Finite Group Databasebeta

← #30595789

Subgroups — #30595789

Order 15616.

600 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 98 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#21461546C211yesmaximal, characteristic, complemented
2#21461480C211yesmaximal, characteristic, complemented
3#21460639C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21454115C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C2×#14519834—21no—
8C2×#14519832—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519753C411yescharacteristic
13C2×#14519748C411yescharacteristic
14C2×C42×D61C2211yescharacteristic
15#16839669C2211yescharacteristic
16#16839665C2211yescharacteristic
17#16839650—21no—
18#16839650—21no—
19#16839638—21no—
20#16839638—21no—
21#16839628C411yescharacteristic
22C2×#124×C61C411yescharacteristic
23C2×D61⋊C8—24no—
24C2×D61⋊C8—42no—
25C2×D61⋊C8—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28#14519834—24no—
29#14519832—42no—
30C22×C22⋊D61—21no—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519753—42no—
35#14519748—42no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×#11758198—21no—
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46C42×D61—42no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61C2×C411yescharacteristic
52C22×D4×C61C2×C411yescharacteristic
53#124×C61—42no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C42×C61C2×C411yescharacteristic
57C24×C61—21no—
58C23×D61C22⋊C411yescharacteristic
59C2×Q8×C61—22no—
60C2×Q8×C61—41no—
61C2×Q8×C61—41no—
62C2×D4×C61—22no—
63C2×D4×C61—41no—
64C2×D4×C61—41no—
65C22×C4×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C2×C22⋊D61—42no—
70C2×C22⋊D61—42no—
71C2×C22⋊D61—42no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—22no—
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×#92420—24no—
88C2×#92420—24no—
89C2×#92420—42no—
90C2×#92420—42no—
91C2×#92420—42no—
92C2×#92420—42no—
93D61⋊C8—48no—
94C22⋊C4×C61—42no—
95C22⋊C4×C61—42no—
96C42×C61—22no—
97C22⋊Dic61—42no—
98C22⋊Dic61—42no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101#11758198—42no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104#11758196—42no—
105C4×Dic61—22no—
106C4×Dic61—41no—
107C4×Dic61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61C2×C22⋊C411yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61#10012yes—
121C22×D61#10412yes—
122C22×D61#10412yes—
123Q8×C61—82no—
124D4×C61—82no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61#9912yes—
136C2×C4×C61#13112yes—
137C22⋊D61—84no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61#13512yes—
152C2×Dic61AGL(1,ℤ/8)11yescharacteristic
153C2×Dic61#13711yescharacteristic
154C4×D61—24no—
155C4×D61—24no—
156C4×D61—44no—
157C4×D61—44no—
158#92420—44no—
159#92420—44no—
160#7690—611nomaximal, Sylow
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61#40811yescharacteristic
169C22×C61C2×#9911yescharacteristic
170C22×C61C2×#10011yescharacteristic
171C22×C61#41611yescharacteristic
172C22×C61#41711yescharacteristic
173C22×C61C2×#10411yescharacteristic
174C22×C61C2×#10411yescharacteristic
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—22no—
180C2×D61—22no—
181C2×D61#32914yes—
182C4×C61—22no—
183C4×C61—22no—
184C4×C61—41no—
185C4×C61—81no—
186Dic61—22no—
187Dic61—21no—
188Dic61—21no—
189Dic61—41no—
190Dic61—81no—
191Dic61—81no—
192#2850—611no—
193#1749—611no—
194C2×#336—611no—
195#1272—612no—
196#1270—612no—
197C2×C61—161no—
198C2×C61#147111yescharacteristic
199C2×C61#148311yescharacteristic
200C2×C61#149411yescharacteristic
201C2×C61#150111yescharacteristic
202C2×C61#150411yescharacteristic
203C2×C61C2×#32911yescharacteristic
204C2×C61#155111yescharacteristic
205D61—24no—
206C23×C8—1221no—
207C2×#124#692311yescharacteristic
208C2×C22⋊Q8—611no—
209C2×#121—611no—
210C22×C42—611no—
211C2×C22⋊C8—1221no—
212C2×#97—1221no—
213#391—611no—
214#390—611no—
215#388—1221no—
216#388—1221no—
217#386—1221no—
218#386—1221no—
219#382—611no—
220#336—612no—
221#336—612no—
222#336—1221no—
223C61#769011yescharacteristic, complemented, Sylow
224C22×Q8C2×#692311yescharacteristic
225C22×D4—1221no—
226C22×D4C2×#692311yescharacteristic
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—611no—
230C22×C8—1222no—
231C22×C8—1222no—
232C22×C8—1224no—
233C22×C8—2442no—
234C22×C8—2442no—
235#124—42no—
236C22⋊Q8—2442no—
237#121—2442no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—1221no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—2442no—
251C2×C42C2×#692311yescharacteristic
252C22⋊C8—1224no—
253#97—2442no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257#95—1221no—
258C24—21no—
259C24—611no—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×D4—22no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—2442no—
267C2×D4—2442no—
268C2×D4—2442no—
269C22×C4—21no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1222no—
276C22×C4—1222no—
277C22×C4—1222no—
278C22×C4—1222no—
279C22×C4—1222no—
280C22×C4—1222no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4C22⋊#692311yescharacteristic
286C22×C4C22⋊#692311yescharacteristic
287C22×C4C22×#692311yescharacteristic
288C2×C8—1224no—
289C2×C8—1224no—
290C2×C8—2442no—
291C2×C8—2442no—
292C2×C8—2442no—
293C2×C8—2448no—
294C2×C8—2442no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2442no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—2442no—
301C22⋊C4—2442no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2442no—
305C42—22no—
306C42—1222no—
307C42—2441no—
308C42—2441no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—612no—
317C23—612no—
318C23—612no—
319C23—1221no—
320C23—1221no—
321C23—1221no—
322C23—1221no—
323C23C2×C22⋊#692311yescharacteristic
324Q8—82no—
325D4—82no—
326D4—4884no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—612no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—1224no—
341C2×C4—1224no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—2444no—
350C2×C4—2444no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4#1451983512yes—
358C2×C4#1451986412yes—
359C8—2444no—
360C8—2444no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—614no—
369C22—1222no—
370C22—1222no—
371C22—1222no—
372C22—1222no—
373C22—1222no—
374C22—1222no—
375C22#1684073611yescharacteristic
376C22C2×#1451983511yescharacteristic
377C22D61⋊#10011yescharacteristic
378C22#1684075211yescharacteristic
379C22#1684075311yescharacteristic
380C22D61⋊#10411yescharacteristic
381C22D61⋊#10411yescharacteristic
382C4—22no—
383C4—22no—
384C4—41no—
385C4—81no—
386C4—1222no—
387C4—1221no—
388C4—1221no—
389C4—4881no—
390C4—4881no—
391C4—2441no—
392C2—161no—
393C2—1224no—
394C2#2146109411yescharacteristic
395C2#2146113511yescharacteristic
396C2#2146117111yescharacteristic
397C2#2146119411yescharacteristic
398C2#2146120511yescharacteristic
399C2D61⋊#32911yescharacteristic
400C2#2146133911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC2×C4×Dic61C23
hypercenterC2×#124#6923
hypocenterC61#7690
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21461546C2semidirect
2. #21461480C2semidirect
3. #21460639C2semidirect
4. #21460635C2semidirect
223. C61#7690semidirect

Maximal subgroups

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

subgroupindex
#214615462
#214614802
#214606392
#214606352
#214541152
#769061