Finite Group Databasebeta

← #29600415

Subgroups — #29600415

Order 15616.

308 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 67 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#21456902C211yesmaximal, characteristic
2#21447494C211yesmaximal, characteristic
3#21443995C212yesmaximal, complemented
4#21443980C212yesmaximal, complemented
5C61×#2133C211yesmaximal, characteristic
6#16840374C411yescharacteristic, complemented
7#16840157C2211yescharacteristic
8#16840141C411yescharacteristic, complemented
9#16840130C411yescharacteristic, complemented
10#16840116C2211yescharacteristic
11#16839981—21no—
12#16839969—21no—
13#16839924—21no—
14#16839918—21no—
15#16839823C411yescharacteristic, complemented
16#16839736—21no—
17#16839557—21no—
18#16839557C2212yes—
19C61×#536C2211yescharacteristic
20C2×#101×C61—21no—
21C61×#356—21no—
22C61×#355C2212yes—
23C2×#11758202—21no—
24C2×#11758202—21no—
25C2×#11758202—21no—
26C2×#11758200—21no—
27#14519777C2×C411yescharacteristic
28#14519770—41no—
29#14519769C2×C411yescharacteristic
30#14519767—41no—
31#14519756—21no—
32C4×Dic122—21no—
33#14519736—41no—
34C4⋊#92418—21no—
35#14519701—21no—
36#14519701—21no—
37#14519701—21no—
38#14519698—21no—
39#14519692—22no—
40#14519692—41no—
41C22⋊#92418—21no—
42#14519688C2×C411yescharacteristic
43C4×#92418C2×C411yescharacteristic
44C2×#41×C61D411yescharacteristic
45C22×Q8×C61D411yescharacteristic
46C2×M16×C61—41no—
47C4⋊Q8×C61C2×C411yescharacteristic
48C4⋊Q8×C61D411yescharacteristic
49#124×C61D411yescharacteristic
50#124×C61C2311yescharacteristic
51#123×C61—41no—
52C22⋊Q8×C61—41no—
53#117×C61C2×C411yescharacteristic
54#101×C61—22no—
55#101×C61—41no—
56#41×C61—81no—
57C2×Q8×C61—21no—
58C2×Q8×C61—81no—
59C2×Q8×C61C22⋊C411yescharacteristic
60C2×Q8×C61C22⋊C411yescharacteristic
61C2×Q8×C61C2×D411yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2×D411yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C2×Dic122—21no—
68M16×C61—42no—
69M16×C61—81no—
70C2×C8×C61—81no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C22⋊C4×C61—21no—
75C22⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C42×C61C22⋊C411yescharacteristic
78C42×C61C22×C411yescharacteristic
79C22⋊Dic61—41no—
80C22⋊Dic61—42no—
81#11758202—81no—
82#11758202—81no—
83#11758202—81no—
84#11758200—81no—
85C4⋊Dic61—21no—
86C4⋊Dic61—41no—
87C4⋊Dic61—81no—
88#11758196—41no—
89#11758196—41no—
90#11758196—41no—
91C4×Dic61—41no—
92C4×Dic61—81no—
93C2×#92418—21no—
94C2×#92418—21no—
95C23×C61—21no—
96C23×C61#9911yescharacteristic
97Q8×C61—41no—
98Q8×C61—41no—
99Q8×C61—41no—
100Q8×C61—81no—
101D4×C61—41no—
102D4×C61—81no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#9911yescharacteristic
114C2×C4×C61C2×C22⋊C411yescharacteristic
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—82no—
118Dic122—41no—
119Dic122—41no—
120C8×C61—82no—
121#92418—41no—
122#92418—41no—
123#13608—611nomaximal, Sylow
124C22×C61—21no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—81no—
128C22×C61C2×#9911yescharacteristic
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—41no—
132C4×C61—41no—
133C4×C61—41no—
134C4×C61—41no—
135C4×C61—41no—
136Dic61—81no—
137Dic61—81no—
138Dic61—162no—
139#3223—611no—
140#2133D6111yescharacteristic
141#2129—611no—
142#1414—612no—
143#1407—612no—
144C2×C61—21no—
145C2×C61—41no—
146C2×C61—81no—
147C2×C61#212711yescharacteristic
148#541—611no—
149#536C2×D6111yescharacteristic
150#497—611no—
151#494—611no—
152#491—611no—
153#488—611no—
154#464—1221no—
155#462—1221no—
156#452—1221no—
157#451—1221no—
158#433—611no—
159C2×#101—21no—
160#410—1221no—
161#356—21no—
162#355C2×D6112yes—
163#354—612no—
164#354—1221no—
165C61#1360811yescharacteristic, complemented, Sylow
166C2×#41D24411yescharacteristic
167C22×Q8C22⋊D6111yescharacteristic
168C2×Q16—1221no—
169C2×Q16—1221no—
170C2×Q16—1221no—
171C2×SD16—1221no—
172C2×M16—41no—
173C4⋊Q8—611no—
174C4⋊Q8C4×D6111yescharacteristic
175C4⋊Q8C22⋊D6111yescharacteristic
176#126—2441no—
177#125—611no—
178#125—2441no—
179#124D24411yescharacteristic
180#124C22×D6111yescharacteristic
181#123—41no—
182C22⋊Q8—41no—
183C22⋊Q8—1221no—
184C4×Q8—1221no—
185#117—2441no—
186#117C4×D6111yescharacteristic
187C4⋊C8—1221no—
188#103—1221no—
189#103—1221no—
190#103—1221no—
191#102—1221no—
192#101—22no—
193#101—41no—
194#99—1222no—
195#99—2441no—
196C22⋊C8—1221no—
197#97—611no—
198C4×C8—611no—
199#41—81no—
200C2×Q8—21no—
201C2×Q8—81no—
202C2×Q8—1221no—
203C2×Q8#1175819811yescharacteristic
204C2×Q8#1175819811yescharacteristic
205C2×Q8C2×C22⋊D6111yescharacteristic
206C2×D4—21no—
207C2×D4C2×D24411yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4#1175819811yescharacteristic
211Q16—4881no—
212Q16—4881no—
213Q16—4881no—
214SD16—4881no—
215M16—42no—
216M16—81no—
217C2×C8—81no—
218C2×C8—1221no—
219C2×C8—1221no—
220C4⋊C4—21no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—1221no—
224C4⋊C4—4881no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C4⋊C4—2441no—
229C22⋊C4—21no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—2442no—
233C22⋊C4—2441no—
234C42—4881no—
235C42—2441no—
236C42#1175819811yescharacteristic
237C42C2×C4×D6111yescharacteristic
238C23—21no—
239C23#1451969111yescharacteristic
240Q8—41no—
241Q8—41no—
242Q8—41no—
243Q8—81no—
244Q8—2441no—
245Q8—2441no—
246D4—41no—
247D4—81no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—4882no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4#1451969111yescharacteristic
262C2×C4C2×#1175819811yescharacteristic
263C8—82no—
264C8—2441no—
265C8—2441no—
266C22—21no—
267C22—41no—
268C22—41no—
269C22—81no—
270C22C2×#1451969111yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—41no—
278C4—9762no—
279C4—4881no—
280C4—4881no—
281C2—21no—
282C2—41no—
283C2—81no—
284C2#2144748611yescharacteristic
subgroupG/H
centerC2#21447486
commutatorC42×C61C22×C4
Frattini#124C22×D61
FittingC61×#2133C2
socleC2×C61#2127
prime radicalC2×#41×C61D4
cosocle#124×C61C23
hypercenter#2133D61
hypocenterC61#13608
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #536 ◁ #2133

Complements

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

NH ≅ G/Ntype
3. #21443995C2semidirect
4. #21443980C2semidirect
6. #16840374C4semidirect
8. #16840141C4semidirect
9. #16840130C4semidirect
15. #16839823C4semidirect
165. C61#13608semidirect

Maximal subgroups

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

subgroupindex
#214569022
#214474942
#214439952
#214439802
C61×#21332
#1360861