Finite Group Databasebeta

← #16950344

Subgroups — #16950344

Order 4352.

420 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14530425C212yesmaximal
2#14528834C211yesmaximal, characteristic, complemented
3#14528830C211yesmaximal, characteristic, complemented
4#14526913C212yesmaximal, complemented
5C17×#2930C211yesmaximal, characteristic
6C2×#10587490—21no—
7#11762847—21no—
8#11762793C2212yes—
9#11762783C2212yes—
10#11762599—22no—
11#11762596—22no—
12#11762567—21no—
13#11762566—21no—
14C2×C17×#131C2211yescharacteristic
15C22×M16×C17C411yescharacteristic, complemented
16C17×#525C2211yescharacteristic
17C17×#436—21no—
18C17×#436—21no—
19C17×#435—21no—
20C17×#435—21no—
21C17×#424C411yescharacteristic, complemented
22C17×#408C2211yescharacteristic
23C17×#407C411yescharacteristic, complemented
24C17×#405C411yescharacteristic, complemented
25C2×#41×C17C2311yescharacteristic
26C23×C4×C17C2×C411yescharacteristic
27C17×#131—41no—
28C17×#131—41no—
29C2×M16×C17—21no—
30C2×M16×C17—21no—
31C2×M16×C17—41no—
32C2×M16×C17—41no—
33C2×M16×C17C2×C411yescharacteristic
34C2×M16×C17C2×C411yescharacteristic
35C2×M16×C17D411yescharacteristic
36C2×M16×C17D411yescharacteristic
37C22×C8×C17C2×C411yescharacteristic
38C22×C8×C17C2×C411yescharacteristic
39C22×C8×C17D411yescharacteristic
40C22×C8×C17D411yescharacteristic
41C17×#123D411yescharacteristic
42C17×#123Q811yescharacteristic
43C17×C22⋊Q8—21no—
44C17×#121—21no—
45C17×#120D411yescharacteristic
46C17×#120Q811yescharacteristic
47C4×D4×C17—21no—
48C4×D4×C17—21no—
49C17×#117C2×C411yescharacteristic
50#10587612—22no—
51C2×#63223—22no—
52C17×C4⋊C8—21no—
53C17×C4⋊C8—21no—
54C17×C22⋊C8—21no—
55C17×C22⋊C8—21no—
56C17×C22⋊C8—21no—
57C17×C22⋊C8—21no—
58C17×#97—21no—
59C4×C8×C17—21no—
60#10587507—22no—
61#10587505—22no—
62#10587505—22no—
63#10587504—22no—
64#10587490—41no—
65#10587490—41no—
66#10587489—41no—
67#10587488—41no—
68C24×C17C4⋊C411yescharacteristic
69#41×C17—41no—
70#41×C17—41no—
71C2×Q8×C17#4111yescharacteristic
72C2×D4×C17—21no—
73C2×D4×C17—21no—
74C2×D4×C17C2×D411yescharacteristic
75C2×D4×C17C2×Q811yescharacteristic
76C2×D4×C17#4111yescharacteristic
77C22×C4×C17—21no—
78C22×C4×C17—21no—
79C22×C4×C17—41no—
80C22×C4×C17—41no—
81C22×C4×C17C4⋊C411yescharacteristic
82C22×C4×C17C22×C411yescharacteristic
83C22×C4×C17C2×D411yescharacteristic
84C22×C4×C17C2×D411yescharacteristic
85M16×C17—41no—
86M16×C17—41no—
87M16×C17—41no—
88M16×C17—42no—
89M16×C17—41no—
90M16×C17—41no—
91M16×C17—41no—
92C2×C8×C17—21no—
93C2×C8×C17—21no—
94C2×C8×C17—21no—
95C2×C8×C17—21no—
96C2×C8×C17—21no—
97C2×C8×C17—21no—
98C2×C8×C17—21no—
99C2×C8×C17—21no—
100C2×C8×C17—41no—
101C2×C8×C17C22⋊C411yescharacteristic
102C2×C8×C17C22⋊C411yescharacteristic
103C2×C8×C17C22⋊C411yescharacteristic
104C2×C8×C17C22⋊C411yescharacteristic
105C4⋊C4×C17—21no—
106C4⋊C4×C17—21no—
107C4⋊C4×C17—21no—
108C22⋊C4×C17—21no—
109C22⋊C4×C17—21no—
110C22⋊C4×C17—21no—
111C22⋊C4×C17—21no—
112C22⋊C4×C17C4⋊C411yescharacteristic
113C22⋊C4×C17C4⋊C411yescharacteristic
114C42×C17—21no—
115C22⋊Dic17—42no—
116C4⋊Dic17—42no—
117C4×Dic17—42no—
118#63223—42no—
119#63223—42no—
120C2×#3622—42no—
121#12806—171nomaximal, Sylow
122C23×C17—21no—
123C23×C17—41no—
124C23×C17—81no—
125C23×C17C2×C4⋊C411yescharacteristic
126C23×C17#12111yescharacteristic
127C23×C17C22⋊Q811yescharacteristic
128Q8×C17—41no—
129D4×C17—41no—
130D4×C17—41no—
131D4×C17—41no—
132D4×C17—81no—
133D4×C17—81no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—21no—
137C2×C4×C17—21no—
138C2×C4×C17—21no—
139C2×C4×C17—21no—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—42no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17C2×C22⋊C411yescharacteristic
148C2×C4×C17#11711yescharacteristic
149C2×C4×C17#12111yescharacteristic
150C2×C4×C17C22⋊Q811yescharacteristic
151C2×Dic17—82no—
152C8×C17—21no—
153C8×C17—21no—
154C8×C17—21no—
155C8×C17—41no—
156C8×C17—41no—
157C8×C17#9911yescharacteristic
158C8×C17#9911yescharacteristic
159#3622—82no—
160#2930D1711yescharacteristic
161#2120—172no—
162#1813—171no—
163#1812—171no—
164#1395—172no—
165C22×C17—21no—
166C22×C17—21no—
167C22×C17—21no—
168C22×C17—41no—
169C22×C17—41no—
170C22×C17—41no—
171C22×C17—41no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17—82no—
175C22×C17#38011yescharacteristic
176C4×C17—21no—
177C4×C17—21no—
178C4×C17—21no—
179C4×C17—41no—
180C4×C17—41no—
181C4×C17—41no—
182C4×C17C2×#9911yescharacteristic
183C4×C17#41011yescharacteristic
184Dic17—162no—
185C2×#131C2×D1711yescharacteristic
186C22×M16Dic1711yescharacteristic, complemented
187#525C2×D1711yescharacteristic
188#436—21no—
189#436—21no—
190#435—21no—
191#435—21no—
192C2×#108—341no—
193#427—341no—
194#424Dic1711yescharacteristic, complemented
195#413—172no—
196#410—172no—
197#408C2×D1711yescharacteristic
198#407Dic1711yescharacteristic, complemented
199#405Dic1711yescharacteristic, complemented
200#352—342no—
201AΣL(1,𝔽16)—342no—
202#338—341no—
203H(3,ℤ/4)—341no—
204C2×C17—21no—
205C2×C17—41no—
206C2×C17—41no—
207C2×C17—41no—
208C2×C17—81no—
209C2×C17#179911yescharacteristic
210C2×#41C22×D1711yescharacteristic
211C23×C4C2×Dic1711yescharacteristic
212#131—41no—
213#131—41no—
214C2×M16—21no—
215C2×M16—21no—
216C2×M16—41no—
217C2×M16—41no—
218C2×M16—342no—
219C2×M16C2×Dic1711yescharacteristic
220C2×M16C2×Dic1711yescharacteristic
221C2×M16C22⋊D1711yescharacteristic
222C2×M16C22⋊D1711yescharacteristic
223C22×C8C2×Dic1711yescharacteristic
224C22×C8C2×Dic1711yescharacteristic
225C22×C8C22⋊D1711yescharacteristic
226C22×C8C22⋊D1711yescharacteristic
227#123Dic3411yescharacteristic
228#123D6811yescharacteristic
229C22⋊Q8—21no—
230#121—21no—
231#120Dic3411yescharacteristic
232#120D6811yescharacteristic
233C4×D4—21no—
234C4×D4—21no—
235#117—342no—
236#117C2×Dic1711yescharacteristic
237#108—681no—
238#108—681no—
239#107—681no—
240#106—681no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243#101—342no—
244#100—342no—
245#99—342no—
246#99—342no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251#97—21no—
252C4×C8—21no—
253C17#1280611yescharacteristic, complemented, Sylow
254C24C4⋊Dic1711yescharacteristic
255#41—41no—
256#41—41no—
257C2×Q8#6325211yescharacteristic
258C2×D4—21no—
259C2×D4—21no—
260C2×D4C2×Dic3411yescharacteristic
261C2×D4C2×D6811yescharacteristic
262C2×D4#6325211yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4C4⋊Dic1711yescharacteristic
268C22×C4C22×Dic1711yescharacteristic
269C22×C4C2×C22⋊D1711yescharacteristic
270C22×C4C2×C22⋊D1711yescharacteristic
271M16—41no—
272M16—41no—
273M16—41no—
274M16—42no—
275M16—41no—
276M16—41no—
277M16—41no—
278M16—682no—
279M16—682no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—41no—
289C2×C8—682no—
290C2×C8C22⋊Dic1711yescharacteristic
291C2×C8C22⋊Dic1711yescharacteristic
292C2×C8C22⋊Dic1711yescharacteristic
293C2×C8C22⋊Dic1711yescharacteristic
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—682no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—682no—
303C22⋊C4C4⋊Dic1711yescharacteristic
304C22⋊C4C4⋊Dic1711yescharacteristic
305C42—21no—
306C42—682no—
307C23—21no—
308C23—41no—
309C23—81no—
310C23#1058761011yescharacteristic
311C23C2×C4⋊Dic1711yescharacteristic
312C23#1058761611yescharacteristic
313Q8—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317D4—81no—
318D4—81no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—1362no—
333C2×C4#1058761011yescharacteristic
334C2×C4#1058761211yescharacteristic
335C2×C4#1058761611yescharacteristic
336C2×C4C2×C22⋊Dic1711yescharacteristic
337C8—21no—
338C8—21no—
339C8—21no—
340C8—41no—
341C8—41no—
342C8—1362no—
343C8#1058750511yescharacteristic
344C8#1058750511yescharacteristic
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—82no—
355C22#1176266911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—2722no—
363C4C2×#1058750511yescharacteristic
364C4#1176278311yescharacteristic
365C2—21no—
366C2—41no—
367C2—41no—
368C2—41no—
369C2—81no—
370C2#1452877211yescharacteristic
subgroupG/H
centerC4#11762783
commutatorC22×C4×C17C22×C4
FrattiniC2×#41C22×D17
FittingC17×#2930C2
socleC2×C17#1799
prime radicalC17×#525C22
cosocleC2×#41×C17C23
hypercenter#2930D17
hypocenterC17#12806
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×#131 ◁ #2930

Complements

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

NH ≅ G/Ntype
2. #14528834C2semidirect
3. #14528830C2semidirect
4. #14526913C2semidirect
15. C22×M16×C17C4semidirect
21. C17×#424C4semidirect
23. C17×#407C4semidirect
24. C17×#405C4semidirect
186. C22×M16Dic17semidirect
194. #424Dic17semidirect
198. #407Dic17semidirect
199. #405Dic17semidirect
253. C17#12806semidirect

Maximal subgroups

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

subgroupindex
#145304252
#145288342
#145288302
#145269132
C17×#29302
#1280617