Finite Group Databasebeta

← #17950048

Subgroups — #17950048

Order 4352.

488 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 94 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#14544510C211yesmaximal, characteristic
2C4×C22⋊#3624C211yesmaximal, characteristic
3#14543605C212yesmaximal, complemented
4#14543602C212yesmaximal, complemented
5#14537124C211yesmaximal, characteristic
6C2×C22⋊#3624—21no—
7C2×C22⋊#3624—21no—
8C2×#10587542—21no—
9C2×C4×#3624—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587610C411yescharacteristic
13C22×C4×Dic17C2211yescharacteristic
14#11762714C411yescharacteristic
15#11762714C2211yescharacteristic
16#11762708C411yescharacteristic
17#11762708C2211yescharacteristic
18#11762694—21no—
19#11762694—21no—
20#11762684—21no—
21#11762670—21no—
22C17×#380C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C23×Dic17D411yescharacteristic
25C23×Dic17D411yescharacteristic
26C22×Dic34C2×C411yescharacteristic
27C22×#3624—22no—
28C22×#3624—22no—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C22⋊C4×C17—21no—
32C2×C22⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17C2×C411yescharacteristic
36#10587610—42no—
37C2×#63225—21no—
38C2×C4×Dic17—42no—
39C2×C4×Dic17C2×C411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17C2311yescharacteristic
43C22⋊#3624—24no—
44C22⋊#3624—24no—
45#10587542—42no—
46C4×#3624—42no—
47C17×#95—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54C24×C17C22⋊C411yescharacteristic
55C22×C4×C17—22no—
56C22×C4×C17—22no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—41no—
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22×C411yescharacteristic
62C22×Dic17—22no—
63C22×Dic17—22no—
64C22×Dic17—22no—
65C22×Dic17—22no—
66C22×Dic17—21no—
67C22×Dic17—21no—
68C22×Dic17—41no—
69C22×Dic17—41no—
70C22×Dic17C22⋊C411yescharacteristic
71C22×Dic17C22⋊C411yescharacteristic
72C22×Dic17C2×D411yescharacteristic
73C22×Dic17C2×D411yescharacteristic
74C2×Dic34—22no—
75C2×Dic34—41no—
76C2×Dic34—41no—
77C2×#3624—24no—
78C2×#3624—24no—
79C2×#3624—42no—
80C2×#3624—42no—
81C2×#3624—42no—
82C2×#3624—42no—
83C4⋊C4×C17—22no—
84C4⋊C4×C17—41no—
85C22⋊C4×C17—42no—
86C22⋊Dic17—42no—
87C4⋊Dic17—42no—
88C4⋊Dic17—42no—
89C4⋊Dic17—41no—
90#63225—42no—
91C4×Dic17—22no—
92C4×Dic17—22no—
93C4×Dic17—41no—
94C4×Dic17—41no—
95#7675—171nomaximal, Sylow
96C23×C17—21no—
97C23×C17—21no—
98C23×C17—21no—
99C23×C17—21no—
100C23×C17—21no—
101C23×C17—21no—
102C23×C17#10412yes—
103C23×C17C2×C22⋊C411yescharacteristic
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—44no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17#9912yes—
116C2×C4×C17#13112yes—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17—21no—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—21no—
125C2×Dic17—21no—
126C2×Dic17—44no—
127C2×Dic17—44no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17#10412yes—
135C2×Dic17#13512yes—
136C2×Dic17#13712yes—
137Dic34—82no—
138#3624—44no—
139#3624—44no—
140#2855—171no—
141#1749—171no—
142C4×C22⋊C8—171no—
143#1272—172no—
144#1271—172no—
145C22×C17—22no—
146C22×C17—22no—
147C22×C17—22no—
148C22×C17—41no—
149C22×C17—41no—
150C22×C17—41no—
151C22×C17—41no—
152C22×C17#40811yescharacteristic
153C22×C17C2×#9911yescharacteristic
154C22×C17#41311yescharacteristic
155C22×C17#41611yescharacteristic
156C22×C17#41911yescharacteristic
157C22×C17C2×#10411yescharacteristic
158C22×C17C2×#10411yescharacteristic
159C4×C17—22no—
160C4×C17—22no—
161C4×C17—81no—
162C4×C17—81no—
163Dic17—22no—
164Dic17—22no—
165Dic17—22no—
166Dic17—41no—
167Dic17—81no—
168Dic17—81no—
169C2×C22⋊Q8—171no—
170C22×C42—171no—
171C2×C22⋊C8—341no—
172C2×C22⋊C8—341no—
173C2×#97—341no—
174C2×C4×C8—341no—
175#391—171no—
176#391—171no—
177#389—171no—
178#389—171no—
179#387—341no—
180#387—341no—
181#385—341no—
182#381—341no—
183#380#59511yescharacteristic
184#336—172no—
185#336—172no—
186C2×C17—42no—
187C2×C17#146811yescharacteristic
188C2×C17#148511yescharacteristic
189C2×C17#149411yescharacteristic
190C2×C17#150111yescharacteristic
191C2×C17#150811yescharacteristic
192C2×C17#152411yescharacteristic
193C2×C17#155411yescharacteristic
194C22×Q8—171no—
195C23×C4—171no—
196C23×C4—171no—
197C23×C4C2×#59511yescharacteristic
198C22×C8—342no—
199C22×C8—342no—
200C22⋊Q8—682no—
201C2×C4⋊C4—171no—
202C2×C4⋊C4—341no—
203C2×C4⋊C4—341no—
204C2×C4⋊C4—341no—
205C2×C4⋊C4C2×#59511yescharacteristic
206C2×C4⋊C4C2×#59511yescharacteristic
207C2×C22⋊C4—21no—
208C2×C22⋊C4—341no—
209C2×C42—171no—
210C2×C42—171no—
211C2×C42—171no—
212C2×C42—171no—
213C2×C42—682no—
214C22⋊C8—344no—
215C22⋊C8—344no—
216#97—682no—
217C4×C8—682no—
218#95—21no—
219#95—341no—
220#95—341no—
221#95—341no—
222#95—341no—
223#95—341no—
224#95—341no—
225C17#767511yescharacteristic, complemented, Sylow
226C24C22⋊#59511yescharacteristic
227C2×Q8—342no—
228C2×Q8—681no—
229C2×Q8—681no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—41no—
235C22×C4—171no—
236C22×C4—171no—
237C22×C4—171no—
238C22×C4—171no—
239C22×C4—342no—
240C22×C4—342no—
241C22×C4—342no—
242C22×C4—342no—
243C22×C4—341no—
244C22×C4—341no—
245C22×C4—681no—
246C22×C4—681no—
247C22×C4C22⋊#59511yescharacteristic
248C22×C4C22×#59511yescharacteristic
249C2×C8—344no—
250C2×C8—344no—
251C2×C8—682no—
252C2×C8—682no—
253C2×C8—682no—
254C2×C8—682no—
255C4⋊C4—22no—
256C4⋊C4—41no—
257C4⋊C4—681no—
258C4⋊C4—682no—
259C4⋊C4—682no—
260C4⋊C4—682no—
261C22⋊C4—42no—
262C22⋊C4—682no—
263C42—342no—
264C42—342no—
265C42—681no—
266C42—681no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23#1058754812yes—
274C23C2×C22⋊#59511yescharacteristic
275Q8—1362no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—44no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—172no—
288C2×C4—172no—
289C2×C4—172no—
290C2×C4—341no—
291C2×C4—341no—
292C2×C4—341no—
293C2×C4—341no—
294C2×C4—341no—
295C2×C4—341no—
296C2×C4—341no—
297C2×C4—341no—
298C2×C4—341no—
299C2×C4—684no—
300C2×C4—684no—
301C2×C4—681no—
302C2×C4—681no—
303C2×C4—681no—
304C2×C4—681no—
305C2×C4—681no—
306C2×C4—681no—
307C2×C4#1058753912yes—
308C2×C4#1058767812yes—
309C8—684no—
310C8—684no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22#1176378211yescharacteristic
319C22C2×#1058753911yescharacteristic
320C22#1176379611yescharacteristic
321C22#1176379911yescharacteristic
322C22#1176380211yescharacteristic
323C22C2×#1058754811yescharacteristic
324C22D17⋊#10411yescharacteristic
325C4—22no—
326C4—22no—
327C4—81no—
328C4—81no—
329C4—342no—
330C4—342no—
331C4—342no—
332C4—681no—
333C4—1361no—
334C4—1361no—
335C2—42no—
336C2#1454405111yescharacteristic
337C2#1454410611yescharacteristic
338C2#1454413511yescharacteristic
339C2#1454416111yescharacteristic
340C2#1454418311yescharacteristic
341C2#1454423511yescharacteristic
342C2#1454431011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#380C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#380#595
hypocenterC17#7675
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #14543605C2semidirect
4. #14543602C2semidirect
225. C17#7675semidirect

Maximal subgroups

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

subgroupindex
#145445102
C4×C22⋊#36242
#145436052
#145436022
#145371242
#767517