Finite Group Databasebeta

← #16937549

Subgroups — #16937549

Order 4352.

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

normal subgroups only

This group has 396 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#14534981C211yesmaximal, characteristic
2#14527317C211yesmaximal, characteristic
3#14527304C211yesmaximal, characteristic
4#14526690C211yesmaximal, characteristic
5#14526670C211yesmaximal, characteristic
6#14526637C211yesmaximal, characteristic
7C17×#1996C211yesmaximal, characteristic
8#11762773C2211yescharacteristic
9#11762773C2211yescharacteristic
10#11762745—21no—
11#11762742—21no—
12#11762742—21no—
13#11762732—21no—
14#11762706—21no—
15#11762692—21no—
16#11762672C2211yescharacteristic
17C4×C22⋊Dic17C2211yescharacteristic
18#11762546—21no—
19#11762546—21no—
20#11762546—21no—
21#11762546—21no—
22C2×C17×C22⋊Q8C2211yescharacteristic
23C17×#380C2211yescharacteristic
24C4×C22⋊C4×C17C2211yescharacteristic
25C17×#342—21no—
26C17×#342—21no—
27C22×Q8×C17Q811yescharacteristic
28C23×C4×C17C2311yescharacteristic
29C17×C22⋊Q8—21no—
30C17×C22⋊Q8—21no—
31C17×C22⋊Q8—21no—
32C17×C22⋊Q8—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17Q811yescharacteristic
36C2×C22⋊C4×C17—21no—
37C2×C22⋊C4×C17—21no—
38C2×C22⋊C4×C17D411yescharacteristic
39C2×C22⋊C4×C17D411yescharacteristic
40C2×C42×C17—21no—
41C2×C22⋊Dic17—21no—
42C2×C22⋊Dic17—21no—
43C2×C4⋊Dic17—21no—
44C2×C4⋊Dic17—21no—
45C2×#63225—21no—
46C2×#63225—21no—
47C2×#63225—21no—
48C2×#63225—21no—
49C2×C4×Dic17—21no—
50C2×#63223—21no—
51C2×#63223—21no—
52C17×#95—21no—
53C17×#95—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502D411yescharacteristic
58#10587502D411yescharacteristic
59#10587502D411yescharacteristic
60#10587502D411yescharacteristic
61C22⋊#3622—21no—
62C22⋊#3622—21no—
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—41no—
74C22×C4×C17—81no—
75C22×C4×C17C2×D411yescharacteristic
76C22×C4×C17C2×D411yescharacteristic
77C22×C4×C17C2×Q811yescharacteristic
78C22×C4×C17#4111yescharacteristic
79C22×C4×C17#4111yescharacteristic
80C22×C4×C17#4111yescharacteristic
81C22×Dic17—21no—
82C22×Dic17—21no—
83C22×Dic17—21no—
84C22×Dic17—21no—
85C4⋊C4×C17—21no—
86C4⋊C4×C17—21no—
87C4⋊C4×C17—41no—
88C4⋊C4×C17—41no—
89C4⋊C4×C17—81no—
90C22⋊C4×C17—22no—
91C22⋊C4×C17—41no—
92C22⋊C4×C17—41no—
93C22⋊C4×C17—41no—
94C22⋊C4×C17—41no—
95C22⋊C4×C17—41no—
96C42×C17—81no—
97C22⋊Dic17—42no—
98C22⋊Dic17—81no—
99C4⋊Dic17—42no—
100C4⋊Dic17—81no—
101#63225—42no—
102#63225—81no—
103#63225—81no—
104#63225—81no—
105C4×Dic17—81no—
106#63223—81no—
107#63223—81no—
108C2×#3622—41no—
109C2×#3622—41no—
110#10385—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—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—42no—
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—41no—
135C2×C4×C17—81no—
136C2×C4×C17—81no—
137C2×C4×C17—81no—
138C2×C4×C17—81no—
139C2×C4×C17C22⋊Q811yescharacteristic
140C2×C4×C17C22⋊Q811yescharacteristic
141C2×C4×C17#12411yescharacteristic
142C2×C4×C17#12411yescharacteristic
143C2×Dic17—22no—
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—41no—
154C2×Dic17—41no—
155#3622—81no—
156#3622—81no—
157#2667—171no—
158#1996D1711yescharacteristic
159#1511—171no—
160#1508—171no—
161#1305—171no—
162#1297—171no—
163#1284—171no—
164C22×C17—21no—
165C22×C17—21no—
166C22×C17—21no—
167C22×C17—21no—
168C22×C17—21no—
169C22×C17—21no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17—81no—
173C22×C17—81no—
174C22×C17#39311yescharacteristic
175C22×C17#45511yescharacteristic
176C22×C17#45611yescharacteristic
177C4×C17—21no—
178C4×C17—21no—
179C4×C17—21no—
180C4×C17—21no—
181C4×C17—81no—
182C4×C17—81no—
183C4×C17—82no—
184C4×C17—81no—
185C4×C17—81no—
186Dic17—42no—
187Dic17—81no—
188Dic17—81no—
189Dic17—81no—
190C2×C22⋊Q8C2×D1711yescharacteristic
191#407—171no—
192#407—171no—
193#399—341no—
194#398—341no—
195#398—341no—
196#396—341no—
197#389—341no—
198#387—341no—
199#381—171no—
200#380C2×D1711yescharacteristic
201C4×C22⋊C4—171no—
202C4×C22⋊C4C2×D1711yescharacteristic
203#342—21no—
204#342—21no—
205#328—341no—
206#328—341no—
207#328—341no—
208#328—341no—
209C2×C17—21no—
210C2×C17—21no—
211C2×C17—41no—
212C2×C17—41no—
213C2×C17#202811yescharacteristic
214C2×C17#203111yescharacteristic
215C2×C17#203211yescharacteristic
216C22×Q8Dic3411yescharacteristic
217C23×C4C22×D1711yescharacteristic
218C2×M16—341no—
219C2×M16—341no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—341no—
227C2×C4⋊C4—341no—
228C2×C4⋊C4—341no—
229C2×C4⋊C4—341no—
230C2×C4⋊C4—341no—
231C2×C4⋊C4—341no—
232C2×C4⋊C4Dic3411yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—341no—
236C2×C22⋊C4—341no—
237C2×C22⋊C4C22⋊D1711yescharacteristic
238C2×C22⋊C4C22⋊D1711yescharacteristic
239C2×C42—21no—
240C2×C42—341no—
241C22⋊C8—341no—
242C22⋊C8—341no—
243C22⋊C8—341no—
244C22⋊C8—341no—
245#95—21no—
246#95—21no—
247#95—171no—
248#95—171no—
249#95—171no—
250#95—171no—
251#95—341no—
252#95—341no—
253#95—341no—
254C17#1038511yescharacteristic, complemented, Sylow
255C24C2×C22⋊D1711yescharacteristic
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—81no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—81no—
265C22×C4—341no—
266C22×C4—341no—
267C22×C4—341no—
268C22×C4—341no—
269C22×C4C2×Dic3411yescharacteristic
270C22×C4#6325211yescharacteristic
271C22×C4D4×D1711yescharacteristic
272C22×C4D4×D1711yescharacteristic
273C22×C4#6325411yescharacteristic
274C22×C4#6325411yescharacteristic
275M16—1361no—
276M16—1361no—
277C2×C8—681no—
278C2×C8—681no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—81no—
284C4⋊C4—682no—
285C4⋊C4—682no—
286C4⋊C4—1361no—
287C4⋊C4—1361no—
288C4⋊C4—1361no—
289C4⋊C4—1361no—
290C22⋊C4—22no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—682no—
297C22⋊C4—1361no—
298C42—81no—
299C42—1361no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23#1058761011yescharacteristic
305C23#1058762211yescharacteristic
306C23#1058762311yescharacteristic
307Q8—81no—
308Q8—81no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
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—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—342no—
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#1058756411yescharacteristic
341C2×C4#1058756411yescharacteristic
342C2×C4#1058757111yescharacteristic
343C2×C4#1058757111yescharacteristic
344C8—1361no—
345C8—1361no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22#1176272111yescharacteristic
357C22#1176298611yescharacteristic
358C22#1176299111yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—81no—
364C4—81no—
365C4—82no—
366C4—81no—
367C4—81no—
368C4—682no—
369C4—1361no—
370C4—1361no—
371C4—1361no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2#1452994511yescharacteristic
377C2#1452995811yescharacteristic
378C2#1452996111yescharacteristic
subgroupG/H
centerC22#11762721
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#1996C2
socleC22×C17#393
prime radicalC24×C17C2×D4
hypercenter#1996D17
hypocenterC17#10385
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
254. C17#10385semidirect

Maximal subgroups

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

subgroupindex
#145349812
#145273172
#145273042
#145266902
#145266702
#145266372
C17×#19962
#1038517