Finite Group Databasebeta

← #16928639

Subgroups — #16928639

Order 4352.

438 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#14537353C211yesmaximal, characteristic
2#14528805C211yesmaximal, characteristic
3#14527555C211yesmaximal, characteristic, complemented
4#14527539C211yesmaximal, characteristic, complemented
5#14527164C211yesmaximal, characteristic
6#14526625C211yesmaximal, characteristic, complemented
7C17×#1303C211yesmaximal, characteristic, complemented
8C2×#10587593—21no—
9C4×#63252C2211yescharacteristic
10#11762837—21no—
11#11762834—22no—
12#11762833C2211yescharacteristic
13#11762831—21no—
14C2×C4⋊#3622C2211yescharacteristic
15C4⋊C8×D17—21no—
16C2×#10587476—21no—
17C2×C4×#3622C2211yescharacteristic
18#11762569—21no—
19#11762560—21no—
20#11762560—21no—
21#11762559—22no—
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—
40#10587593—42no—
41#10587593—42no—
42C2×#63218—22no—
43C2×C8×D17—22no—
44C4×D68C2×C411yescharacteristic
45C4×D68Q811yescharacteristic
46#10587558—21no—
47C42×D17—21no—
48C4×Dic34C2×C411yescharacteristic
49C4×Dic34Q811yescharacteristic
50C17×C4⋊C8—21no—
51C17×C4⋊C8C2×C411yescharacteristic
52C17×C4⋊C8C2×C411yescharacteristic
53C17×C4⋊C8D412yes—
54C17×C22⋊C8—21no—
55C4×C8×C17—21no—
56C17×#95—21no—
57#10587485—22no—
58#10587485—22no—
59#10587476—42no—
60C4⋊#3622—21no—
61C4⋊#3622—21no—
62C4⋊#3622—21no—
63C4⋊#3622D411yescharacteristic
64C4⋊#3622D411yescharacteristic
65C4×#3622—21no—
66C4×#3622C2×C411yescharacteristic
67C4×#3622C2×C411yescharacteristic
68C22×C4×C17—41no—
69C22×C4×C17C2×D411yescharacteristic
70C22×C4×C17#4111yescharacteristic
71C22×C4×C17#4111yescharacteristic
72C2×C22⋊D17—21no—
73#63252—21no—
74#63252—21no—
75#63252SD1612yes—
76#63252SD1612yes—
77C2×D68C4⋊C411yescharacteristic
78C2×C4×D17—21no—
79C2×C4×D17—21no—
80C2×C4×D17—21no—
81C2×Dic34C4⋊C411yescharacteristic
82M16×C17—41no—
83M16×C17—41no—
84C2×C8×C17—21no—
85C2×C8×C17—21no—
86C2×C8×C17—22no—
87C4⋊C4×C17—22no—
88C4⋊C4×C17—41no—
89C42×C17—41no—
90C42×C17—41no—
91C42×C17C22×C411yescharacteristic
92C42×C17C2×D411yescharacteristic
93C42×C17C2×D411yescharacteristic
94C42×C17C2×Q811yescharacteristic
95C22⋊Dic17—21no—
96#63227—21no—
97#63227—21no—
98C4⋊Dic17C4⋊C411yescharacteristic
99C4⋊Dic17C4⋊C411yescharacteristic
100#63225—21no—
101#63225—21no—
102C4×Dic17—21no—
103C4×Dic17—21no—
104C4×Dic17—21no—
105#63223—41no—
106#63223—41no—
107C2×#3622—21no—
108C2×#3622—21no—
109C2×#3622—21no—
110C2×#3622—21no—
111C2×#3622—42no—
112C2×#3622—41no—
113C2×#3622—41no—
114C2×#3622—41no—
115#63218—44no—
116C8×D17—44no—
117#8904—171nomaximal, Sylow
118C23×C17#12311yescharacteristic
119C22×D17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—41no—
123C2×C4×C17—42no—
124C2×C4×C17—81no—
125C2×C4×C17—81no—
126C2×C4×C17C2×C4⋊C411yescharacteristic
127C2×C4×C17C4×D411yescharacteristic
128C2×C4×C17C4×D411yescharacteristic
129C2×C4×C17#12011yescharacteristic
130C2×C4×C17C22⋊Q811yescharacteristic
131C2×C4×C17C22⋊Q811yescharacteristic
132C2×C4×C17C2×SD1611yescharacteristic
133C2×C4×C17C2×SD1611yescharacteristic
134C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C17#13711yescharacteristic
136C22⋊D17—22no—
137C22⋊D17—22no—
138C2×Dic17—21no—
139C2×Dic17—21no—
140C2×Dic17—21no—
141D68—21no—
142D68#10612yes—
143C4×D17—22no—
144C4×D17—22no—
145C4×D17—41no—
146C4×D17—41no—
147C4×D17—81no—
148Dic34—21no—
149Dic34#10612yes—
150C8×C17—41no—
151C8×C17—41no—
152C8×C17—42no—
153#3622—22no—
154#3622—41no—
155#3622—41no—
156#3622—41no—
157#3622—81no—
158#2906—171no—
159#1806—171no—
160#1570—171no—
161#1566—171no—
162#1476—171no—
163#1303D1711yescharacteristic, complemented
164#1279—171no—
165C22×C17—21no—
166C22×C17—21no—
167C22×C17#38511yescharacteristic
168C22×C17#48111yescharacteristic
169C22×C17#48311yescharacteristic
170C2×D17—22no—
171C2×D17—41no—
172C2×D17—41no—
173C4×C17—21no—
174C4×C17—21no—
175C4×C17—21no—
176C4×C17—82no—
177C4×C17C2×#10611yescharacteristic
178C4×C17#42811yescharacteristic
179C4×C17#44311yescharacteristic
180C4×C17#44411yescharacteristic
181C4×C17#44811yescharacteristic
182C4×C17#45011yescharacteristic
183Dic17—22no—
184Dic17—41no—
185Dic17—41no—
186C2×#131—341no—
187C4×#41—171no—
188#431C2×D1711yescharacteristic
189#424—341no—
190#424—342no—
191#423—171no—
192#423—341no—
193#423C2×D1711yescharacteristic
194C2×C4⋊C8—171no—
195C2×C4⋊C8—341no—
196C2×#104—341no—
197C2×C4×C8—171no—
198C4×C4⋊C4C2×D1711yescharacteristic
199#339—341no—
200#334—341no—
201#334—341no—
202#334—342no—
203Q8⋊C8—171no—
204Q8⋊C8—171no—
205D4⋊C8—171no—
206D4⋊C8—171no—
207C2×C17—21no—
208C2×C17—21no—
209C2×C17#185311yescharacteristic
210C2×C17#186111yescharacteristic
211C2×C17#186611yescharacteristic
212D17—42no—
213C2×#41—171no—
214#131—682no—
215#131—682no—
216C2×M16—21no—
217C2×M16—342no—
218C2×M16—341no—
219C22×C8—342no—
220C22×C8—341no—
221C22×C8—341no—
222C4×Q8—171no—
223C4×Q8—171no—
224C4×D4—171no—
225C4×D4—171no—
226C4×D4—341no—
227C4×D4—341no—
228#117—171no—
229#117—341no—
230C2×C4⋊C4—21no—
231C2×C42—21no—
232C2×C42—341no—
233C2×C42C22×D1711yescharacteristic
234C4⋊C8—21no—
235C4⋊C8—171no—
236C4⋊C8—171no—
237C4⋊C8—342no—
238C4⋊C8—342no—
239C4⋊C8—341no—
240C4⋊C8—341no—
241C4⋊C8—341no—
242C4⋊C8C4×D1711yescharacteristic
243C4⋊C8C4×D1711yescharacteristic
244C4⋊C8D6812yes—
245#104—682no—
246C22⋊C8—21no—
247C4×C8—21no—
248C4×C8—171no—
249C4×C8—171no—
250C4×C8—341no—
251#95—21no—
252C17#890411yescharacteristic, complemented, Sylow
253#41—172no—
254#41—172no—
255#41—341no—
256#41—341no—
257C2×Q8—171no—
258C2×D4—171no—
259C2×D4—341no—
260C22×C4—41no—
261C22×C4—341no—
262C22×C4—341no—
263C22×C4—341no—
264C22×C4#6325211yescharacteristic
265C22×C4D4×D1711yescharacteristic
266C22×C4#6325411yescharacteristic
267M16—41no—
268M16—41no—
269M16—684no—
270M16—681no—
271M16—681no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—22no—
275C2×C8—341no—
276C2×C8—341no—
277C2×C8—341no—
278C2×C8—341no—
279C2×C8—684no—
280C2×C8—682no—
281C2×C8—681no—
282C2×C8—681no—
283C2×C8—681no—
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—171no—
287C4⋊C4—171no—
288C4⋊C4—341no—
289C4⋊C4—341no—
290C22⋊C4—341no—
291C22⋊C4—341no—
292C22⋊C4—341no—
293C42—41no—
294C42—41no—
295C42—341no—
296C42—341no—
297C42—341no—
298C42C2×C4×D1711yescharacteristic
299C42C2×D6811yescharacteristic
300C42D4×D1711yescharacteristic
301C42Q8×D1711yescharacteristic
302C23—341no—
303C23#1058756911yescharacteristic
304Q8—172no—
305Q8—341no—
306D4—172no—
307D4—342no—
308D4—342no—
309D4—341no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—341no—
317C2×C4—342no—
318C2×C4—342no—
319C2×C4—341no—
320C2×C4—341no—
321C2×C4—681no—
322C2×C4—681no—
323C2×C4—1361no—
324C2×C4C4×D6811yescharacteristic
325C2×C4#1058756711yescharacteristic
326C2×C4#1058756811yescharacteristic
327C2×C4C4⋊C4×D1711yescharacteristic
328C2×C4#1058758211yescharacteristic
329C2×C4#1058758311yescharacteristic
330C2×C4#1058759711yescharacteristic
331C2×C4SD16×D1711yescharacteristic
332C2×C4SD16×D1711yescharacteristic
333C2×C4#1058760411yescharacteristic
334C8—42no—
335C8—41no—
336C8—41no—
337C8—342no—
338C8—681no—
339C8—681no—
340C8—681no—
341C8—1361no—
342C22—21no—
343C22—21no—
344C22—342no—
345C22—681no—
346C22—681no—
347C22#1176268311yescharacteristic
348C22#1176312611yescharacteristic
349C22#1176313811yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—82no—
354C4—342no—
355C4—681no—
356C4—681no—
357C4#106×D1711yescharacteristic
358C4#1176285011yescharacteristic
359C4#1176292311yescharacteristic
360C4#1176292811yescharacteristic
361C4#1176294911yescharacteristic
362C4#1176296111yescharacteristic
363C2—21no—
364C2—21no—
365C2—682no—
366C2#1452897811yescharacteristic
367C2#1452902711yescharacteristic
368C2#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#8904
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. #14527539C2semidirect
6. #14526625C2semidirect
7. C17×#1303C2semidirect
22. #11762539C4semidirect
23. #11762539C4semidirect
24. #11762536C4semidirect
25. #11762536C4semidirect
163. #1303D17semidirect
252. C17#8904semidirect

Maximal subgroups

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

subgroupindex
#145373532
#145288052
#145275552
#145275392
#145271642
#145266252
C17×#13032
#890417