Finite Group Databasebeta

← #27179788

Subgroups — #27179788

Order 12928.

402 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#117×D101C211yesmaximal, characteristic
2#20265238C211yesmaximal, characteristic, complemented
3#20265235C211yesmaximal, characteristic, complemented
4#20265235C211yesmaximal, characteristic, complemented
5#20265233C211yesmaximal, characteristic, complemented
6#20265232C211yesmaximal, characteristic, complemented
7#20265229C211yesmaximal, characteristic, complemented
8#20265228C211yesmaximal, characteristic, complemented
9#20265202C211yesmaximal, characteristic, complemented
10#20265202C211yesmaximal, characteristic, complemented
11#20265139C211yesmaximal, characteristic
12C22⋊C8×D101C211yesmaximal, characteristic
13#20265134C211yesmaximal, characteristic, complemented
14#20265131C211yesmaximal, characteristic, complemented
15#433×C101C211yesmaximal, characteristic, complemented
16C22×C4×D101C2211yescharacteristic
17C2×#13108057C2211yescharacteristic
18C2×#13108057C2211yescharacteristic
19C2×C8×D101C2211yescharacteristic
20C2×C8×D101C2211yescharacteristic
21#15692214C2211yescharacteristic
22#15692213C411yescharacteristic
23#15692213C411yescharacteristic
24#15692212C2211yescharacteristic
25#15692212C2211yescharacteristic
26#15692211C411yescharacteristic
27#15692211C411yescharacteristic
28C4⋊C4×D101C411yescharacteristic
29C4⋊C4×D101C411yescharacteristic
30C22⋊C4×D101C411yescharacteristic
31C22⋊C4×D101C411yescharacteristic
32C42×D101C2211yescharacteristic
33C42×D101C2211yescharacteristic
34C4⋊#11717579C2211yescharacteristic, complemented
35C4⋊#11717579C2211yescharacteristic, complemented
36#15692184C2211yescharacteristic, complemented
37#15692184C2211yescharacteristic, complemented
38#15692184C2211yescharacteristic, complemented
39#15692184C2211yescharacteristic, complemented
40C22⋊#11717579C2211yescharacteristic
41C22⋊#11717579C2211yescharacteristic
42#15692167C2211yescharacteristic
43#15692167C2211yescharacteristic
44#15692167C2211yescharacteristic
45#15692167C2211yescharacteristic
46#15692166C2211yescharacteristic, complemented
47#15692165C2211yescharacteristic, complemented
48#15692165C2211yescharacteristic, complemented
49C4×#11717579C2211yescharacteristic, complemented
50C8×Dic101C2211yescharacteristic, complemented
51C8×Dic101C2211yescharacteristic, complemented
52#117×C101C2211yescharacteristic
53C4⋊C8×C101C2211yescharacteristic, complemented
54C4⋊C8×C101C2211yescharacteristic, complemented
55C22⋊C8×C101C2211yescharacteristic
56C22⋊C8×C101C2211yescharacteristic
57#97×C101C2211yescharacteristic, complemented
58C4×C8×C101C2211yescharacteristic, complemented
59C23×D101C2×C411yescharacteristic
60C22×Dic101C2×C411yescharacteristic
61C2×C4×D101—22no—
62C2×C4×D101—22no—
63C2×C4×D101C2×C411yescharacteristic
64C2×C4×D101C2×C411yescharacteristic
65C2×C4×D101C2×C411yescharacteristic
66C2×C4×D101C2×C411yescharacteristic
67C2×C4×D101C2×C411yescharacteristic
68C2×C4×D101C2×C411yescharacteristic
69C2×C4×D101C2311yescharacteristic
70C2×C4×D101C2311yescharacteristic
71#13108057—22no—
72#13108057—22no—
73C2×#11717579C2311yescharacteristic
74C2×#11717579C2311yescharacteristic
75C2×#11717579C2311yescharacteristic
76C2×#11717579C2311yescharacteristic
77C8×D101—22no—
78C8×D101—22no—
79C4⋊Dic101C2×C411yescharacteristic
80C4⋊Dic101C2×C411yescharacteristic
81#13108053C2×C411yescharacteristic
82#13108053C2×C411yescharacteristic
83#13108053C2×C411yescharacteristic
84#13108053C2×C411yescharacteristic
85C22⋊Dic101C2×C411yescharacteristic
86C22⋊Dic101C2×C411yescharacteristic
87#13108051C2×C411yescharacteristic
88#13108051C2×C411yescharacteristic
89#13108051C2×C411yescharacteristic
90#13108051C2×C411yescharacteristic
91C4×Dic101C2×C411yescharacteristic
92C4×Dic101C2×C411yescharacteristic
93C4×Dic101C2×C411yescharacteristic
94C4×Dic101C2×C411yescharacteristic
95C4×Dic101C2311yescharacteristic
96C4×Dic101C2311yescharacteristic
97C22×C4×C101C2311yescharacteristic
98C2×C8×C101C2311yescharacteristic
99C2×C8×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C2×C8×C101C2311yescharacteristic
102C4⋊C4×C101C2×C411yescharacteristic
103C4⋊C4×C101C2×C411yescharacteristic
104C22⋊C4×C101C2×C411yescharacteristic
105C22⋊C4×C101C2×C411yescharacteristic
106C42×C101C2311yescharacteristic
107C42×C101C2311yescharacteristic
108C23×C101C22×C411yescharacteristic
109C22×D101—22no—
110C22×D101—22no—
111C22×D101—41no—
112C22×D101C22×C411yescharacteristic
113C22×D101C22×C411yescharacteristic
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101C22×C411yescharacteristic
117C2×C4×C101C22×C411yescharacteristic
118C2×C4×C101C22×C411yescharacteristic
119C2×C4×C101C22×C411yescharacteristic
120C2×C4×C101C22×C411yescharacteristic
121C2×C4×C101C2411yescharacteristic
122C2×Dic101—22no—
123C2×Dic101C22×C411yescharacteristic
124C2×Dic101C22×C411yescharacteristic
125C2×Dic101C22×C411yescharacteristic
126C2×Dic101C22×C411yescharacteristic
127C2×Dic101C22×C411yescharacteristic
128C2×Dic101C22×C411yescharacteristic
129C4×D101—22no—
130C4×D101—22no—
131C4×D101—22no—
132C4×D101—21no—
133C4×D101—21no—
134C4×D101—22no—
135C4×D101—41no—
136C4×D101—41no—
137C4×D101#4112yes—
138C4×D101#4112yes—
139C8×C101—21no—
140C8×C101—21no—
141C8×C101—21no—
142C8×C101—21no—
143#11717579—21no—
144#11717579—21no—
145#11717579—21no—
146#11717579—21no—
147C22×C101—21no—
148C22×C101—21no—
149C22×C101—21no—
150C22×C101C23×C411yescharacteristic
151C2×D101—21no—
152C2×D101—21no—
153C2×D101—21no—
154C2×D101—21no—
155C2×D101—44no—
156C2×D101#11712yes—
157C2×D101#13112yes—
158C4×C101—21no—
159C4×C101—21no—
160C4×C101—21no—
161C4×C101—21no—
162C4×C101—21no—
163C4×C101C2×#4111yescharacteristic
164C4×C101C2×#4111yescharacteristic
165Dic101—21no—
166Dic101—21no—
167Dic101—21no—
168Dic101—21no—
169Dic101—21no—
170Dic101#11712yes—
171C2×C101—41no—
172C2×C101C2×#11711yescharacteristic
173C2×C101C2×#13111yescharacteristic
174C2×C101#56811yescharacteristic
175D101—22no—
176D101—22no—
177#2924—1011nomaximal, Sylow
178C101#292411yescharacteristic, complemented, Sylow
179C2×#117—1011no—
180#433—1011no—
181#433—1011no—
182#433—1011no—
183#433D10111yescharacteristic, complemented
184#432—1011no—
185#432—1011no—
186#431—1011no—
187#431—1011no—
188#424—1011no—
189#424—1011no—
190#407—1011no—
191C2×C22⋊C8—1011no—
192#405—1011no—
193#405—1011no—
194C23×C4—1011no—
195C2×M16—1011no—
196C2×M16—1011no—
197C22×C8—1011no—
198C22×C8—1011no—
199#117—1011no—
200#117—1011no—
201#117—1011no—
202#117—1011no—
203#117—1011no—
204#117—1011no—
205#117—1011no—
206#117C2×D10111yescharacteristic
207C2×C4⋊C4—1011no—
208C2×C4⋊C4—1011no—
209C2×C22⋊C4—1011no—
210C2×C22⋊C4—1011no—
211C2×C42—1011no—
212C2×C42—1011no—
213C4⋊C8—1011no—
214C4⋊C8—1011no—
215C4⋊C8—1011no—
216C4⋊C8—1011no—
217C4⋊C8—1011no—
218C4⋊C8—1011no—
219C4⋊C8C2×D10111yescharacteristic, complemented
220C4⋊C8C2×D10111yescharacteristic, complemented
221C22⋊C8—1011no—
222C22⋊C8—1011no—
223C22⋊C8—1011no—
224C22⋊C8—1011no—
225C22⋊C8—1011no—
226C22⋊C8—1011no—
227C22⋊C8C2×D10111yescharacteristic
228C22⋊C8C2×D10111yescharacteristic
229#97—1011no—
230#97—1011no—
231#97—1011no—
232#97C2×D10111yescharacteristic, complemented
233C4×C8—1011no—
234C4×C8—1011no—
235C4×C8—1011no—
236C4×C8C2×D10111yescharacteristic, complemented
237C24—1011no—
238C22×C4—1011no—
239C22×C4—1011no—
240C22×C4—1011no—
241C22×C4—1011no—
242C22×C4—1011no—
243C22×C4—1011no—
244C22×C4—1011no—
245C22×C4—1011no—
246C22×C4—1011no—
247C22×C4—2022no—
248C22×C4—2022no—
249C22×C4C22×D10111yescharacteristic
250M16—2022no—
251M16—2022no—
252C2×C8—1011no—
253C2×C8—1011no—
254C2×C8—1011no—
255C2×C8—1011no—
256C2×C8—2022no—
257C2×C8—2022no—
258C2×C8C22×D10111yescharacteristic
259C2×C8C22×D10111yescharacteristic
260C2×C8C22×D10111yescharacteristic
261C2×C8C22×D10111yescharacteristic
262C4⋊C4—1011no—
263C4⋊C4—1011no—
264C4⋊C4—1011no—
265C4⋊C4—1011no—
266C4⋊C4—1011no—
267C4⋊C4—1011no—
268C4⋊C4C4×D10111yescharacteristic
269C4⋊C4C4×D10111yescharacteristic
270C22⋊C4—1011no—
271C22⋊C4—1011no—
272C22⋊C4—1011no—
273C22⋊C4—1011no—
274C22⋊C4—1011no—
275C22⋊C4—1011no—
276C22⋊C4C4×D10111yescharacteristic
277C22⋊C4C4×D10111yescharacteristic
278C42—1011no—
279C42—1011no—
280C42—1011no—
281C42—1011no—
282C42—1011no—
283C42—1011no—
284C42C22×D10111yescharacteristic
285C42C22×D10111yescharacteristic
286C23—1011no—
287C23—1011no—
288C23—4041no—
289C23—2022no—
290C23—2022no—
291C23C2×C4×D10111yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—1011no—
295C2×C4—1012no—
296C2×C4—1012no—
297C2×C4—1011no—
298C2×C4—1011no—
299C2×C4—1011no—
300C2×C4—1011no—
301C2×C4—1011no—
302C2×C4—4041no—
303C2×C4—4041no—
304C2×C4—2022no—
305C2×C4—2022no—
306C2×C4—2022no—
307C2×C4—2022no—
308C2×C4—2022no—
309C2×C4—2021no—
310C2×C4—2021no—
311C2×C4C2×C4×D10111yescharacteristic
312C2×C4C2×C4×D10111yescharacteristic
313C2×C4C2×C4×D10111yescharacteristic
314C2×C4C2×C4×D10111yescharacteristic
315C2×C4C2×C4×D10111yescharacteristic
316C2×C4C23×D10111yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8—21no—
321C8—2021no—
322C8—2021no—
323C8—2021no—
324C8—2021no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—1012no—
329C22—1012no—
330C22—4044no—
331C22—2021no—
332C22—2021no—
333C22—2021no—
334C22—2021no—
335C22C22×C4×D10111yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—1012no—
342C4—2021no—
343C4—2021no—
344C4—2021no—
345C4—2021no—
346C4—2021no—
347C4#41×D10111yescharacteristic
348C4#41×D10111yescharacteristic
349C2—41no—
350C2—2022no—
351C2—2022no—
352C2#117×D10111yescharacteristic
353C2#131×D10111yescharacteristic
354C2#2026594211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D101
commutator, socleC22×C101C23×C4
Fitting#433×C101C2
prime radicalC23×D101C2×C4
cosocleC2×C4×C101C24
hypercenter#433D101
hypocenterC101#2924
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #20265238C2semidirect
3. #20265235C2semidirect
4. #20265235C2semidirect
5. #20265233C2semidirect
6. #20265232C2semidirect
7. #20265229C2semidirect
8. #20265228C2semidirect
9. #20265202C2semidirect
10. #20265202C2semidirect
13. #20265134C2semidirect
14. #20265131C2semidirect
15. #433×C101C2semidirect
34. C4⋊#11717579C22semidirect
35. C4⋊#11717579C22semidirect
36. #15692184C22semidirect
37. #15692184C22semidirect
38. #15692184C22semidirect
39. #15692184C22semidirect
46. #15692166C22semidirect
47. #15692165C22semidirect
48. #15692165C22semidirect
49. C4×#11717579C22semidirect
50. C8×Dic101C22semidirect
51. C8×Dic101C22semidirect
53. C4⋊C8×C101C22semidirect
54. C4⋊C8×C101C22semidirect
57. #97×C101C22semidirect
58. C4×C8×C101C22semidirect
178. C101#2924semidirect
183. #433D101semidirect
219. C4⋊C8C2×D101semidirect
220. C4⋊C8C2×D101semidirect
232. #97C2×D101semidirect
236. C4×C8C2×D101semidirect

Maximal subgroups

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

subgroupindex
#117×D1012
#202652382
#202652352
#202652332
#202652322
#202652292
#202652282
#202652022
#202651392
C22⋊C8×D1012
#202651342
#202651312
#433×C1012
#2924101