Finite Group Databasebeta

← #27183138

Subgroups — #27183138

Order 12928.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265873C211yesmaximal, characteristic, complemented
2#20265541C211yesmaximal, characteristic, complemented
3#20265498C211yesmaximal, characteristic, complemented
4#20265488C211yesmaximal, characteristic, complemented
5#20265484C211yesmaximal, characteristic, complemented
6#20265428C211yesmaximal, characteristic, complemented
7#20265411C211yesmaximal, characteristic, complemented
8#20265369C211yesmaximal, characteristic, complemented
9#20265322C211yesmaximal, characteristic, complemented
10#20265322C211yesmaximal, characteristic, complemented
11#20265275C211yesmaximal, characteristic, complemented
12#20265249C211yesmaximal, characteristic, complemented
13#20265178C211yesmaximal, characteristic, complemented
14#20265173C211yesmaximal, characteristic, complemented
15#550×C101C211yesmaximal, characteristic, complemented
16C2×#13108061C2211yescharacteristic
17C2×#13108059C2211yescharacteristic
18C2×#13108059C2211yescharacteristic
19C2×#13108058C2211yescharacteristic
20C22×#11717579C2211yescharacteristic
21#15692250—21no—
22#15692247C2211yescharacteristic
23#15692237—21no—
24#15692229C2211yescharacteristic
25#15692229C2211yescharacteristic
26#15692227—21no—
27C4×D404C2211yescharacteristic
28#15692215—21no—
29#15692214C2211yescharacteristic
30C2×C4⋊Dic101C2211yescharacteristic
31#15692188C2211yescharacteristic
32#15692188C2211yescharacteristic
33#15692186C2211yescharacteristic
34C4⋊#11717579C2211yescharacteristic
35#15692179C2211yescharacteristic
36#15692179C2211yescharacteristic
37#15692179C2211yescharacteristic
38#15692176C2211yescharacteristic
39#15692176C2211yescharacteristic
40#15692176C2211yescharacteristic
41#15692176C2211yescharacteristic
42#15692176C2211yescharacteristic
43#15692176C2211yescharacteristic
44#15692175C2211yescharacteristic
45C22⋊#11717579C2211yescharacteristic
46C22⋊#11717579C2211yescharacteristic
47#15692166C2211yescharacteristic
48C2×#41×C101C2211yescharacteristic
49C2×#41×C101C2211yescharacteristic
50#127×C101—21no—
51#127×C101C2211yescharacteristic
52#121×C101—21no—
53#121×C101—21no—
54#121×C101C2211yescharacteristic
55#121×C101C2211yescharacteristic
56C4×Q8×C101C2211yescharacteristic
57C4×D4×C101—21no—
58C4×D4×C101C2211yescharacteristic
59C2×D404C2311yescharacteristic
60C2×C22⋊D101—21no—
61C2×C22⋊D101—21no—
62C22×Dic101—21no—
63C2×C4×D101—21no—
64#13108061—22no—
65#13108059—41no—
66#13108059—41no—
67#13108058—41no—
68C2×#11717579—41no—
69C2×#11717579C2311yescharacteristic
70C2×#11717579C2311yescharacteristic
71C2×#11717579C2311yescharacteristic
72C2×#11717579C2311yescharacteristic
73C4⋊Dic101—21no—
74C4⋊Dic101C2311yescharacteristic
75C4⋊Dic101C2311yescharacteristic
76C4⋊Dic101C2311yescharacteristic
77#13108053—21no—
78#13108053—21no—
79C22⋊Dic101—21no—
80#13108051—21no—
81#13108051—21no—
82#13108051—21no—
83C4×Dic101—21no—
84#41×C101—22no—
85#41×C101—22no—
86#41×C101—41no—
87#41×C101—41no—
88C2×Q8×C101C2311yescharacteristic
89C2×D4×C101—21no—
90C2×D4×C101—21no—
91C2×D4×C101—21no—
92C2×D4×C101—21no—
93C2×D4×C101—21no—
94C2×D4×C101—21no—
95C2×D4×C101D411yescharacteristic
96C2×D4×C101C2311yescharacteristic
97C2×D4×C101C2311yescharacteristic
98C22×C4×C101—21no—
99C22×C4×C101—21no—
100C22×C4×C101C2311yescharacteristic
101C22×C4×C101C2311yescharacteristic
102C4⋊C4×C101—21no—
103C4⋊C4×C101D411yescharacteristic
104C4⋊C4×C101C2311yescharacteristic
105C22⋊C4×C101—21no—
106C22⋊C4×C101—21no—
107C22⋊C4×C101D411yescharacteristic
108C22⋊C4×C101D411yescharacteristic
109C42×C101—21no—
110C42×C101C2311yescharacteristic
111C23×C101—21no—
112C23×C101—21no—
113C23×C101C2×D411yescharacteristic
114C23×C101C2×D411yescharacteristic
115C22×D101—21no—
116Q8×C101—21no—
117Q8×C101#4112yes—
118D4×C101—21no—
119D4×C101—21no—
120D4×C101—21no—
121D4×C101—21no—
122D4×C101—41no—
123D4×C101—42no—
124D4×C101—42no—
125D4×C101—42no—
126D4×C101—81no—
127D4×C101—81no—
128D4×C101—81no—
129C2×C4×C101—21no—
130C2×C4×C101—21no—
131C2×C4×C101—21no—
132C2×C4×C101—21no—
133C2×C4×C101—21no—
134C2×C4×C101—21no—
135C2×C4×C101—42no—
136C2×C4×C101—42no—
137C2×C4×C101C2×D411yescharacteristic
138C2×C4×C101C2×D411yescharacteristic
139C2×C4×C101C2×D411yescharacteristic
140C2×C4×C101C2×D411yescharacteristic
141C2×C4×C101C2411yescharacteristic
142C22⋊D101—42no—
143C22⋊D101—81no—
144C2×Dic101—21no—
145C2×Dic101—21no—
146C2×Dic101—21no—
147C2×Dic101—81no—
148D404—21no—
149D404—21no—
150C4×D101—81no—
151#11717579—21no—
152#11717579—21no—
153#11717579—21no—
154#11717579—21no—
155C22×C101—21no—
156C22×C101—21no—
157C22×C101—21no—
158C22×C101—21no—
159C22×C101—21no—
160C22×C101—21no—
161C22×C101—41no—
162C22×C101—41no—
163C22×C101—41no—
164C22×C101—41no—
165C22×C101—41no—
166C22×C101—41no—
167C22×C101C22×D411yescharacteristic
168C2×D101—41no—
169C2×D101—41no—
170C2×D101—41no—
171C4×C101—21no—
172C4×C101—21no—
173C4×C101—22no—
174C4×C101—21no—
175C4×C101—21no—
176C4×C101—41no—
177C4×C101C2×#4111yescharacteristic
178C4×C101H(5,𝔽2)11yescharacteristic
179Dic101—41no—
180Dic101—41no—
181Dic101—41no—
182C2×C101—41no—
183C2×C101—41no—
184C2×C101—81no—
185C2×C101—81no—
186C2×C101#54611yescharacteristic
187C2×C101#57511yescharacteristic
188C2×C101#57611yescharacteristic
189D101—81no—
190#3309—1011nomaximal, Sylow
191C101#330911yescharacteristic, complemented, Sylow
192#553—1011no—
193#550D10111yescharacteristic, complemented
194#490—1011no—
195#482—1011no—
196#480—1011no—
197#479—1011no—
198#469—1011no—
199#466—1011no—
200#459—1011no—
201#449—1011no—
202#449—1011no—
203#440—1011no—
204#435—1011no—
205#417—1011no—
206#416—1011no—
207C2×#41C2×D10111yescharacteristic
208C2×#41C2×D10111yescharacteristic
209C2×SD16—1011no—
210C2×D8—1011no—
211C2×D8—1011no—
212C2×M16—1011no—
213C22×C8—1011no—
214#127—21no—
215#127C2×D10111yescharacteristic
216#126—2021no—
217#125—1011no—
218#123—2021no—
219#121—21no—
220#121—21no—
221#121—1011no—
222#121—1011no—
223#121—2021no—
224#121C2×D10111yescharacteristic
225#121C2×D10111yescharacteristic
226C4×Q8C2×D10111yescharacteristic
227C4×D4—21no—
228C4×D4—1011no—
229C4×D4—2021no—
230C4×D4C2×D10111yescharacteristic
231#117—1011no—
232C2×C4⋊C4—1011no—
233#107—1011no—
234#107—1011no—
235#106—1011no—
236C4⋊C8—1011no—
237#103—1011no—
238#103—1011no—
239#103—1011no—
240#102—1011no—
241#102—1011no—
242#102—1011no—
243#102—1011no—
244#102—1011no—
245#102—1011no—
246#102—1011no—
247C22⋊C8—1011no—
248C22⋊C8—1011no—
249#97—1011no—
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8C22×D10111yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—1011no—
262C2×D4—2021no—
263C2×D4—2021no—
264C2×D4C22⋊D10111yescharacteristic
265C2×D4C22×D10111yescharacteristic
266C2×D4C22×D10111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—2021no—
270C22×C4—2021no—
271C22×C4C22×D10111yescharacteristic
272C22×C4C22×D10111yescharacteristic
273SD16—2022no—
274D8—4041no—
275D8—4041no—
276M16—4041no—
277C2×C8—1011no—
278C2×C8—1011no—
279C2×C8—1011no—
280C2×C8—1011no—
281C2×C8—4041no—
282C4⋊C4—21no—
283C4⋊C4—1011no—
284C4⋊C4—1011no—
285C4⋊C4—1011no—
286C4⋊C4—2021no—
287C4⋊C4—2021no—
288C4⋊C4—2021no—
289C4⋊C4C22⋊D10111yescharacteristic
290C4⋊C4C22×D10111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—2021no—
294C22⋊C4—2021no—
295C22⋊C4—2021no—
296C22⋊C4—2021no—
297C22⋊C4C22⋊D10111yescharacteristic
298C22⋊C4C22⋊D10111yescharacteristic
299C42—21no—
300C42—2021no—
301C42C22×D10111yescharacteristic
302C23—21no—
303C23—21no—
304C23—2021no—
305C23C2×C22⋊D10111yescharacteristic
306C23C2×C22⋊D10111yescharacteristic
307Q8—21no—
308Q8#1310807312yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4—81no—
319D4—81no—
320D4—8081no—
321D4—4042no—
322D4—2021no—
323D4—2021no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—8081no—
333C2×C4—8081no—
334C2×C4—2021no—
335C2×C4—2021no—
336C2×C4—2021no—
337C2×C4C2×C22⋊D10111yescharacteristic
338C2×C4C2×C22⋊D10111yescharacteristic
339C2×C4C2×C22⋊D10111yescharacteristic
340C2×C4C2×C22⋊D10111yescharacteristic
341C2×C4C23×D10111yescharacteristic
342C8—2021no—
343C8—2021no—
344C8—2021no—
345C8—2021no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—4041no—
359C22—4041no—
360C22—4041no—
361C22C22×C22⋊D10111yescharacteristic
362C4—21no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—4041no—
369C4—4041no—
370C4—4041no—
371C4C2×#1310807311yescharacteristic
372C4#1569230011yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—8081no—
378C2#2026582111yescharacteristic
379C2#2026597511yescharacteristic
380C2#2026598011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#550×C101C2
socleC22×C101C22×D4
hypercenter#550D101
hypocenterC101#3309
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #20265873C2semidirect
2. #20265541C2semidirect
3. #20265498C2semidirect
4. #20265488C2semidirect
5. #20265484C2semidirect
6. #20265428C2semidirect
7. #20265411C2semidirect
8. #20265369C2semidirect
9. #20265322C2semidirect
10. #20265322C2semidirect
11. #20265275C2semidirect
12. #20265249C2semidirect
13. #20265178C2semidirect
14. #20265173C2semidirect
15. #550×C101C2semidirect
191. C101#3309semidirect
193. #550D101semidirect

Maximal subgroups

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

subgroupindex
#202658732
#202655412
#202654982
#202654882
#202654842
#202654282
#202654112
#202653692
#202653222
#202652752
#202652492
#202651782
#202651732
#550×C1012
#3309101