Finite Group Databasebeta

← #17981546

Subgroups — #17981546

Order 4352.

630 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 97 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#14545925C212yesmaximal
2#14545785C214yesmaximal, complemented
3C2×(C2×#595)⋊Q8C211yesmaximal, characteristic
4C2×C22⋊#3633—22no—
5(C2×#3633)⋊C4—22no—
6(C2×#3633)⋊C4C2214yes—
7C22×C4⋊#595C411yescharacteristic
8C22×C4×#595C2211yescharacteristic
9(C2×#595)⋊Q8—22no—
10(C2×#595)⋊Q8C412yes—
11(C2×#595)⋊Q8C2212yes—
12C2×(C2×#595)⋊C4—22no—
13C22×Q8×D17C411yescharacteristic
14C23×#595—21no—
15C23×#595D412yes—
16C22×#3633—24no—
17C22×Q8×C17C811yescharacteristic, complemented
18C2×Q8×D17—21no—
19C2×Q8×D17—21no—
20C2×Q8×D17—42no—
21C2×Q8×D17—42no—
22C2×Q8×D17C812yescomplemented
23C2×Q8×D17C2×C412yes—
24C22×C4×D17—21no—
25C22×C4×D17C2×C411yescharacteristic
26C22×Dic34—21no—
27C22×Dic34C811yescharacteristic, complemented
28C2×C4⋊#595—21no—
29C2×C4⋊#595—42no—
30C2×C4⋊#595C2×C412yes—
31C2×C4×#595—42no—
32C2×C4×#595C2×C411yescharacteristic
33C2×C4×#595D412yes—
34C2×C4×#595C2311yescharacteristic
35C22⋊#3633—44no—
36(C2×#595)⋊C4—24no—
37(C2×#595)⋊C4—24no—
38C23×D17C22⋊C411yescharacteristic
39C22×#595—24no—
40C22×#595—24no—
41C22×#595—22no—
42C22×#595—42no—
43C22×#595—44no—
44C22×#595—42no—
45C22×#595C22⋊C412yes—
46C22×#595C2×D412yes—
47C2×#3633—44no—
48C2×#3633—44no—
49C2×#3633—44no—
50C2×Q8×C17—21no—
51C2×Q8×C17—42no—
52C2×Q8×C17C2×C812yes—
53C22×C4×C17—21no—
54C22×C4×C17C2×C811yescharacteristic
55C22×Dic17—21no—
56C22×Dic17M1611yescharacteristic
57Q8×D17—44no—
58Q8×D17—42no—
59Q8×D17—42no—
60Q8×D17—44no—
61Q8×D17—42no—
62Q8×D17—42no—
63C2×C4×D17—22no—
64C2×C4×D17—22no—
65C2×C4×D17—22no—
66C2×C4×D17—22no—
67C2×C4×D17—42no—
68C2×C4×D17—42no—
69C2×C4×D17C22⋊C411yescharacteristic
70C2×C4×D17C2×C811yescharacteristic
71C2×C4×D17M1611yescharacteristic
72C2×C4×D17C22×C411yescharacteristic
73C2×Dic34—21no—
74C2×Dic34—22no—
75C2×Dic34—22no—
76C2×Dic34—44no—
77C2×Dic34—42no—
78C2×Dic34C2×C812yes—
79C4⋊#595—42no—
80C4⋊#595—42no—
81C4×#595—41no—
82C4×#595—42no—
83C4×#595—41no—
84#7595—171nomaximal, Sylow
85C23×C17C22⋊C811yescharacteristic
86C22×D17—22no—
87C22×D17—22no—
88C22×D17C22⋊C811yescharacteristic
89C22×D17#9912yes—
90C22×D17#10012yes—
91C22×D17C2×C22⋊C411yescharacteristic
92C2×#595—22no—
93C2×#595—22no—
94C2×#595—22no—
95C2×#595—22no—
96C2×#595—22no—
97C2×#595—48no—
98C2×#595—42no—
99C2×#595—44no—
100C2×#595—84no—
101C2×#595#13714yes—
102#3633—84no—
103Q8×C17—42no—
104Q8×C17—42no—
105C2×C4×C17—22no—
106C2×C4×C17—22no—
107C2×C4×C17—42no—
108C2×C4×C17C22⋊C811yescharacteristic
109C2×C4×C17C22×C811yescharacteristic
110C2×Dic17—22no—
111C2×Dic17—22no—
112C2×Dic17—42no—
113C2×Dic17C22⋊C811yescharacteristic
114C2×Dic17C2×M1611yescharacteristic
115C4×D17—22no—
116C4×D17—22no—
117C4×D17—21no—
118C4×D17—21no—
119C4×D17—21no—
120C4×D17—21no—
121C4×D17—44no—
122C4×D17—42no—
123C4×D17—42no—
124Dic34—44no—
125Dic34—44no—
126Dic34—42no—
127Dic34—42no—
128C2×#391—171no—
129#1817—172no—
130#1272—174no—
131C22×C17—22no—
132C22×C17#32312yes—
133C22×C17C2×C22⋊C811yescharacteristic
134C2×D17—22no—
135C2×D17—22no—
136C2×D17—24no—
137C2×D17—22no—
138C2×D17#32312yes—
139C2×D17C2×#9911yescharacteristic
140C2×D17C2×#10011yescharacteristic
141C2×D17#41912yes—
142C2×D17#42112yes—
143#595—24no—
144#595—42no—
145#595—82no—
146C4×C17—21no—
147C4×C17—21no—
148C4×C17—42no—
149Dic17—21no—
150Dic17—21no—
151Dic17—42no—
152C23×Q8—171no—
153C22×C4⋊C4—171no—
154C22×C42—171no—
155C2×C22⋊C8—342no—
156#391—172no—
157#391—172no—
158#391—342no—
159C2×#95—342no—
160#336—174no—
161#336—342no—
162C2×C17—22no—
163C2×C17C2×#32311yescharacteristic
164C2×C17#147912yes—
165D17—22no—
166D17#151112yes—
167D17#153311yescharacteristic
168D17#155811yescharacteristic
169C22×Q8—172no—
170C22×Q8—172no—
171C22×Q8—171no—
172C22×Q8—341no—
173C22×Q8—341no—
174C22×Q8—341no—
175C22×Q8—682no—
176C22×Q8—682no—
177C22×Q8#363311yescharacteristic, complemented
178C23×C4—171no—
179C23×C4—172no—
180C23×C4—341no—
181C23×C4—341no—
182C22×C8—344no—
183C2×C4⋊C4—172no—
184C2×C4⋊C4—341no—
185C2×C4⋊C4—682no—
186C2×C42—171no—
187C2×C42—172no—
188C2×C42—171no—
189C2×C42—682no—
190C22⋊C8—684no—
191#95—344no—
192#95—344no—
193C17#759511yescharacteristic, complemented, Sylow
194C24—171no—
195C2×Q8—21no—
196C2×Q8—42no—
197C2×Q8—172no—
198C2×Q8—342no—
199C2×Q8—342no—
200C2×Q8—341no—
201C2×Q8—682no—
202C2×Q8—684no—
203C2×Q8—682no—
204C2×Q8—682no—
205C2×Q8—684no—
206C2×Q8—682no—
207C2×Q8—682no—
208C2×Q8—684no—
209C2×Q8C2×#363312yes—
210C22×C4—21no—
211C22×C4—172no—
212C22×C4—171no—
213C22×C4—171no—
214C22×C4—171no—
215C22×C4—171no—
216C22×C4—171no—
217C22×C4—172no—
218C22×C4—342no—
219C22×C4—342no—
220C22×C4—342no—
221C22×C4—342no—
222C22×C4—344no—
223C22×C4—344no—
224C22×C4—341no—
225C22×C4—342no—
226C22×C4—682no—
227C22×C4—682no—
228C22×C4—682no—
229C22×C4—682no—
230C22×C4—684no—
231C22×C4C2×#363311yescharacteristic
232C2×C8—684no—
233C2×C8—684no—
234C2×C8—684no—
235C4⋊C4—682no—
236C4⋊C4—682no—
237C42—681no—
238C42—682no—
239C42—681no—
240C23—171no—
241C23—172no—
242C23—172no—
243C23—171no—
244C23—342no—
245C23—342no—
246C23C22⋊#363311yescharacteristic
247Q8—42no—
248Q8—42no—
249Q8—682no—
250Q8—682no—
251Q8—684no—
252Q8—684no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—174no—
257C2×C4—171no—
258C2×C4—171no—
259C2×C4—341no—
260C2×C4—341no—
261C2×C4—341no—
262C2×C4—341no—
263C2×C4—342no—
264C2×C4—342no—
265C2×C4—342no—
266C2×C4—342no—
267C2×C4—342no—
268C2×C4—342no—
269C2×C4—342no—
270C2×C4—342no—
271C2×C4—342no—
272C2×C4—682no—
273C2×C4—682no—
274C2×C4—684no—
275C2×C4—688no—
276C2×C4—682no—
277C2×C4—682no—
278C2×C4—684no—
279C2×C4—1364no—
280C2×C4C22⋊#363311yescharacteristic
281C2×C4C22×#363311yescharacteristic
282C8—1364no—
283C22—22no—
284C22—171no—
285C22—171no—
286C22—172no—
287C22—172no—
288C22—172no—
289C22—344no—
290C22—342no—
291C22—342no—
292C22—342no—
293C22#1176389412yes—
294C22C2×C22⋊#363311yescharacteristic
295C4—21no—
296C4—21no—
297C4—42no—
298C4—344no—
299C4—341no—
300C4—341no—
301C4—682no—
302C4—682no—
303C4—1362no—
304C2—22no—
305C2—172no—
306C2—171no—
307C2—171no—
308C2—342no—
309C2C2×#1176389411yescharacteristic
310C2#1454590512yes—
subgroupG/H
centerC22C2×C22⋊#3633
commutatorC2×C4×C17C22×C8
FrattiniC2×C4C22×#3633
FittingC22×Q8×C17C8
socleC22×C17C2×C22⋊C8
prime radicalC23×D17C22⋊C4
cosocleC2×C4×#595C23
hypercenterC22×Q8#3633
hypocenterC17#7595
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #14545785C2semidirect
17. C22×Q8×C17C8semidirect
22. C2×Q8×D17C8semidirect
27. C22×Dic34C8semidirect
177. C22×Q8#3633semidirect
193. C17#7595semidirect

Maximal subgroups

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

subgroupindex
#145459252
#145457852
C2×(C2×#595)⋊Q82
#759517