Finite Group Databasebeta

← #14540865

Subgroups — #14540865

Order 2176.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763516C211yesmaximal, characteristic, complemented
2#11763168C211yesmaximal, characteristic, complemented
3#11763142C211yesmaximal, characteristic, complemented
4#11763120C211yesmaximal, characteristic, complemented
5#11763089C211yesmaximal, characteristic, complemented
6#11763053C211yesmaximal, characteristic, complemented
7#11763048C211yesmaximal, characteristic, complemented
8#11763028C211yesmaximal, characteristic, complemented
9#11762971C211yesmaximal, characteristic, complemented
10#11762960C211yesmaximal, characteristic, complemented
11#11762909C211yesmaximal, characteristic, complemented
12#11762881C211yesmaximal, characteristic, complemented
13#11762810C211yesmaximal, characteristic, complemented
14C2×#10587503C211yesmaximal, characteristic, complemented
15C17×#546C211yesmaximal, characteristic
16C2×#41×C17C2211yescharacteristic
17C22×D4×C17C2211yescharacteristic
18C17×#124C2211yescharacteristic
19C17×#123—21no—
20C17×C22⋊Q8C2211yescharacteristic
21C17×#121—21no—
22C17×#121C2211yescharacteristic
23C17×#120—21no—
24C4×D4×C17C2211yescharacteristic
25C4×D4×C17C2211yescharacteristic
26C2×C22⋊C4×C17—21no—
27C2×#63231C2211yescharacteristic, complemented
28D4×Dic17—21no—
29C2×#63229C2211yescharacteristic
30C2×#63229C2211yescharacteristic
31C2×C4⋊Dic17C2211yescharacteristic
32C2×C4⋊Dic17C2211yescharacteristic, complemented
33#10587610C2211yescharacteristic
34#10587610C2211yescharacteristic, complemented
35C2×#63223C2211yescharacteristic, complemented
36C22×#3622C2211yescharacteristic
37#10587576—21no—
38#10587564—21no—
39#10587564—21no—
40#10587555C2211yescharacteristic, complemented
41C4×Dic34C2211yescharacteristic, complemented
42#10587506C2211yescharacteristic, complemented
43#10587506C2211yescharacteristic, complemented
44#10587506C2211yescharacteristic, complemented
45#10587503C2211yescharacteristic
46#10587503C2211yescharacteristic
47#10587503C2211yescharacteristic
48#10587503C2211yescharacteristic
49#10587503C2211yescharacteristic
50#10587503C2211yescharacteristic
51C22⋊#3622C2211yescharacteristic
52C22⋊#3622C2211yescharacteristic, complemented
53#10587481C2211yescharacteristic, complemented
54#10587478C2211yescharacteristic, complemented
55#10587478C2211yescharacteristic, complemented
56#10587478C2211yescharacteristic, complemented
57C4⋊#3622C2211yescharacteristic, complemented
58#10587474C2211yescharacteristic, complemented
59C24×C17—21no—
60#41×C17—22no—
61#41×C17—41no—
62C2×Q8×C17C2311yescharacteristic
63C2×D4×C17—22no—
64C2×D4×C17—21no—
65C2×D4×C17—21no—
66C2×D4×C17—21no—
67C2×D4×C17—41no—
68C2×D4×C17D411yescharacteristic
69C2×D4×C17C2311yescharacteristic
70C2×D4×C17C2311yescharacteristic
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17C2311yescharacteristic
74C22×C4×C17C2311yescharacteristic
75C22×Dic17—21no—
76C22×Dic17—21no—
77C2×Dic34—21no—
78C2×Dic34C2311yescharacteristic
79C4⋊C4×C17—21no—
80C4⋊C4×C17D411yescharacteristic
81C4⋊C4×C17C2311yescharacteristic
82C22⋊C4×C17—21no—
83C22⋊C4×C17—21no—
84C22⋊C4×C17—21no—
85C22⋊C4×C17—21no—
86C22⋊C4×C17—21no—
87C22⋊C4×C17D411yescharacteristic
88C22⋊C4×C17D411yescharacteristic
89C42×C17C2311yescharacteristic
90C22⋊Dic17—21no—
91C22⋊Dic17—21no—
92#63231—41no—
93#63229—22no—
94#63229—41no—
95C4⋊Dic17—21no—
96C4⋊Dic17—21no—
97C4⋊Dic17—21no—
98C4⋊Dic17C2311yescharacteristic
99C4⋊Dic17C2311yescharacteristic
100C4⋊Dic17C2311yescharacteristic
101#63225—21no—
102#63225—21no—
103#63225—21no—
104C4×Dic17—21no—
105#63223—41no—
106C2×#3622—41no—
107C2×#3622C2311yescharacteristic
108C2×#3622C2311yescharacteristic
109C2×#3622C2311yescharacteristic
110C2×#3622C2311yescharacteristic
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—42no—
114C23×C17—42no—
115C23×C17—81no—
116C23×C17C2×D411yescharacteristic
117C23×C17C2×D411yescharacteristic
118Q8×C17—21no—
119Q8×C17—21no—
120D4×C17—22no—
121D4×C17—21no—
122D4×C17—21no—
123D4×C17—21no—
124D4×C17—42no—
125D4×C17—42no—
126D4×C17—81no—
127D4×C17#4112yes—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—42no—
135C2×C4×C17—81no—
136C2×C4×C17C2×D411yescharacteristic
137C2×C4×C17C2×D411yescharacteristic
138C2×C4×C17C2×D411yescharacteristic
139C2×C4×C17C2×D411yescharacteristic
140C2×C4×C17C2411yescharacteristic
141C2×Dic17—21no—
142C2×Dic17—21no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—81no—
146C2×Dic17—81no—
147Dic34—21no—
148Dic34—21no—
149Dic34—81no—
150#3622—21no—
151#3622—21no—
152#3622—21no—
153#3622—21no—
154#3314—171nomaximal, Sylow
155C22×C17—21no—
156C22×C17—21no—
157C22×C17—21no—
158C22×C17—22no—
159C22×C17—21no—
160C22×C17—21no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17—41no—
164C22×C17—41no—
165C22×C17—41no—
166C22×C17—84no—
167C22×C17#13712yes—
168C22×C17C22×D411yescharacteristic
169C4×C17—21no—
170C4×C17—21no—
171C4×C17—21no—
172C4×C17—21no—
173C4×C17—41no—
174C4×C17—41no—
175C4×C17C2×#4111yescharacteristic
176C4×C17H(5,𝔽2)11yescharacteristic
177Dic17—41no—
178Dic17—41no—
179Dic17—41no—
180Dic17—41no—
181#554—171no—
182#546D1711yescharacteristic
183#489—171no—
184#484—171no—
185#480—171no—
186#474—171no—
187#468—171no—
188#467—171no—
189#464—171no—
190#452—171no—
191#450—171no—
192#440—171no—
193#435—171no—
194#417—171no—
195C2×#102—171no—
196C2×C17—22no—
197C2×C17—41no—
198C2×C17—42no—
199C2×C17—81no—
200C2×C17#54611yescharacteristic
201C2×C17C2×#13711yescharacteristic
202C2×C17#57611yescharacteristic
203C2×#41C2×D1711yescharacteristic
204C22×D4C2×D1711yescharacteristic
205C2×Q16—171no—
206C2×SD16—171no—
207C2×SD16—171no—
208C2×M16—171no—
209C22×C8—171no—
210C4⋊Q8—171no—
211#125—341no—
212#124C2×D1711yescharacteristic
213#123—21no—
214C22⋊Q8—171no—
215C22⋊Q8—171no—
216C22⋊Q8—341no—
217C22⋊Q8—341no—
218C22⋊Q8C2×D1711yescharacteristic
219#121—21no—
220#121C2×D1711yescharacteristic
221#120—21no—
222C4×Q8—171no—
223C4×D4—341no—
224C4×D4C2×D1711yescharacteristic
225C4×D4C2×D1711yescharacteristic
226C2×C4⋊C4—171no—
227C2×C4⋊C4—171no—
228C2×C22⋊C4—21no—
229#107—171no—
230#107—171no—
231#107—171no—
232C4⋊C8—171no—
233#103—171no—
234#103—171no—
235#103—171no—
236#103—171no—
237#102—171no—
238#102—171no—
239#102—171no—
240#102—171no—
241#102—171no—
242#102—171no—
243C22⋊C8—171no—
244C22⋊C8—171no—
245#97—171no—
246C17#331411yescharacteristic, complemented, Sylow
247C24—21no—
248#41—22no—
249#41—41no—
250C2×Q8—171no—
251C2×Q8—341no—
252C2×Q8C22×D1711yescharacteristic
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4C22⋊D1711yescharacteristic
259C2×D4C22×D1711yescharacteristic
260C2×D4C22×D1711yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—341no—
264C22×C4—341no—
265C22×C4C22×D1711yescharacteristic
266C22×C4C22×D1711yescharacteristic
267Q16—681no—
268SD16—342no—
269SD16—681no—
270M16—681no—
271C2×C8—171no—
272C2×C8—171no—
273C2×C8—171no—
274C2×C8—171no—
275C2×C8—681no—
276C4⋊C4—21no—
277C4⋊C4—171no—
278C4⋊C4—171no—
279C4⋊C4—171no—
280C4⋊C4—341no—
281C4⋊C4—341no—
282C4⋊C4—341no—
283C4⋊C4—341no—
284C4⋊C4—341no—
285C4⋊C4—341no—
286C4⋊C4C22⋊D1711yescharacteristic
287C4⋊C4C22×D1711yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—341no—
294C22⋊C4—341no—
295C22⋊C4C22⋊D1711yescharacteristic
296C22⋊C4C22⋊D1711yescharacteristic
297C42—341no—
298C42C22×D1711yescharacteristic
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23C2×C22⋊D1711yescharacteristic
305C23C2×C22⋊D1711yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—341no—
309Q8—341no—
310Q8—1361no—
311D4—22no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4#6325412yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—341no—
328C2×C4—341no—
329C2×C4—341no—
330C2×C4—341no—
331C2×C4—1361no—
332C2×C4—1361no—
333C2×C4C2×C22⋊D1711yescharacteristic
334C2×C4C2×C22⋊D1711yescharacteristic
335C2×C4C2×C22⋊D1711yescharacteristic
336C2×C4C2×C22⋊D1711yescharacteristic
337C2×C4C23×D1711yescharacteristic
338C8—341no—
339C8—341no—
340C8—341no—
341C8—341no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—84no—
354C22#1058763712yes—
355C22C22×C22⋊D1711yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—681no—
363C4—681no—
364C4—681no—
365C4—681no—
366C4C2×#6325411yescharacteristic
367C4#1058769111yescharacteristic
368C2—22no—
369C2—41no—
370C2—42no—
371C2—81no—
372C2#1176345311yescharacteristic
373C2C2×#1058763711yescharacteristic
374C2#1176361211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
Fitting, prime radicalC17×#546C2
socleC22×C17C22×D4
hypercenter#546D17
hypocenterC17#3314
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #11763516C2semidirect
2. #11763168C2semidirect
3. #11763142C2semidirect
4. #11763120C2semidirect
5. #11763089C2semidirect
6. #11763053C2semidirect
7. #11763048C2semidirect
8. #11763028C2semidirect
9. #11762971C2semidirect
10. #11762960C2semidirect
11. #11762909C2semidirect
12. #11762881C2semidirect
13. #11762810C2semidirect
14. C2×#10587503C2semidirect
27. C2×#63231C22semidirect
32. C2×C4⋊Dic17C22semidirect
34. #10587610C22semidirect
35. C2×#63223C22semidirect
40. #10587555C22semidirect
41. C4×Dic34C22semidirect
42. #10587506C22semidirect
43. #10587506C22semidirect
44. #10587506C22semidirect
52. C22⋊#3622C22semidirect
53. #10587481C22semidirect
54. #10587478C22semidirect
55. #10587478C22semidirect
56. #10587478C22semidirect
57. C4⋊#3622C22semidirect
58. #10587474C22semidirect
246. C17#3314semidirect

Maximal subgroups

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

subgroupindex
#117635162
#117631682
#117631422
#117631202
#117630892
#117630532
#117630482
#117630282
#117629712
#117629602
#117629092
#117628812
#117628102
C2×#105875032
C17×#5462
#331417