Finite Group Databasebeta

← #30598335

Subgroups — #30598335

Order 15616.

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

normal subgroups only

This group has 788 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
1C4×#14519838C211yesmaximal, characteristic, complemented
2#21461281C212yesmaximal, complemented
3#21461158C212yesmaximal
4#21461081C211yesmaximal, characteristic, complemented
5C2×#16840469C211yesmaximal, characteristic
6#16840783C2212yes—
7C2×#14519838—21no—
8C4×#11758217C2212yes—
9#16840642—21no—
10#16840619—24no—
11D4⋊#92420—24no—
12#16840608—21no—
13#16840607—21no—
14#16840469—24no—
15#16840469—24no—
16C2×#14519777C411yescharacteristic
17C2×#14519768C411yescharacteristic
18C2×#14519768C2211yescharacteristic
19C2×#14519756—21no—
20C2×#14519754—21no—
21C2×#14519754—21no—
22C2×C4×Dic122C2211yescharacteristic
23C2×D4×Dic61C411yescharacteristic
24C2×D4×Dic61C2211yescharacteristic
25C22×C4⋊Dic61—21no—
26C2×C4×D4×C61C411yescharacteristic
27C2×#11758217—22no—
28C4⋊#92420—22no—
29#14519838—24no—
30C22⋊#92420—22no—
31#14519832—22no—
32#14519832—22no—
33C4×#92420—22no—
34C22×Dic122—21no—
35C22×Dic122D411yescharacteristic
36C23×Dic61—21no—
37C23×Dic61—21no—
38#14519777—22no—
39#14519777—22no—
40#14519768—22no—
41#14519768—22no—
42#14519768—22no—
43#14519768D414yes—
44#14519756—28no—
45#14519754—28no—
46#14519754—28no—
47C4×Dic122—22no—
48C4×Dic122—22no—
49D4×Dic61—22no—
50D4×Dic61—22no—
51D4×Dic61—22no—
52D4×Dic61D414yes—
53C2×C4⋊Dic61—28no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61—21no—
57C2×C4⋊Dic61C2×C411yescharacteristic
58C2×C4⋊Dic61C2×C411yescharacteristic
59C2×C4⋊Dic61D411yescharacteristic
60C2×#11758196—21no—
61C2×#11758196—21no—
62C2×#11758196D411yescharacteristic
63C2×#11758196D411yescharacteristic
64C2×C22⋊Dic61—21no—
65C2×C22⋊Dic61—21no—
66C2×C4×Dic61C2×C411yescharacteristic
67C2×C4×Dic61C2311yescharacteristic
68C22×D4×C61C2×C411yescharacteristic
69C23×C4×C61—21no—
70C4×D4×C61—22no—
71C4×D4×C61—22no—
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C22⋊C4×C61—21no—
74C2×C42×C61C2×C411yescharacteristic
75C24×C61—21no—
76C2×D4×C61—24no—
77C2×D4×C61—21no—
78C2×D4×C61C22⋊C412yes—
79C22×C4×C61—24no—
80C22×C4×C61—21no—
81C22×C4×C61—42no—
82C22×C4×C61—42no—
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22×C411yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—24no—
89C22×Dic61—24no—
90C22×Dic61—82no—
91C22×Dic61—82no—
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C22⋊C411yescharacteristic
94C22×Dic61C2×D411yescharacteristic
95C22×Dic61C2×D411yescharacteristic
96C2×Dic122—22no—
97C2×Dic122—22no—
98C2×Dic122—24no—
99C2×Dic122—41no—
100C2×Dic122—82no—
101#11758217—24no—
102#11758217—42no—
103C2×#92420—42no—
104C2×#92420—42no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61C22⋊C412yes—
107C22⋊C4×C61—24no—
108C42×C61—21no—
109C42×C61—21no—
110C22⋊Dic61—24no—
111C22⋊Dic61—24no—
112C4⋊Dic61—24no—
113C4⋊Dic61—24no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—22no—
117C4⋊Dic61—24no—
118C4⋊Dic61C22⋊C412yes—
119C4⋊Dic61C22⋊C412yes—
120#11758196—24no—
121#11758196—24no—
122#11758196—22no—
123#11758196—22no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61C2×D412yes—
127C4×Dic61C2×D412yes—
128C23×C61—24no—
129C23×C61—22no—
130C23×C61—42no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61C2×C22⋊C411yescharacteristic
134D4×C61—24no—
135D4×C61—22no—
136D4×C61#10114yescomplemented
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—21no—
142C2×C4×C61—48no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61#10412yes—
147C2×C4×C61C2×C22⋊C411yescharacteristic
148C2×C4×C61C2×C22⋊C411yescharacteristic
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—22no—
154C2×Dic61—22no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—41no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160C2×Dic61—41no—
161C2×Dic61—84no—
162C2×Dic61—84no—
163C2×Dic61#12012yes—
164C2×Dic61#12012yes—
165Dic122—44no—
166Dic122—84no—
167#92420—44no—
168#92420—82no—
169#8372—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—24no—
173C22×C61—44no—
174C22×C61—44no—
175C22×C61—42no—
176C22×C61—42no—
177C22×C61#37911yescharacteristic
178C22×C61C2×#10411yescharacteristic
179C22×C61#42111yescharacteristic
180C4×C61—21no—
181C4×C61—22no—
182C4×C61—41no—
183C4×C61—42no—
184C4×C61C2×#10112yes—
185Dic61—22no—
186Dic61—22no—
187Dic61—42no—
188Dic61—42no—
189Dic61—41no—
190Dic61—41no—
191C2×#554—611no—
192C4×#101—611no—
193#1528—612no—
194#1490—612no—
195#1467—611no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61—44no—
199C2×C61#178411yescharacteristic
200C2×C61#178911yescharacteristic
201C2×C61#179511yescharacteristic
202#554—1224no—
203#554—1224no—
204C2×C4⋊Q8—611no—
205C2×#125—611no—
206C2×#125—611no—
207C2×C22⋊Q8—1221no—
208C2×C22⋊Q8—1221no—
209C2×C22⋊Q8—1221no—
210C2×C4×Q8—611no—
211C2×C4×D4—611no—
212C2×C4×D4—611no—
213C2×C4×D4#692311yescharacteristic
214C22×C4⋊C4—1221no—
215#432—612no—
216C2×#101—1221no—
217C4×M16—612no—
218#343—1221no—
219#330—1224no—
220D4⋊C8—1224no—
221#324—1221no—
222#324—1221no—
223C61#837211yescharacteristic, complemented, Sylow
224C22×Q8—611no—
225C22×Q8—1221no—
226C22×D4C2×#692311yescharacteristic
227C23×C4—21no—
228C23×C4—1221no—
229C23×C4—1221no—
230C2×M16—1222no—
231C4⋊Q8—1222no—
232C4⋊Q8—1222no—
233#125—614no—
234#125—1222no—
235#125—1222no—
236#125—1222no—
237C22⋊Q8—1228no—
238C22⋊Q8—1228no—
239C22⋊Q8—1228no—
240C4×Q8—1222no—
241C4×Q8—1222no—
242C4×D4—22no—
243C4×D4—22no—
244C4×D4—614no—
245C4×D4—1222no—
246C4×D4—1222no—
247C4×D4—1222no—
248C2×C4⋊C4—611no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1228no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4C2×#692311yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C42—611no—
264C2×C42—611no—
265C2×C42C2×#692311yescharacteristic
266C4⋊C8—1222no—
267#101—1224no—
268C22⋊C8—1222no—
269#97—1222no—
270#97—1222no—
271C4×C8—1222no—
272C24—21no—
273C2×Q8—1222no—
274C2×Q8—1224no—
275C2×Q8—1222no—
276C2×Q8—4882no—
277C2×Q8—2441no—
278C2×D4—24no—
279C2×D4—21no—
280C2×D4C22⋊#692312yes—
281C22×C4—24no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—1224no—
290C22×C4—1224no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—4882no—
294C22×C4—4882no—
295C22×C4C22⋊#692311yescharacteristic
296C22×C4C22⋊#692311yescharacteristic
297C22×C4C22×#692311yescharacteristic
298M16—1224no—
299M16—2442no—
300C2×C8—2442no—
301C2×C8—2442no—
302C4⋊C4—21no—
303C4⋊C4—612no—
304C4⋊C4—612no—
305C4⋊C4—1222no—
306C4⋊C4—1222no—
307C4⋊C4—1222no—
308C4⋊C4—1224no—
309C4⋊C4—1224no—
310C4⋊C4—1224no—
311C4⋊C4—1224no—
312C4⋊C4—1224no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4C22⋊#692312yes—
316C22⋊C4—24no—
317C22⋊C4—1224no—
318C22⋊C4—1224no—
319C42—21no—
320C42—21no—
321C42—612no—
322C42—612no—
323C42—1221no—
324C42—1221no—
325C23—24no—
326C23—22no—
327C23—42no—
328C23—41no—
329C23—41no—
330C23C2×C22⋊#692311yescharacteristic
331Q8—4884no—
332Q8—2444no—
333D4—24no—
334D4—22no—
335D4#1451983814yescomplemented
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—48no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—612no—
346C2×C4—612no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—4884no—
356C2×C4—4884no—
357C2×C4—2441no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4—2441no—
361C2×C4#1451984112yes—
362C2×C4C2×C22⋊#692311yescharacteristic
363C2×C4C2×C22⋊#692311yescharacteristic
364C8—4882no—
365C8—2444no—
366C22—21no—
367C22—21no—
368C22—24no—
369C22—44no—
370C22—44no—
371C22—42no—
372C22—42no—
373C22#1684070311yescharacteristic
374C22C2×#1451984111yescharacteristic
375C22#1684076011yescharacteristic
376C4—21no—
377C4—22no—
378C4—42no—
379C4—41no—
380C4—1222no—
381C4—1222no—
382C4—2441no—
383C4—2441no—
384C4—2442no—
385C4—2442no—
386C4C2×#1451983812yes—
387C2—21no—
388C2—21no—
389C2—44no—
390C2#2146165311yescharacteristic
391C2#2146166011yescharacteristic
392C2#2146167011yescharacteristic
subgroupG/H
centerC22#16840703
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC22×C61#379
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×D4#6923
hypocenterC61#8372
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×#14519838C2semidirect
2. #21461281C2semidirect
4. #21461081C2semidirect
136. D4×C61#101semidirect
223. C61#8372semidirect
335. D4#14519838semidirect

Maximal subgroups

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

subgroupindex
C4×#145198382
#214612812
#214611582
#214610812
C2×#168404692
#837261