Finite Group Databasebeta

← #16929306

Subgroups — #16929306

Order 4352.

558 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 103 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#14537825C211yesmaximal, characteristic
2#14532043C211yesmaximal, characteristic
3#14528884C212yesmaximal, complemented
4#14526670C212yesmaximal, complemented
5C4×C17×#99C211yesmaximal, characteristic
6C2×#10587612C2211yescharacteristic
7#11762887—24no—
8#11762862—21no—
9#11762773—21no—
10#11762773C2212yes—
11#11762748C411yescharacteristic, complemented
12#11762745C411yescharacteristic, complemented
13#11762739C411yescharacteristic, complemented
14#11762737—21no—
15#11762734C411yescharacteristic, complemented
16#11762723—21no—
17C4×#63225—21no—
18C4×C22⋊Dic17—21no—
19C4×C22⋊Dic17C2211yescharacteristic
20#11762569—24no—
21C2×C4×D4×C17C2211yescharacteristic
22C2×C17×#99—21no—
23C4×C22⋊C4×C17C2212yes—
24C17×#342—21no—
25C22×D4×C17D411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C23×C4×C17C2311yescharacteristic
28C4×D4×C17—22no—
29C4×D4×C17—22no—
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C22⋊C4×C17—22no—
32C2×C22⋊C4×C17C2×C411yescharacteristic
33C2×C22⋊C4×C17D411yescharacteristic
34C2×C42×C17—22no—
35C2×C42×C17D411yescharacteristic
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17—21no—
39C2×C22⋊Dic17—21no—
40#10587612—22no—
41#10587612—22no—
42C2×C4⋊Dic17C2×C411yescharacteristic
43C2×C4⋊Dic17C2×C411yescharacteristic
44C2×#63225—21no—
45C2×#63225—21no—
46C2×C4×Dic17—21no—
47C2×C4×Dic17—21no—
48C2×#63223—22no—
49C2×#63223D414yes—
50C17×#99—24no—
51C17×#95—22no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502C2×C411yescharacteristic
57#10587502C2×C411yescharacteristic
58C22⋊#3622—22no—
59C22⋊#3622—22no—
60C22⋊#3622—22no—
61C4⋊#3622—22no—
62C4×#3622—22no—
63C24×C17C22⋊C411yescharacteristic
64C24×C17C2×D411yescharacteristic
65C2×D4×C17—22no—
66C2×D4×C17—22no—
67C2×D4×C17—41no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—42no—
71C22×C4×C17—42no—
72C22×C4×C17—42no—
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C22⋊C411yescharacteristic
76C22×C4×C17C22×C411yescharacteristic
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17C2×D412yes—
79C22×C4×C17#4112yes—
80C22×Dic17—21no—
81C22×Dic17—21no—
82C22×Dic17—21no—
83C22×Dic17—21no—
84C4⋊C4×C17—22no—
85C22⋊C4×C17—22no—
86C22⋊C4×C17—22no—
87C22⋊C4×C17—24no—
88C22⋊C4×C17—42no—
89C42×C17—21no—
90C42×C17—21no—
91C42×C17—44no—
92C22⋊Dic17—42no—
93C22⋊Dic17—42no—
94C22⋊Dic17—42no—
95C22⋊Dic17—42no—
96C4⋊Dic17—22no—
97C4⋊Dic17—22no—
98#63225—42no—
99#63225—42no—
100C4×Dic17—42no—
101C4×Dic17—41no—
102C4×Dic17—41no—
103#63223—44no—
104#63223—82no—
105C2×#3622—24no—
106#9012—171nomaximal, Sylow
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—41no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17—41no—
116C23×C17C2×C22⋊C411yescharacteristic
117C23×C17#12112yes—
118D4×C17—44no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—24no—
122C2×C4×C17—22no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—41no—
126C2×C4×C17—42no—
127C2×C4×C17—42no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—44no—
131C2×C4×C17—81no—
132C2×C4×C17—82no—
133C2×C4×C17—82no—
134C2×C4×C17#10412yes—
135C2×C4×C17C4×D412yes—
136C2×C4×C17#12011yescharacteristic
137C2×C4×C17#12311yescharacteristic
138C2×Dic17—22no—
139C2×Dic17—41no—
140C2×Dic17—41no—
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—
150#3622—44no—
151#2975—171no—
152#2395—171no—
153#1826—172no—
154C4×#99D1711yescharacteristic
155#1297—172no—
156C22×C17—21no—
157C22×C17—21no—
158C22×C17—22no—
159C22×C17—22no—
160C22×C17—22no—
161C22×C17—42no—
162C22×C17—41no—
163C22×C17—41no—
164C22×C17—41no—
165C22×C17—81no—
166C22×C17—81no—
167C22×C17—81no—
168C22×C17#38611yescharacteristic
169C22×C17C2×#10411yescharacteristic
170C22×C17#42111yescharacteristic
171C4×C17—22no—
172C4×C17—21no—
173C4×C17—22no—
174C4×C17—41no—
175C4×C17—41no—
176C4×C17—84no—
177C4×C17#45812yes—
178Dic17—42no—
179Dic17—81no—
180Dic17—81no—
181Dic17—81no—
182C2×C4×D4C2×D1711yescharacteristic
183C2×#117—171no—
184#436—344no—
185#431—341no—
186C2×#99—21no—
187#407—172no—
188#407—341no—
189#400—171no—
190#399—171no—
191#398—171no—
192#397—171no—
193#397—341no—
194#394—341no—
195C4×C4⋊C4—341no—
196C4×C22⋊C4—171no—
197C4×C22⋊C4—341no—
198C4×C22⋊C4C2×D1712yes—
199#342—21no—
200#339—344no—
201C2×C17—21no—
202C2×C17—21no—
203C2×C17—42no—
204C2×C17—81no—
205C2×C17#187111yescharacteristic
206C2×C17#188411yescharacteristic
207C2×C17#189011yescharacteristic
208C22×D4C22⋊D1711yescharacteristic
209C23×C4D6811yescharacteristic
210C23×C4C22×D1711yescharacteristic
211C2×M16—174no—
212C2×M16—342no—
213C4×D4—22no—
214C4×D4—22no—
215#117—342no—
216#117—342no—
217C2×C4⋊C4—171no—
218C2×C4⋊C4—171no—
219C2×C4⋊C4—341no—
220C2×C4⋊C4—341no—
221C2×C4⋊C4C4×D1711yescharacteristic
222C2×C22⋊C4—22no—
223C2×C22⋊C4—341no—
224C2×C22⋊C4—341no—
225C2×C22⋊C4—341no—
226C2×C22⋊C4—341no—
227C2×C22⋊C4C4×D1711yescharacteristic
228C2×C22⋊C4C22⋊D1711yescharacteristic
229C2×C42—22no—
230C2×C42—341no—
231C2×C42—341no—
232C2×C42D6811yescharacteristic
233C4⋊C8—342no—
234#99—24no—
235C22⋊C8—342no—
236C22⋊C8—342no—
237C22⋊C8—342no—
238C4×C8—342no—
239#95—22no—
240#95—171no—
241#95—171no—
242#95—341no—
243#95—341no—
244#95—341no—
245#95—341no—
246C17#901211yescharacteristic, complemented, Sylow
247C24#6322711yescharacteristic
248C24C2×C22⋊D1711yescharacteristic
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—341no—
258C22×C4—341no—
259C22×C4—341no—
260C22×C4—341no—
261C22×C4#6322711yescharacteristic
262C22×C4#6322711yescharacteristic
263C22×C4#6322711yescharacteristic
264C22×C4C2×C4×D1711yescharacteristic
265C22×C4C2×D6811yescharacteristic
266C22×C4D4×D1712yes—
267C22×C4#6325412yes—
268M16—684no—
269M16—1362no—
270C2×C8—344no—
271C4⋊C4—22no—
272C4⋊C4—342no—
273C4⋊C4—342no—
274C4⋊C4—682no—
275C4⋊C4—682no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—24no—
279C22⋊C4—42no—
280C22⋊C4—682no—
281C22⋊C4—682no—
282C22⋊C4—682no—
283C22⋊C4—682no—
284C42—21no—
285C42—21no—
286C42—44no—
287C42—682no—
288C42—681no—
289C42—681no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23C2×#6322711yescharacteristic
300C23#1058762512yes—
301D4—44no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—44no—
314C2×C4—81no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4—342no—
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#1058747612yes—
330C2×C4#1058756712yes—
331C2×C4#1058756811yescharacteristic
332C2×C4#1058757211yescharacteristic
333C8—684no—
334C22—21no—
335C22—21no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#1176268611yescharacteristic
347C22C2×#1058747611yescharacteristic
348C22#1176282711yescharacteristic
349C4—22no—
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—84no—
355C4—682no—
356C4—1361no—
357C4—1361no—
358C4—1361no—
359C4#1176300012yes—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—81no—
364C2#1452908411yescharacteristic
365C2#1452916511yescharacteristic
366C2#1452919511yescharacteristic
subgroupG/H
centerC2×C4#10587568
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC4×C17×#99C2
socleC22×C17#386
prime radicalC22×D4×C17D4
cosocleC23×C4×C17C23
hypercenterC4×#99D17
hypocenterC17#9012
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #14528884C2semidirect
4. #14526670C2semidirect
11. #11762748C4semidirect
12. #11762745C4semidirect
13. #11762739C4semidirect
15. #11762734C4semidirect
246. C17#9012semidirect

Maximal subgroups

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

subgroupindex
#145378252
#145320432
#145288842
#145266702
C4×C17×#992
#901217