Finite Group Databasebeta

← #16937537

Subgroups — #16937537

Order 4352.

404 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 75 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
1#14534954C211yesmaximal, characteristic
2#14529770C211yesmaximal, characteristic
3#14527317C211yesmaximal, characteristic
4#14526689C211yesmaximal, characteristic
5#14526670C211yesmaximal, characteristic
6#14526638C211yesmaximal, characteristic
7C17×#1508C211yesmaximal, characteristic
8#11762773C2211yescharacteristic
9#11762751—21no—
10#11762732—21no—
11#11762730—21no—
12#11762721—21no—
13#11762715—21no—
14#11762693—21no—
15#11762672C2211yescharacteristic
16#11762669C2211yescharacteristic
17C4×C22⋊Dic17C2211yescharacteristic
18#11762576—21no—
19#11762576—21no—
20#11762546—21no—
21#11762546—21no—
22C2×C17×C22⋊Q8C2211yescharacteristic
23C17×#407C2211yescharacteristic
24C4×C22⋊C4×C17C2211yescharacteristic
25C17×#328—21no—
26C17×#328—21no—
27C22×Q8×C17Q811yescharacteristic, complemented
28C23×C4×C17C2311yescharacteristic
29C22×Dic34—21no—
30C2×M16×C17—21no—
31C17×C22⋊Q8—21no—
32C17×C22⋊Q8—21no—
33C17×C22⋊Q8—21no—
34C17×C22⋊Q8—21no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17Q811yescharacteristic, complemented
37C2×C22⋊C4×C17—21no—
38C2×C22⋊C4×C17—21no—
39C2×C42×C17—21no—
40C2×C22⋊Dic17—21no—
41C2×C22⋊Dic17—21no—
42C2×C22⋊Dic17D411yescharacteristic
43C2×C22⋊Dic17D411yescharacteristic
44C2×C4⋊Dic17—21no—
45C2×C4⋊Dic17—21no—
46C2×#63225—21no—
47C2×#63225—21no—
48C2×C4×Dic17—21no—
49C2×#63223—21no—
50C17×C22⋊C8—21no—
51C17×C22⋊C8—21no—
52C17×#95D411yescharacteristic
53C17×#95D411yescharacteristic
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58#10587502—21no—
59#10587502—21no—
60#10587502—21no—
61#10587502D411yescharacteristic
62#10587502D411yescharacteristic
63C22⋊#3622—21no—
64C22⋊#3622—21no—
65C24×C17C2×D411yescharacteristic
66C2×Q8×C17—21no—
67C2×Q8×C17—21no—
68C2×Q8×C17—81no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—81no—
74C22×C4×C17C2×D411yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76C22×C4×C17C2×Q811yescharacteristic
77C22×C4×C17#4111yescharacteristic
78C22×C4×C17#4111yescharacteristic
79C22×C4×C17#4111yescharacteristic
80C22×Dic17—21no—
81C22×Dic17—21no—
82C22×Dic17—21no—
83C22×Dic17—21no—
84C22×Dic17—41no—
85C2×Dic34—42no—
86C2×Dic34—81no—
87C2×Dic34—81no—
88M16×C17—81no—
89C2×C8×C17—41no—
90C4⋊C4×C17—21no—
91C4⋊C4×C17—21no—
92C4⋊C4×C17—41no—
93C4⋊C4×C17—41no—
94C22⋊C4×C17—42no—
95C22⋊C4×C17—41no—
96C22⋊C4×C17—41no—
97C42×C17—81no—
98C22⋊Dic17—22no—
99C22⋊Dic17—41no—
100C22⋊Dic17—41no—
101C22⋊Dic17—41no—
102C22⋊Dic17—81no—
103C4⋊Dic17—81no—
104C4⋊Dic17—81no—
105#63225—42no—
106#63225—81no—
107C4×Dic17—81no—
108#63223—81no—
109C2×#3622—41no—
110#10383—171nomaximal, Sylow
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17#12011yescharacteristic
116C23×C17C22⋊Q811yescharacteristic
117C23×C17#12411yescharacteristic
118Q8×C17—81no—
119Q8×C17—81no—
120C2×C4×C17—22no—
121C2×C4×C17—41no—
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—81no—
135C2×C4×C17—81no—
136C2×C4×C17C22⋊Q811yescharacteristic
137C2×C4×C17C22⋊Q811yescharacteristic
138C2×C4×C17#12411yescharacteristic
139C2×C4×C17#12411yescharacteristic
140C2×Dic17—42no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—81no—
154C2×Dic17—81no—
155Dic34—84no—
156C8×C17—81no—
157#3622—81no—
158#2665—171no—
159#1996—171no—
160#1511—171no—
161#1508D1711yescharacteristic
162#1305—171no—
163#1297—171no—
164#1284—171no—
165C22×C17—21no—
166C22×C17—21no—
167C22×C17—21no—
168C22×C17—21no—
169C22×C17—21no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17—21no—
173C22×C17—81no—
174C22×C17—81no—
175C22×C17#39311yescharacteristic
176C22×C17#45511yescharacteristic
177C22×C17#45611yescharacteristic
178C4×C17—21no—
179C4×C17—21no—
180C4×C17—21no—
181C4×C17—21no—
182C4×C17—42no—
183C4×C17—81no—
184C4×C17—81no—
185C4×C17—81no—
186Dic17—81no—
187Dic17—81no—
188Dic17—81no—
189Dic17—81no—
190Dic17—82no—
191C2×C22⋊Q8C2×D1711yescharacteristic
192#407—171no—
193#407C2×D1711yescharacteristic
194#400—341no—
195#396—341no—
196#395—341no—
197#393—341no—
198#391—341no—
199#387—341no—
200#381—171no—
201#380—171no—
202C4×C22⋊C4—171no—
203C4×C22⋊C4C2×D1711yescharacteristic
204#342—341no—
205#342—341no—
206#328—21no—
207#328—21no—
208#328—341no—
209#328—341no—
210C2×C17—21no—
211C2×C17—21no—
212C2×C17—41no—
213C2×C17—41no—
214C2×C17#202811yescharacteristic
215C2×C17#203111yescharacteristic
216C2×C17#203211yescharacteristic
217C22×Q8—341no—
218C22×Q8Dic3411yescharacteristic, complemented
219C23×C4C22×D1711yescharacteristic
220C2×M16—21no—
221C2×M16—341no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—341no—
228C2×C4⋊C4—341no—
229C2×C4⋊C4—341no—
230C2×C4⋊C4—341no—
231C2×C4⋊C4Dic3411yescharacteristic, complemented
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—171no—
235C2×C22⋊C4—171no—
236C2×C22⋊C4—341no—
237C2×C22⋊C4—341no—
238C2×C42—21no—
239C2×C42—341no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—341no—
243C22⋊C8—341no—
244#95—171no—
245#95—171no—
246#95—341no—
247#95—341no—
248#95—341no—
249#95—341no—
250#95—341no—
251#95—341no—
252#95—341no—
253#95C22⋊D1711yescharacteristic
254#95C22⋊D1711yescharacteristic
255C17#1038311yescharacteristic, complemented, Sylow
256C24D4×D1711yescharacteristic
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—81no—
260C2×Q8—682no—
261C2×Q8—1361no—
262C2×Q8—1361no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—81no—
268C22×C4—341no—
269C22×C4—341no—
270C22×C4—341no—
271C22×C4—341no—
272C22×C4—681no—
273C22×C4C2×Dic3411yescharacteristic
274C22×C4#6325211yescharacteristic
275C22×C4D4×D1711yescharacteristic
276C22×C4#6325411yescharacteristic
277C22×C4#6325411yescharacteristic
278C22×C4C2×C22⋊D1711yescharacteristic
279M16—81no—
280M16—1361no—
281C2×C8—41no—
282C2×C8—681no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—682no—
288C4⋊C4—1361no—
289C4⋊C4—1361no—
290C4⋊C4—1361no—
291C22⋊C4—42no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—342no—
295C22⋊C4—681no—
296C22⋊C4—681no—
297C22⋊C4—681no—
298C22⋊C4—1361no—
299C42—81no—
300C42—1361no—
301C23—21no—
302C23—21no—
303C23—41no—
304C23—41no—
305C23#1058756411yescharacteristic
306C23#1058757111yescharacteristic
307C23#1058762311yescharacteristic
308Q8—81no—
309Q8—81no—
310Q8—1364no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—682no—
328C2×C4—681no—
329C2×C4—681no—
330C2×C4—681no—
331C2×C4—681no—
332C2×C4—681no—
333C2×C4—681no—
334C2×C4—681no—
335C2×C4—681no—
336C2×C4—681no—
337C2×C4—681no—
338C2×C4—681no—
339C2×C4—681no—
340C2×C4—1361no—
341C2×C4—1361no—
342C2×C4#1058756411yescharacteristic
343C2×C4#1058757111yescharacteristic
344C2×C4#1058761011yescharacteristic
345C2×C4#1058762211yescharacteristic
346C8—81no—
347C8—1361no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—81no—
357C22—81no—
358C22#1176272111yescharacteristic
359C22#1176298511yescharacteristic
360C22#1176299011yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—1361no—
370C4—1361no—
371C4—1361no—
372C4—1361no—
373C4—1362no—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2#1452994311yescharacteristic
379C2#1452995611yescharacteristic
380C2#1452996111yescharacteristic
subgroupG/H
centerC22#11762721
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#1508C2
socleC22×C17#393
prime radicalC24×C17C2×D4
hypercenter#1508D17
hypocenterC17#10383
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
27. C22×Q8×C17Q8semidirect
36. C2×C4⋊C4×C17Q8semidirect
218. C22×Q8Dic34semidirect
231. C2×C4⋊C4Dic34semidirect
255. C17#10383semidirect

Maximal subgroups

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

subgroupindex
#145349542
#145297702
#145273172
#145266892
#145266702
#145266382
C17×#15082
#1038317