Finite Group Databasebeta

← #17957960

Subgroups — #17957960

Order 4352.

926 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 926 conjugacy classes of subgroups — too many to draw. Only its 172 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
1C2×#11763689C212yesmaximal
2C2×#11763689C212yesmaximal
3#14544447C212yesmaximal
4C22×#10587575C211yesmaximal, characteristic
5C22×#63247C2214yes—
6#11763689—24no—
7#11763689—24no—
8#11763675—24no—
9C2×#10587575—24no—
10C2×#10587575—24no—
11C2×#10587575—24no—
12C22×C4⋊Dic17C411yescharacteristic
13C22×#63225C411yescharacteristic
14C22×#63225C411yescharacteristic
15C22×#63225C2211yescharacteristic
16C22×#63225C2211yescharacteristic
17C22×C4×Dic17C2211yescharacteristic
18C22×C4⋊C4×C17C411yescharacteristic
19C23×C4×C17C2×C411yescharacteristic
20C23×C4×C17C2×C411yescharacteristic
21C23×C4×C17C2×C411yescharacteristic
22C23×Dic17C2×C411yescharacteristic
23C23×Dic17C2×C411yescharacteristic
24C23×Dic17C2×C411yescharacteristic
25C23×Dic17C2311yescharacteristic
26C2×#63247—24no—
27C2×#63247—24no—
28C2×#63247—24no—
29C2×#63247—24no—
30C2×#63247—24no—
31C2×#63247Q818yes—
32C22×#3624—24no—
33C2×C4⋊C4×C17—22no—
34C2×C4⋊C4×C17—22no—
35C2×C4⋊C4×C17—22no—
36C2×C4⋊Dic17—22no—
37C2×C4⋊Dic17—22no—
38C2×C4⋊Dic17—22no—
39C2×#63225—22no—
40C2×#63225—22no—
41C2×#63225—22no—
42C2×#63225—22no—
43C2×#63225—22no—
44C2×#63225—22no—
45C2×#63225—22no—
46C2×#63225—22no—
47C2×#63225—22no—
48C2×#63225—22no—
49C2×#63225D414yes—
50C2×#63225D414yes—
51C2×C4×Dic17—22no—
52C2×C4×Dic17—22no—
53C2×C4×Dic17D414yes—
54#10587575—232no—
55C24×C17C22×C411yescharacteristic
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—42no—
63C22×C4×C17—42no—
64C22×C4×C17—42no—
65C22×C4×C17C22⋊C412yes—
66C22×C4×C17C22⋊C412yes—
67C22×C4×C17C22⋊C412yes—
68C22×Dic17—21no—
69C22×Dic17—21no—
70C22×Dic17—21no—
71C22×Dic17—21no—
72C22×Dic17—21no—
73C22×Dic17—21no—
74C22×Dic17—42no—
75C22×Dic17—42no—
76C22×Dic17—42no—
77C22×Dic17C22⋊C412yes—
78C22×Dic17C22⋊C412yes—
79C22×Dic17C22⋊C412yes—
80C22×Dic17C2×D412yes—
81C22×Dic17C2×D412yes—
82C22×Dic17C2×D412yes—
83C22×Dic17C2×Q814yes—
84C22×Dic17#4114yes—
85#63247—28no—
86#63247—28no—
87#63247—44no—
88#63247—44no—
89C2×#3624—28no—
90C2×#3624—44no—
91C2×#3624—44no—
92C4⋊C4×C17—28no—
93C4⋊Dic17—28no—
94#63225—28no—
95#63225—28no—
96#63225—28no—
97#63225—28no—
98C4×Dic17—28no—
99#11383—171nomaximal, Sylow
100C23×C17—22no—
101C23×C17—22no—
102C23×C17C2×C22⋊C411yescharacteristic
103C23×C17C2×C22⋊C411yescharacteristic
104C23×C17C2×C22⋊C411yescharacteristic
105C23×C17C4×Q814yes—
106C2×C4×C17—22no—
107C2×C4×C17—22no—
108C2×C4×C17—22no—
109C2×C4×C17—24no—
110C2×C4×C17—42no—
111C2×C4×C17—42no—
112C2×C4×C17—42no—
113C2×C4×C17—42no—
114C2×C4×C17—42no—
115C2×C4×C17—42no—
116C2×C4×C17—42no—
117C2×C4×C17—42no—
118C2×Dic17—22no—
119C2×Dic17—22no—
120C2×Dic17—22no—
121C2×Dic17—24no—
122C2×Dic17—42no—
123C2×Dic17—42no—
124C2×Dic17—42no—
125C2×Dic17—42no—
126C2×Dic17—42no—
127C2×Dic17—42no—
128C2×Dic17—42no—
129C2×Dic17—42no—
130C2×Dic17#12014yes—
131C2×Dic17C22⋊Q814yes—
132C2×Dic17C22⋊Q814yes—
133C2×Dic17C22⋊Q814yes—
134C2×Dic17#12412yes—
135C2×Dic17#12412yes—
136C2×Dic17#12412yes—
137C2×Dic17C4⋊Q812yes—
138C2×Dic17C4⋊Q812yes—
139C2×Dic17C4⋊Q812yes—
140#3624—48no—
141C22×#125—171no—
142C2×#343—172no—
143C2×#343—172no—
144#1728—172no—
145C22×C17—28no—
146C22×C17—21no—
147C22×C17—21no—
148C22×C17—21no—
149C22×C17—21no—
150C22×C17#37911yescharacteristic
151C22×C17#39112yes—
152C22×C17#39112yes—
153C22×C17#39112yes—
154C22×C17#41312yes—
155C22×C17#41312yes—
156C4×C17—42no—
157C4×C17—42no—
158C4×C17—42no—
159Dic17—42no—
160Dic17—42no—
161Dic17—42no—
162Dic17#39314yes—
163Dic17#39514yes—
164C22×M16—174no—
165C2×#125—344no—
166C2×#125—344no—
167C2×#125—344no—
168C22×C4⋊C4—171no—
169C22×C4⋊C4—171no—
170C22×C4⋊C4—171no—
171C22×C4⋊C4—171no—
172C22×C4⋊C4—171no—
173C22×C4⋊C4#59511yescharacteristic
174C22×C42—171no—
175#343—344no—
176#343—344no—
177#336—344no—
178C2×C17—22no—
179C2×C17—22no—
180C2×C17#144611yescharacteristic
181C2×C17#178511yescharacteristic
182C2×C17#178511yescharacteristic
183C2×C17#199814yes—
184C23×C4—171no—
185C23×C4—171no—
186C23×C4—171no—
187C23×C4—171no—
188C23×C4C2×#59511yescharacteristic
189C23×C4C2×#59511yescharacteristic
190C23×C4C2×#59511yescharacteristic
191C2×M16—178no—
192C2×M16—344no—
193C2×M16—344no—
194C2×M16—344no—
195C2×M16—344no—
196C2×M16—344no—
197C22×C8—344no—
198#125—3432no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—174no—
203C2×C4⋊C4—174no—
204C2×C4⋊C4—342no—
205C2×C4⋊C4—342no—
206C2×C4⋊C4—342no—
207C2×C4⋊C4—342no—
208C2×C4⋊C4—342no—
209C2×C4⋊C4—342no—
210C2×C4⋊C4—342no—
211C2×C4⋊C4—342no—
212C2×C4⋊C4—342no—
213C2×C4⋊C4—342no—
214C2×C4⋊C4—342no—
215C2×C4⋊C4—342no—
216C2×C4⋊C4—342no—
217C2×C42—174no—
218C2×C42—342no—
219C2×C42—342no—
220C17#1138311yescharacteristic, complemented, Sylow
221C24C22×#59511yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—174no—
232C22×C4—174no—
233C22×C4—172no—
234C22×C4—172no—
235C22×C4—172no—
236C22×C4—172no—
237C22×C4—172no—
238C22×C4—172no—
239C22×C4—341no—
240C22×C4—341no—
241C22×C4—341no—
242C22×C4—341no—
243C22×C4—341no—
244C22×C4—341no—
245C22×C4—682no—
246C22×C4—682no—
247C22×C4—682no—
248C22×C4C22⋊#59512yes—
249C22×C4C22⋊#59512yes—
250C22×C4C22⋊#59512yes—
251M16—348no—
252M16—348no—
253M16—684no—
254M16—684no—
255C2×C8—348no—
256C2×C8—684no—
257C2×C8—684no—
258C4⋊C4—28no—
259C4⋊C4—348no—
260C4⋊C4—348no—
261C4⋊C4—348no—
262C4⋊C4—348no—
263C4⋊C4—348no—
264C42—348no—
265C23—22no—
266C23—22no—
267C23Q8×#59514yes—
268C23C2×C22⋊#59511yescharacteristic
269C23C2×C22⋊#59511yescharacteristic
270C23C2×C22⋊#59511yescharacteristic
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—174no—
284C2×C4—174no—
285C2×C4—172no—
286C2×C4—174no—
287C2×C4—174no—
288C2×C4—172no—
289C2×C4—172no—
290C2×C4—172no—
291C2×C4—172no—
292C2×C4—172no—
293C2×C4—342no—
294C2×C4—342no—
295C2×C4—342no—
296C2×C4—344no—
297C2×C4—682no—
298C2×C4—682no—
299C2×C4—682no—
300C2×C4—682no—
301C2×C4—682no—
302C2×C4—682no—
303C2×C4—682no—
304C2×C4—682no—
305C8—688no—
306C22—28no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22#1176375011yescharacteristic
312C22(C2×#595)⋊Q812yes—
313C22(C2×#595)⋊Q812yes—
314C22(C2×#595)⋊Q812yes—
315C22#1176379512yes—
316C22#1176379612yes—
317C4—42no—
318C4—42no—
319C4—42no—
320C4—174no—
321C4—174no—
322C4—682no—
323C4—682no—
324C4—682no—
325C2—22no—
326C2—22no—
327C2#1454397411yescharacteristic
328C2#1454462011yescharacteristic
329C2#1454462111yescharacteristic
330C2#1454497814yes—
subgroupG/H
centerC23C2×C22⋊#595
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
cosocleC23×Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#11383
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
220. C17#11383semidirect

Maximal subgroups

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

subgroupindex
C2×#117636892
#145444472
C22×#105875752
#1138317