Finite Group Databasebeta

← #14541738

Subgroups — #14541738

Order 2176.

348 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763519C211yesmaximal, characteristic, complemented
2#11763219C211yesmaximal, characteristic, complemented
3#11763215C211yesmaximal, characteristic, complemented
4#11763208C211yesmaximal, characteristic, complemented
5#11763109C211yesmaximal, characteristic, complemented
6#11763109C211yesmaximal, characteristic, complemented
7#11763106C211yesmaximal, characteristic, complemented
8#11763106C211yesmaximal, characteristic, complemented
9#11763089C211yesmaximal, characteristic, complemented
10#11763086C211yesmaximal, characteristic, complemented
11#11762940C211yesmaximal, characteristic, complemented
12#11762919C211yesmaximal, characteristic
13#11762919C211yesmaximal, characteristic
14C4×#63228C211yesmaximal, characteristic
15C17×#554C211yesmaximal, characteristic, complemented
16C17×C4⋊Q8C2211yescharacteristic
17C17×#125C2211yescharacteristic
18C17×#125C2211yescharacteristic
19C17×C22⋊Q8—21no—
20C17×C22⋊Q8—21no—
21C17×C22⋊Q8—21no—
22C4×Q8×C17C2211yescharacteristic
23C4×D4×C17C2211yescharacteristic
24C4×D4×C17C2211yescharacteristic
25C4×D4×C17C2211yescharacteristic
26C2×C4⋊C4×C17—21no—
27#10587632—21no—
28C2×#63228C2211yescharacteristic
29#10587582—21no—
30#10587582—21no—
31C4⋊C4×D17—21no—
32C4×D68C2211yescharacteristic
33C4×D68C2211yescharacteristic
34C4×D68C2211yescharacteristic
35#10587556C2211yescharacteristic
36#10587556C2211yescharacteristic
37#10587555C2211yescharacteristic
38#10587503C2211yescharacteristic
39#10587503C2211yescharacteristic
40#10587503C2211yescharacteristic
41#10587480C2211yescharacteristic
42#10587480C2211yescharacteristic
43#10587480C2211yescharacteristic
44#10587479C2211yescharacteristic
45#10587479C2211yescharacteristic
46#10587479C2211yescharacteristic
47#10587479C2211yescharacteristic
48#10587478C2211yescharacteristic
49#10587478C2211yescharacteristic
50#10587478C2211yescharacteristic
51#10587478C2211yescharacteristic
52#10587478C2211yescharacteristic
53C4⋊#3622C2211yescharacteristic
54C4⋊#3622C2211yescharacteristic
55C4⋊#3622C2211yescharacteristic
56#10587474C2211yescharacteristic
57#10587474C2211yescharacteristic
58C4×#3622C2211yescharacteristic
59C2×Q8×C17—21no—
60C2×Q8×C17D411yescharacteristic
61C2×D4×C17C2311yescharacteristic
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C2×D68C2311yescharacteristic
66C2×C4×D17—21no—
67C2×C4×D17—21no—
68C2×C4×D17—21no—
69C2×Dic34—21no—
70C4⋊C4×C17—21no—
71C4⋊C4×C17—21no—
72C4⋊C4×C17—21no—
73C4⋊C4×C17—21no—
74C4⋊C4×C17—21no—
75C4⋊C4×C17D411yescharacteristic
76C4⋊C4×C17D411yescharacteristic
77C4⋊C4×C17D411yescharacteristic
78C4⋊C4×C17C2311yescharacteristic
79C4⋊C4×C17C2311yescharacteristic
80C4⋊C4×C17C2311yescharacteristic
81C22⋊C4×C17—21no—
82C22⋊C4×C17—21no—
83C22⋊C4×C17—21no—
84C42×C17C2311yescharacteristic
85C42×C17C2311yescharacteristic
86C42×C17C2311yescharacteristic
87#63228Q814yescomplemented
88#63227—21no—
89#63227—21no—
90#63227—21no—
91C4⋊Dic17—21no—
92C4⋊Dic17C2311yescharacteristic
93C4⋊Dic17C2311yescharacteristic
94C4⋊Dic17C2311yescharacteristic
95#63225—21no—
96#63225—21no—
97#63225—21no—
98#63225—21no—
99C2×#3622C2311yescharacteristic
100C2×#3622C2311yescharacteristic
101C2×#3622C2311yescharacteristic
102C2×#3622C2311yescharacteristic
103C23×C17—21no—
104C22×D17—21no—
105Q8×C17—41no—
106Q8×C17—81no—
107D4×C17—21no—
108D4×C17C2×Q812yes—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—42no—
113C2×C4×C17—81no—
114C2×C4×C17—81no—
115C2×C4×C17C2×D411yescharacteristic
116C2×C4×C17C2×D411yescharacteristic
117C2×C4×C17C2×D411yescharacteristic
118C2×C4×C17C2×D411yescharacteristic
119C2×C4×C17C2×D411yescharacteristic
120C2×C4×C17C2×D411yescharacteristic
121C2×C4×C17C2411yescharacteristic
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—21no—
125D68—21no—
126D68C2×Q812yes—
127C4×D17—42no—
128C4×D17—81no—
129C4×D17—81no—
130Dic34—81no—
131#3622—21no—
132#3622—21no—
133#3622—21no—
134#3622C2×Q812yes—
135#3389—171nomaximal, Sylow
136C22×C17—22no—
137C22×C17—41no—
138C22×C17—41no—
139C22×C17C22×D411yescharacteristic
140C2×D17—22no—
141C2×D17—41no—
142C2×D17—41no—
143C4×C17—21no—
144C4×C17—21no—
145C4×C17—21no—
146C4×C17—21no—
147C4×C17—21no—
148C4×C17—21no—
149C4×C17—41no—
150C4×C17—41no—
151C4×C17—41no—
152C4×C17C22×Q811yescharacteristic
153C4×C172−1+411yescharacteristic
154Dic17—41no—
155Dic17—41no—
156Dic17—41no—
157#554—171no—
158#554D1711yescharacteristic, complemented
159#501—171no—
160#501—171no—
161#499—171no—
162#478—171no—
163#478—171no—
164#478—171no—
165#478—171no—
166#474—171no—
167#474—171no—
168#446—171no—
169#442—171no—
170#442—171no—
171C4×D8—171no—
172C2×C17—42no—
173C2×C17D4×Q811yescharacteristic
174C2×C17#57511yescharacteristic
175C2×C17#57611yescharacteristic
176D17—42no—
177C2×D8—171no—
178C4⋊Q8—171no—
179C4⋊Q8C2×D1711yescharacteristic
180#125—171no—
181#125—171no—
182#125C2×D1711yescharacteristic
183#125C2×D1711yescharacteristic
184C22⋊Q8—21no—
185C22⋊Q8—21no—
186C22⋊Q8—21no—
187C22⋊Q8—341no—
188C22⋊Q8—341no—
189C22⋊Q8—341no—
190C4×Q8C2×D1711yescharacteristic
191C4×D4—171no—
192C4×D4—171no—
193C4×D4—171no—
194C4×D4C2×D1711yescharacteristic
195C4×D4C2×D1711yescharacteristic
196C4×D4C2×D1711yescharacteristic
197C2×C4⋊C4—21no—
198C2×C4⋊C4—341no—
199#107—171no—
200#107—171no—
201#107—171no—
202#107—171no—
203#107—171no—
204#106—171no—
205#106—171no—
206#106—171no—
207#106—171no—
208C4⋊C8—171no—
209C4⋊C8—171no—
210C4⋊C8—171no—
211#102—171no—
212#102—171no—
213#102—171no—
214#102—171no—
215#102—171no—
216#102—171no—
217#97—171no—
218#97—171no—
219C4×C8—171no—
220C17#338911yescharacteristic, complemented, Sylow
221C2×Q8—21no—
222C2×Q8—341no—
223C2×Q8C22⋊D1711yescharacteristic
224C2×D4—171no—
225C2×D4C22×D1711yescharacteristic
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—341no—
230C22×C4—341no—
231C22×C4—341no—
232D8—174no—
233C2×C8—171no—
234C2×C8—171no—
235C2×C8—171no—
236C2×C8—171no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—171no—
243C4⋊C4—171no—
244C4⋊C4—171no—
245C4⋊C4—341no—
246C4⋊C4—341no—
247C4⋊C4—341no—
248C4⋊C4—341no—
249C4⋊C4—341no—
250C4⋊C4C22⋊D1711yescharacteristic
251C4⋊C4C22⋊D1711yescharacteristic
252C4⋊C4C22⋊D1711yescharacteristic
253C4⋊C4C22×D1711yescharacteristic
254C4⋊C4C22×D1711yescharacteristic
255C4⋊C4C22×D1711yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—341no—
260C22⋊C4—341no—
261C22⋊C4—341no—
262C42C22×D1711yescharacteristic
263C42C22×D1711yescharacteristic
264C42C22×D1711yescharacteristic
265C23—21no—
266C23—341no—
267Q8—41no—
268Q8—81no—
269Q8—1361no—
270D4—21no—
271D4—172no—
272D4—341no—
273D4Q8×D1712yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—341no—
281C2×C4—341no—
282C2×C4—341no—
283C2×C4—682no—
284C2×C4—1361no—
285C2×C4—1361no—
286C2×C4C2×C22⋊D1711yescharacteristic
287C2×C4C2×C22⋊D1711yescharacteristic
288C2×C4C2×C22⋊D1711yescharacteristic
289C2×C4C2×C22⋊D1711yescharacteristic
290C2×C4C2×C22⋊D1711yescharacteristic
291C2×C4C2×C22⋊D1711yescharacteristic
292C2×C4C23×D1711yescharacteristic
293C8—172no—
294C8—341no—
295C8—341no—
296C8—341no—
297C22—22no—
298C22—41no—
299C22—41no—
300C22—342no—
301C22—681no—
302C22—681no—
303C22C22×C22⋊D1711yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—681no—
314C4—681no—
315C4—681no—
316C4C2×Q8×D1711yescharacteristic
317C4#1058769411yescharacteristic
318C2—42no—
319C2—682no—
320C2Q8×C22⋊D1711yescharacteristic
321C2#1176360711yescharacteristic
322C2#1176361211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#554C2
socleC22×C17C22×D4
prime radicalC2×#63228C22
hypercenter#554D17
hypocenterC17#3389
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #11763519C2semidirect
2. #11763219C2semidirect
3. #11763215C2semidirect
4. #11763208C2semidirect
5. #11763109C2semidirect
6. #11763109C2semidirect
7. #11763106C2semidirect
8. #11763106C2semidirect
9. #11763089C2semidirect
10. #11763086C2semidirect
11. #11762940C2semidirect
15. C17×#554C2semidirect
87. #63228Q8semidirect
158. #554D17semidirect
220. C17#3389semidirect

Maximal subgroups

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

subgroupindex
#117635192
#117632192
#117632152
#117632082
#117631092
#117631062
#117630892
#117630862
#117629402
#117629192
C4×#632282
C17×#5542
#338917