Finite Group Databasebeta

← #29579379

Subgroups — #29579379

Order 15616.

416 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456142C211yesmaximal, characteristic
2#21445686C211yesmaximal, characteristic, complemented
3#21444319C211yesmaximal, characteristic, complemented
4#21444315C211yesmaximal, characteristic
5#21444223C211yesmaximal, characteristic, complemented
6#21444219C211yesmaximal, characteristic
7C61×#1564C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9#16840312C2211yescharacteristic
10#16840117—21no—
11#16840117—21no—
12#16840113C411yescharacteristic, complemented
13#16840113C411yescharacteristic, complemented
14#16840109C411yescharacteristic, complemented
15#16840109C411yescharacteristic, complemented
16C2×C4⋊#92418C2211yescharacteristic
17#16839759—21no—
18#16839759—21no—
19C2×#14519687—21no—
20C4×C4⋊Dic61C2211yescharacteristic
21#16839516—21no—
22#16839500—22no—
23#16839497—22no—
24#16839494—22no—
25#16839491—22no—
26C61×#431C2211yescharacteristic
27C61×#431C2211yescharacteristic
28C2×C4×C8×C61C2211yescharacteristic
29C61×#335—21no—
30C61×#334—21no—
31C2×#11758222—21no—
32C22×#92418—21no—
33#14519777C2×C411yescharacteristic
34#14519777C2×C411yescharacteristic
35#14519777C2×C411yescharacteristic
36#14519774C2×C411yescharacteristic
37#14519769—21no—
38#14519765—21no—
39#14519756—21no—
40#14519756—21no—
41#14519751—21no—
42#14519751—21no—
43C4×Dic122—21no—
44C4×Dic122—21no—
45C4×D244—21no—
46C4×D244—21no—
47#14519736—21no—
48C2×C4⋊Dic61—21no—
49C2×C4×Dic61—21no—
50C4⋊#92418—21no—
51C4⋊#92418D412yes—
52#14519702—21no—
53#14519702—21no—
54#14519702—21no—
55#14519702—21no—
56#14519699—21no—
57#14519699—21no—
58#14519699—21no—
59#14519699—21no—
60#14519687—42no—
61#14519684D412yes—
62C22×C8×C61D411yescharacteristic
63C22×C8×C61D411yescharacteristic
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C22⋊C8×C61—21no—
68C22⋊C8×C61—21no—
69C4×C8×C61—21no—
70C4×C8×C61—21no—
71C4×C8×C61C2×C411yescharacteristic
72C4×C8×C61C2×C411yescharacteristic
73C4×C8×C61D411yescharacteristic
74C4×C8×C61D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C2×C22⋊D61—41no—
79C22×Dic61—22no—
80#11758222—41no—
81#11758222—41no—
82#11758222—41no—
83#11758222—41no—
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—21no—
92C2×C8×C61—21no—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61C22⋊C411yescharacteristic
98C2×C8×C61C22⋊C411yescharacteristic
99C2×C8×C61C22⋊C411yescharacteristic
100C2×C8×C61C22⋊C411yescharacteristic
101C42×C61C22×C411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105C22⋊Dic61—41no—
106#11758198—41no—
107#11758198—41no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—42no—
115#11758196—41no—
116#11758196—41no—
117C4×Dic61—41no—
118C4×Dic61—41no—
119C4×Dic61—41no—
120C2×#92418—22no—
121C2×#92418—41no—
122C2×#92418—41no—
123C23×C61#12111yescharacteristic
124C22×D61—41no—
125C2×C4×C61—22no—
126C2×C4×C61—41no—
127C2×C4×C61C2×C22⋊C411yescharacteristic
128C2×C4×C61C4×D411yescharacteristic
129C2×C4×C61C4×D411yescharacteristic
130C2×C4×C61#12111yescharacteristic
131C2×C4×C61#12411yescharacteristic
132C2×C4×C61#12711yescharacteristic
133C2×C4×C61#13511yescharacteristic
134C2×C4×C61#13511yescharacteristic
135C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C61#13711yescharacteristic
137C22⋊D61—81no—
138C22⋊D61—81no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—42no—
145D244—41no—
146D244—41no—
147D244—42no—
148D244—81no—
149C4×D61—81no—
150C4×D61—81no—
151Dic122—41no—
152Dic122—41no—
153Dic122—42no—
154Dic122—81no—
155C8×C61—21no—
156C8×C61—21no—
157C8×C61—21no—
158C8×C61—21no—
159C8×C61—81no—
160C8×C61—81no—
161#92418—42no—
162#9754—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61#39011yescharacteristic
166C22×C61#46311yescharacteristic
167C22×C61#46411yescharacteristic
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61#41611yescharacteristic
175C4×C61#41711yescharacteristic
176C4×C61#44412yes—
177C4×C61#46311yescharacteristic
178C4×C61#46411yescharacteristic
179Dic61—82no—
180Dic61—81no—
181Dic61—81no—
182Dic61—81no—
183#3131—611no—
184#1770—611no—
185#1564D6111yescharacteristic, complemented
186#1503—611no—
187#1502—611no—
188#1481—611no—
189#1480—611no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61#197511yescharacteristic
193C2×C61#197611yescharacteristic
194C2×C61#198311yescharacteristic
195D61—161no—
196#533—611no—
197#532—611no—
198#488—1221no—
199#488—1221no—
200#487—611no—
201#487—611no—
202#486—611no—
203#486—611no—
204#431C2×D6111yescharacteristic
205#431C2×D6111yescharacteristic
206C2×C4⋊C8—611no—
207#416—1221no—
208#416—1221no—
209C2×#97—1221no—
210C2×C4×C8C2×D6111yescharacteristic
211C4×C4⋊C4—611no—
212#336—1221no—
213#335—21no—
214#334—21no—
215#328—1222no—
216#327—1222no—
217Q8⋊C8—1222no—
218D4⋊C8—1222no—
219C61#975411yescharacteristic, complemented, Sylow
220C2×#41—1221no—
221C22×C8—1221no—
222C22×C8D24411yescharacteristic
223C22×C8D24411yescharacteristic
224C4⋊Q8—611no—
225C4⋊Q8—611no—
226C4⋊Q8—611no—
227#127—611no—
228#125—1221no—
229#124—1221no—
230C22⋊Q8—1221no—
231C22⋊Q8—1221no—
232#121—1221no—
233#121—1221no—
234C4×Q8—1221no—
235C4×Q8—1221no—
236C4×D4—1221no—
237C4×D4—1221no—
238#117—1221no—
239C2×C4⋊C4—1221no—
240C2×C42—1221no—
241C2×C42C22×D6111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—612no—
245C4⋊C8—1221no—
246#103—1221no—
247#103—1221no—
248#103—1221no—
249#103—1221no—
250#102—1221no—
251#102—1221no—
252#102—1221no—
253#102—1221no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256#97—2442no—
257C4×C8—21no—
258C4×C8—21no—
259C4×C8C4×D6111yescharacteristic
260C4×C8C4×D6111yescharacteristic
261C4×C8C22⋊D6111yescharacteristic
262C4×C8C22⋊D6111yescharacteristic
263#95—612no—
264#41—2441no—
265#41—2441no—
266#41—2441no—
267#41—2441no—
268C2×Q8—1221no—
269C2×Q8—1221no—
270C2×Q8—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—2441no—
275C22×C4—1222no—
276C22×C4—2441no—
277C22×C4C2×D24411yescharacteristic
278C22×C4D4×D6111yescharacteristic
279C22×C4#1175822611yescharacteristic
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—1222no—
287C2×C8—2441no—
288C2×C8—2441no—
289C2×C8#1175819811yescharacteristic
290C2×C8#1175819811yescharacteristic
291C2×C8#1175819811yescharacteristic
292C2×C8#1175819811yescharacteristic
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—2442no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C42—2441no—
306C42—2441no—
307C42—2441no—
308C42C2×C4×D6111yescharacteristic
309C42D4×D6111yescharacteristic
310C42#1175822611yescharacteristic
311C42C2×C22⋊D6111yescharacteristic
312C23—2441no—
313C23#1451975211yescharacteristic
314Q8—4881no—
315Q8—2441no—
316Q8—2441no—
317Q8—2442no—
318D4—4881no—
319D4—4881no—
320D4—4881no—
321D4—2441no—
322D4—2441no—
323D4—2442no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4C2×#1175819811yescharacteristic
335C2×C4#1451973911yescharacteristic
336C2×C4#1451973911yescharacteristic
337C2×C4#1451975211yescharacteristic
338C2×C4#1451976611yescharacteristic
339C2×C4#1451977311yescharacteristic
340C2×C4#1451979911yescharacteristic
341C2×C4#1451979911yescharacteristic
342C2×C4#1451980511yescharacteristic
343C2×C4#1451981011yescharacteristic
344C8—21no—
345C8—21no—
346C8—21no—
347C8—21no—
348C8—81no—
349C8—81no—
350C8—2442no—
351C22—21no—
352C22—21no—
353C22—4881no—
354C22—4881no—
355C22—4881no—
356C22#1683966311yescharacteristic
357C22#1683997811yescharacteristic
358C22#1683998511yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—4882no—
363C4—4881no—
364C4—4881no—
365C4—4881no—
366C4#1683975911yescharacteristic
367C4#1683976411yescharacteristic
368C4#1683988312yes—
369C4#1683997811yescharacteristic
370C4#1683998511yescharacteristic
371C2—21no—
372C2—21no—
373C2—9761no—
374C2#2144671011yescharacteristic
375C2#2144671511yescharacteristic
376C2#2144674911yescharacteristic
subgroupG/H
centerC2×C4#14519752
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1564C2
socleC22×C61#390
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1564D61
hypocenterC61#9754
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
2. #21445686C2semidirect
3. #21444319C2semidirect
5. #21444223C2semidirect
7. C61×#1564C2semidirect
12. #16840113C4semidirect
13. #16840113C4semidirect
14. #16840109C4semidirect
15. #16840109C4semidirect
185. #1564D61semidirect
219. C61#9754semidirect

Maximal subgroups

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

subgroupindex
#214561422
#214456862
#214443192
#214443152
#214442232
#214442192
C61×#15642
#975461