Finite Group Databasebeta

← #29583140

Subgroups — #29583140

Order 15616.

454 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 93 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#21449113C211yesmaximal, characteristic, complemented
2#21446650C211yesmaximal, characteristic
3#21444315C211yesmaximal, characteristic
4#21444313C211yesmaximal, characteristic
5#21443720C211yesmaximal, characteristic, complemented
6#21443647C211yesmaximal, characteristic, complemented
7C61×#1303C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9C2×C4×Dic122—21no—
10#16839815C2211yescharacteristic
11C2×#14519703—21no—
12C2×#14519703—21no—
13#16839696—21no—
14#16839695—21no—
15#16839683—21no—
16#16839682—21no—
17C4×#11758196—21no—
18C4×C4⋊Dic61C2211yescharacteristic
19#16839608C2211yescharacteristic
20#16839497—21no—
21#16839497—21no—
22#16839495—21no—
23#16839495—21no—
24C61×#431C2211yescharacteristic
25C61×#423C2211yescharacteristic
26C4×C4⋊C4×C61C2211yescharacteristic
27C2×#11758222—21no—
28C22×Dic122—21no—
29#14519777Q811yescharacteristic, complemented
30#14519774Q811yescharacteristic, complemented
31#14519765—21no—
32#14519751—21no—
33#14519751—21no—
34C4×Dic122—42no—
35C4×Dic122—42no—
36C4×D244—21no—
37C4×D244—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C4⋊#92418—21no—
48#14519703—42no—
49#14519703—42no—
50C22⋊#92418—21no—
51C4×#92418—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684D411yescharacteristic
57#14519684D411yescharacteristic
58C2×M16×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C42×C61—21no—
61C2×C42×C61C2311yescharacteristic
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66C4×C8×C61—21no—
67#95×C61D411yescharacteristic
68#95×C61D411yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C2×C22⋊D61—41no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79#11758222—41no—
80#11758222—41no—
81#11758222—41no—
82#11758222—41no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×C4×D61—41no—
87C2×Dic122—21no—
88C2×Dic122—42no—
89C2×Dic122—42no—
90C2×Dic122—42no—
91M16×C61—41no—
92M16×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C4⋊C4×C61—42no—
96C42×C61—41no—
97C42×C61—41no—
98C42×C61C2×Q811yescharacteristic
99C42×C61#4111yescharacteristic
100C42×C61#4111yescharacteristic
101C42×C61#4111yescharacteristic
102#11758198—41no—
103#11758198—41no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—42no—
107C4⋊Dic61—42no—
108#11758196—42no—
109#11758196—42no—
110#11758196—42no—
111#11758196—42no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61—41no—
115C4×Dic61—41no—
116C4×Dic61D812yes—
117C4×Dic61SD1612yes—
118C2×#92418—41no—
119C23×C61#12011yescharacteristic
120C22×D61—41no—
121C2×C4×C61—22no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61C22⋊Q811yescharacteristic
130C2×C4×C61C22⋊Q811yescharacteristic
131C2×C4×C61C22⋊Q811yescharacteristic
132C2×C4×C61#12411yescharacteristic
133C2×C4×C61#12411yescharacteristic
134C2×C4×C61#12411yescharacteristic
135C2×C4×C61C2×D811yescharacteristic
136C2×C4×C61C2×SD1611yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C22⋊D61—81no—
140C22⋊D61—81no—
141C2×Dic61—22no—
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154D244—41no—
155D244—41no—
156D244—81no—
157D244—81no—
158C4×D61—81no—
159C4×D61—81no—
160Dic122—48no—
161Dic122—41no—
162Dic122—41no—
163C8×C61—81no—
164C8×C61—81no—
165#92418—81no—
166#10370—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61#39311yescharacteristic
170C22×C61#44711yescharacteristic
171C22×C61#44811yescharacteristic
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—42no—
180C4×C61—81no—
181C4×C61#47411yescharacteristic
182C4×C61#47611yescharacteristic
183C4×C61#48611yescharacteristic
184C4×C61#48911yescharacteristic
185Dic61—42no—
186Dic61—42no—
187Dic61—42no—
188Dic61—81no—
189Dic61—81no—
190#2399—611no—
191#1963—611no—
192#1502—611no—
193#1502—611no—
194#1303—611no—
195#1303D6111yescharacteristic, complemented
196#1274—611no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61#202311yescharacteristic
200C2×C61#203111yescharacteristic
201C2×C61#203111yescharacteristic
202D61—161no—
203#532—611no—
204C2×C4×Q8—1221no—
205#431—611no—
206#431C2×D6111yescharacteristic
207#423C2×D6111yescharacteristic
208C2×#104—1221no—
209C2×#104—1221no—
210#398—1221no—
211#398—1221no—
212#395—1221no—
213#395—1221no—
214C4×C4⋊C4—611no—
215C4×C4⋊C4—1221no—
216C4×C4⋊C4C2×D6111yescharacteristic
217#376—611no—
218#327—1221no—
219#327—1221no—
220#327—1221no—
221#327—1221no—
222C61#1037011yescharacteristic, complemented, Sylow
223C2×#41—1221no—
224C22×Q8—1221no—
225C2×M16—21no—
226C4⋊Q8—611no—
227#127—611no—
228#124—1221no—
229#121—1221no—
230#121—1221no—
231C4×Q8—2442no—
232C4×Q8—2442no—
233C4×D4—1221no—
234C4×D4—1221no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C42—21no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—1221no—
246C2×C42C22×D6111yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—1221no—
251#104—2442no—
252#104—2442no—
253C22⋊C8—21no—
254C22⋊C8—1221no—
255C4×C8—21no—
256C4×C8—1221no—
257#95—611no—
258#95—611no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263#95D24411yescharacteristic
264#95D24411yescharacteristic
265#41—2441no—
266#41—2441no—
267#41—2441no—
268#41—2441no—
269C2×Q8—1221no—
270C2×Q8—2442no—
271C2×Q8—2442no—
272C2×Q8—2442no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—2441no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—2441no—
284C22×C4C2×D24411yescharacteristic
285C22×C4D4×D6111yescharacteristic
286C22×C4D4×D6111yescharacteristic
287M16—41no—
288M16—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—2441no—
292C4⋊C4—42no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—2442no—
296C4⋊C4—2442no—
297C4⋊C4—2442no—
298C4⋊C4—2442no—
299C4⋊C4—2442no—
300C4⋊C4—2442no—
301C22⋊C4—2441no—
302C22⋊C4—2441no—
303C42—41no—
304C42—41no—
305C42—612no—
306C42—612no—
307C42—1221no—
308C42—1221no—
309C42—2441no—
310C42—2441no—
311C42#1175822211yescharacteristic
312C42#1175822211yescharacteristic
313C42#1175822411yescharacteristic
314C42Q8×D6111yescharacteristic
315C23—2441no—
316C23#1451974711yescharacteristic
317Q8—2448no—
318Q8—2441no—
319Q8—2441no—
320D4—4881no—
321D4—4881no—
322D4—4881no—
323D4—4881no—
324D4—2441no—
325D4—2441no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—1222no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—4881no—
338C2×C4—4881no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4#1451975511yescharacteristic
350C2×C4#1451975511yescharacteristic
351C2×C4#1451975711yescharacteristic
352C2×C4#1451976311yescharacteristic
353C2×C4#1451976311yescharacteristic
354C2×C4#1451976511yescharacteristic
355C2×C4D8×D6111yescharacteristic
356C2×C4SD16×D6111yescharacteristic
357C2×C4#1451980411yescharacteristic
358C2×C4#1451980911yescharacteristic
359C8—81no—
360C8—81no—
361C8—4881no—
362C22—21no—
363C22—21no—
364C22—4881no—
365C22—4881no—
366C22—4881no—
367C22#1683967511yescharacteristic
368C22#1683989711yescharacteristic
369C22#1683990211yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—81no—
376C4—4881no—
377C4—4881no—
378C4—2442no—
379C4—2442no—
380C4—2442no—
381C4#1684004111yescharacteristic
382C4#1684005111yescharacteristic
383C4#1684010711yescharacteristic
384C4#1684012311yescharacteristic
385C2—21no—
386C2—21no—
387C2—9761no—
388C2#2144695411yescharacteristic
389C2#2144699211yescharacteristic
390C2#2144699411yescharacteristic
subgroupG/H
centerC2×C4#14519763
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1303C2
socleC22×C61#393
prime radical#16840312C22
hypercenter#1303D61
hypocenterC61#10370
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
1. #21449113C2semidirect
5. #21443720C2semidirect
6. #21443647C2semidirect
7. C61×#1303C2semidirect
29. #14519777Q8semidirect
30. #14519774Q8semidirect
195. #1303D61semidirect
222. C61#10370semidirect

Maximal subgroups

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

subgroupindex
#214491132
#214466502
#214443152
#214443132
#214437202
#214436472
C61×#13032
#1037061