Finite Group Databasebeta

← #14540949

Subgroups — #14540949

Order 2176.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic34C211yesmaximal, characteristic, complemented
2#11763179C211yesmaximal, characteristic, complemented
3#11763150C211yesmaximal, characteristic, complemented
4#11763144C211yesmaximal, characteristic, complemented
5#11763113C211yesmaximal, characteristic, complemented
6#11763053C211yesmaximal, characteristic, complemented
7#11763036C211yesmaximal, characteristic, complemented
8#11763014C211yesmaximal, characteristic, complemented
9#11762947C211yesmaximal, characteristic, complemented
10#11762947C211yesmaximal, characteristic, complemented
11#11762909C211yesmaximal, characteristic, complemented
12#11762881C211yesmaximal, characteristic, complemented
13#11762817C211yesmaximal, characteristic, complemented
14C2×#10587481C211yesmaximal, characteristic, complemented
15C17×#553C211yesmaximal, characteristic
16C22×Dic34C2211yescharacteristic
17C22×Dic34C2211yescharacteristic
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
29D4×Dic17—21no—
30C2×#63229C2211yescharacteristic
31C2×#63229C2211yescharacteristic
32C2×#63229C2211yescharacteristic
33#10587610C2211yescharacteristic
34#10587610C2211yescharacteristic
35C2×#63223C2211yescharacteristic
36C22×#3622C2211yescharacteristic
37#10587574—21no—
38#10587564—21no—
39#10587564—21no—
40#10587555C2211yescharacteristic
41C4×Dic34C2211yescharacteristic
42#10587503C2211yescharacteristic
43C22⋊#3622C2211yescharacteristic
44C22⋊#3622C2211yescharacteristic
45#10587481C2211yescharacteristic
46#10587481C2211yescharacteristic
47#10587481C2211yescharacteristic
48#10587481C2211yescharacteristic
49#10587481C2211yescharacteristic
50#10587481C2211yescharacteristic
51#10587481C2211yescharacteristic
52#10587481C2211yescharacteristic
53#10587481C2211yescharacteristic
54#10587479C2211yescharacteristic
55#10587478C2211yescharacteristic
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
67C22×Dic17—21no—
68C22×Dic17—21no—
69C2×Dic34—22no—
70C2×Dic34—22no—
71C2×Dic34—21no—
72C2×Dic34—21no—
73C2×Dic34—41no—
74C2×Dic34—41no—
75C2×Dic34C2311yescharacteristic
76C2×Dic34C2311yescharacteristic
77C2×Dic34C2311yescharacteristic
78C4⋊C4×C17—21no—
79C4⋊C4×C17—21no—
80C4⋊C4×C17—21no—
81C4⋊C4×C17D411yescharacteristic
82C4⋊C4×C17C2311yescharacteristic
83C4⋊C4×C17C2311yescharacteristic
84C4⋊C4×C17C2311yescharacteristic
85C22⋊C4×C17—21no—
86C22⋊C4×C17—21no—
87C22⋊C4×C17—21no—
88C22⋊C4×C17—21no—
89C22⋊C4×C17D411yescharacteristic
90C22⋊C4×C17D411yescharacteristic
91C42×C17—21no—
92C42×C17C2311yescharacteristic
93C22⋊Dic17—21no—
94C22⋊Dic17—21no—
95#63229—22no—
96#63229—41no—
97#63229—41no—
98C4⋊Dic17—21no—
99C4⋊Dic17—21no—
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×C17C2×D411yescharacteristic
113C23×C17C2×D411yescharacteristic
114D4×C17—22no—
115D4×C17—21no—
116D4×C17—21no—
117D4×C17—42no—
118D4×C17—81no—
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—
126C2×C4×C17—81no—
127C2×C4×C17—81no—
128C2×C4×C17C2×D411yescharacteristic
129C2×C4×C17C2×D411yescharacteristic
130C2×C4×C17C2×D411yescharacteristic
131C2×C4×C17C2×D411yescharacteristic
132C2×C4×C17C2411yescharacteristic
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—21no—
136C2×Dic17—21no—
137C2×Dic17—42no—
138C2×Dic17—42no—
139Dic34—21no—
140Dic34—21no—
141Dic34—21no—
142Dic34—21no—
143Dic34—21no—
144Dic34—42no—
145Dic34—42no—
146Dic34#4112yes—
147#3622—21no—
148#3622—21no—
149#3622—21no—
150#3622—21no—
151#3320—171nomaximal, Sylow
152C22×C17—21no—
153C22×C17—21no—
154C22×C17—21no—
155C22×C17—21no—
156C22×C17—21no—
157C22×C17—41no—
158C22×C17—41no—
159C22×C17—41no—
160C22×C17#13712yes—
161C22×C17C22×D411yescharacteristic
162C4×C17—21no—
163C4×C17—21no—
164C4×C17—21no—
165C4×C17—21no—
166C4×C17—41no—
167C4×C17—41no—
168C4×C17—41no—
169C4×C17C2×#4111yescharacteristic
170C4×C17H(5,𝔽2)11yescharacteristic
171Dic17—22no—
172Dic17—41no—
173Dic17—41no—
174Dic17—41no—
175#553D1711yescharacteristic
176D4×Q8—171no—
177#491—171no—
178#485—171no—
179#484—171no—
180#479—171no—
181#468—171no—
182#465—171no—
183#461—171no—
184#448—171no—
185#448—171no—
186#440—171no—
187#435—171no—
188#419—171no—
189C2×#103—171no—
190C2×C17—22no—
191C2×C17—41no—
192C2×C17—81no—
193C2×C17#54611yescharacteristic
194C2×C17C2×#13711yescharacteristic
195C2×C17#57711yescharacteristic
196C22×Q8—171no—
197C22×Q8—171no—
198C2×SD16—171no—
199C2×SD16—171no—
200C2×SD16—171no—
201C2×M16—171no—
202C22×C8—171no—
203C4⋊Q8—171no—
204C4⋊Q8—341no—
205#126—21no—
206#125C2×D1711yescharacteristic
207#123—21no—
208C22⋊Q8—171no—
209C22⋊Q8—171no—
210C22⋊Q8—341no—
211C22⋊Q8—341no—
212#121—21no—
213#121C2×D1711yescharacteristic
214#121C2×D1711yescharacteristic
215C4×Q8—171no—
216C4×D4—21no—
217C4×D4—341no—
218C4×D4C2×D1711yescharacteristic
219C4×D4C2×D1711yescharacteristic
220#117C2×D1711yescharacteristic
221C2×C4⋊C4C2×D1711yescharacteristic
222#107—171no—
223#107—171no—
224#106—171no—
225C4⋊C8—171no—
226#103—171no—
227#103—171no—
228#103—171no—
229#103—171no—
230#103—171no—
231#103—171no—
232#103—171no—
233#103—171no—
234#103—171no—
235#102—171no—
236C22⋊C8—171no—
237C22⋊C8—171no—
238#97—171no—
239C17#332011yescharacteristic, complemented, Sylow
240C2×Q8—171no—
241C2×Q8—171no—
242C2×Q8—171no—
243C2×Q8—342no—
244C2×Q8—342no—
245C2×Q8—341no—
246C2×Q8—341no—
247C2×Q8—681no—
248C2×Q8—681no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D1711yescharacteristic
252C2×D4C22×D1711yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—341no—
256C22×C4—341no—
257C22×C4C22×D1711yescharacteristic
258C22×C4C22×D1711yescharacteristic
259SD16—342no—
260SD16—681no—
261SD16—681no—
262M16—681no—
263C2×C8—171no—
264C2×C8—171no—
265C2×C8—171no—
266C2×C8—171no—
267C2×C8—681no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—171no—
272C4⋊C4—341no—
273C4⋊C4—341no—
274C4⋊C4—341no—
275C4⋊C4—341no—
276C4⋊C4—341no—
277C4⋊C4C22⋊D1711yescharacteristic
278C4⋊C4C22×D1711yescharacteristic
279C4⋊C4C22×D1711yescharacteristic
280C4⋊C4C22×D1711yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—341no—
286C22⋊C4—341no—
287C22⋊C4C22⋊D1711yescharacteristic
288C22⋊C4C22⋊D1711yescharacteristic
289C42—21no—
290C42—341no—
291C42C22×D1711yescharacteristic
292C23—21no—
293C23C2×C22⋊D1711yescharacteristic
294C23C2×C22⋊D1711yescharacteristic
295Q8—172no—
296Q8—341no—
297Q8—341no—
298Q8—341no—
299Q8—341no—
300Q8—341no—
301Q8—682no—
302Q8—682no—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—341no—
318C2×C4—341no—
319C2×C4—341no—
320C2×C4—341no—
321C2×C4—682no—
322C2×C4—682no—
323C2×C4C2×C22⋊D1711yescharacteristic
324C2×C4C2×C22⋊D1711yescharacteristic
325C2×C4C2×C22⋊D1711yescharacteristic
326C2×C4C2×C22⋊D1711yescharacteristic
327C2×C4C23×D1711yescharacteristic
328C8—341no—
329C8—341no—
330C8—341no—
331C8—341no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1058763712yes—
341C22C22×C22⋊D1711yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—342no—
350C4—681no—
351C4—681no—
352C4—681no—
353C4#41×D1711yescharacteristic
354C4#1058769611yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1176344711yescharacteristic
359C2C2×#1058763711yescharacteristic
360C2#1176362011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
Fitting, prime radicalC17×#553C2
socleC22×C17C22×D4
hypercenter#553D17
hypocenterC17#3320
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. D4×Dic34C2semidirect
2. #11763179C2semidirect
3. #11763150C2semidirect
4. #11763144C2semidirect
5. #11763113C2semidirect
6. #11763053C2semidirect
7. #11763036C2semidirect
8. #11763014C2semidirect
9. #11762947C2semidirect
10. #11762947C2semidirect
11. #11762909C2semidirect
12. #11762881C2semidirect
13. #11762817C2semidirect
14. C2×#10587481C2semidirect
239. C17#3320semidirect

Maximal subgroups

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

subgroupindex
D4×Dic342
#117631792
#117631502
#117631442
#117631132
#117630532
#117630362
#117630142
#117629472
#117629092
#117628812
#117628172
C2×#105874812
C17×#5532
#332017