Finite Group Databasebeta

← #30610038

Subgroups — #30610038

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462715C212yesmaximal, complemented
2#21461080C214yesmaximal, complemented
3#21461072C214yesmaximal, complemented
4#21461060C212yesmaximal, complemented
5#21461052C212yesmaximal, complemented
6C2×#16840244C211yesmaximal, characteristic
7#16840813—28no—
8#16840782C2218yes—
9#16840778C2214yes—
10#16840608C2214yes—
11#16840606C2214yes—
12#16840606C2218yes—
13C22×#11758226C411yescharacteristic
14#16840244—28no—
15C2×Q8×Dic61C2211yescharacteristic
16C2×C4×D244C412yes—
17C2×C4×D244C411yescharacteristic
18C2×#14519739C2211yescharacteristic
19C2×#14519739C2212yes—
20C2×#14519734C2211yescharacteristic
21C2×#14519734C2212yes—
22C2×C4⋊C4×D61C412yes—
23C2×C4⋊C4×D61C411yescharacteristic
24C2×C4×Q8×C61C411yescharacteristic
25#14519844—28no—
26C4⋊#92420—24no—
27C22⋊#92420C2318yes—
28#14519832—28no—
29C4×#92420—24no—
30C2×#11758226—24no—
31C2×#11758226—24no—
32C2×#11758226—24no—
33C22×D244C2×C412yes—
34C22×D244C2×C411yescharacteristic
35C22×C4×D61C2×C412yes—
36C22×C4×D61C2×C411yescharacteristic
37C22×C4×D61C2×C412yes—
38C22×C4×D61C2×C412yes—
39C22×C4×D61C2×C412yes—
40Q8×Dic61D418yes—
41C4×D244—28no—
42C4×D244—24no—
43#14519739—24no—
44#14519739—28no—
45#14519734—24no—
46#14519734—28no—
47C2×C4⋊Dic61C2×C412yes—
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×#11758196C2×C411yescharacteristic
50C2×#11758196C2×C412yes—
51C2×#11758196C2311yescharacteristic
52C4⋊C4×D61—28no—
53C4⋊C4×D61—24no—
54C2×#11758198C2×C411yescharacteristic
55C2×#11758198C2×C412yes—
56C2×#11758198C2311yescharacteristic
57C2×#11758198C2312yes—
58C2×C4×Dic61C2311yescharacteristic
59C2×C4×Dic61C2312yes—
60C22×Q8×C61C2×C411yescharacteristic
61C4×Q8×C61—24no—
62C2×C4⋊C4×C61C2×C412yes—
63C2×C4⋊C4×C61C2×C411yescharacteristic
64C2×C42×C61C2×C412yes—
65C2×C42×C61C2×C411yescharacteristic
66C23×D61C22×C412yes—
67C23×D61C22×C411yescharacteristic
68C2×Q8×C61—22no—
69C2×Q8×C61—22no—
70C2×Q8×C61C22⋊C414yes—
71C22×C4×C61C22×C412yes—
72C22×C4×C61C22×C412yes—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C22×C411yescharacteristic
76C22×Dic61C22×C411yescharacteristic
77C22×Dic61C22×C411yescharacteristic
78C22×Dic61C22×C412yes—
79C22×Dic61C2411yescharacteristic
80#11758226—232no—
81C2×D244—24no—
82C2×D244—24no—
83C2×D244—24no—
84C2×D244—22no—
85C2×D244—22no—
86C2×D244M1614yes—
87C2×C4×D61—24no—
88C2×C4×D61—24no—
89C2×C4×D61—22no—
90C2×C4×D61—22no—
91C2×C4×D61—24no—
92C2×C4×D61—24no—
93C2×C4×D61—24no—
94C2×C4×D61—24no—
95C2×C4×D61—82no—
96C2×C4×D61—82no—
97C2×C4×D61—82no—
98C2×C4×D61M1614yes—
99C2×#92420—28no—
100C4⋊C4×C61—24no—
101C4⋊C4×C61—22no—
102C42×C61—24no—
103C42×C61—22no—
104#11758198—22no—
105#11758198—24no—
106#11758198—22no—
107#11758198—24no—
108C4⋊Dic61C22⋊C418yes—
109C4⋊Dic61C22⋊C414yes—
110#11758196—22no—
111#11758196—24no—
112#11758196—22no—
113C4×Dic61C2×D414yes—
114C4×Dic61C2×D418yes—
115C23×C61C23×C411yescharacteristic
116C22×D61—22no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—22no—
120C22×D61—42no—
121C22×D61—41no—
122C22×D61—42no—
123C22×D61—41no—
124C22×D61C2×M1614yes—
125C22×D61C2×M1612yes—
126Q8×C61—28no—
127C2×C4×C61—22no—
128C2×C4×C61—22no—
129C2×C4×C61—21no—
130C2×C4×C61—22no—
131C2×C4×C61—21no—
132C2×C4×C61—42no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61C2×C22⋊C414yes—
136C2×C4×C61C2×C22⋊C412yes—
137C2×C4×C61C2×M1612yes—
138C2×C4×C61C2×M1612yes—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—42no—
143C2×Dic61—41no—
144C2×Dic61C2×C22⋊C412yes—
145C2×Dic61C2×C22⋊C414yes—
146C2×Dic61C2×M1612yes—
147C2×Dic61C22×D412yes—
148D244—216no—
149D244—28no—
150C4×D61—216no—
151C4×D61—28no—
152C4×D61—84no—
153C4×D61—84no—
154C4×D61—84no—
155#92420—48no—
156#17372—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61C22×C22⋊C411yescharacteristic
160C22×C61C22×M1611yescharacteristic
161C22×C61C22×M1611yescharacteristic
162C2×D61—24no—
163C2×D61—22no—
164C2×D61—44no—
165C2×D61—42no—
166C2×D61—42no—
167C2×D61—41no—
168C2×D61—42no—
169C2×D61—41no—
170C2×D61—44no—
171C2×D61—42no—
172C4×C61—24no—
173C4×C61—41no—
174C4×C61—42no—
175C4×C61—41no—
176C4×C61#40714yes—
177Dic61—22no—
178Dic61—22no—
179Dic61—22no—
180Dic61—24no—
181C2×#520—611no—
182#2983—612no—
183#1466—614no—
184#1464—614no—
185#1460—612no—
186#1458—612no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61C2×#40711yescharacteristic
190C2×C61#288411yescharacteristic
191C2×C61#288811yescharacteristic
192D61—44no—
193D61—42no—
194C22×#41—611no—
195#520—1228no—
196C2×C4×Q8—611no—
197C2×C4×Q8#692311yescharacteristic
198C2×C4×D4—611no—
199C2×C4×D4—612no—
200C2×C4×D4—611no—
201C2×C4×D4—612no—
202C2×#117—611no—
203C2×#117—612no—
204C22×C4⋊C4—611no—
205C22×C4⋊C4—612no—
206#446—1228no—
207#432—618no—
208#431—614no—
209#324—614no—
210#323—614no—
211#323—618no—
212C61#1737211yescharacteristic, complemented, Sylow
213C2×#41—1224no—
214C2×#41—1224no—
215C2×#41—1224no—
216C22×Q8C2×#692311yescharacteristic
217C22×D4—611no—
218C22×D4—612no—
219C23×C4—611no—
220C23×C4—612no—
221C23×C4—612no—
222C23×C4—612no—
223C23×C4—612no—
224C4×Q8—24no—
225C4×Q8—618no—
226C4×D4—1228no—
227C4×D4—1224no—
228C4×D4—1224no—
229C4×D4—1228no—
230#117—1224no—
231#117—1228no—
232C2×C4⋊C4—612no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—612no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1228no—
238C2×C4⋊C4—1224no—
239C2×C4⋊C4C2×#692312yes—
240C2×C4⋊C4C2×#692311yescharacteristic
241C2×C22⋊C4—611no—
242C2×C22⋊C4—612no—
243C2×C22⋊C4—611no—
244C2×C22⋊C4—612no—
245C2×C42—611no—
246C2×C42—612no—
247C2×C42C2×#692312yes—
248C2×C42C2×#692311yescharacteristic
249C4⋊C8—1224no—
250C4⋊C8—1228no—
251C22⋊C8—618no—
252#97—1228no—
253C4×C8—1224no—
254C24—611no—
255C24—612no—
256#41—12232no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8C22⋊#692314yes—
260C2×D4—614no—
261C2×D4—1224no—
262C2×D4—1224no—
263C2×D4—1224no—
264C2×D4—1222no—
265C2×D4—1222no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—612no—
270C22×C4—614no—
271C22×C4—1224no—
272C22×C4—1224no—
273C22×C4—1224no—
274C22×C4—1224no—
275C22×C4—1224no—
276C22×C4—1224no—
277C22×C4—1222no—
278C22×C4—1222no—
279C22×C4—4882no—
280C22×C4—4882no—
281C22×C4—4882no—
282C22×C4C22×#692312yes—
283C22×C4C22×#692311yescharacteristic
284C22×C4C22×#692312yes—
285C22×C4C22×#692311yescharacteristic
286C22×C4C22×#692311yescharacteristic
287C2×C8—1228no—
288C4⋊C4—24no—
289C4⋊C4—22no—
290C4⋊C4—618no—
291C4⋊C4—614no—
292C4⋊C4—1222no—
293C4⋊C4—1224no—
294C4⋊C4—1222no—
295C22⋊C4—1222no—
296C22⋊C4—1224no—
297C22⋊C4—1222no—
298C22⋊C4—1224no—
299C42—24no—
300C42—22no—
301C42—614no—
302C42—618no—
303C23—612no—
304C23—614no—
305C23—1222no—
306C23—1221no—
307C23—1222no—
308C23—1221no—
309C23—2441no—
310C23—2442no—
311C23—2441no—
312C23—2442no—
313C23C23×#692311yescharacteristic
314Q8—28no—
315D4—12216no—
316D4—1228no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—612no—
326C2×C4—614no—
327C2×C4—612no—
328C2×C4—612no—
329C2×C4—12216no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1228no—
333C2×C4—4884no—
334C2×C4—4884no—
335C2×C4—4884no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2442no—
339C2×C4C2×C22⋊#692314yes—
340C2×C4C2×C22⋊#692312yes—
341C2×C4D61⋊M1612yes—
342C2×C4D61⋊M1612yes—
343C8—2448no—
344C22—21no—
345C22—21no—
346C22—1224no—
347C22—1222no—
348C22—2442no—
349C22—2444no—
350C22—2442no—
351C22—2444no—
352C22—2442no—
353C22—2441no—
354C22—2442no—
355C22—2441no—
356C22C22×C22⋊#692311yescharacteristic
357C22C2×D61⋊M1611yescharacteristic
358C22C2×D61⋊M1611yescharacteristic
359C4—24no—
360C4—41no—
361C4—42no—
362C4—41no—
363C4—1222no—
364C4—1222no—
365C4—1222no—
366C4—1224no—
367C4#1684073414yes—
368C2—21no—
369C2—21no—
370C2—2444no—
371C2—2442no—
372C2C2×#1684073411yescharacteristic
373C2#2146242011yescharacteristic
374C2#2146243011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758226C4
cosocleC22×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61#17372
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×Q8 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #21462715C2semidirect
2. #21461080C2semidirect
3. #21461072C2semidirect
4. #21461060C2semidirect
5. #21461052C2semidirect
212. C61#17372semidirect

Maximal subgroups

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

subgroupindex
#214627152
#214610802
#214610722
#214610602
#214610522
C2×#168402442
#1737261