Finite Group Databasebeta

← #29579187

Subgroups — #29579187

Order 15616.

460 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456378C211yesmaximal, characteristic
2#21446762C211yesmaximal, characteristic, complemented
3#21446737C211yesmaximal, characteristic
4#21444317C211yesmaximal, characteristic, complemented
5#21444313C211yesmaximal, characteristic
6#21444108C211yesmaximal, characteristic, complemented
7C4×#107×C61C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9#16840312C2211yescharacteristic
10#16840160C411yescharacteristic, complemented
11#16840135C411yescharacteristic, complemented
12#16840113C411yescharacteristic, complemented
13#16840109C411yescharacteristic, complemented
14#16839991—21no—
15#16839991—21no—
16C4×#11758190—21no—
17C4×#11758190—21no—
18#16839815C2211yescharacteristic
19C2×#14519705—22no—
20C4×#11758194C2211yescharacteristic
21#16839522—22no—
22#16839498—22no—
23#16839495—22no—
24#16839484—21no—
25#16839483—21no—
26C2×#107×C61—21no—
27C2×C4×C8×C61C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C4×C4⋊C4×C61C2211yescharacteristic
30C61×#340—21no—
31C2×#11758222—21no—
32C2×#11758190—21no—
33C2×#11758190—21no—
34C2×#11758194D412yes—
35#14519777C2×C411yescharacteristic
36#14519777C2×C411yescharacteristic
37#14519777C2×C411yescharacteristic
38#14519774C2×C411yescharacteristic
39#14519769—21no—
40#14519765—21no—
41#14519756—21no—
42#14519756—21no—
43#14519751—21no—
44#14519751—21no—
45C4×Dic122—21no—
46C4×Dic122—21no—
47C4×D244—21no—
48C4×D244—21no—
49#14519736—21no—
50#14519709—21no—
51#14519709—21no—
52C4⋊#92418—21no—
53#14519705—44no—
54#14519702—21no—
55#14519702—21no—
56#14519699—21no—
57#14519699—21no—
58C22⋊#92418D412yes—
59#14519688—21no—
60C4×#92418—21no—
61C4×#92418—21no—
62C22×C8×C61D411yescharacteristic
63C22×C8×C61D411yescharacteristic
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C42×C61—21no—
67C2×C42×C61—21no—
68C2×C42×C61C2311yescharacteristic
69#107×C61—24no—
70C4×C8×C61C2×C411yescharacteristic
71C4×C8×C61C2×C411yescharacteristic
72C4×C8×C61D411yescharacteristic
73C4×C8×C61D411yescharacteristic
74#95×C61—21no—
75#95×C61—21no—
76C22×C4×C61—41no—
77C22×C4×C61—41no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C2×C22⋊D61—41no—
82#11758222—42no—
83#11758222—42no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×C4×D61—41no—
88C2×Dic122—21no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91C2×C8×C61—22no—
92C2×C8×C61—41no—
93C2×C8×C61C22⋊C411yescharacteristic
94C2×C8×C61C22⋊C411yescharacteristic
95C2×C8×C61C22⋊C411yescharacteristic
96C2×C8×C61C22⋊C411yescharacteristic
97C4⋊C4×C61—22no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C42×C61—42no—
102C42×C61—42no—
103C42×C61C22×C411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61#4111yescharacteristic
106C42×C61#4111yescharacteristic
107C22⋊Dic61—41no—
108#11758198—41no—
109#11758198—41no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116#11758196—41no—
117#11758196—41no—
118C4×Dic61—41no—
119#11758194—22no—
120#11758194—22no—
121C2×#92418—22no—
122C2×#92418—22no—
123#11758190—42no—
124#11758190—42no—
125C23×C61#12711yescharacteristic
126C22×D61—41no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—41no—
130C2×C4×C61—42no—
131C2×C4×C61—42no—
132C2×C4×C61—81no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61C2×C22⋊C411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12411yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)12yes—
143C2×C4×C61#13712yes—
144C22⋊D61—81no—
145C22⋊D61—81no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149D244—41no—
150D244—41no—
151D244—42no—
152D244—81no—
153C4×D61—82no—
154Dic122—41no—
155Dic122—41no—
156Dic122—42no—
157Dic122—81no—
158C8×C61—21no—
159C8×C61—21no—
160C8×C61—21no—
161C8×C61#10412yescomplemented
162#92418—42no—
163#92418—42no—
164#9722—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61#39011yescharacteristic
168C22×C61#49611yescharacteristic
169C22×C61#49711yescharacteristic
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—82no—
177C4×C61—82no—
178C4×C61C2×#10411yescharacteristic
179C4×C61#42111yescharacteristic
180C4×C61#44012yes—
181C4×C61#46812yes—
182Dic61—81no—
183Dic61—81no—
184Dic61—81no—
185#3167—611no—
186#1986—611no—
187#1980—611no—
188C4×#107D6111yescharacteristic, complemented
189#1503—611no—
190#1502—611no—
191#1451—611no—
192C2×C61—21no—
193C2×C61—21no—
194C2×C61#197311yescharacteristic
195C2×C61#197611yescharacteristic
196C2×C61#198011yescharacteristic
197D61—161no—
198#533—611no—
199#532—611no—
200#498—611no—
201#492—611no—
202#487—611no—
203#486—611no—
204#465—1221no—
205#465—1221no—
206C4×SD16—1221no—
207C4×SD16—1221no—
208#431—611no—
209C2×#107—21no—
210C2×#104—1222no—
211C4×M16—611no—
212C2×C4×C8C2×D6111yescharacteristic
213C4×C4⋊C4C2×D6111yescharacteristic
214C4×C4⋊C4C2×D6111yescharacteristic
215#340—21no—
216#339—1222no—
217#328—1222no—
218#327—1222no—
219#322—1221no—
220#322—1221no—
221C61#972211yescharacteristic, complemented, Sylow
222C2×#41—1221no—
223C2×SD16—1221no—
224C2×SD16—1221no—
225C2×M16—612no—
226C22×C8C22⋊D6111yescharacteristic
227C22×C8C22⋊D6111yescharacteristic
228C4⋊Q8—611no—
229C4⋊Q8—611no—
230C4⋊Q8—611no—
231#127—611no—
232#125—1221no—
233#124—1221no—
234C22⋊Q8—1221no—
235C22⋊Q8—1221no—
236#121—1221no—
237#121—1221no—
238C4×Q8—1221no—
239C4×Q8—1221no—
240C4×D4—1221no—
241C4×D4—1221no—
242#117—1221no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42C22×D6111yescharacteristic
248#107—24no—
249#106—1221no—
250#106—1221no—
251C4⋊C8—1221no—
252#104—2444no—
253#103—1221no—
254#103—1221no—
255#102—1221no—
256#102—1221no—
257C22⋊C8—612no—
258#97—1221no—
259C4×C8—1221no—
260C4×C8—1221no—
261C4×C8C4×D6111yescharacteristic
262C4×C8C4×D6111yescharacteristic
263C4×C8D24411yescharacteristic
264C4×C8D24411yescharacteristic
265#95—21no—
266#95—21no—
267#41—2442no—
268#41—2442no—
269C2×Q8—1221no—
270C2×Q8—1221no—
271C2×Q8—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—2441no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—2441no—
279C22×C4D4×D6111yescharacteristic
280C22×C4D4×D6111yescharacteristic
281C22×C4C2×C22⋊D6111yescharacteristic
282SD16—2442no—
283SD16—2442no—
284M16—1222no—
285M16—1222no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—1222no—
289C2×C8—1222no—
290C2×C8#1175819811yescharacteristic
291C2×C8#1175819811yescharacteristic
292C2×C8#1175819811yescharacteristic
293C2×C8#1175819811yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C42—42no—
310C42—42no—
311C42—2441no—
312C42C2×C4×D6111yescharacteristic
313C42C2×D24411yescharacteristic
314C42#1175822611yescharacteristic
315C42#1175822611yescharacteristic
316C23—2441no—
317C23#1451977311yescharacteristic
318Q8—4881no—
319Q8—2441no—
320Q8—2441no—
321Q8—2442no—
322D4—4881no—
323D4—4881no—
324D4—4881no—
325D4—2441no—
326D4—2441no—
327D4—2442no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—4882no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4C2×#1175819811yescharacteristic
342C2×C4#1451973911yescharacteristic
343C2×C4#1451973911yescharacteristic
344C2×C4#1451975211yescharacteristic
345C2×C4#1451975211yescharacteristic
346C2×C4#1451976611yescharacteristic
347C2×C4#1451980112yes—
348C2×C4#1451980912yes—
349C8—21no—
350C8—21no—
351C8—21no—
352C8—2442no—
353C8—2442no—
354C8#1451970512yescomplemented
355C22—21no—
356C22—21no—
357C22—4881no—
358C22—4881no—
359C22—4881no—
360C22#1683966311yescharacteristic
361C22#1684015011yescharacteristic
362C22#1684015511yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—4881no—
369C4—4881no—
370C4—4881no—
371C4C2×#1451970511yescharacteristic
372C4#1683978011yescharacteristic
373C4#1683986112yes—
374C4#1684000912yes—
375C2—21no—
376C2—21no—
377C2—9761no—
378C2#2144669811yescharacteristic
379C2#2144671511yescharacteristic
380C2#2144673711yescharacteristic
subgroupG/H
centerC2×C4#14519752
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC4×#107×C61C2
socleC22×C61#390
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenterC4×#107D61
hypocenterC61#9722
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
2. #21446762C2semidirect
4. #21444317C2semidirect
6. #21444108C2semidirect
7. C4×#107×C61C2semidirect
10. #16840160C4semidirect
11. #16840135C4semidirect
12. #16840113C4semidirect
13. #16840109C4semidirect
161. C8×C61#104semidirect
188. C4×#107D61semidirect
221. C61#9722semidirect
354. C8#14519705semidirect

Maximal subgroups

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

subgroupindex
#214563782
#214467622
#214467372
#214443172
#214443132
#214441082
C4×#107×C612
#972261