Finite Group Databasebeta

← #16944924

Subgroups — #16944924

Order 4352.

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

normal subgroups only

This group has 514 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#14527122C211yesmaximal, characteristic, complemented
3#14526790C212yesmaximal, complemented
4#14526787C212yesmaximal, complemented
5C17×#2543C211yesmaximal, characteristic
6C2×#10587504—21no—
7#11762773—21no—
8C4×#63223—21no—
9#11762578C2212yes—
10#11762535C2212yes—
11#11762533—21no—
12C2×C17×#121—21no—
13C2×C17×#121C411yescharacteristic
14C2×C4×D4×C17C2211yescharacteristic
15C17×#398C2211yescharacteristic
16C17×#397C411yescharacteristic
17C17×#394C2211yescharacteristic
18C17×#392C411yescharacteristic
19C17×#388—21no—
20C17×#386—21no—
21C17×#386—21no—
22C2×C17×#95C411yescharacteristic
23C22×D4×C17—21no—
24C22×D4×C17—21no—
25C22×D4×C17C2×C411yescharacteristic
26C22×D4×C17D411yescharacteristic
27C23×C4×C17—21no—
28C23×C4×C17C2×C411yescharacteristic
29C23×C4×C17D411yescharacteristic
30C17×#121—44no—
31C17×#121—41no—
32C17×#121—41no—
33C4×D4×C17—41no—
34C4×D4×C17—41no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17C2×C411yescharacteristic
37C2×C4⋊C4×C17C2311yescharacteristic
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17—21no—
43C2×C22⋊C4×C17C2×C411yescharacteristic
44C2×C22⋊C4×C17D411yescharacteristic
45C2×C42×C17D411yescharacteristic
46C2×#63223—22no—
47C2×#63223—41no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95C2×C411yescharacteristic
52C17×#95C2×C411yescharacteristic
53#10587504—24no—
54C22⋊#3622—22no—
55C22⋊#3622—41no—
56#10587474—41no—
57C4×#3622—41no—
58C24×C17—21no—
59C24×C17C22⋊C411yescharacteristic
60C24×C17C22⋊C411yescharacteristic
61C2×D4×C17—22no—
62C2×D4×C17—22no—
63C2×D4×C17—41no—
64C2×D4×C17—41no—
65C2×D4×C17—42no—
66C2×D4×C17—42no—
67C2×D4×C17—42no—
68C2×D4×C17—42no—
69C2×D4×C17—42no—
70C2×D4×C17—81no—
71C2×D4×C17—81no—
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—21no—
79C22×C4×C17—42no—
80C22×C4×C17—42no—
81C22×C4×C17—81no—
82C22×C4×C17—81no—
83C22×C4×C17—81no—
84C22×C4×C17C22⋊C411yescharacteristic
85C22×C4×C17C22⋊C411yescharacteristic
86C22×C4×C17C22×C411yescharacteristic
87C22×C4×C17C2×D411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C4⋊C4×C17—41no—
90C4⋊C4×C17—41no—
91C4⋊C4×C17—42no—
92C22⋊C4×C17—41no—
93C22⋊C4×C17—41no—
94C22⋊C4×C17—42no—
95C22⋊C4×C17—42no—
96C22⋊C4×C17—41no—
97C22⋊C4×C17—41no—
98C22⋊C4×C17—42no—
99C22⋊C4×C17—81no—
100C42×C17—21no—
101C42×C17—21no—
102#63223—24no—
103#63223—42no—
104#63223—82no—
105C2×#3622—42no—
106C2×#3622—42no—
107#11783—171nomaximal, Sylow
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—21no—
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—41no—
122C23×C17—41no—
123C23×C17—41no—
124C23×C17#10412yes—
125C23×C17C2×C22⋊C411yescharacteristic
126D4×C17—44no—
127D4×C17—84no—
128D4×C17—82no—
129D4×C17—84no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—22no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—41no—
137C2×C4×C17—42no—
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—41no—
147C2×C4×C17—41no—
148C2×C4×C17—41no—
149C2×C4×C17—81no—
150C2×C4×C17—81no—
151C2×C4×C17—81no—
152C2×C4×C17—84no—
153C2×C4×C17#9911yescharacteristic
154C2×C4×C17#9911yescharacteristic
155C2×C4×C17AGL(1,ℤ/8)12yes—
156#3622—44no—
157#3622—82no—
158#2543D1711yescharacteristic
159C4×#100—171no—
160#1465—171no—
161#1346—172no—
162#1345—172no—
163C22×C17—21no—
164C22×C17—21no—
165C22×C17—22no—
166C22×C17—42no—
167C22×C17—42no—
168C22×C17—42no—
169C22×C17—41no—
170C22×C17—41no—
171C22×C17—41no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17—81no—
175C22×C17—81no—
176C22×C17—81no—
177C22×C17—81no—
178C22×C17—81no—
179C22×C17—81no—
180C22×C17—81no—
181C22×C17—81no—
182C22×C17C2×#9911yescharacteristic
183C22×C17#41811yescharacteristic
184C22×C17C2×#10411yescharacteristic
185C4×C17—21no—
186C4×C17—21no—
187C4×C17—22no—
188C4×C17—42no—
189C4×C17—41no—
190C4×C17—41no—
191C4×C17—41no—
192C4×C17—81no—
193C4×C17—81no—
194C2×#121—21no—
195C2×#121Dic1711yescharacteristic
196C2×C4×D4C2×D1711yescharacteristic
197C2×#100—341no—
198#407—341no—
199C4×M16—341no—
200#398C2×D1711yescharacteristic
201#397Dic1711yescharacteristic
202#394C2×D1711yescharacteristic
203#392Dic1711yescharacteristic
204#388—21no—
205#386—21no—
206#386—21no—
207C2×#95Dic1711yescharacteristic
208#343—172no—
209#324—172no—
210#323—341no—
211C2×C17—21no—
212C2×C17—21no—
213C2×C17—42no—
214C2×C17—81no—
215C2×C17—161no—
216C2×C17#150711yescharacteristic
217C2×C17#212111yescharacteristic
218C2×C17#213211yescharacteristic
219C22×D4—21no—
220C22×D4—21no—
221C22×D4C2×Dic1711yescharacteristic
222C22×D4C22⋊D1711yescharacteristic
223C23×C4—21no—
224C23×C4C2×Dic1711yescharacteristic
225C23×C4C22⋊D1711yescharacteristic
226C2×M16—342no—
227C2×M16—681no—
228#121—44no—
229#121—41no—
230#121—41no—
231C4×D4—41no—
232C4×D4—41no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C2×Dic1711yescharacteristic
235C2×C4⋊C4C22×D1711yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4C2×Dic1711yescharacteristic
242C2×C22⋊C4C22⋊D1711yescharacteristic
243C2×C42C22⋊D1711yescharacteristic
244#100—344no—
245C22⋊C8—342no—
246C22⋊C8—681no—
247#97—681no—
248C4×C8—681no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95C2×Dic1711yescharacteristic
253#95C2×Dic1711yescharacteristic
254C17#1178311yescharacteristic, complemented, Sylow
255C24—21no—
256C24C22⋊Dic1711yescharacteristic
257C24C22⋊Dic1711yescharacteristic
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—81no—
268C2×D4—81no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—81no—
279C22×C4—81no—
280C22×C4—81no—
281C22×C4C22⋊Dic1711yescharacteristic
282C22×C4C22⋊Dic1711yescharacteristic
283C22×C4C22×Dic1711yescharacteristic
284C22×C4C2×C22⋊D1711yescharacteristic
285C22×C4C2×C22⋊D1711yescharacteristic
286M16—344no—
287M16—682no—
288M16—1362no—
289C2×C8—682no—
290C2×C8—682no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—81no—
302C42—21no—
303C42—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23#1058750812yes—
321C23C2×C22⋊Dic1711yescharacteristic
322D4—44no—
323D4—84no—
324D4—82no—
325D4—84no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—84no—
349C2×C4#1058750511yescharacteristic
350C2×C4#1058750511yescharacteristic
351C2×C4#1058761812yes—
352C8—684no—
353C8—1362no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22C2×#1058750511yescharacteristic
374C22#1176281411yescharacteristic
375C22C2×#1058750811yescharacteristic
376C4—22no—
377C4—21no—
378C4—21no—
379C4—42no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—81no—
384C4—81no—
385C2—21no—
386C2—21no—
387C2—42no—
388C2—81no—
389C2—161no—
390C2#1452730011yescharacteristic
391C2#1453043011yescharacteristic
392C2#1453046911yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
Fitting, prime radicalC17×#2543C2
socleC22×C17C2×#99
cosocleC2×C4⋊C4×C17C23
hypercenter#2543D17
hypocenterC17#11783
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2543

Complements

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

NH ≅ G/Ntype
1. C4×#10587504C2semidirect
2. #14527122C2semidirect
3. #14526790C2semidirect
4. #14526787C2semidirect
254. C17#11783semidirect

Maximal subgroups

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

subgroupindex
C4×#105875042
#145271222
#145267902
#145267872
C17×#25432
#1178317