Finite Group Databasebeta

← #30595741

Subgroups — #30595741

Order 15616.

458 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 94 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×C4⋊#92420C211yesmaximal, characteristic, complemented
2#21461536C211yesmaximal, characteristic, complemented
3#21460640C212yesmaximal, complemented
4#21460635C212yesmaximal
5#21454190C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×#14519832—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519768C411yescharacteristic
13C2×#14519764C411yescharacteristic
14#16839668C411yescharacteristic
15#16839667C2211yescharacteristic
16#16839665C2211yescharacteristic
17#16839655—21no—
18#16839655—21no—
19#16839650—21no—
20#16839650—21no—
21C42×Dic61C2211yescharacteristic
22C61×#390C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26#14519832—24no—
27C4×#92420—42no—
28C22×Dic122C2×C411yescharacteristic
29#14519768—42no—
30#14519764—42no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×#11758196—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61C2311yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C22×D4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C42×C61C2×C411yescharacteristic
53C24×C61—21no—
54C2×D4×C61—22no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C22×C4×C61—21no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×Dic122—22no—
68C2×Dic122—41no—
69C2×Dic122—41no—
70C2×#92420—24no—
71C2×#92420—24no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C4⋊C4×C61—41no—
77C22⋊C4×C61—42no—
78C22⋊C4×C61—42no—
79C42×C61—22no—
80C22⋊Dic61—42no—
81C22⋊Dic61—42no—
82C22⋊Dic61—42no—
83C22⋊Dic61—41no—
84C22⋊Dic61—41no—
85C4⋊Dic61—42no—
86C4⋊Dic61—41no—
87#11758196—42no—
88C4×Dic61—22no—
89C4×Dic61—22no—
90C4×Dic61—22no—
91C4×Dic61—22no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—41no—
95C23×C61—41no—
96C23×C61—41no—
97C23×C61—41no—
98C23×C61—41no—
99C23×C61—41no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61C2×C22⋊C411yescharacteristic
103D4×C61—82no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#10412yes—
114C2×C4×C61#10412yes—
115C2×C4×C61#13112yes—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61#10012yes—
132C2×Dic61#13512yes—
133C2×Dic61AGL(1,ℤ/8)11yescharacteristic
134C2×Dic61#13711yescharacteristic
135Dic122—82no—
136#92420—44no—
137#92420—44no—
138#7676—611nomaximal, Sylow
139C22×C61—81no—
140C22×C61—81no—
141C22×C61—81no—
142C22×C61—81no—
143C22×C61—81no—
144C22×C61—81no—
145C22×C61—81no—
146C22×C61#40811yescharacteristic
147C22×C61#41011yescharacteristic
148C22×C61C2×#10011yescharacteristic
149C22×C61#41611yescharacteristic
150C22×C61#41711yescharacteristic
151C22×C61C2×#10411yescharacteristic
152C22×C61C2×#10411yescharacteristic
153C4×C61—22no—
154C4×C61—22no—
155C4×C61—22no—
156C4×C61—81no—
157Dic61—22no—
158Dic61—22no—
159Dic61—21no—
160Dic61—21no—
161Dic61—41no—
162Dic61—81no—
163Dic61—81no—
164#2861—611no—
165C4×C4⋊C8—611no—
166#1745—611no—
167#1272—612no—
168#1270—612no—
169C2×C61—161no—
170C2×C61#146911yescharacteristic
171C2×C61#148311yescharacteristic
172C2×C61#149411yescharacteristic
173C2×C61#150011yescharacteristic
174C2×C61#150911yescharacteristic
175C2×C61#152511yescharacteristic
176C2×C61#155111yescharacteristic
177C2×#125—611no—
178C2×#124—611no—
179C2×C4⋊C8—1221no—
180C2×#97—1221no—
181C2×C4×C8—1221no—
182#391—611no—
183#391—611no—
184#390—611no—
185#390#692311yescharacteristic
186#388—1221no—
187#388—1221no—
188#388—1221no—
189#388—1221no—
190C43—611no—
191#336—612no—
192#336—612no—
193#336—1221no—
194C61#767611yescharacteristic, complemented, Sylow
195C22×Q8—611no—
196C22×D4C2×#692311yescharacteristic
197C22×C8—1222no—
198C22×C8—1222no—
199#125—2442no—
200#124—2442no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4C2×#692311yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—1221no—
208C2×C22⋊C4—1221no—
209C2×C22⋊C4—1221no—
210C2×C22⋊C4—1221no—
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—611no—
214C2×C42—611no—
215C2×C42—611no—
216C2×C42—611no—
217C2×C42C2×#692311yescharacteristic
218C4⋊C8—1224no—
219#97—1224no—
220C4×C8—2442no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225C24—21no—
226C2×Q8—1222no—
227C2×Q8—2441no—
228C2×Q8—2441no—
229C2×D4—22no—
230C2×D4—41no—
231C2×D4—41no—
232C22×C4—21no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4C22⋊#692311yescharacteristic
240C22×C4C22⋊#692311yescharacteristic
241C22×C4C22×#692311yescharacteristic
242C2×C8—1224no—
243C2×C8—1224no—
244C2×C8—2442no—
245C2×C8—2442no—
246C2×C8—2442no—
247C2×C8—2442no—
248C4⋊C4—41no—
249C4⋊C4—2441no—
250C4⋊C4—2442no—
251C4⋊C4—2442no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—2442no—
255C22⋊C4—2441no—
256C22⋊C4—2441no—
257C22⋊C4—2442no—
258C22⋊C4—2442no—
259C42—22no—
260C42—1221no—
261C42—1222no—
262C42—1221no—
263C42—1222no—
264C42—1222no—
265C42—1222no—
266C42—2441no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23C2×C22⋊#692311yescharacteristic
275Q8—4882no—
276D4—82no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—612no—
287C2×C4—612no—
288C2×C4—611no—
289C2×C4—611no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4#1451984112yes—
306C2×C4#1451984112yes—
307C2×C4#1451986412yes—
308C8—2444no—
309C8—2444no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22#1684073511yescharacteristic
318C22#1684074111yescharacteristic
319C22D61⋊#10011yescharacteristic
320C22#1684075211yescharacteristic
321C22#1684075311yescharacteristic
322C22C2×#1451984111yescharacteristic
323C22C2×#1451984111yescharacteristic
324C4—22no—
325C4—22no—
326C4—22no—
327C4—81no—
328C4—1222no—
329C4—1222no—
330C4—1221no—
331C4—1221no—
332C4—4881no—
333C4—4881no—
334C4—2441no—
335C2—161no—
336C2#2146108811yescharacteristic
337C2#2146113411yescharacteristic
338C2#2146117011yescharacteristic
339C2#2146119011yescharacteristic
340C2#2146122111yescharacteristic
341C2#2146127411yescharacteristic
342C2#2146133911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#7676
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊#92420C2semidirect
2. #21461536C2semidirect
3. #21460640C2semidirect
194. C61#7676semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#924202
#214615362
#214606402
#214606352
#214541902
#767661