Finite Group Databasebeta

← #17955844

Subgroups — #17955844

Order 4352.

384 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544699C211yesmaximal, characteristic
2C4×C4⋊#3624C211yesmaximal, characteristic
3C2×#11763673C211yesmaximal, characteristic
4C2×#11763671C211yesmaximal, characteristic
5#14543614C211yesmaximal, characteristic
6#14543614C211yesmaximal, characteristic
7C4⋊C8×Dic17C211yesmaximal, characteristic
8C2×C4⋊#3624C2211yescharacteristic
9C2×C4⋊#3624C2211yescharacteristic
10C2×C4⋊#3624C2211yescharacteristic
11C2×C4⋊#3624C2211yescharacteristic
12C2×C4×#3624—21no—
13#11763675—21no—
14#11763675—21no—
15#11763675—21no—
16#11763673—22no—
17#11763671—22no—
18C2×C4⋊#3622C411yescharacteristic
19C2×C8×Dic17C2211yescharacteristic
20C2×C8×Dic17C2211yescharacteristic
21C42×Dic17C2211yescharacteristic
22#11762563C411yescharacteristic
23#11762563C411yescharacteristic
24C2×C17×C4⋊C8C411yescharacteristic
25C22×#3624—21no—
26C22×#3624—21no—
27C22×#3624—21no—
28C22×#3624—21no—
29C22×C8×C17C2×C411yescharacteristic
30C22×C8×C17C2×C411yescharacteristic
31C2×C42×C17C2×C411yescharacteristic
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17D411yescharacteristic
34C2×C4×Dic17D411yescharacteristic
35C2×C4×Dic17Q811yescharacteristic
36C2×C4×Dic17Q811yescharacteristic
37C2×C4×Dic17C2311yescharacteristic
38C22×#3622C2×C411yescharacteristic
39C22×#3622C2×C411yescharacteristic
40C4⋊#3624—21no—
41C4⋊#3624—21no—
42C4⋊#3624—21no—
43C4⋊#3624—21no—
44C4⋊#3624—21no—
45C4⋊#3624—21no—
46C4⋊#3624D412yes—
47C4⋊#3624Q812yes—
48C4×#3624—42no—
49C17×C4⋊C8—22no—
50C8×Dic17—21no—
51C8×Dic17—21no—
52C8×Dic17—21no—
53C8×Dic17—21no—
54C4⋊#3622C814yescomplemented
55C22×C4×C17C4⋊C411yescharacteristic
56C22×C4×C17C4⋊C411yescharacteristic
57C22×C4×C17C22×C411yescharacteristic
58C22×Dic17C4⋊C411yescharacteristic
59C22×Dic17C4⋊C411yescharacteristic
60C22×Dic17C2×D411yescharacteristic
61C22×Dic17C2×Q811yescharacteristic
62C2×#3624—22no—
63C2×#3624—22no—
64C2×#3624—41no—
65C2×#3624—41no—
66C2×#3624—41no—
67C2×#3624—41no—
68C2×#3624—41no—
69C2×#3624—41no—
70C2×#3624—41no—
71C2×#3624—41no—
72C2×#3624—41no—
73C2×#3624—41no—
74C2×C8×C17—21no—
75C2×C8×C17—21no—
76C2×C8×C17—21no—
77C2×C8×C17—21no—
78C2×C8×C17—21no—
79C2×C8×C17—21no—
80C42×C17C2×C812yes—
81C42×C17M1612yes—
82C4×Dic17—21no—
83C4×Dic17—21no—
84C4×Dic17—22no—
85C4×Dic17—21no—
86C4×Dic17—21no—
87C4×Dic17—21no—
88C4×Dic17—21no—
89C4×Dic17—41no—
90C4×Dic17C2×D411yescharacteristic
91C4×Dic17C2×Q811yescharacteristic
92C4×Dic17#4111yescharacteristic
93C4×Dic17#4111yescharacteristic
94C2×#3622—21no—
95C2×#3622—21no—
96C2×#3622—21no—
97C2×#3622—21no—
98C2×#3622C2×C812yes—
99C2×#3622C2×C812yes—
100#9603—171nomaximal, Sylow
101C23×C17C2×C4⋊C411yescharacteristic
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17C4⋊C812yes—
107C2×C4×C17C4⋊C812yes—
108C2×C4×C17C4×D411yescharacteristic
109C2×C4×C17C4×Q811yescharacteristic
110C2×C4×C17C22×C811yescharacteristic
111C2×C4×C17C2×M1611yescharacteristic
112C2×C4×C17#13111yescharacteristic
113C2×C4×C17#13111yescharacteristic
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17—21no—
121C2×Dic17#10812yes—
122C2×Dic17#12111yescharacteristic
123C2×Dic17C22⋊Q811yescharacteristic
124C2×Dic17#12511yescharacteristic
125C2×Dic17C4⋊Q811yescharacteristic
126C2×Dic17#13511yescharacteristic
127C2×Dic17#13511yescharacteristic
128C2×Dic17AGL(1,ℤ/8)11yescharacteristic
129C2×Dic17#13711yescharacteristic
130#3624—42no—
131#3624—42no—
132#3624—81no—
133#3624—81no—
134C8×C17—41no—
135C8×C17—41no—
136#3622—22no—
137#3622—22no—
138#1831—171no—
139C4×C4⋊C8—171no—
140C4×C4⋊C8—171no—
141C2×#335—171no—
142C2×#334—171no—
143#1277—171no—
144#1277—171no—
145C22×C17#38911yescharacteristic
146C22×C17C2×C4⋊C811yescharacteristic
147C22×C17#42411yescharacteristic
148C22×C17#42711yescharacteristic
149C22×C17#42811yescharacteristic
150C22×C17C2×#10811yescharacteristic
151C22×C17#43011yescharacteristic
152C4×C17—22no—
153C4×C17—22no—
154C4×C17C8×D411yescharacteristic
155C4×C17#43611yescharacteristic
156C4×C17C8×Q811yescharacteristic
157C4×C17#44611yescharacteristic
158Dic17—22no—
159Dic17—21no—
160Dic17—21no—
161Dic17—41no—
162Dic17#46311yescharacteristic
163Dic17#46411yescharacteristic
164Dic17#47811yescharacteristic
165Dic17#47911yescharacteristic
166C2×C4⋊C8—171no—
167C2×C4⋊C8—171no—
168C2×C4⋊C8—171no—
169C2×C4⋊C8—171no—
170C2×C4⋊C8—171no—
171C2×C4⋊C8#59511yescharacteristic
172C2×C4×C8—171no—
173C2×C4×C8—171no—
174C2×C4×C8—341no—
175C43—171no—
176#336—171no—
177#336—171no—
178#336—341no—
179#336—341no—
180#336—341no—
181#335—342no—
182#334—342no—
183C2×C17#156411yescharacteristic
184C2×C17#156511yescharacteristic
185C2×C17#157211yescharacteristic
186C2×C17#157311yescharacteristic
187C2×C17#193911yescharacteristic
188C2×C17#194911yescharacteristic
189C2×C17#195011yescharacteristic
190C22×C8—171no—
191C22×C8—171no—
192C22×C8—341no—
193C22×C8—341no—
194C22×C8—341no—
195C22×C8—341no—
196C22×C8C2×#59511yescharacteristic
197C22×C8C2×#59511yescharacteristic
198C2×C42—171no—
199C2×C42—171no—
200C2×C42—171no—
201C2×C42—171no—
202C2×C42—171no—
203C2×C42—171no—
204C2×C42C2×#59511yescharacteristic
205C4⋊C8—22no—
206C4⋊C8—172no—
207C4⋊C8—172no—
208C4⋊C8—174no—
209C4⋊C8—341no—
210C4⋊C8—341no—
211C4⋊C8—341no—
212C4⋊C8—341no—
213C4⋊C8—341no—
214C4⋊C8—341no—
215C4×C8—341no—
216C4×C8—341no—
217C4×C8—341no—
218C4×C8—341no—
219C4×C8—682no—
220C17#960311yescharacteristic, complemented, Sylow
221C22×C4—171no—
222C22×C4—171no—
223C22×C4—171no—
224C22×C4—171no—
225C22×C4C4⋊#59511yescharacteristic
226C22×C4C4⋊#59511yescharacteristic
227C22×C4C22×#59511yescharacteristic
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—172no—
235C2×C8—172no—
236C2×C8—341no—
237C2×C8—341no—
238C2×C8—341no—
239C2×C8—341no—
240C2×C8—342no—
241C2×C8—342no—
242C2×C8—681no—
243C2×C8—681no—
244C2×C8—681no—
245C2×C8—681no—
246C2×C8—681no—
247C2×C8—681no—
248C2×C8—681no—
249C2×C8—681no—
250C2×C8—681no—
251C2×C8—681no—
252C42—171no—
253C42—171no—
254C42—171no—
255C42—171no—
256C42—341no—
257C42—341no—
258C42—341no—
259C42—341no—
260C42—342no—
261C42—341no—
262C42—341no—
263C42—681no—
264C42#6324212yes—
265C42#6324712yes—
266C23C2×C4⋊#59511yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—171no—
272C2×C4—171no—
273C2×C4—171no—
274C2×C4—171no—
275C2×C4—171no—
276C2×C4—171no—
277C2×C4—171no—
278C2×C4—171no—
279C2×C4—172no—
280C2×C4—341no—
281C2×C4—341no—
282C2×C4—341no—
283C2×C4—341no—
284C2×C4—341no—
285C2×C4—341no—
286C2×C4—341no—
287C2×C4#1058754412yes—
288C2×C4#1058754412yes—
289C2×C4C2×#6324211yescharacteristic
290C2×C4#1058767811yescharacteristic
291C2×C4D4×#59511yescharacteristic
292C2×C4#1058768011yescharacteristic
293C2×C4Q8×#59511yescharacteristic
294C2×C4C2×#6324711yescharacteristic
295C8—41no—
296C8—41no—
297C8—342no—
298C8—342no—
299C8—682no—
300C8—682no—
301C8—1361no—
302C8—1361no—
303C22#1176376011yescharacteristic
304C22C2×#1058754411yescharacteristic
305C22#1176381611yescharacteristic
306C22#1176381911yescharacteristic
307C22#1176382011yescharacteristic
308C22D17⋊#10811yescharacteristic
309C22#1176382411yescharacteristic
310C4—22no—
311C4—22no—
312C4—171no—
313C4—171no—
314C4—171no—
315C4—171no—
316C4—341no—
317C4—341no—
318C4—342no—
319C4—681no—
320C4#1176383711yescharacteristic
321C4#1176384411yescharacteristic
322C4#1176385811yescharacteristic
323C4#1176386011yescharacteristic
324C2#1454433311yescharacteristic
325C2#1454433711yescharacteristic
326C2#1454435611yescharacteristic
327C2#1454435811yescharacteristic
328C2#1454488211yescharacteristic
329C2#1454489711yescharacteristic
330C2#1454490011yescharacteristic
subgroupG/H
centerC23C2×C4⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊C8C4
socle, prime radicalC23×C17C2×C4⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4⋊C8#595
hypocenterC17#9603
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
54. C4⋊#3622C8semidirect
220. C17#9603semidirect

Maximal subgroups

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

subgroupindex
#145446992
C4×C4⋊#36242
C2×#117636732
C2×#117636712
#145436142
C4⋊C8×Dic172
#960317