Finite Group Databasebeta

← #16944951

Subgroups — #16944951

Order 4352.

462 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 83 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#14533960C211yesmaximal, characteristic
2C4×#10587505C211yesmaximal, characteristic
3#14526809C212yesmaximal, complemented
4#14526806C212yesmaximal, complemented
5C17×#1466C211yesmaximal, characteristic
6C2×#10587610C411yescharacteristic, complemented
7C2×#10587505—21no—
8#11762748C411yescharacteristic, complemented
9#11762745C2211yescharacteristic
10#11762729C411yescharacteristic, complemented
11#11762721C2211yescharacteristic
12#11762693—21no—
13#11762689—21no—
14#11762682—21no—
15#11762667—21no—
16C4×C22⋊Dic17—21no—
17C2×#10587502C411yescharacteristic, complemented
18#11762576C2212yes—
19C2×C4×D4×C17C2211yescharacteristic
20C17×#432—21no—
21C17×#323—21no—
22C17×#323C2212yes—
23C22×D4×C17D411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C23×Dic17—21no—
27C22×Dic34C2×C411yescharacteristic
28C4×D4×C17—41no—
29C4×D4×C17—41no—
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C22⋊C4×C17D411yescharacteristic
32C2×C22⋊C4×C17C2311yescharacteristic
33C2×C42×C17D411yescharacteristic
34C2×C22⋊Dic17—22no—
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38C2×C4⋊Dic17C2×C411yescharacteristic
39#10587610—41no—
40#10587610—41no—
41C2×#63225—21no—
42C2×#63225—21no—
43C2×#63225—21no—
44C2×C4×Dic17—41no—
45C17×C4⋊C8—41no—
46C17×C22⋊C8—22no—
47C17×#97—41no—
48#10587505—24no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—41no—
55#10587502C2×C411yescharacteristic
56#10587502C2×C411yescharacteristic
57C24×C17C22⋊C411yescharacteristic
58C24×C17C2×D411yescharacteristic
59C2×D4×C17—22no—
60C2×D4×C17—22no—
61C2×D4×C17—41no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—81no—
67C22×C4×C17—81no—
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22×C411yescharacteristic
72C22×C4×C17C2×D411yescharacteristic
73C22×Dic17—21no—
74C22×Dic17—21no—
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17—42no—
78C22×Dic17—42no—
79C22×Dic17—42no—
80C22×Dic17—81no—
81C2×Dic34—41no—
82C2×Dic34—81no—
83C2×C8×C17—42no—
84C4⋊C4×C17—41no—
85C22⋊C4×C17—41no—
86C22⋊C4×C17—41no—
87C42×C17—21no—
88C42×C17—21no—
89C22⋊Dic17—24no—
90C22⋊Dic17—42no—
91C22⋊Dic17—42no—
92C22⋊Dic17—42no—
93C22⋊Dic17—81no—
94C4⋊Dic17—41no—
95#63225—42no—
96#63225—41no—
97#63225—41no—
98#63225—81no—
99C4×Dic17—82no—
100#11789—171nomaximal, Sylow
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17#10412yes—
110C23×C17C2×C22⋊C411yescharacteristic
111C23×C17#13712yes—
112D4×C17—44no—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—41no—
120C2×C4×C17—42no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—81no—
125C2×C4×C17—81no—
126C2×C4×C17—81no—
127C2×C4×C17#9911yescharacteristic
128C2×C4×C17#9911yescharacteristic
129C2×Dic17—22no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—44no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—84no—
143C2×Dic17—82no—
144C2×Dic17—82no—
145Dic34—82no—
146C8×C17—82no—
147#2564—171no—
148C4×#99—171no—
149#1466D1711yescharacteristic
150#1352—172no—
151#1351—172no—
152C22×C17—21no—
153C22×C17—21no—
154C22×C17—22no—
155C22×C17—22no—
156C22×C17—42no—
157C22×C17—42no—
158C22×C17—42no—
159C22×C17—41no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17—81no—
164C22×C17C2×#9911yescharacteristic
165C22×C17#41911yescharacteristic
166C22×C17C2×#10411yescharacteristic
167C4×C17—21no—
168C4×C17—21no—
169C4×C17—41no—
170C4×C17—41no—
171C4×C17—41no—
172C4×C17—41no—
173Dic17—42no—
174Dic17—81no—
175Dic17—84no—
176Dic17—81no—
177Dic17—81no—
178C2×C22⋊Q8—171no—
179C2×C4×D4C2×D1711yescharacteristic
180#432—21no—
181C2×#99—341no—
182#400—171no—
183#399—171no—
184#395—171no—
185#393—171no—
186#387—341no—
187#386—341no—
188#385—341no—
189#380—341no—
190C4×C22⋊C4—341no—
191C2×#95—171no—
192#342—172no—
193#323—21no—
194#323C2×D1712yes—
195C2×C17—21no—
196C2×C17—21no—
197C2×C17—42no—
198C2×C17—42no—
199C2×C17#150811yescharacteristic
200C2×C17#212111yescharacteristic
201C2×C17#212611yescharacteristic
202C22×Q8—171no—
203C22×D4D6811yescharacteristic
204C23×C4—341no—
205C23×C4C4×D1711yescharacteristic
206C23×C4D6811yescharacteristic
207C22⋊Q8—681no—
208C22⋊Q8—681no—
209C4×D4—41no—
210C4×D4—41no—
211C2×C4⋊C4—171no—
212C2×C4⋊C4—341no—
213C2×C4⋊C4—341no—
214C2×C4⋊C4—341no—
215C2×C4⋊C4C4×D1711yescharacteristic
216C2×C22⋊C4—342no—
217C2×C22⋊C4—341no—
218C2×C22⋊C4—341no—
219C2×C22⋊C4—341no—
220C2×C22⋊C4C22⋊D1711yescharacteristic
221C2×C22⋊C4C22×D1711yescharacteristic
222C2×C42—681no—
223C2×C42C22⋊D1711yescharacteristic
224C4⋊C8—41no—
225#99—344no—
226C22⋊C8—22no—
227#97—41no—
228#95—171no—
229#95—171no—
230#95—341no—
231#95—341no—
232#95—341no—
233#95—341no—
234#95—341no—
235#95—681no—
236C17#1178911yescharacteristic, complemented, Sylow
237C24#6322711yescharacteristic
238C24C2×D6811yescharacteristic
239C2×Q8—681no—
240C2×Q8—1361no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—341no—
251C22×C4—341no—
252C22×C4—341no—
253C22×C4—341no—
254C22×C4—682no—
255C22×C4—682no—
256C22×C4—682no—
257C22×C4—1361no—
258C22×C4#6322711yescharacteristic
259C22×C4#6322711yescharacteristic
260C22×C4#6322711yescharacteristic
261C22×C4C2×C4×D1711yescharacteristic
262C22×C4C2×C22⋊D1711yescharacteristic
263C2×C8—42no—
264C4⋊C4—41no—
265C4⋊C4—681no—
266C4⋊C4—682no—
267C4⋊C4—681no—
268C4⋊C4—681no—
269C4⋊C4—1361no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—344no—
273C22⋊C4—682no—
274C22⋊C4—682no—
275C22⋊C4—682no—
276C22⋊C4—1361no—
277C42—21no—
278C42—21no—
279C42—1362no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23#1058749612yes—
289C23#1058759512yes—
290C23C2×#6322711yescharacteristic
291Q8—1362no—
292D4—44no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—342no—
308C2×C4—681no—
309C2×C4—681no—
310C2×C4—684no—
311C2×C4—681no—
312C2×C4—681no—
313C2×C4—681no—
314C2×C4—681no—
315C2×C4—681no—
316C2×C4—681no—
317C2×C4—681no—
318C2×C4—681no—
319C2×C4—681no—
320C2×C4—1364no—
321C2×C4—1362no—
322C2×C4—1362no—
323C2×C4#1058747711yescharacteristic
324C2×C4#1058747711yescharacteristic
325C8—82no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22C2×#1058747711yescharacteristic
339C22#1176281911yescharacteristic
340C22C2×#1058749611yescharacteristic
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—682no—
348C4—1361no—
349C4—1364no—
350C4—1361no—
351C4—1361no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—42no—
356C2#1452730511yescharacteristic
357C2#1453043111yescharacteristic
358C2#1453044711yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1466C2
socleC22×C17C2×#99
prime radicalC22×D4×C17D4
cosocleC2×C22⋊C4×C17C23
hypercenter#1466D17
hypocenterC17#11789
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #14526809C2semidirect
4. #14526806C2semidirect
6. C2×#10587610C4semidirect
8. #11762748C4semidirect
10. #11762729C4semidirect
17. C2×#10587502C4semidirect
236. C17#11789semidirect

Maximal subgroups

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

subgroupindex
#145339602
C4×#105875052
#145268092
#145268062
C17×#14662
#1178917