Finite Group Databasebeta

← #16944708

Subgroups — #16944708

Order 4352.

470 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#10587504C211yesmaximal, characteristic, complemented
2#14527102C211yesmaximal, characteristic, complemented
3#14526811C212yesmaximal, complemented
4#14526787C212yesmaximal, complemented
5C17×#2635C211yesmaximal, characteristic
6C2×#10587504—21no—
7C2×C22⋊#3622—21no—
8C4×#63223—21no—
9#11762578C2212yes—
10#11762535C2212yes—
11#11762533—21no—
12C2×C17×#121C411yescharacteristic
13C2×C4×D4×C17C2211yescharacteristic
14C17×#400C2211yescharacteristic
15C17×#399C411yescharacteristic
16C17×#394—21no—
17C17×#394C2211yescharacteristic
18C17×#392—21no—
19C17×#392C411yescharacteristic
20C17×#388—21no—
21C17×#386—21no—
22C17×#381C411yescharacteristic
23C22×D4×C17—21no—
24C22×D4×C17—21no—
25C22×D4×C17C2×C411yescharacteristic
26C22×D4×C17D411yescharacteristic
27C23×C4×C17C2×C411yescharacteristic
28C23×C4×C17D411yescharacteristic
29C17×#121—41no—
30C17×#121—41no—
31C4×D4×C17—41no—
32C4×D4×C17—41no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C4⋊C4×C17C2311yescharacteristic
36C2×C22⋊C4×C17—21no—
37C2×C22⋊C4×C17—21no—
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17C2×C411yescharacteristic
43C2×C22⋊C4×C17D411yescharacteristic
44C2×C42×C17D411yescharacteristic
45C2×#63223—22no—
46C22×#3622—41no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95C2×C411yescharacteristic
51C17×#95C2×C411yescharacteristic
52#10587504—24no—
53C22⋊#3622—22no—
54C22⋊#3622—41no—
55#10587474—41no—
56C4×#3622—41no—
57C24×C17—21no—
58C24×C17C22⋊C411yescharacteristic
59C24×C17C22⋊C411yescharacteristic
60C2×D4×C17—22no—
61C2×D4×C17—22no—
62C2×D4×C17—41no—
63C2×D4×C17—41no—
64C2×D4×C17—42no—
65C2×D4×C17—42no—
66C2×D4×C17—81no—
67C2×D4×C17—81no—
68C2×D4×C17—81no—
69C2×D4×C17—81no—
70C2×D4×C17—81no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—81no—
79C22×C4×C17—81no—
80C22×C4×C17C22⋊C411yescharacteristic
81C22×C4×C17C22⋊C411yescharacteristic
82C22×C4×C17C22×C411yescharacteristic
83C22×C4×C17C2×D411yescharacteristic
84C22×C4×C17C2×D411yescharacteristic
85C4⋊C4×C17—41no—
86C4⋊C4×C17—41no—
87C4⋊C4×C17—81no—
88C22⋊C4×C17—41no—
89C22⋊C4×C17—41no—
90C22⋊C4×C17—41no—
91C22⋊C4×C17—41no—
92C22⋊C4×C17—42no—
93C22⋊C4×C17—81no—
94C22⋊C4×C17—81no—
95C22⋊C4×C17—81no—
96C22⋊C4×C17—81no—
97C42×C17—21no—
98C42×C17—21no—
99#63223—24no—
100#63223—42no—
101C2×#3622—42no—
102C2×#3622—42no—
103C2×#3622—82no—
104#11737—171nomaximal, Sylow
105C23×C17—21no—
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—41no—
111C23×C17—41no—
112C23×C17—41no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17—41no—
116C23×C17—41no—
117C23×C17—41no—
118C23×C17—41no—
119C23×C17—41no—
120C23×C17—41no—
121C23×C17#10412yes—
122C23×C17C2×C22⋊C411yescharacteristic
123D4×C17—44no—
124D4×C17—82no—
125D4×C17—84no—
126D4×C17—84no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—41no—
133C2×C4×C17—42no—
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×C17#9911yescharacteristic
150C2×C4×C17#9911yescharacteristic
151C2×C4×C17#13512yes—
152#3622—44no—
153#3622—82no—
154#2635D1711yescharacteristic
155C4×#100—171no—
156#1459—171no—
157#1353—172no—
158#1345—172no—
159C22×C17—21no—
160C22×C17—21no—
161C22×C17—22no—
162C22×C17—42no—
163C22×C17—41no—
164C22×C17—41no—
165C22×C17—41no—
166C22×C17—41no—
167C22×C17—41no—
168C22×C17—81no—
169C22×C17—81no—
170C22×C17—81no—
171C22×C17—81no—
172C22×C17—81no—
173C22×C17—81no—
174C22×C17—81no—
175C22×C17—81no—
176C22×C17—81no—
177C22×C17—81no—
178C22×C17C2×#9911yescharacteristic
179C22×C17#41611yescharacteristic
180C22×C17C2×#10411yescharacteristic
181C4×C17—21no—
182C4×C17—21no—
183C4×C17—22no—
184C4×C17—41no—
185C4×C17—41no—
186C4×C17—41no—
187C4×C17—81no—
188C4×C17—81no—
189C4×C17—81no—
190C2×#121Dic1711yescharacteristic
191C2×C4×D4C2×D1711yescharacteristic
192C2×#100—341no—
193C2×C22⋊C8—341no—
194C4×M16—341no—
195#400C2×D1711yescharacteristic
196#399Dic1711yescharacteristic
197#394—21no—
198#394C2×D1711yescharacteristic
199#392—21no—
200#392Dic1711yescharacteristic
201#388—21no—
202#386—21no—
203#381Dic1711yescharacteristic
204#343—172no—
205#324—172no—
206#323—341no—
207C2×C17—21no—
208C2×C17—21no—
209C2×C17—42no—
210C2×C17—81no—
211C2×C17—161no—
212C2×C17#150111yescharacteristic
213C2×C17#212111yescharacteristic
214C2×C17#213411yescharacteristic
215C22×D4—21no—
216C22×D4—21no—
217C22×D4C2×Dic1711yescharacteristic
218C22×D4C22⋊D1711yescharacteristic
219C23×C4C2×Dic1711yescharacteristic
220C23×C4C22⋊D1711yescharacteristic
221C2×M16—342no—
222C22×C8—681no—
223#121—41no—
224#121—41no—
225C4×D4—41no—
226C4×D4—41no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C2×Dic1711yescharacteristic
229C2×C4⋊C4C22×D1711yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4C2×Dic1711yescharacteristic
237C2×C22⋊C4C22⋊D1711yescharacteristic
238C2×C42C22⋊D1711yescharacteristic
239#100—344no—
240C22⋊C8—342no—
241C22⋊C8—681no—
242#97—681no—
243C4×C8—681no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95C2×Dic1711yescharacteristic
248#95C2×Dic1711yescharacteristic
249C17#1173711yescharacteristic, complemented, Sylow
250C24—21no—
251C24C22⋊Dic1711yescharacteristic
252C24C22⋊Dic1711yescharacteristic
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—81no—
260C2×D4—81no—
261C2×D4—81no—
262C2×D4—81no—
263C2×D4—81no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—81no—
272C22×C4—81no—
273C22×C4C22⋊Dic1711yescharacteristic
274C22×C4C22⋊Dic1711yescharacteristic
275C22×C4C22×Dic1711yescharacteristic
276C22×C4C2×C22⋊D1711yescharacteristic
277C22×C4C2×C22⋊D1711yescharacteristic
278M16—344no—
279M16—682no—
280C2×C8—682no—
281C2×C8—682no—
282C2×C8—1362no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—81no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—42no—
291C22⋊C4—81no—
292C22⋊C4—81no—
293C22⋊C4—81no—
294C22⋊C4—81no—
295C42—21no—
296C42—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23#1058750812yes—
314C23C2×C22⋊Dic1711yescharacteristic
315D4—44no—
316D4—82no—
317D4—84no—
318D4—84no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—42no—
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—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4#1058750511yescharacteristic
342C2×C4#1058750511yescharacteristic
343C2×C4#1058763612yes—
344C8—684no—
345C8—1362no—
346C22—21no—
347C22—21no—
348C22—22no—
349C22—42no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22C2×#1058750511yescharacteristic
366C22#1176280511yescharacteristic
367C22C2×#1058750811yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—81no—
375C4—81no—
376C4—81no—
377C2—21no—
378C2—21no—
379C2—42no—
380C2—81no—
381C2—161no—
382C2#1452727511yescharacteristic
383C2#1453043011yescharacteristic
384C2#1453047611yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
Fitting, prime radicalC17×#2635C2
socleC22×C17C2×#99
cosocleC2×C4⋊C4×C17C23
hypercenter#2635D17
hypocenterC17#11737
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2635

Complements

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

NH ≅ G/Ntype
1. C4×#10587504C2semidirect
2. #14527102C2semidirect
3. #14526811C2semidirect
4. #14526787C2semidirect
249. C17#11737semidirect

Maximal subgroups

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

subgroupindex
C4×#105875042
#145271022
#145268112
#145267872
C17×#26352
#1173717