Finite Group Databasebeta

← #16945366

Subgroups — #16945366

Order 4352.

440 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 103 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#14528780C211yesmaximal, characteristic, complemented
2#14527108C211yesmaximal, characteristic, complemented
3#14526790C212yesmaximal, complemented
4#14526787C212yesmaximal
5C17×#2536C211yesmaximal, characteristic
6#11762862—21no—
7#11762833—21no—
8C2×#10587507—21no—
9#11762578C2212yes—
10#11762535—21no—
11#11762535C2212yes—
12C2×C17×C22⋊Q8—21no—
13C2×C4×Q8×C17C2211yescharacteristic
14C2×C4×D4×C17C411yescharacteristic
15C17×#398C411yescharacteristic
16C17×#398C2211yescharacteristic
17C17×#394C411yescharacteristic
18C17×#394C2211yescharacteristic
19C17×#388—21no—
20C17×#388—21no—
21C17×#382C411yescharacteristic
22C17×#380—21no—
23C22×Q8×C17D411yescharacteristic
24C22×D4×C17C2×C411yescharacteristic
25C23×C4×C17—21no—
26C17×C22⋊Q8—42no—
27C17×C22⋊Q8—42no—
28C4×Q8×C17—41no—
29C4×Q8×C17—41no—
30C4×D4×C17—41no—
31C4×D4×C17—41no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17C2×C411yescharacteristic
36C2×C4⋊C4×C17C2×C411yescharacteristic
37C2×C4⋊C4×C17D411yescharacteristic
38C2×C4⋊C4×C17C2311yescharacteristic
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17—21no—
43C2×C22⋊C4×C17—21no—
44C2×C42×C17C2×C411yescharacteristic
45C2×C42×C17D411yescharacteristic
46C2×C42×C17D411yescharacteristic
47C2×#63223—22no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95C2×C411yescharacteristic
52C17×#95C2×C411yescharacteristic
53#10587507—42no—
54C22⋊#3622—22no—
55C4⋊#3622—41no—
56C4⋊#3622—41no—
57C4⋊#3622—41no—
58C4×#3622—41no—
59C24×C17—21no—
60C2×Q8×C17—41no—
61C2×Q8×C17—41no—
62C2×Q8×C17D812yes—
63C2×Q8×C17SD1612yes—
64C2×D4×C17—41no—
65C2×D4×C17—42no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—42no—
70C22×C4×C17—42no—
71C22×C4×C17—42no—
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C22⋊C411yescharacteristic
76C22×C4×C17C22×C411yescharacteristic
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17—42no—
84C4⋊C4×C17—42no—
85C4⋊C4×C17—41no—
86C4⋊C4×C17—41no—
87C22⋊C4×C17—42no—
88C22⋊C4×C17—42no—
89C22⋊C4×C17—41no—
90C22⋊C4×C17—41no—
91C22⋊C4×C17—42no—
92C22⋊C4×C17—41no—
93C22⋊C4×C17—41no—
94C42×C17—21no—
95C42×C17—21no—
96C42×C17—21no—
97C42×C17—21no—
98C42×C17—21no—
99C42×C17—21no—
100#63223—42no—
101#63223—42no—
102C2×#3622—42no—
103C2×#3622—42no—
104#11879—171nomaximal, Sylow
105C23×C17—22no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17—41no—
110C23×C17—41no—
111C23×C17—41no—
112C23×C17C2×C22⋊C411yescharacteristic
113Q8×C17—42no—
114Q8×C17—42no—
115D4×C17—42no—
116D4×C17—42no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—84no—
140C2×C4×C17#9911yescharacteristic
141C2×C4×C17#9911yescharacteristic
142C2×C4×C17#10212yes—
143C2×C4×C17#10212yes—
144C2×C4×C17C2×D811yescharacteristic
145C2×C4×C17C2×SD1611yescharacteristic
146#3622—82no—
147#3622—82no—
148#2536D1711yescharacteristic
149#1801—171no—
150#1461—171no—
151#1346—172no—
152#1345—172no—
153C22×C17—21no—
154C22×C17—21no—
155C22×C17—42no—
156C22×C17—42no—
157C22×C17—42no—
158C22×C17—81no—
159C22×C17—81no—
160C22×C17—81no—
161C22×C17—81no—
162C22×C17C2×#9911yescharacteristic
163C22×C17C2×#10211yescharacteristic
164C22×C17#42111yescharacteristic
165C4×C17—21no—
166C4×C17—21no—
167C4×C17—21no—
168C4×C17—22no—
169C4×C17—22no—
170C4×C17—21no—
171C4×C17—41no—
172C4×C17—41no—
173C4×C17—41no—
174C4×C17—81no—
175C4×C17—81no—
176C4×C17—81no—
177C2×C22⋊Q8—21no—
178C2×C4×Q8C2×D1711yescharacteristic
179C2×C4×D4Dic1711yescharacteristic
180#431—341no—
181#423—341no—
182C2×#101—341no—
183#398Dic1711yescharacteristic
184#398C2×D1711yescharacteristic
185#394Dic1711yescharacteristic
186#394C2×D1711yescharacteristic
187#388—21no—
188#388—21no—
189#382Dic1711yescharacteristic
190#380—21no—
191#343—172no—
192#324—172no—
193#324—341no—
194C2×C17—21no—
195C2×C17—21no—
196C2×C17—82no—
197C2×C17#151911yescharacteristic
198C2×C17#212011yescharacteristic
199C2×C17#213311yescharacteristic
200C22×Q8C22⋊D1711yescharacteristic
201C22×D4C2×Dic1711yescharacteristic
202C23×C4—21no—
203C2×M16—342no—
204C22⋊Q8—42no—
205C22⋊Q8—42no—
206C4×Q8—41no—
207C4×Q8—41no—
208C4×D4—41no—
209C4×D4—41no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×Dic1711yescharacteristic
214C2×C4⋊C4C2×Dic1711yescharacteristic
215C2×C4⋊C4C22⋊D1711yescharacteristic
216C2×C4⋊C4C22×D1711yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C42C2×Dic1711yescharacteristic
223C2×C42C22⋊D1711yescharacteristic
224C2×C42C22⋊D1711yescharacteristic
225C4⋊C8—681no—
226C4⋊C8—681no—
227C4⋊C8—681no—
228#101—682no—
229C22⋊C8—342no—
230C4×C8—681no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95C2×Dic1711yescharacteristic
235#95C2×Dic1711yescharacteristic
236C17#1187911yescharacteristic, complemented, Sylow
237C24—21no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8#6322812yes—
241C2×Q8#6322912yes—
242C2×D4—41no—
243C2×D4—42no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4C22⋊Dic1711yescharacteristic
251C22×C4C22⋊Dic1711yescharacteristic
252C22×C4C22⋊Dic1711yescharacteristic
253C22×C4C22⋊Dic1711yescharacteristic
254C22×C4C22×Dic1711yescharacteristic
255C22×C4C2×C22⋊D1711yescharacteristic
256C22×C4C2×C22⋊D1711yescharacteristic
257M16—682no—
258M16—682no—
259C2×C8—682no—
260C2×C8—682no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—21no—
281C42—21no—
282C23—22no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×C22⋊Dic1711yescharacteristic
290Q8—42no—
291Q8—42no—
292D4—42no—
293D4—42no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—84no—
317C2×C4#1058750312yes—
318C2×C4#1058750312yes—
319C2×C4#1058750511yescharacteristic
320C2×C4#1058750511yescharacteristic
321C2×C4C2×#6322811yescharacteristic
322C2×C4C2×#6322911yescharacteristic
323C8—1362no—
324C8—1362no—
325C22—21no—
326C22—21no—
327C22—42no—
328C22—42no—
329C22—42no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22C2×#1058750511yescharacteristic
335C22C2×#1058750311yescharacteristic
336C22#1176282611yescharacteristic
337C4—21no—
338C4—22no—
339C4—22no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—81no—
349C2—21no—
350C2—21no—
351C2—82no—
352C2#1452735211yescharacteristic
353C2#1453042511yescharacteristic
354C2#1453047311yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2536C2
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2536D17
hypocenterC17#11879
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2536

Complements

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

NH ≅ G/Ntype
1. #14528780C2semidirect
2. #14527108C2semidirect
3. #14526790C2semidirect
236. C17#11879semidirect

Maximal subgroups

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

subgroupindex
#145287802
#145271082
#145267902
#145267872
C17×#25362
#1187917