Finite Group Databasebeta

← #16945216

Subgroups — #16945216

Order 4352.

382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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#14534475C211yesmaximal, characteristic
2#14528860C211yesmaximal, characteristic
3#14527095C211yesmaximal, characteristic
4#14526808C211yesmaximal, characteristic
5#14526785C211yesmaximal, characteristic
6#14526783C211yesmaximal, characteristic
7C17×#1352C211yesmaximal, characteristic
8C2×#10587576C411yescharacteristic, complemented
9C2×#10587563C2211yescharacteristic
10#11762859—21no—
11#11762747C411yescharacteristic, complemented
12#11762741C411yescharacteristic, complemented
13#11762734C2211yescharacteristic
14#11762705—21no—
15#11762697—21no—
16#11762695—21no—
17#11762684—21no—
18#11762670—21no—
19#11762654C411yescharacteristic, complemented
20#11762576C2211yescharacteristic
21#11762575—21no—
22#11762534—21no—
23#11762533C2211yescharacteristic
24C17×#399C2211yescharacteristic
25C17×#342C2211yescharacteristic
26C17×#323C2211yescharacteristic
27C23×Dic17D411yescharacteristic
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C22⋊C4×C17—21no—
31C2×C22⋊C4×C17—21no—
32C2×C22⋊C4×C17C2311yescharacteristic
33C2×C22⋊Dic17—21no—
34C2×C22⋊Dic17—21no—
35C2×C22⋊Dic17D411yescharacteristic
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17C2×C411yescharacteristic
39C2×#63225—21no—
40C2×#63225C2×C411yescharacteristic
41C2×#63225D411yescharacteristic
42C2×C4×Dic17—21no—
43C2×C4×Dic17C2×C411yescharacteristic
44C2×C4×Dic17D411yescharacteristic
45#10587576—41no—
46#10587576—41no—
47#10587563—41no—
48#10587563—41no—
49C17×C22⋊C8—21no—
50C17×#95C2×C411yescharacteristic
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—41no—
57#10587502—41no—
58#10587502C2×C411yescharacteristic
59C22⋊#3622—21no—
60#10587485—41no—
61C8×Dic17—41no—
62C24×C17C2×D411yescharacteristic
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—41no—
66C22×C4×C17C22×C411yescharacteristic
67C22×C4×C17C2×D411yescharacteristic
68C22×Dic17—21no—
69C22×Dic17—21no—
70C22×Dic17—21no—
71C22×Dic17—21no—
72C22×Dic17—21no—
73C22×Dic17—21no—
74C22×Dic17—41no—
75C22×Dic17—41no—
76C22×Dic17C22⋊C411yescharacteristic
77C22×Dic17C22⋊C411yescharacteristic
78C22×Dic17C22⋊C411yescharacteristic
79C22×Dic17C22⋊C411yescharacteristic
80C2×C8×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—42no—
83C22⋊C4×C17—41no—
84C22⋊C4×C17—42no—
85C22⋊C4×C17—41no—
86C22⋊C4×C17—41no—
87C22⋊Dic17—41no—
88C22⋊Dic17—41no—
89C22⋊Dic17—41no—
90C22⋊Dic17—41no—
91C22⋊Dic17—41no—
92C4⋊Dic17—42no—
93C4⋊Dic17—41no—
94C4⋊Dic17—41no—
95C4⋊Dic17—41no—
96#63225—41no—
97#63225—41no—
98#63225—42no—
99C4×Dic17—21no—
100C4×Dic17—21no—
101C4×Dic17—21no—
102C4×Dic17—21no—
103C4×Dic17—42no—
104C2×#3622—41no—
105#11846—171nomaximal, Sylow
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—41no—
109C23×C17—41no—
110C23×C17C2×C22⋊C411yescharacteristic
111C23×C17#13511yescharacteristic
112C23×C17#13511yescharacteristic
113C2×C4×C17—22no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—81no—
124C2×C4×C17—81no—
125C2×C4×C17—81no—
126C2×Dic17—21no—
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—21no—
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—81no—
146C2×Dic17—81no—
147C2×Dic17—81no—
148C2×Dic17#9911yescharacteristic
149C2×Dic17#9911yescharacteristic
150C8×C17—81no—
151#3622—81no—
152#2611—171no—
153#1820—171no—
154#1458—171no—
155#1352—171no—
156#1352D1711yescharacteristic
157#1344—171no—
158#1344—171no—
159C22×C17—21no—
160C22×C17—21no—
161C22×C17—21no—
162C22×C17—21no—
163C22×C17—41no—
164C22×C17—41no—
165C22×C17—41no—
166C22×C17—41no—
167C22×C17—81no—
168C22×C17C2×#9911yescharacteristic
169C22×C17#41611yescharacteristic
170C22×C17#42111yescharacteristic
171C4×C17—42no—
172C4×C17—41no—
173C4×C17—41no—
174C4×C17—81no—
175C4×C17—161no—
176Dic17—21no—
177Dic17—21no—
178Dic17—41no—
179Dic17—41no—
180Dic17—41no—
181Dic17—81no—
182Dic17—81no—
183Dic17—161no—
184C2×#125—171no—
185C2×#117—171no—
186#431—341no—
187#400—171no—
188#399C2×D1711yescharacteristic
189#398—171no—
190#397—171no—
191#389—341no—
192#388—341no—
193#387—341no—
194#385—341no—
195#381—341no—
196#376—171no—
197#342—171no—
198#342—341no—
199#342C2×D1711yescharacteristic
200#324—341no—
201#323—171no—
202#323C2×D1711yescharacteristic
203C2×C17—21no—
204C2×C17—21no—
205C2×C17—41no—
206C2×C17—41no—
207C2×C17#151611yescharacteristic
208C2×C17#212311yescharacteristic
209C2×C17#212611yescharacteristic
210C23×C4—171no—
211#125—681no—
212#125—681no—
213#117—681no—
214#117—681no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—171no—
217C2×C4⋊C4—171no—
218C2×C4⋊C4—171no—
219C2×C4⋊C4—341no—
220C2×C4⋊C4—341no—
221C2×C4⋊C4—341no—
222C2×C4⋊C4C4×D1711yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—171no—
226C2×C22⋊C4—341no—
227C2×C22⋊C4—341no—
228C2×C22⋊C4C22×D1711yescharacteristic
229C2×C42—171no—
230C2×C42—171no—
231C2×C42—341no—
232C4⋊C8—681no—
233C22⋊C8—21no—
234C22⋊C8—341no—
235C4×C8—681no—
236#95—171no—
237#95—341no—
238#95—341no—
239#95—341no—
240#95—341no—
241#95—341no—
242#95—681no—
243#95—681no—
244#95C4×D1711yescharacteristic
245C17#1184611yescharacteristic, complemented, Sylow
246C24D4×D1711yescharacteristic
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—171no—
251C22×C4—171no—
252C22×C4—171no—
253C22×C4—171no—
254C22×C4—341no—
255C22×C4—341no—
256C22×C4—341no—
257C22×C4—341no—
258C22×C4—341no—
259C22×C4—341no—
260C22×C4—681no—
261C22×C4—681no—
262C22×C4C2×C4×D1711yescharacteristic
263C22×C4D4×D1711yescharacteristic
264C2×C8—41no—
265C2×C8—681no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—681no—
269C4⋊C4—681no—
270C4⋊C4—681no—
271C4⋊C4—681no—
272C4⋊C4—681no—
273C4⋊C4—682no—
274C4⋊C4—682no—
275C22⋊C4—41no—
276C22⋊C4—42no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—681no—
280C22⋊C4—681no—
281C22⋊C4—681no—
282C22⋊C4—681no—
283C22⋊C4—681no—
284C42—341no—
285C42—341no—
286C42—341no—
287C42—341no—
288C42—682no—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23C22⋊C4×D1711yescharacteristic
294C23#1058760211yescharacteristic
295C23#1058760511yescharacteristic
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—171no—
310C2×C4—171no—
311C2×C4—341no—
312C2×C4—341no—
313C2×C4—341no—
314C2×C4—341no—
315C2×C4—341no—
316C2×C4—341no—
317C2×C4—341no—
318C2×C4—681no—
319C2×C4—681no—
320C2×C4—681no—
321C2×C4—681no—
322C2×C4—681no—
323C2×C4—681no—
324C2×C4—681no—
325C2×C4—681no—
326C2×C4—681no—
327C2×C4—681no—
328C2×C4—681no—
329C2×C4—681no—
330C2×C4—1361no—
331C2×C4—1361no—
332C2×C4—1361no—
333C8—81no—
334C8—1361no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22#99×D1711yescharacteristic
345C22#1176280411yescharacteristic
346C22#1176282411yescharacteristic
347C4—42no—
348C4—41no—
349C4—41no—
350C4—81no—
351C4—161no—
352C4—2721no—
353C4—341no—
354C4—341no—
355C4—681no—
356C4—681no—
357C4—681no—
358C4—1361no—
359C4—1361no—
360C2—21no—
361C2—21no—
362C2—41no—
363C2—41no—
364C2#1452733911yescharacteristic
365C2#1453043611yescharacteristic
366C2#1453044611yescharacteristic
subgroupG/H
centerC22#99×D17
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1352C2
socleC22×C17C2×#99
prime radicalC24×C17C2×D4
cosocleC2×C22⋊C4×C17C23
hypercenter#1352D17
hypocenterC17#11846
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
8. C2×#10587576C4semidirect
11. #11762747C4semidirect
12. #11762741C4semidirect
19. #11762654C4semidirect
245. C17#11846semidirect

Maximal subgroups

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

subgroupindex
#145344752
#145288602
#145270952
#145268082
#145267852
#145267832
C17×#13522
#1184617