Finite Group Databasebeta

← #30603796

Subgroups — #30603796

Order 15616.

666 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 102 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#21462047C212yesmaximal, complemented
2#21460740C212yesmaximal, complemented
3#21460739C212yesmaximal, complemented
4C2×C22⋊C8×D61C211yesmaximal, characteristic
5C2×#14519852—22no—
6#16840657—22no—
7C22⋊#11758187C2214yescomplemented
8C23×C4×D61C411yescharacteristic
9C22×C8×D61C411yescharacteristic
10C22×C8×D61C2211yescharacteristic
11C2×C22⋊#92418C2211yescharacteristic
12C2×#14519689C411yescharacteristic
13C2×#14519689C2211yescharacteristic
14C22⋊C8×D61—22no—
15C22⋊C8×D61—22no—
16C2×C22⋊C8×C61C411yescharacteristic
17#14519852—44no—
18C2×#11758187—24no—
19C24×D61C811yescharacteristic
20C23×Dic61C811yescharacteristic
21C22×C4×D61—21no—
22C22×C4×D61—21no—
23C22×C4×D61—21no—
24C22×C4×D61—21no—
25C22×C4×D61—42no—
26C22×C4×D61—42no—
27C22×C4×D61C811yescharacteristic
28C22×C4×D61C811yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61C2×C411yescharacteristic
31C22×#92418C2×C411yescharacteristic
32C22×#92418C2311yescharacteristic
33C2×C8×D61—21no—
34C2×C8×D61—21no—
35C2×C8×D61—42no—
36C2×C8×D61—42no—
37C2×C8×D61D412yes—
38C2×C8×D61D412yes—
39C22⋊#92418—22no—
40#14519689—22no—
41#14519689—22no—
42C23×C4×C61C2×C411yescharacteristic
43C22×C8×C61C2×C411yescharacteristic
44C22×C8×C61C2×C411yescharacteristic
45C22⋊C8×C61—22no—
46C24×C61C2×C811yescharacteristic
47C23×D61—22no—
48C23×D61—21no—
49C23×D61—21no—
50C23×D61—22no—
51C23×D61—42no—
52C23×D61—42no—
53C23×D61C2×C811yescharacteristic
54C23×D61C2×C811yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—41no—
58C22×C4×C61—41no—
59C22×C4×C61C2×C811yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61—42no—
64C22×Dic61C2×C811yescharacteristic
65C22×Dic61C2×C811yescharacteristic
66C2×C4×D61—22no—
67C2×C4×D61—22no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—44no—
75C2×C4×D61—42no—
76C2×C4×D61—42no—
77C2×C4×D61—44no—
78C2×C4×D61—42no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—42no—
84C2×C4×D61C22⋊C411yescharacteristic
85C2×C4×D61C22⋊C411yescharacteristic
86C2×C4×D61M1611yescharacteristic
87C2×C4×D61M1611yescharacteristic
88C2×C8×C61—21no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61C22⋊C412yes—
92C2×#92418—21no—
93C2×#92418—41no—
94C2×#92418—41no—
95C2×#92418C2×D412yes—
96C8×D61—24no—
97C8×D61—42no—
98C8×D61—42no—
99C8×D61—42no—
100#11758187—44no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61M3212yescomplemented
106C23×C61C22×C811yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—22no—
110C22×D61—22no—
111C22×D61—24no—
112C22×D61—24no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—42no—
116C22×D61—48no—
117C22×D61—48no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61C22⋊C811yescharacteristic
124C22×D61C22⋊C811yescharacteristic
125C22×D61M3212yescomplemented
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—42no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61C2×M1611yescharacteristic
135C2×Dic61—22no—
136C2×Dic61—21no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—41no—
140C2×Dic61C22⋊C811yescharacteristic
141C2×Dic61C22⋊C811yescharacteristic
142C4×D61—22no—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—22no—
146C4×D61—42no—
147C4×D61—42no—
148C4×D61—42no—
149C4×D61—42no—
150C4×D61—41no—
151C4×D61—41no—
152C4×D61—42no—
153C4×D61#9912yes—
154C4×D61#10012yes—
155C8×C61—22no—
156C8×C61—41no—
157#92418—22no—
158#92418—41no—
159#11418—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—22no—
163C22×C61—42no—
164C22×C61—42no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61C2×C22⋊C811yescharacteristic
168C22×C61C2×M3211yescharacteristic
169C22×C61C2×M3211yescharacteristic
170C2×D61—24no—
171C2×D61—24no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—22no—
177C2×D61—48no—
178C2×D61—48no—
179C2×D61—42no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—42no—
183C2×D61#32312yes—
184C2×D61#34912yes—
185C4×C61—21no—
186C4×C61—41no—
187C4×C61C2×#9911yescharacteristic
188C4×C61C2×#10011yescharacteristic
189Dic61—21no—
190Dic61—41no—
191Dic61#32312yes—
192C22×C22⋊C8—611no—
193#2112—612no—
194#1314—612no—
195#1314—612no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61—42no—
199C2×C61C2×#32311yescharacteristic
200C2×C61#211211yescharacteristic
201C2×C61C2×#34911yescharacteristic
202D61—22no—
203D61—22no—
204D61—42no—
205C24×C4—611no—
206C23×C8—611no—
207C23×C8—611no—
208C2×M32—1222no—
209C2×C22⋊C8—611no—
210C2×C22⋊C8—611no—
211C2×C22⋊C8—611no—
212C2×C22⋊C8—1222no—
213C2×C22⋊C8—1222no—
214C2×C22⋊C8#692311yescharacteristic
215C22⋊C16—614no—
216C22⋊C16—1222no—
217C61#1141811yescharacteristic, complemented, Sylow
218C25—611no—
219C23×C4—611no—
220C23×C4—611no—
221C23×C4—611no—
222C23×C4—611no—
223C23×C4—611no—
224C23×C4—1221no—
225C23×C4—1221no—
226C23×C4—1221no—
227C23×C4—1221no—
228C23×C4—2442no—
229C23×C4—2442no—
230C23×C4C2×#692311yescharacteristic
231C22×C8—611no—
232C22×C8—612no—
233C22×C8—612no—
234C22×C8—611no—
235C22×C8—1221no—
236C22×C8—1221no—
237C22×C8—2442no—
238C22×C8—2442no—
239C22×C8C2×#692311yescharacteristic
240C22×C8C2×#692311yescharacteristic
241M32—2444no—
242C2×C16—1224no—
243C22⋊C8—22no—
244C22⋊C8—1222no—
245C22⋊C8—1222no—
246C22⋊C8—1222no—
247C24—611no—
248C24—611no—
249C24—1221no—
250C24—1221no—
251C24—1222no—
252C24—1222no—
253C24—2442no—
254C24—2442no—
255C24D61⋊C811yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—1222no—
267C22×C4—1222no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—2441no—
277C22×C4—2441no—
278C22×C4—2442no—
279C22×C4—2442no—
280C22×C4—2444no—
281C22×C4—2444no—
282C22×C4—2442no—
283C22×C4—2442no—
284C22×C4—2442no—
285C22×C4—2442no—
286C22×C4—2442no—
287C22×C4D61⋊C811yescharacteristic
288C22×C4C22×#692311yescharacteristic
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—612no—
293C2×C8—1224no—
294C2×C8—1221no—
295C2×C8—2442no—
296C2×C8—2442no—
297C2×C8—2442no—
298C2×C8—2441no—
299C2×C8—2441no—
300C2×C8C22⋊#692312yes—
301C16—2444no—
302C23—21no—
303C23—21no—
304C23—41no—
305C23—41no—
306C23—611no—
307C23—611no—
308C23—612no—
309C23—1222no—
310C23—1222no—
311C23—1224no—
312C23—1224no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—2441no—
318C23—2441no—
319C23—2442no—
320C23—2442no—
321C23—2442no—
322C23—2448no—
323C23—2448no—
324C23—2442no—
325C23#1451985212yescomplemented
326C23C2×D61⋊C811yescharacteristic
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—611no—
335C2×C4—612no—
336C2×C4—612no—
337C2×C4—611no—
338C2×C4—1222no—
339C2×C4—1222no—
340C2×C4—1222no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4C2×C22⋊#692311yescharacteristic
355C2×C4D61⋊M1611yescharacteristic
356C8—22no—
357C8—41no—
358C8—1222no—
359C8—2441no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—42no—
364C22—42no—
365C22—41no—
366C22—41no—
367C22—612no—
368C22—612no—
369C22—1224no—
370C22—1224no—
371C22—1221no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22—1222no—
376C22—2442no—
377C22—2442no—
378C22—2448no—
379C22—2448no—
380C22—2441no—
381C22—2441no—
382C22D61⋊(C22⋊C8)11yescharacteristic
383C22D61⋊M3211yescharacteristic
384C22C2×#1451985211yescharacteristic
385C4—21no—
386C4—41no—
387C4—612no—
388C4—1221no—
389C4—2441no—
390C4D61⋊#9911yescharacteristic
391C4D61⋊#10011yescharacteristic
392C2—21no—
393C2—21no—
394C2—42no—
395C2—1222no—
396C2—1222no—
397C2—2442no—
398C2D61⋊#32311yescharacteristic
399C2#2146204711yescharacteristic
400C2D61⋊#34911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC24×D61C8
cosocleC22×#92418C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#11418
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #21462047C2semidirect
2. #21460740C2semidirect
3. #21460739C2semidirect
7. C22⋊#11758187C22semidirect
105. C23×C61M32semidirect
125. C22×D61M32semidirect
217. C61#11418semidirect
325. C23#14519852semidirect

Maximal subgroups

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

subgroupindex
#214620472
#214607402
#214607392
C2×C22⋊C8×D612
#1141861