Finite Group Databasebeta

← #16928632

Subgroups — #16928632

Order 4352.

392 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
1#14537452C211yesmaximal, characteristic
2#14528805C211yesmaximal, characteristic
3#14527555C211yesmaximal, characteristic, complemented
4#14527542C211yesmaximal, characteristic, complemented
5#14527164C211yesmaximal, characteristic
6#14526625C211yesmaximal, characteristic, complemented
7C17×#1303C211yesmaximal, characteristic, complemented
8C4×#63252C2211yescharacteristic
9#11762869—22no—
10#11762865—21no—
11#11762861—21no—
12#11762833C2211yescharacteristic
13C2×C4⋊#3622C2211yescharacteristic
14C2×#10587476—21no—
15#11762777—21no—
16#11762767—21no—
17C2×C4×#3622C2211yescharacteristic
18#11762569—21no—
19#11762561—22no—
20#11762560—21no—
21#11762560—21no—
22#11762539C411yescharacteristic, complemented
23#11762539C411yescharacteristic, complemented
24#11762536C411yescharacteristic, complemented
25#11762536C411yescharacteristic, complemented
26C17×#431C2211yescharacteristic
27C17×#423C2211yescharacteristic
28C4×C4⋊C4×C17C2211yescharacteristic
29C2×#63252D411yescharacteristic
30C2×M16×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C42×C17—21no—
33C2×C42×C17C2311yescharacteristic
34C4×C22⋊D17—21no—
35C4×C22⋊D17—21no—
36#10587612D411yescharacteristic
37C2×#63223—21no—
38C22×#3622—21no—
39C22×#3622—21no—
40C4×D68C2×C411yescharacteristic
41C4×D68Q811yescharacteristic
42#10587558—21no—
43C42×D17—21no—
44C4×Dic34C2×C411yescharacteristic
45C4×Dic34Q811yescharacteristic
46C17×C4⋊C8—21no—
47C17×C4⋊C8C2×C411yescharacteristic
48C17×C4⋊C8C2×C411yescharacteristic
49C17×C4⋊C8D412yes—
50C17×C22⋊C8—21no—
51C4×C8×C17—21no—
52C17×#95—21no—
53#10587491—22no—
54#10587491—22no—
55#10587486—22no—
56C8×Dic17—22no—
57#10587476—42no—
58C4⋊#3622—21no—
59C4⋊#3622—21no—
60C4⋊#3622—21no—
61C4⋊#3622D411yescharacteristic
62C4⋊#3622D411yescharacteristic
63C4×#3622—21no—
64C4×#3622C2×C411yescharacteristic
65C4×#3622C2×C411yescharacteristic
66C22×C4×C17—41no—
67C22×C4×C17C2×D411yescharacteristic
68C22×C4×C17#4111yescharacteristic
69C22×C4×C17#4111yescharacteristic
70C2×C22⋊D17—21no—
71#63252—21no—
72#63252—21no—
73#63252—21no—
74#63252—21no—
75C2×D68C4⋊C411yescharacteristic
76C2×C4×D17—21no—
77C2×C4×D17—21no—
78C2×C4×D17—21no—
79C2×Dic34C4⋊C411yescharacteristic
80M16×C17—41no—
81M16×C17—41no—
82C2×C8×C17—21no—
83C2×C8×C17—21no—
84C2×C8×C17—22no—
85C4⋊C4×C17—22no—
86C4⋊C4×C17—41no—
87C42×C17—41no—
88C42×C17—41no—
89C42×C17C22×C411yescharacteristic
90C42×C17C2×D411yescharacteristic
91C42×C17C2×D411yescharacteristic
92C42×C17C2×Q811yescharacteristic
93C22⋊Dic17—21no—
94#63227—21no—
95#63227—21no—
96C4⋊Dic17C4⋊C411yescharacteristic
97C4⋊Dic17C4⋊C411yescharacteristic
98#63225—21no—
99#63225—21no—
100C4×Dic17—21no—
101C4×Dic17—21no—
102C4×Dic17—21no—
103#63223—41no—
104#63223—41no—
105C2×#3622—21no—
106C2×#3622—21no—
107C2×#3622—21no—
108C2×#3622—21no—
109C2×#3622—42no—
110C2×#3622—41no—
111C2×#3622—41no—
112C2×#3622—41no—
113#8903—171nomaximal, Sylow
114C23×C17#12311yescharacteristic
115C22×D17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—41no—
119C2×C4×C17—42no—
120C2×C4×C17—81no—
121C2×C4×C17—81no—
122C2×C4×C17C2×C4⋊C411yescharacteristic
123C2×C4×C17C4×D411yescharacteristic
124C2×C4×C17C4×D411yescharacteristic
125C2×C4×C17#12011yescharacteristic
126C2×C4×C17C22⋊Q811yescharacteristic
127C2×C4×C17C22⋊Q811yescharacteristic
128C2×C4×C17#13511yescharacteristic
129C2×C4×C17#13511yescharacteristic
130C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C17#13711yescharacteristic
132C22⋊D17—41no—
133C22⋊D17—41no—
134C2×Dic17—21no—
135C2×Dic17—21no—
136C2×Dic17—21no—
137D68—21no—
138D68—21no—
139C4×D17—41no—
140C4×D17—41no—
141C4×D17—41no—
142C4×D17—41no—
143C4×D17—81no—
144Dic34—21no—
145Dic34—21no—
146C8×C17—41no—
147C8×C17—41no—
148C8×C17—42no—
149#3622—22no—
150#3622—41no—
151#3622—41no—
152#3622—41no—
153#3622—81no—
154#2925—171no—
155#1806—171no—
156#1570—171no—
157#1567—171no—
158#1476—171no—
159#1303D1711yescharacteristic, complemented
160#1279—171no—
161C22×C17—21no—
162C22×C17—21no—
163C22×C17#38511yescharacteristic
164C22×C17#48211yescharacteristic
165C22×C17#48511yescharacteristic
166C2×D17—41no—
167C2×D17—41no—
168C2×D17—41no—
169C4×C17—21no—
170C4×C17—21no—
171C4×C17—21no—
172C4×C17—82no—
173C4×C17#42711yescharacteristic
174C4×C17#42811yescharacteristic
175C4×C17#44311yescharacteristic
176C4×C17#44411yescharacteristic
177C4×C17#44911yescharacteristic
178C4×C17#45211yescharacteristic
179Dic17—41no—
180Dic17—41no—
181Dic17—41no—
182C4×#41—171no—
183#433—342no—
184#432—341no—
185#431—341no—
186#431C2×D1711yescharacteristic
187#423—171no—
188#423C2×D1711yescharacteristic
189C2×C4⋊C8—171no—
190C2×#104—341no—
191#408—341no—
192#405—341no—
193C2×C4×C8—171no—
194C4×C4⋊C4C2×D1711yescharacteristic
195#339—341no—
196#335—342no—
197#334—341no—
198#334—341no—
199Q8⋊C8—171no—
200Q8⋊C8—171no—
201D4⋊C8—171no—
202D4⋊C8—171no—
203C2×C17—21no—
204C2×C17—21no—
205C2×C17#185411yescharacteristic
206C2×C17#186111yescharacteristic
207C2×C17#186611yescharacteristic
208D17—81no—
209C2×#41—171no—
210C2×M16—21no—
211C2×M16—341no—
212C22×C8—341no—
213C22×C8—341no—
214C4×Q8—171no—
215C4×Q8—171no—
216C4×D4—171no—
217C4×D4—171no—
218C4×D4—341no—
219C4×D4—341no—
220#117—171no—
221#117—341no—
222C2×C4⋊C4—21no—
223C2×C42—21no—
224C2×C42—341no—
225C2×C42C22×D1711yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—171no—
228C4⋊C8—171no—
229C4⋊C8—341no—
230C4⋊C8—341no—
231C4⋊C8—341no—
232C4⋊C8C4×D1711yescharacteristic
233C4⋊C8C4×D1711yescharacteristic
234C4⋊C8D6812yes—
235#104—682no—
236C22⋊C8—21no—
237C22⋊C8—342no—
238C22⋊C8—342no—
239#97—342no—
240C4×C8—21no—
241C4×C8—171no—
242C4×C8—171no—
243C4×C8—342no—
244C4×C8—341no—
245#95—21no—
246C17#890311yescharacteristic, complemented, Sylow
247#41—341no—
248#41—341no—
249#41—341no—
250#41—341no—
251C2×Q8—171no—
252C2×D4—171no—
253C2×D4—341no—
254C22×C4—41no—
255C22×C4—341no—
256C22×C4—341no—
257C22×C4—341no—
258C22×C4#6325211yescharacteristic
259C22×C4D4×D1711yescharacteristic
260C22×C4#6325411yescharacteristic
261M16—41no—
262M16—41no—
263M16—681no—
264M16—681no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—22no—
268C2×C8—341no—
269C2×C8—341no—
270C2×C8—341no—
271C2×C8—341no—
272C2×C8—682no—
273C2×C8—681no—
274C2×C8—681no—
275C2×C8—681no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—171no—
279C4⋊C4—171no—
280C4⋊C4—341no—
281C4⋊C4—341no—
282C22⋊C4—341no—
283C22⋊C4—341no—
284C22⋊C4—341no—
285C42—41no—
286C42—41no—
287C42—341no—
288C42—341no—
289C42—341no—
290C42C2×C4×D1711yescharacteristic
291C42C2×D6811yescharacteristic
292C42D4×D1711yescharacteristic
293C42Q8×D1711yescharacteristic
294C23—341no—
295C23#1058756911yescharacteristic
296Q8—341no—
297Q8—341no—
298D4—341no—
299D4—341no—
300D4—681no—
301D4—681no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—341no—
309C2×C4—341no—
310C2×C4—341no—
311C2×C4—681no—
312C2×C4—681no—
313C2×C4—681no—
314C2×C4—681no—
315C2×C4—1361no—
316C2×C4C4×D6811yescharacteristic
317C2×C4#1058756711yescharacteristic
318C2×C4#1058756811yescharacteristic
319C2×C4C4⋊C4×D1711yescharacteristic
320C2×C4#1058758211yescharacteristic
321C2×C4#1058758311yescharacteristic
322C2×C4#1058759711yescharacteristic
323C2×C4#1058760211yescharacteristic
324C2×C4#1058760211yescharacteristic
325C2×C4#1058760411yescharacteristic
326C8—42no—
327C8—41no—
328C8—41no—
329C8—342no—
330C8—681no—
331C8—681no—
332C8—681no—
333C8—1361no—
334C22—21no—
335C22—21no—
336C22—681no—
337C22—681no—
338C22—681no—
339C22#1176268311yescharacteristic
340C22#1176313211yescharacteristic
341C22#1176314811yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—82no—
346C4—681no—
347C4—681no—
348C4—681no—
349C4#1176284411yescharacteristic
350C4#1176285011yescharacteristic
351C4#1176292311yescharacteristic
352C4#1176292811yescharacteristic
353C4#1176295511yescharacteristic
354C4#1176297411yescharacteristic
355C2—21no—
356C2—21no—
357C2—1361no—
358C2#1452898411yescharacteristic
359C2#1452902711yescharacteristic
360C2#1452906011yescharacteristic
subgroupG/H
centerC2×C4#10587568
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1303C2
socleC22×C17#385
prime radicalC2×#63252D4
cosocleC2×C42×C17C23
hypercenter#1303D17
hypocenterC17#8903
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #14527555C2semidirect
4. #14527542C2semidirect
6. #14526625C2semidirect
7. C17×#1303C2semidirect
22. #11762539C4semidirect
23. #11762539C4semidirect
24. #11762536C4semidirect
25. #11762536C4semidirect
159. #1303D17semidirect
246. C17#8903semidirect

Maximal subgroups

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

subgroupindex
#145374522
#145288052
#145275552
#145275422
#145271642
#145266252
C17×#13032
#890317