Finite Group Databasebeta

← #27173731

Subgroups — #27173731

Order 12928.

512 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D101C211yesmaximal, characteristic
2#20265064C211yesmaximal, characteristic, complemented
3#20265063C211yesmaximal, characteristic, complemented
4#20265062C211yesmaximal, characteristic, complemented
5#20265061C211yesmaximal, characteristic, complemented
6#20265060C211yesmaximal, characteristic, complemented
7#20265059C211yesmaximal, characteristic, complemented
8#20265058C211yesmaximal, characteristic, complemented
9#20265039C211yesmaximal, characteristic
10#20265039C211yesmaximal, characteristic
11#20265036C211yesmaximal, characteristic
12#20265034C211yesmaximal, characteristic
13C4×#13108051C211yesmaximal, characteristic
14#20265024C211yesmaximal, characteristic
15#387×C101C211yesmaximal, characteristic, complemented
16C22×C4×D101C2211yescharacteristic
17C22×C4×D101C2211yescharacteristic
18C22×C4×D101C2211yescharacteristic
19C2×C4⋊Dic101C2211yescharacteristic
20C2×C4⋊Dic101C2211yescharacteristic
21C2×#13108053C2211yescharacteristic
22C2×#13108053C2211yescharacteristic
23C2×#13108053C2211yescharacteristic
24C2×#13108053C2211yescharacteristic
25C4⋊C4×D101C418yescomplemented
26C2×#13108051C2211yescharacteristic
27C2×#13108051C2211yescharacteristic
28C2×#13108051C2211yescharacteristic
29C2×#13108051C2211yescharacteristic
30C2×C4×Dic101C2211yescharacteristic
31C2×C4×Dic101C2211yescharacteristic
32C2×C4×Dic101C2211yescharacteristic
33#15692162C2211yescharacteristic
34#15692162C2211yescharacteristic
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
52C23×D101C2311yescharacteristic
53C22×Dic101C2311yescharacteristic
54C22×Dic101C2311yescharacteristic
55C22×Dic101C2311yescharacteristic
56C22×Dic101C2311yescharacteristic
57C22×Dic101C2311yescharacteristic
58C22×Dic101C2311yescharacteristic
59C22×Dic101C2311yescharacteristic
60C2×C4×D101—22no—
61C2×C4×D101—22no—
62C2×C4×D101—41no—
63C2×C4×D101—41no—
64C2×C4×D101—41no—
65C2×C4×D101—41no—
66C2×C4×D101C2×C414yes—
67C2×C4×D101C2×C414yes—
68C2×C4×D101C2×C414yes—
69C4⋊Dic101—41no—
70C4⋊Dic101C2×C414yes—
71#13108053—41no—
72#13108053—41no—
73#13108053C2×C414yes—
74#13108053C2×C414yes—
75#13108051—22no—
76#13108051—22no—
77#13108051—22no—
78#13108051—22no—
79C4×Dic101—41no—
80C4×Dic101—41no—
81C4×Dic101—41no—
82C22×C4×C101C2311yescharacteristic
83C22×C4×C101C2311yescharacteristic
84C22×C4×C101C2311yescharacteristic
85C22×C4×C101C2311yescharacteristic
86C22×C4×C101C2311yescharacteristic
87C22×C4×C101C2311yescharacteristic
88C22×C4×C101C2311yescharacteristic
89C4⋊C4×C101—41no—
90C4⋊C4×C101C2×C414yes—
91C42×C101—41no—
92C23×C101C2411yescharacteristic
93C22×D101—21no—
94C22×D101—21no—
95C22×D101—21no—
96C22×D101—21no—
97C22×D101C22×C412yes—
98C22×D101#4112yes—
99C22×D101#4112yes—
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×C101—21no—
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—21no—
118C2×C4×C101C22×C412yes—
119C2×C4×C101C22×C412yes—
120C2×C4×C101C22×C412yes—
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×Dic101—21no—
133C2×Dic101—21no—
134C2×Dic101—21no—
135C2×Dic101—21no—
136C2×Dic101—21no—
137C2×Dic101—21no—
138C2×Dic101—21no—
139C2×Dic101C22×C412yes—
140C2×Dic101C22×C412yes—
141C2×Dic101C22×C412yes—
142C4×D101—28no—
143C4×D101—44no—
144C4×D101—44no—
145C22×C101C23×C411yescharacteristic
146C22×C101C2×#4111yescharacteristic
147C22×C101C2×#4111yescharacteristic
148C22×C101H(5,𝔽2)11yescharacteristic
149C22×C101H(5,𝔽2)11yescharacteristic
150C22×C1012−1+411yescharacteristic
151C22×C1012−1+411yescharacteristic
152C2×D101—22no—
153C2×D101—22no—
154C2×D101—22no—
155C2×D101—22no—
156C2×D101—22no—
157C2×D101—22no—
158C2×D101#11714yes—
159C4×C101—22no—
160C4×C101—22no—
161C4×C101—22no—
162C4×C101—41no—
163C4×C101—41no—
164C4×C101—41no—
165C4×C101—41no—
166Dic101—22no—
167Dic101—22no—
168Dic101—22no—
169Dic101—41no—
170Dic101—41no—
171Dic101—41no—
172Dic101—41no—
173C2×C101C2×#11711yescharacteristic
174C2×C101#51811yescharacteristic
175C2×C101#51911yescharacteristic
176C2×C101#53911yescharacteristic
177C2×C101#53911yescharacteristic
178C2×C101#53911yescharacteristic
179C2×C101#53911yescharacteristic
180D101—24no—
181#2313—1011nomaximal, Sylow
182C101#231311yescharacteristic, complemented, Sylow
183C22×C4⋊C4—1011no—
184#387—1011no—
185#387—1011no—
186#387—1011no—
187#387—1011no—
188#387—1011no—
189#387—1011no—
190#387—1011no—
191#387D10111yescharacteristic, complemented
192#381—1011no—
193#381—1011no—
194#380—1011no—
195#380—1011no—
196C4×C22⋊C4—1011no—
197C4×C22⋊C4—1011no—
198C23×C4—1011no—
199C23×C4—1011no—
200C23×C4—1011no—
201C2×C4⋊C4—1011no—
202C2×C4⋊C4—1011no—
203C2×C4⋊C4—1011no—
204C2×C4⋊C4—1018no—
205C2×C4⋊C4—1011no—
206C2×C4⋊C4—1011no—
207C2×C4⋊C4—1011no—
208C2×C4⋊C4C2×D10111yescharacteristic
209C2×C4⋊C4C2×D10111yescharacteristic
210C2×C22⋊C4—1011no—
211C2×C22⋊C4—1011no—
212C2×C22⋊C4—1011no—
213C2×C22⋊C4—1011no—
214C2×C42—1011no—
215C2×C42—1011no—
216C2×C42—1011no—
217C2×C42C2×D10111yescharacteristic
218#95—1011no—
219#95—1011no—
220#95—1011no—
221#95—1011no—
222#95—1011no—
223#95—1011no—
224#95—1011no—
225#95—1011no—
226#95—1011no—
227#95—1011no—
228#95—1011no—
229#95—1011no—
230#95C2×D10111yescharacteristic
231#95C2×D10111yescharacteristic
232#95C2×D10111yescharacteristic
233#95C2×D10111yescharacteristic
234C24—1011no—
235C22×C4—1011no—
236C22×C4—1011no—
237C22×C4—1011no—
238C22×C4—1014no—
239C22×C4—1014no—
240C22×C4—1014no—
241C22×C4—1011no—
242C22×C4—1011no—
243C22×C4—1011no—
244C22×C4—1011no—
245C22×C4—4041no—
246C22×C4—4041no—
247C22×C4—4041no—
248C22×C4—4041no—
249C22×C4—2022no—
250C22×C4—2022no—
251C22×C4C22×D10111yescharacteristic
252C22×C4C22×D10111yescharacteristic
253C22×C4C22×D10111yescharacteristic
254C22×C4C22×D10111yescharacteristic
255C22×C4C22×D10111yescharacteristic
256C22×C4C22×D10111yescharacteristic
257C22×C4C22×D10111yescharacteristic
258C4⋊C4—41no—
259C4⋊C4—1014no—
260C4⋊C4—1014no—
261C4⋊C4—1014no—
262C4⋊C4—4041no—
263C4⋊C4—4041no—
264C4⋊C4—4041no—
265C4⋊C4C4×D10114yes—
266C22⋊C4—2022no—
267C22⋊C4—2022no—
268C22⋊C4—2022no—
269C22⋊C4—2022no—
270C42—41no—
271C42—4041no—
272C42—4041no—
273C42—4041no—
274C23—1012no—
275C23—1012no—
276C23—1012no—
277C23—2021no—
278C23—2021no—
279C23—2021no—
280C23—2021no—
281C23C23×D10111yescharacteristic
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—1012no—
301C2×C4—1012no—
302C2×C4—1012no—
303C2×C4—4044no—
304C2×C4—4044no—
305C2×C4—2028no—
306C2×C4—2021no—
307C2×C4—2021no—
308C2×C4—2021no—
309C2×C4—2021no—
310C2×C4—2021no—
311C2×C4—2021no—
312C2×C4—2021no—
313C2×C4—2021no—
314C2×C4—2021no—
315C2×C4—2021no—
316C2×C4—2021no—
317C2×C4—2021no—
318C2×C4—2021no—
319C2×C4—2021no—
320C2×C4—2021no—
321C2×C4—2021no—
322C2×C4—2021no—
323C2×C4—2021no—
324C2×C4C2×C4×D10112yes—
325C2×C4C2×C4×D10112yes—
326C2×C4C2×C4×D10112yes—
327C22—1014no—
328C22—2022no—
329C22—2022no—
330C22—2022no—
331C22—2022no—
332C22—2022no—
333C22—2022no—
334C22C22×C4×D10111yescharacteristic
335C22#41×D10111yescharacteristic
336C22#41×D10111yescharacteristic
337C22#1569230011yescharacteristic
338C22#1569230111yescharacteristic
339C22#1569230211yescharacteristic
340C22#1569230311yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—4041no—
349C4—4041no—
350C4—4041no—
351C4—4041no—
352C4—2022no—
353C4—2022no—
354C4—2022no—
355C2—2024no—
356C2#117×D10111yescharacteristic
357C2#2026564911yescharacteristic
358C2#2026565311yescharacteristic
359C2#2026576811yescharacteristic
360C2#2026577011yescharacteristic
361C2#2026577311yescharacteristic
362C2#2026577511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutatorC22×C101C23×C4
Fitting#387×C101C2
socle, cosocleC23×C101C24
prime radicalC23×D101C23
hypercenter#387D101
hypocenterC101#2313
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #20265064C2semidirect
3. #20265063C2semidirect
4. #20265062C2semidirect
5. #20265061C2semidirect
6. #20265060C2semidirect
7. #20265059C2semidirect
8. #20265058C2semidirect
15. #387×C101C2semidirect
25. C4⋊C4×D101C4semidirect
182. C101#2313semidirect
191. #387D101semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D1012
#202650642
#202650632
#202650622
#202650612
#202650602
#202650592
#202650582
#202650392
#202650362
#202650342
C4×#131080512
#202650242
#387×C1012
#2313101