Finite Group Databasebeta

← #29579381

Subgroups — #29579381

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#21444567C211yesmaximal, characteristic, complemented
3#21444317C211yesmaximal, characteristic, complemented
4#21444313C211yesmaximal, characteristic
5#21444221C211yesmaximal, characteristic, complemented
6#21444217C211yesmaximal, characteristic
7C61×#1770C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9#16840312C2211yescharacteristic
10#16840117—21no—
11#16840117—21no—
12#16840113C411yescharacteristic, complemented
13#16840113C411yescharacteristic, complemented
14#16840109C411yescharacteristic, complemented
15#16840109C411yescharacteristic, complemented
16#16839815C2211yescharacteristic
17#16839815C2211yescharacteristic
18#16839759—21no—
19#16839759—21no—
20#16839515—21no—
21#16839513—21no—
22#16839498—22no—
23#16839495—22no—
24#16839492—22no—
25#16839489—22no—
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×#97×C61—21no—
28C2×C4×C8×C61C2211yescharacteristic
29C4×C4⋊C4×C61C2211yescharacteristic
30C61×#336—21no—
31C2×#11758222—21no—
32#14519777C2×C411yescharacteristic
33#14519777C2×C411yescharacteristic
34#14519777C2×C411yescharacteristic
35#14519774C2×C411yescharacteristic
36#14519769—21no—
37#14519765—21no—
38#14519756—21no—
39#14519756—21no—
40#14519751—21no—
41#14519751—21no—
42C4×Dic122—21no—
43C4×Dic122—21no—
44C4×D244—21no—
45C4×D244—21no—
46#14519736—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49#14519702—21no—
50#14519702—21no—
51#14519702—21no—
52#14519702—21no—
53#14519699—21no—
54#14519699—21no—
55#14519699—21no—
56#14519699—21no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59C4×#92418—21no—
60C4×#92418—21no—
61C22×C8×C61—21no—
62C22×C8×C61D411yescharacteristic
63C22×C8×C61D411yescharacteristic
64C2×C4⋊C4×C61—21no—
65C2×C42×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61D412yes—
69#97×C61—42no—
70C4×C8×C61C2×C411yescharacteristic
71C4×C8×C61C2×C411yescharacteristic
72C4×C8×C61D411yescharacteristic
73C4×C8×C61D411yescharacteristic
74#95×C61D412yes—
75C22×C4×C61—22no—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C2×C22⋊D61—41no—
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—22no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61C22⋊C411yescharacteristic
99C2×C8×C61C22⋊C411yescharacteristic
100C2×C8×C61C22⋊C411yescharacteristic
101C2×C8×C61C22⋊C411yescharacteristic
102C4⋊C4×C61—42no—
103C42×C61—41no—
104C42×C61—41no—
105C42×C61C22×C411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61#4111yescharacteristic
109C22⋊Dic61—41no—
110#11758198—41no—
111#11758198—41no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118#11758196—41no—
119#11758196—41no—
120C4×Dic61—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C23×C61#12111yescharacteristic
124C22×D61—41no—
125C2×C4×C61—22no—
126C2×C4×C61—41no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12411yescharacteristic
135C2×C4×C61#12711yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61#13511yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C61#13711yescharacteristic
140C22⋊D61—81no—
141C22⋊D61—81no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
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—42no—
160#92418—81no—
161#92418—81no—
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—82no—
175C4×C61#41611yescharacteristic
176C4×C61#41711yescharacteristic
177C4×C61#44412yes—
178C4×C61#46311yescharacteristic
179C4×C61#46411yescharacteristic
180Dic61—81no—
181Dic61—81no—
182Dic61—81no—
183#3131—611no—
184#1770D6111yescharacteristic, complemented
185#1564—611no—
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#431—611no—
205#431—611no—
206C2×C4⋊C8C2×D6111yescharacteristic
207#416—1221no—
208#416—1221no—
209C2×#97—21no—
210C2×C4×C8C2×D6111yescharacteristic
211C4×C4⋊C4C2×D6111yescharacteristic
212#336—21no—
213#335—1221no—
214#334—1221no—
215#328—1222no—
216#327—1222no—
217Q8⋊C8—1222no—
218D4⋊C8—1222no—
219C61#975411yescharacteristic, complemented, Sylow
220C2×#41—1221no—
221C22×C8—21no—
222C22×C8C22⋊D6111yescharacteristic
223C22×C8C22⋊D6111yescharacteristic
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—21no—
240C2×C42—21no—
241C2×C42C22×D6111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—1221no—
244C4⋊C8—1221no—
245C4⋊C8D24412yes—
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—1221no—
255C22⋊C8—1221no—
256#97—42no—
257C4×C8—1221no—
258C4×C8—1221no—
259C4×C8C4×D6111yescharacteristic
260C4×C8C4×D6111yescharacteristic
261C4×C8D24411yescharacteristic
262C4×C8D24411yescharacteristic
263#95D24412yes—
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—22no—
276C22×C4—2441no—
277C22×C4C2×D24411yescharacteristic
278C22×C4#1175822211yescharacteristic
279C22×C4C2×C22⋊D6111yescharacteristic
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—22no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—2441no—
288C2×C8—2441no—
289C2×C8#1175819811yescharacteristic
290C2×C8#1175819811yescharacteristic
291C2×C8#1175819811yescharacteristic
292C2×C8#1175819811yescharacteristic
293C4⋊C4—42no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C42—41no—
306C42—41no—
307C42—2441no—
308C42C2×C4×D6111yescharacteristic
309C42C2×D24411yescharacteristic
310C42C2×D24411yescharacteristic
311C42#1175822211yescharacteristic
312C23—2441no—
313C23#1451975111yescharacteristic
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—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4C2×#1175819811yescharacteristic
335C2×C4C4×D24411yescharacteristic
336C2×C4C4×D24411yescharacteristic
337C2×C4#1451975111yescharacteristic
338C2×C4#1451976511yescharacteristic
339C2×C4#1451977411yescharacteristic
340C2×C4#1451979711yescharacteristic
341C2×C4#1451979711yescharacteristic
342C2×C4#1451980311yescharacteristic
343C2×C4#1451980811yescharacteristic
344C8—21no—
345C8—21no—
346C8—21no—
347C8—21no—
348C8—42no—
349C8—4881no—
350C8—4881no—
351C22—21no—
352C22—21no—
353C22—4881no—
354C22—4881no—
355C22—4881no—
356C22#1683966411yescharacteristic
357C22#1683997711yescharacteristic
358C22#1683998411yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—4881no—
364C4—4881no—
365C4—4881no—
366C4#1683975611yescharacteristic
367C4#1683976111yescharacteristic
368C4#1683988512yes—
369C4#1683997711yescharacteristic
370C4#1683998411yescharacteristic
371C2—21no—
372C2—21no—
373C2—9761no—
374C2#2144671211yescharacteristic
375C2#2144671711yescharacteristic
376C2#2144675111yescharacteristic
subgroupG/H
centerC2×C4#14519751
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1770C2
socleC22×C61#390
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1770D61
hypocenterC61#9754
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1770

Complements

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

NH ≅ G/Ntype
2. #21444567C2semidirect
3. #21444317C2semidirect
5. #21444221C2semidirect
7. C61×#1770C2semidirect
12. #16840113C4semidirect
13. #16840113C4semidirect
14. #16840109C4semidirect
15. #16840109C4semidirect
184. #1770D61semidirect
219. C61#9754semidirect

Maximal subgroups

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

subgroupindex
#214561422
#214445672
#214443172
#214443132
#214442212
#214442172
C61×#17702
#975461