Finite Group Databasebeta

← #27174187

Subgroups — #27174187

Order 12928.

552 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692254C211yesmaximal, characteristic
2C2×C4×Dic202C211yesmaximal, characteristic
3C2×#15692220C211yesmaximal, characteristic
4#20265081C211yesmaximal, characteristic
5#20265081C211yesmaximal, characteristic
6#20265074C211yesmaximal, characteristic
7#20265072C211yesmaximal, characteristic
8#20265063C211yesmaximal, characteristic
9#20265062C211yesmaximal, characteristic
10#20265060C211yesmaximal, characteristic
11C4×#13108053C211yesmaximal, characteristic
12#20265028C211yesmaximal, characteristic
13#20265028C211yesmaximal, characteristic
14#20265028C211yesmaximal, characteristic
15#387×C101C211yesmaximal, characteristic
16C22×Dic202C2211yescharacteristic
17C22×Dic202C2211yescharacteristic
18#15692254C418yescomplemented
19C4×Dic202—24no—
20#15692220—24no—
21C2×C4⋊Dic101C2211yescharacteristic
22C2×C4⋊Dic101C2211yescharacteristic
23C2×#13108053C2211yescharacteristic
24C2×#13108053C2211yescharacteristic
25C2×#13108053C2211yescharacteristic
26C2×#13108053C2211yescharacteristic
27C2×#13108053C2211yescharacteristic
28C2×#13108053C2211yescharacteristic
29C2×#13108053C2211yescharacteristic
30C2×#13108053C2211yescharacteristic
31C2×C4×Dic101C2211yescharacteristic
32C2×C4×Dic101C2211yescharacteristic
33C2×C4×Dic101C2211yescharacteristic
34C2×C4×Dic101C2211yescharacteristic
35C2×C4×Dic101C2211yescharacteristic
36C2×C4×Dic101C2211yescharacteristic
37C2×C4×Dic101C2211yescharacteristic
38C2×C4×Dic101C2211yescharacteristic
39#15692162C2211yescharacteristic
40#15692162C2211yescharacteristic
41#15692162C2211yescharacteristic
42#15692162C2211yescharacteristic
43#15692162C2211yescharacteristic
44#15692162C2211yescharacteristic
45#15692162C2211yescharacteristic
46#15692162C2211yescharacteristic
47C2×C4⋊C4×C101C2211yescharacteristic
48C2×C4⋊C4×C101C2211yescharacteristic
49C2×C42×C101C2211yescharacteristic
50#95×C101C2211yescharacteristic
51#95×C101C2211yescharacteristic
52#95×C101C2211yescharacteristic
53#95×C101C2211yescharacteristic
54C2×Dic202—22no—
55C2×Dic202—22no—
56C2×Dic202—22no—
57C2×Dic202—22no—
58C2×Dic202C2×C414yes—
59C2×Dic202C2×C414yes—
60C22×Dic101C2311yescharacteristic
61C22×Dic101C2311yescharacteristic
62C22×Dic101C2311yescharacteristic
63C22×Dic101C2311yescharacteristic
64C22×Dic101C2311yescharacteristic
65C22×Dic101C2311yescharacteristic
66C22×Dic101C2311yescharacteristic
67C22×Dic101C2311yescharacteristic
68C4⋊Dic101—22no—
69C4⋊Dic101C2×C414yes—
70#13108053—22no—
71#13108053—22no—
72#13108053—22no—
73#13108053—22no—
74#13108053C2×C414yes—
75#13108053C2×C414yes—
76#13108053D414yes—
77#13108053Q814yescomplemented
78C4×Dic101—22no—
79C4×Dic101—22no—
80C4×Dic101—22no—
81C4×Dic101—22no—
82C4×Dic101—22no—
83C4×Dic101—22no—
84C4×Dic101—22no—
85C4×Dic101C2×C414yes—
86C22×C4×C101C2311yescharacteristic
87C22×C4×C101C2311yescharacteristic
88C22×C4×C101C2311yescharacteristic
89C22×C4×C101C2311yescharacteristic
90C22×C4×C101C2311yescharacteristic
91C22×C4×C101C2311yescharacteristic
92C22×C4×C101C2311yescharacteristic
93C4⋊C4×C101—22no—
94C4⋊C4×C101C2×C414yes—
95C42×C101—22no—
96C23×C101C2411yescharacteristic
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×C101—21no—
109C2×C4×C101—21no—
110C2×C4×C101—21no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101C22×C412yes—
114C2×C4×C101C22×C412yes—
115C2×C4×C101C22×C412yes—
116C2×C4×C101C2×D412yes—
117C2×C4×C101C2×Q812yes—
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×Dic101—21no—
128C2×Dic101—21no—
129C2×Dic101—21no—
130C2×Dic101—21no—
131C2×Dic101—21no—
132C2×Dic101C22×C412yes—
133C2×Dic101C22×C412yes—
134C2×Dic101C22×C412yes—
135C2×Dic101C22×C412yes—
136C2×Dic101C2×D412yes—
137C2×Dic101C2×D412yes—
138C2×Dic101C2×Q812yes—
139C2×Dic101C2×Q812yes—
140C2×Dic101#4112yes—
141C2×Dic101#4112yes—
142Dic202—28no—
143Dic202—28no—
144C22×C101C23×C411yescharacteristic
145C22×C101C22×D411yescharacteristic
146C22×C101C22×Q811yescharacteristic
147C22×C101C2×#4111yescharacteristic
148C22×C101C2×#4111yescharacteristic
149C22×C1012−1+411yescharacteristic
150C22×C1012−1+411yescharacteristic
151C4×C101—22no—
152C4×C101—22no—
153C4×C101—22no—
154C4×C101—22no—
155C4×C101—22no—
156C4×C101—41no—
157C4×C101—41no—
158Dic101—22no—
159Dic101—22no—
160Dic101—22no—
161Dic101—22no—
162Dic101—41no—
163Dic101—41no—
164Dic101C4×D414yes—
165Dic101C4×Q814yescomplemented
166C2×C101C2×C4×D411yescharacteristic
167C2×C101C2×C4×Q811yescharacteristic
168C2×C101#51911yescharacteristic
169C2×C101#54711yescharacteristic
170C2×C101D4×Q811yescharacteristic
171C2×C101#55611yescharacteristic
172C2×C101#55711yescharacteristic
173#2365—1011nomaximal, Sylow
174C101#236511yescharacteristic, complemented, Sylow
175C2×C4⋊Q8—1011no—
176C2×C4×Q8—1011no—
177C2×C4×Q8—1011no—
178#391—1011no—
179#391—1011no—
180#389—1011no—
181#389—1011no—
182#387—1011no—
183#387—1011no—
184#387—1011no—
185#387D10111yescharacteristic
186C4×C4⋊C4—1011no—
187C4×C4⋊C4—1011no—
188C4×C4⋊C4—1011no—
189C4×C4⋊C4—1011no—
190C22×Q8—1011no—
191C22×Q8—1011no—
192C4⋊Q8—1018no—
193C4×Q8—2024no—
194C4×Q8—2024no—
195C2×C4⋊C4—1011no—
196C2×C4⋊C4—1011no—
197C2×C4⋊C4—1011no—
198C2×C4⋊C4—1011no—
199C2×C4⋊C4—1011no—
200C2×C4⋊C4—1011no—
201C2×C4⋊C4—1011no—
202C2×C4⋊C4—1011no—
203C2×C4⋊C4—1011no—
204C2×C4⋊C4—1011no—
205C2×C4⋊C4C2×D10111yescharacteristic
206C2×C4⋊C4C2×D10111yescharacteristic
207C2×C42—1011no—
208C2×C42—1011no—
209C2×C42—1011no—
210C2×C42—1011no—
211C2×C42—1011no—
212C2×C42—1011no—
213C2×C42—1011no—
214C2×C42—1011no—
215C2×C42C2×D10111yescharacteristic
216#95—1011no—
217#95—1011no—
218#95—1011no—
219#95—1011no—
220#95—1011no—
221#95—1011no—
222#95—1011no—
223#95—1011no—
224#95C2×D10111yescharacteristic
225#95C2×D10111yescharacteristic
226#95C2×D10111yescharacteristic
227#95C2×D10111yescharacteristic
228C2×Q8—1014no—
229C2×Q8—1014no—
230C2×Q8—2022no—
231C2×Q8—2022no—
232C2×Q8—2022no—
233C2×Q8—2022no—
234C22×C4—1011no—
235C22×C4—1011no—
236C22×C4—1011no—
237C22×C4—1011no—
238C22×C4—1011no—
239C22×C4—1011no—
240C22×C4—1011no—
241C22×C4—1011no—
242C22×C4C22×D10111yescharacteristic
243C22×C4C22×D10111yescharacteristic
244C22×C4C22×D10111yescharacteristic
245C22×C4C22×D10111yescharacteristic
246C22×C4C22×D10111yescharacteristic
247C22×C4C22×D10111yescharacteristic
248C22×C4C22×D10111yescharacteristic
249C4⋊C4—22no—
250C4⋊C4—1014no—
251C4⋊C4—1014no—
252C4⋊C4—1014no—
253C4⋊C4—1014no—
254C4⋊C4—1014no—
255C4⋊C4—2022no—
256C4⋊C4—2022no—
257C4⋊C4—2022no—
258C4⋊C4—2022no—
259C4⋊C4—2022no—
260C4⋊C4C4×D10114yes—
261C42—22no—
262C42—1014no—
263C42—2022no—
264C42—2022no—
265C42—2022no—
266C42—2022no—
267C42—2022no—
268C42—2022no—
269C42—2022no—
270C23C23×D10111yescharacteristic
271Q8—2028no—
272Q8—2028no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—1012no—
290C2×C4—1012no—
291C2×C4—1012no—
292C2×C4—1012no—
293C2×C4—1012no—
294C2×C4—1012no—
295C2×C4—1012no—
296C2×C4—1012no—
297C2×C4—1012no—
298C2×C4—1012no—
299C2×C4—2021no—
300C2×C4—2021no—
301C2×C4—2021no—
302C2×C4—2021no—
303C2×C4—2021no—
304C2×C4—2021no—
305C2×C4—2021no—
306C2×C4—2021no—
307C2×C4—2021no—
308C2×C4—2021no—
309C2×C4—2021no—
310C2×C4—2021no—
311C2×C4—2021no—
312C2×C4—2021no—
313C2×C4C2×C4×D10112yes—
314C2×C4C2×C4×D10112yes—
315C2×C4C2×C4×D10112yes—
316C2×C4D4×D10112yes—
317C2×C4Q8×D10112yes—
318C22C22×C4×D10111yescharacteristic
319C22C2×D4×D10111yescharacteristic
320C22C2×Q8×D10111yescharacteristic
321C22#41×D10111yescharacteristic
322C22#41×D10111yescharacteristic
323C22#1569230211yescharacteristic
324C22#1569230211yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—22no—
329C4—22no—
330C4—41no—
331C4—41no—
332C4—1014no—
333C4—1014no—
334C4—4041no—
335C4—4041no—
336C4—2022no—
337C4—2022no—
338C4—2022no—
339C4—2022no—
340C2C4×D4×D10111yescharacteristic
341C2C4×Q8×D10111yescharacteristic
342C2#2026565411yescharacteristic
343C2#2026582511yescharacteristic
344C2#2026584011yescharacteristic
345C2#2026589411yescharacteristic
346C2#2026590411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutatorC22×C101C23×C4
Fitting#387×C101C2
socle, prime radical, cosocleC23×C101C24
hypercenter#387D101
hypocenterC101#2365
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
18. #15692254C4semidirect
77. #13108053Q8semidirect
165. Dic101C4×Q8semidirect
174. C101#2365semidirect

Maximal subgroups

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

subgroupindex
C2×#156922542
C2×C4×Dic2022
C2×#156922202
#202650812
#202650742
#202650722
#202650632
#202650622
#202650602
C4×#131080532
#202650282
#387×C1012
#2365101