Finite Group Databasebeta

← #16939055

Subgroups — #16939055

Order 4352.

366 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#14529721C211yesmaximal, characteristic
2#14528940C211yesmaximal, characteristic
3#14528789C211yesmaximal, characteristic
4#14526668C211yesmaximal, characteristic
5#14526667C211yesmaximal, characteristic
6#14526618C211yesmaximal, characteristic
7C17×#1803C211yesmaximal, characteristic
8C2×#10587479—21no—
9C2×#10587479—21no—
10C2×C4⋊#3622C2211yescharacteristic
11C2×C4⋊#3622C2211yescharacteristic
12C2×#10587506—21no—
13C2×C4×#3622C2211yescharacteristic
14#11762679C2211yescharacteristic
15#11762571—21no—
16#11762564—21no—
17#11762564—21no—
18C2×C4×Q8×C17C2211yescharacteristic
19C2×C17×C4⋊C8C2211yescharacteristic
20C2×C17×#103—21no—
21C17×#384C2211yescharacteristic
22C17×#340—21no—
23C22×Q8×C17D411yescharacteristic
24C22×C8×C17—21no—
25C4×Q8×C17—21no—
26C4×Q8×C17—21no—
27C4×Q8×C17—21no—
28C4×Q8×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C42×C17—21no—
35C2×C42×C17C2311yescharacteristic
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17—21no—
39C22×#3622—21no—
40C22×#3622—21no—
41C22×#3622D411yescharacteristic
42C22×#3622D411yescharacteristic
43C17×C4⋊C8—21no—
44C17×C4⋊C8—21no—
45C17×#103—42no—
46#10587506—42no—
47#10587479—42no—
48#10587479—42no—
49C4⋊#3622—21no—
50C4⋊#3622—21no—
51C4⋊#3622—21no—
52C4⋊#3622—21no—
53C4×#3622—21no—
54C4×#3622—21no—
55C2×Q8×C17—21no—
56C2×Q8×C17—21no—
57C2×Q8×C17—21no—
58C2×Q8×C17—21no—
59C2×Q8×C17—21no—
60C2×Q8×C17SD1612yes—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—41no—
64C22×C4×C17C2×D411yescharacteristic
65C22×C4×C17C2×D411yescharacteristic
66C22×C4×C17#4111yescharacteristic
67C22×Dic17—41no—
68C2×C8×C17—41no—
69C2×C8×C17—41no—
70C2×C8×C17—41no—
71C4⋊C4×C17—21no—
72C4⋊C4×C17—21no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—81no—
80C42×C17—41no—
81C42×C17—41no—
82C42×C17#4111yescharacteristic
83C42×C17#4111yescharacteristic
84C42×C17#4111yescharacteristic
85C42×C17#4111yescharacteristic
86C4⋊Dic17—41no—
87C4⋊Dic17—41no—
88C4⋊Dic17—41no—
89C4⋊Dic17—41no—
90C4⋊Dic17—81no—
91C2×#3622—21no—
92C2×#3622—21no—
93C2×#3622—21no—
94C2×#3622—21no—
95C2×#3622—41no—
96C2×#3622—41no—
97C2×#3622—41no—
98C2×#3622—41no—
99C2×#3622—41no—
100C2×#3622—41no—
101C2×#3622SD1612yes—
102C2×#3622Q1612yes—
103#10620—171nomaximal, Sylow
104C23×C17#12111yescharacteristic
105Q8×C17—22no—
106Q8×C17—22no—
107Q8×C17—41no—
108Q8×C17—41no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—22no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—81no—
118C2×C4×C17—81no—
119C2×C4×C17—81no—
120C2×C4×C17#12311yescharacteristic
121C2×C4×C17#12311yescharacteristic
122C2×C4×C17#12311yescharacteristic
123C2×C4×C17#12411yescharacteristic
124C2×C4×C17#12611yescharacteristic
125C2×C4×C17#12611yescharacteristic
126C2×C4×C17C2×SD1611yescharacteristic
127C2×C4×C17C2×SD1611yescharacteristic
128C2×C4×C17C2×Q1611yescharacteristic
129C2×C4×C17#13511yescharacteristic
130C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C17#13711yescharacteristic
133C2×C4×C17#13711yescharacteristic
134C2×Dic17—81no—
135C2×Dic17—81no—
136C2×Dic17—81no—
137C8×C17—81no—
138#3622—22no—
139#3622—22no—
140#3622—81no—
141#3622—81no—
142#1984—171no—
143#1844—171no—
144#1803—171no—
145#1803D1711yescharacteristic
146#1296—171no—
147#1296—171no—
148#1277—171no—
149C22×C17#39711yescharacteristic
150C22×C17#46011yescharacteristic
151C22×C17#46211yescharacteristic
152C22×C17#46511yescharacteristic
153C22×C17#46811yescharacteristic
154C22×C17#47111yescharacteristic
155C22×C17#47111yescharacteristic
156C4×C17—21no—
157C4×C17—21no—
158C4×C17—42no—
159C4×C17—81no—
160C4×C17—161no—
161C4×C17#48111yescharacteristic
162C4×C17#48211yescharacteristic
163C4×C17#48311yescharacteristic
164C4×C17#48311yescharacteristic
165C4×C17#48411yescharacteristic
166C4×C17#48511yescharacteristic
167C4×C17#48711yescharacteristic
168C4×C17#48911yescharacteristic
169Dic17—161no—
170C2×C4×Q8C2×D1711yescharacteristic
171C2×#106—341no—
172C2×#106—341no—
173C2×C4⋊C8—171no—
174C2×C4⋊C8—171no—
175C2×C4⋊C8C2×D1711yescharacteristic
176C2×#103—21no—
177C2×#103—341no—
178C2×C4×C8—171no—
179#384—171no—
180#384C2×D1711yescharacteristic
181#340—21no—
182#340—341no—
183#336—341no—
184#336—341no—
185C2×C17#166611yescharacteristic
186C2×C17#167211yescharacteristic
187C2×C17#168611yescharacteristic
188C2×C17#169211yescharacteristic
189C2×C17#207211yescharacteristic
190C2×C17#207711yescharacteristic
191C2×C17#207911yescharacteristic
192C22×Q8C22⋊D1711yescharacteristic
193C22×C8—21no—
194C22×C8—171no—
195C22×C8—171no—
196C22×C8—341no—
197C22×C8—341no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—341no—
207C2×C4⋊C4—341no—
208C2×C4⋊C4—341no—
209C2×C4⋊C4C22⋊D1711yescharacteristic
210C2×C42—21no—
211C2×C42C22×D1711yescharacteristic
212#106—682no—
213#106—682no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—341no—
217C4⋊C8—341no—
218C4⋊C8—341no—
219C4⋊C8—341no—
220#103—42no—
221#103—682no—
222C4×C8—341no—
223C4×C8—341no—
224C17#1062011yescharacteristic, complemented, Sylow
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8#6323012yes—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—681no—
235C22×C4D4×D1711yescharacteristic
236C22×C4#6325411yescharacteristic
237C22×C4C2×C22⋊D1711yescharacteristic
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—172no—
242C2×C8—172no—
243C2×C8—341no—
244C2×C8—341no—
245C2×C8—341no—
246C2×C8—341no—
247C2×C8—681no—
248C2×C8—681no—
249C2×C8—681no—
250C2×C8—681no—
251C2×C8—681no—
252C2×C8—681no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—681no—
263C4⋊C4—681no—
264C4⋊C4—681no—
265C4⋊C4—681no—
266C4⋊C4—1361no—
267C42—41no—
268C42—41no—
269C42#6325211yescharacteristic
270C42#6325211yescharacteristic
271C42#6325411yescharacteristic
272C42#6325411yescharacteristic
273C23#1058762511yescharacteristic
274Q8—22no—
275Q8—22no—
276Q8—41no—
277Q8—41no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—1361no—
290C2×C4—1361no—
291C2×C4—1361no—
292C2×C4#1058756511yescharacteristic
293C2×C4#1058756511yescharacteristic
294C2×C4#1058756911yescharacteristic
295C2×C4#1058757111yescharacteristic
296C2×C4SD16×D1711yescharacteristic
297C2×C4#1058760011yescharacteristic
298C2×C4Q16×D1711yescharacteristic
299C2×C4#1058760411yescharacteristic
300C2×C4#1058761511yescharacteristic
301C2×C4#1058761811yescharacteristic
302C2×C4#1058762111yescharacteristic
303C2×C4C2×#6323011yescharacteristic
304C2×C4#1058763611yescharacteristic
305C2×C4#1058763711yescharacteristic
306C8—81no—
307C8—342no—
308C8—342no—
309C8—1361no—
310C8—1361no—
311C22#1176273711yescharacteristic
312C22#1176300711yescharacteristic
313C22#1176301711yescharacteristic
314C22#1176304011yescharacteristic
315C22#1176305311yescharacteristic
316C22#1176307011yescharacteristic
317C22#1176307411yescharacteristic
318C4—21no—
319C4—21no—
320C4—42no—
321C4—81no—
322C4—161no—
323C4—2721no—
324C4#1176312711yescharacteristic
325C4#1176313011yescharacteristic
326C4#1176313711yescharacteristic
327C4#1176313811yescharacteristic
328C4#1176314311yescharacteristic
329C4#1176315011yescharacteristic
330C4#1176315811yescharacteristic
331C4#1176317011yescharacteristic
332C2#1452813411yescharacteristic
333C2#1452816811yescharacteristic
334C2#1452825411yescharacteristic
335C2#1452828811yescharacteristic
336C2#1453019511yescharacteristic
337C2#1453022111yescharacteristic
338C2#1453023211yescharacteristic
subgroupG/H
centerC23#10587625
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1803C2
socle, prime radicalC23×C17#121
hypercenter#1803D17
hypocenterC17#10620
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
224. C17#10620semidirect

Maximal subgroups

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

subgroupindex
#145297212
#145289402
#145287892
#145266682
#145266672
#145266182
C17×#18032
#1062017