Finite Group Databasebeta

← #16939043

Subgroups — #16939043

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#14529719C211yesmaximal, characteristic
2#14528943C211yesmaximal, characteristic
3#14528790C211yesmaximal, characteristic
4#14528786C211yesmaximal, characteristic
5#14526668C211yesmaximal, characteristic
6#14526618C211yesmaximal, characteristic
7C17×#1296C211yesmaximal, characteristic
8C2×C4×Dic34C2211yescharacteristic
9C2×#10587478—21no—
10C2×#10587478—21no—
11C2×C4⋊#3622C2211yescharacteristic
12C2×#10587487—21no—
13C2×#10587481—21no—
14C2×C4×#3622C2211yescharacteristic
15#11762679C2211yescharacteristic
16#11762572—21no—
17#11762571—21no—
18#11762563—21no—
19#11762563—21no—
20C2×C17×C4⋊C8C2211yescharacteristic
21C2×C17×C4⋊C8C2211yescharacteristic
22C17×#384C2211yescharacteristic
23C22×Dic34D411yescharacteristic
24C22×C8×C17—21no—
25C22×C8×C17—21no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C42×C17C2311yescharacteristic
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17D411yescharacteristic
34C2×#63225—21no—
35C2×C4×Dic17—21no—
36C22×#3622—21no—
37C22×#3622D411yescharacteristic
38C22×#3622D411yescharacteristic
39C4×Dic34—21no—
40C4×Dic34—21no—
41C4×Dic34—21no—
42C4×Dic34—21no—
43C17×C4⋊C8—21no—
44C17×C4⋊C8—21no—
45C17×C4⋊C8—21no—
46C17×C4⋊C8—21no—
47#10587487—42no—
48#10587481—42no—
49#10587478—42no—
50#10587478—42no—
51C4⋊#3622—21no—
52C4⋊#3622—21no—
53C4×#3622—21no—
54C4×#3622—21no—
55C22×C4×C17—41no—
56C22×C4×C17C2×D411yescharacteristic
57C22×C4×C17C2×D411yescharacteristic
58C22×C4×C17#4111yescharacteristic
59C22×Dic17—21no—
60C22×Dic17—21no—
61C22×Dic17—41no—
62C2×Dic34—21no—
63C2×Dic34—21no—
64C2×Dic34—21no—
65C2×Dic34—21no—
66C2×Dic34—21no—
67C2×Dic34Q1612yes—
68C2×C8×C17—41no—
69C2×C8×C17—41no—
70C2×C8×C17—41no—
71C2×C8×C17—41no—
72C2×C8×C17—41no—
73C2×C8×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—81no—
79C42×C17#4111yescharacteristic
80C42×C17#4111yescharacteristic
81C42×C17#4111yescharacteristic
82C42×C17#4111yescharacteristic
83C4⋊Dic17—21no—
84C4⋊Dic17—21no—
85C4⋊Dic17—41no—
86C4⋊Dic17—41no—
87C4⋊Dic17—41no—
88C4⋊Dic17—41no—
89C4⋊Dic17—81no—
90#63225—41no—
91#63225—41no—
92C4×Dic17—41no—
93C4×Dic17—41no—
94C2×#3622—21no—
95C2×#3622—21no—
96C2×#3622—21no—
97C2×#3622—21no—
98C2×#3622—41no—
99C2×#3622—41no—
100C2×#3622—41no—
101C2×#3622SD1612yes—
102C2×#3622Q1612yes—
103#10618—171nomaximal, Sylow
104C23×C17#12111yescharacteristic
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—81no—
108C2×C4×C17—81no—
109C2×C4×C17—81no—
110C2×C4×C17#12311yescharacteristic
111C2×C4×C17#12311yescharacteristic
112C2×C4×C17#12311yescharacteristic
113C2×C4×C17#12411yescharacteristic
114C2×C4×C17#12611yescharacteristic
115C2×C4×C17#12611yescharacteristic
116C2×C4×C17C2×SD1611yescharacteristic
117C2×C4×C17C2×Q1611yescharacteristic
118C2×C4×C17C2×Q1611yescharacteristic
119C2×C4×C17#13511yescharacteristic
120C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C17#13711yescharacteristic
124C2×Dic17—22no—
125C2×Dic17—41no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—81no—
131C2×Dic17—81no—
132C2×Dic17—81no—
133Dic34—22no—
134Dic34—22no—
135Dic34—41no—
136Dic34—41no—
137C8×C17—81no—
138C8×C17—81no—
139#3622—22no—
140#3622—22no—
141#3622—81no—
142#1984—171no—
143#1845—171no—
144#1803—171no—
145#1803—171no—
146#1296—171no—
147#1296D1711yescharacteristic
148#1277—171no—
149C22×C17#39711yescharacteristic
150C22×C17#46011yescharacteristic
151C22×C17#46211yescharacteristic
152C22×C17#46711yescharacteristic
153C22×C17#46911yescharacteristic
154C22×C17#47211yescharacteristic
155C22×C17#47311yescharacteristic
156C4×C17—21no—
157C4×C17—21no—
158C4×C17—161no—
159C4×C17#48211yescharacteristic
160C4×C17#48211yescharacteristic
161C4×C17#48311yescharacteristic
162C4×C17#48411yescharacteristic
163C4×C17#48411yescharacteristic
164C4×C17#48411yescharacteristic
165C4×C17#48711yescharacteristic
166C4×C17#48911yescharacteristic
167Dic17—42no—
168Dic17—81no—
169Dic17—161no—
170C2×C4×Q8—171no—
171C2×#107—341no—
172C2×#107—341no—
173C2×C4⋊C8—171no—
174C2×C4⋊C8C2×D1711yescharacteristic
175C2×C4⋊C8C2×D1711yescharacteristic
176C2×#103—341no—
177C2×#103—341no—
178C2×C4×C8—171no—
179#384—171no—
180#384C2×D1711yescharacteristic
181#340—341no—
182#340—341no—
183#336—341no—
184#336—341no—
185C2×C17#167011yescharacteristic
186C2×C17#167611yescharacteristic
187C2×C17#168811yescharacteristic
188C2×C17#169411yescharacteristic
189C2×C17#207211yescharacteristic
190C2×C17#207611yescharacteristic
191C2×C17#207811yescharacteristic
192C22×Q8—171no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—171no—
196C22×C8—171no—
197C22×C8—341no—
198C4×Q8—341no—
199C4×Q8—341no—
200C4×Q8—341no—
201C4×Q8—341no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—171no—
206C2×C4⋊C4—341no—
207C2×C4⋊C4—341no—
208C2×C4⋊C4—341no—
209C2×C4⋊C4—341no—
210C2×C42—341no—
211C2×C42C22×D1711yescharacteristic
212#107—682no—
213#107—682no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—341no—
219C4⋊C8—341no—
220#103—682no—
221#103—682no—
222C4×C8—341no—
223C4×C8—341no—
224C17#1061811yescharacteristic, complemented, Sylow
225C2×Q8—172no—
226C2×Q8—341no—
227C2×Q8—341no—
228C2×Q8—341no—
229C2×Q8—341no—
230C2×Q8—341no—
231C22×C4—41no—
232C22×C4—341no—
233C22×C4—341no—
234C22×C4—681no—
235C22×C4#6325211yescharacteristic
236C22×C4D4×D1711yescharacteristic
237C22×C4D4×D1711yescharacteristic
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—172no—
245C2×C8—172no—
246C2×C8—341no—
247C2×C8—341no—
248C2×C8—341no—
249C2×C8—341no—
250C2×C8—681no—
251C2×C8—681no—
252C2×C8—681no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—341no—
259C4⋊C4—341no—
260C4⋊C4—681no—
261C4⋊C4—681no—
262C4⋊C4—681no—
263C4⋊C4—681no—
264C4⋊C4—681no—
265C4⋊C4—681no—
266C4⋊C4—1361no—
267C42—681no—
268C42—681no—
269C42#6325211yescharacteristic
270C42#6325211yescharacteristic
271C42#6325411yescharacteristic
272C42#6325611yescharacteristic
273C23#1058757011yescharacteristic
274Q8—342no—
275Q8—342no—
276Q8—681no—
277Q8—681no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—342no—
284C2×C4—681no—
285C2×C4—681no—
286C2×C4—681no—
287C2×C4—681no—
288C2×C4—681no—
289C2×C4—1361no—
290C2×C4—1361no—
291C2×C4—1361no—
292C2×C4#1058756211yescharacteristic
293C2×C4#1058756911yescharacteristic
294C2×C4#1058757111yescharacteristic
295C2×C4#1058758011yescharacteristic
296C2×C4#1058758011yescharacteristic
297C2×C4#1058758411yescharacteristic
298C2×C4#1058759711yescharacteristic
299C2×C4#1058759711yescharacteristic
300C2×C4SD16×D1711yescharacteristic
301C2×C4#1058760011yescharacteristic
302C2×C4#1058760111yescharacteristic
303C2×C4#1058760211yescharacteristic
304C2×C4Q16×D1711yescharacteristic
305C2×C4Q16×D1711yescharacteristic
306C8—81no—
307C8—81no—
308C8—342no—
309C8—342no—
310C8—1361no—
311C22#1176273811yescharacteristic
312C22#1176300811yescharacteristic
313C22#1176301811yescharacteristic
314C22#1176304911yescharacteristic
315C22#1176306111yescharacteristic
316C22#1176307811yescharacteristic
317C22#1176308311yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—2721no—
322C4—682no—
323C4—1361no—
324C4#1176313211yescharacteristic
325C4#1176313511yescharacteristic
326C4#1176314111yescharacteristic
327C4#1176314311yescharacteristic
328C4#1176314611yescharacteristic
329C4#1176314611yescharacteristic
330C4#1176315811yescharacteristic
331C4#1176316711yescharacteristic
332C2#1452815311yescharacteristic
333C2#1452818711yescharacteristic
334C2#1452826711yescharacteristic
335C2#1452830111yescharacteristic
336C2#1453019611yescharacteristic
337C2#1453021611yescharacteristic
338C2#1453022811yescharacteristic
subgroupG/H
centerC23#10587570
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1296C2
socle, prime radicalC23×C17#121
hypercenter#1296D17
hypocenterC17#10618
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
224. C17#10618semidirect

Maximal subgroups

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

subgroupindex
#145297192
#145289432
#145287902
#145287862
#145266682
#145266182
C17×#12962
#1061817