Finite Group Databasebeta

← #14540820

Subgroups — #14540820

Order 2176.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763529C211yesmaximal, characteristic, complemented
2#11763168C211yesmaximal, characteristic, complemented
3#11763147C211yesmaximal, characteristic, complemented
4#11763130C211yesmaximal, characteristic, complemented
5#11763099C211yesmaximal, characteristic, complemented
6#11763065C211yesmaximal, characteristic, complemented
7#11763036C211yesmaximal, characteristic, complemented
8#11763028C211yesmaximal, characteristic, complemented
9#11762971C211yesmaximal, characteristic, complemented
10#11762960C211yesmaximal, characteristic, complemented
11#11762909C211yesmaximal, characteristic, complemented
12#11762881C211yesmaximal, characteristic, complemented
13#11762814C211yesmaximal, characteristic, complemented
14#11762805C211yesmaximal, 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
28#10587622—21no—
29C2×#63229C2211yescharacteristic
30C2×#63229C2211yescharacteristic
31#10587612C2211yescharacteristic
32#10587612C2211yescharacteristic, complemented
33#10587610C2211yescharacteristic
34#10587610C2211yescharacteristic, complemented
35C2×#63223C2211yescharacteristic
36C22×#3622C2211yescharacteristic, complemented
37#10587573—21no—
38#10587565—21no—
39#10587565—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#10587479C2211yescharacteristic, complemented
55#10587479C2211yescharacteristic, 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
75C2×Dic34—21no—
76C2×Dic34C2311yescharacteristic
77C4⋊C4×C17—21no—
78C4⋊C4×C17D411yescharacteristic
79C4⋊C4×C17C2311yescharacteristic
80C22⋊C4×C17—21no—
81C22⋊C4×C17—21no—
82C22⋊C4×C17—21no—
83C22⋊C4×C17—21no—
84C22⋊C4×C17—21no—
85C22⋊C4×C17D411yescharacteristic
86C22⋊C4×C17D411yescharacteristic
87C42×C17C2311yescharacteristic
88C22⋊Dic17—21no—
89C22⋊Dic17—21no—
90C22⋊Dic17—21no—
91C22⋊Dic17—21no—
92#63231—41no—
93#63229—22no—
94#63229—41no—
95C4⋊Dic17—21no—
96C4⋊Dic17C2311yescharacteristic
97C4⋊Dic17C2311yescharacteristic
98C4⋊Dic17C2311yescharacteristic
99#63225—21no—
100#63225—21no—
101#63225—21no—
102C4×Dic17—21no—
103C4×Dic17—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—21no—
121D4×C17—21no—
122D4×C17—21no—
123D4×C17—41no—
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—
145Dic34—21no—
146Dic34—21no—
147Dic34—42no—
148#3622—21no—
149#3622—21no—
150#3622—21no—
151#3622—21no—
152#3311—171nomaximal, Sylow
153C22×C17—21no—
154C22×C17—21no—
155C22×C17—22no—
156C22×C17—21no—
157C22×C17—21no—
158C22×C17—21no—
159C22×C17—21no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17—41no—
164C22×C17—41no—
165C22×C17—84no—
166C22×C17C22×D411yescharacteristic
167C4×C17—21no—
168C4×C17—21no—
169C4×C17—21no—
170C4×C17—21no—
171C4×C17—41no—
172C4×C17—41no—
173C4×C17C2×#4111yescharacteristic
174C4×C17H(5,𝔽2)11yescharacteristic
175Dic17—41no—
176Dic17—41no—
177Dic17—41no—
178Dic17—41no—
179#556—171no—
180#546D1711yescharacteristic
181#489—171no—
182#485—171no—
183#482—171no—
184#476—171no—
185#470—171no—
186#465—171no—
187#464—171no—
188#452—171no—
189#450—171no—
190#440—171no—
191#435—171no—
192#418—171no—
193#416—171no—
194C2×C17—41no—
195C2×C17—41no—
196C2×C17—42no—
197C2×C17—81no—
198C2×C17#54611yescharacteristic
199C2×C17#57511yescharacteristic
200C2×C17#57711yescharacteristic
201C2×#41C2×D1711yescharacteristic
202C22×D4C2×D1711yescharacteristic
203C2×Q16—171no—
204C2×SD16—171no—
205C2×SD16—171no—
206C2×M16—171no—
207C22×C8—171no—
208C4⋊Q8—171no—
209#126—341no—
210#126—341no—
211#124—341no—
212#124C2×D1711yescharacteristic
213#123—21no—
214C22⋊Q8—171no—
215C22⋊Q8—171no—
216C22⋊Q8C2×D1711yescharacteristic
217#121—21no—
218#121C2×D1711yescharacteristic
219#120—21no—
220C4×Q8—171no—
221C4×Q8—341no—
222C4×D4C2×D1711yescharacteristic
223C4×D4C2×D1711yescharacteristic
224#117—171no—
225#117—171no—
226C2×C22⋊C4—21no—
227#107—171no—
228#106—171no—
229#106—171no—
230C4⋊C8—171no—
231#103—171no—
232#103—171no—
233#103—171no—
234#103—171no—
235#102—171no—
236#102—171no—
237#102—171no—
238#102—171no—
239#102—171no—
240#102—171no—
241C22⋊C8—171no—
242C22⋊C8—171no—
243#97—171no—
244C17#331111yescharacteristic, complemented, Sylow
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—171no—
249C2×Q8—341no—
250C2×Q8C22×D1711yescharacteristic
251C2×D4—22no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4C22⋊D1711yescharacteristic
257C2×D4C22×D1711yescharacteristic
258C2×D4C22×D1711yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4C22×D1711yescharacteristic
262C22×C4C22×D1711yescharacteristic
263Q16—681no—
264SD16—342no—
265SD16—681no—
266M16—681no—
267C2×C8—171no—
268C2×C8—171no—
269C2×C8—171no—
270C2×C8—171no—
271C2×C8—681no—
272C4⋊C4—21no—
273C4⋊C4—171no—
274C4⋊C4—171no—
275C4⋊C4—171no—
276C4⋊C4—341no—
277C4⋊C4—341no—
278C4⋊C4—341no—
279C4⋊C4—341no—
280C4⋊C4C22⋊D1711yescharacteristic
281C4⋊C4C22×D1711yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—341no—
288C22⋊C4—341no—
289C22⋊C4—341no—
290C22⋊C4—341no—
291C22⋊C4C22⋊D1711yescharacteristic
292C22⋊C4C22⋊D1711yescharacteristic
293C42—341no—
294C42—341no—
295C42—341no—
296C42C22×D1711yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D1711yescharacteristic
303C23C2×C22⋊D1711yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—341no—
307Q8—341no—
308Q8—682no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—42no—
314D4—42no—
315D4—81no—
316D4#6325412yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—341no—
326C2×C4—341no—
327C2×C4—341no—
328C2×C4—341no—
329C2×C4C2×C22⋊D1711yescharacteristic
330C2×C4C2×C22⋊D1711yescharacteristic
331C2×C4C2×C22⋊D1711yescharacteristic
332C2×C4C2×C22⋊D1711yescharacteristic
333C2×C4C23×D1711yescharacteristic
334C8—341no—
335C8—341no—
336C8—341no—
337C8—341no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22C22×C22⋊D1711yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—681no—
359C4—681no—
360C4—681no—
361C4—681no—
362C4C2×#6325411yescharacteristic
363C4#1058769111yescharacteristic
364C2—41no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#1176345311yescharacteristic
369C2#1176360711yescharacteristic
370C2#1176362011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
Fitting, prime radicalC17×#546C2
socleC22×C17C22×D4
hypercenter#546D17
hypocenterC17#3311
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. #11763529C2semidirect
2. #11763168C2semidirect
3. #11763147C2semidirect
4. #11763130C2semidirect
5. #11763099C2semidirect
6. #11763065C2semidirect
7. #11763036C2semidirect
8. #11763028C2semidirect
9. #11762971C2semidirect
10. #11762960C2semidirect
11. #11762909C2semidirect
12. #11762881C2semidirect
13. #11762814C2semidirect
14. #11762805C2semidirect
27. C2×#63231C22semidirect
32. #10587612C22semidirect
34. #10587610C22semidirect
36. C22×#3622C22semidirect
40. #10587555C22semidirect
41. C4×Dic34C22semidirect
42. #10587506C22semidirect
43. #10587506C22semidirect
44. #10587506C22semidirect
52. C22⋊#3622C22semidirect
53. #10587481C22semidirect
54. #10587479C22semidirect
55. #10587479C22semidirect
56. #10587478C22semidirect
57. C4⋊#3622C22semidirect
58. #10587474C22semidirect
244. C17#3311semidirect

Maximal subgroups

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

subgroupindex
#117635292
#117631682
#117631472
#117631302
#117630992
#117630652
#117630362
#117630282
#117629712
#117629602
#117629092
#117628812
#117628142
#117628052
C17×#5462
#331117