Finite Group Databasebeta

← #27181494

Subgroups — #27181494

Order 12928.

372 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265804C211yesmaximal, characteristic, complemented
2#20265747C211yesmaximal, characteristic
3#20265546C211yesmaximal, characteristic, complemented
4#20265544C211yesmaximal, characteristic, complemented
5#20265535C211yesmaximal, characteristic, complemented
6#20265531C211yesmaximal, characteristic, complemented
7#20265530C211yesmaximal, characteristic, complemented
8#20265529C211yesmaximal, characteristic, complemented
9#20265526C211yesmaximal, characteristic, complemented
10#20265184C211yesmaximal, characteristic, complemented
11#20265175C211yesmaximal, characteristic
12#20265170C211yesmaximal, characteristic
13#103×D101C211yesmaximal, characteristic, complemented
14#20265134C211yesmaximal, characteristic, complemented
15#489×C101C211yesmaximal, characteristic, complemented
16C2×#13108073C2211yescharacteristic
17C2×Q8×D101C2211yescharacteristic
18C2×#13108057C2211yescharacteristic
19C2×C8×D101C2211yescharacteristic
20#15692255C2211yescharacteristic
21#15692254C2211yescharacteristic
22#15692253—21no—
23#15692253C2211yescharacteristic
24#15692247C2211yescharacteristic
25#15692246C2211yescharacteristic
26#15692245—21no—
27#15692242C2211yescharacteristic
28#15692237—21no—
29#15692237—21no—
30#15692233—21no—
31#15692232—21no—
32#15692232—21no—
33#15692231—21no—
34#15692213C2211yescharacteristic
35#15692212C2211yescharacteristic
36C4⋊C4×D101C2211yescharacteristic
37#15692180C2211yescharacteristic
38#15692180C2211yescharacteristic
39#15692180C2211yescharacteristic
40#15692180C2211yescharacteristic
41#15692179C2211yescharacteristic
42#15692179C2211yescharacteristic
43#15692178C2211yescharacteristic
44#15692178C2211yescharacteristic
45#15692178C2211yescharacteristic
46#15692178C2211yescharacteristic
47#15692176C2211yescharacteristic
48#15692176C2211yescharacteristic
49#15692165C2211yescharacteristic
50C4×#11717579C2211yescharacteristic
51C8×Dic101C2211yescharacteristic
52C4⋊Q8×C101C2211yescharacteristic
53#124×C101C2211yescharacteristic
54#103×C101C2211yescharacteristic
55#103×C101C2211yescharacteristic
56#102×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic
58#97×C101C2211yescharacteristic
59#13108073—22no—
60#13108073—22no—
61C2×Dic202—21no—
62C2×Dic202—21no—
63C2×Dic202C2311yescharacteristic
64C2×Dic202C2311yescharacteristic
65Q8×D101—22no—
66Q8×D101—22no—
67C2×C22⋊D101—21no—
68C22×Dic101—21no—
69C2×C4×D101—21no—
70C2×C4×D101—21no—
71C2×C4×D101C2311yescharacteristic
72#13108057—22no—
73C2×#11717579C2311yescharacteristic
74C2×#11717579C2311yescharacteristic
75C8×D101—22no—
76C4⋊Dic101—21no—
77C4⋊Dic101—21no—
78C4⋊Dic101—21no—
79C4⋊Dic101C2311yescharacteristic
80C4⋊Dic101C2311yescharacteristic
81#13108053—21no—
82#13108053—21no—
83#13108053—21no—
84#13108053—21no—
85#13108053—21no—
86#13108053—21no—
87#13108053—21no—
88#13108053D411yescharacteristic
89#13108053D411yescharacteristic
90C22⋊Dic101—21no—
91C22⋊Dic101—21no—
92#13108051—21no—
93#13108051D411yescharacteristic
94#13108051D411yescharacteristic
95C4×Dic101—21no—
96C4×Dic101C2311yescharacteristic
97C2×Q8×C101—21no—
98C2×Q8×C101C2311yescharacteristic
99C2×D4×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C2×C8×C101C2311yescharacteristic
102C4⋊C4×C101—21no—
103C4⋊C4×C101C2311yescharacteristic
104C4⋊C4×C101C2311yescharacteristic
105C22⋊C4×C101—21no—
106C22⋊C4×C101—21no—
107C42×C101C2311yescharacteristic
108C23×C101—21no—
109C22×D101C2×D411yescharacteristic
110Q8×C101—21no—
111Q8×C101—21no—
112Q8×C101—81no—
113D4×C101—21no—
114D4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—21no—
118C2×C4×C101C2×D411yescharacteristic
119C2×C4×C101C2×D411yescharacteristic
120C2×C4×C101C2411yescharacteristic
121C22⋊D101—42no—
122C2×Dic101—21no—
123C2×Dic101—21no—
124C2×Dic101—21no—
125C2×Dic101—21no—
126C2×Dic101—42no—
127C2×Dic101C2×D411yescharacteristic
128C2×Dic101C2×D411yescharacteristic
129C2×Dic101C2×D411yescharacteristic
130C4×D101—42no—
131C4×D101—81no—
132C4×D101#4112yes—
133C4×D101#4112yes—
134Dic202—21no—
135Dic202—21no—
136Dic202—21no—
137Dic202—21no—
138Dic202—42no—
139Dic202—81no—
140C8×C101—21no—
141C8×C101—21no—
142#11717579—21no—
143#11717579—21no—
144C22×C101—41no—
145C22×C101—41no—
146C22×C101—41no—
147C22×C101C22×D411yescharacteristic
148C2×D101—21no—
149C2×D101—21no—
150C2×D101#12412yes—
151C4×C101—21no—
152C4×C101—21no—
153C4×C101—41no—
154C4×C101—41no—
155C4×C101—41no—
156C4×C101C2×#4111yescharacteristic
157C4×C101C2×#4111yescharacteristic
158Dic101—21no—
159Dic101—21no—
160Dic101—41no—
161Dic101—41no—
162Dic101—41no—
163Dic101—41no—
164Dic101#12412yes—
165C2×C101—81no—
166C2×C101C2×#12411yescharacteristic
167C2×C101#57711yescharacteristic
168C2×C101#57811yescharacteristic
169D101—22no—
170#3137—1011nomaximal, Sylow
171C101#313711yescharacteristic, complemented, Sylow
172#544—1011no—
173#536—1011no—
174#491—1011no—
175#491—1011no—
176#489—1011no—
177#489D10111yescharacteristic, complemented
178#488—1011no—
179#488—1011no—
180#487—1011no—
181#487—1011no—
182#419—1011no—
183#417—1011no—
184#416—1011no—
185C2×#103—1011no—
186#405—1011no—
187C2×#41—1011no—
188C22×Q8—1011no—
189C2×M16—1011no—
190C22×C8—1011no—
191C4⋊Q8—1011no—
192C4⋊Q8—1011no—
193C4⋊Q8—1011no—
194C4⋊Q8—2021no—
195C4⋊Q8C2×D10111yescharacteristic
196#125—1011no—
197#125—1011no—
198#125—2021no—
199#124—1011no—
200#124C2×D10111yescharacteristic
201#123—2021no—
202#123—2021no—
203C22⋊Q8—2021no—
204C22⋊Q8—2021no—
205C22⋊Q8—2021no—
206C22⋊Q8—2021no—
207#117—1011no—
208#117—1011no—
209C2×C4⋊C4—1011no—
210#103—1011no—
211#103—1011no—
212#103—1011no—
213#103—1011no—
214#103—1011no—
215#103—1011no—
216#103—1011no—
217#103—1011no—
218#103—1011no—
219#103—1011no—
220#103C2×D10111yescharacteristic
221#103C2×D10111yescharacteristic
222#102—1011no—
223#102—1011no—
224#102C2×D10111yescharacteristic
225#102C2×D10111yescharacteristic
226#97—1011no—
227#97C2×D10111yescharacteristic
228C4×C8—1011no—
229C4×C8—1011no—
230#41—2022no—
231#41—2022no—
232C2×Q8—21no—
233C2×Q8—1011no—
234C2×Q8—1011no—
235C2×Q8—2021no—
236C2×Q8—2021no—
237C2×Q8—2022no—
238C2×Q8—2022no—
239C2×Q8C22×D10111yescharacteristic
240C2×D4—2021no—
241C2×D4C22×D10111yescharacteristic
242C22×C4—1011no—
243C22×C4—2021no—
244C22×C4—2021no—
245C22×C4—2021no—
246M16—2022no—
247C2×C8—1011no—
248C2×C8—1011no—
249C2×C8—2022no—
250C2×C8C22×D10111yescharacteristic
251C2×C8C22×D10111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—1011no—
254C4⋊C4—1011no—
255C4⋊C4—1011no—
256C4⋊C4—1011no—
257C4⋊C4—2021no—
258C4⋊C4—2021no—
259C4⋊C4—2021no—
260C4⋊C4—2021no—
261C4⋊C4—2021no—
262C4⋊C4—2021no—
263C4⋊C4—2021no—
264C4⋊C4—2021no—
265C4⋊C4—2021no—
266C4⋊C4—2021no—
267C4⋊C4C22×D10111yescharacteristic
268C4⋊C4C22×D10111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—1011no—
272C22⋊C4—1011no—
273C22⋊C4—2021no—
274C22⋊C4—2021no—
275C22⋊C4—2021no—
276C42—1011no—
277C42—2021no—
278C42C22×D10111yescharacteristic
279C23—21no—
280C23—1011no—
281Q8—21no—
282Q8—21no—
283Q8—81no—
284Q8—8081no—
285Q8—4042no—
286Q8—2021no—
287Q8—2021no—
288Q8—2021no—
289Q8—2021no—
290D4—21no—
291D4—21no—
292D4—4042no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—8081no—
297C2×C4—1011no—
298C2×C4—1012no—
299C2×C4—1012no—
300C2×C4—1011no—
301C2×C4—1011no—
302C2×C4—4042no—
303C2×C4—4042no—
304C2×C4—2021no—
305C2×C4—2021no—
306C2×C4—2021no—
307C2×C4—2021no—
308C2×C4D4×D10111yescharacteristic
309C2×C4D4×D10111yescharacteristic
310C2×C4C23×D10111yescharacteristic
311C8—21no—
312C8—21no—
313C8—2021no—
314C8—2021no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—1012no—
319C22—2021no—
320C22—2021no—
321C22C2×D4×D10111yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—1012no—
328C4—4041no—
329C4—4041no—
330C4—4041no—
331C4—4041no—
332C4—2021no—
333C4—2021no—
334C4#41×D10111yescharacteristic
335C4#41×D10111yescharacteristic
336C2—81no—
337C2—2022no—
338C2#124×D10111yescharacteristic
339C2#2026598711yescharacteristic
340C2#2026599311yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#489×C101C2
socleC22×C101C22×D4
prime radicalC2×#13108073C22
hypercenter#489D101
hypocenterC101#3137
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #20265804C2semidirect
3. #20265546C2semidirect
4. #20265544C2semidirect
5. #20265535C2semidirect
6. #20265531C2semidirect
7. #20265530C2semidirect
8. #20265529C2semidirect
9. #20265526C2semidirect
10. #20265184C2semidirect
13. #103×D101C2semidirect
14. #20265134C2semidirect
15. #489×C101C2semidirect
171. C101#3137semidirect
177. #489D101semidirect

Maximal subgroups

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

subgroupindex
#202658042
#202657472
#202655462
#202655442
#202655352
#202655312
#202655302
#202655292
#202655262
#202651842
#202651752
#202651702
#103×D1012
#202651342
#489×C1012
#3137101