Finite Group Databasebeta

← #16932913

Subgroups — #16932913

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#14528901C211yesmaximal, characteristic
2C4×C4⋊#3622C211yesmaximal, characteristic
3C2×#11762562C211yesmaximal, characteristic
4C2×#11762560C211yesmaximal, characteristic
5#14526619C211yesmaximal, characteristic
6#14526619C211yesmaximal, characteristic
7C4×C17×C4⋊C8C211yesmaximal, characteristic
8C2×C4⋊#3622C2211yescharacteristic
9C2×C4⋊#3622C2211yescharacteristic
10C2×C4⋊#3622C2211yescharacteristic
11C2×C4⋊#3622C2211yescharacteristic
12C2×C4×#3622—21no—
13#11762564—21no—
14#11762564—21no—
15#11762564—21no—
16#11762562—22no—
17#11762560—22no—
18C2×C17×C4⋊C8C411yescharacteristic
19C2×C17×C4⋊C8C411yescharacteristic
20C2×C4×C8×C17C2211yescharacteristic
21C2×C4×C8×C17C2211yescharacteristic
22C43×C17C2211yescharacteristic
23C17×#336C411yescharacteristic
24C17×#336C411yescharacteristic
25C22×C8×C17C2×C411yescharacteristic
26C22×C8×C17C2×C411yescharacteristic
27C22×C8×C17C2×C411yescharacteristic
28C22×C8×C17C2×C411yescharacteristic
29C2×C42×C17C2×C411yescharacteristic
30C2×C42×C17C2×C411yescharacteristic
31C2×C42×C17D411yescharacteristic
32C2×C42×C17D411yescharacteristic
33C2×C42×C17Q811yescharacteristic
34C2×C42×C17Q811yescharacteristic
35C2×C42×C17C2311yescharacteristic
36C22×#3622—21no—
37C22×#3622—21no—
38C22×#3622—21no—
39C22×#3622—21no—
40C17×C4⋊C8—22no—
41C17×C4⋊C8C814yescomplemented
42C4×C8×C17—21no—
43C4×C8×C17—21no—
44C4×C8×C17—21no—
45C4×C8×C17—21no—
46C4⋊#3622—21no—
47C4⋊#3622—21no—
48C4⋊#3622—21no—
49C4⋊#3622—21no—
50C4⋊#3622—21no—
51C4⋊#3622—21no—
52C4⋊#3622D412yes—
53C4⋊#3622Q812yes—
54C4×#3622—42no—
55C22×C4×C17C4⋊C411yescharacteristic
56C22×C4×C17C4⋊C411yescharacteristic
57C22×C4×C17C4⋊C411yescharacteristic
58C22×C4×C17C4⋊C411yescharacteristic
59C22×C4×C17C22×C411yescharacteristic
60C22×C4×C17C2×D411yescharacteristic
61C22×C4×C17C2×Q811yescharacteristic
62C2×C8×C17—21no—
63C2×C8×C17—21no—
64C2×C8×C17—21no—
65C2×C8×C17—21no—
66C2×C8×C17—21no—
67C2×C8×C17—21no—
68C2×C8×C17—21no—
69C2×C8×C17—21no—
70C2×C8×C17—21no—
71C2×C8×C17—21no—
72C2×C8×C17C2×C812yes—
73C2×C8×C17C2×C812yes—
74C42×C17—22no—
75C42×C17—21no—
76C42×C17—21no—
77C42×C17—21no—
78C42×C17—21no—
79C42×C17—21no—
80C42×C17—21no—
81C42×C17—41no—
82C42×C17C2×C812yes—
83C42×C17M1612yes—
84C42×C17C2×D411yescharacteristic
85C42×C17C2×Q811yescharacteristic
86C42×C17#4111yescharacteristic
87C42×C17#4111yescharacteristic
88C2×#3622—22no—
89C2×#3622—22no—
90C2×#3622—41no—
91C2×#3622—41no—
92C2×#3622—41no—
93C2×#3622—41no—
94C2×#3622—41no—
95C2×#3622—41no—
96C2×#3622—41no—
97C2×#3622—41no—
98C2×#3622—41no—
99C2×#3622—41no—
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×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17C4⋊C812yes—
114C2×C4×C17C4⋊C812yes—
115C2×C4×C17#10812yes—
116C2×C4×C17C4×D411yescharacteristic
117C2×C4×C17C4×Q811yescharacteristic
118C2×C4×C17#12111yescharacteristic
119C2×C4×C17C22⋊Q811yescharacteristic
120C2×C4×C17#12511yescharacteristic
121C2×C4×C17C4⋊Q811yescharacteristic
122C2×C4×C17C22×C811yescharacteristic
123C2×C4×C17C2×M1611yescharacteristic
124C2×C4×C17#13111yescharacteristic
125C2×C4×C17#13111yescharacteristic
126C2×C4×C17#13511yescharacteristic
127C2×C4×C17#13511yescharacteristic
128C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C17#13711yescharacteristic
130C8×C17—22no—
131C8×C17—22no—
132C8×C17—41no—
133C8×C17—41no—
134#3622—42no—
135#3622—42no—
136#3622—81no—
137#3622—81no—
138#1831—171no—
139C4×C4⋊C8—171no—
140C4×C4⋊C8D1711yescharacteristic
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×C17—22no—
155C4×C17—21no—
156C4×C17—21no—
157C4×C17—41no—
158C4×C17C8×D411yescharacteristic
159C4×C17#43611yescharacteristic
160C4×C17C8×Q811yescharacteristic
161C4×C17#44611yescharacteristic
162C4×C17#46311yescharacteristic
163C4×C17#46411yescharacteristic
164C4×C17#47811yescharacteristic
165C4×C17#47911yescharacteristic
166C2×C4⋊C8—171no—
167C2×C4⋊C8—171no—
168C2×C4⋊C8—171no—
169C2×C4⋊C8—171no—
170C2×C4⋊C8Dic1711yescharacteristic
171C2×C4⋊C8Dic1711yescharacteristic
172C2×C4×C8—341no—
173C2×C4×C8C2×D1711yescharacteristic
174C2×C4×C8C2×D1711yescharacteristic
175C43C2×D1711yescharacteristic
176#336—341no—
177#336—341no—
178#336—341no—
179#336Dic1711yescharacteristic
180#336Dic1711yescharacteristic
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—341no—
191C22×C8—341no—
192C22×C8—341no—
193C22×C8—341no—
194C22×C8C2×Dic1711yescharacteristic
195C22×C8C2×Dic1711yescharacteristic
196C22×C8C2×Dic1711yescharacteristic
197C22×C8C2×Dic1711yescharacteristic
198C2×C42Dic3411yescharacteristic
199C2×C42Dic3411yescharacteristic
200C2×C42D6811yescharacteristic
201C2×C42D6811yescharacteristic
202C2×C42C2×Dic1711yescharacteristic
203C2×C42C2×Dic1711yescharacteristic
204C2×C42C22×D1711yescharacteristic
205C4⋊C8—22no—
206C4⋊C8—172no—
207C4⋊C8—172no—
208C4⋊C8—341no—
209C4⋊C8—341no—
210C4⋊C8—341no—
211C4⋊C8—341no—
212C4⋊C8—341no—
213C4⋊C8—341no—
214C4⋊C8#362214yescomplemented
215C4×C8—21no—
216C4×C8—21no—
217C4×C8—21no—
218C4×C8—21no—
219C4×C8—682no—
220C17#960311yescharacteristic, complemented, Sylow
221C22×C4C4⋊Dic1711yescharacteristic
222C22×C4C4⋊Dic1711yescharacteristic
223C22×C4C4⋊Dic1711yescharacteristic
224C22×C4C4⋊Dic1711yescharacteristic
225C22×C4C2×Dic3411yescharacteristic
226C22×C4C2×D6811yescharacteristic
227C22×C4C22×Dic1711yescharacteristic
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—342no—
239C2×C8—342no—
240C2×C8—681no—
241C2×C8—681no—
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×C8C2×#362212yes—
251C2×C8C2×#362212yes—
252C42—22no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—41no—
260C42C2×#362212yes—
261C42#6322312yes—
262C42D4×D1711yescharacteristic
263C42#6325411yescharacteristic
264C42Q8×D1711yescharacteristic
265C42#6325611yescharacteristic
266C23C2×C4⋊Dic1711yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4C4⋊#362212yes—
279C2×C4C4⋊#362212yes—
280C2×C4#1058749012yes—
281C2×C4#1058757411yescharacteristic
282C2×C4#1058757611yescharacteristic
283C2×C4#1058758111yescharacteristic
284C2×C4#1058758311yescharacteristic
285C2×C4#1058759011yescharacteristic
286C2×C4#1058759011yescharacteristic
287C2×C4#1058759411yescharacteristic
288C2×C4#1058759511yescharacteristic
289C2×C4C22×#362211yescharacteristic
290C2×C4C2×#6322311yescharacteristic
291C2×C4D4×Dic1711yescharacteristic
292C2×C4Q8×Dic1711yescharacteristic
293C2×C4#1058763411yescharacteristic
294C2×C4#1058763411yescharacteristic
295C8—22no—
296C8—22no—
297C8—41no—
298C8—41no—
299C8—682no—
300C8—682no—
301C8—1361no—
302C8—1361no—
303C22#1176270811yescharacteristic
304C22C2×C4⋊#362211yescharacteristic
305C22#1176283611yescharacteristic
306C22#1176284711yescharacteristic
307C22#1176285111yescharacteristic
308C22C2×#1058749011yescharacteristic
309C22#1176285811yescharacteristic
310C4—21no—
311C4—21no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4D4×#362211yescharacteristic
317C4#1176288711yescharacteristic
318C4Q8×#362211yescharacteristic
319C4#1176294011yescharacteristic
320C4#1176302511yescharacteristic
321C4#1176303211yescharacteristic
322C4#1176311011yescharacteristic
323C4#1176311711yescharacteristic
324C2#1452753211yescharacteristic
325C2#1452753611yescharacteristic
326C2#1452756411yescharacteristic
327C2#1452756911yescharacteristic
328C2#1452950311yescharacteristic
329C2#1452955411yescharacteristic
330C2#1452956011yescharacteristic
subgroupG/H
centerC22×C4C2×D68
commutatorC2×C4×C17C22×C8
FrattiniC2×C42C22×D17
FittingC4×C17×C4⋊C8C2
socle, prime radicalC23×C17C2×C4⋊C4
cosocleC2×C42×C17C23
hypercenterC4×C4⋊C8D17
hypocenterC17#9603
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
41. C17×C4⋊C8C8semidirect
214. C4⋊C8#3622semidirect
220. C17#9603semidirect

Maximal subgroups

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

subgroupindex
#145289012
C4×C4⋊#36222
C2×#117625622
C2×#117625602
#145266192
C4×C17×C4⋊C82
#960317