Finite Group Databasebeta

← #17955841

Subgroups — #17955841

Order 4352.

404 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#14544717C211yesmaximal, characteristic
2C4×C4⋊#3624C211yesmaximal, characteristic
3C2×#11763671C211yesmaximal, characteristic
4C2×#11763670C211yesmaximal, characteristic
5#14543614C211yesmaximal, characteristic
6#14543614C211yesmaximal, characteristic
7#14528632C211yesmaximal, characteristic
8C2×#10587544—21no—
9C2×#10587544—21no—
10C2×C4⋊#3624C2211yescharacteristic
11C2×C4⋊#3624C2211yescharacteristic
12C2×C4⋊#3624C2211yescharacteristic
13C2×C4⋊#3624C2211yescharacteristic
14C2×C4×#3624—21no—
15#11763675—21no—
16#11763671—22no—
17#11763670—22no—
18C2×#10587485C411yescharacteristic
19C2×#10587485C411yescharacteristic
20C2×C8×Dic17C2211yescharacteristic
21C2×C8×Dic17C2211yescharacteristic
22C42×Dic17C2211yescharacteristic
23#11762564C411yescharacteristic
24C17×#336C411yescharacteristic
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
40#10587544—42no—
41#10587544—42no—
42C4⋊#3624—21no—
43C4⋊#3624—21no—
44C4⋊#3624—21no—
45C4⋊#3624—21no—
46C4⋊#3624—21no—
47C4⋊#3624—21no—
48C4⋊#3624D412yes—
49C4⋊#3624Q812yes—
50C4×#3624—42no—
51#10587485—22no—
52#10587485C814yescomplemented
53C8×Dic17—21no—
54C8×Dic17—21no—
55C8×Dic17—21no—
56C8×Dic17—21no—
57C22×C4×C17C4⋊C411yescharacteristic
58C22×C4×C17C4⋊C411yescharacteristic
59C22×C4×C17C22×C411yescharacteristic
60C22×Dic17C4⋊C411yescharacteristic
61C22×Dic17C4⋊C411yescharacteristic
62C22×Dic17C2×D411yescharacteristic
63C22×Dic17C2×Q811yescharacteristic
64C2×#3624—22no—
65C2×#3624—22no—
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×#3624—41no—
75C2×#3624—41no—
76C2×C8×C17—21no—
77C2×C8×C17—21no—
78C2×C8×C17—21no—
79C2×C8×C17—21no—
80C2×C8×C17—21no—
81C2×C8×C17C2×C812yes—
82C42×C17—21no—
83C42×C17—21no—
84C4×Dic17—22no—
85C4×Dic17—21no—
86C4×Dic17—21no—
87C4×Dic17—41no—
88C4×Dic17C2×C812yes—
89C4×Dic17M1612yes—
90C4×Dic17SD1612yes—
91C4×Dic17SD1612yes—
92C4×Dic17C2×D411yescharacteristic
93C4×Dic17C2×Q811yescharacteristic
94C4×Dic17#4111yescharacteristic
95C4×Dic17#4111yescharacteristic
96C2×#3622—21no—
97C2×#3622—21no—
98C2×#3622—21no—
99C2×#3622—21no—
100C2×#3622—21no—
101C2×#3622C2×C812yes—
102#9602—171nomaximal, Sylow
103C23×C17C2×C4⋊C411yescharacteristic
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17#10612yes—
110C2×C4×C17C4×D411yescharacteristic
111C2×C4×C17C4×Q811yescharacteristic
112C2×C4×C17C22×C811yescharacteristic
113C2×C4×C17C2×M1611yescharacteristic
114C2×C4×C17#13111yescharacteristic
115C2×C4×C17#13111yescharacteristic
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17C4⋊C812yes—
121C2×Dic17C4⋊C812yes—
122C2×Dic17#10612yes—
123C2×Dic17#10812yes—
124C2×Dic17#12111yescharacteristic
125C2×Dic17C22⋊Q811yescharacteristic
126C2×Dic17#12511yescharacteristic
127C2×Dic17C4⋊Q811yescharacteristic
128C2×Dic17C2×SD1611yescharacteristic
129C2×Dic17C2×SD1611yescharacteristic
130C2×Dic17AGL(1,ℤ/8)11yescharacteristic
131C2×Dic17#13711yescharacteristic
132#3624—42no—
133#3624—42no—
134#3624—81no—
135#3624—81no—
136C8×C17—22no—
137C8×C17—41no—
138#3622—22no—
139#3622—41no—
140#1842—171no—
141C4×C4⋊C8—171no—
142C4×C4⋊C8—171no—
143C2×#334—171no—
144C2×#334—171no—
145#1277—171no—
146#1277—171no—
147C22×C17#38911yescharacteristic
148C22×C17C2×C4⋊C811yescharacteristic
149C22×C17#42411yescharacteristic
150C22×C17C2×#10611yescharacteristic
151C22×C17#42811yescharacteristic
152C22×C17C2×#10811yescharacteristic
153C22×C17#43011yescharacteristic
154C4×C17—22no—
155C4×C17—41no—
156C4×C17C8×D411yescharacteristic
157C4×C17#43611yescharacteristic
158C4×C17C8×Q811yescharacteristic
159C4×C17#44611yescharacteristic
160Dic17—22no—
161Dic17—21no—
162Dic17—21no—
163Dic17#33414yescomplemented
164Dic17#46011yescharacteristic
165Dic17#46111yescharacteristic
166Dic17#47511yescharacteristic
167Dic17#47611yescharacteristic
168C2×C4⋊C8—171no—
169C2×C4⋊C8—171no—
170C2×C4⋊C8—171no—
171C2×C4⋊C8—171no—
172C2×C4⋊C8—171no—
173C2×C4⋊C8—171no—
174C2×C4⋊C8—341no—
175C2×C4⋊C8—341no—
176C2×C4×C8—171no—
177C2×C4×C8—171no—
178C2×C4×C8—341no—
179C43—171no—
180#336—171no—
181#336—341no—
182#336#59511yescharacteristic
183#334—342no—
184#334—342no—
185C2×C17C2×#33411yescharacteristic
186C2×C17#156511yescharacteristic
187C2×C17#157011yescharacteristic
188C2×C17#157411yescharacteristic
189C2×C17#193911yescharacteristic
190C2×C17#194811yescharacteristic
191C2×C17#195011yescharacteristic
192C22×C8—171no—
193C22×C8—171no—
194C22×C8—341no—
195C22×C8—341no—
196C22×C8—341no—
197C22×C8—341no—
198C22×C8C2×#59511yescharacteristic
199C22×C8C2×#59511yescharacteristic
200C2×C42—171no—
201C2×C42—171no—
202C2×C42—171no—
203C2×C42—171no—
204C2×C42—171no—
205C2×C42—171no—
206C2×C42C2×#59511yescharacteristic
207C4⋊C8—174no—
208C4⋊C8—172no—
209C4⋊C8—172no—
210C4⋊C8—342no—
211C4⋊C8—341no—
212C4⋊C8—341no—
213C4⋊C8—341no—
214C4⋊C8—341no—
215C4⋊C8—341no—
216C4⋊C8—341no—
217C4⋊C8—682no—
218C4⋊C8—682no—
219C4×C8—341no—
220C4×C8—341no—
221C4×C8—341no—
222C4×C8—341no—
223C4×C8—682no—
224C17#960211yescharacteristic, complemented, Sylow
225C22×C4—171no—
226C22×C4—171no—
227C22×C4—171no—
228C22×C4—171no—
229C22×C4C4⋊#59511yescharacteristic
230C22×C4C4⋊#59511yescharacteristic
231C22×C4C22×#59511yescharacteristic
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—172no—
238C2×C8—341no—
239C2×C8—341no—
240C2×C8—342no—
241C2×C8—342no—
242C2×C8—341no—
243C2×C8—341no—
244C2×C8—341no—
245C2×C8—681no—
246C2×C8—681no—
247C2×C8—681no—
248C2×C8—681no—
249C2×C8—681no—
250C2×C8—681no—
251C2×C8—681no—
252C2×C8—681no—
253C2×C8—681no—
254C2×C8—681no—
255C2×C8#6324212yes—
256C42—21no—
257C42—21no—
258C42—172no—
259C42—172no—
260C42—171no—
261C42—171no—
262C42—171no—
263C42—171no—
264C42—172no—
265C42—172no—
266C42—341no—
267C42—341no—
268C42—342no—
269C42—681no—
270C23C2×C4⋊#59511yescharacteristic
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—171no—
277C2×C4—171no—
278C2×C4—172no—
279C2×C4—171no—
280C2×C4—171no—
281C2×C4—172no—
282C2×C4—171no—
283C2×C4—171no—
284C2×C4—172no—
285C2×C4—171no—
286C2×C4—171no—
287C2×C4—172no—
288C2×C4—341no—
289C2×C4—341no—
290C2×C4—341no—
291C2×C4—341no—
292C2×C4#1058753312yes—
293C2×C4C2×#6324211yescharacteristic
294C2×C4D17⋊M1611yescharacteristic
295C2×C4#1058767811yescharacteristic
296C2×C4#1058767811yescharacteristic
297C2×C4D4×#59511yescharacteristic
298C2×C4Q8×#59511yescharacteristic
299C8—22no—
300C8—41no—
301C8—342no—
302C8—682no—
303C8—682no—
304C8—681no—
305C8—1361no—
306C8—1361no—
307C22#1176376011yescharacteristic
308C22#1176381011yescharacteristic
309C22#1176381511yescharacteristic
310C22C2×#1058753311yescharacteristic
311C22#1176382011yescharacteristic
312C22D17⋊#10811yescharacteristic
313C22#1176382411yescharacteristic
314C4—22no—
315C4—41no—
316C4—171no—
317C4—171no—
318C4—171no—
319C4—171no—
320C4—174no—
321C4—341no—
322C4—341no—
323C4—342no—
324C4#1176383611yescharacteristic
325C4#1176384211yescharacteristic
326C4#1176385811yescharacteristic
327C4#1176386111yescharacteristic
328C2#1454432611yescharacteristic
329C2#1454433611yescharacteristic
330C2#1454435111yescharacteristic
331C2#1454436011yescharacteristic
332C2#1454488311yescharacteristic
333C2#1454489611yescharacteristic
334C2#1454490011yescharacteristic
subgroupG/H
centerC23C2×C4⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#336C4
socle, prime radicalC23×C17C2×C4⋊C4
cosocleC2×C4×Dic17C23
hypercenter#336#595
hypocenterC17#9602
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
52. #10587485C8semidirect
163. Dic17#334semidirect
224. C17#9602semidirect

Maximal subgroups

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

subgroupindex
#145447172
C4×C4⋊#36242
C2×#117636712
C2×#117636702
#145436142
#145286322
#960217