Finite Group Databasebeta

← #30600474

Subgroups — #30600474

Order 15616.

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

normal subgroups only

This group has 478 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#21462467C211yesmaximal, characteristic
2#21461335C211yesmaximal, characteristic, complemented
3D61⋊#333C211yesmaximal, characteristic, complemented
4#21461117C211yesmaximal, characteristic
5#21460709C211yesmaximal, characteristic, complemented
6#21460688C211yesmaximal, characteristic, complemented
7#21455629C211yesmaximal, characteristic
8C2×#14519865—21no—
9#16840780C2211yescharacteristic
10#16840769—21no—
11#16840769—22no—
12#16840767—21no—
13#16840767C2211yescharacteristic
14D61⋊(C4⋊C8)—21no—
15D61⋊(C4⋊C8)C2211yescharacteristic
16D61⋊(C4⋊C8)C2211yescharacteristic
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
33#14519865—42no—
34#14519865—42no—
35C2×#11758213—22no—
36C2×#11758213—21no—
37C2×D61⋊C8—22no—
38C2×D61⋊C8—21no—
39C2×D61⋊C8—21no—
40#14519844—22no—
41#14519844—21no—
42#14519844—21no—
43#14519844—21no—
44#14519844D411yescharacteristic
45#14519844D411yescharacteristic
46#14519844D412yes—
47C4⋊#92420—22no—
48C4⋊#92420—21no—
49C4⋊#92420—21no—
50#14519834—21no—
51C4×#92420—21no—
52C2×#11758226D411yescharacteristic
53C2×Q8×D61—21no—
54C2×#11758189—21no—
55#14519777C2×C411yescharacteristic
56#14519776—21no—
57#14519776—21no—
58#14519775—21no—
59Q8×Dic61D411yescharacteristic
60C4×D244—21no—
61C4×D244C2×C411yescharacteristic
62#14519739—21no—
63#14519739D411yescharacteristic
64#14519735—21no—
65#14519735D411yescharacteristic
66C4⋊C4×D61—21no—
67C4⋊C4×D61—21no—
68C42×D61—21no—
69C42×D61C2311yescharacteristic
70#14519711—21no—
71#14519710—21no—
72#14519708—21no—
73C4⋊#92418C2×C411yescharacteristic
74#14519706—21no—
75#14519701—21no—
76#14519699—21no—
77#14519697—21no—
78C4⋊Q8×C61C2×C411yescharacteristic
79C4×Q8×C61C2×C411yescharacteristic
80#106×C61—21no—
81C4⋊C8×C61C2×C411yescharacteristic
82#103×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61C22⋊C411yescharacteristic
85#11758226—21no—
86#11758226—21no—
87#11758226SD1612yes—
88#11758226Q1612yes—
89Q8×D61—82no—
90C2×D244—21no—
91C2×D244C22⋊C411yescharacteristic
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—41no—
96C2×C4×D61C2×D411yescharacteristic
97C2×C4×D61#4111yescharacteristic
98C2×C4×D61#4111yescharacteristic
99C2×Dic122—21no—
100C2×Dic122—41no—
101C2×#92420—21no—
102C2×#92420—22no—
103C2×#92420—21no—
104C2×#92420—41no—
105C2×#92420—41no—
106#11758213—44no—
107#11758213—41no—
108#11758213—41no—
109D61⋊C8—44no—
110D61⋊C8—41no—
111D61⋊C8—41no—
112D61⋊C8—81no—
113C2×C8×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61C22⋊C411yescharacteristic
118C42×C61—21no—
119C42×C61C22×C411yescharacteristic
120#11758198—21no—
121#11758198—21no—
122#11758198—21no—
123C4⋊Dic61—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61C22⋊C411yescharacteristic
127#11758196—41no—
128#11758196—41no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61C2×D411yescharacteristic
132C4×Dic61C2×D411yescharacteristic
133C4×Dic61C2×D411yescharacteristic
134C2×#92418—21no—
135#11758189—41no—
136#11758189—41no—
137C22×D61—21no—
138C22×D61#12311yescharacteristic
139Q8×C61—21no—
140Q8×C61—81no—
141Q8×C61#10312yes—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61C2×C22⋊C411yescharacteristic
146C2×C4×C61C4×D411yescharacteristic
147C2×C4×C61C4×D411yescharacteristic
148C2×Dic61—21no—
149C2×Dic61—41no—
150C2×Dic61#12011yescharacteristic
151C2×Dic61#12111yescharacteristic
152C2×Dic61#12111yescharacteristic
153D244—22no—
154D244—22no—
155D244—21no—
156D244#10312yes—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—21no—
160C4×D61—21no—
161C4×D61—41no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—81no—
165C4×D61—82no—
166C4×D61C2×SD1611yescharacteristic
167C4×D61C2×Q1611yescharacteristic
168C4×D61AGL(1,ℤ/8)11yescharacteristic
169C4×D61#13711yescharacteristic
170Dic122—82no—
171Dic122—81no—
172#92420—41no—
173#92420—42no—
174#92420—41no—
175#92420—81no—
176#92420—81no—
177C8×C61—41no—
178#92418—41no—
179#9169—611nomaximal, Sylow
180C22×C61#38611yescharacteristic
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—22no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61#48311yescharacteristic
187C2×D61#48411yescharacteristic
188C4×C61—22no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—81no—
193C4×C61C2×#10311yescharacteristic
194C4×C61#41711yescharacteristic
195Dic61—21no—
196Dic61—41no—
197Dic61—81no—
198Dic61#45011yescharacteristic
199Dic61#45111yescharacteristic
200Dic61#47111yescharacteristic
201Dic61#47311yescharacteristic
202#3079—611no—
203#2906—611no—
204#1549—611no—
205C2×#333—611no—
206#1477—611no—
207#1301—611no—
208#1292—611no—
209C2×C61#187211yescharacteristic
210C2×C61#190311yescharacteristic
211C2×C61#190811yescharacteristic
212D61—21no—
213D61—21no—
214D61—42no—
215C2×#131—1221no—
216C2×C4⋊Q8—611no—
217C4×#41—611no—
218#477—1221no—
219#476—1221no—
220#475—611no—
221#475#692311yescharacteristic
222#474—611no—
223#474—611no—
224#431—611no—
225#428—1221no—
226#424—1222no—
227#424—1221no—
228#423—611no—
229#423—611no—
230#423—1221no—
231C2×C4⋊C8—611no—
232C2×C4⋊C8—611no—
233C2×C4⋊C8—1221no—
234#417—1221no—
235#333—1221no—
236#333—1221no—
237#332—1222no—
238Q8⋊C8—1221no—
239D4⋊C8—1221no—
240C61#916911yescharacteristic, complemented, Sylow
241C2×#41—611no—
242C22×Q8—1221no—
243#131—2442no—
244#131—2442no—
245C2×M16—1221no—
246C2×M16—1221no—
247C2×M16—1222no—
248C22×C8—1221no—
249C22×C8—1222no—
250C22×C8—1221no—
251C4⋊Q8—611no—
252C4⋊Q8—1221no—
253C4⋊Q8—1221no—
254C4⋊Q8—1221no—
255C4⋊Q8C2×#692311yescharacteristic
256C4×Q8—611no—
257C4×Q8C2×#692311yescharacteristic
258C4×D4—611no—
259C4×D4—611no—
260C4×D4—1221no—
261C4×D4—1221no—
262#117—611no—
263#117—1221no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4—1221no—
266C2×C42—611no—
267C2×C42—1221no—
268#107—1221no—
269#107—1221no—
270#106—21no—
271#106—1221no—
272C4⋊C8—612no—
273C4⋊C8—611no—
274C4⋊C8—611no—
275C4⋊C8—611no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278C4⋊C8—1221no—
279C4⋊C8—1221no—
280C4⋊C8—1221no—
281C4⋊C8—1221no—
282C4⋊C8—1222no—
283C4⋊C8—1222no—
284C4⋊C8C2×#692311yescharacteristic
285#103—21no—
286#103—1221no—
287#102—1221no—
288#102—1221no—
289C22⋊C8—1221no—
290C4×C8—1221no—
291#41—612no—
292#41—612no—
293#41—1221no—
294#41—1221no—
295C2×Q8—21no—
296C2×Q8—1221no—
297C2×Q8—4882no—
298C2×Q8—2441no—
299C2×Q8C22⋊#692311yescharacteristic
300C2×D4—611no—
301C2×D4—1221no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—2441no—
309M16—2441no—
310M16—2441no—
311M16—2441no—
312M16—2441no—
313M16—2444no—
314C2×C8—21no—
315C2×C8—1221no—
316C2×C8—1222no—
317C2×C8—1221no—
318C2×C8—1221no—
319C2×C8—4881no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8—2444no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—611no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—2441no—
333C4⋊C4—2441no—
334C4⋊C4C22⋊#692311yescharacteristic
335C22⋊C4—1221no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C42—21no—
339C42—611no—
340C42—611no—
341C42—611no—
342C42—1221no—
343C42—1221no—
344C42C22×#692311yescharacteristic
345C23—611no—
346C23—1221no—
347Q8—21no—
348Q8—81no—
349Q8—4881no—
350Q8—4882no—
351Q8#1451984012yes—
352D4—612no—
353D4—1222no—
354D4—1222no—
355D4—1221no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—611no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—611no—
363C2×C4—611no—
364C2×C4—611no—
365C2×C4—611no—
366C2×C4—1221no—
367C2×C4—1222no—
368C2×C4—1221no—
369C2×C4—1222no—
370C2×C4—1221no—
371C2×C4—4881no—
372C2×C4—4882no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4C2×C22⋊#692311yescharacteristic
378C2×C4D4×#692311yescharacteristic
379C2×C4D4×#692311yescharacteristic
380C8—41no—
381C8—4881no—
382C8—4881no—
383C8—2441no—
384C8—2441no—
385C8—2442no—
386C8—2441no—
387C22—611no—
388C22—611no—
389C22—1221no—
390C22—1221no—
391C22—1222no—
392C22—2441no—
393C22—2441no—
394C22#1684071011yescharacteristic
395C4—22no—
396C4—21no—
397C4—21no—
398C4—41no—
399C4—81no—
400C4—611no—
401C4—611no—
402C4—611no—
403C4—611no—
404C4—1221no—
405C4—4881no—
406C4—2441no—
407C4C2×#1451984011yescharacteristic
408C4#1684075311yescharacteristic
409C2—1221no—
410C2—1221no—
411C2—2442no—
412C2#2146180411yescharacteristic
413C2#2146185111yescharacteristic
414C2#2146185911yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#475C4
socleC22×C61#386
prime radicalC2×#11758226D4
cosocleC42×D61C23
hypercenter#475#6923
hypocenterC61#9169
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
240. C61#9169semidirect

Maximal subgroups

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

subgroupindex
#214624672
#214613352
D61⋊#3332
#214611172
#214607092
#214606882
#214556292
#916961