Finite Group Databasebeta

← #16933754

Subgroups — #16933754

Order 4352.

396 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14528535C211yesmaximal, characteristic, complemented
2#14527547C211yesmaximal, characteristic, complemented
3#14527399C211yesmaximal, characteristic, complemented
4#14527395C211yesmaximal, characteristic
5#14527296C211yesmaximal, characteristic, complemented
6#14527292C211yesmaximal, characteristic
7C17×#3167C211yesmaximal, characteristic
8#11762866C2211yescharacteristic
9#11762866C2211yescharacteristic
10C2×#10587474C2211yescharacteristic
11#11762655C2211yescharacteristic
12#11762563—21no—
13#11762563—21no—
14#11762562—21no—
15#11762560—21no—
16#11762551—22no—
17#11762549—22no—
18#11762546—22no—
19#11762543—22no—
20C17×#533C2211yescharacteristic
21C17×#532C2211yescharacteristic
22C17×#498C411yescharacteristic, complemented
23C17×#492C411yescharacteristic, complemented
24C17×#487C411yescharacteristic, complemented
25C17×#486C411yescharacteristic, complemented
26C17×#465—21no—
27C17×#465—21no—
28C4×SD16×C17—21no—
29C4×SD16×C17—21no—
30C2×C4×C8×C17C2211yescharacteristic
31C2×#41×C17—21no—
32C2×SD16×C17—21no—
33C2×SD16×C17—21no—
34C22×C8×C17D411yescharacteristic
35C22×C8×C17D411yescharacteristic
36C17×C4⋊Q8C2×C411yescharacteristic
37C17×C4⋊Q8C2×C411yescharacteristic
38C17×C4⋊Q8C2×C411yescharacteristic
39C17×#127C2×C411yescharacteristic
40C17×#125—21no—
41C17×#124—21no—
42C17×C22⋊Q8—21no—
43C17×C22⋊Q8—21no—
44C17×#121—21no—
45C17×#121—21no—
46C4×Q8×C17—21no—
47C4×Q8×C17—21no—
48C4×D4×C17—21no—
49C4×D4×C17—21no—
50C17×#117—21no—
51C2×C42×C17C2311yescharacteristic
52C2×C4×Dic17—21no—
53C22×#3622—21no—
54C17×#106—21no—
55C17×#106—21no—
56C17×#103—21no—
57C17×#103—21no—
58C17×#102—21no—
59C17×#102—21no—
60C4×C8×C17C2×C411yescharacteristic
61C4×C8×C17C2×C411yescharacteristic
62C4×C8×C17D411yescharacteristic
63C4×C8×C17D411yescharacteristic
64#10587502—21no—
65#10587502D412yes—
66C22⋊#3622—21no—
67C22⋊#3622—21no—
68C4⋊#3622—21no—
69C4⋊#3622—21no—
70#10587474—21no—
71#10587474—21no—
72#10587474—21no—
73#10587474D412yes—
74#41×C17—82no—
75C2×Q8×C17—21no—
76C2×Q8×C17—21no—
77C2×Q8×C17—21no—
78C2×D4×C17—21no—
79C2×D4×C17—21no—
80C2×D4×C17—21no—
81C2×D4×C17—41no—
82C22×C4×C17—41no—
83C22×C4×C17C2×D411yescharacteristic
84C22×C4×C17C2×D411yescharacteristic
85C22×C4×C17#4111yescharacteristic
86C22×Dic17—22no—
87SD16×C17—42no—
88SD16×C17—42no—
89C2×C8×C17—41no—
90C2×C8×C17—41no—
91C2×C8×C17C22⋊C411yescharacteristic
92C2×C8×C17C22⋊C411yescharacteristic
93C2×C8×C17C22⋊C411yescharacteristic
94C2×C8×C17C22⋊C411yescharacteristic
95C4⋊C4×C17—21no—
96C4⋊C4×C17—21no—
97C4⋊C4×C17—21no—
98C4⋊C4×C17—21no—
99C4⋊C4×C17—21no—
100C4⋊C4×C17—21no—
101C4⋊C4×C17—41no—
102C4⋊C4×C17—41no—
103C22⋊C4×C17—41no—
104C22⋊C4×C17—41no—
105C22⋊C4×C17—41no—
106C42×C17—41no—
107C42×C17C22×C411yescharacteristic
108C42×C17C2×D411yescharacteristic
109C42×C17C2×D411yescharacteristic
110C42×C17#4111yescharacteristic
111C4×Dic17—41no—
112C4×Dic17—41no—
113C2×#3622—22no—
114C2×#3622—41no—
115C2×#3622—41no—
116C2×#3622—41no—
117C2×#3622—41no—
118#9766—171nomaximal, Sylow
119C23×C17—41no—
120C23×C17#12111yescharacteristic
121Q8×C17—41no—
122Q8×C17—41no—
123Q8×C17—81no—
124Q8×C17—81no—
125D4×C17—41no—
126D4×C17—41no—
127D4×C17—81no—
128D4×C17—81no—
129D4×C17—82no—
130C2×C4×C17—22no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—82no—
138C2×C4×C17C2×C22⋊C411yescharacteristic
139C2×C4×C17C4×D411yescharacteristic
140C2×C4×C17C4×D411yescharacteristic
141C2×C4×C17#12111yescharacteristic
142C2×C4×C17#12411yescharacteristic
143C2×C4×C17#12711yescharacteristic
144C2×Dic17—42no—
145C2×Dic17—42no—
146C2×Dic17—42no—
147C8×C17—21no—
148C8×C17—21no—
149C8×C17—21no—
150C8×C17—21no—
151#3622—42no—
152#3622—81no—
153#3622—81no—
154#3167D1711yescharacteristic
155#1746—171no—
156#1568—171no—
157#1531—171no—
158#1530—171no—
159#1506—171no—
160#1505—171no—
161C22×C17—21no—
162C22×C17—21no—
163C22×C17—81no—
164C22×C17—81no—
165C22×C17—81no—
166C22×C17#39011yescharacteristic
167C22×C17#47112yes—
168C4×C17—21no—
169C4×C17—21no—
170C4×C17—21no—
171C4×C17—21no—
172C4×C17—21no—
173C4×C17—81no—
174C4×C17—81no—
175C4×C17—81no—
176C4×C17#42111yescharacteristic
177C4×C17#42111yescharacteristic
178Dic17—82no—
179#533C2×D1711yescharacteristic
180#532C2×D1711yescharacteristic
181#498Dic1711yescharacteristic, complemented
182#492Dic1711yescharacteristic, complemented
183#487Dic1711yescharacteristic, complemented
184#486Dic1711yescharacteristic, complemented
185#465—21no—
186#465—21no—
187C4×SD16—21no—
188C4×SD16—21no—
189#432—171no—
190#432—171no—
191C2×#97—171no—
192C2×C4×C8C2×D1711yescharacteristic
193#376—171no—
194#336—341no—
195#336—341no—
196#335—341no—
197#334—341no—
198#330—342no—
199#329—342no—
200#328—342no—
201#327—342no—
202C2×C17—22no—
203C2×C17—161no—
204C2×C17#196311yescharacteristic
205C2×C17#197611yescharacteristic
206C2×C17#197711yescharacteristic
207C2×#41—21no—
208C2×SD16—21no—
209C2×SD16—21no—
210C22×C8—341no—
211C22×C8C22⋊D1711yescharacteristic
212C22×C8C22⋊D1711yescharacteristic
213C4⋊Q8C2×Dic1711yescharacteristic
214C4⋊Q8C2×Dic1711yescharacteristic
215C4⋊Q8C2×Dic1711yescharacteristic
216#127C2×Dic1711yescharacteristic
217#125—21no—
218#124—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221#121—21no—
222#121—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×D4—21no—
226C4×D4—21no—
227#117—21no—
228C2×C42—341no—
229C2×C42C22×D1711yescharacteristic
230#106—21no—
231#106—21no—
232C4⋊C8—341no—
233C4⋊C8—341no—
234#103—21no—
235#103—21no—
236#102—21no—
237#102—21no—
238C22⋊C8—341no—
239C22⋊C8—341no—
240#97—172no—
241#97—341no—
242#97—341no—
243#97—341no—
244C4×C8C2×Dic1711yescharacteristic
245C4×C8C2×Dic1711yescharacteristic
246C4×C8C22⋊D1711yescharacteristic
247C4×C8C22⋊D1711yescharacteristic
248#95—172no—
249#95—341no—
250C17#976611yescharacteristic, complemented, Sylow
251#41—82no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C22×C4—41no—
260C22×C4—342no—
261C22×C4D4×D1711yescharacteristic
262C22×C4#6325411yescharacteristic
263C22×C4C2×C22⋊D1711yescharacteristic
264SD16—42no—
265SD16—42no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—342no—
269C2×C8—681no—
270C2×C8—681no—
271C2×C8—681no—
272C2×C8—681no—
273C2×C8C22⋊Dic1711yescharacteristic
274C2×C8C22⋊Dic1711yescharacteristic
275C2×C8C22⋊Dic1711yescharacteristic
276C2×C8C22⋊Dic1711yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C42—41no—
289C42—681no—
290C42—681no—
291C42D4×D1711yescharacteristic
292C42#6325411yescharacteristic
293C42C22×Dic1711yescharacteristic
294C42C2×C22⋊D1711yescharacteristic
295C23—41no—
296C23#1058762411yescharacteristic
297Q8—41no—
298Q8—41no—
299Q8—81no—
300Q8—81no—
301D4—41no—
302D4—41no—
303D4—81no—
304D4—81no—
305D4—82no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—82no—
314C2×C4—682no—
315C2×C4—682no—
316C2×C4—682no—
317C2×C4D4×Dic1711yescharacteristic
318C2×C4D4×Dic1711yescharacteristic
319C2×C4#1058762211yescharacteristic
320C2×C4#1058762411yescharacteristic
321C2×C4#1058762611yescharacteristic
322C2×C4C2×C22⋊Dic1711yescharacteristic
323C8—21no—
324C8—21no—
325C8—21no—
326C8—21no—
327C8—682no—
328C8—1361no—
329C8—1361no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#1176271211yescharacteristic
336C22#1176306912yes—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—1362no—
346C4#1176282611yescharacteristic
347C4#1176282611yescharacteristic
348C2—22no—
349C2—161no—
350C2#1452961711yescharacteristic
351C2#1452968311yescharacteristic
352C2#1452968911yescharacteristic
subgroupG/H
centerC22#11762712
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#3167C2
socleC22×C17#390
prime radicalC17×#532C22
cosocleC2×C42×C17C23
hypercenter#3167D17
hypocenterC17#9766
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #14528535C2semidirect
2. #14527547C2semidirect
3. #14527399C2semidirect
5. #14527296C2semidirect
22. C17×#498C4semidirect
23. C17×#492C4semidirect
24. C17×#487C4semidirect
25. C17×#486C4semidirect
181. #498Dic17semidirect
182. #492Dic17semidirect
183. #487Dic17semidirect
184. #486Dic17semidirect
250. C17#9766semidirect

Maximal subgroups

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

subgroupindex
#145285352
#145275472
#145273992
#145273952
#145272962
#145272922
C17×#31672
#976617