Finite Group Databasebeta

← #17950044

Subgroups — #17950044

Order 4352.

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

normal subgroups only

This group has 550 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, complemented
2C4×C22⋊#3624C211yesmaximal, characteristic, complemented
3#14543603C212yesmaximal, complemented
4#14543600C212yesmaximal, complemented
5#14537110C211yesmaximal, characteristic
6C2×C22⋊#3624—21no—
7C2×C22⋊#3624—21no—
8C2×#10587542—21no—
9C2×C4×#3624—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587621—21no—
13C22×C4×Dic17C2211yescharacteristic
14#11762712C411yescharacteristic
15#11762712C2211yescharacteristic
16#11762705C411yescharacteristic
17#11762705C2211yescharacteristic
18#11762697—21no—
19#11762697—21no—
20#11762689—21no—
21#11762669C411yescharacteristic
22C2×C17×#121C411yescharacteristic
23C22×D4×C17—21no—
24C22×D4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×Dic17D411yescharacteristic
27C23×Dic17D411yescharacteristic
28C22×#3624—22no—
29C22×#3624—22no—
30C17×#121—42no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C22⋊C4×C17—21no—
33C2×C22⋊Dic17—21no—
34C2×C22⋊Dic17—21no—
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38#10587621—44no—
39C2×C4⋊Dic17C2×C411yescharacteristic
40C2×C4⋊Dic17C2×C411yescharacteristic
41C2×#63225—21no—
42C2×#63225—21no—
43C2×C4×Dic17—42no—
44C2×C4×Dic17C2×C411yescharacteristic
45C2×C4×Dic17D411yescharacteristic
46C2×C4×Dic17D411yescharacteristic
47C2×C4×Dic17C2311yescharacteristic
48C22⋊#3624—24no—
49C22⋊#3624—24no—
50#10587542—42no—
51C4×#3624—42no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55C24×C17—21no—
56C24×C17C22⋊C411yescharacteristic
57C2×D4×C17—22no—
58C2×D4×C17—41no—
59C2×D4×C17—41no—
60C2×D4×C17—42no—
61C2×D4×C17—42no—
62C2×D4×C17—42no—
63C22×C4×C17—22no—
64C22×C4×C17—22no—
65C22×C4×C17—21no—
66C22×C4×C17—41no—
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22×C411yescharacteristic
69C22×Dic17—22no—
70C22×Dic17—22no—
71C22×Dic17—22no—
72C22×Dic17—22no—
73C22×Dic17—21no—
74C22×Dic17—21no—
75C22×Dic17—41no—
76C22×Dic17—41no—
77C22×Dic17C22⋊C411yescharacteristic
78C22×Dic17C22⋊C411yescharacteristic
79C22×Dic17C2×D411yescharacteristic
80C22×Dic17C2×D411yescharacteristic
81C2×#3624—24no—
82C2×#3624—24no—
83C2×#3624—42no—
84C2×#3624—42no—
85C2×#3624—42no—
86C2×#3624—42no—
87C4⋊C4×C17—41no—
88C22⋊C4×C17—42no—
89C22⋊Dic17—42no—
90C22⋊Dic17—42no—
91C22⋊Dic17—42no—
92C22⋊Dic17—42no—
93C22⋊Dic17—42no—
94C4⋊Dic17—22no—
95C4⋊Dic17—41no—
96#63225—42no—
97#63225—42no—
98C4×Dic17—22no—
99C4×Dic17—22no—
100C4×Dic17—41no—
101C4×Dic17—41no—
102#7674—171nomaximal, Sylow
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—41no—
110C23×C17—41no—
111C23×C17—41no—
112C23×C17—41no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17—41no—
116C23×C17#10412yes—
117C23×C17C2×C22⋊C411yescharacteristic
118D4×C17—82no—
119D4×C17—84no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—44no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17#9912yes—
129C2×C4×C17#13112yes—
130C2×Dic17—21no—
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—21no—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—21no—
139C2×Dic17—44no—
140C2×Dic17—44no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146C2×Dic17—41no—
147C2×Dic17#10412yes—
148C2×Dic17#13512yes—
149C2×Dic17AGL(1,ℤ/8)12yes—
150#3624—44no—
151#3624—44no—
152#2854—171no—
153#1749—171no—
154C4×C22⋊C8—171no—
155#1271—172no—
156#1270—172no—
157C22×C17—22no—
158C22×C17—22no—
159C22×C17—22no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17—41no—
164C22×C17—81no—
165C22×C17—81no—
166C22×C17—81no—
167C22×C17—81no—
168C22×C17—81no—
169C22×C17—81no—
170C22×C17—81no—
171C22×C17#40811yescharacteristic
172C22×C17C2×#9911yescharacteristic
173C22×C17#41311yescharacteristic
174C22×C17#41611yescharacteristic
175C22×C17#41811yescharacteristic
176C22×C17C2×#10411yescharacteristic
177C22×C17C2×#10411yescharacteristic
178C4×C17—22no—
179C4×C17—22no—
180C4×C17—81no—
181Dic17—22no—
182Dic17—22no—
183Dic17—22no—
184Dic17—41no—
185Dic17—81no—
186Dic17—81no—
187C2×#123—341no—
188C2×#121#59511yescharacteristic
189C22×C42—171no—
190C2×C22⋊C8—341no—
191C2×C22⋊C8—341no—
192C2×#97—341no—
193C2×C4×C8—341no—
194#390—171no—
195#390—171no—
196#389—171no—
197#389—171no—
198#388—341no—
199#388—341no—
200#386—341no—
201#380—171no—
202#336—172no—
203#336—172no—
204C2×C17—42no—
205C2×C17—161no—
206C2×C17#146811yescharacteristic
207C2×C17#148411yescharacteristic
208C2×C17#149411yescharacteristic
209C2×C17#150111yescharacteristic
210C2×C17#150711yescharacteristic
211C2×C17#152411yescharacteristic
212C2×C17#155311yescharacteristic
213C22×D4—21no—
214C22×D4C2×#59511yescharacteristic
215C23×C4—171no—
216C23×C4—171no—
217C23×C4C2×#59511yescharacteristic
218C22×C8—342no—
219C22×C8—342no—
220#123—684no—
221#121—42no—
222C2×C4⋊C4—171no—
223C2×C4⋊C4—171no—
224C2×C4⋊C4—341no—
225C2×C4⋊C4—341no—
226C2×C4⋊C4C2×#59511yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—341no—
229C2×C22⋊C4—341no—
230C2×C22⋊C4—341no—
231C2×C22⋊C4—341no—
232C2×C22⋊C4—341no—
233C2×C42—171no—
234C2×C42—171no—
235C2×C42—171no—
236C2×C42—171no—
237C2×C42—682no—
238C22⋊C8—344no—
239C22⋊C8—344no—
240#97—682no—
241C4×C8—682no—
242#95—341no—
243#95—341no—
244#95—341no—
245C17#767411yescharacteristic, complemented, Sylow
246C24—21no—
247C24C22⋊#59511yescharacteristic
248C2×D4—22no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—42no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—171no—
259C22×C4—171no—
260C22×C4—171no—
261C22×C4—171no—
262C22×C4—342no—
263C22×C4—342no—
264C22×C4—342no—
265C22×C4—342no—
266C22×C4—341no—
267C22×C4—341no—
268C22×C4—681no—
269C22×C4—681no—
270C22×C4C22⋊#59511yescharacteristic
271C22×C4C22×#59511yescharacteristic
272C2×C8—344no—
273C2×C8—344no—
274C2×C8—682no—
275C2×C8—682no—
276C2×C8—682no—
277C2×C8—682no—
278C4⋊C4—41no—
279C4⋊C4—342no—
280C4⋊C4—681no—
281C4⋊C4—682no—
282C4⋊C4—682no—
283C22⋊C4—42no—
284C22⋊C4—682no—
285C22⋊C4—682no—
286C22⋊C4—682no—
287C22⋊C4—682no—
288C22⋊C4—682no—
289C42—342no—
290C42—342no—
291C42—681no—
292C42—681no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23#1058754812yes—
307C23C2×C22⋊#59511yescharacteristic
308D4—82no—
309D4—84no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—44no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—172no—
319C2×C4—172no—
320C2×C4—172no—
321C2×C4—341no—
322C2×C4—341no—
323C2×C4—341no—
324C2×C4—341no—
325C2×C4—341no—
326C2×C4—341no—
327C2×C4—341no—
328C2×C4—341no—
329C2×C4—341no—
330C2×C4—684no—
331C2×C4—684no—
332C2×C4—681no—
333C2×C4—681no—
334C2×C4—681no—
335C2×C4—681no—
336C2×C4—681no—
337C2×C4—681no—
338C2×C4#1058755112yes—
339C2×C4#1058767812yes—
340C8—684no—
341C8—684no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1176378211yescharacteristic
357C22C2×#1058755111yescharacteristic
358C22#1176379611yescharacteristic
359C22#1176379911yescharacteristic
360C22#1176380111yescharacteristic
361C22C2×#1058754811yescharacteristic
362C22D17⋊#10411yescharacteristic
363C4—22no—
364C4—22no—
365C4—81no—
366C4—342no—
367C4—342no—
368C4—342no—
369C4—681no—
370C4—1361no—
371C4—1361no—
372C2—42no—
373C2—161no—
374C2#1454404911yescharacteristic
375C2#1454410311yescharacteristic
376C2#1454413511yescharacteristic
377C2#1454415911yescharacteristic
378C2#1454418011yescharacteristic
379C2#1454423511yescharacteristic
380C2#1454430811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
Fitting, prime radicalC2×C17×#121C4
socleC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×#121#595
hypocenterC17#7674
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #14544510C2semidirect
2. C4×C22⋊#3624C2semidirect
3. #14543603C2semidirect
4. #14543600C2semidirect
245. C17#7674semidirect

Maximal subgroups

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

subgroupindex
#145445102
C4×C22⋊#36242
#145436032
#145436002
#145371102
#767417