Finite Group Databasebeta

← #16944006

Subgroups — #16944006

Order 4352.

424 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 91 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#14527122C211yesmaximal, characteristic
2#14527105C211yesmaximal, characteristic
3#14526732C212yesmaximal, complemented
4#14526732C212yesmaximal, complemented
5C17×#2579C211yesmaximal, characteristic
6#11762862—21no—
7#11762773—21no—
8#11762535—21no—
9#11762533—21no—
10#11762533C2212yes—
11#11762533C2212yes—
12C2×C4×D4×C17C2211yescharacteristic
13C22×C4⋊C4×C17C411yescharacteristic
14C17×#398—21no—
15C17×#396—21no—
16C17×#387—21no—
17C17×#386C411yescharacteristic
18C17×#386C411yescharacteristic
19C17×#385—21no—
20C17×#385C2211yescharacteristic
21C17×#385C2211yescharacteristic
22C17×#380C411yescharacteristic
23C22×D4×C17C2×C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17C2×C411yescharacteristic
27C23×C4×C17D411yescharacteristic
28C4×D4×C17—41no—
29C4×D4×C17—41no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17—41no—
36C2×C4⋊C4×C17—41no—
37C2×C4⋊C4×C17D411yescharacteristic
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17C2×C411yescharacteristic
41C2×C22⋊C4×C17C2×C411yescharacteristic
42C2×C22⋊C4×C17D411yescharacteristic
43C2×C22⋊C4×C17C2311yescharacteristic
44C2×C42×C17D411yescharacteristic
45C2×#63223—41no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95—21no—
51C22⋊#3622—22no—
52C22⋊#3622—22no—
53C22⋊#3622—41no—
54C4⋊#3622—41no—
55C4×#3622—41no—
56C24×C17C22⋊C411yescharacteristic
57C24×C17C22×C411yescharacteristic
58C2×D4×C17—22no—
59C2×D4×C17—22no—
60C2×D4×C17—41no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—42no—
70C22×C4×C17—41no—
71C22×C4×C17—41no—
72C22×C4×C17—81no—
73C22×C4×C17—81no—
74C22×C4×C17—81no—
75C22×C4×C17C22⋊C411yescharacteristic
76C22×C4×C17C22⋊C411yescharacteristic
77C22×C4×C17C22⋊C411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17C2×D411yescharacteristic
80C4⋊C4×C17—41no—
81C4⋊C4×C17—42no—
82C4⋊C4×C17—42no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—41no—
85C4⋊C4×C17—81no—
86C4⋊C4×C17—81no—
87C22⋊C4×C17—22no—
88C22⋊C4×C17—22no—
89C22⋊C4×C17—41no—
90C22⋊C4×C17—41no—
91C22⋊C4×C17—42no—
92C22⋊C4×C17—81no—
93C42×C17—21no—
94C42×C17—21no—
95#63223—82no—
96C2×#3622—42no—
97C2×#3622—42no—
98#11577—171nomaximal, Sylow
99C23×C17—21no—
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—41no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17C2×C22⋊C411yescharacteristic
109C23×C17#13112yes—
110D4×C17—44no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—22no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—41no—
118C2×C4×C17—42no—
119C2×C4×C17—41no—
120C2×C4×C17—42no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—42no—
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—41no—
135C2×C4×C17—81no—
136C2×C4×C17—81no—
137C2×C4×C17—81no—
138C2×C4×C17—82no—
139C2×C4×C17#9911yescharacteristic
140C2×C4×C17#9911yescharacteristic
141C2×C4×C17#10112yes—
142#3622—82no—
143#3622—82no—
144#2579D1711yescharacteristic
145#1465—171no—
146#1460—171no—
147#1326—172no—
148#1326—172no—
149C22×C17—21no—
150C22×C17—21no—
151C22×C17—22no—
152C22×C17—42no—
153C22×C17—42no—
154C22×C17—42no—
155C22×C17—41no—
156C22×C17—41no—
157C22×C17—41no—
158C22×C17—41no—
159C22×C17—41no—
160C22×C17—81no—
161C22×C17#40811yescharacteristic
162C22×C17C2×#9911yescharacteristic
163C22×C17C2×#10111yescharacteristic
164C4×C17—21no—
165C4×C17—21no—
166C4×C17—22no—
167C4×C17—41no—
168C4×C17—42no—
169C4×C17—41no—
170C4×C17—41no—
171C4×C17—81no—
172C4×C17—81no—
173C4×C17—81no—
174C2×C4×D4C2×D1711yescharacteristic
175C22×C4⋊C4Dic1711yescharacteristic
176#431—341no—
177#407—341no—
178#398—21no—
179#396—21no—
180#387—21no—
181#386Dic1711yescharacteristic
182#386Dic1711yescharacteristic
183#385—21no—
184#385C2×D1711yescharacteristic
185#385C2×D1711yescharacteristic
186#380Dic1711yescharacteristic
187#324—341no—
188#323—172no—
189#323—172no—
190#323—341no—
191C2×C17—21no—
192C2×C17—21no—
193C2×C17—42no—
194C2×C17—81no—
195C2×C17#147211yescharacteristic
196C2×C17#212011yescharacteristic
197C2×C17#212111yescharacteristic
198C22×D4C2×Dic1711yescharacteristic
199C23×C4C2×Dic1711yescharacteristic
200C23×C4C2×Dic1711yescharacteristic
201C23×C4C2×Dic1711yescharacteristic
202C23×C4C22⋊D1711yescharacteristic
203C2×M16—681no—
204C4×D4—41no—
205C4×D4—41no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—41no—
213C2×C4⋊C4C22⋊D1711yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4C2×Dic1711yescharacteristic
217C2×C22⋊C4C2×Dic1711yescharacteristic
218C2×C22⋊C4C22⋊D1711yescharacteristic
219C2×C22⋊C4C22×D1711yescharacteristic
220C2×C42C22⋊D1711yescharacteristic
221C4⋊C8—681no—
222C22⋊C8—342no—
223C22⋊C8—342no—
224C22⋊C8—681no—
225C4×C8—681no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231C17#1157711yescharacteristic, complemented, Sylow
232C24C22⋊Dic1711yescharacteristic
233C24C22×Dic1711yescharacteristic
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—41no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—42no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4C22⋊Dic1711yescharacteristic
252C22×C4C22⋊Dic1711yescharacteristic
253C22×C4C22⋊Dic1711yescharacteristic
254C22×C4C2×C22⋊D1711yescharacteristic
255C22×C4C2×C22⋊D1711yescharacteristic
256M16—1362no—
257C2×C8—682no—
258C2×C8—682no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—42no—
271C22⋊C4—81no—
272C42—21no—
273C42—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23#1058763412yes—
284C23C2×C22⋊Dic1711yescharacteristic
285D4—44no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—82no—
314C2×C4#1058750511yescharacteristic
315C2×C4#1058750511yescharacteristic
316C2×C4#1058750712yes—
317C8—1362no—
318C8—1362no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—42no—
323C22—42no—
324C22—42no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22#1176277611yescharacteristic
332C22C2×#1058750511yescharacteristic
333C22C2×#1058750711yescharacteristic
334C4—21no—
335C4—21no—
336C4—22no—
337C4—41no—
338C4—42no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—81no—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—81no—
348C2#1452714811yescharacteristic
349C2#1453042511yescharacteristic
350C2#1453043011yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC24×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#2579C2
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC2×C22⋊C4×C17C23
hypercenter#2579D17
hypocenterC17#11577
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2579

Complements

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

NH ≅ G/Ntype
3. #14526732C2semidirect
4. #14526732C2semidirect
231. C17#11577semidirect

Maximal subgroups

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

subgroupindex
#145271222
#145271052
#145267322
C17×#25792
#1157717