Finite Group Databasebeta

← #16944903

Subgroups — #16944903

Order 4352.

446 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10587507C211yesmaximal, characteristic, complemented
2#14527128C211yesmaximal, characteristic, complemented
3#14526790C212yesmaximal, complemented
4#14526787C212yesmaximal
5C17×#2536C211yesmaximal, characteristic
6#11762866—21no—
7C2×#10587507—21no—
8C4×#63223—21no—
9#11762578C2212yes—
10#11762535—21no—
11#11762535C2212yes—
12C2×C17×C22⋊Q8—21no—
13C2×C4×Q8×C17C2211yescharacteristic
14C2×C4×D4×C17C411yescharacteristic
15C17×#398C411yescharacteristic
16C17×#398C2211yescharacteristic
17C17×#394C411yescharacteristic
18C17×#394C2211yescharacteristic
19C17×#388—21no—
20C17×#388—21no—
21C17×#382C411yescharacteristic
22C17×#380—21no—
23C22×Q8×C17D411yescharacteristic
24C22×D4×C17C2×C411yescharacteristic
25C23×C4×C17—21no—
26C17×C22⋊Q8—44no—
27C4×Q8×C17—41no—
28C4×Q8×C17—41no—
29C4×D4×C17—41no—
30C4×D4×C17—41no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C4⋊C4×C17C2×C411yescharacteristic
36C2×C4⋊C4×C17D411yescharacteristic
37C2×C4⋊C4×C17C2311yescharacteristic
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17—21no—
43C2×C42×C17C2×C411yescharacteristic
44C2×C42×C17D411yescharacteristic
45C2×C42×C17D411yescharacteristic
46C2×#63223—22no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95C2×C411yescharacteristic
51C17×#95C2×C411yescharacteristic
52#10587507—24no—
53C22⋊#3622—22no—
54C4⋊#3622—41no—
55#10587474—41no—
56#10587474—41no—
57C4×#3622—41no—
58C24×C17—21no—
59C2×Q8×C17—22no—
60C2×Q8×C17—22no—
61C2×Q8×C17—41no—
62C2×D4×C17—41no—
63C2×D4×C17—42no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—42no—
68C22×C4×C17—42no—
69C22×C4×C17—42no—
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22×C411yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76C22×C4×C17C2×D411yescharacteristic
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—42no—
82C4⋊C4×C17—42no—
83C4⋊C4×C17—42no—
84C22⋊C4×C17—42no—
85C22⋊C4×C17—42no—
86C22⋊C4×C17—42no—
87C22⋊C4×C17—41no—
88C22⋊C4×C17—41no—
89C22⋊C4×C17—42no—
90C42×C17—21no—
91C42×C17—21no—
92C42×C17—21no—
93C42×C17—21no—
94C42×C17—21no—
95C42×C17—21no—
96#63223—24no—
97#63223—42no—
98C2×#3622—42no—
99C2×#3622—42no—
100#11778—171nomaximal, Sylow
101C23×C17—22no—
102C23×C17—41no—
103C23×C17—41no—
104C23×C17—41no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17C2×C22⋊C411yescharacteristic
109Q8×C17—44no—
110D4×C17—42no—
111D4×C17—42no—
112C2×C4×C17—21no—
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—21no—
121C2×C4×C17—21no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—84no—
136C2×C4×C17#9911yescharacteristic
137C2×C4×C17#9911yescharacteristic
138C2×C4×C17#10412yes—
139C2×C4×C17AGL(1,ℤ/8)12yes—
140#3622—44no—
141#3622—82no—
142#2536D1711yescharacteristic
143C4×#101—171no—
144#1467—171no—
145#1346—172no—
146#1345—172no—
147C22×C17—21no—
148C22×C17—21no—
149C22×C17—42no—
150C22×C17—42no—
151C22×C17—42no—
152C22×C17—81no—
153C22×C17—81no—
154C22×C17—81no—
155C22×C17—81no—
156C22×C17C2×#9911yescharacteristic
157C22×C17#41811yescharacteristic
158C22×C17C2×#10411yescharacteristic
159C4×C17—21no—
160C4×C17—21no—
161C4×C17—22no—
162C4×C17—22no—
163C4×C17—41no—
164C4×C17—41no—
165C4×C17—41no—
166C4×C17—41no—
167C4×C17—81no—
168C4×C17—81no—
169C4×C17—81no—
170C2×C22⋊Q8—21no—
171C2×C4×Q8C2×D1711yescharacteristic
172C2×C4×D4Dic1711yescharacteristic
173#432—341no—
174C2×#101—341no—
175C4×M16—341no—
176#398Dic1711yescharacteristic
177#398C2×D1711yescharacteristic
178#394Dic1711yescharacteristic
179#394C2×D1711yescharacteristic
180#388—21no—
181#388—21no—
182#382Dic1711yescharacteristic
183#380—21no—
184#343—172no—
185#324—172no—
186#324—341no—
187C2×C17—21no—
188C2×C17—21no—
189C2×C17—82no—
190C2×C17#150711yescharacteristic
191C2×C17#212011yescharacteristic
192C2×C17#213311yescharacteristic
193C22×Q8C22⋊D1711yescharacteristic
194C22×D4C2×Dic1711yescharacteristic
195C23×C4—21no—
196C2×M16—342no—
197C22⋊Q8—44no—
198C4×Q8—41no—
199C4×Q8—41no—
200C4×D4—41no—
201C4×D4—41no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×Dic1711yescharacteristic
206C2×C4⋊C4C2×Dic1711yescharacteristic
207C2×C4⋊C4C22⋊D1711yescharacteristic
208C2×C4⋊C4C22×D1711yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C42C2×Dic1711yescharacteristic
215C2×C42C22⋊D1711yescharacteristic
216C2×C42C22⋊D1711yescharacteristic
217C4⋊C8—681no—
218#101—344no—
219C22⋊C8—342no—
220#97—681no—
221#97—681no—
222C4×C8—681no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95C2×Dic1711yescharacteristic
227#95C2×Dic1711yescharacteristic
228C17#1177811yescharacteristic, complemented, Sylow
229C24—21no—
230C2×Q8—22no—
231C2×Q8—22no—
232C2×Q8—41no—
233C2×D4—41no—
234C2×D4—42no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4C22⋊Dic1711yescharacteristic
242C22×C4C22⋊Dic1711yescharacteristic
243C22×C4C22⋊Dic1711yescharacteristic
244C22×C4C22⋊Dic1711yescharacteristic
245C22×C4C22×Dic1711yescharacteristic
246C22×C4C2×C22⋊D1711yescharacteristic
247C22×C4C2×C22⋊D1711yescharacteristic
248M16—344no—
249M16—682no—
250C2×C8—682no—
251C2×C8—682no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—42no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C23—22no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23C2×C22⋊Dic1711yescharacteristic
279Q8—44no—
280D4—42no—
281D4—42no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—84no—
306C2×C4#1058750511yescharacteristic
307C2×C4#1058750511yescharacteristic
308C2×C4#1058750812yes—
309C2×C4#1058761812yes—
310C8—684no—
311C8—1362no—
312C22—21no—
313C22—21no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22C2×#1058750511yescharacteristic
322C22#1176281411yescharacteristic
323C22C2×#1058750811yescharacteristic
324C4—22no—
325C4—22no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—81no—
333C4—81no—
334C4—81no—
335C2—21no—
336C2—21no—
337C2—82no—
338C2#1452730011yescharacteristic
339C2#1453042511yescharacteristic
340C2#1453047311yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2536C2
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2536D17
hypocenterC17#11778
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2536

Complements

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

NH ≅ G/Ntype
1. C4×#10587507C2semidirect
2. #14527128C2semidirect
3. #14526790C2semidirect
228. C17#11778semidirect

Maximal subgroups

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

subgroupindex
C4×#105875072
#145271282
#145267902
#145267872
C17×#25362
#1177817