Finite Group Databasebeta

← #29594987

Subgroups — #29594987

Order 15616.

826 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 826 conjugacy classes of subgroups — too many to draw. Only its 151 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×#16839734C212yesmaximal
2#21448409C211yesmaximal, characteristic
3#21443944C211yesmaximal, characteristic, complemented
4#21443943C212yesmaximal, complemented
5C61×#1393C211yesmaximal, characteristic, complemented
6C22×#11758224C2211yescharacteristic
7C2×#14519734C411yescharacteristic, complemented
8C2×#14519733—22no—
9C2×C4⋊C4×D61C411yescharacteristic, complemented
10#16839734—24no—
11#16839734C418yescomplemented
12C2×#14519692C2212yes—
13C2×#14519691—22no—
14#16839668C411yescharacteristic, complemented
15#16839667C411yescharacteristic, complemented
16#16839665C2211yescharacteristic
17#16839638—22no—
18#16839620—22no—
19C2×#99×C61C2212yes—
20C61×#390C2211yescharacteristic
21C2×#11758224—42no—
22C2×#11758224—42no—
23C2×#11758224C2×C414yes—
24C2×#11758224D412yes—
25C2×#11758224Q812yes—
26C22×Dic122C2×C411yescharacteristic
27C22×C22⋊D61D412yes—
28C23×Dic61D412yes—
29C22×C4×D61—21no—
30C22×C4×D61C2×C411yescharacteristic
31#14519734—42no—
32#14519733—28no—
33#14519733—44no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—42no—
38C4⋊C4×D61—42no—
39C2×C22⋊Dic61—22no—
40C2×C22⋊Dic61—22no—
41C2×#11758198—21no—
42C2×C4×Dic61—42no—
43C2×C4×Dic61C2×C411yescharacteristic
44#14519692—22no—
45#14519692C2×C414yescomplemented
46#14519691—28no—
47#14519684—22no—
48#14519684—22no—
49C22×D4×C61C2311yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61—22no—
52C2×C22⋊C4×C61—22no—
53C2×C42×C61C2×C411yescharacteristic
54#99×C61—22no—
55#99×C61C2×C414yescomplemented
56C24×C61C2×D412yes—
57C23×D61C22⋊C411yescharacteristic
58C2×D4×C61—41no—
59C2×D4×C61—41no—
60C2×D4×C61C22×C412yes—
61C2×D4×C61C2×D411yescharacteristic
62C2×D4×C61C2×Q811yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—42no—
66C22×C4×C61C22×C411yescharacteristic
67C2×C22⋊D61—42no—
68C2×C22⋊D61—42no—
69C2×C22⋊D61C22⋊C414yes—
70C2×C22⋊D61C4⋊C414yes—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—24no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—42no—
77C22×Dic61C22⋊C412yes—
78C22×Dic61C22⋊C414yes—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C4⋊C414yes—
81#11758224—44no—
82#11758224—44no—
83#11758224—44no—
84#11758224—44no—
85C2×C4×D61—22no—
86C2×C4×D61—22no—
87C2×C4×D61—42no—
88C2×C4×D61—82no—
89C2×C4×D61C4212yes—
90C2×C4×D61C4⋊C412yes—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122C4212yes—
94C2×Dic122C4⋊C412yes—
95C4⋊C4×C61—41no—
96C22⋊C4×C61—24no—
97C22⋊C4×C61—42no—
98C22⋊C4×C61—82no—
99C42×C61—41no—
100C22⋊Dic61—24no—
101C22⋊Dic61—42no—
102C22⋊Dic61—82no—
103#11758198—42no—
104C4⋊Dic61—41no—
105#11758196—48no—
106#11758196—42no—
107#11758196—42no—
108C4×Dic61—48no—
109C4×Dic61—41no—
110C23×C61—22no—
111C23×C61—22no—
112C23×C61—42no—
113C23×C61—42no—
114C23×C61C2×C22⋊C411yescharacteristic
115C23×C61C2×C22⋊C412yes—
116C23×C61C2×C4⋊C412yes—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61#9512yes—
122D4×C61—42no—
123D4×C61—41no—
124D4×C61—41no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—44no—
128C2×C4×C61—41no—
129C2×C4×C61—42no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—82no—
134C2×C4×C61—82no—
135C2×C4×C61C2×C4211yescharacteristic
136C2×C4×C61C2×C4⋊C411yescharacteristic
137C22⋊D61—44no—
138C22⋊D61—44no—
139C2×Dic61—22no—
140C2×Dic61—22no—
141C2×Dic61—24no—
142C2×Dic61—24no—
143C2×Dic61—24no—
144C2×Dic61—24no—
145C2×Dic61—44no—
146C2×Dic61—41no—
147C2×Dic61—42no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—82no—
152C2×Dic61—82no—
153C2×Dic61#9514yes—
154C2×Dic61#9512yes—
155C2×Dic61#9912yes—
156C2×Dic61#9912yes—
157C4×D61—24no—
158C4×D61—24no—
159C4×D61—84no—
160Dic122—42no—
161Dic122—42no—
162#12583—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—22no—
166C22×C61—22no—
167C22×C61—42no—
168C22×C61—42no—
169C22×C61—42no—
170C22×C61—42no—
171C22×C61—82no—
172C22×C61C2×#9511yescharacteristic
173C22×C61C2×#9911yescharacteristic
174C22×C61C2×#9911yescharacteristic
175C2×D61—22no—
176C2×D61—42no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—42no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—81no—
183C4×C61—84no—
184C4×C61—81no—
185Dic61—24no—
186Dic61—81no—
187Dic61—84no—
188Dic61—81no—
189Dic61#34214yes—
190C2×#410—612no—
191#2311—611no—
192#1393—612no—
193#1393—611no—
194#1393D6111yescharacteristic, complemented
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—42no—
198C2×C61—42no—
199C2×C61C2×#34211yescharacteristic
200C2×C61#212811yescharacteristic
201C2×C61#212911yescharacteristic
202D61—42no—
203C22×#41—611no—
204C2×#117—611no—
205C2×#117—1222no—
206C22×C4⋊C4—611no—
207#410—618no—
208#410—1224no—
209C2×#99—612no—
210C2×#99—1222no—
211C2×#99C2×D6112yes—
212#391—611no—
213#391—611no—
214#390—611no—
215#390C2×D6111yescharacteristic
216#386—1222no—
217#380—1222no—
218C61#1258311yescharacteristic, complemented, Sylow
219C2×#41—614no—
220C2×#41—612no—
221C2×#41—612no—
222C2×#41—2442no—
223C2×#41—2442no—
224C22×Q8—611no—
225C22×D4—612no—
226C22×D4C22×D6111yescharacteristic
227C23×C4—612no—
228C23×C4—611no—
229C23×C4—1221no—
230#117—1228no—
231#117—2442no—
232#117—2444no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—2442no—
237C2×C4⋊C4—2442no—
238C2×C4⋊C4C4×D6111yescharacteristic
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—1222no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4—1221no—
244C2×C42—611no—
245C2×C42—2442no—
246C2×C42C4×D6111yescharacteristic
247#99—22no—
248#99—614no—
249#99—1228no—
250#99—1222no—
251#99C4×D6114yescomplemented
252#95—1222no—
253#95—1222no—
254C24—611no—
255C24D4×D6112yes—
256#41—2444no—
257#41—2444no—
258#41—2444no—
259#41—2444no—
260C2×Q8—612no—
261C2×Q8—612no—
262C2×Q8—2441no—
263C2×Q8—2441no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—614no—
267C2×D4—614no—
268C2×D4—2442no—
269C2×D4—2442no—
270C2×D4C2×C4×D6112yes—
271C2×D4D4×D6111yescharacteristic
272C2×D4Q8×D6111yescharacteristic
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—611no—
277C22×C4—614no—
278C22×C4—612no—
279C22×C4—614no—
280C22×C4—612no—
281C22×C4—612no—
282C22×C4—1222no—
283C22×C4—1222no—
284C22×C4—1222no—
285C22×C4—1222no—
286C22×C4—1224no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—4882no—
290C22×C4—2442no—
291C22×C4—2442no—
292C22×C4C2×C4×D6111yescharacteristic
293C4⋊C4—41no—
294C4⋊C4—2441no—
295C4⋊C4—2442no—
296C4⋊C4—2442no—
297C4⋊C4—2448no—
298C22⋊C4—24no—
299C22⋊C4—42no—
300C22⋊C4—82no—
301C22⋊C4—1224no—
302C22⋊C4—4882no—
303C22⋊C4—2442no—
304C22⋊C4—2442no—
305C42—41no—
306C42—2441no—
307C42—2448no—
308C23—22no—
309C23—22no—
310C23—42no—
311C23—42no—
312C23—612no—
313C23—1221no—
314C23—1221no—
315C23—2441no—
316C23—2441no—
317C23C22⋊C4×D6112yes—
318C23C22⋊C4×D6111yescharacteristic
319C23C4⋊C4×D6112yes—
320Q8—2442no—
321Q8—2442no—
322D4—42no—
323D4—41no—
324D4—41no—
325D4—2444no—
326D4—2444no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—44no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—612no—
338C2×C4—612no—
339C2×C4—612no—
340C2×C4—614no—
341C2×C4—1224no—
342C2×C4—1224no—
343C2×C4—1224no—
344C2×C4—1224no—
345C2×C4—1224no—
346C2×C4—1224no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—4884no—
350C2×C4—4882no—
351C2×C4—4882no—
352C2×C4—2444no—
353C2×C4—2441no—
354C2×C4—2442no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4C42×D6111yescharacteristic
359C2×C4C4⋊C4×D6111yescharacteristic
360C22—21no—
361C22—21no—
362C22—22no—
363C22—22no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—42no—
368C22—82no—
369C22—1222no—
370C22—2442no—
371C22—2442no—
372C22—2441no—
373C22—2441no—
374C22#95×D6111yescharacteristic
375C22#99×D6111yescharacteristic
376C22#99×D6111yescharacteristic
377C4—21no—
378C4—21no—
379C4—81no—
380C4—84no—
381C4—81no—
382C4—614no—
383C4—1224no—
384C4—4881no—
385C4—4884no—
386C4—4881no—
387C2—21no—
388C2—21no—
389C2—42no—
390C2—42no—
391C2—2442no—
392C2#342×D6111yescharacteristic
393C2#2144748911yescharacteristic
394C2#2144749211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C2×C42
FrattiniC22×D4C22×D61
FittingC61×#1393C2
socleC22×C61C2×#99
prime radicalC22×#11758224C22
cosocleC22×D4×C61C23
hypercenter#1393D61
hypocenterC61#12583
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
3. #21443944C2semidirect
4. #21443943C2semidirect
5. C61×#1393C2semidirect
7. C2×#14519734C4semidirect
9. C2×C4⋊C4×D61C4semidirect
11. #16839734C4semidirect
14. #16839668C4semidirect
15. #16839667C4semidirect
45. #14519692C2×C4semidirect
55. #99×C61C2×C4semidirect
194. #1393D61semidirect
218. C61#12583semidirect
251. #99C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397342
#214484092
#214439442
#214439432
C61×#13932
#1258361