Finite Group Databasebeta

← #17981289

Subgroups — #17981289

Order 4352.

462 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 75 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×#11763895C212yesmaximal
2#14543962C211yesmaximal, characteristic
3C2×C22⋊#3633—22no—
4#11763895—22no—
5#11763895C414yescomplemented
6C22×C4⋊#595C411yescharacteristic
7C22×C4⋊#595C2211yescharacteristic
8C2×(C2×#595)⋊C4—22no—
9C2×C42×D17C411yescharacteristic
10C23×#595—21no—
11C23×#595D412yes—
12C22×#3633—42no—
13C22×C4×D17—21no—
14C22×C4×D17C2×C411yescharacteristic
15C2×C4⋊#595—21no—
16C2×C4⋊#595—41no—
17C2×C4⋊#595—41no—
18C2×C4⋊#595—41no—
19C2×C4⋊#595—41no—
20C2×C4⋊#595C812yescomplemented
21C2×C4⋊#595C2×C412yes—
22C2×C4⋊#595D411yescharacteristic
23C2×C4⋊#595Q811yescharacteristic
24C22⋊#3633—24no—
25C22⋊#3633—42no—
26C2×C42×C17C811yescharacteristic, complemented
27C2×C4×Dic17—21no—
28C2×C4×Dic17C811yescharacteristic, complemented
29C42×D17—41no—
30C42×D17—41no—
31(C2×#595)⋊C4—44no—
32C23×D17C22⋊C411yescharacteristic
33C22×#595—22no—
34C22×#595—22no—
35C22×#595—22no—
36C22×#595—42no—
37C22×#595—42no—
38C22×#595—42no—
39C22×#595—42no—
40C22×#595—41no—
41C22×#595—41no—
42C22×#595C22⋊C412yes—
43C22×#595C4⋊C412yes—
44C2×#3633—44no—
45C2×#3633—82no—
46C2×#3633—82no—
47C22×C4×C17—21no—
48C22×C4×C17C2×C811yescharacteristic
49C22×Dic17—21no—
50C22×Dic17M1611yescharacteristic
51C2×C4×D17—21no—
52C2×C4×D17—21no—
53C2×C4×D17—21no—
54C2×C4×D17—21no—
55C2×C4×D17—22no—
56C2×C4×D17—22no—
57C2×C4×D17—41no—
58C2×C4×D17—41no—
59C2×C4×D17—41no—
60C2×C4×D17—41no—
61C2×C4×D17C4211yescharacteristic
62C2×C4×D17C4⋊C411yescharacteristic
63C2×C4×D17C2×C811yescharacteristic
64C2×C4×D17M1611yescharacteristic
65C4⋊#595—42no—
66C4⋊#595—41no—
67C4⋊#595—41no—
68C4⋊#595—42no—
69C4⋊#595—42no—
70C42×C17—41no—
71C4×Dic17—42no—
72C4×Dic17—41no—
73#7189—171nomaximal, Sylow
74C23×C17C22⋊C811yescharacteristic
75C22×D17—21no—
76C22×D17—21no—
77C22×D17—21no—
78C22×D17—21no—
79C22×D17#9511yescharacteristic
80C22×D17C22⋊C811yescharacteristic
81C22×D17#9911yescharacteristic
82C22×D17#9911yescharacteristic
83C22×D17#10011yescharacteristic
84C22×D17#10111yescharacteristic
85C2×#595—22no—
86C2×#595—22no—
87C2×#595—42no—
88C2×#595—42no—
89C2×#595—42no—
90C2×#595—42no—
91C2×#595—44no—
92C2×#595—42no—
93C2×#595—82no—
94C2×#595—82no—
95C2×#595—81no—
96C2×#595—81no—
97#3633—84no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—22no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17C4×C811yescharacteristic
104C2×C4×C17C4⋊C811yescharacteristic
105C2×Dic17—21no—
106C2×Dic17—21no—
107C2×Dic17—22no—
108C2×Dic17—41no—
109C2×Dic17—41no—
110C2×Dic17#9711yescharacteristic
111C2×Dic17C4⋊C811yescharacteristic
112C4×D17—21no—
113C4×D17—21no—
114C4×D17—21no—
115C4×D17—21no—
116C4×D17—21no—
117C4×D17—21no—
118C4×D17—21no—
119C4×D17—21no—
120C4×D17—42no—
121C4×D17—42no—
122C4×D17—42no—
123C4×D17—42no—
124C2×#324—172no—
125C4⋊#95—171no—
126C22×C17—21no—
127C22×C17—21no—
128C22×C17#32311yescharacteristic
129C22×C17#32411yescharacteristic
130C22×C17#33611yescharacteristic
131C2×D17—21no—
132C2×D17—21no—
133C2×D17—21no—
134C2×D17—21no—
135C2×D17—21no—
136C2×D17—21no—
137C2×D17—21no—
138C2×D17—21no—
139C2×D17—21no—
140C2×D17—21no—
141C2×D17#32311yescharacteristic
142C2×D17#32411yescharacteristic
143C2×D17#34211yescharacteristic
144C2×D17#34311yescharacteristic
145C2×D17#35311yescharacteristic
146C2×D17#35411yescharacteristic
147C2×D17#35511yescharacteristic
148C2×D17#35611yescharacteristic
149#595—42no—
150#595—42no—
151#595—82no—
152C4×C17—21no—
153C4×C17—21no—
154C4×C17—42no—
155Dic17—21no—
156Dic17—21no—
157Dic17—42no—
158C22×C4⋊C4—171no—
159C22×C4⋊C4—171no—
160C22×C42—171no—
161C2×C22⋊C8—342no—
162C2×#95—342no—
163#324—174no—
164#324—342no—
165C2×C17—21no—
166C2×C17—21no—
167C2×C17#128011yescharacteristic
168C2×C17#132411yescharacteristic
169C2×C17#132511yescharacteristic
170D17—21no—
171D17—21no—
172D17#131811yescharacteristic
173D17#131911yescharacteristic
174D17#139311yescharacteristic
175D17#139411yescharacteristic
176C23×C4—171no—
177C23×C4—172no—
178C23×C4—341no—
179C23×C4—341no—
180C22×C8—682no—
181C2×C4⋊C4—172no—
182C2×C4⋊C4—171no—
183C2×C4⋊C4—171no—
184C2×C4⋊C4—172no—
185C2×C4⋊C4—341no—
186C2×C4⋊C4—681no—
187C2×C4⋊C4—681no—
188C2×C4⋊C4—681no—
189C2×C4⋊C4—681no—
190C2×C42—171no—
191C2×C42—341no—
192C2×C42—681no—
193C2×C42—681no—
194C2×C42#363311yescharacteristic, complemented
195C22⋊C8—344no—
196C22⋊C8—682no—
197#95—684no—
198C17#718911yescharacteristic, complemented, Sylow
199C24—171no—
200C22×C4—21no—
201C22×C4—171no—
202C22×C4—171no—
203C22×C4—171no—
204C22×C4—171no—
205C22×C4—171no—
206C22×C4—172no—
207C22×C4—172no—
208C22×C4—341no—
209C22×C4—341no—
210C22×C4—341no—
211C22×C4—341no—
212C22×C4—342no—
213C22×C4—342no—
214C22×C4—342no—
215C22×C4—341no—
216C22×C4—342no—
217C22×C4—342no—
218C22×C4—681no—
219C22×C4—681no—
220C22×C4—681no—
221C22×C4—681no—
222C22×C4—682no—
223C22×C4—682no—
224C22×C4—681no—
225C22×C4—681no—
226C22×C4—682no—
227C22×C4—682no—
228C22×C4C2×#363311yescharacteristic
229C2×C8—684no—
230C2×C8—1362no—
231C2×C8—1362no—
232C4⋊C4—681no—
233C4⋊C4—682no—
234C4⋊C4—681no—
235C4⋊C4—682no—
236C4⋊C4—682no—
237C42—41no—
238C42—681no—
239C42—682no—
240C23—171no—
241C23—171no—
242C23—171no—
243C23—171no—
244C23—171no—
245C23—171no—
246C23—341no—
247C23—341no—
248C23—341no—
249C23—341no—
250C23C22⋊#363311yescharacteristic
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—171no—
257C2×C4—171no—
258C2×C4—341no—
259C2×C4—341no—
260C2×C4—341no—
261C2×C4—341no—
262C2×C4—341no—
263C2×C4—341no—
264C2×C4—341no—
265C2×C4—341no—
266C2×C4—341no—
267C2×C4—341no—
268C2×C4—342no—
269C2×C4—342no—
270C2×C4—342no—
271C2×C4—682no—
272C2×C4—682no—
273C2×C4—682no—
274C2×C4—682no—
275C2×C4—681no—
276C2×C4—682no—
277C2×C4—682no—
278C2×C4—681no—
279C2×C4—682no—
280C2×C4—682no—
281C2×C4—682no—
282C2×C4—684no—
283C2×C4—1362no—
284C2×C4—1361no—
285C2×C4—1361no—
286C2×C4—1362no—
287C2×C4C4×#363311yescharacteristic
288C2×C4C4⋊#363311yescharacteristic
289C8—1364no—
290C22—21no—
291C22—21no—
292C22—171no—
293C22—171no—
294C22—171no—
295C22—171no—
296C22—171no—
297C22—171no—
298C22—171no—
299C22—171no—
300C22—341no—
301C22—341no—
302C22—341no—
303C22—341no—
304C22—341no—
305C22—341no—
306C22—341no—
307C22—341no—
308C22—341no—
309C22—341no—
310C22#1176389411yescharacteristic
311C22#1176389511yescharacteristic
312C22(C2×#3633)⋊C411yescharacteristic
313C4—21no—
314C4—21no—
315C4—42no—
316C4—341no—
317C4—341no—
318C4—682no—
319C4—682no—
320C4—682no—
321C4—1362no—
322C2—21no—
323C2—21no—
324C2—171no—
325C2—171no—
326C2—171no—
327C2—171no—
328C2—341no—
329C2—341no—
330C2#1454579311yescharacteristic
331C2#1454582011yescharacteristic
332C2#1454582111yescharacteristic
subgroupG/H
centerC22#11763895
commutatorC2×C4×C17C4×C8
FrattiniC22×C4C2×#3633
FittingC2×C42×C17C8
socleC22×C17#324
prime radicalC23×D17C22⋊C4
cosocleC22×C4⋊#595C22
hypercenterC2×C42#3633
hypocenterC17#7189
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
5. #11763895C4semidirect
20. C2×C4⋊#595C8semidirect
26. C2×C42×C17C8semidirect
28. C2×C4×Dic17C8semidirect
194. C2×C42#3633semidirect
198. C17#7189semidirect

Maximal subgroups

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

subgroupindex
C2×#117638952
#145439622
#718917