Finite Group Databasebeta

← #16939085

Subgroups — #16939085

Order 4352.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14528912C211yesmaximal, characteristic
2#14528789C211yesmaximal, characteristic
3#14528789C211yesmaximal, characteristic
4#14526668C211yesmaximal, characteristic
5#14526668C211yesmaximal, characteristic
6#14526619C211yesmaximal, characteristic
7C17×#1984C211yesmaximal, characteristic
8C2×C4⋊#3622C2211yescharacteristic
9C2×C4⋊#3622C2211yescharacteristic
10C2×#10587506—21no—
11C2×#10587506—21no—
12#11762679C2211yescharacteristic
13#11762679C2211yescharacteristic
14#11762572—21no—
15#11762572—21no—
16#11762571—21no—
17#11762571—21no—
18C2×C4×Q8×C17C2211yescharacteristic
19C2×C17×C4⋊C8C2211yescharacteristic
20C2×C4×C8×C17C2211yescharacteristic
21C17×#336—21no—
22C17×#336—21no—
23C22×Q8×C17D411yescharacteristic
24C22×C8×C17—21no—
25C22×C8×C17D411yescharacteristic
26C22×C8×C17D411yescharacteristic
27C4×Q8×C17—21no—
28C4×Q8×C17—21no—
29C4×Q8×C17—21no—
30C4×Q8×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C42×C17—21no—
34C2×C42×C17C2311yescharacteristic
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17—21no—
39C2×C4⋊Dic17—21no—
40C2×C4⋊Dic17—21no—
41C22×#3622—21no—
42C22×#3622—21no—
43C17×C4⋊C8—21no—
44C17×C4⋊C8—21no—
45C4×C8×C17—21no—
46C4×C8×C17—21no—
47#10587506—42no—
48#10587506—42no—
49C4⋊#3622—21no—
50C4⋊#3622—21no—
51C4⋊#3622—21no—
52C4⋊#3622—21no—
53C2×Q8×C17—21no—
54C2×Q8×C17—21no—
55C2×Q8×C17—21no—
56C2×Q8×C17—21no—
57C2×Q8×C17—21no—
58C2×Q8×C17SD1612yes—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C22×C4×C17#4111yescharacteristic
64C22×Dic17—41no—
65C22×Dic17—41no—
66C2×C8×C17—21no—
67C2×C8×C17—21no—
68C2×C8×C17—21no—
69C2×C8×C17—21no—
70C2×C8×C17—21no—
71C2×C8×C17—21no—
72C2×C8×C17—41no—
73C2×C8×C17—41no—
74C2×C8×C17—41no—
75C4⋊C4×C17—21no—
76C4⋊C4×C17—21no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C42×C17—41no—
80C42×C17—41no—
81C42×C17#4111yescharacteristic
82C42×C17#4111yescharacteristic
83C42×C17#4111yescharacteristic
84C42×C17#4111yescharacteristic
85C4⋊Dic17—41no—
86C4⋊Dic17—41no—
87C4⋊Dic17—41no—
88C4⋊Dic17—41no—
89C4⋊Dic17—41no—
90C4⋊Dic17—41no—
91C4⋊Dic17—41no—
92C4⋊Dic17—41no—
93C4⋊Dic17—81no—
94C4⋊Dic17—81no—
95C2×#3622—41no—
96C2×#3622—41no—
97C2×#3622—41no—
98C2×#3622—41no—
99C2×#3622—41no—
100C2×#3622—41no—
101#10626—171nomaximal, Sylow
102C23×C17#12111yescharacteristic
103Q8×C17—22no—
104Q8×C17—22no—
105Q8×C17—41no—
106Q8×C17—41no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—22no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17#12311yescharacteristic
116C2×C4×C17#12311yescharacteristic
117C2×C4×C17#12311yescharacteristic
118C2×C4×C17#12411yescharacteristic
119C2×C4×C17#12611yescharacteristic
120C2×C4×C17#12611yescharacteristic
121C2×C4×C17C2×SD1611yescharacteristic
122C2×C4×C17#13511yescharacteristic
123C2×C4×C17#13511yescharacteristic
124C2×C4×C17#13511yescharacteristic
125C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C17#13711yescharacteristic
127C2×C4×C17#13711yescharacteristic
128C2×C4×C17#13711yescharacteristic
129C2×Dic17—81no—
130C2×Dic17—81no—
131C2×Dic17—81no—
132C2×Dic17—81no—
133C2×Dic17—81no—
134C2×Dic17—81no—
135C8×C17—41no—
136C8×C17—41no—
137C8×C17—81no—
138#3622—81no—
139#3622—81no—
140#1984D1711yescharacteristic
141#1834—171no—
142#1803—171no—
143#1803—171no—
144#1296—171no—
145#1296—171no—
146#1277—171no—
147C22×C17#39711yescharacteristic
148C22×C17#46411yescharacteristic
149C22×C17#46411yescharacteristic
150C22×C17#46511yescharacteristic
151C22×C17#46811yescharacteristic
152C22×C17#47211yescharacteristic
153C22×C17#47311yescharacteristic
154C4×C17—21no—
155C4×C17—21no—
156C4×C17—42no—
157C4×C17—81no—
158C4×C17#48111yescharacteristic
159C4×C17#48211yescharacteristic
160C4×C17#48311yescharacteristic
161C4×C17#48511yescharacteristic
162C4×C17#48511yescharacteristic
163C4×C17#48511yescharacteristic
164C4×C17#48811yescharacteristic
165C4×C17#49111yescharacteristic
166Dic17—161no—
167Dic17—161no—
168C2×C4×Q8C2×D1711yescharacteristic
169C2×C4⋊C8—171no—
170C2×C4⋊C8—171no—
171C2×C4⋊C8C2×D1711yescharacteristic
172C2×#103—341no—
173C2×#103—341no—
174C2×C4×C8C2×D1711yescharacteristic
175#384—171no—
176#384—171no—
177#340—341no—
178#340—341no—
179#340—341no—
180#340—341no—
181#336—21no—
182#336—21no—
183C2×C17#167811yescharacteristic
184C2×C17#168011yescharacteristic
185C2×C17#169811yescharacteristic
186C2×C17#170011yescharacteristic
187C2×C17#207411yescharacteristic
188C2×C17#207711yescharacteristic
189C2×C17#207811yescharacteristic
190C22×Q8D6811yescharacteristic
191C22×C8—21no—
192C22×C8—341no—
193C22×C8—341no—
194C22×C8C22⋊D1711yescharacteristic
195C22×C8C22⋊D1711yescharacteristic
196C4×Q8—21no—
197C4×Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—341no—
202C2×C4⋊C4—341no—
203C2×C4⋊C4—341no—
204C2×C4⋊C4—341no—
205C2×C4⋊C4—341no—
206C2×C4⋊C4—341no—
207C2×C4⋊C4D6811yescharacteristic
208C2×C42—21no—
209C2×C42C22×D1711yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—341no—
213C4⋊C8—341no—
214C4⋊C8—341no—
215C4⋊C8—341no—
216#103—682no—
217#103—682no—
218C4×C8—21no—
219C4×C8—21no—
220C17#1062611yescharacteristic, complemented, Sylow
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×Q8#6321912yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—681no—
230C22×C4—681no—
231C22×C4C2×D6811yescharacteristic
232C22×C4#6325211yescharacteristic
233C22×C4C2×C22⋊D1711yescharacteristic
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—681no—
244C2×C8—681no—
245C2×C8—681no—
246C2×C8—681no—
247C2×C8—681no—
248C2×C8—681no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—681no—
254C4⋊C4—681no—
255C4⋊C4—681no—
256C4⋊C4—681no—
257C4⋊C4—681no—
258C4⋊C4—681no—
259C4⋊C4—681no—
260C4⋊C4—681no—
261C4⋊C4—1361no—
262C4⋊C4—1361no—
263C42—41no—
264C42—41no—
265C42#6325411yescharacteristic
266C42#6325411yescharacteristic
267C42#6325411yescharacteristic
268C42#6325411yescharacteristic
269C23#1058761611yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—1361no—
283C2×C4—1361no—
284C2×C4—1361no—
285C2×C4—1361no—
286C2×C4—1361no—
287C2×C4—1361no—
288C2×C4#1058756511yescharacteristic
289C2×C4#1058756511yescharacteristic
290C2×C4#1058757211yescharacteristic
291C2×C4#1058757211yescharacteristic
292C2×C4C2×#6321911yescharacteristic
293C2×C4#1058759011yescharacteristic
294C2×C4#1058759411yescharacteristic
295C2×C4#1058759511yescharacteristic
296C2×C4#1058762111yescharacteristic
297C2×C4#1058762211yescharacteristic
298C2×C4#1058762811yescharacteristic
299C2×C4#1058762811yescharacteristic
300C2×C4#1058763611yescharacteristic
301C2×C4#1058763611yescharacteristic
302C8—41no—
303C8—41no—
304C8—81no—
305C8—1361no—
306C8—1361no—
307C22#1176273411yescharacteristic
308C22#1176303111yescharacteristic
309C22#1176303111yescharacteristic
310C22#1176303811yescharacteristic
311C22#1176305511yescharacteristic
312C22#1176307911yescharacteristic
313C22#1176308411yescharacteristic
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—2721no—
319C4—2721no—
320C4#1176312811yescharacteristic
321C4#1176313411yescharacteristic
322C4#1176314011yescharacteristic
323C4#1176314711yescharacteristic
324C4#1176314711yescharacteristic
325C4#1176315111yescharacteristic
326C4#1176316311yescharacteristic
327C4#1176317711yescharacteristic
328C2#1452820011yescharacteristic
329C2#1452821411yescharacteristic
330C2#1452832411yescharacteristic
331C2#1452833811yescharacteristic
332C2#1453020211yescharacteristic
333C2#1453021711yescharacteristic
334C2#1453022411yescharacteristic
subgroupG/H
centerC23#10587616
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1984C2
socle, prime radicalC23×C17#121
hypercenter#1984D17
hypocenterC17#10626
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
220. C17#10626semidirect

Maximal subgroups

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

subgroupindex
#145289122
#145287892
#145266682
#145266192
C17×#19842
#1062617