Finite Group Databasebeta

← #30598730

Subgroups — #30598730

Order 15616.

694 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 96 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#21461348C212yesmaximal, complemented
2#21461301C212yesmaximal, complemented
3#21461072C211yesmaximal, characteristic
4#21461072C211yesmaximal, characteristic
5C2×#16840392C211yesmaximal, characteristic
6#16840782C2212yes—
7#16840782C2212yes—
8#16840621—24no—
9#16840619—24no—
10#16840608—21no—
11#16840608—21no—
12#16840606—21no—
13#16840606—21no—
14#16840392—24no—
15#16840392—24no—
16C2×#14519777C411yescharacteristic
17C2×#14519776—21no—
18C2×#14519776C2211yescharacteristic
19C2×#14519768C2211yescharacteristic
20C2×#14519767—21no—
21C2×#14519757—21no—
22C2×#14519755—21no—
23C2×#14519735C411yescharacteristic
24C2×#14519734C2211yescharacteristic
25C2×C4⋊C4×D61C411yescharacteristic
26C2×#125×C61C411yescharacteristic
27#14519844—22no—
28#14519844—22no—
29C22⋊#92420—22no—
30C22⋊#92420—22no—
31#14519832—22no—
32#14519832—22no—
33C22×Dic122—21no—
34C22×Dic122—21no—
35C22×C4×D61—21no—
36C22×C4×D61C2×C411yescharacteristic
37#14519777—22no—
38#14519777—22no—
39#14519776—28no—
40#14519776—22no—
41#14519776D414yes—
42#14519768—22no—
43#14519768D414yes—
44#14519767—28no—
45#14519757—28no—
46#14519755—28no—
47#14519735—22no—
48#14519735—22no—
49#14519734—22no—
50#14519734—22no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61C2×C411yescharacteristic
54C2×C4⋊Dic61C2×C411yescharacteristic
55C2×#11758196—21no—
56C2×#11758196—21no—
57C2×#11758196—21no—
58C2×#11758196D411yescharacteristic
59C2×#11758196D411yescharacteristic
60C4⋊C4×D61—22no—
61C4⋊C4×D61—22no—
62C2×#11758198—21no—
63C2×#11758198D411yescharacteristic
64C2×#11758198D411yescharacteristic
65C2×C4×Dic61—21no—
66C2×C4×Dic61C2311yescharacteristic
67#125×C61—22no—
68#125×C61—22no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61C2×C411yescharacteristic
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C42×C61C2×C411yescharacteristic
74C23×D61C22⋊C411yescharacteristic
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22×C411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84C22×Dic61C2×D411yescharacteristic
85C2×C4×D61—22no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—22no—
89C2×C4×D61—24no—
90C2×C4×D61—82no—
91C2×Dic122—24no—
92C2×Dic122—24no—
93C2×Dic122—82no—
94C2×Dic122—82no—
95C2×#92420—42no—
96C2×#92420—42no—
97C4⋊C4×C61—24no—
98C4⋊C4×C61—24no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61C22⋊C412yes—
102C4⋊C4×C61C22⋊C412yes—
103C42×C61—21no—
104C42×C61—21no—
105#11758198—24no—
106#11758198—22no—
107#11758198—22no—
108C4⋊Dic61—24no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—24no—
112C4⋊Dic61C22⋊C412yes—
113C4⋊Dic61C22⋊C412yes—
114#11758196—24no—
115#11758196—24no—
116#11758196—24no—
117#11758196—22no—
118#11758196—22no—
119C4×Dic61—24no—
120C4×Dic61C2×D412yes—
121C4×Dic61C2×D412yes—
122C23×C61C2×C22⋊C411yescharacteristic
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61#10112yes—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148C2×Dic61#10112yes—
149C2×Dic61#12012yes—
150C2×Dic61#12012yes—
151C4×D61—24no—
152C4×D61—24no—
153C4×D61—84no—
154Dic122—84no—
155Dic122—84no—
156#92420—82no—
157#92420—82no—
158#8525—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61#37911yescharacteristic
162C22×C61C2×#10111yescharacteristic
163C22×C61C2×#10111yescharacteristic
164C2×D61—22no—
165C2×D61—42no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—42no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—41no—
172C4×C61—42no—
173C4×C61—41no—
174C4×C61—42no—
175Dic61—22no—
176Dic61—22no—
177Dic61—22no—
178Dic61—42no—
179Dic61—42no—
180C2×#544—611no—
181#1556—612no—
182#1534—612no—
183#1464—611no—
184#1464—611no—
185C2×C61—21no—
186C2×C61—21no—
187C2×C61#178411yescharacteristic
188C2×C61#179511yescharacteristic
189C2×C61#179611yescharacteristic
190D61—42no—
191#544—1224no—
192#544—1224no—
193C2×C4⋊Q8—611no—
194C2×C4⋊Q8—611no—
195C2×C4⋊Q8—1221no—
196C2×#125—611no—
197C2×#125—1221no—
198C2×#125#692311yescharacteristic
199C2×C22⋊Q8—1221no—
200C2×C22⋊Q8—1221no—
201C2×#117—611no—
202C2×#117—611no—
203C22×C4⋊C4—611no—
204#432—612no—
205#432—612no—
206#332—1224no—
207#330—1224no—
208#324—1221no—
209#324—1221no—
210#323—1221no—
211#323—1221no—
212C61#852511yescharacteristic, complemented, Sylow
213C22×Q8—1221no—
214C22×Q8—1221no—
215C23×C4—611no—
216C23×C4—1221no—
217C4⋊Q8—614no—
218C4⋊Q8—1222no—
219C4⋊Q8—1222no—
220C4⋊Q8—1222no—
221C4⋊Q8—1228no—
222#125—22no—
223#125—22no—
224#125—614no—
225#125—1222no—
226#125—1228no—
227C22⋊Q8—1228no—
228C22⋊Q8—1228no—
229#117—1222no—
230#117—1222no—
231#117—1222no—
232#117—1222no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1222no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1222no—
246C2×C4⋊C4C2×#692311yescharacteristic
247C2×C4⋊C4C2×#692311yescharacteristic
248C2×C22⋊C4—611no—
249C2×C22⋊C4—611no—
250C2×C22⋊C4—1221no—
251C2×C42—611no—
252C2×C42—1221no—
253C2×C42C2×#692311yescharacteristic
254C4⋊C8—1222no—
255C4⋊C8—1222no—
256C22⋊C8—1222no—
257C22⋊C8—1222no—
258#97—1222no—
259#97—1222no—
260C24—611no—
261C2×Q8—1224no—
262C2×Q8—1224no—
263C2×Q8—4882no—
264C2×Q8—4882no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—1222no—
271C22×C4—1222no—
272C22×C4—1224no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—4882no—
278C22×C4C22⋊#692311yescharacteristic
279C22×C4C22⋊#692311yescharacteristic
280C22×C4C22×#692311yescharacteristic
281C2×C8—2442no—
282C2×C8—2442no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—612no—
288C4⋊C4—612no—
289C4⋊C4—1222no—
290C4⋊C4—1222no—
291C4⋊C4—1224no—
292C4⋊C4—1224no—
293C4⋊C4—1224no—
294C4⋊C4—1224no—
295C4⋊C4—1224no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4C22⋊#692312yes—
299C4⋊C4C22⋊#692312yes—
300C22⋊C4—1222no—
301C22⋊C4—1222no—
302C22⋊C4—1224no—
303C42—21no—
304C42—21no—
305C42—612no—
306C42—612no—
307C42—1224no—
308C23—612no—
309C23—1221no—
310C23—1221no—
311C23—2441no—
312C23—2441no—
313C23C2×C22⋊#692311yescharacteristic
314Q8—4884no—
315Q8—4884no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—612no—
327C2×C4—612no—
328C2×C4—612no—
329C2×C4—1224no—
330C2×C4—1224no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1222no—
334C2×C4—1222no—
335C2×C4—4884no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4C2×C22⋊#692311yescharacteristic
341C2×C4C2×C22⋊#692311yescharacteristic
342C8—4882no—
343C8—4882no—
344C22—21no—
345C22—21no—
346C22—1222no—
347C22—2442no—
348C22—2442no—
349C22—2441no—
350C22—2441no—
351C22#1684070311yescharacteristic
352C22D61⋊#10111yescharacteristic
353C22D61⋊#10111yescharacteristic
354C4—21no—
355C4—21no—
356C4—42no—
357C4—41no—
358C4—41no—
359C4—42no—
360C4—1222no—
361C4—1222no—
362C4—1222no—
363C4—2442no—
364C4—2442no—
365C2—21no—
366C2—21no—
367C2—2442no—
368C2#2146165411yescharacteristic
369C2#2146167011yescharacteristic
370C2#2146167211yescharacteristic
subgroupG/H
centerC22#16840703
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#125×C61C4
socleC22×C61#379
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#125#6923
hypocenterC61#8525
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #21461348C2semidirect
2. #21461301C2semidirect
212. C61#8525semidirect

Maximal subgroups

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

subgroupindex
#214613482
#214613012
#214610722
C2×#168403922
#852561