Finite Group Databasebeta

← #16945020

Subgroups — #16945020

Order 4352.

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

normal subgroups only

This group has 448 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#14528864C211yesmaximal, characteristic, complemented
2#14527114C211yesmaximal, characteristic, complemented
3#14526790C212yesmaximal, complemented
4#14526787C212yesmaximal, complemented
5C17×#2618C211yesmaximal, characteristic
6#11762773—21no—
7#11762773—21no—
8#11762578—21no—
9#11762578C2212yes—
10#11762535—21no—
11#11762535C2212yes—
12C2×C17×#123—21no—
13C2×C17×#121C411yescharacteristic
14C22×C4⋊C4×C17C2211yescharacteristic
15C17×#398C411yescharacteristic
16C17×#398C2211yescharacteristic
17C17×#396—21no—
18C17×#396—21no—
19C17×#394C411yescharacteristic
20C17×#394C2211yescharacteristic
21C17×#386—21no—
22C17×#380C411yescharacteristic
23C22×D4×C17—21no—
24C22×D4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C23×C4×C17D411yescharacteristic
28C17×#123—44no—
29C17×#121—41no—
30C17×#121—41no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—41no—
35C2×C4⋊C4×C17—41no—
36C2×C4⋊C4×C17C2×C411yescharacteristic
37C2×C4⋊C4×C17C2×C411yescharacteristic
38C2×C4⋊C4×C17D411yescharacteristic
39C2×C4⋊C4×C17D411yescharacteristic
40C2×C4⋊C4×C17C2311yescharacteristic
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17—21no—
43C2×C22⋊C4×C17—21no—
44C2×C22⋊C4×C17—21no—
45C2×C22⋊C4×C17—21no—
46C2×C22⋊C4×C17—21no—
47C2×#63223—22no—
48C2×#63223—41no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95C2×C411yescharacteristic
52C17×#95C2×C411yescharacteristic
53C22⋊#3622—22no—
54C22⋊#3622—41no—
55C22⋊#3622—41no—
56C22⋊#3622—41no—
57C24×C17—21no—
58C24×C17C22⋊C411yescharacteristic
59C2×D4×C17—41no—
60C2×D4×C17—42no—
61C2×D4×C17—42no—
62C2×D4×C17—41no—
63C2×D4×C17—41no—
64C2×D4×C17—81no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—22no—
72C22×C4×C17—21no—
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—41no—
76C22×C4×C17—81no—
77C22×C4×C17—81no—
78C22×C4×C17C22⋊C411yescharacteristic
79C22×C4×C17C22⋊C411yescharacteristic
80C22×C4×C17C22⋊C411yescharacteristic
81C22×C4×C17C22×C411yescharacteristic
82C22×C4×C17C2×D411yescharacteristic
83C22×C4×C17C2×D411yescharacteristic
84C4⋊C4×C17—41no—
85C4⋊C4×C17—41no—
86C4⋊C4×C17—41no—
87C4⋊C4×C17—41no—
88C4⋊C4×C17—41no—
89C4⋊C4×C17—42no—
90C4⋊C4×C17—42no—
91C4⋊C4×C17—81no—
92C22⋊C4×C17—42no—
93C22⋊C4×C17—42no—
94C22⋊C4×C17—42no—
95C22⋊C4×C17—42no—
96C22⋊C4×C17—81no—
97C22⋊C4×C17—81no—
98#63223—42no—
99#63223—42no—
100#63223—82no—
101C2×#3622—42no—
102C2×#3622—42no—
103#11805—171nomaximal, Sylow
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17—41no—
110C23×C17—41no—
111C23×C17—41no—
112C23×C17—41no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17#9911yescharacteristic
116C23×C17#9911yescharacteristic
117C23×C17C2×C22⋊C411yescharacteristic
118D4×C17—82no—
119D4×C17—82no—
120D4×C17—82no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—42no—
131C2×C4×C17—42no—
132C2×C4×C17—42no—
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—41no—
140C2×C4×C17—41no—
141C2×C4×C17—41no—
142C2×C4×C17—41no—
143C2×C4×C17—41no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17—81no—
147C2×C4×C17—81no—
148C2×C4×C17—81no—
149C2×C4×C17AGL(1,ℤ/8)12yes—
150#3622—82no—
151#3622—82no—
152#2618D1711yescharacteristic
153#1821—171no—
154#1463—171no—
155#1346—172no—
156#1345—172no—
157C22×C17—21no—
158C22×C17—21no—
159C22×C17—21no—
160C22×C17—21no—
161C22×C17—21no—
162C22×C17—21no—
163C22×C17—21no—
164C22×C17—21no—
165C22×C17—42no—
166C22×C17—42no—
167C22×C17—81no—
168C22×C17—81no—
169C22×C17—81no—
170C22×C17—81no—
171C22×C17—81no—
172C22×C17—81no—
173C22×C17—81no—
174C22×C17C2×#9911yescharacteristic
175C22×C17#41811yescharacteristic
176C22×C17#42111yescharacteristic
177C4×C17—22no—
178C4×C17—41no—
179C4×C17—41no—
180C4×C17—41no—
181C4×C17—41no—
182C4×C17—41no—
183C4×C17—81no—
184C4×C17—81no—
185C4×C17—81no—
186C2×#123—21no—
187C2×#121Dic1711yescharacteristic
188C22×C4⋊C4C2×D1711yescharacteristic
189#407—341no—
190#407—341no—
191#398Dic1711yescharacteristic
192#398C2×D1711yescharacteristic
193#396—21no—
194#396—21no—
195#394Dic1711yescharacteristic
196#394C2×D1711yescharacteristic
197#386—21no—
198#380Dic1711yescharacteristic
199#343—172no—
200#343—341no—
201#324—172no—
202#324—341no—
203C2×C17—21no—
204C2×C17—21no—
205C2×C17—41no—
206C2×C17—41no—
207C2×C17—161no—
208C2×C17#151011yescharacteristic
209C2×C17#212111yescharacteristic
210C2×C17#213311yescharacteristic
211C22×D4—21no—
212C22×D4C2×Dic1711yescharacteristic
213C23×C4C2×Dic1711yescharacteristic
214C23×C4C22⋊D1711yescharacteristic
215C23×C4C22⋊D1711yescharacteristic
216C2×M16—342no—
217C2×M16—681no—
218#123—44no—
219#121—41no—
220#121—41no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—41no—
225C2×C4⋊C4—41no—
226C2×C4⋊C4C2×Dic1711yescharacteristic
227C2×C4⋊C4C2×Dic1711yescharacteristic
228C2×C4⋊C4C22⋊D1711yescharacteristic
229C2×C4⋊C4C22⋊D1711yescharacteristic
230C2×C4⋊C4C22×D1711yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C22⋊C8—342no—
238C22⋊C8—681no—
239C22⋊C8—681no—
240C22⋊C8—681no—
241#95—21no—
242#95—21no—
243#95C2×Dic1711yescharacteristic
244#95C2×Dic1711yescharacteristic
245C17#1180511yescharacteristic, complemented, Sylow
246C24—21no—
247C24C22⋊Dic1711yescharacteristic
248C2×D4—41no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—81no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—81no—
266C22×C4—81no—
267C22×C4C22⋊Dic1711yescharacteristic
268C22×C4C22⋊Dic1711yescharacteristic
269C22×C4C22⋊Dic1711yescharacteristic
270C22×C4C22×Dic1711yescharacteristic
271C22×C4C2×C22⋊D1711yescharacteristic
272C22×C4C2×C22⋊D1711yescharacteristic
273M16—682no—
274M16—682no—
275M16—1362no—
276C2×C8—682no—
277C2×C8—682no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—81no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23#1058750511yescharacteristic
304C23#1058750511yescharacteristic
305C23C2×C22⋊Dic1711yescharacteristic
306D4—82no—
307D4—82no—
308D4—82no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#1058761812yes—
338C8—1362no—
339C8—1362no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—42no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C2×#1058750511yescharacteristic
358C22#1176281411yescharacteristic
359C22#1176282611yescharacteristic
360C4—22no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—81no—
367C4—81no—
368C4—81no—
369C2—21no—
370C2—21no—
371C2—41no—
372C2—41no—
373C2—161no—
374C2#1452731311yescharacteristic
375C2#1453043011yescharacteristic
376C2#1453047311yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2618C2
socleC22×C17C2×#99
prime radicalC2×C17×#121C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2618D17
hypocenterC17#11805
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2618

Complements

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

NH ≅ G/Ntype
1. #14528864C2semidirect
2. #14527114C2semidirect
3. #14526790C2semidirect
4. #14526787C2semidirect
245. C17#11805semidirect

Maximal subgroups

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

subgroupindex
#145288642
#145271142
#145267902
#145267872
C17×#26182
#1180517