Finite Group Databasebeta

← #14534792

Subgroups — #14534792

Order 2176.

434 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11762750C211yesmaximal, characteristic, complemented
2#11762747C211yesmaximal, characteristic, complemented
3#11762744C211yesmaximal, characteristic, complemented
4#11762737C211yesmaximal, characteristic, complemented
5#11762735C211yesmaximal, characteristic, complemented
6#11762724C211yesmaximal, characteristic
7#11762724C211yesmaximal, characteristic
8#11762704C211yesmaximal, characteristic, complemented
9#11762703C211yesmaximal, characteristic, complemented
10#11762697C211yesmaximal, characteristic, complemented
11#11762690C211yesmaximal, characteristic, complemented
12#11762685C211yesmaximal, characteristic
13#11762680C211yesmaximal, characteristic, complemented
14#11762656C211yesmaximal, characteristic, complemented
15C17×#396C211yesmaximal, characteristic, complemented
16C22×C22⋊D17C2211yescharacteristic
17C22×C4×D17C2211yescharacteristic
18C2×C4⋊C4×C17C2211yescharacteristic
19C2×C4⋊C4×C17C2211yescharacteristic
20C2×C4⋊C4×C17C2211yescharacteristic
21C2×C22⋊C4×C17C2211yescharacteristic
22C2×C22⋊C4×C17C2211yescharacteristic
23C2×C22⋊C4×C17C2211yescharacteristic
24C2×C22⋊Dic17C2211yescharacteristic
25C2×C22⋊Dic17C2211yescharacteristic
26C2×C22⋊Dic17C2211yescharacteristic
27C2×#63227C2211yescharacteristic
28C2×#63227C2211yescharacteristic
29C2×#63227C2211yescharacteristic
30C2×#63227C2211yescharacteristic
31C2×#63227C2211yescharacteristic
32C2×#63225C2211yescharacteristic
33C2×#63225C2211yescharacteristic
34C2×#63225C2211yescharacteristic
35C2×#63225C2211yescharacteristic
36C2×#63225C2211yescharacteristic
37C2×C4×Dic17C2211yescharacteristic
38C2×C4×Dic17C2211yescharacteristic
39C17×#95C2211yescharacteristic
40#10587502C2211yescharacteristic
41#10587502C2211yescharacteristic
42#10587502C2211yescharacteristic
43#10587502C2211yescharacteristic
44#10587502C2211yescharacteristic
45#10587502C2211yescharacteristic
46#10587502C2211yescharacteristic
47#10587502C2211yescharacteristic
48#10587502C2211yescharacteristic
49#10587502C2211yescharacteristic
50#10587502C2211yescharacteristic
51C24×C17C2311yescharacteristic
52C23×D17C2311yescharacteristic
53C22×C4×C17C2311yescharacteristic
54C22×C4×C17C2311yescharacteristic
55C22×C4×C17C2311yescharacteristic
56C22×C4×C17C2311yescharacteristic
57C22×C4×C17C2311yescharacteristic
58C22×C4×C17C2311yescharacteristic
59C2×C22⋊D17—22no—
60C2×C22⋊D17—41no—
61C2×C22⋊D17—41no—
62C22×Dic17C2311yescharacteristic
63C22×Dic17C2311yescharacteristic
64C22×Dic17C2311yescharacteristic
65C22×Dic17C2311yescharacteristic
66C22×Dic17C2311yescharacteristic
67C22×Dic17C2311yescharacteristic
68C22×Dic17C2311yescharacteristic
69C2×C4×D17—22no—
70C2×C4×D17—41no—
71C2×C4×D17—41no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C22⋊C4×C17—41no—
76C22⋊C4×C17—41no—
77C22⋊C4×C17—41no—
78C22⋊Dic17—22no—
79C22⋊Dic17—22no—
80C22⋊Dic17—41no—
81#63227—22no—
82#63227—22no—
83#63227—22no—
84#63227—41no—
85#63227—41no—
86#63225—22no—
87#63225—22no—
88#63225—41no—
89#63225—41no—
90#63225—41no—
91C4×Dic17—41no—
92C4×Dic17—41no—
93C23×C17—21no—
94C23×C17—21no—
95C23×C17—21no—
96C23×C17—21no—
97C23×C17—21no—
98C23×C17—21no—
99C23×C17—21no—
100C23×C17C2411yescharacteristic
101C22×D17—21no—
102C22×D17—21no—
103C22×D17—21no—
104C22×D17—21no—
105C22×D17—21no—
106C22×D17—21no—
107C22×D17#4112yes—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
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—
126C22⋊D17—44no—
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—21no—
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—21no—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—21no—
139C2×Dic17—21no—
140C2×Dic17—21no—
141C2×Dic17—21no—
142C2×Dic17—21no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17#4112yes—
147C2×Dic17#4112yes—
148C4×D17—44no—
149#2649—171nomaximal, Sylow
150C22×C17—41no—
151C22×C17—41no—
152C22×C17—41no—
153C22×C17—41no—
154C22×C17—41no—
155C22×C17—41no—
156C22×C17—41no—
157C22×C17C2×#4111yescharacteristic
158C22×C17C2×#4111yescharacteristic
159C22×C17C2×#4111yescharacteristic
160C22×C17H(5,𝔽2)11yescharacteristic
161C22×C17H(5,𝔽2)11yescharacteristic
162C22×C17H(5,𝔽2)11yescharacteristic
163C22×C172−1+411yescharacteristic
164C2×D17—22no—
165C2×D17—22no—
166C2×D17—22no—
167C2×D17—41no—
168C2×D17—41no—
169C2×D17—41no—
170C2×D17—41no—
171C4×C17—41no—
172C4×C17—41no—
173C4×C17—41no—
174C4×C17—41no—
175C4×C17—41no—
176C4×C17—41no—
177Dic17—22no—
178Dic17—22no—
179Dic17—41no—
180Dic17—41no—
181Dic17—41no—
182Dic17—41no—
183Dic17—41no—
184#400—171no—
185#400—171no—
186#399—171no—
187#397—171no—
188#397—171no—
189#396D1711yescharacteristic, complemented
190#394—171no—
191#394—171no—
192#389—171no—
193#388—171no—
194#388—171no—
195#387—171no—
196#386—171no—
197#385—171no—
198C4×C22⋊C4—171no—
199C2×C17—81no—
200C2×C17#52911yescharacteristic
201C2×C17#53811yescharacteristic
202C2×C17#53811yescharacteristic
203C2×C17#53911yescharacteristic
204C2×C17#53911yescharacteristic
205C2×C17#54011yescharacteristic
206C2×C17#54211yescharacteristic
207D17—42no—
208C22×D4—171no—
209C23×C4—171no—
210C2×C4⋊C4—171no—
211C2×C4⋊C4—171no—
212C2×C4⋊C4—171no—
213C2×C4⋊C4—171no—
214C2×C4⋊C4—171no—
215C2×C4⋊C4C2×D1711yescharacteristic
216C2×C4⋊C4C2×D1711yescharacteristic
217C2×C4⋊C4C2×D1711yescharacteristic
218C2×C22⋊C4—171no—
219C2×C22⋊C4—171no—
220C2×C22⋊C4—171no—
221C2×C22⋊C4—171no—
222C2×C22⋊C4—171no—
223C2×C22⋊C4—171no—
224C2×C22⋊C4—171no—
225C2×C22⋊C4—171no—
226C2×C22⋊C4C2×D1711yescharacteristic
227C2×C22⋊C4C2×D1711yescharacteristic
228C2×C22⋊C4C2×D1711yescharacteristic
229C2×C42—171no—
230C2×C42—171no—
231#95—171no—
232#95—171no—
233#95—171no—
234#95—171no—
235#95—171no—
236#95—171no—
237#95—171no—
238#95—171no—
239#95—171no—
240#95—171no—
241#95—171no—
242#95C2×D1711yescharacteristic
243C17#264911yescharacteristic, complemented, Sylow
244C24—171no—
245C24C22×D1711yescharacteristic
246C2×D4—342no—
247C2×D4—681no—
248C2×D4—681no—
249C22×C4—171no—
250C22×C4—171no—
251C22×C4—171no—
252C22×C4—171no—
253C22×C4—171no—
254C22×C4—171no—
255C22×C4—171no—
256C22×C4—342no—
257C22×C4—681no—
258C22×C4—681no—
259C22×C4C22×D1711yescharacteristic
260C22×C4C22×D1711yescharacteristic
261C22×C4C22×D1711yescharacteristic
262C22×C4C22×D1711yescharacteristic
263C22×C4C22×D1711yescharacteristic
264C22×C4C22×D1711yescharacteristic
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—342no—
269C4⋊C4—342no—
270C4⋊C4—681no—
271C4⋊C4—681no—
272C4⋊C4—681no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—342no—
277C22⋊C4—342no—
278C22⋊C4—342no—
279C22⋊C4—342no—
280C22⋊C4—342no—
281C22⋊C4—681no—
282C22⋊C4—681no—
283C22⋊C4—681no—
284C42—681no—
285C42—681no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—172no—
294C23—341no—
295C23—341no—
296C23—341no—
297C23—341no—
298C23—341no—
299C23—341no—
300C23C23×D1711yescharacteristic
301D4—684no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
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—21no—
319C2×C4—21no—
320C2×C4—172no—
321C2×C4—172no—
322C2×C4—341no—
323C2×C4—341no—
324C2×C4—341no—
325C2×C4—341no—
326C2×C4—341no—
327C2×C4—341no—
328C2×C4—341no—
329C2×C4—341no—
330C2×C4—341no—
331C2×C4—341no—
332C2×C4—341no—
333C2×C4—341no—
334C2×C4—341no—
335C2×C4—341no—
336C2×C4—341no—
337C2×C4—341no—
338C2×C4—341no—
339C2×C4—341no—
340C2×C4—341no—
341C2×C4—684no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—342no—
350C22—342no—
351C22—342no—
352C22—681no—
353C22—681no—
354C22—681no—
355C22—681no—
356C22#1058769111yescharacteristic
357C22#1058769111yescharacteristic
358C22#1058769111yescharacteristic
359C22#1058769411yescharacteristic
360C22#41×D1711yescharacteristic
361C22#41×D1711yescharacteristic
362C22#41×D1711yescharacteristic
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—342no—
370C4—342no—
371C4—681no—
372C4—681no—
373C4—681no—
374C4—681no—
375C4—681no—
376C2—81no—
377C2—682no—
378C2#1176334211yescharacteristic
379C2#1176339111yescharacteristic
380C2#1176339111yescharacteristic
381C2#1176340511yescharacteristic
382C2#1176340511yescharacteristic
383C2#1176340911yescharacteristic
384C2#1176342911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, cosocleC23×C17C24
FittingC17×#396C2
prime radicalC22×C22⋊D17C22
hypercenter#396D17
hypocenterC17#2649
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #11762750C2semidirect
2. #11762747C2semidirect
3. #11762744C2semidirect
4. #11762737C2semidirect
5. #11762735C2semidirect
8. #11762704C2semidirect
9. #11762703C2semidirect
10. #11762697C2semidirect
11. #11762690C2semidirect
13. #11762680C2semidirect
14. #11762656C2semidirect
15. C17×#396C2semidirect
189. #396D17semidirect
243. C17#2649semidirect

Maximal subgroups

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

subgroupindex
#117627502
#117627472
#117627442
#117627372
#117627352
#117627242
#117627042
#117627032
#117626972
#117626902
#117626852
#117626802
#117626562
C17×#3962
#264917