Finite Group Databasebeta

← #27181388

Subgroups — #27181388

Order 12928.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265657C211yesmaximal, characteristic, complemented
2#20265510C211yesmaximal, characteristic, complemented
3#20265488C211yesmaximal, characteristic, complemented
4#20265469C211yesmaximal, characteristic, complemented
5#20265454C211yesmaximal, characteristic, complemented
6#20265396C211yesmaximal, characteristic, complemented
7#20265389C211yesmaximal, characteristic, complemented
8#20265337C211yesmaximal, characteristic, complemented
9#20265320C211yesmaximal, characteristic
10#20265277C211yesmaximal, characteristic, complemented
11#20265275C211yesmaximal, characteristic, complemented
12C4×#13108064C211yesmaximal, characteristic, complemented
13C4×#13108059C211yesmaximal, characteristic, complemented
14#20265238C211yesmaximal, characteristic, complemented
15#542×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×#13108064C2211yescharacteristic
18C2×#13108062C2211yescharacteristic
19C2×#13108061C2211yescharacteristic
20C2×#13108059C2211yescharacteristic
21C4×Dic202C2211yescharacteristic
22C4×Dic202C2211yescharacteristic
23C4×D404C2211yescharacteristic
24C4×D404C2211yescharacteristic
25#15692215—21no—
26#15692215—21no—
27#15692213—21no—
28C2×C4⋊Dic101C2211yescharacteristic
29C4⋊C4×D101—21no—
30#15692188C2211yescharacteristic
31#15692188C2211yescharacteristic
32#15692188C2211yescharacteristic
33#15692188C2211yescharacteristic
34C4⋊#11717579C2211yescharacteristic
35C4⋊#11717579C2211yescharacteristic
36#15692179C2211yescharacteristic
37#15692179C2211yescharacteristic
38#15692178C2211yescharacteristic
39#15692178C2211yescharacteristic
40#15692176C2211yescharacteristic
41#15692176C2211yescharacteristic
42#15692175C2211yescharacteristic
43#15692175C2211yescharacteristic
44C22⋊#11717579C2211yescharacteristic
45C22⋊#11717579C2211yescharacteristic
46#15692166C2211yescharacteristic
47C4×#11717579C2211yescharacteristic
48C4⋊Q8×C101C2211yescharacteristic
49#126×C101—21no—
50#124×C101—21no—
51#124×C101C2211yescharacteristic
52#123×C101—21no—
53C22⋊Q8×C101—21no—
54C22⋊Q8×C101C2211yescharacteristic
55#121×C101C2211yescharacteristic
56C4×Q8×C101C2211yescharacteristic
57C4×D4×C101C2211yescharacteristic
58#117×C101C2211yescharacteristic
59#13108074—22no—
60#13108074—22no—
61C2×Dic202C2311yescharacteristic
62C2×D404C2311yescharacteristic
63C2×C22⋊D101—21no—
64C22×Dic101—21no—
65C2×C4×D101—21no—
66C2×C4×D101—21no—
67C2×C4×D101—21no—
68#13108064—22no—
69#13108062—22no—
70#13108061—22no—
71#13108059—22no—
72C2×#11717579C2311yescharacteristic
73C2×#11717579C2311yescharacteristic
74C2×#11717579C2311yescharacteristic
75C2×#11717579C2311yescharacteristic
76C4⋊Dic101—21no—
77C4⋊Dic101C2311yescharacteristic
78C4⋊Dic101C2311yescharacteristic
79#13108053—21no—
80#13108053—21no—
81#13108051—21no—
82#13108051—21no—
83C4×Dic101—21no—
84C4×Dic101—21no—
85C2×Q8×C101—21no—
86C2×Q8×C101C2311yescharacteristic
87C2×D4×C101—21no—
88C2×D4×C101C2311yescharacteristic
89C22×C4×C101—21no—
90C22×C4×C101C2311yescharacteristic
91C4⋊C4×C101—21no—
92C4⋊C4×C101—21no—
93C4⋊C4×C101—21no—
94C4⋊C4×C101D411yescharacteristic
95C4⋊C4×C101D411yescharacteristic
96C4⋊C4×C101C2311yescharacteristic
97C4⋊C4×C101C2311yescharacteristic
98C22⋊C4×C101—21no—
99C22⋊C4×C101—21no—
100C22⋊C4×C101—21no—
101C22⋊C4×C101—21no—
102C22⋊C4×C101—21no—
103C22⋊C4×C101D411yescharacteristic
104C22⋊C4×C101D411yescharacteristic
105C42×C101—21no—
106C42×C101C2311yescharacteristic
107C42×C101C2311yescharacteristic
108C23×C101—21no—
109C23×C101C2×D411yescharacteristic
110C22×D101—21no—
111Q8×C101—21no—
112Q8×C101—21no—
113Q8×C101—81no—
114D4×C101—21no—
115D4×C101—21no—
116D4×C101—81no—
117C2×C4×C101—21no—
118C2×C4×C101—21no—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—81no—
123C2×C4×C101C2×D411yescharacteristic
124C2×C4×C101C2×D411yescharacteristic
125C2×C4×C101C2×D411yescharacteristic
126C2×C4×C101C2×D411yescharacteristic
127C2×C4×C101C2×D411yescharacteristic
128C2×C4×C101C2411yescharacteristic
129C22⋊D101—24no—
130C2×Dic101—21no—
131C2×Dic101—21no—
132C2×Dic101—21no—
133C2×Dic101—81no—
134D404—21no—
135D404#4112yes—
136C4×D101—24no—
137C4×D101—81no—
138C4×D101—81no—
139Dic202—21no—
140Dic202#4112yes—
141#11717579—21no—
142#11717579—21no—
143#11717579—21no—
144#11717579—21no—
145C22×C101—21no—
146C22×C101—21no—
147C22×C101—21no—
148C22×C101—41no—
149C22×C101—41no—
150C22×C101—41no—
151C22×C101C22×D411yescharacteristic
152C2×D101—22no—
153C2×D101—41no—
154C2×D101—41no—
155C4×C101—21no—
156C4×C101—21no—
157C4×C101—21no—
158C4×C101—21no—
159C4×C101—21no—
160C4×C101—41no—
161C4×C101—41no—
162C4×C101—41no—
163C4×C101C2×#4111yescharacteristic
164C4×C101C2×#4111yescharacteristic
165Dic101—22no—
166Dic101—41no—
167Dic101—41no—
168C2×C101—41no—
169C2×C101—81no—
170C2×C101#52511yescharacteristic
171C2×C101#57611yescharacteristic
172C2×C101#57811yescharacteristic
173D101—42no—
174#3124—1011nomaximal, Sylow
175C101#312411yescharacteristic, complemented, Sylow
176#542D10111yescharacteristic, complemented
177#520—1011no—
178#484—1011no—
179#480—1011no—
180#477—1011no—
181#474—1011no—
182#464—1011no—
183#463—1011no—
184#452—1011no—
185#449—1011no—
186#440—1011no—
187#440—1011no—
188C4×Q16—1011no—
189C4×D8—1011no—
190#433—1011no—
191C2×#41—1011no—
192C2×Q16—1011no—
193C2×SD16—1011no—
194C2×SD16—1011no—
195C2×D8—1011no—
196C4⋊Q8C2×D10111yescharacteristic
197#126—21no—
198#124—21no—
199#124C2×D10111yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C2×D10111yescharacteristic
203#121C2×D10111yescharacteristic
204C4×Q8—1011no—
205C4×Q8—1011no—
206C4×Q8C2×D10111yescharacteristic
207C4×D4—1011no—
208C4×D4—1011no—
209C4×D4—2021no—
210C4×D4—2021no—
211C4×D4C2×D10111yescharacteristic
212#117—2021no—
213#117C2×D10111yescharacteristic
214C2×C4⋊C4—1011no—
215C2×C4⋊C4—2021no—
216#107—1011no—
217#107—1011no—
218#107—1011no—
219#107—1011no—
220C4⋊C8—1011no—
221C4⋊C8—1011no—
222#103—1011no—
223#103—1011no—
224#103—1011no—
225#103—1011no—
226#102—1011no—
227#102—1011no—
228#102—1011no—
229#102—1011no—
230C22⋊C8—1011no—
231C22⋊C8—1011no—
232#97—1011no—
233C4×C8—1011no—
234#41—2022no—
235#41—2022no—
236C2×Q8—21no—
237C2×Q8—1011no—
238C2×Q8C22×D10111yescharacteristic
239C2×D4—21no—
240C2×D4—1011no—
241C2×D4—2021no—
242C2×D4C22×D10111yescharacteristic
243C22×C4—21no—
244C22×C4—2021no—
245C22×C4—2021no—
246C22×C4—2021no—
247C22×C4—2021no—
248C22×C4C22×D10111yescharacteristic
249Q16—2022no—
250SD16—2022no—
251SD16—2022no—
252D8—2022no—
253C2×C8—1011no—
254C2×C8—1011no—
255C2×C8—1011no—
256C2×C8—1011no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—1011no—
261C4⋊C4—1011no—
262C4⋊C4—2021no—
263C4⋊C4—2021no—
264C4⋊C4—2021no—
265C4⋊C4C22⋊D10111yescharacteristic
266C4⋊C4C22⋊D10111yescharacteristic
267C4⋊C4C22×D10111yescharacteristic
268C4⋊C4C22×D10111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—2021no—
275C22⋊C4—2021no—
276C22⋊C4C22⋊D10111yescharacteristic
277C22⋊C4C22⋊D10111yescharacteristic
278C42—21no—
279C42—2021no—
280C42—2021no—
281C42C22×D10111yescharacteristic
282C42C22×D10111yescharacteristic
283C23—21no—
284C23—2021no—
285C23C2×C22⋊D10111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—1012no—
290Q8—2021no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—1012no—
295D4—2024no—
296D4—2021no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—8081no—
304C2×C4—8081no—
305C2×C4—8081no—
306C2×C4—2024no—
307C2×C4—2021no—
308C2×C4—2021no—
309C2×C4—2021no—
310C2×C4C2×C22⋊D10111yescharacteristic
311C2×C4C2×C22⋊D10111yescharacteristic
312C2×C4C2×C22⋊D10111yescharacteristic
313C2×C4C2×C22⋊D10111yescharacteristic
314C2×C4C2×C22⋊D10111yescharacteristic
315C2×C4C23×D10111yescharacteristic
316C8—2021no—
317C8—2021no—
318C8—2021no—
319C8—2021no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—4041no—
327C22—4041no—
328C22—2022no—
329C22C22×C22⋊D10111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—4041no—
339C4—4041no—
340C4—2022no—
341C4#41×D10111yescharacteristic
342C4#41×D10111yescharacteristic
343C2—41no—
344C2—81no—
345C2—4042no—
346C2#2026568411yescharacteristic
347C2#2026598011yescharacteristic
348C2#2026599211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#542×C101C2
socleC22×C101C22×D4
prime radical#20265320C2
hypercenter#542D101
hypocenterC101#3124
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #20265657C2semidirect
2. #20265510C2semidirect
3. #20265488C2semidirect
4. #20265469C2semidirect
5. #20265454C2semidirect
6. #20265396C2semidirect
7. #20265389C2semidirect
8. #20265337C2semidirect
10. #20265277C2semidirect
11. #20265275C2semidirect
12. C4×#13108064C2semidirect
13. C4×#13108059C2semidirect
14. #20265238C2semidirect
15. #542×C101C2semidirect
175. C101#3124semidirect
176. #542D101semidirect

Maximal subgroups

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

subgroupindex
#202656572
#202655102
#202654882
#202654692
#202654542
#202653962
#202653892
#202653372
#202653202
#202652772
#202652752
C4×#131080642
C4×#131080592
#202652382
#542×C1012
#3124101