Finite Group Databasebeta

← #29589662

Subgroups — #29589662

Order 15616.

480 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 73 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#21450771C211yesmaximal, characteristic
2#21444156C211yesmaximal, characteristic
3#21444136C211yesmaximal, characteristic
4#21443765C211yesmaximal, characteristic, complemented
5#21443764C211yesmaximal, characteristic, complemented
6#21443764C211yesmaximal, characteristic, complemented
7C61×#1325C211yesmaximal, characteristic, complemented
8C2×#14519776C411yescharacteristic
9C2×#14519755—21no—
10C2×#14519755—21no—
11C2×#14519739C2211yescharacteristic
12#16839724—21no—
13C22⋊C8×D61—21no—
14#16839697—21no—
15#16839697—21no—
16#16839664C411yescharacteristic
17#16839663C411yescharacteristic
18#16839631C2211yescharacteristic
19C4×#11758196C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839485—21no—
23#16839485—21no—
24C61×#384C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758189—41no—
32C2×C8×D61—41no—
33#14519776—41no—
34#14519776—41no—
35#14519755—44no—
36#14519755—44no—
37#14519739—41no—
38#14519739—41no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198D411yescharacteristic
49C2×#11758198D411yescharacteristic
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61C2×C411yescharacteristic
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54#14519689—41no—
55#14519689—41no—
56#14519684—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2311yescharacteristic
61C2×C42×C61C2×C411yescharacteristic
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64C23×D61C22⋊C411yescharacteristic
65C23×D61C22⋊C411yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C2×D244—22no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—41no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—42no—
84C2×C4×D61—42no—
85C2×Dic122—42no—
86C2×Dic122—42no—
87C2×Dic122—41no—
88C2×Dic122—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—42no—
93C4⋊C4×C61—42no—
94C4⋊C4×C61—41no—
95C42×C61—21no—
96C42×C61—21no—
97#11758198—41no—
98#11758198—41no—
99#11758198—42no—
100#11758198—42no—
101#11758198—42no—
102#11758198—42no—
103C4⋊Dic61—41no—
104#11758196—24no—
105#11758196—42no—
106#11758196—42no—
107#11758196—42no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C2×#92418—41no—
113C2×#92418—41no—
114#11758189—82no—
115C8×D61—82no—
116C23×C61C2×C22⋊C411yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61#10112yes—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—22no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61#13111yescharacteristic
140C2×C4×C61#13111yescharacteristic
141C2×Dic61—22no—
142C2×Dic61—22no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61#9911yescharacteristic
151C2×Dic61#9911yescharacteristic
152D244—42no—
153D244—42no—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—81no—
157C4×D61—81no—
158Dic122—82no—
159Dic122—82no—
160C8×C61—81no—
161C8×C61—81no—
162#92418—81no—
163#92418—81no—
164#11570—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61#40811yescharacteristic
168C22×C61C2×#9911yescharacteristic
169C22×C61C2×#10111yescharacteristic
170C2×D61—22no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—42no—
174C2×D61—42no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—81no—
179C2×D61—81no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—42no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—81no—
186Dic61—21no—
187Dic61—42no—
188Dic61—41no—
189Dic61—81no—
190Dic61#35312yes—
191#2542—611no—
192#1465—611no—
193#1459—611no—
194#1325—611no—
195#1325—611no—
196#1325—611no—
197#1325D6111yescharacteristic, complemented
198C2×C61—21no—
199C2×C61—21no—
200C2×C61#147211yescharacteristic
201C2×C61C2×#35311yescharacteristic
202C2×C61#213511yescharacteristic
203D61—42no—
204D61—81no—
205C2×C4⋊Q8—611no—
206C2×C22⋊Q8—1221no—
207C2×C22⋊Q8—1221no—
208C2×C4×D4—611no—
209#407—1221no—
210C2×C22⋊C8—1221no—
211#399—1221no—
212#399—1221no—
213#390—611no—
214#390—611no—
215#384—611no—
216#384C2×D6111yescharacteristic
217C4×C4⋊C4—611no—
218#324—611no—
219#324—611no—
220#324C2×D6111yescharacteristic
221#324C2×D6111yescharacteristic
222#323—1221no—
223#323—1221no—
224C61#1157011yescharacteristic, complemented, Sylow
225C22×Q8—1221no—
226C22×D4—611no—
227C23×C4—611no—
228C23×C4—611no—
229C2×M16—2441no—
230C22×C8—2441no—
231C4⋊Q8—2441no—
232C4⋊Q8—2441no—
233C22⋊Q8—2444no—
234C22⋊Q8—2444no—
235C4×D4—2441no—
236C4×D4—2441no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4C4×D6111yescharacteristic
245C2×C4⋊C4C22×D6111yescharacteristic
246C2×C22⋊C4—611no—
247C2×C22⋊C4—611no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42C4×D6111yescharacteristic
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—1221no—
258C22⋊C8—1221no—
259C22⋊C8—2441no—
260C22⋊C8—2441no—
261#95—1221no—
262C24—611no—
263C24—611no—
264C2×Q8—2441no—
265C2×Q8—2441no—
266C2×Q8—2442no—
267C2×Q8—2442no—
268C2×D4—1222no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—2441no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—2442no—
283C22×C4—2442no—
284C22×C4C2×C4×D6111yescharacteristic
285C22×C4D4×D6111yescharacteristic
286C22×C4D4×D6111yescharacteristic
287M16—4882no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—4882no—
291C2×C8—2441no—
292C2×C8—2441no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—1224no—
298C4⋊C4—2441no—
299C4⋊C4—2442no—
300C4⋊C4—2442no—
301C4⋊C4—2442no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2442no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C22⋊C4—2442no—
308C42—21no—
309C42—21no—
310C42—1221no—
311C42—1221no—
312C42—1221no—
313C42—1221no—
314C23—612no—
315C23—1221no—
316C23—1221no—
317C23—1221no—
318C23—1221no—
319C23—1221no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23—2441no—
324C23C22⋊C4×D6111yescharacteristic
325Q8—4882no—
326Q8—4882no—
327D4—2442no—
328D4—2442no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1221no—
346C2×C4—4881no—
347C2×C4—4881no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4#1451978311yescharacteristic
357C2×C4#1451978511yescharacteristic
358C8—81no—
359C8—81no—
360C8—4881no—
361C8—4881no—
362C22—21no—
363C22—21no—
364C22—1222no—
365C22—4881no—
366C22—4881no—
367C22—2442no—
368C22—2442no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22#1683972711yescharacteristic
375C22#99×D6111yescharacteristic
376C22#101×D6111yescharacteristic
377C4—21no—
378C4—21no—
379C4—42no—
380C4—41no—
381C4—41no—
382C4—81no—
383C4—612no—
384C4—1221no—
385C4—4881no—
386C4—2442no—
387C4—2441no—
388C2—21no—
389C2—21no—
390C2—4881no—
391C2—2442no—
392C2#2144418111yescharacteristic
393C2#353×D6111yescharacteristic
394C2#2144751211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1325C2
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1325D61
hypocenterC61#11570
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
4. #21443765C2semidirect
5. #21443764C2semidirect
6. #21443764C2semidirect
7. C61×#1325C2semidirect
197. #1325D61semidirect
224. C61#11570semidirect

Maximal subgroups

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

subgroupindex
#214507712
#214441562
#214441362
#214437652
#214437642
C61×#13252
#1157061