Finite Group Databasebeta

← #30601778

Subgroups — #30601778

Order 15616.

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

normal subgroups only

This group has 482 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
1#21461604C211yesmaximal, characteristic, complemented
2#21461536C211yesmaximal, characteristic, complemented
3C2×#16840619C212yesmaximal, complemented
4C2×#16840617C212yesmaximal
5#21454190C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519832C2212yes—
8C2×#14519832C2212yes—
9#16840628—21no—
10#16840628—21no—
11#16840628—21no—
12#16840619—24no—
13#16840617—24no—
14C2×#14519768C2211yescharacteristic
15C2×#14519764C2211yescharacteristic
16#16839668C411yescharacteristic
17#16839667C411yescharacteristic
18#16839665C411yescharacteristic
19#16839655—21no—
20#16839655—21no—
21#16839650—21no—
22#16839650—21no—
23C42×Dic61C2211yescharacteristic
24C61×#390C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27#14519844—24no—
28#14519832—22no—
29#14519832—22no—
30#14519832—22no—
31#14519832D414yes—
32C22×Dic122C2×C411yescharacteristic
33#14519768—22no—
34#14519768—22no—
35#14519764—22no—
36#14519764—22no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61C2311yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54C22×D4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C42×C61C2×C411yescharacteristic
59C24×C61—21no—
60C2×D4×C61—22no—
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C2×Dic122—22no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×#92420—24no—
77C2×#92420—24no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C4⋊C4×C61—22no—
83C22⋊C4×C61—42no—
84C22⋊C4×C61—42no—
85C42×C61—41no—
86C22⋊Dic61—42no—
87C22⋊Dic61—42no—
88C22⋊Dic61—42no—
89C22⋊Dic61—41no—
90C22⋊Dic61—41no—
91C4⋊Dic61—22no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94#11758196—42no—
95C4×Dic61—22no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C4×Dic61C2×D412yes—
101C4×Dic61#4112yes—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61C2×C22⋊C411yescharacteristic
110D4×C61—82no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61C4×D412yes—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61#10412yes—
139C2×Dic61#12112yes—
140C2×Dic61#12411yescharacteristic
141C2×Dic61#12711yescharacteristic
142Dic122—82no—
143#92420—44no—
144#92420—44no—
145#9688—611nomaximal, Sylow
146C22×C61—81no—
147C22×C61—81no—
148C22×C61—81no—
149C22×C61—81no—
150C22×C61—81no—
151C22×C61—81no—
152C22×C61—81no—
153C22×C61#39011yescharacteristic
154C22×C61#41311yescharacteristic
155C22×C61#41311yescharacteristic
156C22×C61C2×#10411yescharacteristic
157C22×C61#42111yescharacteristic
158C22×C61#42111yescharacteristic
159C22×C61#42111yescharacteristic
160C4×C61—22no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—81no—
164Dic61—22no—
165Dic61—21no—
166Dic61—21no—
167Dic61—22no—
168Dic61—41no—
169Dic61—81no—
170Dic61—81no—
171#2861—611no—
172#1767—611no—
173#1745—611no—
174C2×#330—612no—
175C2×#329—612no—
176C2×C61—161no—
177C2×C61#152911yescharacteristic
178C2×C61#153211yescharacteristic
179C2×C61#153511yescharacteristic
180C2×C61#153511yescharacteristic
181C2×C61#196311yescharacteristic
182C2×C61#196711yescharacteristic
183C2×C61#198011yescharacteristic
184C2×#125—611no—
185C2×#124—611no—
186C2×C4⋊C8—1221no—
187C2×#97—612no—
188C2×#97—612no—
189#391—611no—
190#391—611no—
191#390—611no—
192#390#692311yescharacteristic
193#388—1221no—
194#388—1221no—
195#388—1221no—
196#388—1221no—
197C43—611no—
198#336—1221no—
199#336—1221no—
200#336—1221no—
201#330—1224no—
202#329—1224no—
203C61#968811yescharacteristic, complemented, Sylow
204C22×Q8—611no—
205C22×D4C2×#692311yescharacteristic
206C22×C8—1222no—
207C22×C8—1222no—
208#125—1222no—
209#125—1222no—
210#124—1222no—
211#124—1222no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4C2×#692311yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—611no—
226C2×C42—611no—
227C2×C42—611no—
228C2×C42C2×#692311yescharacteristic
229C4⋊C8—1224no—
230#97—614no—
231#97—1222no—
232#97—1222no—
233#97—1222no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238C24—21no—
239C2×Q8—1222no—
240C2×Q8—2441no—
241C2×Q8—2441no—
242C2×D4—22no—
243C2×D4—41no—
244C2×D4—41no—
245C22×C4—21no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4C22⋊#692311yescharacteristic
253C22×C4C22⋊#692311yescharacteristic
254C22×C4C22×#692311yescharacteristic
255C2×C8—1224no—
256C2×C8—1224no—
257C2×C8—2442no—
258C2×C8—2442no—
259C2×C8—2442no—
260C2×C8—2442no—
261C4⋊C4—22no—
262C4⋊C4—1222no—
263C4⋊C4—2442no—
264C4⋊C4—2441no—
265C4⋊C4—2441no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—2442no—
269C22⋊C4—2442no—
270C22⋊C4—2441no—
271C22⋊C4—2441no—
272C22⋊C4—2442no—
273C42—41no—
274C42—612no—
275C42—612no—
276C42—1222no—
277C42—2441no—
278C42—2441no—
279C42—2441no—
280C42—2441no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23C2×C22⋊#692311yescharacteristic
289Q8—4882no—
290D4—82no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—612no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—612no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4D4×#692312yes—
322C8—2444no—
323C8—2444no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22#1684071411yescharacteristic
332C22#1684074811yescharacteristic
333C22#1684074911yescharacteristic
334C22D61⋊#10411yescharacteristic
335C22#1684075911yescharacteristic
336C22#1684076011yescharacteristic
337C22#1684076011yescharacteristic
338C4—22no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—1222no—
343C4—1222no—
344C4—1221no—
345C4—1221no—
346C4—4881no—
347C4—4881no—
348C4—2441no—
349C2—161no—
350C2#2146128511yescharacteristic
351C2#2146129411yescharacteristic
352C2#2146130311yescharacteristic
353C2#2146130411yescharacteristic
354C2#2146195711yescharacteristic
355C2#2146196311yescharacteristic
356C2#2146198411yescharacteristic
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#9688
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. #21461604C2semidirect
2. #21461536C2semidirect
3. C2×#16840619C2semidirect
203. C61#9688semidirect

Maximal subgroups

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

subgroupindex
#214616042
#214615362
C2×#168406192
C2×#168406172
#214541902
#968861