Finite Group Databasebeta

← #30601775

Subgroups — #30601775

Order 15616.

482 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 96 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#21461605C211yesmaximal, characteristic, complemented
2#21461536C211yesmaximal, characteristic, complemented
3C2×#16840619C212yesmaximal, complemented
4C2×#16840618C212yesmaximal
5#21454193C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×#14519832C2212yes—
8C2×#14519832C2212yes—
9#16840628—21no—
10#16840628—21no—
11#16840628—21no—
12#16840619—24no—
13#16840618—24no—
14C2×#14519768C2211yescharacteristic
15C2×#14519766C2211yescharacteristic
16#16839669C411yescharacteristic
17#16839664C411yescharacteristic
18#16839663C411yescharacteristic
19#16839654—21no—
20#16839654—21no—
21#16839651—21no—
22#16839651—21no—
23C42×Dic61C2211yescharacteristic
24C61×#391C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27C4⋊#92420—24no—
28#14519832—22no—
29#14519832—22no—
30#14519832—22no—
31#14519832D414yes—
32C22×D244C2×C411yescharacteristic
33#14519768—22no—
34#14519768—22no—
35#14519766—22no—
36#14519766—22no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61C2311yescharacteristic
52#14519684—21no—
53#14519684—21no—
54C22×Q8×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57#95×C61—21no—
58#95×C61—21no—
59C23×D61—21no—
60C2×Q8×C61—22no—
61C2×Q8×C61—41no—
62C2×Q8×C61—41no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C2×D244—22no—
74C2×D244—41no—
75C2×D244—41no—
76C2×#92420—24no—
77C2×#92420—24no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C4⋊C4×C61—22no—
83C42×C61—41no—
84#11758198—42no—
85#11758198—42no—
86#11758198—42no—
87#11758198—42no—
88#11758198—42no—
89#11758198—41no—
90#11758198—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×C61C2×C22⋊C411yescharacteristic
103C22×D61—41no—
104C22×D61—41no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—41no—
110Q8×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—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61#10412yes—
125C2×C4×C61C4×D412yes—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61#12112yes—
140C2×Dic61#12411yescharacteristic
141C2×Dic61#12711yescharacteristic
142D244—82no—
143#92420—44no—
144#92420—44no—
145#9688—611nomaximal, Sylow
146C22×C61#39011yescharacteristic
147C22×C61#41311yescharacteristic
148C22×C61#41311yescharacteristic
149C22×C61C2×#10411yescharacteristic
150C22×C61#42111yescharacteristic
151C22×C61#42111yescharacteristic
152C22×C61#42111yescharacteristic
153C2×D61—81no—
154C2×D61—81no—
155C2×D61—81no—
156C2×D61—81no—
157C2×D61—81no—
158C2×D61—81no—
159C2×D61—81no—
160C4×C61—22no—
161C4×C61—22no—
162C4×C61—41no—
163C4×C61—81no—
164C4×C61—81no—
165Dic61—22no—
166Dic61—21no—
167Dic61—21no—
168Dic61—41no—
169Dic61—41no—
170Dic61—81no—
171#2861—611no—
172#1767—611no—
173#1745—611no—
174C2×#330—612no—
175C2×#329—612no—
176C2×C61#152911yescharacteristic
177C2×C61#153211yescharacteristic
178C2×C61#153511yescharacteristic
179C2×C61#153511yescharacteristic
180C2×C61#196311yescharacteristic
181C2×C61#196711yescharacteristic
182C2×C61#198011yescharacteristic
183D61—161no—
184C2×#125—611no—
185C2×#124—611no—
186C2×C4⋊C8—1221no—
187C2×#97—612no—
188C2×#97—612no—
189#391—611no—
190#391#692311yescharacteristic
191#390—611no—
192#390—611no—
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×Q8C2×#692311yescharacteristic
205C22×D4—611no—
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—1221no—
217C2×C22⋊C4—1221no—
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—21no—
235#95—21no—
236#95—1221no—
237#95—1221no—
238C24—1221no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×D4—1222no—
243C2×D4—2441no—
244C2×D4—2441no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
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—2442no—
267C22⋊C4—2442no—
268C22⋊C4—2441no—
269C22⋊C4—2441no—
270C22⋊C4—2442no—
271C22⋊C4—2442no—
272C22⋊C4—2442no—
273C42—41no—
274C42—612no—
275C42—612no—
276C42—1222no—
277C42—2441no—
278C42—2441no—
279C42—2441no—
280C42—2441no—
281C23—2441no—
282C23—2441no—
283C23—2441no—
284C23—2441no—
285C23—2441no—
286C23—2441no—
287C23—2441no—
288C23C2×C22⋊#692311yescharacteristic
289Q8—82no—
290D4—4882no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—612no—
305C2×C4—611no—
306C2×C4—611no—
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—1221no—
316C2×C4—1221no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4#1451984212yes—
321C2×C4D4×#692312yes—
322C8—2444no—
323C8—2444no—
324C22—4881no—
325C22—4881no—
326C22—4881no—
327C22—4881no—
328C22—4881no—
329C22—4881no—
330C22—4881no—
331C22#1684071411yescharacteristic
332C22#1684074811yescharacteristic
333C22#1684074911yescharacteristic
334C22C2×#1451984211yescharacteristic
335C22#1684075911yescharacteristic
336C22#1684075911yescharacteristic
337C22#1684076111yescharacteristic
338C4—22no—
339C4—22no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—1222no—
344C4—1221no—
345C4—1221no—
346C4—4881no—
347C4—2441no—
348C4—2441no—
349C2—9761no—
350C2#2146128611yescharacteristic
351C2#2146129711yescharacteristic
352C2#2146130511yescharacteristic
353C2#2146130611yescharacteristic
354C2#2146195611yescharacteristic
355C2#2146196311yescharacteristic
356C2#2146198211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#9688
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #21461605C2semidirect
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
#214616052
#214615362
C2×#168406192
C2×#168406182
#214541932
#968861