Finite Group Databasebeta

← #16950835

Subgroups — #16950835

Order 4352.

442 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762846C211yesmaximal, characteristic
2C2×#11762637C211yesmaximal, characteristic, complemented
3C2×#11762634C211yesmaximal, characteristic, complemented
4C2×#11762588C211yesmaximal, characteristic
5#14528810C211yesmaximal, characteristic
6#14526875C211yesmaximal, characteristic, complemented
7C17×#1380C211yesmaximal, characteristic, complemented
8C22×C8×D17C2211yescharacteristic
9C2×#10587578—21no—
10C22×#63214C2211yescharacteristic
11#11762846—22no—
12#11762846—22no—
13C2×#10587489C2211yescharacteristic
14C2×#10587489C2211yescharacteristic
15C2×#10587479—21no—
16#11762666—21no—
17#11762637—22no—
18#11762634—22no—
19#11762588C414yescomplemented
20#11762571—21no—
21C22×C16×C17C2211yescharacteristic
22C2×C17×#107C2211yescharacteristic
23C2×C17×#107C2211yescharacteristic
24C22×C4×D17D411yescharacteristic
25C22×C8×C17C2311yescharacteristic
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×#63227—41no—
29C2×#63227—41no—
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17—21no—
32C2×C4×Dic17—41no—
33C22×#3622D411yescharacteristic
34C2×C8×D17—21no—
35C2×C8×D17—21no—
36C2×C8×D17—21no—
37C2×C8×D17—21no—
38C2×C8×D17C2×C412yes—
39C2×C8×D17Q812yes—
40#10587578—24no—
41#10587578—42no—
42C2×C16×C17—21no—
43C2×C16×C17—21no—
44C2×C16×C17C2×C412yes—
45C17×#107—21no—
46C17×#107—21no—
47C17×#107—21no—
48C17×#107D412yes—
49#10587502—41no—
50#10587489—21no—
51#10587489—21no—
52#10587489—21no—
53#10587489D412yes—
54C2×#63214—21no—
55C2×#63214—21no—
56C2×#63214C2×C412yes—
57#10587479—24no—
58C23×D17D811yescharacteristic
59C22×C4×C17—41no—
60C22×C4×C17—41no—
61C22×C4×C17C2×D411yescharacteristic
62C22×Dic17—41no—
63C22×Dic17—41no—
64C22×Dic17D811yescharacteristic
65C2×C4×D17—21no—
66C2×C4×D17—21no—
67C2×C4×D17—21no—
68C2×C4×D17—21no—
69C2×C4×D17C4⋊C412yes—
70C2×C4×D17Q1612yes—
71C2×C8×C17C22×C411yescharacteristic
72C2×C8×C17C2×D411yescharacteristic
73C2×C8×C17C2×D411yescharacteristic
74C2×C8×C17C2×Q811yescharacteristic
75C2×C8×C17#4111yescharacteristic
76C2×C8×C17#4111yescharacteristic
77C4⋊C4×C17—22no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81#63227—44no—
82#63227—82no—
83C4⋊Dic17—22no—
84C4⋊Dic17—41no—
85C4⋊Dic17—41no—
86C4⋊Dic17—41no—
87C4×Dic17—44no—
88C2×#3622—21no—
89C2×#3622—21no—
90C2×#3622C4⋊C412yes—
91C8×D17—22no—
92C8×D17—22no—
93C8×D17—22no—
94C8×D17—22no—
95C16×C17—22no—
96#63214—22no—
97#12921—171nomaximal, Sylow
98C23×C17C2×D811yescharacteristic
99C22×D17—21no—
100C22×D17—21no—
101C22×D17—21no—
102C22×D17—21no—
103C22×D17—21no—
104C22×D17—21no—
105C22×D17#10712yes—
106C2×C4×C17—42no—
107C2×C4×C17—81no—
108C2×C4×C17—81no—
109C2×C4×C17—81no—
110C2×C4×C17—81no—
111C2×C4×C17—81no—
112C2×C4×C17C2×C4⋊C411yescharacteristic
113C2×C4×C17#12011yescharacteristic
114C2×C4×C17#12311yescharacteristic
115C2×C4×C17C2×Q1611yescharacteristic
116C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C17#13711yescharacteristic
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17—42no—
121C2×Dic17—81no—
122C2×Dic17—81no—
123C2×Dic17—81no—
124C2×Dic17—81no—
125C2×Dic17—81no—
126C2×Dic17#10712yes—
127C4×D17—22no—
128C4×D17—22no—
129C4×D17—22no—
130C4×D17—22no—
131C8×C17C4×D411yescharacteristic
132C8×C17C4×D411yescharacteristic
133C8×C17C22⋊Q811yescharacteristic
134C8×C17C22⋊Q811yescharacteristic
135#3622—22no—
136C2×#427—171no—
137C2×#367—171no—
138C2×#366—171no—
139C2×C22⋊C16—171no—
140#1808—171no—
141#1380—171no—
142#1380D1711yescharacteristic, complemented
143C22×C17C2×#10711yescharacteristic
144C22×C17#44711yescharacteristic
145C22×C17#48011yescharacteristic
146C22×C17#50811yescharacteristic
147C22×C17#50811yescharacteristic
148C22×C17#50911yescharacteristic
149C22×C17#51011yescharacteristic
150C2×D17—22no—
151C2×D17—22no—
152C2×D17—22no—
153C2×D17—41no—
154C2×D17—41no—
155C2×D17—41no—
156C2×D17—41no—
157C4×C17—82no—
158C4×C17—161no—
159C4×C17#38511yescharacteristic
160C4×C17#42811yescharacteristic
161C4×C17#45111yescharacteristic
162C4×C17#48411yescharacteristic
163Dic17—22no—
164Dic17—82no—
165Dic17—161no—
166C23×C8—171no—
167C2×#117—341no—
168C22×C16—171no—
169C22×C16C2×D1711yescharacteristic
170#427—342no—
171#427—342no—
172C2×#107—171no—
173C2×#107—171no—
174C2×#107C2×D1711yescharacteristic
175C2×#107C2×D1711yescharacteristic
176C2×#106—341no—
177#380—341no—
178#367—342no—
179#366—342no—
180C22⋊C16—174no—
181#340—341no—
182C2×C17#185211yescharacteristic
183C2×C17#215811yescharacteristic
184C2×C17#215911yescharacteristic
185C2×C17#218611yescharacteristic
186C2×C17#218911yescharacteristic
187C2×C17#223411yescharacteristic
188C2×C17#223711yescharacteristic
189D17—42no—
190C23×C4—171no—
191C22×C8—171no—
192C22×C8—172no—
193C22×C8—172no—
194C22×C8—341no—
195C22×C8—341no—
196C22×C8—341no—
197C22×C8—341no—
198C22×C8C22×D1711yescharacteristic
199#117—344no—
200#117—682no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—341no—
204C2×C4⋊C4—341no—
205C2×C22⋊C4—681no—
206C2×C22⋊C4—681no—
207C2×C42—681no—
208C2×C16—21no—
209C2×C16—21no—
210C2×C16—172no—
211C2×C16—341no—
212C2×C16—341no—
213C2×C16C4×D1712yes—
214#107—21no—
215#107—21no—
216#107—21no—
217#107—172no—
218#107—341no—
219#107—341no—
220#107—341no—
221#107D6812yes—
222#106—344no—
223#95—681no—
224C17#1292111yescharacteristic, complemented, Sylow
225C24—171no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—171no—
229C22×C4—172no—
230C22×C4—172no—
231C22×C4—341no—
232C22×C4—341no—
233C22×C4—341no—
234C22×C4—341no—
235C22×C4—681no—
236C22×C4—681no—
237C22×C4D4×D1711yescharacteristic
238C2×C8—172no—
239C2×C8—341no—
240C2×C8—341no—
241C2×C8—342no—
242C2×C8—342no—
243C2×C8—342no—
244C2×C8—342no—
245C2×C8C2×C4×D1711yescharacteristic
246C2×C8C2×D6811yescharacteristic
247C2×C8#6325211yescharacteristic
248C2×C8D4×D1711yescharacteristic
249C2×C8#6325411yescharacteristic
250C2×C8Q8×D1711yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—342no—
256C4⋊C4—681no—
257C4⋊C4—681no—
258C4⋊C4—681no—
259C22⋊C4—684no—
260C22⋊C4—1362no—
261C42—684no—
262C16—22no—
263C16—342no—
264C23—172no—
265C23—341no—
266C23—341no—
267C23—341no—
268C23—341no—
269C23—341no—
270C23—341no—
271C23D8×D1711yescharacteristic
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—172no—
279C2×C4—341no—
280C2×C4—341no—
281C2×C4—342no—
282C2×C4—342no—
283C2×C4—342no—
284C2×C4—342no—
285C2×C4—682no—
286C2×C4—1361no—
287C2×C4—1361no—
288C2×C4—1361no—
289C2×C4—1361no—
290C2×C4—1361no—
291C2×C4#1058756811yescharacteristic
292C2×C4#1058756911yescharacteristic
293C2×C4C4⋊C4×D1711yescharacteristic
294C2×C4#1058760011yescharacteristic
295C2×C4#1058760111yescharacteristic
296C2×C4Q16×D1711yescharacteristic
297C8—342no—
298C8C4×D6811yescharacteristic
299C8#1058756711yescharacteristic
300C8#1058758211yescharacteristic
301C8#1058758311yescharacteristic
302C22—342no—
303C22—342no—
304C22—342no—
305C22—681no—
306C22—681no—
307C22—681no—
308C22—681no—
309C22#107×D1711yescharacteristic
310C22#1176294411yescharacteristic
311C22#1176312111yescharacteristic
312C22#1176324011yescharacteristic
313C22#1176324011yescharacteristic
314C22#1176324311yescharacteristic
315C22#1176325111yescharacteristic
316C4—82no—
317C4—161no—
318C4—2721no—
319C4—342no—
320C4—1362no—
321C4#1176268311yescharacteristic
322C4#1176284811yescharacteristic
323C4#1176296611yescharacteristic
324C4#1176314311yescharacteristic
325C2—682no—
326C2#1452897311yescharacteristic
327C2#1453056711yescharacteristic
328C2#1453056911yescharacteristic
329C2#1453070811yescharacteristic
330C2#1453072711yescharacteristic
331C2#1453097411yescharacteristic
332C2#1453099011yescharacteristic
subgroupG/H
centerC23D8×D17
commutatorC2×C8×C17C22×C4
FrattiniC22×C8C22×D17
FittingC17×#1380C2
socleC23×C17C2×D8
prime radicalC23×D17D8
cosocleC22×C8×C17C23
hypercenter#1380D17
hypocenterC17#12921
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×#11762637C2semidirect
3. C2×#11762634C2semidirect
6. #14526875C2semidirect
7. C17×#1380C2semidirect
19. #11762588C4semidirect
142. #1380D17semidirect
224. C17#12921semidirect

Maximal subgroups

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

subgroupindex
C2×#117628462
C2×#117626372
C2×#117626342
C2×#117625882
#145288102
#145268752
C17×#13802
#1292117