Finite Group Databasebeta

← #17958149

Subgroups — #17958149

Order 4352.

602 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 104 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#14544015C212yesmaximal, complemented
2#14543715C212yesmaximal, complemented
3#14543713C212yesmaximal, complemented
4#14531274C211yesmaximal, characteristic
5#11763825—22no—
6#11763654C2214yes—
7#11763652—22no—
8C22×#63252C411yescharacteristic
9C2×#10587612C2211yescharacteristic
10#11762715C411yescharacteristic
11#11762715C2211yescharacteristic
12#11762711C411yescharacteristic
13#11762711C2211yescharacteristic
14#11762688—22no—
15C4×#63227—22no—
16C22×C42×C17C411yescharacteristic
17C23×C4×C17—21no—
18C23×C4×C17C2×C411yescharacteristic
19C22×C22⋊D17—21no—
20C2×#63252—22no—
21C2×#63252—41no—
22C2×#63252—41no—
23C2×#63252—42no—
24C2×#63252C814yescomplemented
25C22×D68C2×C411yescharacteristic
26C22×C4×D17—21no—
27C22×Dic34C2×C411yescharacteristic
28C2×C42×C17—21no—
29C2×C42×C17—42no—
30C2×C42×C17C2×C411yescharacteristic
31C2×C42×C17C2×C411yescharacteristic
32C2×C22⋊Dic17D412yes—
33C2×#63227—22no—
34C2×#63227—22no—
35#10587612—41no—
36#10587612—41no—
37C2×C4⋊Dic17C2×C411yescharacteristic
38C2×C4⋊Dic17C2311yescharacteristic
39C2×C4×Dic17D412yes—
40C22⋊#3624—24no—
41C4⋊#3624—42no—
42C4×#3624—42no—
43#10587502—22no—
44#10587502—22no—
45C24×C17C22⋊C411yescharacteristic
46C23×D17—21no—
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17—22no—
50C22×C4×C17—21no—
51C22×C4×C17—21no—
52C22×C4×C17—42no—
53C22×C4×C17—42no—
54C22×C4×C17—42no—
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C2×C812yes—
57C22×C4×C17M1612yes—
58C22×C4×C17C22×C411yescharacteristic
59C2×C22⋊D17—24no—
60C2×C22⋊D17—42no—
61C2×C22⋊D17—42no—
62C22×Dic17—21no—
63C22×Dic17C22⋊C412yes—
64C22×Dic17C2×D412yes—
65#63252—44no—
66#63252—44no—
67#63252—44no—
68#63252—44no—
69C2×D68—21no—
70C2×D68—41no—
71C2×D68—41no—
72C2×D68C2×C812yes—
73C2×C4×D17—24no—
74C2×C4×D17—41no—
75C2×C4×D17—41no—
76C2×C4×D17—42no—
77C2×Dic34—21no—
78C2×Dic34—41no—
79C2×Dic34—41no—
80C2×Dic34C2×C812yes—
81C2×#3624—44no—
82C42×C17—41no—
83C42×C17—41no—
84C42×C17—42no—
85C22⋊Dic17—42no—
86#63227—44no—
87#63227—44no—
88C4⋊Dic17—41no—
89C4⋊Dic17—41no—
90C4×Dic17—22no—
91C4×Dic17—22no—
92#11431—171nomaximal, Sylow
93C23×C17—21no—
94C23×C17—21no—
95C23×C17—41no—
96C23×C17—41no—
97C23×C17C22⋊C812yes—
98C23×C17C2×C22⋊C411yescharacteristic
99C22×D17—22no—
100C22×D17—42no—
101C22×D17—42no—
102C22×D17—41no—
103C22×D17—41no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—22no—
107C2×C4×C17—22no—
108C2×C4×C17—22no—
109C2×C4×C17—22no—
110C2×C4×C17—22no—
111C2×C4×C17—22no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—48no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17C22⋊C812yes—
118C2×C4×C17#9911yescharacteristic
119C2×C4×C17#9911yescharacteristic
120C2×C4×C17#10012yes—
121C2×C4×C17C22×C811yescharacteristic
122C2×C4×C17C2×M1611yescharacteristic
123C22⋊D17—48no—
124C2×Dic17—22no—
125C2×Dic17—22no—
126C2×Dic17—22no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—42no—
130C2×Dic17—42no—
131D68—42no—
132D68—42no—
133C4×D17—44no—
134C4×D17—44no—
135Dic34—42no—
136Dic34—42no—
137#3624—84no—
138#2297—171no—
139#1458—172no—
140#1319—172no—
141#1318—172no—
142C22×C17—21no—
143C22×C17—21no—
144C22×C17—22no—
145C22×C17—42no—
146C22×C17—42no—
147C22×C17—41no—
148C22×C17—41no—
149C22×C17C2×C22⋊C811yescharacteristic
150C22×C17C2×#9911yescharacteristic
151C22×C17C2×#10011yescharacteristic
152C2×D17—44no—
153C2×D17—42no—
154C2×D17—82no—
155C2×D17—81no—
156C2×D17—81no—
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—42no—
160C4×C17—42no—
161C4×C17#32312yes—
162C4×C17#32312yes—
163Dic17—42no—
164Dic17—42no—
165Dic17—42no—
166C22×#41—171no—
167C2×#117—171no—
168C22×C42#59511yescharacteristic
169#431—342no—
170#391—171no—
171#391—171no—
172#390—171no—
173#390—171no—
174#386—342no—
175C4×C22⋊C4—342no—
176#324—174no—
177#323—342no—
178C2×C17—21no—
179C2×C17—21no—
180C2×C17—42no—
181C2×C17C2×#32311yescharacteristic
182C2×C17#212611yescharacteristic
183C2×C17#213211yescharacteristic
184D17—82no—
185C2×#41—174no—
186C2×#41—342no—
187C2×#41—681no—
188C2×#41—681no—
189C2×#41—682no—
190C22×Q8—171no—
191C22×D4—171no—
192C22×D4—341no—
193C23×C4—21no—
194C23×C4—341no—
195C23×C4C2×#59511yescharacteristic
196#117—681no—
197#117—681no—
198C2×C4⋊C4—171no—
199C2×C4⋊C4—171no—
200C2×C22⋊C4—172no—
201C2×C22⋊C4—342no—
202C2×C22⋊C4—342no—
203C2×C42—21no—
204C2×C42—42no—
205C2×C42—172no—
206C2×C42C2×#59511yescharacteristic
207C2×C42C2×#59511yescharacteristic
208C4⋊C8—682no—
209C22⋊C8—344no—
210C4×C8—682no—
211#95—342no—
212#95—342no—
213C17#1143111yescharacteristic, complemented, Sylow
214C24—341no—
215C24C22⋊#59511yescharacteristic
216#41—684no—
217#41—684no—
218#41—684no—
219#41—684no—
220C2×Q8—172no—
221C2×Q8—341no—
222C2×Q8—681no—
223C2×Q8—681no—
224C2×D4—172no—
225C2×D4—344no—
226C2×D4—341no—
227C2×D4—681no—
228C2×D4—681no—
229C2×D4—682no—
230C2×D4—682no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—172no—
240C22×C4—172no—
241C22×C4—341no—
242C22×C4—344no—
243C22×C4—681no—
244C22×C4—681no—
245C22×C4—682no—
246C22×C4#6324212yes—
247C22×C4#6324312yes—
248C22×C4C22⋊#59511yescharacteristic
249C22×C4C22×#59511yescharacteristic
250C2×C8—684no—
251C4⋊C4—681no—
252C4⋊C4—681no—
253C22⋊C4—684no—
254C22⋊C4—684no—
255C22⋊C4—682no—
256C42—41no—
257C42—41no—
258C42—42no—
259C42—342no—
260C42—342no—
261C23—21no—
262C23—21no—
263C23—41no—
264C23—41no—
265C23—342no—
266C23—682no—
267C23—682no—
268C23—681no—
269C23—681no—
270C23#1058754312yes—
271C23C2×C22⋊#59511yescharacteristic
272Q8—682no—
273Q8—682no—
274D4—682no—
275D4—682no—
276D4—688no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—48no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—342no—
291C2×C4—342no—
292C2×C4—342no—
293C2×C4—681no—
294C2×C4—681no—
295C2×C4—684no—
296C2×C4—684no—
297C2×C4—682no—
298C2×C4—682no—
299C2×C4#1058753911yescharacteristic
300C2×C4#1058753911yescharacteristic
301C2×C4#1058754312yes—
302C2×C4#1058755312yes—
303C2×C4C2×#6324211yescharacteristic
304C2×C4C2×#6324311yescharacteristic
305C8—1364no—
306C22—21no—
307C22—21no—
308C22—22no—
309C22—42no—
310C22—42no—
311C22—41no—
312C22—41no—
313C22—684no—
314C22—682no—
315C22—1362no—
316C22—1361no—
317C22—1361no—
318C22C2×#1058754311yescharacteristic
319C22C2×#1058753911yescharacteristic
320C22C2×#1058755311yescharacteristic
321C4—21no—
322C4—21no—
323C4—42no—
324C4—42no—
325C4—682no—
326C4—682no—
327C4—682no—
328C4#1176365312yes—
329C4#1176365312yes—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—1362no—
334C2C2×#1176365311yescharacteristic
335C2#1454505711yescharacteristic
336C2#1454507711yescharacteristic
subgroupG/H
centerC2×C4#10587539
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC22×C42×C17C4
socleC22×C17C2×#99
prime radicalC22×#63252C4
cosocleC2×C4⋊Dic17C23
hypercenterC22×C42#595
hypocenterC17#11431
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. #14544015C2semidirect
2. #14543715C2semidirect
3. #14543713C2semidirect
24. C2×#63252C8semidirect
213. C17#11431semidirect

Maximal subgroups

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

subgroupindex
#145440152
#145437152
#145437132
#145312742
#1143117