Finite Group Databasebeta

← #14540754

Subgroups — #14540754

Order 2176.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763464C211yesmaximal, characteristic, complemented
2#11763179C211yesmaximal, characteristic, complemented
3#11763150C211yesmaximal, characteristic, complemented
4#11763139C211yesmaximal, characteristic, complemented
5#11763106C211yesmaximal, characteristic, complemented
6#11763053C211yesmaximal, characteristic, complemented
7#11763036C211yesmaximal, characteristic, complemented
8#11763014C211yesmaximal, characteristic, complemented
9#11762952C211yesmaximal, characteristic, complemented
10#11762952C211yesmaximal, characteristic, complemented
11#11762919C211yesmaximal, characteristic, complemented
12#11762881C211yesmaximal, characteristic, complemented
13#11762808C211yesmaximal, characteristic, complemented
14#11762803C211yesmaximal, characteristic, complemented
15C17×#553C211yesmaximal, characteristic, complemented
16C2×#63252C2211yescharacteristic
17C2×#63252C2211yescharacteristic
18C17×#126—21no—
19C17×#125C2211yescharacteristic
20C17×#123—21no—
21C17×#121—21no—
22C17×#121C2211yescharacteristic
23C17×#121C2211yescharacteristic
24C4×D4×C17—21no—
25C4×D4×C17C2211yescharacteristic
26C4×D4×C17C2211yescharacteristic
27C17×#117C2211yescharacteristic
28C2×C4⋊C4×C17C2211yescharacteristic
29#10587624—21no—
30C2×#63229C2211yescharacteristic
31C2×#63229C2211yescharacteristic
32C2×#63228C2211yescharacteristic
33#10587610C2211yescharacteristic
34#10587610C2211yescharacteristic
35C2×#63223C2211yescharacteristic
36C22×#3622C2211yescharacteristic
37C4⋊C4×D17—21no—
38#10587569—21no—
39#10587569—21no—
40C4×D68C2211yescharacteristic
41#10587555C2211yescharacteristic
42#10587503C2211yescharacteristic
43C22⋊#3622C2211yescharacteristic
44C22⋊#3622C2211yescharacteristic
45#10587481C2211yescharacteristic
46#10587481C2211yescharacteristic
47#10587481C2211yescharacteristic
48#10587481C2211yescharacteristic
49#10587481C2211yescharacteristic
50#10587481C2211yescharacteristic
51#10587480C2211yescharacteristic
52#10587480C2211yescharacteristic
53#10587480C2211yescharacteristic
54#10587479C2211yescharacteristic
55#10587479C2211yescharacteristic
56#10587478C2211yescharacteristic
57C4⋊#3622C2211yescharacteristic
58#10587474C2211yescharacteristic
59C2×D4×C17—21no—
60C2×D4×C17—21no—
61C2×D4×C17D411yescharacteristic
62C2×D4×C17C2311yescharacteristic
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17C2311yescharacteristic
66C22×C4×C17C2311yescharacteristic
67C2×C22⋊D17—21no—
68C2×C22⋊D17—21no—
69#63252—22no—
70#63252—22no—
71#63252—41no—
72#63252—41no—
73C2×D68C2311yescharacteristic
74C2×C4×D17—21no—
75C2×C4×D17—21no—
76C2×C4×D17—21no—
77C2×Dic34C2311yescharacteristic
78C2×Dic34C2311yescharacteristic
79C4⋊C4×C17—21no—
80C4⋊C4×C17—21no—
81C4⋊C4×C17—21no—
82C4⋊C4×C17D411yescharacteristic
83C4⋊C4×C17C2311yescharacteristic
84C4⋊C4×C17C2311yescharacteristic
85C4⋊C4×C17C2311yescharacteristic
86C22⋊C4×C17—21no—
87C22⋊C4×C17—21no—
88C22⋊C4×C17—21no—
89C22⋊C4×C17—21no—
90C22⋊C4×C17D411yescharacteristic
91C22⋊C4×C17D411yescharacteristic
92C42×C17—21no—
93C42×C17C2311yescharacteristic
94C22⋊Dic17—21no—
95C22⋊Dic17—21no—
96#63229—41no—
97#63229—41no—
98#63228—22no—
99#63227—21no—
100C4⋊Dic17—21no—
101C4⋊Dic17—21no—
102C4⋊Dic17C2311yescharacteristic
103#63225—21no—
104#63225—21no—
105#63223—41no—
106C2×#3622—41no—
107C2×#3622C2311yescharacteristic
108C2×#3622C2311yescharacteristic
109C2×#3622C2311yescharacteristic
110C2×#3622C2311yescharacteristic
111C23×C17—21no—
112C23×C17C2×D411yescharacteristic
113C23×C17C2×D411yescharacteristic
114C22×D17—21no—
115D4×C17—21no—
116D4×C17—21no—
117D4×C17—41no—
118D4×C17—42no—
119D4×C17—81no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—81no—
128C2×C4×C17—81no—
129C2×C4×C17C2×D411yescharacteristic
130C2×C4×C17C2×D411yescharacteristic
131C2×C4×C17C2×D411yescharacteristic
132C2×C4×C17C2×D411yescharacteristic
133C2×C4×C17C2411yescharacteristic
134C22⋊D17—42no—
135C22⋊D17—42no—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—21no—
139D68—21no—
140D68#4112yes—
141C4×D17—42no—
142C4×D17—42no—
143C4×D17—42no—
144Dic34—21no—
145Dic34—21no—
146Dic34—21no—
147Dic34—21no—
148#3622—21no—
149#3622—21no—
150#3622—21no—
151#3622—21no—
152#3307—171nomaximal, Sylow
153C22×C17—21no—
154C22×C17—21no—
155C22×C17—21no—
156C22×C17—21no—
157C22×C17—21no—
158C22×C17—21no—
159C22×C17—41no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17C22×D411yescharacteristic
163C2×D17—22no—
164C2×D17—41no—
165C2×D17—41no—
166C4×C17—21no—
167C4×C17—21no—
168C4×C17—21no—
169C4×C17—21no—
170C4×C17—41no—
171C4×C17—41no—
172C4×C17—41no—
173C4×C17C2×#4111yescharacteristic
174C4×C17H(5,𝔽2)11yescharacteristic
175Dic17—41no—
176Dic17—41no—
177Dic17—41no—
178#553D1711yescharacteristic, complemented
179#547—171no—
180#491—171no—
181#485—171no—
182#483—171no—
183#478—171no—
184#468—171no—
185#465—171no—
186#461—171no—
187#449—171no—
188#449—171no—
189#442—171no—
190#435—171no—
191#417—171no—
192#416—171no—
193C2×C17—41no—
194C2×C17—41no—
195C2×C17—81no—
196C2×C17#54611yescharacteristic
197C2×C17#57511yescharacteristic
198C2×C17#57711yescharacteristic
199D17—42no—
200C2×#41—171no—
201C2×#41—171no—
202C2×SD16—171no—
203C2×SD16—171no—
204C2×D8—171no—
205C2×M16—171no—
206C22×C8—171no—
207C4⋊Q8—171no—
208#126—21no—
209#125C2×D1711yescharacteristic
210#123—21no—
211#123—341no—
212#123—341no—
213C22⋊Q8—171no—
214C22⋊Q8—171no—
215#121—21no—
216#121—341no—
217#121C2×D1711yescharacteristic
218#121C2×D1711yescharacteristic
219C4×D4—21no—
220C4×D4—171no—
221C4×D4C2×D1711yescharacteristic
222C4×D4C2×D1711yescharacteristic
223#117C2×D1711yescharacteristic
224C2×C4⋊C4—341no—
225C2×C4⋊C4C2×D1711yescharacteristic
226#107—171no—
227#106—171no—
228#106—171no—
229C4⋊C8—171no—
230#103—171no—
231#103—171no—
232#103—171no—
233#103—171no—
234#103—171no—
235#103—171no—
236#102—171no—
237#102—171no—
238#102—171no—
239#102—171no—
240C22⋊C8—171no—
241C22⋊C8—171no—
242#97—171no—
243C17#330711yescharacteristic, complemented, Sylow
244#41—342no—
245#41—342no—
246#41—681no—
247#41—681no—
248C2×Q8—171no—
249C2×Q8—171no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—171no—
253C2×D4—341no—
254C2×D4—341no—
255C2×D4C22⋊D1711yescharacteristic
256C2×D4C22×D1711yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—341no—
260C22×C4—341no—
261C22×C4—341no—
262C22×C4C22×D1711yescharacteristic
263C22×C4C22×D1711yescharacteristic
264SD16—681no—
265SD16—681no—
266D8—342no—
267M16—681no—
268C2×C8—171no—
269C2×C8—171no—
270C2×C8—171no—
271C2×C8—171no—
272C2×C8—681no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—171no—
277C4⋊C4—341no—
278C4⋊C4—341no—
279C4⋊C4—341no—
280C4⋊C4—341no—
281C4⋊C4C22⋊D1711yescharacteristic
282C4⋊C4C22×D1711yescharacteristic
283C4⋊C4C22×D1711yescharacteristic
284C4⋊C4C22×D1711yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—341no—
290C22⋊C4—341no—
291C22⋊C4—341no—
292C22⋊C4C22⋊D1711yescharacteristic
293C22⋊C4C22⋊D1711yescharacteristic
294C42—21no—
295C42C22×D1711yescharacteristic
296C23—21no—
297C23—341no—
298C23C2×C22⋊D1711yescharacteristic
299C23C2×C22⋊D1711yescharacteristic
300Q8—341no—
301Q8—341no—
302Q8—341no—
303Q8—341no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—42no—
308D4—81no—
309D4—172no—
310D4—341no—
311D4—682no—
312D4—682no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—341no—
323C2×C4—341no—
324C2×C4—341no—
325C2×C4—682no—
326C2×C4—682no—
327C2×C4—682no—
328C2×C4C2×C22⋊D1711yescharacteristic
329C2×C4C2×C22⋊D1711yescharacteristic
330C2×C4C2×C22⋊D1711yescharacteristic
331C2×C4C2×C22⋊D1711yescharacteristic
332C2×C4C23×D1711yescharacteristic
333C8—341no—
334C8—341no—
335C8—341no—
336C8—341no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—342no—
347C22—681no—
348C22—681no—
349C22C22×C22⋊D1711yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—681no—
358C4—681no—
359C4—681no—
360C4#41×D1711yescharacteristic
361C4#1058769611yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—682no—
366C2#1176344711yescharacteristic
367C2#1176360711yescharacteristic
368C2#1176362011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#553C2
socleC22×C17C22×D4
hypercenter#553D17
hypocenterC17#3307
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #11763464C2semidirect
2. #11763179C2semidirect
3. #11763150C2semidirect
4. #11763139C2semidirect
5. #11763106C2semidirect
6. #11763053C2semidirect
7. #11763036C2semidirect
8. #11763014C2semidirect
9. #11762952C2semidirect
10. #11762952C2semidirect
11. #11762919C2semidirect
12. #11762881C2semidirect
13. #11762808C2semidirect
14. #11762803C2semidirect
15. C17×#553C2semidirect
178. #553D17semidirect
243. C17#3307semidirect

Maximal subgroups

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

subgroupindex
#117634642
#117631792
#117631502
#117631392
#117631062
#117630532
#117630362
#117630142
#117629522
#117629192
#117628812
#117628082
#117628032
C17×#5532
#330717