Finite Group Databasebeta

← #30600476

Subgroups — #30600476

Order 15616.

432 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 86 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#21462518C211yesmaximal, characteristic
2#21461335C211yesmaximal, characteristic, complemented
3D61⋊#333C211yesmaximal, characteristic, complemented
4#21461117C211yesmaximal, characteristic
5#21460709C211yesmaximal, characteristic, complemented
6#21460688C211yesmaximal, characteristic, complemented
7#21455629C211yesmaximal, characteristic
8#16840787—22no—
9#16840785—21no—
10#16840780—21no—
11#16840780C2211yescharacteristic
12#16840767C2211yescharacteristic
13D61⋊(C4⋊C8)C2211yescharacteristic
14D61⋊(C4⋊C8)C2211yescharacteristic
15#16840737—21no—
16#16840727—21no—
17#16840622—21no—
18#16840622—21no—
19#16840621—22no—
20Q8⋊#92420—21no—
21#16840610—21no—
22C4⋊Q8×D61C2211yescharacteristic
23C4×#11758226C2211yescharacteristic
24#16840055—21no—
25#16840051—21no—
26#16840047C411yescharacteristic
27#16840043C411yescharacteristic
28#16840039C411yescharacteristic
29#16839801—21no—
30#16839784C2211yescharacteristic
31#16839762—21no—
32C61×#475C411yescharacteristic
33C2×#11758213—21no—
34C2×D61⋊C8—21no—
35C2×D61⋊C8—21no—
36#14519844—21no—
37#14519844—21no—
38#14519844—21no—
39#14519844D411yescharacteristic
40#14519844D411yescharacteristic
41#14519844D412yes—
42C4⋊#92420—21no—
43C4⋊#92420—21no—
44#14519834—22no—
45#14519834—22no—
46#14519834—21no—
47#14519832—22no—
48C4×#92420—22no—
49C4×#92420—21no—
50C2×#11758226D411yescharacteristic
51C2×Q8×D61—21no—
52C2×#11758189—21no—
53#14519777C2×C411yescharacteristic
54#14519776—21no—
55#14519776—21no—
56#14519775—21no—
57Q8×Dic61D411yescharacteristic
58C4×D244—21no—
59C4×D244C2×C411yescharacteristic
60#14519739—21no—
61#14519739D411yescharacteristic
62#14519735—21no—
63#14519735D411yescharacteristic
64C4⋊C4×D61—21no—
65C4⋊C4×D61—21no—
66C42×D61—21no—
67C42×D61C2311yescharacteristic
68#14519711—21no—
69#14519710—21no—
70#14519708—21no—
71C4⋊#92418C2×C411yescharacteristic
72#14519706—21no—
73#14519701—21no—
74#14519699—21no—
75#14519697—21no—
76C4⋊Q8×C61C2×C411yescharacteristic
77C4×Q8×C61C2×C411yescharacteristic
78#106×C61—21no—
79C4⋊C8×C61C2×C411yescharacteristic
80#103×C61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61C22⋊C411yescharacteristic
83#11758226—21no—
84#11758226—21no—
85#11758226—21no—
86#11758226—21no—
87Q8×D61—82no—
88C2×D244—21no—
89C2×D244C22⋊C411yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—41no—
94C2×C4×D61C2×D411yescharacteristic
95C2×C4×D61#4111yescharacteristic
96C2×C4×D61#4111yescharacteristic
97C2×Dic122—21no—
98C2×Dic122—41no—
99C2×#92420—21no—
100C2×#92420—22no—
101C2×#92420—21no—
102C2×#92420—41no—
103C2×#92420—41no—
104#11758213—41no—
105#11758213—41no—
106D61⋊C8—41no—
107D61⋊C8—41no—
108D61⋊C8—81no—
109C2×C8×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61C22⋊C411yescharacteristic
114C42×C61—21no—
115C42×C61C22×C411yescharacteristic
116#11758198—21no—
117#11758198—21no—
118#11758198—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61C22⋊C411yescharacteristic
123#11758196—41no—
124#11758196—41no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61C2×D411yescharacteristic
128C4×Dic61C2×D411yescharacteristic
129C4×Dic61C2×D411yescharacteristic
130C2×#92418—21no—
131#11758189—41no—
132#11758189—41no—
133C22×D61—21no—
134C22×D61#12311yescharacteristic
135Q8×C61—21no—
136Q8×C61—21no—
137Q8×C61—81no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61C2×C22⋊C411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×Dic61—21no—
145C2×Dic61—41no—
146C2×Dic61#12011yescharacteristic
147C2×Dic61#12111yescharacteristic
148C2×Dic61#12111yescharacteristic
149D244—21no—
150D244—21no—
151D244—41no—
152D244—41no—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—41no—
156C4×D61—41no—
157C4×D61—41no—
158C4×D61—41no—
159C4×D61—41no—
160C4×D61—81no—
161C4×D61—82no—
162C4×D61#13511yescharacteristic
163C4×D61#13511yescharacteristic
164C4×D61#13711yescharacteristic
165C4×D61#13711yescharacteristic
166Dic122—82no—
167Dic122—81no—
168#92420—41no—
169#92420—41no—
170#92420—42no—
171#92420—81no—
172#92420—81no—
173C8×C61—41no—
174#92418—41no—
175#9170—611nomaximal, Sylow
176C22×C61#38611yescharacteristic
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61#48511yescharacteristic
183C2×D61#48511yescharacteristic
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61—81no—
189C4×C61#41611yescharacteristic
190C4×C61#41911yescharacteristic
191Dic61—21no—
192Dic61—41no—
193Dic61—81no—
194Dic61#45211yescharacteristic
195Dic61#45211yescharacteristic
196Dic61#47111yescharacteristic
197Dic61#47311yescharacteristic
198#3079—611no—
199#2925—611no—
200#1549—611no—
201C2×#333—611no—
202#1477—611no—
203#1301—611no—
204#1292—611no—
205C2×C61#187311yescharacteristic
206C2×C61#190311yescharacteristic
207C2×C61#190811yescharacteristic
208D61—21no—
209D61—21no—
210D61—81no—
211C2×C4⋊Q8—611no—
212C4×#41—611no—
213#477—1221no—
214#476—1221no—
215#475—611no—
216#475#692311yescharacteristic
217#474—611no—
218#474—611no—
219#433—1222no—
220#432—1221no—
221#431—611no—
222#431—1221no—
223#428—1221no—
224#423—611no—
225#423—611no—
226C2×C4⋊C8—611no—
227C2×C4⋊C8—611no—
228#417—1221no—
229#408—1221no—
230#405—1221no—
231#333—1221no—
232#333—1221no—
233#332—1222no—
234Q8⋊C8—1221no—
235D4⋊C8—1221no—
236C61#917011yescharacteristic, complemented, Sylow
237C2×#41—611no—
238C22×Q8—1221no—
239C2×M16—1221no—
240C2×M16—1221no—
241C22×C8—1221no—
242C22×C8—1221no—
243C4⋊Q8—611no—
244C4⋊Q8—1221no—
245C4⋊Q8—1221no—
246C4⋊Q8—1221no—
247C4⋊Q8C2×#692311yescharacteristic
248C4×Q8—611no—
249C4×Q8C2×#692311yescharacteristic
250C4×D4—611no—
251C4×D4—611no—
252C4×D4—1221no—
253C4×D4—1221no—
254#117—611no—
255#117—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1221no—
258C2×C42—611no—
259C2×C42—1221no—
260#107—1221no—
261#107—1221no—
262#106—21no—
263#106—1221no—
264C4⋊C8—612no—
265C4⋊C8—611no—
266C4⋊C8—611no—
267C4⋊C8—611no—
268C4⋊C8—1221no—
269C4⋊C8—1221no—
270C4⋊C8—1221no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274C4⋊C8C2×#692311yescharacteristic
275#103—21no—
276#103—1221no—
277#102—1221no—
278#102—1221no—
279C22⋊C8—1222no—
280C22⋊C8—1222no—
281C22⋊C8—1221no—
282#97—1222no—
283C4×C8—1221no—
284C4×C8—1222no—
285#41—1221no—
286#41—1221no—
287#41—1221no—
288#41—1221no—
289C2×Q8—21no—
290C2×Q8—1221no—
291C2×Q8—4882no—
292C2×Q8—2441no—
293C2×Q8C22⋊#692311yescharacteristic
294C2×D4—611no—
295C2×D4—1221no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—2441no—
303M16—2441no—
304M16—2441no—
305M16—2441no—
306M16—2441no—
307C2×C8—21no—
308C2×C8—1221no—
309C2×C8—1222no—
310C2×C8—1221no—
311C2×C8—1221no—
312C2×C8—4881no—
313C2×C8—2441no—
314C2×C8—2441no—
315C2×C8—2441no—
316C2×C8—2441no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—611no—
321C4⋊C4—1221no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C4⋊C4—2441no—
325C4⋊C4—2441no—
326C4⋊C4C22⋊#692311yescharacteristic
327C22⋊C4—1221no—
328C22⋊C4—1221no—
329C22⋊C4—1221no—
330C42—21no—
331C42—611no—
332C42—611no—
333C42—611no—
334C42—1221no—
335C42—1221no—
336C42C22×#692311yescharacteristic
337C23—611no—
338C23—1221no—
339Q8—21no—
340Q8—21no—
341Q8—81no—
342Q8—4881no—
343Q8—4882no—
344D4—1221no—
345D4—1221no—
346D4—2441no—
347D4—2441no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—611no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—4881no—
362C2×C4—4882no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4C2×C22⋊#692311yescharacteristic
370C2×C4D4×#692311yescharacteristic
371C2×C4D4×#692311yescharacteristic
372C8—41no—
373C8—4881no—
374C8—4881no—
375C8—2441no—
376C8—2441no—
377C8—2442no—
378C8—2441no—
379C22—611no—
380C22—611no—
381C22—1221no—
382C22—1221no—
383C22—2441no—
384C22—2441no—
385C22—2441no—
386C22#1684071011yescharacteristic
387C4—21no—
388C4—21no—
389C4—41no—
390C4—41no—
391C4—81no—
392C4—611no—
393C4—611no—
394C4—611no—
395C4—611no—
396C4—1221no—
397C4—4881no—
398C4—2441no—
399C4#1684075211yescharacteristic
400C4#1684075511yescharacteristic
401C2—1221no—
402C2—1221no—
403C2—4881no—
404C2#2146180511yescharacteristic
405C2#2146185111yescharacteristic
406C2#2146185911yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#475C4
socleC22×C61#386
prime radicalC2×#11758226D4
cosocleC42×D61C23
hypercenter#475#6923
hypocenterC61#9170
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #21461335C2semidirect
3. D61⋊#333C2semidirect
5. #21460709C2semidirect
6. #21460688C2semidirect
236. C61#9170semidirect

Maximal subgroups

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

subgroupindex
#214625182
#214613352
D61⋊#3332
#214611172
#214607092
#214606882
#214556292
#917061