Finite Group Databasebeta

← #30599261

Subgroups — #30599261

Order 15616.

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

normal subgroups only

This group has 588 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#21461711C211yesmaximal, characteristic
2#21460995C211yesmaximal, characteristic
3#21460692C212yesmaximal
4#21460692C212yesmaximal
5#21448223C211yesmaximal, characteristic
6C2×#14519834C2212yes—
7C2×(C2×#6923)⋊C4—21no—
8C2×(C2×#6923)⋊C4—21no—
9C2×(C2×#6923)⋊C4C2212yes—
10#16840628—21no—
11#16840628—21no—
12C2×#14519734—21no—
13C2×C42×D61C2211yescharacteristic
14#16839631C411yescharacteristic, complemented
15#16839631C411yescharacteristic, complemented
16#16839626—21no—
17#16839621—21no—
18#16839619C2211yescharacteristic
19#16839619C2211yescharacteristic
20C4×#11758196—21no—
21C4×C4⋊Dic61C411yescharacteristic, complemented
22C4×C4⋊C4×C61C411yescharacteristic, complemented
23C23×#6923—22no—
24C22×#92420—22no—
25#14519834—24no—
26(C2×#6923)⋊C4—24no—
27(C2×#6923)⋊C4—24no—
28(C2×#6923)⋊C4—42no—
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61C2311yescharacteristic
32#14519734—42no—
33#14519734—42no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C42×D61—24no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C42×C61—21no—
53C2×C42×C61C2×C411yescharacteristic
54#95×C61—21no—
55C23×D61C2×D411yescharacteristic
56C22×#6923—24no—
57C22×#6923—42no—
58C22×#6923—42no—
59C22×#6923—42no—
60C22×#6923—42no—
61C22×#6923—42no—
62C22×#6923—42no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61D812yes—
81C2×C4×D61SD1612yes—
82C2×C4×D61#4114yes—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C42×C61—22no—
89C42×C61—42no—
90#11758198—41no—
91#11758198—41no—
92#11758198—41no—
93#11758198—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96#11758196—42no—
97#11758196—42no—
98#11758196—42no—
99#11758196—42no—
100C4×Dic61—22no—
101C4×Dic61—22no—
102C4×Dic61—22no—
103C4×Dic61—42no—
104C23×C61C2×C22⋊C411yescharacteristic
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61#12312yes—
110C22×D61C2×D811yescharacteristic
111C22×D61C2×SD1611yescharacteristic
112C22×D61#13712yes—
113C2×#6923—44no—
114C2×#6923—44no—
115C2×#6923—44no—
116C2×#6923—82no—
117C2×#6923—82no—
118C2×#6923—82no—
119C2×#6923—82no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61#10212yes—
134C2×C4×C61#11712yes—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61#10212yes—
148C2×Dic61#10412yes—
149C2×Dic61#12312yes—
150C4×D61—24no—
151C4×D61—24no—
152C4×D61—44no—
153C4×D61—44no—
154#92420—82no—
155#8716—611nomaximal, Sylow
156C22×C61#38111yescharacteristic
157C22×C61#41011yescharacteristic
158C22×C61#41011yescharacteristic
159C22×C61C2×#10211yescharacteristic
160C22×C61#41911yescharacteristic
161C22×C61C2×#10411yescharacteristic
162C22×C61#42111yescharacteristic
163C2×D61—22no—
164C2×D61—22no—
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—22no—
168C2×D61—22no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61#48012yes—
172C2×D61#48312yes—
173#6923—84no—
174C4×C61—22no—
175C4×C61—22no—
176C4×C61—41no—
177C4×C61—81no—
178C4×C61—81no—
179Dic61—22no—
180Dic61—22no—
181Dic61—22no—
182Dic61—81no—
183Dic61—81no—
184#2285—611no—
185#1817—611no—
186#1434—611no—
187#1294—612no—
188#1294—612no—
189C2×C61#150211yescharacteristic
190C2×C61#150611yescharacteristic
191C2×C61#151511yescharacteristic
192C2×C61#151711yescharacteristic
193C2×C61#182011yescharacteristic
194C2×C61#182311yescharacteristic
195C2×C61#182611yescharacteristic
196D61—22no—
197D61—22no—
198C2×#117—1221no—
199C22×C42—611no—
200C2×C22⋊C8—612no—
201#384—611no—
202#384—611no—
203#382—1221no—
204#380—611no—
205#380—611no—
206#380—1221no—
207C4×C4⋊C4—611no—
208C4×C4⋊C4—1221no—
209C4×C4⋊C4#692311yescharacteristic, complemented
210C2×#95—612no—
211C2×#95—1221no—
212C2×#95—1221no—
213#336—1221no—
214#336—1221no—
215C61#871611yescharacteristic, complemented, Sylow
216C23×C4—611no—
217C23×C4—611no—
218C23×C4—611no—
219C23×C4—1222no—
220C22×C8—1222no—
221#117—2442no—
222#117—2442no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4C2×#692311yescharacteristic
230C2×C4⋊C4C2×#692311yescharacteristic
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C42—21no—
234C2×C42—611no—
235C2×C42—611no—
236C2×C42—611no—
237C2×C42—1224no—
238C2×C42—1221no—
239C2×C42C2×#692311yescharacteristic
240C22⋊C8—1224no—
241#95—21no—
242#95—1221no—
243#95—1221no—
244#95—1224no—
245#95—1224no—
246#95—1221no—
247#95—2442no—
248C24—611no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—612no—
255C22×C4—612no—
256C22×C4—614no—
257C22×C4—1222no—
258C22×C4—1222no—
259C22×C4—1222no—
260C22×C4—1222no—
261C22×C4—1224no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—2441no—
265C22×C4—2441no—
266C22×C4—2441no—
267C22×C4—2442no—
268C22×C4—2442no—
269C22×C4—2442no—
270C22×C4—2442no—
271C22×C4—2442no—
272C22×C4—2442no—
273C22×C4C22⋊#692311yescharacteristic
274C22×C4C22⋊#692311yescharacteristic
275C22×C4C22×#692311yescharacteristic
276C2×C8—2442no—
277C2×C8—2442no—
278C2×C8—2442no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2442no—
284C4⋊C4—2442no—
285C4⋊C4—2442no—
286C4⋊C4—2442no—
287C22⋊C4—2441no—
288C22⋊C4—2441no—
289C22⋊C4—2441no—
290C22⋊C4—2441no—
291C42—22no—
292C42—42no—
293C42—1222no—
294C42—1222no—
295C42—1222no—
296C42—2442no—
297C23—612no—
298C23—611no—
299C23—611no—
300C23—612no—
301C23—1221no—
302C23—1221no—
303C23—1221no—
304C23—1221no—
305C23C2×C22⋊#692311yescharacteristic
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—612no—
320C2×C4—612no—
321C2×C4—612no—
322C2×C4—1224no—
323C2×C4—1224no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—4882no—
331C2×C4—4882no—
332C2×C4—4882no—
333C2×C4—4882no—
334C2×C4—2444no—
335C2×C4—2444no—
336C2×C4—2444no—
337C2×C4—2444no—
338C2×C4—2444no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4#1451983912yes—
346C2×C4#1451985612yes—
347C8—4882no—
348C22—612no—
349C22—612no—
350C22—1221no—
351C22—1221no—
352C22—1221no—
353C22—1221no—
354C22—1222no—
355C22—1222no—
356C22—1222no—
357C22—1222no—
358C22#1684070511yescharacteristic
359C22#1684074111yescharacteristic
360C22#1684074111yescharacteristic
361C22C2×#1451983911yescharacteristic
362C22#1684075511yescharacteristic
363C22D61⋊#10411yescharacteristic
364C22#1684075911yescharacteristic
365C4—22no—
366C4—22no—
367C4—41no—
368C4—81no—
369C4—81no—
370C4—1222no—
371C4—1222no—
372C4—1222no—
373C4—4884no—
374C4—4881no—
375C4—4881no—
376C2—1222no—
377C2—1222no—
378C2#2146119811yescharacteristic
379C2#2146121211yescharacteristic
380C2#2146124111yescharacteristic
381C2#2146124911yescharacteristic
382C2#2146171611yescharacteristic
383C2#2146172211yescharacteristic
384C2#2146172711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8716
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
14. #16839631C4semidirect
15. #16839631C4semidirect
21. C4×C4⋊Dic61C4semidirect
22. C4×C4⋊C4×C61C4semidirect
209. C4×C4⋊C4#6923semidirect
215. C61#8716semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214609952
#214606922
#214482232
#871661