Finite Group Databasebeta

← #30600471

Subgroups — #30600471

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#21462516C211yesmaximal, characteristic
2#21461333C211yesmaximal, characteristic, complemented
3D61⋊#332C211yesmaximal, characteristic, complemented
4#21461115C211yesmaximal, characteristic
5#21460709C211yesmaximal, characteristic, complemented
6#21460688C211yesmaximal, characteristic, complemented
7#21455631C211yesmaximal, characteristic
8#16840786—22no—
9#16840782—21no—
10#16840780C2211yescharacteristic
11#16840779—21no—
12#16840767C2211yescharacteristic
13D61⋊(C4⋊C8)C2211yescharacteristic
14D61⋊(C4⋊C8)C2211yescharacteristic
15#16840736—21no—
16#16840727—21no—
17#16840622—22no—
18#16840621—21no—
19#16840621—21no—
20#16840612—21no—
21D4⋊#92420—21no—
22C4⋊Q8×D61C2211yescharacteristic
23C4×#11758224C2211yescharacteristic
24#16840058C411yescharacteristic
25#16840054C411yescharacteristic
26#16840052C411yescharacteristic
27#16840046—21no—
28#16840040—21no—
29#16839801—21no—
30#16839784C2211yescharacteristic
31#16839760—21no—
32C61×#476C411yescharacteristic
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—21no—
45C22⋊#92420—22no—
46C22⋊#92420—22no—
47#14519832—22no—
48C4×#92420—22no—
49C4×#92420—21no—
50C2×#11758224D411yescharacteristic
51C2×Q8×D61—21no—
52C2×#11758189—21no—
53#14519777C2×C411yescharacteristic
54#14519776—21no—
55#14519776—21no—
56#14519775—21no—
57C4×Dic122C2×C411yescharacteristic
58#14519742D411yescharacteristic
59D4×Dic61D411yescharacteristic
60C4×C22⋊D61—21no—
61#14519737—21no—
62#14519735D411yescharacteristic
63#14519733—21no—
64C4⋊C4×D61—21no—
65C4⋊C4×D61—21no—
66C2×C4×Dic61—21no—
67C42×D61C2311yescharacteristic
68#14519711—21no—
69#14519710—21no—
70#14519708—21no—
71C4⋊#92418C2×C411yescharacteristic
72#14519706—21no—
73#14519702—21no—
74#14519700—21no—
75#14519698—21no—
76C4⋊Q8×C61C2×C411yescharacteristic
77C4×D4×C61C2×C411yescharacteristic
78#106×C61—21no—
79C4⋊C8×C61C2×C411yescharacteristic
80#102×C61—21no—
81C2×Q8×C61—21no—
82C2×D4×C61C22⋊C411yescharacteristic
83C22×C4×C61—21no—
84C2×C22⋊D61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87Q8×D61—81no—
88Q8×D61—81no—
89#11758224—21no—
90#11758224—21no—
91#11758224—21no—
92#11758224—21no—
93C2×C4×D61—41no—
94C2×C4×D61C2×D411yescharacteristic
95C2×C4×D61#4111yescharacteristic
96C2×C4×D61#4111yescharacteristic
97C2×Dic122—21no—
98C2×Dic122—41no—
99C2×Dic122C22⋊C411yescharacteristic
100C2×#92420—21no—
101C2×#92420—22no—
102C2×#92420—21no—
103C2×#92420—41no—
104C2×#92420—41no—
105#11758213—41no—
106#11758213—41no—
107D61⋊C8—41no—
108D61⋊C8—41no—
109D61⋊C8—81no—
110C2×C8×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61C22⋊C411yescharacteristic
114C22⋊C4×C61—21no—
115C42×C61C22×C411yescharacteristic
116C22⋊Dic61—21no—
117#11758198—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61C22⋊C411yescharacteristic
121#11758196—21no—
122#11758196—21no—
123#11758196—41no—
124#11758196—41no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61C2×D411yescharacteristic
129C4×Dic61C2×D411yescharacteristic
130C4×Dic61C2×D411yescharacteristic
131C2×#92418—21no—
132#11758189—41no—
133#11758189—41no—
134C23×C61—21no—
135C22×D61#12311yescharacteristic
136Q8×C61—81no—
137D4×C61—21no—
138D4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—81no—
142C2×C4×C61C2×C22⋊C411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61C4×D411yescharacteristic
145C22⋊D61—41no—
146C22⋊D61—41no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61#12011yescharacteristic
155C2×Dic61#12111yescharacteristic
156C2×Dic61#12111yescharacteristic
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—41no—
160C4×D61—82no—
161C4×D61#13511yescharacteristic
162C4×D61#13511yescharacteristic
163C4×D61#13711yescharacteristic
164C4×D61#13711yescharacteristic
165Dic122—21no—
166Dic122—21no—
167Dic122—81no—
168Dic122—81no—
169Dic122—81no—
170#92420—41no—
171#92420—41no—
172#92420—42no—
173#92420—81no—
174#92420—81no—
175C8×C61—41no—
176#92418—41no—
177#9168—611nomaximal, Sylow
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61#38611yescharacteristic
182C2×D61—21no—
183C2×D61—21no—
184C2×D61#48511yescharacteristic
185C2×D61#48511yescharacteristic
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—41no—
189C4×C61—81no—
190C4×C61#41611yescharacteristic
191C4×C61#41911yescharacteristic
192Dic61—21no—
193Dic61—41no—
194Dic61—41no—
195Dic61—81no—
196Dic61#45211yescharacteristic
197Dic61#45211yescharacteristic
198Dic61#47111yescharacteristic
199Dic61#47211yescharacteristic
200#3079—611no—
201#2925—611no—
202#1548—611no—
203C2×#332—611no—
204#1477—611no—
205#1301—611no—
206#1292—611no—
207C2×C61—81no—
208C2×C61#187311yescharacteristic
209C2×C61#190211yescharacteristic
210C2×C61#190711yescharacteristic
211D61—21no—
212D61—21no—
213C2×C4⋊Q8—611no—
214C4×#41—611no—
215#477—611no—
216#477—611no—
217#476—611no—
218#476#692311yescharacteristic
219#475—1221no—
220#474—1221no—
221#433—1222no—
222#432—1221no—
223#431—611no—
224#431—1221no—
225#428—1221no—
226#423—611no—
227#423—611no—
228C2×C4⋊C8—611no—
229C2×C4⋊C8—611no—
230#417—1221no—
231#408—1221no—
232#405—1221no—
233#333—1222no—
234#332—1221no—
235#332—1221no—
236Q8⋊C8—1221no—
237D4⋊C8—1221no—
238C61#916811yescharacteristic, complemented, Sylow
239C2×#41—611no—
240C22×Q8—1221no—
241C2×M16—1221no—
242C2×M16—1221no—
243C22×C8—1221no—
244C22×C8—1221no—
245C4⋊Q8—611no—
246C4⋊Q8—1221no—
247C4⋊Q8—1221no—
248C4⋊Q8—1221no—
249C4⋊Q8C2×#692311yescharacteristic
250C4×Q8—611no—
251C4×Q8—611no—
252C4×D4—611no—
253C4×D4—1221no—
254C4×D4—1221no—
255C4×D4C2×#692311yescharacteristic
256#117—611no—
257#117—1221no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4—1221no—
260C2×C42—611no—
261C2×C42—1221no—
262#107—1221no—
263#107—1221no—
264#106—21no—
265#106—1221no—
266C4⋊C8—611no—
267C4⋊C8—611no—
268C4⋊C8—612no—
269C4⋊C8—611no—
270C4⋊C8—1221no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274C4⋊C8—1221no—
275C4⋊C8—1221no—
276C4⋊C8C2×#692311yescharacteristic
277#103—1221no—
278#103—1221no—
279#102—21no—
280#102—1221no—
281C22⋊C8—1222no—
282C22⋊C8—1222no—
283C22⋊C8—1221no—
284#97—1222no—
285C4×C8—1221no—
286C4×C8—1222no—
287#41—1221no—
288#41—1221no—
289#41—1221no—
290#41—1221no—
291C2×Q8—21no—
292C2×Q8—611no—
293C2×Q8—1221no—
294C2×Q8—4881no—
295C2×Q8—4881no—
296C2×Q8—2441no—
297C2×D4—1221no—
298C2×D4C22⋊#692311yescharacteristic
299C22×C4—21no—
300C22×C4—611no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—2441no—
306M16—2441no—
307M16—2441no—
308M16—2441no—
309M16—2441no—
310C2×C8—21no—
311C2×C8—1221no—
312C2×C8—1222no—
313C2×C8—1221no—
314C2×C8—1221no—
315C2×C8—4881no—
316C2×C8—2441no—
317C2×C8—2441no—
318C2×C8—2441no—
319C2×C8—2441no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—611no—
323C4⋊C4—1221no—
324C4⋊C4—1221no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4—2441no—
328C4⋊C4—2441no—
329C4⋊C4C22⋊#692311yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—1221no—
332C22⋊C4—1221no—
333C42—611no—
334C42—611no—
335C42—611no—
336C42—1221no—
337C42—1221no—
338C42—1221no—
339C42C22×#692311yescharacteristic
340C23—21no—
341C23—611no—
342Q8—81no—
343Q8—1221no—
344Q8—1221no—
345Q8—4881no—
346Q8—4881no—
347Q8—4881no—
348D4—21no—
349D4—21no—
350D4—2441no—
351D4—2441no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—81no—
355C2×C4—611no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—611no—
359C2×C4—611no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—4882no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4C2×C22⋊#692311yescharacteristic
374C2×C4D4×#692311yescharacteristic
375C2×C4D4×#692311yescharacteristic
376C8—41no—
377C8—4881no—
378C8—4881no—
379C8—2441no—
380C8—2441no—
381C8—2442no—
382C8—2441no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—611no—
387C22—611no—
388C22—1221no—
389C22—1221no—
390C22#1684071011yescharacteristic
391C4—21no—
392C4—21no—
393C4—41no—
394C4—81no—
395C4—611no—
396C4—611no—
397C4—611no—
398C4—611no—
399C4—1221no—
400C4—4881no—
401C4—2441no—
402C4—2441no—
403C4#1684075211yescharacteristic
404C4#1684075511yescharacteristic
405C2—81no—
406C2—1221no—
407C2—1221no—
408C2#2146180511yescharacteristic
409C2#2146184811yescharacteristic
410C2#2146185811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#476C4
socleC22×C61#386
prime radicalC2×#11758224D4
cosocleC42×D61C23
hypercenter#476#6923
hypocenterC61#9168
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #21461333C2semidirect
3. D61⋊#332C2semidirect
5. #21460709C2semidirect
6. #21460688C2semidirect
238. C61#9168semidirect

Maximal subgroups

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

subgroupindex
#214625162
#214613332
D61⋊#3322
#214611152
#214607092
#214606882
#214556312
#916861