Finite Group Databasebeta

← #16930318

Subgroups — #16930318

Order 4352.

502 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 107 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#14537813C211yesmaximal, characteristic
2C4×#10587504C211yesmaximal, characteristic
3#14527386C212yesmaximal, complemented
4#14526648C212yesmaximal, complemented
5C17×#2633C211yesmaximal, characteristic
6#11762881—24no—
7#11762866C2212yes—
8C2×#10587504—21no—
9#11762773—21no—
10C2×C22⋊#3622—21no—
11C4×#63223C2212yes—
12#11762578—21no—
13#11762551—24no—
14C2×C17×#125C2211yescharacteristic
15C2×C4×D4×C17C2211yescharacteristic
16C17×#399C411yescharacteristic
17C17×#399C411yescharacteristic
18C17×#398—21no—
19C17×#397C411yescharacteristic
20C17×#397C411yescharacteristic
21C17×#394—21no—
22C17×#385—21no—
23C17×#385—21no—
24C17×#383C2211yescharacteristic
25C22×D4×C17D411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C23×C4×C17D411yescharacteristic
28C17×#125—22no—
29C17×#125—22no—
30C4×D4×C17—22no—
31C4×D4×C17—22no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17C2×C411yescharacteristic
37C2×C4⋊C4×C17C2×C411yescharacteristic
38C2×C4⋊C4×C17D411yescharacteristic
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×C17C2×C411yescharacteristic
45C2×C42×C17C2311yescharacteristic
46C2×#63223—22no—
47C2×#63223—22no—
48C22×#3622—22no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95—21no—
52C17×#95—21no—
53C17×#95C2×C411yescharacteristic
54C17×#95C2×C411yescharacteristic
55#10587504—24no—
56C22⋊#3622—22no—
57C22⋊#3622—22no—
58C22⋊#3622—22no—
59C4⋊#3622—22no—
60#10587474—22no—
61#10587474D414yes—
62C4×#3622—22no—
63C24×C17C22⋊C411yescharacteristic
64C24×C17C22⋊C411yescharacteristic
65C2×D4×C17—22no—
66C2×D4×C17—22no—
67C2×D4×C17—41no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—21no—
76C22×C4×C17—81no—
77C22×C4×C17—81no—
78C22×C4×C17C22⋊C411yescharacteristic
79C22×C4×C17C22⋊C411yescharacteristic
80C22×C4×C17C22×C411yescharacteristic
81C22×C4×C17C2×D411yescharacteristic
82C22×C4×C17C2×D411yescharacteristic
83C4⋊C4×C17—22no—
84C4⋊C4×C17—22no—
85C4⋊C4×C17—22no—
86C4⋊C4×C17—41no—
87C4⋊C4×C17—42no—
88C4⋊C4×C17—41no—
89C4⋊C4×C17—81no—
90C4⋊C4×C17—81no—
91C22⋊C4×C17—22no—
92C22⋊C4×C17—22no—
93C22⋊C4×C17—42no—
94C22⋊C4×C17—42no—
95C22⋊C4×C17—81no—
96C22⋊C4×C17—81no—
97C42×C17C2×D412yes—
98C42×C17#4112yes—
99#63223—24no—
100#63223—42no—
101#63223—82no—
102C2×#3622—24no—
103C2×#3622—42no—
104C2×#3622—82no—
105#9189—171nomaximal, Sylow
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—41no—
112C23×C17—41no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17#10412yes—
116C23×C17C2×C22⋊C411yescharacteristic
117D4×C17—44no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—42no—
125C2×C4×C17—42no—
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—41no—
140C2×C4×C17—81no—
141C2×C4×C17—81no—
142C2×C4×C17C4×D412yes—
143C2×C4×C17#12011yescharacteristic
144C2×C4×C17#12112yes—
145C2×C4×C17#12311yescharacteristic
146#3622—44no—
147#3622—44no—
148#2973—171no—
149#2633D1711yescharacteristic
150C4×#100—171no—
151#1528—172no—
152#1288—172no—
153C22×C17—21no—
154C22×C17—21no—
155C22×C17—22no—
156C22×C17—42no—
157C22×C17—42no—
158C22×C17—41no—
159C22×C17—41no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17—81no—
164C22×C17—81no—
165C22×C17#38611yescharacteristic
166C22×C17C2×#10411yescharacteristic
167C22×C17#42111yescharacteristic
168C4×C17—22no—
169C4×C17—21no—
170C4×C17—21no—
171C4×C17—22no—
172C4×C17—41no—
173C4×C17—41no—
174C4×C17—81no—
175C4×C17—81no—
176C4×C17—81no—
177C4×C17—81no—
178C2×#125C2×D1711yescharacteristic
179C2×C4×D4C2×D1711yescharacteristic
180#435—344no—
181#432—172no—
182C2×#100—341no—
183#407—341no—
184C2×C22⋊C8—341no—
185C4×M16—172no—
186#399Dic1711yescharacteristic
187#399Dic1711yescharacteristic
188#398—21no—
189#397Dic1711yescharacteristic
190#397Dic1711yescharacteristic
191#394—21no—
192#385—21no—
193#385—21no—
194#383C2×D1711yescharacteristic
195#343—341no—
196#330—344no—
197C2×C17—21no—
198C2×C17—21no—
199C2×C17—42no—
200C2×C17—81no—
201C2×C17#187111yescharacteristic
202C2×C17#191111yescharacteristic
203C2×C17#191511yescharacteristic
204C22×D4C22⋊D1711yescharacteristic
205C23×C4C22⋊D1711yescharacteristic
206C23×C4C22⋊D1711yescharacteristic
207C2×M16—342no—
208C2×M16—342no—
209C22×C8—342no—
210#125—22no—
211#125—22no—
212C4×D4—22no—
213C4×D4—22no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×Dic1711yescharacteristic
219C2×C4⋊C4C2×Dic1711yescharacteristic
220C2×C4⋊C4C22⋊D1711yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4C2×Dic1711yescharacteristic
226C2×C22⋊C4C2×Dic1711yescharacteristic
227C2×C42C22×D1711yescharacteristic
228C4⋊C8—342no—
229#100—344no—
230C22⋊C8—342no—
231C22⋊C8—342no—
232C22⋊C8—342no—
233#97—174no—
234#97—342no—
235C4×C8—342no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95C2×Dic1711yescharacteristic
241#95C2×Dic1711yescharacteristic
242C17#918911yescharacteristic, complemented, Sylow
243C24C22⋊Dic1711yescharacteristic
244C24C22⋊Dic1711yescharacteristic
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—41no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4C22⋊Dic1711yescharacteristic
259C22×C4C22⋊Dic1711yescharacteristic
260C22×C4C22×Dic1711yescharacteristic
261C22×C4C2×C22⋊D1711yescharacteristic
262C22×C4C2×C22⋊D1711yescharacteristic
263M16—344no—
264M16—682no—
265M16—1362no—
266C2×C8—344no—
267C2×C8—682no—
268C2×C8—1362no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—42no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—81no—
282C22⋊C4—81no—
283C42D4×D1712yes—
284C42#6325412yes—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#1058750812yes—
295C23C2×C22⋊Dic1711yescharacteristic
296D4—44no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
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—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4D4×Dic1712yes—
322C2×C4#1058762111yescharacteristic
323C2×C4#1058762311yescharacteristic
324C2×C4#1058762512yes—
325C8—684no—
326C8—684no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22#1176268911yescharacteristic
340C22C2×#1058750811yescharacteristic
341C22#1176282611yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—22no—
346C4—41no—
347C4—41no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—81no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—81no—
356C2#1452908711yescharacteristic
357C2#1452931711yescharacteristic
358C2#1452933711yescharacteristic
subgroupG/H
centerC22#11762689
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2633C2
socleC22×C17#386
prime radicalC22×D4×C17D4
cosocleC2×C42×C17C23
hypercenter#2633D17
hypocenterC17#9189
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2633

Complements

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

NH ≅ G/Ntype
3. #14527386C2semidirect
4. #14526648C2semidirect
242. C17#9189semidirect

Maximal subgroups

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

subgroupindex
#145378132
C4×#105875042
#145273862
#145266482
C17×#26332
#918917