2×C4⋊Q8—611no—
160C2×C4×Q8—611no—
161#477—1222no—
162#477—1222no—
163#431—611no—
164#431C2×D6111yescharacteristic
165C2×#107—1221no—
166#423—611no—
167#423C2×D6111yescharacteristic
168C2×C4⋊C8C2×D6111yescharacteristic
169C2×#103—1221no—
170C2×#101—1221no—
171#343—1221no—
172#334—1222no—
173#333—1222no—
174#332—1222no—
175Q8⋊C8—1222no—
176C61#1045411yescharacteristic, complemented, Sylow
177C22×Q8—611no—
178C22×Q8—1221no—
179C2×M16—21no—
180C2×M16—1221no—
181C22×C8—21no—
182C4⋊Q8—612no—
183C4⋊Q8—1221no—
184C4⋊Q8—1221no—
185C4⋊Q8—1221no—
186C4×Q8—1221no—
187C4×Q8—1221no—
188C4×Q8—1221no—
189C4×Q8—1221no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C42—1221no—
195C2×C42C22×D6111yescharacteristic
196#107—1224no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—612no—
202C4⋊C8—1221no—
203C4⋊C8—1221no—
204C4⋊C8D24412yes—
205#103—1224no—
206#101—2442no—
207C22⋊C8—21no—
208C22⋊C8—1221no—
209C4×C8—21no—
210C4×C8—1221no—
211C2×Q8—612no—
212C2×Q8—1221no—
213C2×Q8—1221no—
214C2×Q8—1221no—
215C2×Q8—1221no—
216C2×Q8—1222no—
217C2×Q8—1221no—
218C2×Q8—4882no—
219C2×Q8—2441no—
220C22×C4—1221no—
221C22×C4—1221no—
222C22×C4—2441no—
223C22×C4#1175822211yescharacteristic
224C22×C4D4×D6111yescharacteristic
225C22×C4#1175822611yescharacteristic
226M16—41no—
227M16—41no—
228M16—2441no—
229M16—2441no—
230C2×C8—22no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—1222no—
236C2×C8—2441no—
237C4⋊C4—1222no—
238C4⋊C4—1221no—
239C4⋊C4—1221no—
240C4⋊C4—1222no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4—2441no—
245C42—2441no—
246C42—2441no—
247C42C2×D24411yescharacteristic
248C42#1175822211yescharacteristic
249C42D4×D6111yescharacteristic
250C42D4×D6111yescharacteristic
251C23#1451976211yescharacteristic
252Q8—1222no—
253Q8—1222no—
254Q8—4882no—
255Q8—4882no—
256Q8—2441no—
257Q8—2441no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—1222no—
261C2×C4—4882no—
262C2×C4—4881no—
263C2×C4—2441no—
264C2×C4—2442no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4#1451974711yescharacteristic
268C2×C4#1451975011yescharacteristic
269C2×C4#1451975011yescharacteristic
270C2×C4#1451975211yescharacteristic
271C2×C4#1451976211yescharacteristic
272C2×C4#1451976511yescharacteristic
273C2×C4SD16×D6111yescharacteristic
274C2×C4#1451979611yescharacteristic
275C2×C4#1451980611yescharacteristic
276C2×C4#1451980911yescharacteristic
277C8—42no—
278C8—81no—
279C8—81no—
280C8—4881no—
281C8—2442no—
282C22—21no—
283C22—21no—
284C22#1683968011yescharacteristic
285C22#1684009411yescharacteristic
286C22#1684010511yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—4882no—
291C4—4881no—
292C4—2442no—
293C4#1683990211yescharacteristic
294C4#1683992511yescharacteristic
295C4#1683999011yescharacteristic
296C4#1684001911yescharacteristic
297C4#1684003812yes—
298C2—21no—
299C2—21no—
300C2#2144701811yescharacteristic
301C2#2144708811yescharacteristic
302C2#2144709511yescharacteristic
subgroupG/H
centerC22#16839680
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1301C2
socleC22×C61#394
prime radicalC23×C61#123
hypercenter#1301D61
hypocenterC61#10454
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
176. C61#10454semidirect

Maximal subgroups

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

subgroupindex
C2×#168400582
#214458122
#214445892
#214445032
#214445012
#214442152
C61×#13012
#1045461