Finite Group Databasebeta

← #14541266

Subgroups — #14541266

Order 2176.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763520C211yesmaximal, characteristic, complemented
2#11763509C211yesmaximal, characteristic
3#11763215C211yesmaximal, characteristic, complemented
4#11763152C211yesmaximal, characteristic, complemented
5#11763146C211yesmaximal, characteristic, complemented
6#11763126C211yesmaximal, characteristic, complemented
7#11763121C211yesmaximal, characteristic, complemented
8#11763117C211yesmaximal, characteristic, complemented
9#11763054C211yesmaximal, characteristic, complemented
10#11763037C211yesmaximal, characteristic, complemented
11#11762909C211yesmaximal, characteristic, complemented
12#11762879C211yesmaximal, characteristic, complemented
13#11762850C211yesmaximal, characteristic, complemented
14#107×D17C211yesmaximal, characteristic, complemented
15C17×#474C211yesmaximal, characteristic, complemented
16C17×C4⋊Q8C2211yescharacteristic
17C4×D4×C17C2211yescharacteristic
18#10587632—21no—
19#10587632—21no—
20#10587624C2211yescharacteristic
21#10587624C2211yescharacteristic
22C2×#63229C2211yescharacteristic
23#10587615—21no—
24C4×C22⋊D17—21no—
25C2×#63218C2211yescharacteristic
26C2×C8×D17C2211yescharacteristic
27#10587583C2211yescharacteristic
28#10587583C2211yescharacteristic
29#10587579—21no—
30#10587578C2211yescharacteristic
31C4⋊C4×D17C2211yescharacteristic
32C4⋊C4×D17C2211yescharacteristic
33C4⋊C4×D17C2211yescharacteristic
34#10587576—21no—
35#10587570—21no—
36#10587565—21no—
37C4×D68C2211yescharacteristic
38#10587556C2211yescharacteristic
39C4×Dic34C2211yescharacteristic
40C17×#107C2211yescharacteristic
41C17×#107C2211yescharacteristic
42C17×C4⋊C8C2211yescharacteristic
43C17×#102C2211yescharacteristic
44C17×#102C2211yescharacteristic
45#10587503C2211yescharacteristic
46#10587491C2211yescharacteristic
47#10587491C2211yescharacteristic
48#10587489C2211yescharacteristic
49#10587488C2211yescharacteristic
50#10587487C2211yescharacteristic
51#10587487C2211yescharacteristic
52#10587481C2211yescharacteristic
53#10587479C2211yescharacteristic
54#10587479C2211yescharacteristic
55#10587478C2211yescharacteristic
56#10587478C2211yescharacteristic
57#10587478C2211yescharacteristic
58#10587474C2211yescharacteristic
59C2×Q8×C17—21no—
60C2×D4×C17C2311yescharacteristic
61C22×C4×C17—21no—
62C2×C22⋊D17—21no—
63C2×C22⋊D17—21no—
64C2×D68D411yescharacteristic
65C2×C4×D17—21no—
66C2×C4×D17—21no—
67C2×C4×D17—21no—
68C2×C4×D17C2311yescharacteristic
69C2×C4×D17C2311yescharacteristic
70C2×Dic34C2311yescharacteristic
71C2×C8×C17C2311yescharacteristic
72C2×C8×C17C2311yescharacteristic
73C4⋊C4×C17—21no—
74C4⋊C4×C17C2311yescharacteristic
75C4⋊C4×C17C2311yescharacteristic
76C4⋊C4×C17C2311yescharacteristic
77C22⋊C4×C17—21no—
78C42×C17C2311yescharacteristic
79C22⋊Dic17—21no—
80C22⋊Dic17—21no—
81#63229—22no—
82#63227—21no—
83#63227—21no—
84#63227—21no—
85#63227D411yescharacteristic
86#63227D411yescharacteristic
87C4⋊Dic17—21no—
88C4⋊Dic17—21no—
89C4⋊Dic17D411yescharacteristic
90C4⋊Dic17C2311yescharacteristic
91C4⋊Dic17C2311yescharacteristic
92C4⋊Dic17C2311yescharacteristic
93#63225—21no—
94#63225—21no—
95#63225—21no—
96#63225—21no—
97#63225—21no—
98#63225—21no—
99C4×Dic17—21no—
100C4×Dic17—21no—
101C2×#3622C2311yescharacteristic
102C2×#3622C2311yescharacteristic
103#63218—22no—
104C8×D17—22no—
105C23×C17—21no—
106C22×D17C2×D411yescharacteristic
107C22×D17C2×D411yescharacteristic
108Q8×C17—81no—
109D4×C17—21no—
110D4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—81no—
115C2×C4×C17C2×D411yescharacteristic
116C2×C4×C17C2×D411yescharacteristic
117C2×C4×C17C2411yescharacteristic
118C22⋊D17—42no—
119C22⋊D17—81no—
120C2×Dic17—21no—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17C2×D411yescharacteristic
125C2×Dic17C2×D411yescharacteristic
126D68—22no—
127C4×D17—21no—
128C4×D17—21no—
129C4×D17—21no—
130C4×D17—21no—
131C4×D17—81no—
132C4×D17—81no—
133C4×D17—81no—
134Dic34—21no—
135Dic34—21no—
136C8×C17—21no—
137C8×C17—21no—
138#3622—21no—
139#3622#4112yes—
140#3346—171nomaximal, Sylow
141C22×C17—41no—
142C22×C17—41no—
143C22×C17—41no—
144C22×C17C22×D411yescharacteristic
145C2×D17—21no—
146C2×D17—21no—
147C2×D17—21no—
148C2×D17—21no—
149C2×D17—21no—
150C2×D17#13712yes—
151C4×C17—21no—
152C4×C17—21no—
153C4×C17—41no—
154C4×C17—41no—
155C4×C17—41no—
156C4×C17C2×#4111yescharacteristic
157C4×C172−1+411yescharacteristic
158Dic17—21no—
159Dic17—21no—
160Dic17—41no—
161Dic17—41no—
162Dic17—41no—
163Dic17—41no—
164#554—171no—
165#553—171no—
166#501—171no—
167#485—171no—
168#484—171no—
169#481—171no—
170#480—171no—
171#479—171no—
172#474D1711yescharacteristic, complemented
173#468—171no—
174#465—171no—
175#440—171no—
176#435—171no—
177#428—171no—
178C2×#107—171no—
179C2×C17—81no—
180C2×C17#54711yescharacteristic
181C2×C17C2×#13711yescharacteristic
182C2×C17#57611yescharacteristic
183D17—22no—
184D17—41no—
185C2×SD16—171no—
186C2×M16—171no—
187C22×C8—171no—
188C4⋊Q8C2×D1711yescharacteristic
189#126—341no—
190#125—171no—
191#125—341no—
192#123—341no—
193C22⋊Q8—171no—
194C22⋊Q8—171no—
195C22⋊Q8—341no—
196C22⋊Q8—341no—
197#121—171no—
198#121—171no—
199#121—341no—
200C4×Q8—171no—
201C4×D4—171no—
202C4×D4—341no—
203C4×D4—341no—
204C4×D4C2×D1711yescharacteristic
205#117—171no—
206C2×C4⋊C4—171no—
207C2×C4⋊C4—171no—
208C2×C4⋊C4—171no—
209#107—171no—
210#107—171no—
211#107—171no—
212#107—171no—
213#107C2×D1711yescharacteristic
214#107C2×D1711yescharacteristic
215#106—171no—
216#106—171no—
217#106—171no—
218C4⋊C8C2×D1711yescharacteristic
219#103—171no—
220#103—171no—
221#103—171no—
222#102—171no—
223#102C2×D1711yescharacteristic
224#102C2×D1711yescharacteristic
225C22⋊C8—171no—
226C22⋊C8—171no—
227#97—171no—
228C17#334611yescharacteristic, complemented, Sylow
229C2×Q8—21no—
230C2×Q8—171no—
231C2×D4—171no—
232C2×D4—341no—
233C2×D4—341no—
234C2×D4C22×D1711yescharacteristic
235C22×C4—21no—
236C22×C4—171no—
237C22×C4—171no—
238C22×C4—341no—
239C22×C4—341no—
240C22×C4—341no—
241SD16—342no—
242M16—342no—
243C2×C8—171no—
244C2×C8—171no—
245C2×C8—342no—
246C2×C8C22×D1711yescharacteristic
247C2×C8C22×D1711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—171no—
250C4⋊C4—171no—
251C4⋊C4—171no—
252C4⋊C4—171no—
253C4⋊C4—341no—
254C4⋊C4—341no—
255C4⋊C4—341no—
256C4⋊C4—341no—
257C4⋊C4—341no—
258C4⋊C4—341no—
259C4⋊C4—341no—
260C4⋊C4—341no—
261C4⋊C4C22×D1711yescharacteristic
262C4⋊C4C22×D1711yescharacteristic
263C4⋊C4C22×D1711yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—171no—
266C22⋊C4—171no—
267C22⋊C4—341no—
268C22⋊C4—341no—
269C22⋊C4—341no—
270C22⋊C4—341no—
271C22⋊C4—341no—
272C42—341no—
273C42—341no—
274C42C22×D1711yescharacteristic
275C23—21no—
276C23—171no—
277C23—171no—
278Q8—81no—
279Q8—341no—
280Q8—341no—
281D4—21no—
282D4—21no—
283D4—342no—
284D4—682no—
285D4—1361no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—81no—
290C2×C4—171no—
291C2×C4—171no—
292C2×C4—341no—
293C2×C4—341no—
294C2×C4—341no—
295C2×C4—341no—
296C2×C4—341no—
297C2×C4—341no—
298C2×C4—341no—
299C2×C4—341no—
300C2×C4—1361no—
301C2×C4—1361no—
302C2×C4—1361no—
303C2×C4D4×D1711yescharacteristic
304C2×C4D4×D1711yescharacteristic
305C2×C4C23×D1711yescharacteristic
306C8—21no—
307C8—21no—
308C8—172no—
309C8—341no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—172no—
314C22—341no—
315C22—341no—
316C22—341no—
317C22—341no—
318C22—341no—
319C22C2×D4×D1711yescharacteristic
320C4—21no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—341no—
326C4—341no—
327C4—681no—
328C4—681no—
329C4—681no—
330C4—681no—
331C4#1058769411yescharacteristic
332C4#41×D1711yescharacteristic
333C2—81no—
334C2—342no—
335C2—681no—
336C2#1176346111yescharacteristic
337C2#137×D1711yescharacteristic
338C2#1176361011yescharacteristic
subgroupG/H
centerC22C2×D4×D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#474C2
socleC22×C17C22×D4
prime radical#11763509C2
hypercenter#474D17
hypocenterC17#3346
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11763520C2semidirect
3. #11763215C2semidirect
4. #11763152C2semidirect
5. #11763146C2semidirect
6. #11763126C2semidirect
7. #11763121C2semidirect
8. #11763117C2semidirect
9. #11763054C2semidirect
10. #11763037C2semidirect
11. #11762909C2semidirect
12. #11762879C2semidirect
13. #11762850C2semidirect
14. #107×D17C2semidirect
15. C17×#474C2semidirect
172. #474D17semidirect
228. C17#3346semidirect

Maximal subgroups

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

subgroupindex
#117635202
#117635092
#117632152
#117631522
#117631462
#117631262
#117631212
#117631172
#117630542
#117630372
#117629092
#117628792
#117628502
#107×D172
C17×#4742
#334617