Finite Group Databasebeta

← #14541157

Subgroups — #14541157

Order 2176.

354 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763499C211yesmaximal, characteristic, complemented
2#11763208C211yesmaximal, characteristic, complemented
3#11763150C211yesmaximal, characteristic, complemented
4#11763144C211yesmaximal, characteristic, complemented
5#11763130C211yesmaximal, characteristic, complemented
6#11763120C211yesmaximal, characteristic, complemented
7#11763113C211yesmaximal, characteristic, complemented
8#11763109C211yesmaximal, characteristic, complemented
9#11763036C211yesmaximal, characteristic, complemented
10#11763036C211yesmaximal, characteristic, complemented
11C4×#63229C211yesmaximal, characteristic, complemented
12D4×#3622C211yesmaximal, characteristic, complemented
13#11762845C211yesmaximal, characteristic, complemented
14C2×#10587479C211yesmaximal, characteristic, complemented
15C17×#553C211yesmaximal, characteristic
16C17×#126—21no—
17C17×#125C2211yescharacteristic
18C17×#123—21no—
19C17×#121—21no—
20C17×#121C2211yescharacteristic
21C17×#121C2211yescharacteristic
22C4×D4×C17—21no—
23C4×D4×C17C2211yescharacteristic
24C4×D4×C17C2211yescharacteristic
25C17×#117C2211yescharacteristic
26C2×C4⋊C4×C17C2211yescharacteristic
27#10587621—21no—
28C2×#63229C2211yescharacteristic
29#10587612C2211yescharacteristic
30C2×C4⋊Dic17C2211yescharacteristic
31#10587610C2211yescharacteristic
32#10587610C2211yescharacteristic
33C22×#3622C2211yescharacteristic
34C22×#3622C2211yescharacteristic
35#10587575—21no—
36#10587565—21no—
37#10587563—21no—
38#10587556C2211yescharacteristic
39C4×Dic34C2211yescharacteristic
40#10587503C2211yescharacteristic
41#10587503C2211yescharacteristic
42#10587503C2211yescharacteristic
43C22⋊#3622C2211yescharacteristic
44C22⋊#3622C2211yescharacteristic
45#10587481C2211yescharacteristic
46#10587481C2211yescharacteristic
47#10587481C2211yescharacteristic
48#10587479C2211yescharacteristic
49#10587479C2211yescharacteristic
50#10587479C2211yescharacteristic
51#10587479C2211yescharacteristic
52#10587479C2211yescharacteristic
53#10587478C2211yescharacteristic
54#10587478C2211yescharacteristic
55#10587478C2211yescharacteristic
56#10587478C2211yescharacteristic
57C4⋊#3622C2211yescharacteristic
58C4×#3622C2211yescharacteristic
59C2×D4×C17—21no—
60C2×D4×C17—21no—
61C2×D4×C17D411yescharacteristic
62C2×D4×C17C2311yescharacteristic
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17C2311yescharacteristic
66C22×C4×C17C2311yescharacteristic
67C22×Dic17—21no—
68C2×Dic34C2311yescharacteristic
69C4⋊C4×C17—21no—
70C4⋊C4×C17—21no—
71C4⋊C4×C17—21no—
72C4⋊C4×C17D411yescharacteristic
73C4⋊C4×C17C2311yescharacteristic
74C4⋊C4×C17C2311yescharacteristic
75C4⋊C4×C17C2311yescharacteristic
76C22⋊C4×C17—21no—
77C22⋊C4×C17—21no—
78C22⋊C4×C17—21no—
79C22⋊C4×C17—21no—
80C22⋊C4×C17D411yescharacteristic
81C22⋊C4×C17D411yescharacteristic
82C42×C17—21no—
83C42×C17C2311yescharacteristic
84C22⋊Dic17—21no—
85C22⋊Dic17—21no—
86C22⋊Dic17—21no—
87#63229—22no—
88C4⋊Dic17—21no—
89C4⋊Dic17C2311yescharacteristic
90C4⋊Dic17C2311yescharacteristic
91C4⋊Dic17C2311yescharacteristic
92#63225—21no—
93#63225—21no—
94#63225—21no—
95#63225—21no—
96#63225—21no—
97C4×Dic17—21no—
98C4×Dic17—21no—
99C2×#3622—22no—
100C2×#3622—22no—
101C2×#3622C2311yescharacteristic
102C2×#3622C2311yescharacteristic
103C2×#3622C2311yescharacteristic
104C2×#3622C2311yescharacteristic
105C23×C17—21no—
106C23×C17C2×D411yescharacteristic
107C23×C17C2×D411yescharacteristic
108D4×C17—22no—
109D4×C17—21no—
110D4×C17—21no—
111D4×C17—42no—
112D4×C17—81no—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—81no—
121C2×C4×C17—81no—
122C2×C4×C17C2×D411yescharacteristic
123C2×C4×C17C2×D411yescharacteristic
124C2×C4×C17C2×D411yescharacteristic
125C2×C4×C17C2×D411yescharacteristic
126C2×C4×C17C2411yescharacteristic
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—21no—
131C2×Dic17—42no—
132Dic34—21no—
133Dic34—21no—
134#3622—21no—
135#3622—21no—
136#3622—21no—
137#3622#4112yes—
138#3337—171nomaximal, Sylow
139C22×C17—21no—
140C22×C17—21no—
141C22×C17—21no—
142C22×C17—21no—
143C22×C17—21no—
144C22×C17—41no—
145C22×C17—41no—
146C22×C17—41no—
147C22×C17#13512yes—
148C22×C17C22×D411yescharacteristic
149C4×C17—21no—
150C4×C17—21no—
151C4×C17—21no—
152C4×C17—21no—
153C4×C17—41no—
154C4×C17—41no—
155C4×C17—41no—
156C4×C17C2×#4111yescharacteristic
157C4×C172−1+411yescharacteristic
158Dic17—41no—
159Dic17—41no—
160Dic17—41no—
161Dic17—41no—
162#553D1711yescharacteristic
163#552—171no—
164#499—171no—
165#485—171no—
166#484—171no—
167#482—171no—
168#480—171no—
169#479—171no—
170#478—171no—
171#465—171no—
172#465—171no—
173C4×SD16—171no—
174C8×D4—171no—
175#427—171no—
176C2×#106—171no—
177C2×C17—22no—
178C2×C17—41no—
179C2×C17—81no—
180C2×C17#54711yescharacteristic
181C2×C17C2×#13511yescharacteristic
182C2×C17#57711yescharacteristic
183C2×SD16—171no—
184C22×C8—171no—
185C22×C8—171no—
186#126—21no—
187#126—341no—
188#125—171no—
189#125—341no—
190#125C2×D1711yescharacteristic
191#123—21no—
192#123—341no—
193C22⋊Q8—171no—
194C22⋊Q8—171no—
195#121—21no—
196#121C2×D1711yescharacteristic
197#121C2×D1711yescharacteristic
198C4×Q8—171no—
199C4×D4—21no—
200C4×D4C2×D1711yescharacteristic
201C4×D4C2×D1711yescharacteristic
202#117—171no—
203#117—341no—
204#117C2×D1711yescharacteristic
205C2×C4⋊C4—171no—
206C2×C4⋊C4C2×D1711yescharacteristic
207#107—171no—
208#107—171no—
209#107—171no—
210#107—171no—
211#106—171no—
212#106—171no—
213#106—171no—
214#106—171no—
215#106—171no—
216C4⋊C8—171no—
217#103—171no—
218#103—171no—
219#103—171no—
220#102—171no—
221#102—171no—
222#102—171no—
223C22⋊C8—171no—
224C22⋊C8—171no—
225C4×C8—171no—
226C17#333711yescharacteristic, complemented, Sylow
227C2×Q8—171no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4C22⋊D1711yescharacteristic
231C2×D4C22×D1711yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—341no—
235C22×C4C22×D1711yescharacteristic
236C22×C4C22×D1711yescharacteristic
237SD16—342no—
238C2×C8—171no—
239C2×C8—171no—
240C2×C8—171no—
241C2×C8—171no—
242C2×C8—342no—
243C2×C8—342no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—171no—
248C4⋊C4—171no—
249C4⋊C4—171no—
250C4⋊C4—341no—
251C4⋊C4—341no—
252C4⋊C4—341no—
253C4⋊C4—341no—
254C4⋊C4—341no—
255C4⋊C4—341no—
256C4⋊C4C22⋊D1711yescharacteristic
257C4⋊C4C22×D1711yescharacteristic
258C4⋊C4C22×D1711yescharacteristic
259C4⋊C4C22×D1711yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—341no—
265C22⋊C4—341no—
266C22⋊C4—341no—
267C22⋊C4C22⋊D1711yescharacteristic
268C22⋊C4C22⋊D1711yescharacteristic
269C42—21no—
270C42—341no—
271C42—341no—
272C42C22×D1711yescharacteristic
273C23—21no—
274C23C2×C22⋊D1711yescharacteristic
275C23C2×C22⋊D1711yescharacteristic
276Q8—341no—
277Q8—341no—
278D4—22no—
279D4—21no—
280D4—21no—
281D4—42no—
282D4—81no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—341no—
293C2×C4—341no—
294C2×C4—341no—
295C2×C4—341no—
296C2×C4—682no—
297C2×C4C2×C22⋊D1711yescharacteristic
298C2×C4C2×C22⋊D1711yescharacteristic
299C2×C4C2×C22⋊D1711yescharacteristic
300C2×C4C2×C22⋊D1711yescharacteristic
301C2×C4C23×D1711yescharacteristic
302C8—172no—
303C8—341no—
304C8—341no—
305C8—341no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22#1058763612yes—
315C22C22×C22⋊D1711yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—681no—
324C4—681no—
325C4—681no—
326C4—681no—
327C4#41×D1711yescharacteristic
328C4#1058769711yescharacteristic
329C2—22no—
330C2—41no—
331C2—81no—
332C2#1176345811yescharacteristic
333C2C2×#1058763611yescharacteristic
334C2#1176362011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
Fitting, prime radicalC17×#553C2
socleC22×C17C22×D4
hypercenter#553D17
hypocenterC17#3337
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #11763499C2semidirect
2. #11763208C2semidirect
3. #11763150C2semidirect
4. #11763144C2semidirect
5. #11763130C2semidirect
6. #11763120C2semidirect
7. #11763113C2semidirect
8. #11763109C2semidirect
9. #11763036C2semidirect
10. #11763036C2semidirect
11. C4×#63229C2semidirect
12. D4×#3622C2semidirect
13. #11762845C2semidirect
14. C2×#10587479C2semidirect
226. C17#3337semidirect

Maximal subgroups

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

subgroupindex
#117634992
#117632082
#117631502
#117631442
#117631302
#117631202
#117631132
#117631092
#117630362
C4×#632292
D4×#36222
#117628452
C2×#105874792
C17×#5532
#333717