Finite Group Databasebeta

← #17950194

Subgroups — #17950194

Order 4352.

464 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 98 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#14544638C211yesmaximal, characteristic
3#14543604C212yesmaximal, complemented
4#14543603C212yesmaximal, complemented
5#14537118C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×C4⋊#3624—21no—
8C2×C22⋊#3624—21no—
9C2×C22⋊#3624—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C22×C4×Dic17C2211yescharacteristic
13#11762716C411yescharacteristic
14#11762716C2211yescharacteristic
15#11762705C411yescharacteristic
16#11762705C2211yescharacteristic
17#11762690—21no—
18#11762690—21no—
19#11762681—21no—
20#11762670—21no—
21#11762669C411yescharacteristic
22C2×C17×C22⋊Q8C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×Dic17D411yescharacteristic
26C23×Dic17D411yescharacteristic
27C22×#3624—22no—
28C22×#3624—22no—
29C17×C22⋊Q8—42no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C22⋊C4×C17—21no—
33C2×C22⋊Dic17—21no—
34C2×C4⋊Dic17C2×C411yescharacteristic
35C2×C4⋊Dic17C2×C411yescharacteristic
36C2×#63225—21no—
37C2×#63225—21no—
38C2×C4×Dic17—42no—
39C2×C4×Dic17C2×C411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17C2311yescharacteristic
43C22⋊#3624—42no—
44C22⋊#3624—42no—
45#10587544—42no—
46C4⋊#3624—42no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54C24×C17C22⋊C411yescharacteristic
55C2×Q8×C17—22no—
56C2×Q8×C17—41no—
57C2×Q8×C17—41no—
58C22×C4×C17—22no—
59C22×C4×C17—22no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—41no—
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22×C411yescharacteristic
65C22×Dic17—21no—
66C22×Dic17—21no—
67C22×Dic17—21no—
68C22×Dic17—21no—
69C22×Dic17—41no—
70C22×Dic17—41no—
71C22×Dic17—41no—
72C22×Dic17—41no—
73C22×Dic17C22⋊C411yescharacteristic
74C22×Dic17C22⋊C411yescharacteristic
75C22×Dic17SD1612yes—
76C22×Dic17Q1612yes—
77C22×Dic17C2×D411yescharacteristic
78C22×Dic17C2×D411yescharacteristic
79C2×#3624—42no—
80C2×#3624—42no—
81C2×#3624—42no—
82C2×#3624—42no—
83C2×#3624—42no—
84C2×#3624—42no—
85C4⋊C4×C17—41no—
86C4⋊C4×C17—42no—
87C22⋊C4×C17—42no—
88C22⋊Dic17—42no—
89C4⋊Dic17—22no—
90C4⋊Dic17—41no—
91#63225—42no—
92#63225—41no—
93#63225—41no—
94C4×Dic17—22no—
95C4×Dic17—22no—
96C4×Dic17—41no—
97C4×Dic17—41no—
98#7715—171nomaximal, Sylow
99C23×C17—21no—
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17#10312yes—
106C23×C17C2×C22⋊C411yescharacteristic
107Q8×C17—82no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—44no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17#9912yes—
120C2×C4×C17#13112yes—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—21no—
125C2×Dic17—21no—
126C2×Dic17—21no—
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—42no—
131C2×Dic17—42no—
132C2×Dic17—42no—
133C2×Dic17—42no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17#10312yes—
141C2×Dic17C2×SD1611yescharacteristic
142C2×Dic17C2×Q1611yescharacteristic
143C2×Dic17AGL(1,ℤ/8)11yescharacteristic
144C2×Dic17#13711yescharacteristic
145#3624—82no—
146#3624—82no—
147#2855—171no—
148#1797—171no—
149#1797—171no—
150#1272—172no—
151#1271—172no—
152C22×C17—22no—
153C22×C17—22no—
154C22×C17—22no—
155C22×C17—41no—
156C22×C17—41no—
157C22×C17—41no—
158C22×C17—41no—
159C22×C17#40811yescharacteristic
160C22×C17C2×#9911yescharacteristic
161C22×C17#41311yescharacteristic
162C22×C17C2×#10311yescharacteristic
163C22×C17#41711yescharacteristic
164C22×C17#42111yescharacteristic
165C22×C17#42111yescharacteristic
166C4×C17—22no—
167C4×C17—22no—
168C4×C17—81no—
169C4×C17—81no—
170Dic17—21no—
171Dic17—21no—
172Dic17—21no—
173Dic17—22no—
174Dic17—21no—
175Dic17—41no—
176Dic17—81no—
177Dic17—81no—
178C2×C22⋊Q8#59511yescharacteristic
179C22×C42—171no—
180C2×C4⋊C8—341no—
181C2×C4⋊C8—341no—
182C2×C22⋊C8—341no—
183C2×C22⋊C8—341no—
184#391—171no—
185#391—171no—
186#389—171no—
187#389—171no—
188#387—341no—
189#387—341no—
190#385—341no—
191#381—341no—
192#380—171no—
193#336—172no—
194#336—172no—
195C2×C17—42no—
196C2×C17#146811yescharacteristic
197C2×C17#148111yescharacteristic
198C2×C17#149511yescharacteristic
199C2×C17#151311yescharacteristic
200C2×C17#152011yescharacteristic
201C2×C17#153511yescharacteristic
202C2×C17#155011yescharacteristic
203C22×Q8C2×#59511yescharacteristic
204C23×C4—171no—
205C23×C4—171no—
206C23×C4C2×#59511yescharacteristic
207C22×C8—342no—
208C22×C8—342no—
209C22⋊Q8—42no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—171no—
212C2×C4⋊C4—171no—
213C2×C4⋊C4—341no—
214C2×C4⋊C4—341no—
215C2×C4⋊C4C2×#59511yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—341no—
218C2×C42—171no—
219C2×C42—171no—
220C2×C42—171no—
221C2×C42—171no—
222C2×C42—682no—
223C4⋊C8—682no—
224C4⋊C8—682no—
225C22⋊C8—682no—
226C22⋊C8—682no—
227#95—341no—
228#95—341no—
229#95—341no—
230#95—341no—
231#95—341no—
232#95—341no—
233#95—341no—
234C17#771511yescharacteristic, complemented, Sylow
235C24C22⋊#59511yescharacteristic
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8—41no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—171no—
245C22×C4—171no—
246C22×C4—171no—
247C22×C4—172no—
248C22×C4—172no—
249C22×C4—171no—
250C22×C4—341no—
251C22×C4—341no—
252C22×C4—341no—
253C22×C4—341no—
254C22×C4—681no—
255C22×C4—681no—
256C22×C4—681no—
257C22×C4—681no—
258C22×C4C22⋊#59511yescharacteristic
259C22×C4C22×#59511yescharacteristic
260C2×C8—682no—
261C2×C8—682no—
262C2×C8—682no—
263C2×C8—682no—
264C2×C8—682no—
265C2×C8—682no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—342no—
269C4⋊C4—681no—
270C4⋊C4—681no—
271C4⋊C4—681no—
272C4⋊C4—682no—
273C22⋊C4—42no—
274C22⋊C4—682no—
275C42—342no—
276C42—342no—
277C42—681no—
278C42—681no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23#1058754912yes—
286C23C2×C22⋊#59511yescharacteristic
287Q8—82no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—44no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—171no—
300C2×C4—172no—
301C2×C4—171no—
302C2×C4—171no—
303C2×C4—171no—
304C2×C4—341no—
305C2×C4—341no—
306C2×C4—341no—
307C2×C4—341no—
308C2×C4—341no—
309C2×C4—341no—
310C2×C4—341no—
311C2×C4—341no—
312C2×C4—341no—
313C2×C4—682no—
314C2×C4—682no—
315C2×C4—682no—
316C2×C4—682no—
317C2×C4—681no—
318C2×C4—681no—
319C2×C4—681no—
320C2×C4—681no—
321C2×C4—681no—
322C2×C4—681no—
323C2×C4#1058755112yes—
324C2×C4#1058767812yes—
325C8—1362no—
326C8—1362no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22#1176378211yescharacteristic
335C22C2×#1058755111yescharacteristic
336C22#1176379611yescharacteristic
337C22C2×#1058754911yescharacteristic
338C22#1176380011yescharacteristic
339C22#1176380611yescharacteristic
340C22#1176380811yescharacteristic
341C4—22no—
342C4—22no—
343C4—81no—
344C4—81no—
345C4—341no—
346C4—341no—
347C4—341no—
348C4—342no—
349C4—341no—
350C4—681no—
351C4—1361no—
352C4—1361no—
353C2—42no—
354C2#1454404911yescharacteristic
355C2#1454409211yescharacteristic
356C2#1454414111yescharacteristic
357C2#1454419911yescharacteristic
358C2#1454422411yescharacteristic
359C2#1454427111yescharacteristic
360C2#1454430211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C22⋊Q8C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×C22⋊Q8#595
hypocenterC17#7715
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #14543604C2semidirect
4. #14543603C2semidirect
234. C17#7715semidirect

Maximal subgroups

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

subgroupindex
#145446402
#145446382
#145436042
#145436032
#145371182
#771517