Finite Group Databasebeta

← #16944241

Subgroups — #16944241

Order 4352.

422 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C8×D4×D17C211yesmaximal, characteristic
2#14530586C211yesmaximal, characteristic, complemented
3#14530581C211yesmaximal, characteristic, complemented
4#14526740C211yesmaximal, characteristic, complemented
5D4⋊#63214C211yesmaximal, characteristic, complemented
6#14526738C211yesmaximal, characteristic, complemented
7C17×D4⋊C16C211yesmaximal, characteristic, complemented
8C22×C8×D17—21no—
9C4×D4×D17C411yescharacteristic
10C8×D68C2211yescharacteristic
11D4×#3622C411yescharacteristic
12#11762874C411yescharacteristic
13C8×C22⋊D17—21no—
14#11762872—21no—
15C4⋊C8×D17C411yescharacteristic
16C22⋊C8×D17—21no—
17C4×C8×D17C2211yescharacteristic
18C4⋊#63214C2211yescharacteristic, complemented
19#11762627—21no—
20#11762588—21no—
21#11762588—21no—
22#11762584—21no—
23C4×#63214C2211yescharacteristic, complemented
24C8×D4×C17C2211yescharacteristic
25C17×C4⋊C16C2211yescharacteristic, complemented
26C4×C16×C17C2211yescharacteristic, complemented
27C2×D4×D17C811yescharacteristic
28C22×C4×D17—21no—
29C22×C8×C17—21no—
30C4×D4×C17C2×C411yescharacteristic
31D4×Dic17C811yescharacteristic
32C4×C22⋊D17—21no—
33C22×#3622—21no—
34C2×C8×D17—21no—
35C2×C8×D17—21no—
36C2×C8×D17—21no—
37C2×C8×D17—42no—
38C2×C8×D17—42no—
39C2×C8×D17D411yescharacteristic
40C2×C8×D17D411yescharacteristic
41#10587579C811yescharacteristic
42C4⋊C4×D17C811yescharacteristic
43#10587567—21no—
44C22⋊C4×D17—21no—
45C4×D68C2×C411yescharacteristic
46C42×D17C2×C411yescharacteristic
47C2×C16×C17—21no—
48C2×C16×C17—21no—
49C17×C4⋊C8C2×C411yescharacteristic
50C17×C22⋊C8—21no—
51C4×C8×C17C2311yescharacteristic
52C22⋊#3622—21no—
53#10587491—21no—
54#10587491—21no—
55#10587485—21no—
56C8×Dic17D411yescharacteristic
57C8×Dic17D411yescharacteristic
58C2×#63214—21no—
59C2×#63214—21no—
60C4⋊#3622C2×C411yescharacteristic
61C4×#3622C2×C411yescharacteristic
62C23×D17—21no—
63C2×D4×C17C2×C811yescharacteristic
64C22×C4×C17—21no—
65C2×C22⋊D17—21no—
66C22×Dic17—21no—
67D4×D17—22no—
68D4×D17—22no—
69C2×D68C2×C811yescharacteristic
70C2×C4×D17—21no—
71C2×C4×D17—21no—
72C2×C4×D17—21no—
73C2×C4×D17—42no—
74C2×C4×D17—42no—
75C2×C4×D17C22⋊C411yescharacteristic
76C2×C4×D17C2×C811yescharacteristic
77C2×C4×D17M1611yescharacteristic
78C2×C8×C17—21no—
79C2×C8×C17—41no—
80C2×C8×C17—41no—
81C2×C8×C17C2×D411yescharacteristic
82C2×C8×C17C2×D411yescharacteristic
83C4⋊C4×C17C2×C811yescharacteristic
84C22⋊C4×C17—21no—
85C42×C17C22×C411yescharacteristic
86C22⋊Dic17—21no—
87#63227—21no—
88#63227—21no—
89C4⋊Dic17C2×C811yescharacteristic
90#63225—21no—
91C4×Dic17C22⋊C411yescharacteristic
92C4×Dic17C2×C811yescharacteristic
93C4×Dic17M1611yescharacteristic
94C2×#3622—21no—
95C2×#3622—42no—
96C2×#3622C22⋊C411yescharacteristic
97C2×#3622C22⋊C411yescharacteristic
98C8×D17—21no—
99C8×D17—21no—
100C8×D17—41no—
101C8×D17—42no—
102C8×D17—42no—
103C8×D17—41no—
104C8×D17—41no—
105C16×C17—41no—
106C16×C17—41no—
107#63214—41no—
108#63214—41no—
109#11631—171nomaximal, Sylow
110C23×C17—21no—
111C22×D17—24no—
112C22×D17—21no—
113C22×D17—42no—
114C22×D17—42no—
115C22×D17C22⋊C811yescharacteristic
116D4×C17—21no—
117D4×C17M3212yes—
118C2×C4×C17—21no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17C2×C22⋊C411yescharacteristic
122C2×C4×C17C22×C811yescharacteristic
123C2×C4×C17C2×M1611yescharacteristic
124C22⋊D17—24no—
125C2×Dic17—21no—
126C2×Dic17—42no—
127C2×Dic17C22⋊C811yescharacteristic
128C2×Dic17C22⋊C811yescharacteristic
129C2×Dic17C22⋊C811yescharacteristic
130D68—21no—
131D68M3212yes—
132C4×D17—22no—
133C4×D17—21no—
134C4×D17—21no—
135C4×D17—21no—
136C4×D17—21no—
137C4×D17—42no—
138C4×D17—42no—
139C4×D17—41no—
140C4×D17—41no—
141C8×C17—21no—
142C8×C17—41no—
143C8×C17AGL(1,ℤ/8)11yescharacteristic
144C8×C17AGL(1,ℤ/8)11yescharacteristic
145#3622—21no—
146#3622—21no—
147#3622—41no—
148C2×C8×D4—171no—
149#2163—171no—
150#2162—171no—
151D4⋊C16—171no—
152D4⋊C16—171no—
153D4⋊C16—171no—
154D4⋊C16D1711yescharacteristic, complemented
155C22×C17—22no—
156C22×C17—41no—
157C22×C17—41no—
158C22×C17C2×C22⋊C811yescharacteristic
159C2×D17—21no—
160C2×D17—21no—
161C2×D17—22no—
162C2×D17—48no—
163C2×D17—41no—
164C2×D17—41no—
165C2×D17#35012yes—
166C4×C17—21no—
167C4×C17—41no—
168C4×C17#41811yescharacteristic
169C4×C17#42111yescharacteristic
170C4×C17C2×M3211yescharacteristic
171C4×C17C2×M3211yescharacteristic
172Dic17—21no—
173Dic17—21no—
174Dic17—21no—
175Dic17—41no—
176C23×C8—341no—
177C2×C4×D4—171no—
178C8×D4—171no—
179C8×D4—171no—
180C8×D4—171no—
181C8×D4—341no—
182C8×D4—341no—
183C8×D4C2×D1711yescharacteristic
184C2×C4⋊C8—171no—
185C2×C22⋊C8—341no—
186C2×C4×C8—171no—
187C4⋊C16—171no—
188C4⋊C16—341no—
189C4⋊C16C2×D1711yescharacteristic, complemented
190C22⋊C16—341no—
191C22⋊C16—341no—
192#346—341no—
193C4×C16—171no—
194C4×C16C2×D1711yescharacteristic, complemented
195C2×C17—42no—
196C2×C17#147811yescharacteristic
197C2×C17#211211yescharacteristic
198C2×C17C2×#35011yescharacteristic
199D17—22no—
200D17—42no—
201C22×D4—171no—
202C23×C4—341no—
203C22×C8—21no—
204C22×C8—171no—
205C22×C8—171no—
206C22×C8—341no—
207C22×C8—341no—
208C22×C8—341no—
209C22×C8—341no—
210C22×C8—682no—
211C22×C8—682no—
212C4×D4—171no—
213C4×D4—171no—
214C4×D4—171no—
215C4×D4—341no—
216C4×D4—341no—
217C4×D4C4×D1711yescharacteristic
218C2×C4⋊C4—171no—
219C2×C22⋊C4—341no—
220C2×C42—171no—
221C2×C16—21no—
222C2×C16—21no—
223C2×C16—341no—
224C2×C16—341no—
225C4⋊C8—171no—
226C4⋊C8—341no—
227C4⋊C8C4×D1711yescharacteristic
228C22⋊C8—21no—
229C22⋊C8—341no—
230C22⋊C8—341no—
231C22⋊C8—341no—
232C4×C8—171no—
233C4×C8—171no—
234C4×C8—171no—
235C4×C8C22×D1711yescharacteristic
236C17#1163111yescharacteristic, complemented, Sylow
237C24—341no—
238C2×D4—171no—
239C2×D4—341no—
240C2×D4—342no—
241C2×D4—342no—
242C2×D4C8×D1711yescharacteristic
243C22×C4—21no—
244C22×C4—171no—
245C22×C4—171no—
246C22×C4—171no—
247C22×C4—341no—
248C22×C4—341no—
249C22×C4—341no—
250C22×C4—341no—
251C22×C4—682no—
252C22×C4—682no—
253C2×C8—21no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—171no—
257C2×C8—171no—
258C2×C8—341no—
259C2×C8—341no—
260C2×C8—341no—
261C2×C8—681no—
262C2×C8—682no—
263C2×C8—682no—
264C2×C8—682no—
265C2×C8—681no—
266C2×C8—681no—
267C2×C8D4×D1711yescharacteristic
268C2×C8D4×D1711yescharacteristic
269C4⋊C4—171no—
270C4⋊C4—341no—
271C4⋊C4C8×D1711yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—341no—
274C22⋊C4—341no—
275C22⋊C4—341no—
276C42—171no—
277C42—171no—
278C42—171no—
279C42C2×C4×D1711yescharacteristic
280C16—41no—
281C16—41no—
282C16—681no—
283C16—681no—
284C23—21no—
285C23—171no—
286C23—344no—
287C23—341no—
288C23—682no—
289C23—682no—
290D4—21no—
291D4—172no—
292D4—344no—
293D4—341no—
294D4#1058746912yes—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—171no—
299C2×C4—171no—
300C2×C4—171no—
301C2×C4—342no—
302C2×C4—341no—
303C2×C4—341no—
304C2×C4—341no—
305C2×C4—341no—
306C2×C4—341no—
307C2×C4—682no—
308C2×C4—682no—
309C2×C4—682no—
310C2×C4—681no—
311C2×C4—681no—
312C2×C4C22⋊C4×D1711yescharacteristic
313C2×C4C2×C8×D1711yescharacteristic
314C2×C4M16×D1711yescharacteristic
315C8—21no—
316C8—41no—
317C8—341no—
318C8—341no—
319C8—681no—
320C8#1058759711yescharacteristic
321C8#1058760011yescharacteristic
322C22—22no—
323C22—41no—
324C22—41no—
325C22—172no—
326C22—341no—
327C22—341no—
328C22—342no—
329C22—688no—
330C22—681no—
331C22—681no—
332C22C22⋊C8×D1711yescharacteristic
333C4—21no—
334C4—41no—
335C4—341no—
336C4—341no—
337C4—341no—
338C4—681no—
339C4#1176281211yescharacteristic
340C4#1176282411yescharacteristic
341C4M32×D1711yescharacteristic
342C4C2×#1058746911yescharacteristic
343C2—42no—
344C2—342no—
345C2—682no—
346C2#1452717311yescharacteristic
347C2#1453039311yescharacteristic
348C2D17×#35011yescharacteristic
subgroupG/H
centerC2×C8D4×D17
commutatorC2×C4×C17C22×C8
FrattiniC4×C8C22×D17
FittingC17×D4⋊C16C2
socleC22×C17C2×C22⋊C8
prime radicalC2×D4×D17C8
cosocleC4×C8×C17C23
hypercenterD4⋊C16D17
hypocenterC17#11631
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ D4⋊C16

Complements

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

NH ≅ G/Ntype
2. #14530586C2semidirect
3. #14530581C2semidirect
4. #14526740C2semidirect
5. D4⋊#63214C2semidirect
6. #14526738C2semidirect
7. C17×D4⋊C16C2semidirect
18. C4⋊#63214C22semidirect
23. C4×#63214C22semidirect
25. C17×C4⋊C16C22semidirect
26. C4×C16×C17C22semidirect
154. D4⋊C16D17semidirect
189. C4⋊C16C2×D17semidirect
194. C4×C16C2×D17semidirect
236. C17#11631semidirect

Maximal subgroups

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

subgroupindex
C8×D4×D172
#145305862
#145305812
#145267402
D4⋊#632142
#145267382
C17×D4⋊C162
#1163117