Finite Group Databasebeta

← #17949828

Subgroups — #17949828

Order 4352.

516 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 102 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#14544640C211yesmaximal, characteristic
2#14544510C211yesmaximal, characteristic
3#14543602C212yesmaximal, complemented
4#14543602C212yesmaximal, complemented
5#14531268C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×C22⋊#3624—21no—
8C2×C22⋊#3624—21no—
9C2×#10587542—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587612C411yescharacteristic
13C22×C4×Dic17C2211yescharacteristic
14#11762708C411yescharacteristic
15#11762708C411yescharacteristic
16#11762708C2211yescharacteristic
17#11762708C2211yescharacteristic
18#11762684—21no—
19#11762684—21no—
20C4×C4⋊Dic17—21no—
21C4×C4⋊Dic17—21no—
22C2×C17×#117C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C23×Dic17D411yescharacteristic
25C23×Dic17D411yescharacteristic
26C22×#3624—22no—
27C22×#3624—22no—
28C17×#117—22no—
29C17×#117—22no—
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C22⋊C4×C17—21no—
33C2×C42×C17—21no—
34C2×C22⋊Dic17—21no—
35#10587612—42no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17—21no—
39C2×C4⋊Dic17—21no—
40C2×C4⋊Dic17C2×C411yescharacteristic
41C2×C4⋊Dic17C2×C411yescharacteristic
42C2×C4×Dic17—21no—
43C2×C4×Dic17—42no—
44C2×C4×Dic17C2×C411yescharacteristic
45C2×C4×Dic17D411yescharacteristic
46C2×C4×Dic17D411yescharacteristic
47C2×C4×Dic17C2311yescharacteristic
48C22⋊#3624—24no—
49C22⋊#3624—42no—
50#10587544—42no—
51#10587542—42no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56C24×C17C22⋊C411yescharacteristic
57C22×C4×C17—22no—
58C22×C4×C17—22no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22×C411yescharacteristic
65C22×Dic17—22no—
66C22×Dic17—22no—
67C22×Dic17—21no—
68C22×Dic17—21no—
69C22×Dic17—21no—
70C22×Dic17—21no—
71C22×Dic17—41no—
72C22×Dic17—41no—
73C22×Dic17—41no—
74C22×Dic17C22⋊C411yescharacteristic
75C22×Dic17C22⋊C411yescharacteristic
76C22×Dic17C2×D411yescharacteristic
77C22×Dic17C2×D411yescharacteristic
78C2×#3624—24no—
79C2×#3624—42no—
80C2×#3624—42no—
81C2×#3624—42no—
82C2×#3624—42no—
83C2×#3624—42no—
84C4⋊C4×C17—21no—
85C4⋊C4×C17—21no—
86C4⋊C4×C17M1612yes—
87C4⋊C4×C17M1612yes—
88C22⋊C4×C17—24no—
89C42×C17—24no—
90C22⋊Dic17—42no—
91C4⋊Dic17—42no—
92C4⋊Dic17—42no—
93C4⋊Dic17—42no—
94C4⋊Dic17—41no—
95C4⋊Dic17—41no—
96C4⋊Dic17—41no—
97C4⋊Dic17—41no—
98C4×Dic17—22no—
99C4×Dic17—22no—
100C4×Dic17—41no—
101C4×Dic17—41no—
102C4×Dic17—42no—
103#7613—171nomaximal, Sylow
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17#10112yes—
111C23×C17C2×C22⋊C411yescharacteristic
112C2×C4×C17—24no—
113C2×C4×C17—24no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—22no—
119C2×C4×C17—22no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17#9912yes—
125C2×C4×C17C2×M1611yescharacteristic
126C2×C4×C17C2×M1611yescharacteristic
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—21no—
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—21no—
136C2×Dic17—44no—
137C2×Dic17—42no—
138C2×Dic17—42no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17#10412yes—
146C2×Dic17#13512yes—
147C2×Dic17AGL(1,ℤ/8)11yescharacteristic
148C2×Dic17#13711yescharacteristic
149#3624—44no—
150#3624—82no—
151#2296—171no—
152#1797—171no—
153#1749—171no—
154#1271—172no—
155#1271—172no—
156C22×C17—22no—
157C22×C17—22no—
158C22×C17—22no—
159C22×C17—41no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17#40711yescharacteristic
164C22×C17C2×#9911yescharacteristic
165C22×C17C2×#10111yescharacteristic
166C22×C17#41611yescharacteristic
167C22×C17#41711yescharacteristic
168C22×C17C2×#10411yescharacteristic
169C22×C17#42111yescharacteristic
170C4×C17—22no—
171C4×C17—21no—
172C4×C17—21no—
173C4×C17—42no—
174C4×C17—42no—
175Dic17—22no—
176Dic17—22no—
177Dic17—21no—
178Dic17—21no—
179Dic17—41no—
180Dic17—81no—
181Dic17—81no—
182C2×#117—171no—
183C2×#117#59511yescharacteristic
184C22×C42—171no—
185C2×C4⋊C8—341no—
186C2×C22⋊C8—341no—
187C2×C22⋊C8—341no—
188C2×#97—341no—
189#389—171no—
190#389—171no—
191#389—171no—
192#389—171no—
193#385—341no—
194#385—341no—
195C4×C4⋊C4—341no—
196C4×C4⋊C4—341no—
197#336—172no—
198#336—172no—
199C2×C17—42no—
200C2×C17#146311yescharacteristic
201C2×C17#148811yescharacteristic
202C2×C17#148911yescharacteristic
203C2×C17#150111yescharacteristic
204C2×C17#151311yescharacteristic
205C2×C17#153111yescharacteristic
206C2×C17#155211yescharacteristic
207C23×C4—171no—
208C23×C4—171no—
209C23×C4C2×#59511yescharacteristic
210C22×C8—342no—
211C22×C8—342no—
212#117—22no—
213#117—22no—
214#117—682no—
215C2×C4⋊C4—171no—
216C2×C4⋊C4—171no—
217C2×C4⋊C4—341no—
218C2×C4⋊C4—341no—
219C2×C4⋊C4—341no—
220C2×C4⋊C4—341no—
221C2×C4⋊C4C2×#59511yescharacteristic
222C2×C4⋊C4C2×#59511yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—341no—
225C2×C42—21no—
226C2×C42—171no—
227C2×C42—171no—
228C2×C42—171no—
229C2×C42—171no—
230C2×C42—341no—
231C2×C42—682no—
232C4⋊C8—682no—
233C22⋊C8—344no—
234C22⋊C8—682no—
235#97—682no—
236#95—341no—
237#95—341no—
238#95—341no—
239#95—341no—
240C17#761311yescharacteristic, complemented, Sylow
241C24C22⋊#59511yescharacteristic
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—171no—
249C22×C4—171no—
250C22×C4—171no—
251C22×C4—171no—
252C22×C4—342no—
253C22×C4—341no—
254C22×C4—342no—
255C22×C4—341no—
256C22×C4—341no—
257C22×C4—341no—
258C22×C4—681no—
259C22×C4—681no—
260C22×C4—681no—
261C22×C4C22⋊#59511yescharacteristic
262C22×C4C22×#59511yescharacteristic
263C2×C8—344no—
264C2×C8—682no—
265C2×C8—682no—
266C2×C8—682no—
267C2×C8—682no—
268C2×C8—682no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—681no—
272C4⋊C4—681no—
273C4⋊C4—682no—
274C4⋊C4—681no—
275C4⋊C4—681no—
276C4⋊C4—682no—
277C4⋊C4—682no—
278C4⋊C4#6324712yes—
279C4⋊C4#6324712yes—
280C22⋊C4—24no—
281C22⋊C4—682no—
282C42—24no—
283C42—342no—
284C42—342no—
285C42—681no—
286C42—681no—
287C42—682no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23#1058754512yes—
295C23C2×C22⋊#59511yescharacteristic
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—172no—
309C2×C4—171no—
310C2×C4—171no—
311C2×C4—172no—
312C2×C4—341no—
313C2×C4—341no—
314C2×C4—341no—
315C2×C4—341no—
316C2×C4—341no—
317C2×C4—341no—
318C2×C4—341no—
319C2×C4—341no—
320C2×C4—341no—
321C2×C4—684no—
322C2×C4—682no—
323C2×C4—682no—
324C2×C4—681no—
325C2×C4—681no—
326C2×C4—681no—
327C2×C4—681no—
328C2×C4—681no—
329C2×C4—681no—
330C2×C4#1058753912yes—
331C2×C4C2×#6324711yescharacteristic
332C2×C4C2×#6324711yescharacteristic
333C8—684no—
334C8—1362no—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22#1176377911yescharacteristic
343C22C2×#1058753911yescharacteristic
344C22C2×#1058754511yescharacteristic
345C22#1176379911yescharacteristic
346C22#1176380011yescharacteristic
347C22D17⋊#10411yescharacteristic
348C22#1176380611yescharacteristic
349C4—21no—
350C4—21no—
351C4—22no—
352C4—42no—
353C4—42no—
354C4—342no—
355C4—342no—
356C4—341no—
357C4—341no—
358C4—681no—
359C4—1361no—
360C4—1361no—
361C2—42no—
362C2#1454403211yescharacteristic
363C2#1454411511yescharacteristic
364C2#1454411911yescharacteristic
365C2#1454416111yescharacteristic
366C2#1454420111yescharacteristic
367C2#1454425611yescharacteristic
368C2#1454430511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×#117#595
hypocenterC17#7613
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #14543602C2semidirect
4. #14543602C2semidirect
240. C17#7613semidirect

Maximal subgroups

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

subgroupindex
#145446402
#145445102
#145436022
#145312682
#761317