Finite Group Databasebeta

← #27181105

Subgroups — #27181105

Order 12928.

398 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
1#20265756C211yesmaximal, characteristic
2#20265658C211yesmaximal, characteristic, complemented
3#20265520C211yesmaximal, characteristic, complemented
4#20265519C211yesmaximal, characteristic, complemented
5#20265514C211yesmaximal, characteristic, complemented
6#20265512C211yesmaximal, characteristic, complemented
7#20265500C211yesmaximal, characteristic, complemented
8#20265498C211yesmaximal, characteristic, complemented
9#20265489C211yesmaximal, characteristic, complemented
10#20265218C211yesmaximal, characteristic, complemented
11#107×D101C211yesmaximal, characteristic, complemented
12#20265175C211yesmaximal, characteristic, complemented
13#20265170C211yesmaximal, characteristic, complemented
14#20265142C211yesmaximal, characteristic, complemented
15#480×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×#13108073C2211yescharacteristic
18C2×#13108057C2211yescharacteristic
19C2×C8×D101C2211yescharacteristic
20#15692235C2211yescharacteristic
21#15692234C2211yescharacteristic
22#15692232—21no—
23#15692228—21no—
24#15692227—21no—
25#15692226—21no—
26#15692226C2211yescharacteristic
27#15692220—21no—
28#15692217—21no—
29C4×C22⋊D101—21no—
30C4×C22⋊D101—21no—
31#15692214C2211yescharacteristic
32#15692213C2211yescharacteristic
33#15692213C2211yescharacteristic
34C4⋊C4×D101C2211yescharacteristic
35C4⋊C4×D101C2211yescharacteristic
36C4⋊C4×D101C2211yescharacteristic
37#15692189C2211yescharacteristic
38#15692188C2211yescharacteristic
39#15692188C2211yescharacteristic
40#15692188C2211yescharacteristic
41#15692187C2211yescharacteristic
42#15692186C2211yescharacteristic
43#15692180C2211yescharacteristic
44#15692180C2211yescharacteristic
45#15692178C2211yescharacteristic
46#15692178C2211yescharacteristic
47#15692176C2211yescharacteristic
48#15692176C2211yescharacteristic
49C22⋊#11717579C2211yescharacteristic
50#15692167C2211yescharacteristic
51#15692167C2211yescharacteristic
52#121×C101C2211yescharacteristic
53C2×C4⋊C4×C101C2211yescharacteristic
54#107×C101C2211yescharacteristic
55#107×C101C2211yescharacteristic
56#102×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic
58C22⋊C8×C101C2211yescharacteristic
59#13108074—22no—
60#13108074—22no—
61#13108073—22no—
62#13108073—22no—
63C2×Dic202D411yescharacteristic
64C2×Dic202C2311yescharacteristic
65C2×D404D411yescharacteristic
66C2×C22⋊D101—21no—
67C2×C22⋊D101—21no—
68C2×C22⋊D101D411yescharacteristic
69C2×C22⋊D101D411yescharacteristic
70C22×Dic101—21no—
71C2×C4×D101—21no—
72C2×C4×D101—21no—
73C2×C4×D101—21no—
74C2×C4×D101C2311yescharacteristic
75C2×C4×D101C2311yescharacteristic
76#13108057—22no—
77C2×#11717579C2311yescharacteristic
78C2×#11717579C2311yescharacteristic
79C8×D101—22no—
80C4⋊Dic101—21no—
81C4⋊Dic101C2311yescharacteristic
82C4⋊Dic101C2311yescharacteristic
83C4⋊Dic101C2311yescharacteristic
84#13108053—21no—
85#13108053—21no—
86#13108053—21no—
87#13108053—21no—
88C22⋊Dic101—21no—
89C22⋊Dic101—21no—
90C22⋊Dic101—21no—
91#13108051—21no—
92#13108051—21no—
93#13108051—21no—
94C4×Dic101—21no—
95C4×Dic101—21no—
96C4×Dic101—21no—
97C2×D4×C101—21no—
98C2×D4×C101C2311yescharacteristic
99C22×C4×C101—21no—
100C22×C4×C101C2311yescharacteristic
101C2×C8×C101C2311yescharacteristic
102C2×C8×C101C2311yescharacteristic
103C4⋊C4×C101—21no—
104C4⋊C4×C101C2311yescharacteristic
105C4⋊C4×C101C2311yescharacteristic
106C4⋊C4×C101C2311yescharacteristic
107C22⋊C4×C101—21no—
108C23×C101—21no—
109C23×C101C2×D411yescharacteristic
110C22×D101C2×D411yescharacteristic
111C22×D101C2×D411yescharacteristic
112D4×C101—21no—
113D4×C101—21no—
114D4×C101—81no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—21no—
118C2×C4×C101—21no—
119C2×C4×C101—21no—
120C2×C4×C101—81no—
121C2×C4×C101C2×D411yescharacteristic
122C2×C4×C101C2411yescharacteristic
123C22⋊D101—22no—
124C22⋊D101—22no—
125C22⋊D101—42no—
126C22⋊D101—81no—
127C2×Dic101—21no—
128C2×Dic101—21no—
129C2×Dic101—21no—
130C2×Dic101—21no—
131C2×Dic101—42no—
132C2×Dic101C2×D411yescharacteristic
133C2×Dic101C2×D411yescharacteristic
134D404—22no—
135C4×D101—21no—
136C4×D101—21no—
137C4×D101—81no—
138C4×D101—81no—
139C4×D101—81no—
140C4×D101#4112yes—
141C4×D101#4112yes—
142Dic202—22no—
143Dic202—21no—
144Dic202—21no—
145C8×C101—21no—
146C8×C101—21no—
147#11717579—21no—
148#11717579—21no—
149C22×C101—21no—
150C22×C101—21no—
151C22×C101—21no—
152C22×C101—41no—
153C22×C101—41no—
154C22×C101—41no—
155C22×C101C22×D411yescharacteristic
156C2×D101—21no—
157C2×D101—21no—
158C2×D101—21no—
159C2×D101—21no—
160C2×D101—21no—
161C2×D101#12312yes—
162C4×C101—21no—
163C4×C101—41no—
164C4×C101—41no—
165C4×C101—41no—
166C4×C101C2×#4111yescharacteristic
167C4×C101C2×#4111yescharacteristic
168Dic101—21no—
169Dic101—41no—
170Dic101—41no—
171Dic101—41no—
172Dic101—41no—
173Dic101#12312yes—
174C2×C101—41no—
175C2×C101—81no—
176C2×C101C2×#12311yescharacteristic
177C2×C101#57611yescharacteristic
178C2×C101#57811yescharacteristic
179D101—22no—
180D101—41no—
181#3098—1011nomaximal, Sylow
182C101#309811yescharacteristic, complemented, Sylow
183#537—1011no—
184#520—1011no—
185#485—1011no—
186#485—1011no—
187#484—1011no—
188#484—1011no—
189#482—1011no—
190#482—1011no—
191#480—1011no—
192#480D10111yescharacteristic, complemented
193#428—1011no—
194C2×#107—1011no—
195#417—1011no—
196#416—1011no—
197#408—1011no—
198C2×#41—1011no—
199C2×#41—1011no—
200C2×M16—1011no—
201C22×C8—1011no—
202C22⋊Q8—1011no—
203C22⋊Q8—1011no—
204C22⋊Q8—2021no—
205#121—1011no—
206#121—2021no—
207#121—2021no—
208#121—2021no—
209#121C2×D10111yescharacteristic
210C4×Q8—2021no—
211C4×D4—2021no—
212C4×D4—2021no—
213C4×D4—2021no—
214#117—1011no—
215#117—1011no—
216#117—1011no—
217C2×C4⋊C4—1011no—
218C2×C4⋊C4—1011no—
219C2×C4⋊C4—1011no—
220C2×C4⋊C4C2×D10111yescharacteristic
221#107—1011no—
222#107—1011no—
223#107—1011no—
224#107—1011no—
225#107C2×D10111yescharacteristic
226#107C2×D10111yescharacteristic
227#106—1011no—
228#106—1011no—
229#103—1011no—
230#103—1011no—
231#103—1011no—
232#103—1011no—
233#102—1011no—
234#102—1011no—
235#102C2×D10111yescharacteristic
236#102C2×D10111yescharacteristic
237C22⋊C8—1011no—
238C22⋊C8—1011no—
239C22⋊C8—1011no—
240C22⋊C8C2×D10111yescharacteristic
241#41—2022no—
242#41—2022no—
243#41—2022no—
244#41—2022no—
245C2×Q8—1011no—
246C2×Q8—1011no—
247C2×D4—21no—
248C2×D4—1011no—
249C2×D4—1011no—
250C2×D4—1011no—
251C2×D4—2021no—
252C2×D4—2021no—
253C2×D4C22×D10111yescharacteristic
254C22×C4—21no—
255C22×C4—1011no—
256C22×C4—1011no—
257C22×C4—2021no—
258C22×C4—2021no—
259C22×C4—2021no—
260C22×C4—2021no—
261C22×C4C22×D10111yescharacteristic
262M16—2022no—
263C2×C8—1011no—
264C2×C8—1011no—
265C2×C8—2022no—
266C2×C8C22×D10111yescharacteristic
267C2×C8C22×D10111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—1011no—
270C4⋊C4—1011no—
271C4⋊C4—1011no—
272C4⋊C4—2021no—
273C4⋊C4—2021no—
274C4⋊C4—2021no—
275C4⋊C4—2021no—
276C4⋊C4—2021no—
277C4⋊C4C22×D10111yescharacteristic
278C4⋊C4C22×D10111yescharacteristic
279C4⋊C4C22×D10111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—2021no—
282C22⋊C4—2021no—
283C22⋊C4—2021no—
284C22⋊C4—2021no—
285C22⋊C4—2021no—
286C22⋊C4—2021no—
287C42—2021no—
288C42—2021no—
289C42—2021no—
290C23—21no—
291C23—1011no—
292C23—1011no—
293C23D4×D10111yescharacteristic
294Q8—2022no—
295Q8—2021no—
296Q8—2021no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—8081no—
301D4—4042no—
302D4—2022no—
303D4—2022no—
304D4—2022no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—8081no—
312C2×C4—8081no—
313C2×C4—8081no—
314C2×C4—1011no—
315C2×C4—1012no—
316C2×C4—1012no—
317C2×C4—1011no—
318C2×C4—4042no—
319C2×C4—2021no—
320C2×C4—2021no—
321C2×C4—2021no—
322C2×C4—2021no—
323C2×C4—2021no—
324C2×C4—2021no—
325C2×C4D4×D10111yescharacteristic
326C2×C4C23×D10111yescharacteristic
327C8—21no—
328C8—21no—
329C8—2021no—
330C8—2021no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—1012no—
338C22—2021no—
339C22—2021no—
340C22—2021no—
341C22—2021no—
342C22—2021no—
343C22C2×D4×D10111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—1012no—
349C4—4041no—
350C4—4041no—
351C4—4041no—
352C4—4041no—
353C4—2021no—
354C4#41×D10111yescharacteristic
355C4#41×D10111yescharacteristic
356C2—41no—
357C2—81no—
358C2—4041no—
359C2—2022no—
360C2#123×D10111yescharacteristic
361C2#2026597811yescharacteristic
362C2#2026599311yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#480×C101C2
socleC22×C101C22×D4
prime radical#20265756C2
hypercenter#480D101
hypocenterC101#3098
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #20265658C2semidirect
3. #20265520C2semidirect
4. #20265519C2semidirect
5. #20265514C2semidirect
6. #20265512C2semidirect
7. #20265500C2semidirect
8. #20265498C2semidirect
9. #20265489C2semidirect
10. #20265218C2semidirect
11. #107×D101C2semidirect
12. #20265175C2semidirect
13. #20265170C2semidirect
14. #20265142C2semidirect
15. #480×C101C2semidirect
182. C101#3098semidirect
192. #480D101semidirect

Maximal subgroups

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

subgroupindex
#202657562
#202656582
#202655202
#202655192
#202655142
#202655122
#202655002
#202654982
#202654892
#202652182
#107×D1012
#202651752
#202651702
#202651422
#480×C1012
#3098101