Finite Group Databasebeta

← #17949774

Subgroups — #17949774

Order 4352.

654 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 110 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#14544641C212yesmaximal, complemented
2#14543605C212yesmaximal, complemented
3#14543600C212yesmaximal, complemented
4#14531271C211yesmaximal, characteristic
5C2×#10587544—22no—
6C2×#10587543—22no—
7#11763675C2214yes—
8C22×#63254C411yescharacteristic
9C2×#10587578C411yescharacteristic
10C2×C42×D17C2211yescharacteristic
11#11762715C411yescharacteristic
12#11762714C2211yescharacteristic
13#11762712C2211yescharacteristic
14#11762685—22no—
15C22⋊C4×Dic17—22no—
16C17×#390C411yescharacteristic
17C22×D4×C17C2×C411yescharacteristic
18C22×C22⋊D17—21no—
19C23×Dic17—21no—
20C2×#63254—22no—
21C2×#63254—42no—
22C2×#63254—42no—
23C2×#63254C814yescomplemented
24C22×C4×D17C2×C411yescharacteristic
25C22×C4×D17D412yes—
26C22×Dic34C2×C411yescharacteristic
27C22×#3624—24no—
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C22⋊C4×C17—22no—
30C2×C42×C17C2×C411yescharacteristic
31C2×C22⋊Dic17—22no—
32C2×#63227—21no—
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×C4×Dic17—21no—
35C2×C4×Dic17D412yes—
36C2×C4×Dic17C2311yescharacteristic
37#10587578—42no—
38C42×D17—42no—
39#10587544—44no—
40#10587543—44no—
41#10587502—22no—
42#10587502—22no—
43C24×C17—21no—
44C23×D17C22⋊C411yescharacteristic
45C2×D4×C17—21no—
46C2×D4×C17—41no—
47C2×D4×C17—41no—
48C2×D4×C17C2×C812yes—
49C22×C4×C17—21no—
50C22×C4×C17C22⋊C412yes—
51C22×C4×C17C22×C411yescharacteristic
52C2×C22⋊D17—24no—
53C2×C22⋊D17—42no—
54C2×C22⋊D17—42no—
55C22×Dic17—21no—
56C22×Dic17—24no—
57C22×Dic17—21no—
58C22×Dic17—42no—
59C22×Dic17—42no—
60C22×Dic17C22⋊C411yescharacteristic
61C22×Dic17C2×D412yes—
62#63254—48no—
63#63254—48no—
64C2×C4×D17—22no—
65C2×C4×D17—22no—
66C2×C4×D17—22no—
67C2×C4×D17—22no—
68C2×C4×D17—42no—
69C2×C4×D17—42no—
70C2×C4×D17C2×C812yes—
71C2×C4×D17M1612yes—
72C2×Dic34—21no—
73C2×Dic34—41no—
74C2×Dic34—41no—
75C2×Dic34C2×C812yes—
76C2×#3624—44no—
77C2×#3624—44no—
78C2×#3624—44no—
79C4⋊C4×C17—41no—
80C22⋊C4×C17—44no—
81C42×C17—41no—
82C22⋊Dic17—42no—
83C22⋊Dic17—42no—
84#63227—42no—
85C4⋊Dic17—41no—
86C4×Dic17—24no—
87C4×Dic17—41no—
88C4×Dic17—42no—
89#7597—171nomaximal, Sylow
90C23×C17—22no—
91C23×C17—41no—
92C23×C17—41no—
93C23×C17—42no—
94C23×C17—42no—
95C23×C17C2×C22⋊C411yescharacteristic
96C22×D17—21no—
97C22×D17—21no—
98C22×D17—22no—
99C22×D17—22no—
100C22×D17C22⋊C812yes—
101D4×C17—42no—
102D4×C17—42no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—22no—
106C2×C4×C17—22no—
107C2×C4×C17—22no—
108C2×C4×C17—41no—
109C2×C4×C17—42no—
110C2×C4×C17C22×C811yescharacteristic
111C2×C4×C17C2×M1611yescharacteristic
112C22⋊D17—48no—
113C2×Dic17—22no—
114C2×Dic17—22no—
115C2×Dic17—22no—
116C2×Dic17—41no—
117C2×Dic17—41no—
118C2×Dic17—48no—
119C2×Dic17—41no—
120C2×Dic17—42no—
121C2×Dic17C22⋊C812yes—
122C2×Dic17#9912yes—
123C2×Dic17#10012yes—
124C2×Dic17AGL(1,ℤ/8)12yes—
125C2×Dic17#13712yes—
126C4×D17—24no—
127C4×D17—24no—
128C4×D17—44no—
129C4×D17—44no—
130Dic34—42no—
131Dic34—42no—
132#3624—84no—
133#2297—171no—
134#1797—172no—
135#1272—172no—
136#1270—172no—
137C22×C17—42no—
138C22×C17—44no—
139C22×C17—81no—
140C22×C17—81no—
141C22×C17—82no—
142C22×C17C2×C22⋊C811yescharacteristic
143C22×C17C2×#9911yescharacteristic
144C22×C17C2×#10011yescharacteristic
145C22×C17#41712yes—
146C22×C17#42112yes—
147C2×D17—22no—
148C2×D17—24no—
149C2×D17—41no—
150C2×D17—41no—
151C2×D17—42no—
152C4×C17—21no—
153C4×C17—21no—
154C4×C17—42no—
155C4×C17—81no—
156Dic17—22no—
157Dic17—22no—
158Dic17—42no—
159Dic17—81no—
160Dic17#32314yes—
161C22×#41—171no—
162C2×#117—171no—
163C22×C42—171no—
164C2×C4⋊C8—342no—
165C2×C22⋊C8—342no—
166#391—171no—
167#391—171no—
168#390—171no—
169#390#59511yescharacteristic
170#386—342no—
171C4×C22⋊C4—342no—
172#336—174no—
173C2×C17—82no—
174C2×C17C2×#32311yescharacteristic
175C2×C17#147712yes—
176C2×C17#151312yes—
177C2×C17#153611yescharacteristic
178C2×C17#156011yescharacteristic
179D17—42no—
180C2×#41—174no—
181C2×#41—342no—
182C2×#41—682no—
183C2×#41—682no—
184C22×Q8—171no—
185C22×D4—341no—
186C22×D4C2×#59511yescharacteristic
187C23×C4—171no—
188C23×C4—172no—
189C23×C4—341no—
190C22×C8—344no—
191#117—682no—
192C2×C4⋊C4—171no—
193C2×C4⋊C4C2×#59511yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—341no—
196C2×C22⋊C4—342no—
197C2×C42—172no—
198C2×C42—171no—
199C2×C42—341no—
200C2×C42—682no—
201C2×C42C2×#59511yescharacteristic
202C4⋊C8—684no—
203C22⋊C8—684no—
204#95—342no—
205#95—342no—
206C17#759711yescharacteristic, complemented, Sylow
207C24—21no—
208C24—171no—
209#41—688no—
210#41—688no—
211C2×Q8—172no—
212C2×Q8—341no—
213C2×Q8—681no—
214C2×Q8—681no—
215C2×D4—21no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—344no—
219C2×D4—682no—
220C2×D4—682no—
221C2×D4#6324212yes—
222C22×C4—21no—
223C22×C4—171no—
224C22×C4—172no—
225C22×C4—172no—
226C22×C4—172no—
227C22×C4—342no—
228C22×C4—342no—
229C22×C4—342no—
230C22×C4—342no—
231C22×C4—344no—
232C22×C4—341no—
233C22×C4—341no—
234C22×C4—682no—
235C22×C4—682no—
236C22×C4—682no—
237C22×C4—682no—
238C22×C4C22⋊#59512yes—
239C22×C4C22×#59511yescharacteristic
240C2×C8—684no—
241C2×C8—684no—
242C2×C8—684no—
243C4⋊C4—41no—
244C4⋊C4—681no—
245C22⋊C4—44no—
246C22⋊C4—682no—
247C22⋊C4—682no—
248C22⋊C4—682no—
249C42—41no—
250C42—344no—
251C42—681no—
252C42—682no—
253C23—22no—
254C23—41no—
255C23—41no—
256C23—42no—
257C23—42no—
258C23—172no—
259C23—341no—
260C23—341no—
261C23—342no—
262C23—342no—
263C23C2×C22⋊#59511yescharacteristic
264Q8—682no—
265Q8—682no—
266D4—42no—
267D4—42no—
268D4—688no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—172no—
277C2×C4—172no—
278C2×C4—172no—
279C2×C4—172no—
280C2×C4—172no—
281C2×C4—344no—
282C2×C4—344no—
283C2×C4—342no—
284C2×C4—342no—
285C2×C4—342no—
286C2×C4—684no—
287C2×C4—684no—
288C2×C4—688no—
289C2×C4—681no—
290C2×C4—681no—
291C2×C4—681no—
292C2×C4—682no—
293C2×C4C2×#6324211yescharacteristic
294C2×C4D17⋊M1611yescharacteristic
295C8—1364no—
296C22—42no—
297C22—44no—
298C22—82no—
299C22—81no—
300C22—81no—
301C22—342no—
302C22—344no—
303C22—682no—
304C22—681no—
305C22—681no—
306C22#1176377711yescharacteristic
307C22D17⋊#9911yescharacteristic
308C22D17⋊#10011yescharacteristic
309C22#1176380012yes—
310C22#1176380712yes—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—81no—
315C4—174no—
316C4—342no—
317C4—342no—
318C4—682no—
319C4—1361no—
320C2—82no—
321C2—682no—
322C2#1454401011yescharacteristic
323C2#1454408012yes—
324C2#1454420012yes—
325C2#1454427311yescharacteristic
326C2#1454432211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#390C4
socleC23×C17C2×C22⋊C4
prime radicalC22×#63254C4
cosocleC2×C4×Dic17C23
hypercenter#390#595
hypocenterC17#7597
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #14544641C2semidirect
2. #14543605C2semidirect
3. #14543600C2semidirect
23. C2×#63254C8semidirect
206. C17#7597semidirect

Maximal subgroups

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

subgroupindex
#145446412
#145436052
#145436002
#145312712
#759717