Finite Group Databasebeta

← #30598394

Subgroups — #30598394

Order 15616.

706 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 108 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#21461685C211yesmaximal, characteristic
2#21461328C212yesmaximal
3#21461149C212yesmaximal
4#21461061C211yesmaximal, characteristic
5C2×#16840489C211yesmaximal, characteristic
6#16840779C2212yes—
7#16840765C2212yes—
8C2×#14519838—21no—
9#16840642—21no—
10#16840621—24no—
11#16840612—24no—
12#16840608—21no—
13#16840607—21no—
14#16840489—24no—
15#16840489—24no—
16C2×#14519776—21no—
17C2×#14519776C2211yescharacteristic
18C2×#14519768C411yescharacteristic
19C2×#14519767—21no—
20C2×#14519767—21no—
21C2×C4×Dic122C411yescharacteristic
22C2×C4×Dic122C2211yescharacteristic
23C2×#14519742—21no—
24C2×#14519742C411yescharacteristic
25C2×#14519742C2211yescharacteristic
26C2×#125×C61C411yescharacteristic
27C2×#11758217—22no—
28#14519844—22no—
29#14519844—22no—
30C4⋊#92420—22no—
31#14519838—42no—
32C22⋊#92420—22no—
33C4×#92420—22no—
34C22×Dic122—21no—
35C22×Dic122C2×C411yescharacteristic
36C22×Dic122D411yescharacteristic
37#14519776—28no—
38#14519776—22no—
39#14519776D414yes—
40#14519768—22no—
41#14519768—22no—
42#14519767—28no—
43#14519767—28no—
44C4×Dic122—22no—
45C4×Dic122—22no—
46C4×Dic122—22no—
47C4×Dic122—22no—
48#14519742—28no—
49#14519742—22no—
50#14519742—22no—
51#14519742—22no—
52#14519742D414yes—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61C2×C411yescharacteristic
55C2×C4⋊Dic61D411yescharacteristic
56C2×#11758196—21no—
57C2×#11758196—21no—
58C2×#11758196—21no—
59C2×#11758196—21no—
60C2×#11758196—21no—
61C2×#11758196D411yescharacteristic
62C2×#11758196D411yescharacteristic
63C2×C4×Dic61—21no—
64C2×C4×Dic61—21no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61C2×C411yescharacteristic
67C2×C4×Dic61C2311yescharacteristic
68#125×C61—22no—
69#125×C61—22no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C4⋊C4×C61C2×C411yescharacteristic
74C2×C42×C61C2×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×Dic61C22⋊C411yescharacteristic
84C22×Dic61C2×D411yescharacteristic
85C22×Dic61C2×D411yescharacteristic
86C2×Dic122—21no—
87C2×Dic122—24no—
88C2×Dic122—24no—
89C2×Dic122—22no—
90C2×Dic122—22no—
91C2×Dic122—21no—
92C2×Dic122—21no—
93C2×Dic122—42no—
94C2×Dic122—41no—
95C2×Dic122—41no—
96C2×Dic122C22⋊C412yes—
97#11758217—42no—
98#11758217—42no—
99C2×#92420—42no—
100C2×#92420—42no—
101C4⋊C4×C61—24no—
102C4⋊C4×C61—24no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61C22⋊C412yes—
106C4⋊C4×C61C22⋊C412yes—
107C42×C61—21no—
108C42×C61—21no—
109C4⋊Dic61—24no—
110C4⋊Dic61—21no—
111C4⋊Dic61—22no—
112C4⋊Dic61C22⋊C412yes—
113#11758196—24no—
114#11758196—24no—
115#11758196—24no—
116#11758196—24no—
117#11758196—24no—
118#11758196—22no—
119#11758196—22no—
120C4×Dic61—24no—
121C4×Dic61—24no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124C4×Dic61—24no—
125C4×Dic61C2×D412yes—
126C4×Dic61C2×D412yes—
127C23×C61C2×C22⋊C411yescharacteristic
128C2×C4×C61—22no—
129C2×C4×C61—21no—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—42no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×Dic61—24no—
142C2×Dic61—22no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—22no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61#12012yes—
153C2×Dic61#12012yes—
154C2×Dic61#13512yes—
155C2×Dic61AGL(1,ℤ/8)11yescharacteristic
156C2×Dic61#13711yescharacteristic
157Dic122—24no—
158Dic122—22no—
159Dic122—42no—
160Dic122—44no—
161Dic122—42no—
162Dic122—44no—
163Dic122#10114yescomplemented
164#92420—82no—
165#92420—82no—
166#8390—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61#37911yescharacteristic
170C22×C61#41611yescharacteristic
171C22×C61#41711yescharacteristic
172C4×C61—21no—
173C4×C61—41no—
174C4×C61—42no—
175C4×C61—41no—
176C4×C61—42no—
177C4×C61C2×#10112yes—
178Dic61—22no—
179Dic61—24no—
180Dic61—41no—
181Dic61—41no—
182Dic61—42no—
183Dic61#44912yes—
184Dic61#45212yes—
185C2×#557—611no—
186#1801—611no—
187#1546—612no—
188#1487—612no—
189#1461—611no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61#178411yescharacteristic
193C2×C61#178811yescharacteristic
194C2×C61#179611yescharacteristic
195#557—1224no—
196#557—1224no—
197C2×C4⋊Q8—611no—
198C2×C4⋊Q8—1221no—
199C2×#125—611no—
200C2×#125—1221no—
201C2×#125—1221no—
202C2×#125#692311yescharacteristic
203C2×C4×Q8—611no—
204C2×C4×Q8—611no—
205C2×C4×Q8—611no—
206C2×C4×Q8—611no—
207C2×C4×Q8—1221no—
208#431—612no—
209#423—612no—
210C2×#101—1221no—
211#343—1221no—
212#332—1224no—
213Q8⋊C8—1224no—
214#324—1221no—
215#324—1221no—
216C61#839011yescharacteristic, complemented, Sylow
217C22×Q8—611no—
218C22×Q8—611no—
219C22×Q8—1221no—
220C2×M16—1222no—
221C4⋊Q8—614no—
222C4⋊Q8—1222no—
223C4⋊Q8—1228no—
224#125—22no—
225#125—22no—
226#125—1222no—
227#125—1228no—
228#125—1228no—
229#125—1222no—
230C4×Q8—614no—
231C4×Q8—1222no—
232C4×Q8—1222no—
233C4×Q8—1222no—
234C4×Q8—1222no—
235C4×Q8—1222no—
236C4×Q8—1222no—
237C4×Q8—1228no—
238C4×Q8—1222no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—1221no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4C2×#692311yescharacteristic
252C2×C4⋊C4C2×#692311yescharacteristic
253C2×C42—611no—
254C2×C42—611no—
255C2×C42—1221no—
256C2×C42—1221no—
257C2×C42—1221no—
258C2×C42C2×#692311yescharacteristic
259C4⋊C8—1222no—
260C4⋊C8—1222no—
261C4⋊C8—1222no—
262#101—2442no—
263C22⋊C8—1222no—
264C4×C8—1222no—
265C2×Q8—612no—
266C2×Q8—1221no—
267C2×Q8—1224no—
268C2×Q8—1222no—
269C2×Q8—1222no—
270C2×Q8—1221no—
271C2×Q8—1224no—
272C2×Q8—1221no—
273C2×Q8—2442no—
274C2×Q8—2441no—
275C2×Q8—2441no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4C22⋊#692311yescharacteristic
285C22×C4C22⋊#692311yescharacteristic
286C22×C4C22×#692311yescharacteristic
287M16—2442no—
288M16—2442no—
289C2×C8—2442no—
290C2×C8—2442no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—612no—
296C4⋊C4—1222no—
297C4⋊C4—1222no—
298C4⋊C4—1222no—
299C4⋊C4—1224no—
300C4⋊C4—1224no—
301C4⋊C4—1224no—
302C4⋊C4—1224no—
303C4⋊C4—1224no—
304C4⋊C4—1224no—
305C4⋊C4—1221no—
306C4⋊C4C22⋊#692312yes—
307C4⋊C4C22⋊#692312yes—
308C42—21no—
309C42—21no—
310C42—612no—
311C42—612no—
312C42—1224no—
313C42—1224no—
314C42—1224no—
315C42—1221no—
316C42—1221no—
317C23C2×C22⋊#692311yescharacteristic
318Q8—614no—
319Q8—1224no—
320Q8—1222no—
321Q8—2442no—
322Q8—2442no—
323Q8—2444no—
324Q8—2444no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—612no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—612no—
340C2×C4—612no—
341C2×C4—1224no—
342C2×C4—1222no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1222no—
347C2×C4—1221no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4C2×C22⋊#692311yescharacteristic
353C2×C4C2×C22⋊#692311yescharacteristic
354C8—4882no—
355C8—4882no—
356C22—21no—
357C22—21no—
358C22#1684070311yescharacteristic
359C22#1684075211yescharacteristic
360C22#1684075311yescharacteristic
361C4—21no—
362C4—41no—
363C4—42no—
364C4—41no—
365C4—42no—
366C4—612no—
367C4—612no—
368C4—1224no—
369C4—1222no—
370C4—2441no—
371C4—2442no—
372C4—2441no—
373C4D61⋊#10112yes—
374C2—21no—
375C2—21no—
376C2#2146165411yescharacteristic
377C2#2146165911yescharacteristic
378C2#2146167211yescharacteristic
subgroupG/H
centerC22#16840703
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#125×C61C4
socleC22×C61#379
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#125#6923
hypocenterC61#8390
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
163. Dic122#101semidirect
216. C61#8390semidirect

Maximal subgroups

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

subgroupindex
#214616852
#214613282
#214611492
#214610612
C2×#168404892
#839061