Finite Group Databasebeta

← #27181260

Subgroups — #27181260

Order 12928.

380 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265731C211yesmaximal, characteristic
2C4×Q8×D101C211yesmaximal, characteristic
3#20265509C211yesmaximal, characteristic
4#20265506C211yesmaximal, characteristic
5#20265461C211yesmaximal, characteristic, complemented
6#20265460C211yesmaximal, characteristic, complemented
7#20265386C211yesmaximal, characteristic, complemented
8#20265385C211yesmaximal, characteristic, complemented
9#20265334C211yesmaximal, characteristic
10#20265331C211yesmaximal, characteristic
11#20265285C211yesmaximal, characteristic, complemented
12#20265282C211yesmaximal, characteristic, complemented
13#20265282C211yesmaximal, characteristic, complemented
14#20265232C211yesmaximal, characteristic
15#441×C101C211yesmaximal, characteristic, complemented
16C2×Q8×D101C2211yescharacteristic
17C2×Dic404C2211yescharacteristic
18C2×#13108064C2211yescharacteristic
19C2×#13108064C2211yescharacteristic
20#15692254C2211yescharacteristic
21#15692253C2211yescharacteristic
22#15692245—21no—
23#15692235C2211yescharacteristic
24#15692233—21no—
25#15692231C2211yescharacteristic
26Q8×Dic101C2211yescharacteristic
27C4×Dic202—21no—
28C4×Dic202—21no—
29C4×Dic202C2211yescharacteristic
30C4×Dic202C2211yescharacteristic
31#15692220—21no—
32#15692220C2211yescharacteristic
33#15692212—21no—
34C4⋊C4×D101—21no—
35C4⋊C4×D101C2211yescharacteristic
36C42×D101—21no—
37C42×D101C2211yescharacteristic
38#15692187C2211yescharacteristic
39#15692186C2211yescharacteristic
40#15692186C2211yescharacteristic
41#15692184C2211yescharacteristic
42#15692184C2211yescharacteristic
43#15692180C2211yescharacteristic
44#15692180C2211yescharacteristic
45#15692179C2211yescharacteristic
46#15692179C2211yescharacteristic
47#15692178C2211yescharacteristic
48#15692178C2211yescharacteristic
49#15692167C2211yescharacteristic
50#15692167C2211yescharacteristic
51#15692166C2211yescharacteristic
52C2×Q16×C101C2211yescharacteristic
53C4×Q8×C101C2211yescharacteristic
54C4×Q8×C101C2211yescharacteristic
55#106×C101C2211yescharacteristic
56#103×C101C2211yescharacteristic
57#103×C101C2211yescharacteristic
58#97×C101C2211yescharacteristic
59C2×Dic202—21no—
60C2×Dic202—21no—
61C2×Dic202C2311yescharacteristic
62C2×Dic202C2311yescharacteristic
63Q8×D101—22no—
64Q8×D101—22no—
65C2×C4×D101—21no—
66C2×C4×D101—21no—
67C2×C4×D101D411yescharacteristic
68C2×C4×D101D411yescharacteristic
69C2×C4×D101C2311yescharacteristic
70Dic404—22no—
71#13108064—22no—
72#13108064—22no—
73C2×#11717579C2311yescharacteristic
74C2×#11717579C2311yescharacteristic
75C4⋊Dic101—21no—
76C4⋊Dic101—21no—
77C4⋊Dic101C2311yescharacteristic
78C4⋊Dic101C2311yescharacteristic
79#13108053—21no—
80#13108053—21no—
81#13108053—21no—
82#13108053—21no—
83#13108053—21no—
84#13108053—21no—
85#13108053—21no—
86#13108053—21no—
87#13108051—21no—
88#13108051—21no—
89C4×Dic101—21no—
90C4×Dic101—21no—
91C4×Dic101—21no—
92C4×Dic101—21no—
93C4×Dic101D411yescharacteristic
94C4×Dic101D411yescharacteristic
95C4×Dic101C2311yescharacteristic
96C2×Q8×C101C2311yescharacteristic
97C2×Q8×C101C2311yescharacteristic
98Q16×C101—22no—
99C2×C8×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C4⋊C4×C101—21no—
102C4⋊C4×C101—21no—
103C4⋊C4×C101C2311yescharacteristic
104C4⋊C4×C101C2311yescharacteristic
105C42×C101—21no—
106C42×C101—21no—
107C42×C101C2311yescharacteristic
108C22×D101C2×D411yescharacteristic
109Q8×C101—21no—
110Q8×C101—21no—
111Q8×C101—21no—
112Q8×C101#4112yes—
113C2×C4×C101—21no—
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101C2×D411yescharacteristic
118C2×C4×C101C2×D411yescharacteristic
119C2×C4×C101C2411yescharacteristic
120C2×Dic101—21no—
121C2×Dic101—21no—
122C2×Dic101—21no—
123C2×Dic101—21no—
124C2×Dic101C2×D411yescharacteristic
125C2×Dic101C2×D411yescharacteristic
126C2×Dic101C2×D411yescharacteristic
127C4×D101—24no—
128C4×D101—22no—
129C4×D101—21no—
130C4×D101—21no—
131C4×D101—22no—
132C4×D101—42no—
133Dic202—24no—
134Dic202—21no—
135Dic202—21no—
136Dic202—21no—
137Dic202—42no—
138Dic202#4112yes—
139C8×C101—21no—
140C8×C101—21no—
141#11717579—21no—
142#11717579—21no—
143C22×C101C22×D411yescharacteristic
144C2×D101—21no—
145C2×D101—21no—
146C2×D101#13712yes—
147C4×C101—22no—
148C4×C101—21no—
149C4×C101—21no—
150C4×C101—41no—
151C4×C101—41no—
152C4×C101—41no—
153C4×C101C2×#4111yescharacteristic
154C4×C101C2×#4111yescharacteristic
155Dic101—21no—
156Dic101—22no—
157Dic101—21no—
158Dic101—41no—
159Dic101—41no—
160Dic101—41no—
161Dic101#13712yes—
162C2×C101#52511yescharacteristic
163C2×C101C2×#13711yescharacteristic
164C2×C101C2×#13711yescharacteristic
165D101—22no—
166#3113—1011nomaximal, Sylow
167C101#311311yescharacteristic, complemented, Sylow
168#533—1011no—
169C2×C4×Q8—1011no—
170#483—1011no—
171#483—1011no—
172#475—1011no—
173#475—1011no—
174#462—1011no—
175#462—1011no—
176#451—1011no—
177#451—1011no—
178#441—1011no—
179#441—1011no—
180#441—1011no—
181#441D10111yescharacteristic, complemented
182#432—1011no—
183C22×Q8—1011no—
184C2×Q16—1011no—
185C2×Q16—1011no—
186C2×Q16—1011no—
187C2×Q16C2×D10111yescharacteristic
188C4⋊Q8—1011no—
189C4⋊Q8—1011no—
190#125—2021no—
191C22⋊Q8—1011no—
192C22⋊Q8—1011no—
193C22⋊Q8—2021no—
194C4×Q8—1011no—
195C4×Q8—1011no—
196C4×Q8—1011no—
197C4×Q8—1011no—
198C4×Q8—2021no—
199C4×Q8—2021no—
200C4×Q8—2021no—
201C4×Q8C2×D10111yescharacteristic
202C4×Q8C2×D10111yescharacteristic
203#117—2021no—
204C2×C4⋊C4—1011no—
205C2×C4⋊C4—2021no—
206C2×C42—1011no—
207C2×C42—2021no—
208#106—1011no—
209#106—1011no—
210#106—1011no—
211#106C2×D10111yescharacteristic
212C4⋊C8—1011no—
213C4⋊C8—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
222C22⋊C8—1011no—
223C22⋊C8—1011no—
224#97—1011no—
225#97C2×D10111yescharacteristic
226C2×Q8—1011no—
227C2×Q8—1011no—
228C2×Q8—2021no—
229C2×Q8—2021no—
230C2×Q8—2022no—
231C2×Q8—2022no—
232C2×Q8C22×D10111yescharacteristic
233C2×Q8C22×D10111yescharacteristic
234C22×C4—1011no—
235C22×C4—1011no—
236C22×C4—1011no—
237C22×C4—2021no—
238C22×C4—2021no—
239Q16—22no—
240Q16—2022no—
241Q16—2022no—
242Q16—2022no—
243C2×C8—1011no—
244C2×C8—1011no—
245C2×C8C22×D10111yescharacteristic
246C2×C8C22×D10111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—1011no—
250C4⋊C4—1011no—
251C4⋊C4—2021no—
252C4⋊C4—2021no—
253C4⋊C4—2021no—
254C4⋊C4—2021no—
255C4⋊C4—2021no—
256C4⋊C4—2021no—
257C4⋊C4—2021no—
258C4⋊C4—2021no—
259C4⋊C4—2021no—
260C4⋊C4—2021no—
261C4⋊C4C22×D10111yescharacteristic
262C4⋊C4C22×D10111yescharacteristic
263C22⋊C4—2021no—
264C22⋊C4—2021no—
265C42—21no—
266C42—21no—
267C42—1011no—
268C42—1011no—
269C42—1011no—
270C42—2021no—
271C42—2021no—
272C42—2021no—
273C42—2021no—
274C42C22×D10111yescharacteristic
275C23—1011no—
276Q8—21no—
277Q8—21no—
278Q8—21no—
279Q8—1012no—
280Q8—4042no—
281Q8—2024no—
282Q8—2021no—
283Q8—2021no—
284Q8—2021no—
285Q8#1310807412yes—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—1011no—
291C2×C4—1011no—
292C2×C4—1011no—
293C2×C4—4042no—
294C2×C4—2022no—
295C2×C4—2022no—
296C2×C4—2024no—
297C2×C4—2021no—
298C2×C4—2021no—
299C2×C4—2021no—
300C2×C4—2021no—
301C2×C4—2021no—
302C2×C4—2021no—
303C2×C4D4×D10111yescharacteristic
304C2×C4D4×D10111yescharacteristic
305C2×C4C23×D10111yescharacteristic
306C8—21no—
307C8—21no—
308C8—2021no—
309C8—2021no—
310C22—1012no—
311C22—2021no—
312C22—2021no—
313C22C2×D4×D10111yescharacteristic
314C4—22no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—1012no—
321C4—4041no—
322C4—4041no—
323C4—4041no—
324C4—2021no—
325C4—2022no—
326C4—2021no—
327C4#41×D10111yescharacteristic
328C4C2×#1310807411yescharacteristic
329C2—2022no—
330C2#2026568611yescharacteristic
331C2#137×D10111yescharacteristic
332C2#137×D10111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#441×C101C2
socleC22×C101C22×D4
prime radicalC22×D101C2×D4
hypercenter#441D101
hypocenterC101#3113
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
5. #20265461C2semidirect
6. #20265460C2semidirect
7. #20265386C2semidirect
8. #20265385C2semidirect
11. #20265285C2semidirect
12. #20265282C2semidirect
13. #20265282C2semidirect
15. #441×C101C2semidirect
167. C101#3113semidirect
181. #441D101semidirect

Maximal subgroups

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

subgroupindex
#202657312
C4×Q8×D1012
#202655092
#202655062
#202654612
#202654602
#202653862
#202653852
#202653342
#202653312
#202652852
#202652822
#202652322
#441×C1012
#3113101