Finite Group Databasebeta

← #27183087

Subgroups — #27183087

Order 12928.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265823C211yesmaximal, characteristic, complemented
2#20265539C211yesmaximal, characteristic, complemented
3#20265507C211yesmaximal, characteristic, complemented
4#20265495C211yesmaximal, characteristic, complemented
5#20265464C211yesmaximal, characteristic, complemented
6#20265428C211yesmaximal, characteristic, complemented
7#20265404C211yesmaximal, characteristic, complemented
8#20265392C211yesmaximal, characteristic, complemented
9#20265320C211yesmaximal, characteristic, complemented
10#20265310C211yesmaximal, characteristic, complemented
11#20265287C211yesmaximal, characteristic, complemented
12#20265249C211yesmaximal, characteristic, complemented
13#20265176C211yesmaximal, characteristic, complemented
14C2×#15692175C211yesmaximal, characteristic, complemented
15#547×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C22×D404C2211yescharacteristic
18C2×#13108062C2211yescharacteristic, complemented
19C2×#13108059C2211yescharacteristic
20C2×#13108059C2211yescharacteristic
21C2×#13108058C2211yescharacteristic, complemented
22C22×#11717579C2211yescharacteristic
23#15692243C2211yescharacteristic
24#15692240—21no—
25#15692234C2211yescharacteristic
26#15692229C2211yescharacteristic
27#15692228—21no—
28#15692223—21no—
29C4×D404C2211yescharacteristic
30C22⋊C4×D101—21no—
31#15692186C2211yescharacteristic, complemented
32#15692186C2211yescharacteristic, complemented
33#15692186C2211yescharacteristic, complemented
34C4⋊#11717579C2211yescharacteristic, complemented
35#15692178C2211yescharacteristic, complemented
36#15692178C2211yescharacteristic, complemented
37#15692178C2211yescharacteristic, complemented
38#15692176C2211yescharacteristic, complemented
39#15692175C2211yescharacteristic
40#15692175C2211yescharacteristic
41#15692175C2211yescharacteristic
42#15692175C2211yescharacteristic
43#15692175C2211yescharacteristic
44#15692175C2211yescharacteristic
45C22⋊#11717579C2211yescharacteristic
46C22⋊#11717579C2211yescharacteristic, complemented
47#15692166C2211yescharacteristic, complemented
48C2×#41×C101—21no—
49C4⋊Q8×C101C2211yescharacteristic, complemented
50#123×C101—21no—
51#123×C101—21no—
52C22⋊Q8×C101—21no—
53#121×C101C2211yescharacteristic
54#121×C101C2211yescharacteristic, complemented
55C4×D4×C101C2211yescharacteristic
56C4×D4×C101C2211yescharacteristic, complemented
57C2×C4⋊C4×C101C2211yescharacteristic
58C2×C4⋊C4×C101C2211yescharacteristic, complemented
59C23×D101—21no—
60#13108074—22no—
61#13108074—41no—
62C2×Dic202C2311yescharacteristic
63C2×D404—22no—
64C2×D404—21no—
65C2×D404—41no—
66C2×D404C2311yescharacteristic
67C2×D404C2311yescharacteristic
68C2×C22⋊D101—21no—
69C2×C22⋊D101—21no—
70C2×C4×D101—21no—
71C2×C4×D101—21no—
72#13108062—41no—
73#13108059—22no—
74#13108059—41no—
75#13108058—41no—
76C2×#11717579—41no—
77C2×#11717579C2311yescharacteristic
78C2×#11717579C2311yescharacteristic
79C2×#11717579C2311yescharacteristic
80C2×#11717579C2311yescharacteristic
81C4⋊Dic101C2311yescharacteristic
82#13108053—21no—
83C22⋊Dic101—21no—
84#13108051—21no—
85#13108051—21no—
86#13108051—21no—
87#13108051—21no—
88#41×C101—44no—
89C2×Q8×C101—21no—
90C2×D4×C101—21no—
91C2×D4×C101—21no—
92C2×D4×C101D411yescharacteristic
93C2×D4×C101C2311yescharacteristic
94C22×C4×C101—21no—
95C22×C4×C101—21no—
96C22×C4×C101—21no—
97C22×C4×C101C2311yescharacteristic
98C22×C4×C101C2311yescharacteristic
99C4⋊C4×C101—21no—
100C4⋊C4×C101—21no—
101C4⋊C4×C101—21no—
102C4⋊C4×C101D411yescharacteristic
103C4⋊C4×C101C2311yescharacteristic
104C4⋊C4×C101C2311yescharacteristic
105C4⋊C4×C101C2311yescharacteristic
106C22⋊C4×C101—21no—
107C22⋊C4×C101—21no—
108C22⋊C4×C101—21no—
109C22⋊C4×C101D411yescharacteristic
110C22⋊C4×C101D411yescharacteristic
111C42×C101C2311yescharacteristic
112C23×C101—21no—
113C23×C101C2×D411yescharacteristic
114C23×C101C2×D411yescharacteristic
115C22×D101—21no—
116C22×D101—21no—
117C22×D101—42no—
118C22×D101—42no—
119C22×D101—81no—
120Q8×C101—42no—
121D4×C101—22no—
122D4×C101—21no—
123D4×C101—21no—
124D4×C101—42no—
125D4×C101—42no—
126C2×C4×C101—21no—
127C2×C4×C101—21no—
128C2×C4×C101—21no—
129C2×C4×C101—21no—
130C2×C4×C101—21no—
131C2×C4×C101—21no—
132C2×C4×C101—21no—
133C2×C4×C101—42no—
134C2×C4×C101—42no—
135C2×C4×C101—42no—
136C2×C4×C101C2×D411yescharacteristic
137C2×C4×C101C2×D411yescharacteristic
138C2×C4×C101C2×D411yescharacteristic
139C2×C4×C101C2×D411yescharacteristic
140C2×C4×C101C2411yescharacteristic
141C22⋊D101—42no—
142C22⋊D101—81no—
143C2×Dic101—21no—
144C2×Dic101—21no—
145D404—21no—
146D404—21no—
147D404—21no—
148D404—42no—
149D404#4112yescomplemented
150C4×D101—42no—
151C4×D101—81no—
152Dic202—21no—
153Dic202—21no—
154#11717579—21no—
155#11717579—21no—
156#11717579—21no—
157#11717579—21no—
158C22×C101—21no—
159C22×C101—21no—
160C22×C101—21no—
161C22×C101—21no—
162C22×C101—21no—
163C22×C101—41no—
164C22×C101—41no—
165C22×C101—41no—
166C22×C101AGL(1,ℤ/8)12yes—
167C22×C101C22×D411yescharacteristic
168C2×D101—22no—
169C2×D101—41no—
170C2×D101—41no—
171C2×D101—41no—
172C2×D101—41no—
173C2×D101—41no—
174C2×D101—84no—
175C4×C101—21no—
176C4×C101—21no—
177C4×C101—21no—
178C4×C101—21no—
179C4×C101—41no—
180C4×C101—41no—
181C4×C101—41no—
182C4×C101C2×#4111yescharacteristic
183C4×C101H(5,𝔽2)11yescharacteristic
184Dic101—41no—
185Dic101—41no—
186C2×C101—22no—
187C2×C101—41no—
188C2×C101—81no—
189C2×C101#54611yescharacteristic
190C2×C101C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C101#57711yescharacteristic
192D101—42no—
193D101—81no—
194#3306—1011nomaximal, Sylow
195C101#330611yescharacteristic, complemented, Sylow
196#547D10111yescharacteristic, complemented
197#546—1011no—
198#489—1011no—
199#483—1011no—
200#481—1011no—
201#476—1011no—
202#469—1011no—
203#465—1011no—
204#463—1011no—
205#449—1011no—
206#447—1011no—
207#442—1011no—
208#435—1011no—
209#417—1011no—
210C2×#102—1011no—
211C2×#41—21no—
212C2×#41—1011no—
213C22×D4—1011no—
214C2×SD16—1011no—
215C2×D8—1011no—
216C2×D8—1011no—
217C2×M16—1011no—
218C22×C8—1011no—
219C4⋊Q8C2×D10111yescharacteristic, complemented
220#124—1011no—
221#123—21no—
222#123—21no—
223#123—2021no—
224C22⋊Q8—21no—
225C22⋊Q8—1011no—
226#121—1011no—
227#121—2021no—
228#121C2×D10111yescharacteristic
229#121C2×D10111yescharacteristic, complemented
230#120—2021no—
231C4×D4—1011no—
232C4×D4C2×D10111yescharacteristic
233C4×D4C2×D10111yescharacteristic, complemented
234C2×C4⋊C4C2×D10111yescharacteristic
235C2×C4⋊C4C2×D10111yescharacteristic, complemented
236C2×C22⋊C4—2021no—
237#106—1011no—
238#106—1011no—
239#106—1011no—
240C4⋊C8—1011no—
241#103—1011no—
242#103—1011no—
243#103—1011no—
244#102—1011no—
245#102—1011no—
246#102—1011no—
247#102—1011no—
248#102—1011no—
249#102—1011no—
250#102—1011no—
251C22⋊C8—1011no—
252C22⋊C8—1011no—
253#97—1011no—
254C24—2021no—
255#41—44no—
256#41—4041no—
257#41—2022no—
258C2×Q8—21no—
259C2×Q8—1011no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—1011no—
263C2×D4—1011no—
264C2×D4—4041no—
265C2×D4—2022no—
266C2×D4—2021no—
267C2×D4—2021no—
268C2×D4—2021no—
269C2×D4C22⋊D10111yescharacteristic
270C2×D4C22×D10111yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—2021no—
275C22×C4—2021no—
276C22×C4C22×D10111yescharacteristic
277C22×C4C22×D10111yescharacteristic
278SD16—4041no—
279D8—4041no—
280D8—2022no—
281M16—4041no—
282C2×C8—1011no—
283C2×C8—1011no—
284C2×C8—1011no—
285C2×C8—1011no—
286C2×C8—4041no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—1011no—
291C4⋊C4—2021no—
292C4⋊C4C22⋊D10111yescharacteristic
293C4⋊C4C22×D10111yescharacteristic
294C4⋊C4C22×D10111yescharacteristic
295C4⋊C4C22×D10111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—2021no—
300C22⋊C4—2021no—
301C22⋊C4—2021no—
302C22⋊C4—2021no—
303C22⋊C4—2021no—
304C22⋊C4C22⋊D10111yescharacteristic
305C22⋊C4C22⋊D10111yescharacteristic
306C42C22×D10111yescharacteristic
307C23—21no—
308C23—8081no—
309C23—4042no—
310C23—4042no—
311C23—2021no—
312C23—2021no—
313C23C2×C22⋊D10111yescharacteristic
314C23C2×C22⋊D10111yescharacteristic
315Q8—42no—
316Q8—2021no—
317Q8—2021no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—8081no—
324D4—1012no—
325D4—4042no—
326D4—4042no—
327D4—2021no—
328D4—2021no—
329D4—2021no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—8081no—
341C2×C4—4042no—
342C2×C4—2021no—
343C2×C4—2021no—
344C2×C4C2×C22⋊D10111yescharacteristic
345C2×C4C2×C22⋊D10111yescharacteristic
346C2×C4C2×C22⋊D10111yescharacteristic
347C2×C4C2×C22⋊D10111yescharacteristic
348C2×C4C23×D10111yescharacteristic
349C8—2021no—
350C8—2021no—
351C8—2021no—
352C8—2021no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—8084no—
362C22—4041no—
363C22—4041no—
364C22—4041no—
365C22—4041no—
366C22—4041no—
367C22—2022no—
368C22#1569228112yes—
369C22C22×C22⋊D10111yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—4041no—
378C4—4041no—
379C4#41×D10111yescharacteristic
380C4#1569230111yescharacteristic
381C2—22no—
382C2—41no—
383C2—81no—
384C2—8081no—
385C2—4042no—
386C2#2026581511yescharacteristic
387C2C2×#1569228111yescharacteristic
388C2#2026598511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#547×C101C2
socleC22×C101C22×D4
hypercenter#547D101
hypocenterC101#3306
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #20265823C2semidirect
2. #20265539C2semidirect
3. #20265507C2semidirect
4. #20265495C2semidirect
5. #20265464C2semidirect
6. #20265428C2semidirect
7. #20265404C2semidirect
8. #20265392C2semidirect
9. #20265320C2semidirect
10. #20265310C2semidirect
11. #20265287C2semidirect
12. #20265249C2semidirect
13. #20265176C2semidirect
14. C2×#15692175C2semidirect
15. #547×C101C2semidirect
18. C2×#13108062C22semidirect
21. C2×#13108058C22semidirect
31. #15692186C22semidirect
32. #15692186C22semidirect
33. #15692186C22semidirect
34. C4⋊#11717579C22semidirect
35. #15692178C22semidirect
36. #15692178C22semidirect
37. #15692178C22semidirect
38. #15692176C22semidirect
46. C22⋊#11717579C22semidirect
47. #15692166C22semidirect
49. C4⋊Q8×C101C22semidirect
54. #121×C101C22semidirect
56. C4×D4×C101C22semidirect
58. C2×C4⋊C4×C101C22semidirect
149. D404#41semidirect
195. C101#3306semidirect
196. #547D101semidirect
219. C4⋊Q8C2×D101semidirect
229. #121C2×D101semidirect
233. C4×D4C2×D101semidirect
235. C2×C4⋊C4C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202658232
#202655392
#202655072
#202654952
#202654642
#202654282
#202654042
#202653922
#202653202
#202653102
#202652872
#202652492
#202651762
C2×#156921752
#547×C1012
#3306101