Finite Group Databasebeta

← #17958131

Subgroups — #17958131

Order 4352.

734 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C2×#11763652C212yesmaximal, complemented
2#14543710C212yesmaximal, complemented
3#14543708C212yesmaximal, complemented
4#14531362C211yesmaximal, characteristic
5C2×C22⋊#3624—22no—
6#11763652—22no—
7#11763652C2214yes—
8C22×C22⋊Dic17C411yescharacteristic
9C22×C22⋊Dic17C2211yescharacteristic
10#11762689—22no—
11#11762689—22no—
12#11762672C411yescharacteristic
13#11762672C2211yescharacteristic
14#11762665C411yescharacteristic
15#11762665C2211yescharacteristic
16C23×D4×C17C411yescharacteristic
17C25×C17C2×C411yescharacteristic
18C25×C17C2×C411yescharacteristic
19C22×D4×C17—21no—
20C22×D4×C17—21no—
21C22×D4×C17—22no—
22C22×D4×C17—42no—
23C22×D4×C17—42no—
24C22×D4×C17C814yescomplemented
25C23×C4×C17C2×C411yescharacteristic
26C23×Dic17—21no—
27C23×Dic17D412yes—
28C22×#3624—42no—
29C2×C22⋊Dic17—21no—
30C2×C22⋊Dic17—22no—
31C2×C22⋊Dic17—22no—
32C2×C22⋊Dic17—42no—
33C2×C22⋊Dic17—42no—
34C2×C22⋊Dic17C2×C411yescharacteristic
35C2×C22⋊Dic17C2×C411yescharacteristic
36C2×C22⋊Dic17C2×C411yescharacteristic
37C2×C22⋊Dic17D412yes—
38C2×C22⋊Dic17C2311yescharacteristic
39C22⋊#3624—24no—
40C22⋊#3624—42no—
41#10587502—22no—
42#10587502—22no—
43C24×C17—22no—
44C24×C17—22no—
45C24×C17—21no—
46C24×C17—21no—
47C24×C17—41no—
48C24×C17—41no—
49C24×C17—82no—
50C24×C17—82no—
51C24×C17C22⋊C411yescharacteristic
52C24×C17C22⋊C411yescharacteristic
53C24×C17C2×C812yes—
54C24×C17C2×C812yescomplemented
55C24×C17M1612yes—
56C24×C17C22×C411yescharacteristic
57C2×D4×C17—24no—
58C2×D4×C17—24no—
59C2×D4×C17—48no—
60C2×D4×C17—42no—
61C2×D4×C17—42no—
62C2×D4×C17—42no—
63C2×D4×C17—42no—
64C2×D4×C17—48no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—41no—
68C22×C4×C17—41no—
69C22×C4×C17C2×C812yescomplemented
70C22×Dic17—22no—
71C22×Dic17—22no—
72C22×Dic17—21no—
73C22×Dic17—21no—
74C22×Dic17—42no—
75C22×Dic17—82no—
76C22×Dic17—82no—
77C22×Dic17C22⋊C412yes—
78C22×Dic17C2×D412yes—
79C2×#3624—44no—
80C2×#3624—84no—
81C22⋊Dic17—41no—
82C22⋊Dic17—42no—
83C22⋊Dic17—41no—
84C22⋊Dic17—42no—
85C22⋊Dic17—41no—
86C22⋊Dic17—41no—
87C22⋊Dic17—82no—
88C22⋊Dic17—82no—
89#11426—171nomaximal, Sylow
90C23×C17—21no—
91C23×C17—21no—
92C23×C17—21no—
93C23×C17—21no—
94C23×C17—24no—
95C23×C17—24no—
96C23×C17—22no—
97C23×C17—42no—
98C23×C17—42no—
99C23×C17—42no—
100C23×C17—42no—
101C23×C17—42no—
102C23×C17—42no—
103C23×C17—42no—
104C23×C17—41no—
105C23×C17—41no—
106C23×C17—82no—
107C23×C17—82no—
108C23×C17—82no—
109C23×C17—82no—
110C23×C17—82no—
111C23×C17—84no—
112C23×C17—82no—
113C23×C17—84no—
114C23×C17—84no—
115C23×C17C22⋊C812yes—
116C23×C17C22⋊C812yes—
117C23×C17#9912yes—
118C23×C17#10012yes—
119C23×C17C2×C22⋊C411yescharacteristic
120C23×C17C22×C811yescharacteristic
121C23×C17C2×M1611yescharacteristic
122D4×C17—48no—
123D4×C17—48no—
124C2×C4×C17—22no—
125C2×C4×C17—42no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—42no—
129C2×Dic17—22no—
130C2×Dic17—22no—
131C2×Dic17—44no—
132C2×Dic17—42no—
133C2×Dic17—42no—
134C2×Dic17—42no—
135C2×Dic17—42no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—82no—
139C2×Dic17—84no—
140#3624—84no—
141#2308—171no—
142C2×#323—172no—
143#1317—172no—
144#1316—172no—
145C22×C17—22no—
146C22×C17—22no—
147C22×C17—22no—
148C22×C17—21no—
149C22×C17—21no—
150C22×C17—22no—
151C22×C17—42no—
152C22×C17—42no—
153C22×C17—41no—
154C22×C17—41no—
155C22×C17—42no—
156C22×C17—42no—
157C22×C17—42no—
158C22×C17—42no—
159C22×C17—42no—
160C22×C17—42no—
161C22×C17—42no—
162C22×C17—42no—
163C22×C17—84no—
164C22×C17—84no—
165C22×C17—82no—
166C22×C17—84no—
167C22×C17—84no—
168C22×C17—82no—
169C22×C17#32314yes—
170C22×C17C2×C22⋊C811yescharacteristic
171C22×C17C2×#9911yescharacteristic
172C22×C17C2×#10011yescharacteristic
173C4×C17—42no—
174Dic17—42no—
175Dic17—42no—
176Dic17—81no—
177Dic17—81no—
178C23×D4#59511yescharacteristic
179C22×C22⋊C4—171no—
180C22×C22⋊C4—171no—
181C2×C22⋊C8—342no—
182#386—342no—
183#386—342no—
184#381—171no—
185#381—171no—
186#379—171no—
187#379—171no—
188#323—174no—
189#323—342no—
190C2×C17—21no—
191C2×C17—21no—
192C2×C17—24no—
193C2×C17—42no—
194C2×C17—41no—
195C2×C17—41no—
196C2×C17—82no—
197C2×C17C2×#32311yescharacteristic
198C2×C17#212112yes—
199C25C2×#59511yescharacteristic
200C25C2×#59511yescharacteristic
201C22×D4—22no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—42no—
205C22×D4—42no—
206C22×D4#362414yescomplemented
207C23×C4—172no—
208C23×C4—341no—
209C23×C4C2×#59511yescharacteristic
210C22×C8—682no—
211C2×C22⋊C4—172no—
212C2×C22⋊C4—171no—
213C2×C22⋊C4—171no—
214C2×C22⋊C4—171no—
215C2×C22⋊C4—171no—
216C2×C22⋊C4—341no—
217C2×C22⋊C4—342no—
218C2×C22⋊C4—342no—
219C2×C22⋊C4—682no—
220C2×C22⋊C4—682no—
221C22⋊C8—344no—
222C22⋊C8—682no—
223#95—342no—
224#95—342no—
225C17#1142611yescharacteristic, complemented, Sylow
226C24—22no—
227C24—22no—
228C24—21no—
229C24—21no—
230C24—41no—
231C24—41no—
232C24—82no—
233C24—82no—
234C24C2×#362412yes—
235C24C2×#362412yescomplemented
236C24#6324712yes—
237C24C22⋊#59511yescharacteristic
238C24C22⋊#59511yescharacteristic
239C24C22×#59511yescharacteristic
240C2×D4—24no—
241C2×D4—24no—
242C2×D4—48no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—48no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—172no—
253C22×C4—172no—
254C22×C4—342no—
255C22×C4—342no—
256C22×C4—341no—
257C22×C4—341no—
258C22×C4—682no—
259C22×C4—1362no—
260C22×C4—1362no—
261C22×C4C2×#362412yescomplemented
262C2×C8—684no—
263C2×C8—1364no—
264C22⋊C4—681no—
265C22⋊C4—682no—
266C22⋊C4—681no—
267C22⋊C4—682no—
268C22⋊C4—681no—
269C22⋊C4—681no—
270C22⋊C4—1362no—
271C22⋊C4—1362no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—24no—
277C23—24no—
278C23—22no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—42no—
283C23—42no—
284C23—42no—
285C23—42no—
286C23—41no—
287C23—41no—
288C23—82no—
289C23—82no—
290C23—82no—
291C23—82no—
292C23—82no—
293C23—84no—
294C23—82no—
295C23—84no—
296C23—84no—
297C23#1058755112yes—
298C23C22⋊#362412yes—
299C23C22⋊#362412yes—
300C23#1058755312yes—
301C23C22×#362411yescharacteristic
302C23C2×#6324711yescharacteristic
303C23C2×C22⋊#59511yescharacteristic
304D4—48no—
305D4—48no—
306C2×C4—22no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—342no—
312C2×C4—342no—
313C2×C4—684no—
314C2×C4—682no—
315C2×C4—682no—
316C2×C4—682no—
317C2×C4—682no—
318C2×C4—681no—
319C2×C4—681no—
320C2×C4—1362no—
321C2×C4—1364no—
322C8—1364no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—42no—
330C22—42no—
331C22—41no—
332C22—41no—
333C22—42no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22—84no—
342C22—84no—
343C22—82no—
344C22—84no—
345C22—84no—
346C22—82no—
347C22#1176365214yes—
348C22C2×C22⋊#362411yescharacteristic
349C22C2×#1058755111yescharacteristic
350C22C2×#1058755311yescharacteristic
351C4—42no—
352C4—682no—
353C4—682no—
354C4—1361no—
355C4—1361no—
356C2—21no—
357C2—21no—
358C2—24no—
359C2—41no—
360C2—41no—
361C2—42no—
362C2—82no—
363C2C2×#1176365211yescharacteristic
364C2#1454503912yes—
subgroupG/H
centerC22C2×#10587551
commutatorC23×C17C22×C8
FrattiniC24C22×#595
Fitting, prime radicalC23×D4×C17C4
socleC22×C17C2×#99
cosocleC2×C22⋊Dic17C23
hypercenterC23×D4#595
hypocenterC17#11426
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C25 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#11763652C2semidirect
2. #14543710C2semidirect
3. #14543708C2semidirect
24. C22×D4×C17C8semidirect
54. C24×C17C2×C8semidirect
69. C22×C4×C17C2×C8semidirect
206. C22×D4#3624semidirect
225. C17#11426semidirect
235. C24C2×#3624semidirect
261. C22×C4C2×#3624semidirect

Maximal subgroups

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

subgroupindex
C2×#117636522
#145437102
#145437082
#145313622
#1142617