Finite Group Databasebeta

← #16944664

Subgroups — #16944664

Order 4352.

470 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 87 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#14532068C211yesmaximal, characteristic
2C4×#10587505C211yesmaximal, characteristic
3#14526806C212yesmaximal, complemented
4#14526785C212yesmaximal, complemented
5C17×#1459C211yesmaximal, characteristic
6C2×C4×Dic34C411yescharacteristic, complemented
7C2×#10587505—21no—
8#11762747—21no—
9#11762734C411yescharacteristic, complemented
10#11762734C2211yescharacteristic
11#11762723—21no—
12#11762721C411yescharacteristic, complemented
13#11762721C2211yescharacteristic
14C4×C22⋊Dic17—21no—
15C4×C22⋊Dic17—21no—
16C4×C22⋊Dic17—21no—
17#11762655C411yescharacteristic, complemented
18#11762576C2212yes—
19C2×C4×D4×C17C2211yescharacteristic
20C2×C17×C22⋊C8—21no—
21C17×#324—21no—
22C17×#323C2212yes—
23C22×D4×C17D411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C22×Dic34C2×C411yescharacteristic
27C22×C8×C17—41no—
28C4×D4×C17—41no—
29C4×D4×C17—41no—
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C22⋊C4×C17C2×C411yescharacteristic
32C2×C22⋊C4×C17C2311yescharacteristic
33C2×C42×C17C2×C411yescharacteristic
34C2×C22⋊Dic17—22no—
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17—21no—
39C2×C4⋊Dic17C2×C411yescharacteristic
40C2×#63225—21no—
41C2×C4×Dic17—21no—
42C2×C4×Dic17—21no—
43C2×C4×Dic17—41no—
44C4×Dic34—41no—
45C4×Dic34—41no—
46C17×C22⋊C8—22no—
47C17×C22⋊C8—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—42no—
67C22×C4×C17—42no—
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—
78C2×Dic34—41no—
79C2×Dic34—42no—
80C2×C8×C17—42no—
81C2×C8×C17—82no—
82C4⋊C4×C17—41no—
83C22⋊C4×C17—41no—
84C22⋊C4×C17—41no—
85C42×C17—21no—
86C42×C17—21no—
87C22⋊Dic17—24no—
88C22⋊Dic17—42no—
89C22⋊Dic17—42no—
90C22⋊Dic17—42no—
91C22⋊Dic17—42no—
92C22⋊Dic17—42no—
93C4⋊Dic17—41no—
94#63225—42no—
95C4×Dic17—42no—
96C4×Dic17—41no—
97C4×Dic17—41no—
98C4×Dic17—82no—
99#11728—171nomaximal, Sylow
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—41no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17#10412yes—
109C23×C17C2×C22⋊C411yescharacteristic
110C23×C17#13512yes—
111D4×C17—44no—
112C2×C4×C17—22no—
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—42no—
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#9911yescharacteristic
127C2×C4×C17#9911yescharacteristic
128C2×Dic17—22no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—44no—
132C2×Dic17—41no—
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—82no—
142C2×Dic17—82no—
143Dic34—42no—
144Dic34—42no—
145C8×C17—82no—
146#2398—171no—
147C4×#99—171no—
148#1459D1711yescharacteristic
149#1351—172no—
150#1344—172no—
151C22×C17—21no—
152C22×C17—21no—
153C22×C17—22no—
154C22×C17—22no—
155C22×C17—42no—
156C22×C17—42no—
157C22×C17—41no—
158C22×C17—41no—
159C22×C17—41no—
160C22×C17—41no—
161C22×C17—81no—
162C22×C17—81no—
163C22×C17C2×#9911yescharacteristic
164C22×C17#41611yescharacteristic
165C22×C17C2×#10411yescharacteristic
166C4×C17—21no—
167C4×C17—41no—
168C4×C17—41no—
169C4×C17—41no—
170C4×C17—41no—
171C4×C17#35412yes—
172Dic17—42no—
173Dic17—81no—
174Dic17—81no—
175Dic17—84no—
176Dic17—81no—
177C2×C4×Q8—171no—
178C2×C4×D4C2×D1711yescharacteristic
179C2×#99—341no—
180C2×C22⋊C8—21no—
181#400—341no—
182#397—171no—
183#397—171no—
184#394—341no—
185#393—171no—
186#393—171no—
187C4×C22⋊C4—341no—
188C4×C22⋊C4—341no—
189C4×C22⋊C4—341no—
190#376—171no—
191#342—172no—
192#324—21no—
193#323C2×D1712yes—
194C2×C17—21no—
195C2×C17—21no—
196C2×C17—42no—
197C2×C17—42no—
198C2×C17#150111yescharacteristic
199C2×C17#212011yescharacteristic
200C2×C17C2×#35411yescharacteristic
201C22×Q8—171no—
202C22×D4D6811yescharacteristic
203C23×C4D6811yescharacteristic
204C23×C4C22⋊D1711yescharacteristic
205C22×C8—41no—
206C4×Q8—681no—
207C4×Q8—681no—
208C4×D4—41no—
209C4×D4—41no—
210C2×C4⋊C4—171no—
211C2×C4⋊C4—341no—
212C2×C4⋊C4C22⋊D1711yescharacteristic
213C2×C22⋊C4—342no—
214C2×C22⋊C4—341no—
215C2×C22⋊C4—341no—
216C2×C22⋊C4—341no—
217C2×C22⋊C4—341no—
218C2×C22⋊C4C4×D1711yescharacteristic
219C2×C22⋊C4C22×D1711yescharacteristic
220C2×C42—341no—
221C2×C42—341no—
222C2×C42—681no—
223C2×C42C4×D1711yescharacteristic
224#99—344no—
225C22⋊C8—22no—
226C22⋊C8—41no—
227#95—171no—
228#95—171no—
229#95—341no—
230#95—341no—
231#95—341no—
232#95—341no—
233#95—341no—
234#95—681no—
235C17#1172811yescharacteristic, complemented, Sylow
236C24#6322711yescharacteristic
237C24C2×D6811yescharacteristic
238C2×Q8—681no—
239C2×Q8—682no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—341no—
250C22×C4—341no—
251C22×C4—341no—
252C22×C4—341no—
253C22×C4—682no—
254C22×C4#6322711yescharacteristic
255C22×C4#6322711yescharacteristic
256C22×C4#6322711yescharacteristic
257C22×C4C2×C4×D1711yescharacteristic
258C22×C4C2×C22⋊D1711yescharacteristic
259C2×C8—42no—
260C2×C8—82no—
261C4⋊C4—41no—
262C4⋊C4—681no—
263C4⋊C4—682no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—344no—
267C22⋊C4—682no—
268C22⋊C4—682no—
269C22⋊C4—682no—
270C22⋊C4—682no—
271C22⋊C4—682no—
272C42—21no—
273C42—21no—
274C42—682no—
275C42—681no—
276C42—681no—
277C42—1362no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23#1058749612yes—
287C23#1058759012yes—
288C23C2×#6322711yescharacteristic
289Q8—682no—
290Q8—682no—
291D4—44no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—342no—
307C2×C4—681no—
308C2×C4—681no—
309C2×C4—681no—
310C2×C4—681no—
311C2×C4—684no—
312C2×C4—681no—
313C2×C4—681no—
314C2×C4—681no—
315C2×C4—681no—
316C2×C4—681no—
317C2×C4—681no—
318C2×C4—681no—
319C2×C4—1362no—
320C2×C4—1362no—
321C2×C4#1058747711yescharacteristic
322C2×C4#1058747711yescharacteristic
323C8—82no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—22no—
328C22—42no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—81no—
335C22—81no—
336C22C2×#1058747711yescharacteristic
337C22#1176280611yescharacteristic
338C22C2×#1058749611yescharacteristic
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—682no—
345C4—1361no—
346C4—1361no—
347C4—1364no—
348C4—1361no—
349C4#1176260312yes—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—42no—
354C2#1452727611yescharacteristic
355C2#1453042611yescharacteristic
356C2C2×#1176260311yescharacteristic
subgroupG/H
centerC2×C4#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1459C2
socleC22×C17C2×#99
prime radicalC22×D4×C17D4
cosocleC2×C22⋊C4×C17C23
hypercenter#1459D17
hypocenterC17#11728
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #14526806C2semidirect
4. #14526785C2semidirect
6. C2×C4×Dic34C4semidirect
9. #11762734C4semidirect
12. #11762721C4semidirect
17. #11762655C4semidirect
235. C17#11728semidirect

Maximal subgroups

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

subgroupindex
#145320682
C4×#105875052
#145268062
#145267852
C17×#14592
#1172817