Finite Group Databasebeta

← #30595385

Subgroups — #30595385

Order 15616.

668 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 146 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#21461673C211yesmaximal, characteristic
2C4×C22⋊#92420C211yesmaximal, characteristic
3#21460640C214yesmaximal, complemented
4C2×#16839667C211yesmaximal, characteristic
5C2×C4⋊#92420—21no—
6C2×C22⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C4×#92420—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C23×Dic122C411yescharacteristic
12C22×C4×Dic61C2211yescharacteristic
13#16839667—21no—
14#16839667—21no—
15#16839667C412yes—
16#16839667C2212yes—
17C2×#14519684—21no—
18C2×#14519684—21no—
19C22×C4⋊C4×C61C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22C4⋊#92420—42no—
23C22⋊#92420—24no—
24C22⋊#92420—42no—
25C4×#92420—42no—
26C22×Dic122—21no—
27C22×Dic122—22no—
28C22×Dic122—42no—
29C22×Dic122—42no—
30C22×Dic122C814yescomplemented
31C22×Dic122C2×C412yes—
32C23×Dic61—21no—
33C23×Dic61D411yescharacteristic
34C23×Dic61D411yescharacteristic
35C2×C4×Dic61—42no—
36C2×C4×Dic61C2×C411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61C2311yescharacteristic
40#14519684—22no—
41#14519684—22no—
42#14519684—22no—
43#14519684—22no—
44C23×C4×C61—21no—
45C23×C4×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—42no—
48C2×C4⋊C4×C61C2×C412yes—
49C24×C61C22⋊C411yescharacteristic
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—42no—
54C22×C4×C61—42no—
55C22×C4×C61—42no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C2×C812yes—
58C22×C4×C61M1612yes—
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—24no—
61C22×Dic61—22no—
62C22×Dic61—22no—
63C22×Dic61—22no—
64C22×Dic61—41no—
65C22×Dic61—41no—
66C22×Dic61—41no—
67C22×Dic61—42no—
68C22×Dic61—42no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61SD1612yes—
72C22×Dic61Q1612yes—
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×Dic122—24no—
76C2×Dic122—22no—
77C2×Dic122—48no—
78C2×Dic122—42no—
79C2×Dic122—42no—
80C2×Dic122—42no—
81C2×Dic122—42no—
82C2×Dic122—48no—
83C2×Dic122C2×C814yes—
84C2×#92420—24no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C2×#92420—42no—
90C4⋊C4×C61—42no—
91C4⋊C4×C61—42no—
92C4×Dic61—22no—
93C4×Dic61—22no—
94C4×Dic61—41no—
95C4×Dic61—41no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61C22⋊C812yes—
101C23×C61#10312yes—
102C23×C61#10412yes—
103C23×C61C2×C22⋊C411yescharacteristic
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—24no—
107C2×C4×C61—24no—
108C2×C4×C61—42no—
109C2×C4×C61—42no—
110C2×C4×C61—42no—
111C2×C4×C61—84no—
112C2×C4×C61C22⋊C812yes—
113C2×C4×C61#9912yes—
114C2×C4×C61#10012yes—
115C2×C4×C61C22×C811yescharacteristic
116C2×C4×C61C2×M1611yescharacteristic
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—24no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—42no—
128C2×Dic61—42no—
129C2×Dic61—44no—
130C2×Dic61—48no—
131C2×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61#10312yes—
134C2×Dic61C2×SD1611yescharacteristic
135C2×Dic61C2×Q1611yescharacteristic
136C2×Dic61#13712yes—
137Dic122—44no—
138Dic122—48no—
139Dic122—44no—
140#92420—44no—
141#92420—82no—
142#7575—611nomaximal, Sylow
143C22×C61—22no—
144C22×C61—22no—
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—22no—
149C22×C61Q8⋊C814yes—
150C22×C61C2×C22⋊C811yescharacteristic
151C22×C61C2×#9911yescharacteristic
152C22×C61C2×#10011yescharacteristic
153C22×C61C2×#10311yescharacteristic
154C22×C61#41911yescharacteristic
155C22×C61C2×#10411yescharacteristic
156C22×C61#42111yescharacteristic
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—82no—
160C4×C61#32314yes—
161Dic61—22no—
162Dic61—21no—
163Dic61—22no—
164Dic61—21no—
165Dic61—44no—
166Dic61—41no—
167C2×#391—611no—
168#1797—611no—
169C4×C22⋊C8—611no—
170#1272—614no—
171C2×C61—24no—
172C2×C61C2×#32311yescharacteristic
173C2×C61C2×Q8⋊C811yescharacteristic
174C2×C61#147911yescharacteristic
175C2×C61#150811yescharacteristic
176C2×C61#152011yescharacteristic
177C2×C61#152711yescharacteristic
178C2×C61#154811yescharacteristic
179C23×Q8—611no—
180C22×C4⋊C4#692311yescharacteristic
181C22×C42—611no—
182C2×C4⋊C8—1221no—
183C2×C22⋊C8—1221no—
184C2×C22⋊C8—1221no—
185C2×C4×C8—1221no—
186#391—612no—
187#391—612no—
188#391—1221no—
189#391—1221no—
190C2×#95—1221no—
191C2×#95—1221no—
192#336—612no—
193#336—612no—
194C61#757511yescharacteristic, complemented, Sylow
195C22×Q8—614no—
196C22×Q8—612no—
197C22×Q8—1222no—
198C22×Q8—1221no—
199C22×Q8—2442no—
200C22×Q8—2442no—
201C23×C4—21no—
202C23×C4—611no—
203C23×C4—611no—
204C23×C4—1221no—
205C23×C4C2×#692311yescharacteristic
206C22×C8—1222no—
207C22×C8—1222no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—42no—
210C2×C4⋊C4C2×#692312yes—
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—611no—
214C2×C42—611no—
215C2×C42—2442no—
216C4⋊C8—2442no—
217C22⋊C8—1224no—
218C22⋊C8—2442no—
219C4×C8—2442no—
220#95—1222no—
221#95—1222no—
222#95—1222no—
223#95—1222no—
224C24C22⋊#692311yescharacteristic
225C2×Q8—614no—
226C2×Q8—1224no—
227C2×Q8—1222no—
228C2×Q8—2448no—
229C2×Q8—2448no—
230C2×Q8—2442no—
231C2×Q8—2442no—
232C2×Q8—2442no—
233C2×Q8—2442no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—612no—
244C22×C4—612no—
245C22×C4—611no—
246C22×C4—1222no—
247C22×C4—1224no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4—2441no—
251C22×C4—2441no—
252C22×C4—2441no—
253C22×C4—2442no—
254C22×C4—2442no—
255C22×C4D61⋊C812yes—
256C22×C4#1175821312yes—
257C22×C4C22⋊#692311yescharacteristic
258C22×C4C22×#692311yescharacteristic
259C2×C8—1224no—
260C2×C8—2442no—
261C2×C8—2442no—
262C2×C8—2442no—
263C2×C8—2442no—
264C2×C8—2442no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C42—1222no—
268C42—1222no—
269C42—2441no—
270C42—2441no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23#1451983412yes—
276C23#1451984012yes—
277C23#1451984112yes—
278C23C2×C22⋊#692311yescharacteristic
279Q8—2444no—
280Q8—2444no—
281Q8—2448no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—84no—
290C2×C4—612no—
291C2×C4—611no—
292C2×C4—611no—
293C2×C4—612no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1224no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—2442no—
305C2×C4—2442no—
306C2×C4—2444no—
307C2×C4—2448no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4#1451983412yes—
311C2×C4#1451983612yes—
312C2×C4#1451983712yes—
313C2×C4C2×D61⋊C811yescharacteristic
314C2×C4C2×#1175821311yescharacteristic
315C8—4882no—
316C8—2444no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22#1684061214yes—
324C22C2×#1451983411yescharacteristic
325C22C2×#1451983611yescharacteristic
326C22C2×#1451983711yescharacteristic
327C22C2×#1451984011yescharacteristic
328C22#1684075511yescharacteristic
329C22C2×#1451984111yescharacteristic
330C22#1684076011yescharacteristic
331C4—21no—
332C4—21no—
333C4—82no—
334C4—1221no—
335C4—1222no—
336C4—1221no—
337C4—1222no—
338C4—2444no—
339C4—2441no—
340C4#1684060614yes—
341C2—24no—
342C2C2×#1684060611yescharacteristic
343C2C2×#1684061211yescharacteristic
344C2#2146112311yescharacteristic
345C2#2146121811yescharacteristic
346C2#2146125811yescharacteristic
347C2#2146127811yescharacteristic
348C2#2146133211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#7575
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460640C2semidirect
30. C22×Dic122C8semidirect
194. C61#7575semidirect

Maximal subgroups

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

subgroupindex
#214616732
C4×C22⋊#924202
#214606402
C2×#168396672
#757561