Finite Group Databasebeta

← #17959792

Subgroups — #17959792

Order 4352.

452 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 76 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#14544644C211yesmaximal, characteristic
2#14544023C211yesmaximal, characteristic
3#14543781C212yesmaximal, complemented
4#14543779C212yesmaximal, complemented
5#14533966C211yesmaximal, characteristic
6#11763826—21no—
7C2×#10587551—21no—
8#11763751—21no—
9#11763687C2212yes—
10#11763653C2212yes—
11#11763652—21no—
12C2×C4×C22⋊D17C2211yescharacteristic
13#11762747C411yescharacteristic, complemented
14#11762744C2211yescharacteristic
15#11762728C411yescharacteristic, complemented
16#11762720C2211yescharacteristic
17#11762690—21no—
18#11762686—21no—
19#11762680—21no—
20#11762667—21no—
21C2×#10587502C411yescharacteristic, complemented
22C2×C17×C22⋊Q8C411yescharacteristic, complemented
23C22×Q8×C17C2×C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C22×C22⋊D17D411yescharacteristic
26C23×Dic17—21no—
27C22×C4×D17D411yescharacteristic
28C2×C22⋊#595—22no—
29C2×C4⋊#595—41no—
30C17×C22⋊Q8—41no—
31C17×C22⋊Q8—41no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C22⋊C4×C17—21no—
35C2×C22⋊Dic17D411yescharacteristic
36C4×C22⋊D17—41no—
37C4×C22⋊D17—41no—
38C2×#63227—21no—
39C2×#63227—21no—
40C2×#63227C2311yescharacteristic
41C2×#63225—21no—
42C2×#63225—21no—
43C2×#63225C2×C411yescharacteristic
44C2×C4×Dic17D411yescharacteristic
45C22⋊#3624—22no—
46#10587551—42no—
47(C2×#595)⋊C4—41no—
48#10587544—41no—
49C4×#3624—41no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502C2×C411yescharacteristic
56#10587502C2×C411yescharacteristic
57C24×C17C22⋊C411yescharacteristic
58C23×D17C2×D411yescharacteristic
59C22×#595—42no—
60C2×Q8×C17—41no—
61C2×Q8×C17—81no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—81no—
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22×C411yescharacteristic
69C2×C22⋊D17—41no—
70C2×C22⋊D17—41no—
71C2×C22⋊D17SD1612yes—
72C2×C22⋊D17Q1612yes—
73C22×Dic17—21no—
74C22×Dic17—21no—
75C22×Dic17—42no—
76C22×Dic17—42no—
77C22×Dic17—81no—
78C22×Dic17C22⋊C411yescharacteristic
79C22×Dic17C22⋊C411yescharacteristic
80C22×Dic17C2×D411yescharacteristic
81C2×C4×D17—21no—
82C2×C4×D17—21no—
83C2×C4×D17—81no—
84C22⋊#595—42no—
85C22⋊#595—42no—
86C2×#3624—42no—
87C4⋊#595—82no—
88C4⋊C4×C17—41no—
89C4⋊C4×C17—41no—
90C4⋊C4×C17—41no—
91C22⋊C4×C17—42no—
92C22⋊Dic17—41no—
93#63227—41no—
94#63227—42no—
95#63227—81no—
96#63225—41no—
97#63225—42no—
98#63225—81no—
99C4×Dic17—21no—
100C4×Dic17—21no—
101#11902—171nomaximal, Sylow
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—41no—
105C23×C17—41no—
106C23×C17#10312yes—
107C23×C17C2×C22⋊C411yescharacteristic
108C22×D17—21no—
109C22×D17—21no—
110C22×D17—41no—
111C22×D17—41no—
112C22×D17C2×SD1611yescharacteristic
113C22×D17C2×Q1611yescharacteristic
114C2×#595—82no—
115C2×#595—82no—
116C2×#595—82no—
117Q8×C17—82no—
118C2×C4×C17—21no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—81no—
128C2×C4×C17—81no—
129C2×C4×C17#9911yescharacteristic
130C2×C4×C17#9911yescharacteristic
131C22⋊D17—42no—
132C22⋊D17—42no—
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—22no—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—84no—
146C2×Dic17#10312yes—
147C4×D17—42no—
148C4×D17—81no—
149#3624—82no—
150#2564—171no—
151#1799—171no—
152#1460—171no—
153#1352—172no—
154#1351—172no—
155C22×C17—21no—
156C22×C17—21no—
157C22×C17—22no—
158C22×C17—42no—
159C22×C17—42no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17C2×#9911yescharacteristic
163C22×C17C2×#10311yescharacteristic
164C22×C17#42111yescharacteristic
165C2×D17—21no—
166C2×D17—21no—
167C2×D17—41no—
168C2×D17—41no—
169C2×D17—41no—
170C2×D17—41no—
171C2×D17—81no—
172#595—162no—
173C4×C17—21no—
174C4×C17—21no—
175C4×C17—41no—
176C4×C17—81no—
177C4×C17—81no—
178Dic17—22no—
179Dic17—42no—
180Dic17—41no—
181Dic17—41no—
182Dic17—81no—
183C2×C22⋊Q8#59511yescharacteristic, complemented
184C2×C4×D4—171no—
185#431—341no—
186C2×#99—341no—
187#400—171no—
188#399—171no—
189#395—171no—
190#393—171no—
191#387—341no—
192#386—341no—
193#385—341no—
194#380—341no—
195#380—341no—
196C2×#95—171no—
197#342—172no—
198#323—172no—
199#323—341no—
200C2×C17—21no—
201C2×C17—21no—
202C2×C17—42no—
203C2×C17#152011yescharacteristic
204C2×C17#212111yescharacteristic
205C2×C17#212611yescharacteristic
206D17—41no—
207D17—41no—
208C22×Q8C2×#59511yescharacteristic
209C22×D4—171no—
210C23×C4—171no—
211C23×C4—341no—
212C23×C4C2×#59511yescharacteristic
213C22⋊Q8—41no—
214C22⋊Q8—41no—
215C4×D4—681no—
216C4×D4—681no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—171no—
219C2×C4⋊C4—341no—
220C2×C4⋊C4—341no—
221C2×C4⋊C4—681no—
222C2×C4⋊C4C2×#59511yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—171no—
225C2×C22⋊C4—171no—
226C2×C22⋊C4—341no—
227C2×C22⋊C4—342no—
228C2×C22⋊C4—341no—
229C2×C42—171no—
230C4⋊C8—681no—
231#99—682no—
232C22⋊C8—342no—
233C4×C8—681no—
234#95—171no—
235#95—171no—
236#95—341no—
237#95—341no—
238#95—341no—
239#95—341no—
240#95—341no—
241#95—681no—
242C17#1190211yescharacteristic, complemented, Sylow
243C24—171no—
244C24C22⋊#59511yescharacteristic
245C2×Q8—41no—
246C2×Q8—81no—
247C2×D4—172no—
248C2×D4—172no—
249C2×D4—681no—
250C2×D4—681no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—81no—
256C22×C4—171no—
257C22×C4—171no—
258C22×C4—171no—
259C22×C4—341no—
260C22×C4—341no—
261C22×C4—341no—
262C22×C4—341no—
263C22×C4—682no—
264C22×C4—682no—
265C22×C4—682no—
266C22×C4—1361no—
267C22×C4—1361no—
268C22×C4C22⋊#59511yescharacteristic
269C22×C4C22×#59511yescharacteristic
270C2×C8—682no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—681no—
275C4⋊C4—682no—
276C4⋊C4—1361no—
277C4⋊C4—1362no—
278C22⋊C4—42no—
279C22⋊C4—681no—
280C22⋊C4—682no—
281C22⋊C4—681no—
282C22⋊C4—682no—
283C22⋊C4—682no—
284C22⋊C4—1361no—
285C42—341no—
286C42—341no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23—171no—
292C23—171no—
293C23—341no—
294C23—341no—
295C23—681no—
296C23—681no—
297C23#1058754912yes—
298C23C2×C22⋊#59511yescharacteristic
299Q8—82no—
300D4—682no—
301D4—682no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—172no—
314C2×C4—341no—
315C2×C4—341no—
316C2×C4—342no—
317C2×C4—341no—
318C2×C4—341no—
319C2×C4—682no—
320C2×C4—681no—
321C2×C4—681no—
322C2×C4—681no—
323C2×C4—681no—
324C2×C4—681no—
325C2×C4—681no—
326C2×C4—681no—
327C2×C4—1361no—
328C2×C4—1362no—
329C2×C4—1362no—
330C2×C4—1362no—
331C2×C4—1364no—
332C2×C4#1058755111yescharacteristic
333C2×C4#1058755111yescharacteristic
334C8—1362no—
335C22—21no—
336C22—21no—
337C22—22no—
338C22—42no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—341no—
343C22—341no—
344C22—681no—
345C22—681no—
346C22—681no—
347C22—681no—
348C22—1361no—
349C22C2×#1058755111yescharacteristic
350C22C2×#1058754911yescharacteristic
351C22#1176380811yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—2722no—
358C4—342no—
359C4—682no—
360C4—681no—
361C4—681no—
362C4—1361no—
363C2—21no—
364C2—21no—
365C2—42no—
366C2—681no—
367C2—681no—
368C2#1454422411yescharacteristic
369C2#1454503911yescharacteristic
370C2#1454505511yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C22⋊Q8C4
socleC22×C17C2×#99
prime radicalC22×C22⋊D17D4
cosocleC2×#63227C23
hypercenterC2×C22⋊Q8#595
hypocenterC17#11902
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #14543781C2semidirect
4. #14543779C2semidirect
13. #11762747C4semidirect
15. #11762728C4semidirect
21. C2×#10587502C4semidirect
22. C2×C17×C22⋊Q8C4semidirect
183. C2×C22⋊Q8#595semidirect
242. C17#11902semidirect

Maximal subgroups

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

subgroupindex
#145446442
#145440232
#145437812
#145437792
#145339662
#1190217