Finite Group Databasebeta

← #17950235

Subgroups — #17950235

Order 4352.

494 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 100 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#14544675C211yesmaximal, characteristic
2#14544638C211yesmaximal, characteristic
3#14543605C212yesmaximal, complemented
4#14543604C212yesmaximal, complemented
5#14537132C211yesmaximal, characteristic
6C2×C4⋊#3624—21no—
7C2×C22⋊#3624—21no—
8C2×C22⋊#3624—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587630C411yescharacteristic
13C2×#10587610C411yescharacteristic
14C22×C4×Dic17C2211yescharacteristic
15#11762716C2211yescharacteristic
16#11762714C2211yescharacteristic
17#11762704—21no—
18#11762704—21no—
19#11762678C411yescharacteristic
20#11762667—21no—
21#11762667—21no—
22C2×C17×C22⋊Q8C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×Dic17D411yescharacteristic
26C23×Dic17D411yescharacteristic
27C22×Dic34C2×C411yescharacteristic
28C22×#3624—22no—
29C22×#3624—22no—
30C17×C22⋊Q8—42no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C22⋊C4×C17—21no—
34C2×C22⋊Dic17—21no—
35#10587630—42no—
36C2×C4⋊Dic17C2×C411yescharacteristic
37#10587610—42no—
38C2×#63225—21no—
39C2×#63225—21no—
40C2×#63225—21no—
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—42no—
49C22⋊#3624—42no—
50C4⋊#3624—42no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55C24×C17C22⋊C411yescharacteristic
56C2×Q8×C17—22no—
57C2×Q8×C17—41no—
58C2×Q8×C17—41no—
59C22×C4×C17—22no—
60C22×C4×C17—22no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—41no—
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22×C411yescharacteristic
66C22×Dic17—22no—
67C22×Dic17—22no—
68C22×Dic17—21no—
69C22×Dic17—21no—
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×Dic34—22no—
80C2×Dic34—41no—
81C2×Dic34—41no—
82C2×#3624—42no—
83C2×#3624—42no—
84C2×#3624—42no—
85C2×#3624—42no—
86C2×#3624—42no—
87C2×#3624—42no—
88C4⋊C4×C17—41no—
89C4⋊C4×C17—42no—
90C22⋊C4×C17—42no—
91C22⋊Dic17—42no—
92C4⋊Dic17—41no—
93#63225—42no—
94#63225—42no—
95#63225—42no—
96#63225—42no—
97#63225—42no—
98C4×Dic17—22no—
99C4×Dic17—22no—
100C4×Dic17—41no—
101C4×Dic17—41no—
102#7727—171nomaximal, Sylow
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17#10312yes—
110C23×C17C2×C22⋊C411yescharacteristic
111Q8×C17—82no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—44no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17#10012yes—
124C2×C4×C17#13112yes—
125C2×Dic17—21no—
126C2×Dic17—21no—
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—21no—
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17—42no—
134C2×Dic17—42no—
135C2×Dic17—44no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17#9912yes—
143C2×Dic17#10312yes—
144C2×Dic17C2×SD1611yescharacteristic
145C2×Dic17C2×Q1611yescharacteristic
146C2×Dic17#13712yes—
147Dic34—82no—
148#3624—82no—
149#3624—82no—
150#2857—171no—
151#1817—171no—
152#1797—171no—
153#1272—172no—
154#1272—172no—
155C22×C17—22no—
156C22×C17—22no—
157C22×C17—22no—
158C22×C17—41no—
159C22×C17—41no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17#40811yescharacteristic
163C22×C17C2×#9911yescharacteristic
164C22×C17C2×#10011yescharacteristic
165C22×C17C2×#10311yescharacteristic
166C22×C17#41911yescharacteristic
167C22×C17#42111yescharacteristic
168C22×C17#42111yescharacteristic
169C4×C17—22no—
170C4×C17—22no—
171C4×C17—81no—
172C4×C17—81no—
173Dic17—22no—
174Dic17—22no—
175Dic17—21no—
176Dic17—22no—
177Dic17—21no—
178Dic17—81no—
179Dic17—81no—
180C2×C4⋊Q8—171no—
181C2×C22⋊Q8—171no—
182C2×C22⋊Q8#59511yescharacteristic
183C22×C42—171no—
184C2×C4⋊C8—341no—
185C2×C22⋊C8—341no—
186C2×C22⋊C8—341no—
187#391—171no—
188#391—171no—
189#389—341no—
190#389—341no—
191#384—171no—
192#380—341no—
193#380—341no—
194#336—172no—
195#336—172no—
196#336—341no—
197C2×C17—42no—
198C2×C17#147111yescharacteristic
199C2×C17#148111yescharacteristic
200C2×C17#149711yescharacteristic
201C2×C17#151111yescharacteristic
202C2×C17#152011yescharacteristic
203C2×C17#153611yescharacteristic
204C2×C17#154811yescharacteristic
205C22×Q8—171no—
206C22×Q8C2×#59511yescharacteristic
207C23×C4—171no—
208C23×C4—171no—
209C23×C4C2×#59511yescharacteristic
210C22×C8—342no—
211C22×C8—342no—
212C4⋊Q8—682no—
213C22⋊Q8—42no—
214C22⋊Q8—682no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—171no—
217C2×C4⋊C4—341no—
218C2×C4⋊C4—341no—
219C2×C4⋊C4—341no—
220C2×C4⋊C4—341no—
221C2×C4⋊C4—341no—
222C2×C4⋊C4C2×#59511yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—341no—
225C2×C42—171no—
226C2×C42—171no—
227C2×C42—171no—
228C2×C42—171no—
229C2×C42—682no—
230C4⋊C8—682no—
231C22⋊C8—682no—
232C22⋊C8—682no—
233#95—341no—
234#95—341no—
235#95—341no—
236#95—341no—
237C17#772711yescharacteristic, complemented, Sylow
238C24C22⋊#59511yescharacteristic
239C2×Q8—22no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—342no—
243C2×Q8—681no—
244C2×Q8—681no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—171no—
251C22×C4—171no—
252C22×C4—171no—
253C22×C4—171no—
254C22×C4—172no—
255C22×C4—172no—
256C22×C4—342no—
257C22×C4—342no—
258C22×C4—341no—
259C22×C4—341no—
260C22×C4—681no—
261C22×C4—681no—
262C22×C4—681no—
263C22×C4C22⋊#59511yescharacteristic
264C22×C4C22×#59511yescharacteristic
265C2×C8—682no—
266C2×C8—682no—
267C2×C8—682no—
268C2×C8—682no—
269C2×C8—682no—
270C2×C8—682no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—681no—
274C4⋊C4—682no—
275C4⋊C4—682no—
276C4⋊C4—682no—
277C4⋊C4—682no—
278C4⋊C4—682no—
279C22⋊C4—42no—
280C22⋊C4—682no—
281C42—342no—
282C42—342no—
283C42—681no—
284C42—681no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23#1058754912yes—
292C23C2×C22⋊#59511yescharacteristic
293Q8—82no—
294Q8—1362no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—44no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—172no—
307C2×C4—171no—
308C2×C4—172no—
309C2×C4—171no—
310C2×C4—172no—
311C2×C4—341no—
312C2×C4—341no—
313C2×C4—341no—
314C2×C4—341no—
315C2×C4—341no—
316C2×C4—341no—
317C2×C4—341no—
318C2×C4—341no—
319C2×C4—682no—
320C2×C4—682no—
321C2×C4—684no—
322C2×C4—681no—
323C2×C4—681no—
324C2×C4—681no—
325C2×C4—681no—
326C2×C4—681no—
327C2×C4—681no—
328C2×C4#1058755312yes—
329C2×C4#1058767812yes—
330C8—1362no—
331C8—1362no—
332C22—22no—
333C22—22no—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22#1176378211yescharacteristic
340C22D17⋊#9911yescharacteristic
341C22C2×#1058755311yescharacteristic
342C22C2×#1058754911yescharacteristic
343C22#1176380211yescharacteristic
344C22#1176380611yescharacteristic
345C22#1176380611yescharacteristic
346C4—22no—
347C4—22no—
348C4—81no—
349C4—81no—
350C4—342no—
351C4—342no—
352C4—341no—
353C4—342no—
354C4—341no—
355C4—1361no—
356C4—1361no—
357C2—42no—
358C2#1454406011yescharacteristic
359C2#1454409211yescharacteristic
360C2#1454414611yescharacteristic
361C2#1454419311yescharacteristic
362C2#1454422211yescharacteristic
363C2#1454427211yescharacteristic
364C2#1454429711yescharacteristic
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#7727
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. #14543605C2semidirect
4. #14543604C2semidirect
237. C17#7727semidirect

Maximal subgroups

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

subgroupindex
#145446752
#145446382
#145436052
#145436042
#145371322
#772717