Finite Group Databasebeta

← #27182967

Subgroups — #27182967

Order 12928.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265867C211yesmaximal, characteristic, complemented
2#20265531C211yesmaximal, characteristic, complemented
3#20265505C211yesmaximal, characteristic, complemented
4#20265498C211yesmaximal, characteristic, complemented
5#20265477C211yesmaximal, characteristic, complemented
6#20265416C211yesmaximal, characteristic, complemented
7#20265404C211yesmaximal, characteristic, complemented
8#20265396C211yesmaximal, characteristic, complemented
9#20265339C211yesmaximal, characteristic, complemented
10#20265328C211yesmaximal, characteristic, complemented
11C4×#13108062C211yesmaximal, characteristic, complemented
12D4×#11717579C211yesmaximal, characteristic, complemented
13#20265173C211yesmaximal, characteristic, complemented
14C2×#15692176C211yesmaximal, characteristic, complemented
15#546×C101C211yesmaximal, characteristic
16C2×#13108064C2211yescharacteristic, complemented
17C2×#13108062C2211yescharacteristic
18C2×#13108062C2211yescharacteristic
19C22×#11717579C2211yescharacteristic
20C22×#11717579C2211yescharacteristic, complemented
21#15692248—21no—
22#15692247C2211yescharacteristic, complemented
23#15692245—21no—
24#15692236—21no—
25#15692234C2211yescharacteristic
26#15692234C2211yescharacteristic, complemented
27C4×Dic202C2211yescharacteristic, complemented
28#15692214C2211yescharacteristic, complemented
29#15692211—21no—
30C2×C4⋊Dic101C2211yescharacteristic
31#15692188C2211yescharacteristic, complemented
32#15692186C2211yescharacteristic, complemented
33#15692186C2211yescharacteristic, complemented
34C4⋊#11717579C2211yescharacteristic, complemented
35#15692179C2211yescharacteristic, complemented
36#15692179C2211yescharacteristic, complemented
37#15692179C2211yescharacteristic, complemented
38#15692178C2211yescharacteristic, complemented
39#15692176C2211yescharacteristic
40#15692176C2211yescharacteristic
41#15692176C2211yescharacteristic
42#15692176C2211yescharacteristic
43#15692176C2211yescharacteristic
44#15692176C2211yescharacteristic
45C22⋊#11717579C2211yescharacteristic
46C22⋊#11717579C2211yescharacteristic, complemented
47C4×#11717579C2211yescharacteristic, complemented
48C2×#41×C101C2211yescharacteristic
49C22×D4×C101C2211yescharacteristic
50#124×C101C2211yescharacteristic
51#123×C101—21no—
52C22⋊Q8×C101C2211yescharacteristic
53#121×C101—21no—
54#121×C101C2211yescharacteristic
55#120×C101—21no—
56C4×D4×C101C2211yescharacteristic
57C4×D4×C101C2211yescharacteristic
58C2×C22⋊C4×C101—21no—
59C2×Dic202C2311yescharacteristic
60C22×Dic101—21no—
61#13108064—41no—
62#13108062—22no—
63#13108062—41no—
64C2×#11717579—41no—
65C2×#11717579—41no—
66C2×#11717579C2311yescharacteristic
67C2×#11717579C2311yescharacteristic
68C2×#11717579C2311yescharacteristic
69C2×#11717579C2311yescharacteristic
70C4⋊Dic101—21no—
71C4⋊Dic101C2311yescharacteristic
72C4⋊Dic101C2311yescharacteristic
73C4⋊Dic101C2311yescharacteristic
74#13108053—21no—
75#13108053—21no—
76#13108053—21no—
77#13108053—21no—
78#13108053—21no—
79C22⋊Dic101—21no—
80C22⋊Dic101—21no—
81C22⋊Dic101—21no—
82C4×Dic101—21no—
83C4×Dic101—21no—
84C24×C101—21no—
85#41×C101—22no—
86#41×C101—41no—
87C2×Q8×C101C2311yescharacteristic
88C2×D4×C101—22no—
89C2×D4×C101—21no—
90C2×D4×C101—21no—
91C2×D4×C101—21no—
92C2×D4×C101—41no—
93C2×D4×C101D411yescharacteristic
94C2×D4×C101C2311yescharacteristic
95C2×D4×C101C2311yescharacteristic
96C22×C4×C101—21no—
97C22×C4×C101—21no—
98C22×C4×C101C2311yescharacteristic
99C22×C4×C101C2311yescharacteristic
100C4⋊C4×C101—21no—
101C4⋊C4×C101D411yescharacteristic
102C4⋊C4×C101C2311yescharacteristic
103C22⋊C4×C101—21no—
104C22⋊C4×C101—21no—
105C22⋊C4×C101—21no—
106C22⋊C4×C101—21no—
107C22⋊C4×C101—21no—
108C22⋊C4×C101D411yescharacteristic
109C22⋊C4×C101D411yescharacteristic
110C42×C101C2311yescharacteristic
111C23×C101—21no—
112C23×C101—21no—
113C23×C101—42no—
114C23×C101—42no—
115C23×C101—81no—
116C23×C101C2×D411yescharacteristic
117C23×C101C2×D411yescharacteristic
118Q8×C101—21no—
119Q8×C101—21no—
120D4×C101—22no—
121D4×C101—21no—
122D4×C101—21no—
123D4×C101—21no—
124D4×C101—42no—
125D4×C101—42no—
126D4×C101—81no—
127D4×C101#4112yes—
128C2×C4×C101—21no—
129C2×C4×C101—21no—
130C2×C4×C101—21no—
131C2×C4×C101—21no—
132C2×C4×C101—21no—
133C2×C4×C101—21no—
134C2×C4×C101—42no—
135C2×C4×C101—81no—
136C2×C4×C101C2×D411yescharacteristic
137C2×C4×C101C2×D411yescharacteristic
138C2×C4×C101C2×D411yescharacteristic
139C2×C4×C101C2×D411yescharacteristic
140C2×C4×C101C2411yescharacteristic
141C2×Dic101—21no—
142C2×Dic101—21no—
143C2×Dic101—21no—
144C2×Dic101—21no—
145C2×Dic101—42no—
146Dic202—21no—
147Dic202—21no—
148#11717579—21no—
149#11717579—21no—
150#11717579—21no—
151#11717579—21no—
152C22×C101—21no—
153C22×C101—21no—
154C22×C101—21no—
155C22×C101—22no—
156C22×C101—21no—
157C22×C101—21no—
158C22×C101—41no—
159C22×C101—41no—
160C22×C101—41no—
161C22×C101—41no—
162C22×C101—41no—
163C22×C101—84no—
164C22×C101#13512yes—
165C22×C101C22×D411yescharacteristic
166C4×C101—21no—
167C4×C101—21no—
168C4×C101—21no—
169C4×C101—21no—
170C4×C101—41no—
171C4×C101—41no—
172C4×C101C2×#4111yescharacteristic
173C4×C101H(5,𝔽2)11yescharacteristic
174Dic101—41no—
175Dic101—41no—
176Dic101—41no—
177Dic101—41no—
178C2×C101—22no—
179C2×C101—41no—
180C2×C101—42no—
181C2×C101—81no—
182C2×C101#54611yescharacteristic
183C2×C101C2×#13511yescharacteristic
184C2×C101#57711yescharacteristic
185#3296—1011nomaximal, Sylow
186C101#329611yescharacteristic, complemented, Sylow
187#552—1011no—
188#546D10111yescharacteristic
189#488—1011no—
190#483—1011no—
191#482—1011no—
192#478—1011no—
193#467—1011no—
194#465—1011no—
195#464—1011no—
196#452—1011no—
197#450—1011no—
198C4×SD16—1011no—
199C8×D4—1011no—
200#416—1011no—
201C2×#102—1011no—
202C2×#41C2×D10111yescharacteristic
203C22×D4C2×D10111yescharacteristic
204C2×Q16—1011no—
205C2×SD16—1011no—
206C2×SD16—1011no—
207C22×C8—1011no—
208C22×C8—1011no—
209#126—2021no—
210#125—1011no—
211#125—2021no—
212#124C2×D10111yescharacteristic
213#123—21no—
214#123—2021no—
215C22⋊Q8—1011no—
216C22⋊Q8—1011no—
217C22⋊Q8C2×D10111yescharacteristic
218#121—21no—
219#121C2×D10111yescharacteristic
220#120—21no—
221C4×Q8—1011no—
222C4×D4C2×D10111yescharacteristic
223C4×D4C2×D10111yescharacteristic
224#117—1011no—
225#117—2021no—
226C2×C4⋊C4—1011no—
227C2×C22⋊C4—21no—
228#107—1011no—
229#106—1011no—
230#106—1011no—
231C4⋊C8—1011no—
232#103—1011no—
233#103—1011no—
234#103—1011no—
235#103—1011no—
236#102—1011no—
237#102—1011no—
238#102—1011no—
239#102—1011no—
240#102—1011no—
241#102—1011no—
242C22⋊C8—1011no—
243C22⋊C8—1011no—
244C4×C8—1011no—
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—1011no—
249C2×Q8C22×D10111yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D10111yescharacteristic
256C2×D4C22×D10111yescharacteristic
257C2×D4C22×D10111yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—2021no—
261C22×C4C22×D10111yescharacteristic
262C22×C4C22×D10111yescharacteristic
263Q16—4041no—
264SD16—4041no—
265SD16—2022no—
266C2×C8—1011no—
267C2×C8—1011no—
268C2×C8—1011no—
269C2×C8—1011no—
270C2×C8—4041no—
271C2×C8—4041no—
272C4⋊C4—21no—
273C4⋊C4—1011no—
274C4⋊C4—1011no—
275C4⋊C4—1011no—
276C4⋊C4—2021no—
277C4⋊C4—2021no—
278C4⋊C4—2021no—
279C4⋊C4—2021no—
280C4⋊C4—2021no—
281C4⋊C4—2021no—
282C4⋊C4C22⋊D10111yescharacteristic
283C4⋊C4C22×D10111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—2021no—
290C22⋊C4—2021no—
291C22⋊C4—2021no—
292C22⋊C4C22⋊D10111yescharacteristic
293C22⋊C4C22⋊D10111yescharacteristic
294C42—2021no—
295C42—2021no—
296C42C22×D10111yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D10111yescharacteristic
303C23C2×C22⋊D10111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2021no—
307Q8—2021no—
308D4—22no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#1310807312yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—4042no—
325C2×C4—2021no—
326C2×C4—2021no—
327C2×C4—2021no—
328C2×C4—2021no—
329C2×C4C2×C22⋊D10111yescharacteristic
330C2×C4C2×C22⋊D10111yescharacteristic
331C2×C4C2×C22⋊D10111yescharacteristic
332C2×C4C2×C22⋊D10111yescharacteristic
333C2×C4C23×D10111yescharacteristic
334C8—2021no—
335C8—2021no—
336C8—2021no—
337C8—2021no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—84no—
350C22#1569227512yes—
351C22C22×C22⋊D10111yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—4041no—
359C4—4041no—
360C4—4041no—
361C4—4041no—
362C4C2×#1310807311yescharacteristic
363C4#1569230011yescharacteristic
364C2—22no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#2026582111yescharacteristic
369C2C2×#1569227511yescharacteristic
370C2#2026598811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting, prime radical#546×C101C2
socleC22×C101C22×D4
hypercenter#546D101
hypocenterC101#3296
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #20265867C2semidirect
2. #20265531C2semidirect
3. #20265505C2semidirect
4. #20265498C2semidirect
5. #20265477C2semidirect
6. #20265416C2semidirect
7. #20265404C2semidirect
8. #20265396C2semidirect
9. #20265339C2semidirect
10. #20265328C2semidirect
11. C4×#13108062C2semidirect
12. D4×#11717579C2semidirect
13. #20265173C2semidirect
14. C2×#15692176C2semidirect
16. C2×#13108064C22semidirect
20. C22×#11717579C22semidirect
22. #15692247C22semidirect
26. #15692234C22semidirect
27. C4×Dic202C22semidirect
28. #15692214C22semidirect
31. #15692188C22semidirect
32. #15692186C22semidirect
33. #15692186C22semidirect
34. C4⋊#11717579C22semidirect
35. #15692179C22semidirect
36. #15692179C22semidirect
37. #15692179C22semidirect
38. #15692178C22semidirect
46. C22⋊#11717579C22semidirect
47. C4×#11717579C22semidirect
186. C101#3296semidirect

Maximal subgroups

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

subgroupindex
#202658672
#202655312
#202655052
#202654982
#202654772
#202654162
#202654042
#202653962
#202653392
#202653282
C4×#131080622
D4×#117175792
#202651732
C2×#156921762
#546×C1012
#3296101