Finite Group Databasebeta

← #16954128

Subgroups — #16954128

Order 4352.

362 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762611C211yesmaximal, characteristic
2C2×#11762609C211yesmaximal, characteristic
3#14529648C211yesmaximal, characteristic
4#14528947C211yesmaximal, characteristic, complemented
5#14526875C211yesmaximal, characteristic, complemented
6#14526861C211yesmaximal, characteristic, complemented
7C17×#1380C211yesmaximal, characteristic, complemented
8C22×D136C2211yescharacteristic
9C22×#63214C2211yescharacteristic
10C2×#10587489C2211yescharacteristic
11C2×#10587479—21no—
12C2×#10587480—21no—
13C2×C8×Dic17C2211yescharacteristic
14#11762710—21no—
15#11762674—21no—
16#11762611—22no—
17#11762609—22no—
18C22×C16×C17C2211yescharacteristic
19C2×C17×#107C2211yescharacteristic
20C2×C17×#107C2211yescharacteristic
21C22×D68—21no—
22C22×C8×C17C2311yescharacteristic
23C2×C4⋊C4×C17—21no—
24C2×C4⋊C4×C17—21no—
25C2×#63227—41no—
26C2×#63227—41no—
27C2×C4⋊Dic17—21no—
28C2×C4×Dic17D411yescharacteristic
29C22×#3622D411yescharacteristic
30C2×D136—21no—
31C2×D136—21no—
32C2×D136—21no—
33C2×D136—21no—
34C2×D136—21no—
35C2×D136D412yes—
36C2×C16×C17—21no—
37C2×C16×C17—21no—
38C2×C16×C17—21no—
39C17×#107—21no—
40C17×#107—21no—
41C17×#107—21no—
42C17×#107—21no—
43#10587502—41no—
44#10587502—41no—
45#10587489—21no—
46#10587489—21no—
47C8×Dic17—21no—
48C8×Dic17—21no—
49C2×#63214—21no—
50C2×#63214—21no—
51C2×#63214—21no—
52#10587480—42no—
53#10587479—42no—
54C23×D17—41no—
55C22×C4×C17—41no—
56C22×C4×C17—41no—
57C22×C4×C17C2×D411yescharacteristic
58C22×Dic17—41no—
59C22×Dic17D811yescharacteristic
60C22×Dic17D811yescharacteristic
61C2×D68—22no—
62C2×D68—41no—
63C2×D68—41no—
64C2×D68—41no—
65C2×D68—41no—
66C2×D68—41no—
67C2×C8×C17C2×D411yescharacteristic
68C2×C8×C17#4111yescharacteristic
69C2×C8×C17#4111yescharacteristic
70C2×C8×C17#4111yescharacteristic
71C2×C8×C17#4111yescharacteristic
72C2×C8×C17#4111yescharacteristic
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77#63227—82no—
78#63227—82no—
79C4⋊Dic17—41no—
80C4⋊Dic17—41no—
81C4×Dic17—21no—
82C4×Dic17—21no—
83C2×#3622—21no—
84C2×#3622—21no—
85C2×#3622SD1612yes—
86D136—22no—
87D136—22no—
88D136—41no—
89D136—41no—
90C16×C17—41no—
91#63214—41no—
92#13482—171nomaximal, Sylow
93C23×C17C2×D811yescharacteristic
94C22×D17—42no—
95C22×D17—81no—
96C22×D17—81no—
97C22×D17—81no—
98C22×D17—81no—
99C22×D17—81no—
100C22×D17—81no—
101C2×C4×C17—81no—
102C2×C4×C17—81no—
103C2×C4×C17—81no—
104C2×C4×C17—81no—
105C2×C4×C17—81no—
106C2×C4×C17—81no—
107C2×C4×C17#12111yescharacteristic
108C2×C4×C17#12311yescharacteristic
109C2×C4×C17#12411yescharacteristic
110C2×C4×C17C2×SD1611yescharacteristic
111C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C17#13711yescharacteristic
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—81no—
120C2×Dic17—81no—
121C2×Dic17—81no—
122D68—42no—
123D68—42no—
124D68—81no—
125D68—81no—
126C8×C17#12311yescharacteristic
127C8×C17#12311yescharacteristic
128C8×C17#12611yescharacteristic
129C8×C17#12611yescharacteristic
130#3622—22no—
131C2×#357—171no—
132C2×#357—171no—
133#1970—171no—
134#1846—171no—
135#1380—171no—
136#1380D1711yescharacteristic, complemented
137#1374—171no—
138C22×C17#45911yescharacteristic
139C22×C17#48011yescharacteristic
140C22×C17#48611yescharacteristic
141C22×C17#50811yescharacteristic
142C22×C17#50811yescharacteristic
143C22×C17#50911yescharacteristic
144C22×C17#50911yescharacteristic
145C2×D17—82no—
146C2×D17—82no—
147C2×D17—82no—
148C2×D17—161no—
149C2×D17—161no—
150C2×D17—161no—
151C2×D17—161no—
152C4×C17—161no—
153C4×C17—161no—
154C4×C17#39711yescharacteristic
155C4×C17#46111yescharacteristic
156C4×C17#48111yescharacteristic
157C4×C17#48911yescharacteristic
158Dic17—41no—
159Dic17—41no—
160Dic17—161no—
161C22×D8—171no—
162C22×C16—171no—
163C22×C16C2×D1711yescharacteristic
164C2×#107—171no—
165C2×#107C2×D1711yescharacteristic
166C2×#107C2×D1711yescharacteristic
167C2×#106—341no—
168C2×#102—341no—
169C2×C4×C8—171no—
170#390—341no—
171#382—341no—
172#357—342no—
173#357—342no—
174C2×C17#207111yescharacteristic
175C2×C17#221011yescharacteristic
176C2×C17#221011yescharacteristic
177C2×C17#223411yescharacteristic
178C2×C17#223411yescharacteristic
179C2×C17#224211yescharacteristic
180C2×C17#224411yescharacteristic
181D17—162no—
182C22×D4—341no—
183C2×D8—172no—
184C2×D8—341no—
185C2×D8—341no—
186C2×D8—341no—
187C2×D8—341no—
188C2×D8—341no—
189C22×C8—171no—
190C22×C8C22×D1711yescharacteristic
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—341no—
194C2×C22⋊C4—681no—
195C2×C22⋊C4—681no—
196C2×C42—171no—
197C2×C16—21no—
198C2×C16—21no—
199C2×C16—21no—
200C2×C16—341no—
201C2×C16—341no—
202C2×C16—341no—
203#107—21no—
204#107—21no—
205#107—21no—
206#107—21no—
207#107—341no—
208#107—341no—
209#106—682no—
210#102—682no—
211C4×C8—341no—
212C4×C8—341no—
213#95—681no—
214#95—681no—
215C17#1348211yescharacteristic, complemented, Sylow
216C24—681no—
217C2×D4—342no—
218C2×D4—681no—
219C2×D4—681no—
220C2×D4—681no—
221C2×D4—681no—
222C2×D4—681no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—171no—
226C22×C4—171no—
227C22×C4—681no—
228C22×C4D4×D1711yescharacteristic
229D8—342no—
230D8—342no—
231D8—681no—
232D8—681no—
233C2×C8—172no—
234C2×C8—341no—
235C2×C8—341no—
236C2×C8#6325211yescharacteristic
237C2×C8#6325211yescharacteristic
238C2×C8#6325211yescharacteristic
239C2×C8D4×D1711yescharacteristic
240C2×C8#6325411yescharacteristic
241C2×C8#6325611yescharacteristic
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—681no—
247C4⋊C4—681no—
248C22⋊C4—1362no—
249C22⋊C4—1362no—
250C42—341no—
251C42—341no—
252C16—41no—
253C16—681no—
254C23—682no—
255C23—1361no—
256C23—1361no—
257C23—1361no—
258C23—1361no—
259C23—1361no—
260C23—1361no—
261C23D8×D1711yescharacteristic
262D4—682no—
263D4—682no—
264D4—1361no—
265D4—1361no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—341no—
273C2×C4—341no—
274C2×C4—341no—
275C2×C4—341no—
276C2×C4—341no—
277C2×C4—341no—
278C2×C4—1361no—
279C2×C4—1361no—
280C2×C4—1361no—
281C2×C4#1058757011yescharacteristic
282C2×C4#1058757111yescharacteristic
283C2×C4#1058758011yescharacteristic
284C2×C4SD16×D1711yescharacteristic
285C2×C4#1058760011yescharacteristic
286C2×C4#1058760411yescharacteristic
287C8—342no—
288C8#1058756211yescharacteristic
289C8#1058756911yescharacteristic
290C8#1058758011yescharacteristic
291C8#1058758411yescharacteristic
292C22—2721no—
293C22—2721no—
294C22—2721no—
295C22—2721no—
296C22—1362no—
297C22—1362no—
298C22—1362no—
299C22#1176300311yescharacteristic
300C22#1176312411yescharacteristic
301C22#1176315411yescharacteristic
302C22#1176324011yescharacteristic
303C22#1176324211yescharacteristic
304C22#1176324311yescharacteristic
305C22#1176324611yescharacteristic
306C4—161no—
307C4—161no—
308C4—2721no—
309C4—681no—
310C4—681no—
311C4#1176273811yescharacteristic
312C4#1176301311yescharacteristic
313C4#1176312911yescharacteristic
314C4#1176317011yescharacteristic
315C2—2722no—
316C2#1453019111yescharacteristic
317C2#1453083811yescharacteristic
318C2#1453084211yescharacteristic
319C2#1453097711yescharacteristic
320C2#1453097811yescharacteristic
321C2#1453101711yescharacteristic
322C2#1453102411yescharacteristic
subgroupG/H
centerC23D8×D17
commutator, cosocleC22×C8×C17C23
FrattiniC22×C8C22×D17
FittingC17×#1380C2
socleC23×C17C2×D8
prime radicalC22×D136C22
hypercenter#1380D17
hypocenterC17#13482
LCSG ▷ C22×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
4. #14528947C2semidirect
5. #14526875C2semidirect
6. #14526861C2semidirect
7. C17×#1380C2semidirect
136. #1380D17semidirect
215. C17#13482semidirect

Maximal subgroups

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

subgroupindex
C2×#117626112
C2×#117626092
#145296482
#145289472
#145268752
#145268612
C17×#13802
#1348217