Finite Group Databasebeta

← #30595861

Subgroups — #30595861

Order 15616.

570 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 92 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#21461676C211yesmaximal, characteristic, complemented
2#21461483C211yesmaximal, characteristic, complemented
3#21460639C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21454115C211yesmaximal, characteristic
6C22×#11758213—21no—
7C2×#14519844—21no—
8C2×#14519834—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×#11758213—24no—
24C2×#11758213—42no—
25C2×#11758213—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28#14519844—42no—
29#14519834—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—21no—
84C2×C4×D61—21no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×#92420—24no—
89C2×#92420—42no—
90C2×#92420—42no—
91C2×#92420—42no—
92C2×#92420—42no—
93C2×#92420—42no—
94#11758213—48no—
95C22⋊C4×C61—42no—
96C22⋊C4×C61—42no—
97C42×C61—22no—
98C22⋊Dic61—42no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101C22⋊Dic61—41no—
102C22⋊Dic61—41no—
103#11758198—42no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106#11758196—42no—
107C4×Dic61—22no—
108C4×Dic61—41no—
109C4×Dic61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61#10412yes—
125Q8×C61—82no—
126D4×C61—82no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61#9912yes—
138C2×C4×C61#13112yes—
139C22⋊D61—84no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61#10012yes—
153C2×Dic61AGL(1,ℤ/8)11yescharacteristic
154C2×Dic61AGL(1,ℤ/8)11yescharacteristic
155C2×Dic61#13711yescharacteristic
156C2×Dic61#13711yescharacteristic
157C4×D61—24no—
158C4×D61—24no—
159C4×D61—44no—
160C4×D61—42no—
161C4×D61—42no—
162#92420—44no—
163#92420—82no—
164#7710—611nomaximal, Sylow
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61#40811yescharacteristic
173C22×C61C2×#9911yescharacteristic
174C22×C61C2×#10011yescharacteristic
175C22×C61#41711yescharacteristic
176C22×C61#41711yescharacteristic
177C22×C61C2×#10411yescharacteristic
178C22×C61#42111yescharacteristic
179C2×D61—22no—
180C2×D61—22no—
181C2×D61—22no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C4×C61—22no—
187C4×C61—22no—
188C4×C61—41no—
189C4×C61—81no—
190Dic61—22no—
191Dic61—21no—
192Dic61—21no—
193Dic61—21no—
194Dic61—21no—
195Dic61—81no—
196Dic61—81no—
197#2850—611no—
198#1797—611no—
199#1728—611no—
200#1272—612no—
201#1270—612no—
202C2×C61—161no—
203C2×C61#147111yescharacteristic
204C2×C61#148311yescharacteristic
205C2×C61#149511yescharacteristic
206C2×C61#150411yescharacteristic
207C2×C61#151311yescharacteristic
208C2×C61#152711yescharacteristic
209C2×C61#156011yescharacteristic
210D61—42no—
211C22×M16—1221no—
212C2×#124#692311yescharacteristic
213C2×C22⋊Q8—611no—
214C2×#121—611no—
215C22×C42—611no—
216C2×C4⋊C8—1221no—
217C2×C22⋊C8—1221no—
218#391—611no—
219#390—611no—
220#388—1221no—
221#388—1221no—
222#386—1221no—
223#386—1221no—
224#382—611no—
225#336—612no—
226#336—612no—
227#336—1221no—
228C61#771011yescharacteristic, complemented, Sylow
229C22×Q8C2×#692311yescharacteristic
230C22×D4—1221no—
231C22×D4C2×#692311yescharacteristic
232C23×C4—611no—
233C23×C4—611no—
234C23×C4—611no—
235C2×M16—1224no—
236C2×M16—2442no—
237C2×M16—2442no—
238C22×C8—1222no—
239C22×C8—1222no—
240#124—42no—
241C22⋊Q8—2442no—
242#121—2442no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—1221no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—611no—
255C2×C42—2442no—
256C2×C42C2×#692311yescharacteristic
257C4⋊C8—2442no—
258C22⋊C8—2442no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263C24—21no—
264C24—611no—
265C2×Q8—22no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×D4—22no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—2442no—
272C2×D4—2442no—
273C2×D4—2442no—
274C22×C4—21no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1222no—
282C22×C4—1221no—
283C22×C4—1222no—
284C22×C4—1222no—
285C22×C4—1222no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—2441no—
289C22×C4—2441no—
290C22×C4—2441no—
291C22×C4C22⋊#692311yescharacteristic
292C22×C4C22⋊#692311yescharacteristic
293C22×C4C22×#692311yescharacteristic
294M16—2448no—
295C2×C8—1224no—
296C2×C8—2442no—
297C2×C8—2442no—
298C2×C8—2442no—
299C2×C8—2442no—
300C2×C8—2442no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C4⋊C4—2442no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—2442no—
307C22⋊C4—2442no—
308C22⋊C4—2441no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C42—22no—
313C42—1222no—
314C42—2441no—
315C42—2441no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—612no—
324C23—1221no—
325C23—1221no—
326C23—1221no—
327C23—1221no—
328C23—1221no—
329C23—1221no—
330C23C2×C22⋊#692311yescharacteristic
331Q8—82no—
332D4—82no—
333D4—4884no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—612no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—1224no—
350C2×C4—1224no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—2444no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4#1451983512yes—
367C2×C4#1451986412yes—
368C8—4882no—
369C8—2444no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—1222no—
378C22—1222no—
379C22—1222no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22#1684073611yescharacteristic
385C22C2×#1451983511yescharacteristic
386C22D61⋊#10011yescharacteristic
387C22#1684075311yescharacteristic
388C22#1684075311yescharacteristic
389C22D61⋊#10411yescharacteristic
390C22#1684075911yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—81no—
395C4—1222no—
396C4—1221no—
397C4—1221no—
398C4—1221no—
399C4—1221no—
400C4—4881no—
401C4—4881no—
402C2—161no—
403C2—2442no—
404C2#2146109411yescharacteristic
405C2#2146113511yescharacteristic
406C2#2146117511yescharacteristic
407C2#2146120511yescharacteristic
408C2#2146123411yescharacteristic
409C2#2146127911yescharacteristic
410C2#2146135711yescharacteristic
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#7710
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. #21461676C2semidirect
2. #21461483C2semidirect
3. #21460639C2semidirect
4. #21460635C2semidirect
228. C61#7710semidirect

Maximal subgroups

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

subgroupindex
#214616762
#214614832
#214606392
#214606352
#214541152
#771061