Finite Group Databasebeta

← #16928621

Subgroups — #16928621

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#14528801C211yesmaximal, characteristic
3#14527560C211yesmaximal, characteristic, complemented
4#14527167C211yesmaximal, characteristic
5#14526685C211yesmaximal, characteristic, complemented
6#14526624C211yesmaximal, characteristic, complemented
7C17×#1567C211yesmaximal, characteristic, complemented
8C2×#10587593—21no—
9C4×#63252C2211yescharacteristic
10#11762862C2211yescharacteristic
11#11762837—21no—
12#11762834—22no—
13#11762831—21no—
14C2×C4⋊#3622C2211yescharacteristic
15C4⋊C8×D17—21no—
16C2×#10587496—21no—
17C4×C4⋊Dic17C2211yescharacteristic
18#11762570—21no—
19#11762561—21no—
20#11762561—21no—
21#11762541C411yescharacteristic, complemented
22#11762541C411yescharacteristic, complemented
23#11762538C411yescharacteristic, complemented
24#11762538C411yescharacteristic, complemented
25C17×#423C2211yescharacteristic
26C17×#423C2211yescharacteristic
27C2×C4×C8×C17C2211yescharacteristic
28C17×#335—22no—
29C2×#63252D411yescharacteristic
30C2×M16×C17—21no—
31C2×M16×C17—21no—
32C22×C8×C17—21no—
33C2×C42×C17C2311yescharacteristic
34C4×C22⋊D17—21no—
35C4×C22⋊D17—21no—
36#10587612D411yescharacteristic
37C2×C4⋊Dic17—21no—
38C2×C4×Dic17—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⋊C8—21no—
52C17×C4⋊C8—21no—
53C17×C4⋊C8D412yes—
54C4×C8×C17—21no—
55C4×C8×C17C2×C411yescharacteristic
56C4×C8×C17C2×C411yescharacteristic
57#10587502—21no—
58C22⋊#3622—21no—
59#10587496—42no—
60#10587485—22no—
61#10587485—22no—
62C4⋊#3622—21no—
63C4⋊#3622C2×C411yescharacteristic
64C4⋊#3622C2×C411yescharacteristic
65C4⋊#3622D411yescharacteristic
66C4⋊#3622D411yescharacteristic
67C4×#3622—21no—
68C22×C4×C17C2×D411yescharacteristic
69C22×C4×C17#4111yescharacteristic
70C22×C4×C17#4111yescharacteristic
71C2×C22⋊D17—21no—
72C22×Dic17—41no—
73#63252—21no—
74#63252—21no—
75#63252D812yes—
76#63252Q1612yes—
77C2×D68C4⋊C411yescharacteristic
78C2×C4×D17—21no—
79C2×C4×D17—21no—
80C2×C4×D17—21no—
81C2×Dic34C4⋊C411yescharacteristic
82M16×C17—41no—
83M16×C17—41no—
84M16×C17—41no—
85M16×C17—41no—
86C2×C8×C17—21no—
87C2×C8×C17—21no—
88C2×C8×C17—22no—
89C2×C8×C17—42no—
90C2×C8×C17—41no—
91C42×C17C22×C411yescharacteristic
92C42×C17C2×D411yescharacteristic
93C42×C17C2×D411yescharacteristic
94C42×C17C2×Q811yescharacteristic
95C22⋊Dic17—21no—
96#63227—21no—
97#63227—21no—
98C4⋊Dic17—22no—
99C4⋊Dic17—41no—
100C4⋊Dic17C4⋊C411yescharacteristic
101C4⋊Dic17C4⋊C411yescharacteristic
102#63225—21no—
103#63225—21no—
104C4×Dic17—21no—
105C4×Dic17—21no—
106C4×Dic17—21no—
107C4×Dic17—41no—
108C4×Dic17—41no—
109C2×#3622—21no—
110C2×#3622—21no—
111C2×#3622—21no—
112C2×#3622—21no—
113C2×#3622—41no—
114C2×#3622—41no—
115#63218—44no—
116C8×D17—44no—
117#8902—171nomaximal, Sylow
118C23×C17#12311yescharacteristic
119C22×D17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—41no—
123C2×C4×C17C2×C4⋊C411yescharacteristic
124C2×C4×C17C4×D411yescharacteristic
125C2×C4×C17C4×D411yescharacteristic
126C2×C4×C17#12011yescharacteristic
127C2×C4×C17C22⋊Q811yescharacteristic
128C2×C4×C17C22⋊Q811yescharacteristic
129C2×C4×C17C2×D811yescharacteristic
130C2×C4×C17C2×Q1611yescharacteristic
131C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C17#13711yescharacteristic
133C22⋊D17—22no—
134C22⋊D17—22no—
135C2×Dic17—21no—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—42no—
139C2×Dic17—81no—
140C2×Dic17—81no—
141D68—21no—
142D68#10712yes—
143C4×D17—22no—
144C4×D17—22no—
145C4×D17—41no—
146C4×D17—41no—
147C4×D17—81no—
148Dic34—21no—
149Dic34#10712yes—
150C8×C17—22no—
151C8×C17—41no—
152C8×C17—42no—
153C8×C17—81no—
154#3622—41no—
155#3622—41no—
156#3622—41no—
157#3622—41no—
158#2906—171no—
159#1806—171no—
160#1571—171no—
161#1567D1711yescharacteristic, complemented
162#1476—171no—
163#1303—171no—
164#1279—171no—
165C22×C17—21no—
166C22×C17—21no—
167C22×C17#38511yescharacteristic
168C22×C17#48011yescharacteristic
169C22×C17#48411yescharacteristic
170C2×D17—22no—
171C2×D17—41no—
172C2×D17—41no—
173C4×C17—21no—
174C4×C17—21no—
175C4×C17—21no—
176C4×C17C2×#10711yescharacteristic
177C4×C17#42811yescharacteristic
178C4×C17#44311yescharacteristic
179C4×C17#44411yescharacteristic
180C4×C17#44711yescharacteristic
181C4×C17#45111yescharacteristic
182Dic17—22no—
183Dic17—41no—
184Dic17—41no—
185Dic17—82no—
186C2×#131—341no—
187C4×#41—171no—
188#431—171no—
189#424—341no—
190#424—342no—
191#423—341no—
192#423C2×D1711yescharacteristic
193#423C2×D1711yescharacteristic
194C2×C4⋊C8—171no—
195C2×C4⋊C8—341no—
196C2×#104—341no—
197C2×C4×C8C2×D1711yescharacteristic
198C4×C4⋊C4—171no—
199#339—341no—
200#335—22no—
201#335—341no—
202#335—341no—
203Q8⋊C8—171no—
204Q8⋊C8—171no—
205D4⋊C8—171no—
206D4⋊C8—171no—
207C2×C17—21no—
208C2×C17—21no—
209C2×C17#185211yescharacteristic
210C2×C17#186111yescharacteristic
211C2×C17#186611yescharacteristic
212D17—42no—
213C2×#41—171no—
214#131—682no—
215#131—682no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16—342no—
219C22×C8—21no—
220C22×C8—342no—
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—341no—
231C2×C42—341no—
232C2×C42—341no—
233C2×C42C22×D1711yescharacteristic
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—171no—
238C4⋊C8—171no—
239C4⋊C8—171no—
240C4⋊C8—171no—
241C4⋊C8—342no—
242C4⋊C8—342no—
243C4⋊C8—341no—
244C4⋊C8C22⋊D1712yes—
245#104—682no—
246C22⋊C8—341no—
247C4×C8—21no—
248C4×C8—341no—
249C4×C8C4×D1711yescharacteristic
250C4×C8C4×D1711yescharacteristic
251#95—341no—
252C17#890211yescharacteristic, 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—341no—
261C22×C4—341no—
262C22×C4—341no—
263C22×C4—681no—
264C22×C4#6325211yescharacteristic
265C22×C4D4×D1711yescharacteristic
266C22×C4#6325611yescharacteristic
267M16—41no—
268M16—41no—
269M16—41no—
270M16—41no—
271M16—684no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—22no—
275C2×C8—42no—
276C2×C8—41no—
277C2×C8—341no—
278C2×C8—341no—
279C2×C8—341no—
280C2×C8—341no—
281C2×C8—684no—
282C2×C8—681no—
283C2×C8—681no—
284C4⋊C4—171no—
285C4⋊C4—171no—
286C4⋊C4—342no—
287C4⋊C4—341no—
288C4⋊C4—341no—
289C4⋊C4—681no—
290C22⋊C4—341no—
291C22⋊C4—341no—
292C22⋊C4—341no—
293C42—341no—
294C42—341no—
295C42—341no—
296C42—681no—
297C42—681no—
298C42C2×C4×D1711yescharacteristic
299C42D4×D1711yescharacteristic
300C42Q8×D1711yescharacteristic
301C42C2×C22⋊D1711yescharacteristic
302C23—341no—
303C23#1058758011yescharacteristic
304Q8—172no—
305Q8—341no—
306D4—172no—
307D4—342no—
308D4—342no—
309D4—341no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—341no—
314C2×C4—342no—
315C2×C4—342no—
316C2×C4—341no—
317C2×C4—341no—
318C2×C4—681no—
319C2×C4—681no—
320C2×C4—682no—
321C2×C4—1361no—
322C2×C4—1361no—
323C2×C4—1361no—
324C2×C4C4⋊C4×D1711yescharacteristic
325C2×C4#1058757911yescharacteristic
326C2×C4#1058758211yescharacteristic
327C2×C4D8×D1711yescharacteristic
328C2×C4#1058759711yescharacteristic
329C2×C4Q16×D1711yescharacteristic
330C2×C4#1058760411yescharacteristic
331C2×C4C4×C22⋊D1711yescharacteristic
332C2×C4#1058762311yescharacteristic
333C2×C4#1058763211yescharacteristic
334C8—22no—
335C8—41no—
336C8—42no—
337C8—81no—
338C8—681no—
339C8—681no—
340C8—681no—
341C8—681no—
342C22—21no—
343C22—21no—
344C22—342no—
345C22—681no—
346C22—681no—
347C22#1176268011yescharacteristic
348C22#1176312411yescharacteristic
349C22#1176314611yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—342no—
354C4—681no—
355C4—681no—
356C4—1362no—
357C4#107×D1711yescharacteristic
358C4#1176285011yescharacteristic
359C4#1176292511yescharacteristic
360C4#1176293011yescharacteristic
361C4#1176294111yescharacteristic
362C4#1176296311yescharacteristic
363C2—21no—
364C2—21no—
365C2—682no—
366C2#1452897011yescharacteristic
367C2#1452902311yescharacteristic
368C2#1452905611yescharacteristic
subgroupG/H
centerC2×C4#10587623
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1567C2
socleC22×C17#385
prime radicalC2×#63252D4
cosocleC2×C42×C17C23
hypercenter#1567D17
hypocenterC17#8902
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1567

Complements

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

NH ≅ G/Ntype
3. #14527560C2semidirect
5. #14526685C2semidirect
6. #14526624C2semidirect
7. C17×#1567C2semidirect
21. #11762541C4semidirect
22. #11762541C4semidirect
23. #11762538C4semidirect
24. #11762538C4semidirect
161. #1567D17semidirect
252. C17#8902semidirect

Maximal subgroups

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

subgroupindex
#145373532
#145288012
#145275602
#145271672
#145266852
#145266242
C17×#15672
#890217