Finite Group Databasebeta

← #16938816

Subgroups — #16938816

Order 4352.

426 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533815C211yesmaximal, characteristic
2#14529545C211yesmaximal, characteristic
3#14528911C211yesmaximal, characteristic
4#14526668C211yesmaximal, characteristic
5#14526625C211yesmaximal, characteristic
6#14526623C211yesmaximal, characteristic
7C17×#1948C211yesmaximal, characteristic
8C2×#10587576—21no—
9C2×#10587479—21no—
10C2×C4⋊#3622C2211yescharacteristic
11C2×C4×#3622C2211yescharacteristic
12#11762741—22no—
13#11762708—21no—
14#11762707—21no—
15#11762679—21no—
16#11762679C2211yescharacteristic
17C4×C4⋊Dic17C2211yescharacteristic
18#11762571—21no—
19#11762571—22no—
20C2×C17×#106—21no—
21C2×C17×C4⋊C8C2211yescharacteristic
22C17×#384C2211yescharacteristic
23C4×C4⋊C4×C17C2211yescharacteristic
24C17×#340—21no—
25C22×C8×C17—21no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17D411yescharacteristic
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C42×C17—21no—
32C2×C42×C17C2311yescharacteristic
33C2×C4⋊Dic17—22no—
34C2×C4⋊Dic17—22no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17D411yescharacteristic
38C2×C4⋊Dic17D411yescharacteristic
39C2×C4⋊Dic17D412yes—
40C2×#63225—22no—
41C2×C4×Dic17—21no—
42C22×#3622—21no—
43C22×#3622—21no—
44#10587576—42no—
45#10587576—42no—
46C17×#106—42no—
47C17×C4⋊C8—21no—
48C17×C4⋊C8Q812yes—
49C17×#95—21no—
50#10587502—22no—
51#10587502—21no—
52#10587479—42no—
53C4⋊#3622—21no—
54C4⋊#3622Q812yes—
55C4×#3622—21no—
56C4×#3622Q812yes—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—41no—
60C22×C4×C17C2×D411yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C22×Dic17—21no—
64C22×Dic17—21no—
65C22×Dic17—22no—
66C2×C8×C17—22no—
67C2×C8×C17—41no—
68C2×C8×C17—41no—
69C4⋊C4×C17—21no—
70C4⋊C4×C17—21no—
71C4⋊C4×C17—42no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17SD1612yes—
77C4⋊C4×C17SD1612yes—
78C42×C17—41no—
79C42×C17—41no—
80C42×C17C2×Q811yescharacteristic
81C42×C17C2×Q811yescharacteristic
82C42×C17C2×Q811yescharacteristic
83C42×C17#4111yescharacteristic
84C4⋊Dic17—21no—
85C4⋊Dic17—21no—
86C4⋊Dic17—21no—
87C4⋊Dic17—21no—
88C4⋊Dic17—44no—
89C4⋊Dic17—41no—
90C4⋊Dic17—41no—
91C4⋊Dic17—41no—
92C4⋊Dic17—41no—
93C4⋊Dic17—42no—
94C4⋊Dic17—82no—
95#63225—44no—
96C4×Dic17—41no—
97C4×Dic17—41no—
98C2×#3622—22no—
99C2×#3622—22no—
100C2×#3622—41no—
101C2×#3622—41no—
102C2×#3622—41no—
103C2×#3622—41no—
104#10582—171nomaximal, Sylow
105C23×C17#12011yescharacteristic
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—22no—
109C2×C4×C17—22no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—81no—
115C2×C4×C17—81no—
116C2×C4×C17—81no—
117C2×C4×C17C22⋊Q811yescharacteristic
118C2×C4×C17C22⋊Q811yescharacteristic
119C2×C4×C17C22⋊Q811yescharacteristic
120C2×C4×C17C4⋊Q811yescharacteristic
121C2×C4×C17C4⋊Q811yescharacteristic
122C2×C4×C17C4⋊Q811yescharacteristic
123C2×C4×C17C2×SD1611yescharacteristic
124C2×C4×C17C2×SD1611yescharacteristic
125C2×C4×C17#13511yescharacteristic
126C2×C4×C17#13511yescharacteristic
127C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C17#13711yescharacteristic
130C2×C4×C17#13711yescharacteristic
131C2×Dic17—41no—
132C2×Dic17—42no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—42no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—42no—
139C2×Dic17—41no—
140C8×C17—42no—
141#3622—42no—
142#3622—42no—
143#2552—171no—
144#1948—171no—
145#1948D1711yescharacteristic
146#1834—171no—
147#1296—171no—
148#1279—171no—
149#1279—171no—
150C22×C17#39511yescharacteristic
151C22×C17#44811yescharacteristic
152C22×C17#44911yescharacteristic
153C22×C17#45011yescharacteristic
154C22×C17#45211yescharacteristic
155C22×C17#45411yescharacteristic
156C22×C17#45511yescharacteristic
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—42no—
160C4×C17—42no—
161C4×C17—161no—
162C4×C17#47511yescharacteristic
163C4×C17#47611yescharacteristic
164C4×C17#47811yescharacteristic
165C4×C17#47911yescharacteristic
166C4×C17#49811yescharacteristic
167C4×C17#49911yescharacteristic
168C4×C17#50111yescharacteristic
169C4×C17#50111yescharacteristic
170Dic17—81no—
171Dic17—81no—
172Dic17—82no—
173C2×#125—341no—
174C2×#106—21no—
175C2×#106—341no—
176C2×C4⋊C8—171no—
177C2×C4⋊C8C2×D1711yescharacteristic
178C2×C4×C8—171no—
179#398—342no—
180#389—341no—
181#389—341no—
182#384—171no—
183#384—341no—
184#384C2×D1711yescharacteristic
185C4×C4⋊C4—171no—
186C4×C4⋊C4C2×D1711yescharacteristic
187#340—21no—
188#340—342no—
189#340—341no—
190C2×C17#162611yescharacteristic
191C2×C17#163511yescharacteristic
192C2×C17#164211yescharacteristic
193C2×C17#164311yescharacteristic
194C2×C17#205811yescharacteristic
195C2×C17#205911yescharacteristic
196C2×C17#206111yescharacteristic
197C22×C8—21no—
198C22×C8—341no—
199C22×C8—341no—
200#125—682no—
201#125—682no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—171no—
206C2×C4⋊C4—171no—
207C2×C4⋊C4—172no—
208C2×C4⋊C4—342no—
209C2×C4⋊C4—342no—
210C2×C4⋊C4—341no—
211C2×C4⋊C4—341no—
212C2×C4⋊C4—342no—
213C2×C4⋊C4C22⋊D1711yescharacteristic
214C2×C4⋊C4C22⋊D1711yescharacteristic
215C2×C42—21no—
216C2×C42—341no—
217C2×C42C22×D1711yescharacteristic
218#106—42no—
219#106—682no—
220C4⋊C8—21no—
221C4⋊C8—172no—
222C4⋊C8—341no—
223C4⋊C8Dic3412yes—
224C4×C8—172no—
225C4×C8—341no—
226#95—21no—
227#95—342no—
228#95—341no—
229C17#1058211yescharacteristic, complemented, Sylow
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4—341no—
234C22×C4—341no—
235C22×C4—342no—
236C22×C4D4×D1711yescharacteristic
237C22×C4D4×D1711yescharacteristic
238C22×C4C2×C22⋊D1711yescharacteristic
239C2×C8—22no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—342no—
243C2×C8—342no—
244C2×C8—681no—
245C2×C8—681no—
246C2×C8—681no—
247C2×C8—681no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—341no—
256C4⋊C4—341no—
257C4⋊C4—341no—
258C4⋊C4—341no—
259C4⋊C4—682no—
260C4⋊C4—684no—
261C4⋊C4—684no—
262C4⋊C4—681no—
263C4⋊C4—681no—
264C4⋊C4—681no—
265C4⋊C4—681no—
266C4⋊C4—1362no—
267C4⋊C4#6322912yes—
268C4⋊C4#6323012yes—
269C42—41no—
270C42—41no—
271C42—681no—
272C42—681no—
273C42C2×Dic3411yescharacteristic
274C42#6325211yescharacteristic
275C42Q8×D1711yescharacteristic
276C42Q8×D1711yescharacteristic
277C23#1058762311yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—681no—
290C2×C4—682no—
291C2×C4—681no—
292C2×C4—681no—
293C2×C4—682no—
294C2×C4—681no—
295C2×C4—681no—
296C2×C4—682no—
297C2×C4—681no—
298C2×C4#1058757411yescharacteristic
299C2×C4#1058757411yescharacteristic
300C2×C4#1058758211yescharacteristic
301C2×C4#1058758211yescharacteristic
302C2×C4#1058760011yescharacteristic
303C2×C4#1058760111yescharacteristic
304C2×C4#1058760211yescharacteristic
305C2×C4#1058760211yescharacteristic
306C2×C4#1058761011yescharacteristic
307C2×C4C2×#6322911yescharacteristic
308C2×C4C2×#6323011yescharacteristic
309C2×C4#1058763011yescharacteristic
310C2×C4#1058763511yescharacteristic
311C2×C4#1058763711yescharacteristic
312C8—42no—
313C8—682no—
314C8—682no—
315C22#1176272911yescharacteristic
316C22#1176294711yescharacteristic
317C22#1176295311yescharacteristic
318C22#1176295911yescharacteristic
319C22#1176296811yescharacteristic
320C22#1176298011yescharacteristic
321C22#1176298511yescharacteristic
322C4—21no—
323C4—21no—
324C4—42no—
325C4—42no—
326C4—161no—
327C4—1361no—
328C4—1361no—
329C4—1362no—
330C4#1176309411yescharacteristic
331C4#1176309911yescharacteristic
332C4#1176310811yescharacteristic
333C4#1176311911yescharacteristic
334C4#1176320511yescharacteristic
335C4#1176320911yescharacteristic
336C4#1176321611yescharacteristic
337C4#1176321911yescharacteristic
338C2#1452787911yescharacteristic
339C2#1452793311yescharacteristic
340C2#1452798311yescharacteristic
341C2#1452798911yescharacteristic
342C2#1453011711yescharacteristic
343C2#1453012411yescharacteristic
344C2#1453013211yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1948C2
socle, prime radicalC23×C17#120
hypercenter#1948D17
hypocenterC17#10582
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
229. C17#10582semidirect

Maximal subgroups

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

subgroupindex
#145338152
#145295452
#145289112
#145266682
#145266252
#145266232
C17×#19482
#1058217