Finite Group Databasebeta

← #27174086

Subgroups — #27174086

Order 12928.

480 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692220C211yesmaximal, characteristic
2#20265081C211yesmaximal, characteristic
3#20265081C211yesmaximal, characteristic
4#20265064C211yesmaximal, characteristic
5#20265063C211yesmaximal, characteristic
6#20265058C211yesmaximal, characteristic
7#20265046C211yesmaximal, characteristic
8#20265041C211yesmaximal, characteristic
9#20265041C211yesmaximal, characteristic
10C4×#13108053C211yesmaximal, characteristic
11C4×#13108053C211yesmaximal, characteristic
12#20265028C211yesmaximal, characteristic
13#20265028C211yesmaximal, characteristic
14#20265028C211yesmaximal, characteristic
15#387×C101C211yesmaximal, characteristic
16C22×Dic202C2211yescharacteristic
17#15692220C418yescomplemented
18C2×C4⋊Dic101C2211yescharacteristic
19C2×#13108053C2211yescharacteristic
20C2×#13108053C2211yescharacteristic
21C2×#13108053C2211yescharacteristic
22C2×#13108053C2211yescharacteristic
23C2×#13108053C2211yescharacteristic
24C2×#13108053C2211yescharacteristic
25C2×#13108053C2211yescharacteristic
26C2×#13108053C2211yescharacteristic
27C2×C4×Dic101C2211yescharacteristic
28C2×C4×Dic101C2211yescharacteristic
29C2×C4×Dic101C2211yescharacteristic
30C2×C4×Dic101C2211yescharacteristic
31C2×C4×Dic101C2211yescharacteristic
32C2×C4×Dic101C2211yescharacteristic
33C2×C4×Dic101C2211yescharacteristic
34C2×C4×Dic101C2211yescharacteristic
35#15692162C2211yescharacteristic
36#15692162C2211yescharacteristic
37#15692162C2211yescharacteristic
38#15692162C2211yescharacteristic
39#15692162C2211yescharacteristic
40#15692162C2211yescharacteristic
41#15692162C2211yescharacteristic
42#15692162C2211yescharacteristic
43#15692162C2211yescharacteristic
44#15692162C2211yescharacteristic
45C2×C4⋊C4×C101C2211yescharacteristic
46C2×C4⋊C4×C101C2211yescharacteristic
47C2×C42×C101C2211yescharacteristic
48#95×C101C2211yescharacteristic
49#95×C101C2211yescharacteristic
50#95×C101C2211yescharacteristic
51#95×C101C2211yescharacteristic
52C2×Dic202—22no—
53C2×Dic202—22no—
54C2×Dic202C2×C414yes—
55C22×Dic101C2311yescharacteristic
56C22×Dic101C2311yescharacteristic
57C22×Dic101C2311yescharacteristic
58C22×Dic101C2311yescharacteristic
59C22×Dic101C2311yescharacteristic
60C22×Dic101C2311yescharacteristic
61C22×Dic101C2311yescharacteristic
62C22×Dic101C2311yescharacteristic
63C4⋊Dic101—41no—
64#13108053—22no—
65#13108053—22no—
66#13108053—22no—
67#13108053—22no—
68#13108053—22no—
69#13108053C2×C414yes—
70#13108053C2×C414yes—
71#13108053Q814yescomplemented
72C4×Dic101—22no—
73C4×Dic101—22no—
74C4×Dic101—41no—
75C4×Dic101—41no—
76C4×Dic101—41no—
77C4×Dic101C2×C414yes—
78C4×Dic101C2×C414yes—
79C4×Dic101C2×C414yes—
80C22×C4×C101C2311yescharacteristic
81C22×C4×C101C2311yescharacteristic
82C22×C4×C101C2311yescharacteristic
83C22×C4×C101C2311yescharacteristic
84C22×C4×C101C2311yescharacteristic
85C22×C4×C101C2311yescharacteristic
86C22×C4×C101C2311yescharacteristic
87C4⋊C4×C101—41no—
88C4⋊C4×C101C2×C414yes—
89C42×C101—41no—
90C23×C101C2411yescharacteristic
91C2×C4×C101—21no—
92C2×C4×C101—21no—
93C2×C4×C101—21no—
94C2×C4×C101—21no—
95C2×C4×C101—21no—
96C2×C4×C101—21no—
97C2×C4×C101—21no—
98C2×C4×C101—21no—
99C2×C4×C101—21no—
100C2×C4×C101—21no—
101C2×C4×C101—21no—
102C2×C4×C101—21no—
103C2×C4×C101—21no—
104C2×C4×C101—21no—
105C2×C4×C101—21no—
106C2×C4×C101—21no—
107C2×C4×C101—21no—
108C2×C4×C101C22×C412yes—
109C2×C4×C101C22×C412yes—
110C2×C4×C101C22×C412yes—
111C2×C4×C101C2×Q812yes—
112C2×Dic101—21no—
113C2×Dic101—21no—
114C2×Dic101—21no—
115C2×Dic101—21no—
116C2×Dic101—21no—
117C2×Dic101—21no—
118C2×Dic101—21no—
119C2×Dic101—21no—
120C2×Dic101—21no—
121C2×Dic101—21no—
122C2×Dic101—21no—
123C2×Dic101—21no—
124C2×Dic101—21no—
125C2×Dic101—21no—
126C2×Dic101—21no—
127C2×Dic101C22×C412yes—
128C2×Dic101C22×C412yes—
129C2×Dic101C22×C412yes—
130C2×Dic101C22×C412yes—
131C2×Dic101C2×Q812yes—
132C2×Dic101C2×Q812yes—
133C2×Dic101#4112yes—
134C2×Dic101#4112yes—
135C2×Dic101#4112yes—
136Dic202—28no—
137C22×C101C23×C411yescharacteristic
138C22×C101C22×Q811yescharacteristic
139C22×C101C2×#4111yescharacteristic
140C22×C101C2×#4111yescharacteristic
141C22×C101C2×#4111yescharacteristic
142C22×C101H(5,𝔽2)11yescharacteristic
143C22×C1012−1+411yescharacteristic
144C4×C101—22no—
145C4×C101—22no—
146C4×C101—22no—
147C4×C101—22no—
148C4×C101—41no—
149C4×C101—41no—
150C4×C101—41no—
151Dic101—22no—
152Dic101—22no—
153Dic101—22no—
154Dic101—41no—
155Dic101—41no—
156Dic101—41no—
157Dic101#11714yes—
158Dic101C4×Q814yes—
159C2×C101C2×#11711yescharacteristic
160C2×C101C2×C4×Q811yescharacteristic
161C2×C101#52011yescharacteristic
162C2×C101#55411yescharacteristic
163C2×C101#55611yescharacteristic
164C2×C101#55711yescharacteristic
165C2×C101#55911yescharacteristic
166#2355—1011nomaximal, Sylow
167C101#235511yescharacteristic, complemented, Sylow
168C2×C4×Q8—1011no—
169#391—1011no—
170#391—1011no—
171#387—1011no—
172#387—1011no—
173#387—1011no—
174#387D10111yescharacteristic
175#384—1011no—
176#382—1011no—
177#382—1011no—
178C4×C4⋊C4—1011no—
179C4×C4⋊C4—1011no—
180C4×C4⋊C4—1011no—
181C4×C4⋊C4—1011no—
182C4×C4⋊C4—1011no—
183C22×Q8—1011no—
184C4×Q8—1018no—
185C2×C4⋊C4—1011no—
186C2×C4⋊C4—1011no—
187C2×C4⋊C4—1011no—
188C2×C4⋊C4—1011no—
189C2×C4⋊C4—1011no—
190C2×C4⋊C4—1011no—
191C2×C4⋊C4—1011no—
192C2×C4⋊C4—1011no—
193C2×C4⋊C4—1011no—
194C2×C4⋊C4C2×D10111yescharacteristic
195C2×C4⋊C4C2×D10111yescharacteristic
196C2×C42—1011no—
197C2×C42—1011no—
198C2×C42—1011no—
199C2×C42—1011no—
200C2×C42—1011no—
201C2×C42—1011no—
202C2×C42—1011no—
203C2×C42—1011no—
204C2×C42C2×D10111yescharacteristic
205#95—1011no—
206#95—1011no—
207#95—1011no—
208#95—1011no—
209#95—1011no—
210#95—1011no—
211#95—1011no—
212#95—1011no—
213#95—1011no—
214#95—1011no—
215#95C2×D10111yescharacteristic
216#95C2×D10111yescharacteristic
217#95C2×D10111yescharacteristic
218#95C2×D10111yescharacteristic
219C2×Q8—1014no—
220C2×Q8—2022no—
221C2×Q8—2022no—
222C22×C4—1011no—
223C22×C4—1011no—
224C22×C4—1011no—
225C22×C4—1011no—
226C22×C4—1011no—
227C22×C4—1011no—
228C22×C4—1011no—
229C22×C4—1011no—
230C22×C4C22×D10111yescharacteristic
231C22×C4C22×D10111yescharacteristic
232C22×C4C22×D10111yescharacteristic
233C22×C4C22×D10111yescharacteristic
234C22×C4C22×D10111yescharacteristic
235C22×C4C22×D10111yescharacteristic
236C22×C4C22×D10111yescharacteristic
237C4⋊C4—41no—
238C4⋊C4—1014no—
239C4⋊C4—1014no—
240C4⋊C4—1014no—
241C4⋊C4—4041no—
242C4⋊C4—2022no—
243C4⋊C4—2022no—
244C4⋊C4—2022no—
245C4⋊C4—2022no—
246C4⋊C4—2022no—
247C4⋊C4C4×D10114yes—
248C42—41no—
249C42—1014no—
250C42—1014no—
251C42—1014no—
252C42—4041no—
253C42—4041no—
254C42—4041no—
255C42—2022no—
256C42—2022no—
257C23C23×D10111yescharacteristic
258Q8—2028no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—1012no—
277C2×C4—1012no—
278C2×C4—1012no—
279C2×C4—1012no—
280C2×C4—1012no—
281C2×C4—1012no—
282C2×C4—1012no—
283C2×C4—1012no—
284C2×C4—1012no—
285C2×C4—2021no—
286C2×C4—2021no—
287C2×C4—2021no—
288C2×C4—2021no—
289C2×C4—2021no—
290C2×C4—2021no—
291C2×C4—2021no—
292C2×C4—2021no—
293C2×C4—2021no—
294C2×C4—2021no—
295C2×C4—2021no—
296C2×C4—2021no—
297C2×C4—2021no—
298C2×C4—2021no—
299C2×C4—2021no—
300C2×C4C2×C4×D10112yes—
301C2×C4C2×C4×D10112yes—
302C2×C4C2×C4×D10112yes—
303C2×C4Q8×D10112yes—
304C22C22×C4×D10111yescharacteristic
305C22C2×Q8×D10111yescharacteristic
306C22#41×D10111yescharacteristic
307C22#41×D10111yescharacteristic
308C22#41×D10111yescharacteristic
309C22#1569230011yescharacteristic
310C22#1569230211yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—1014no—
319C4—1014no—
320C4—4041no—
321C4—4041no—
322C4—4041no—
323C4—2022no—
324C4—2022no—
325C4—2022no—
326C2#117×D10111yescharacteristic
327C2C4×Q8×D10111yescharacteristic
328C2#2026565611yescharacteristic
329C2#2026588111yescharacteristic
330C2#2026589411yescharacteristic
331C2#2026590411yescharacteristic
332C2#2026591111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutatorC22×C101C23×C4
Fitting#387×C101C2
socle, prime radical, cosocleC23×C101C24
hypercenter#387D101
hypocenterC101#2355
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
17. #15692220C4semidirect
71. #13108053Q8semidirect
167. C101#2355semidirect

Maximal subgroups

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

subgroupindex
C2×#156922202
#202650812
#202650642
#202650632
#202650582
#202650462
#202650412
C4×#131080532
#202650282
#387×C1012
#2355101