Finite Group Databasebeta

← #16954092

Subgroups — #16954092

Order 4352.

382 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762636C211yesmaximal, characteristic, complemented
2C2×#11762627C211yesmaximal, characteristic, complemented
3C2×#11762611C211yesmaximal, characteristic
4C2×#11762609C211yesmaximal, characteristic
5#14529648C211yesmaximal, characteristic
6#14529515C211yesmaximal, characteristic, complemented
7C17×#1380C211yesmaximal, characteristic, complemented
8C22×D136C2211yescharacteristic
9C22×#63214C2211yescharacteristic
10C2×#10587489C2211yescharacteristic
11C2×#10587480—21no—
12C2×C8×Dic17C2211yescharacteristic
13#11762710—21no—
14#11762705—21no—
15#11762636—22no—
16#11762627—22no—
17#11762611—22no—
18#11762609—22no—
19#11762571—21no—
20C22×C16×C17C2211yescharacteristic
21C2×C17×#107C2211yescharacteristic
22C2×C17×#107C2211yescharacteristic
23C22×D68—21no—
24C22×C8×C17C2311yescharacteristic
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17—21no—
27C2×#63227—41no—
28C2×#63227—41no—
29C2×C4⋊Dic17—21no—
30C2×#63225—41no—
31C2×C4×Dic17D411yescharacteristic
32C22×#3622D411yescharacteristic
33C2×D136—21no—
34C2×D136—21no—
35C2×D136—21no—
36C2×D136—21no—
37C2×D136—21no—
38C2×D136Q812yes—
39C2×C16×C17—21no—
40C2×C16×C17—21no—
41C2×C16×C17—21no—
42C17×#107—21no—
43C17×#107—21no—
44C17×#107—21no—
45C17×#107—21no—
46#10587502—41no—
47#10587489—21no—
48#10587489D412yes—
49C8×Dic17—21no—
50C8×Dic17—21no—
51C2×#63214—21no—
52C2×#63214—21no—
53C2×#63214D412yes—
54#10587480—42no—
55C23×D17—41no—
56C22×C4×C17—41no—
57C22×C4×C17—41no—
58C22×C4×C17C2×D411yescharacteristic
59C22×Dic17—41no—
60C22×Dic17D811yescharacteristic
61C22×Dic17D811yescharacteristic
62C2×D68—22no—
63C2×D68—41no—
64C2×D68—41no—
65C2×D68—41no—
66C2×D68—41no—
67C2×D68—41no—
68C2×C8×C17C2×D411yescharacteristic
69C2×C8×C17C2×D411yescharacteristic
70C2×C8×C17C2×Q811yescharacteristic
71C2×C8×C17#4111yescharacteristic
72C2×C8×C17#4111yescharacteristic
73C2×C8×C17#4111yescharacteristic
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78#63227—82no—
79#63227—82no—
80C4⋊Dic17—22no—
81C4⋊Dic17—41no—
82#63225—82no—
83C4×Dic17—21no—
84C4×Dic17—21no—
85C2×#3622—21no—
86C2×#3622—21no—
87C2×#3622—21no—
88D136—22no—
89D136—22no—
90D136—41no—
91D136—41no—
92C16×C17—41no—
93#63214—22no—
94#13476—171nomaximal, Sylow
95C23×C17C2×D811yescharacteristic
96C22×D17—42no—
97C22×D17—81no—
98C22×D17—81no—
99C22×D17—81no—
100C22×D17—81no—
101C22×D17—81no—
102C22×D17—81no—
103C2×C4×C17—81no—
104C2×C4×C17—81no—
105C2×C4×C17—81no—
106C2×C4×C17—81no—
107C2×C4×C17—81no—
108C2×C4×C17—81no—
109C2×C4×C17#12111yescharacteristic
110C2×C4×C17#12111yescharacteristic
111C2×C4×C17C22⋊Q811yescharacteristic
112C2×C4×C17#13511yescharacteristic
113C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C17#13711yescharacteristic
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17—42no—
121C2×Dic17—81no—
122C2×Dic17—81no—
123C2×Dic17SD3212yes—
124D68—42no—
125D68—42no—
126D68—81no—
127D68—81no—
128C8×C17#12111yescharacteristic
129C8×C17C22⋊Q811yescharacteristic
130C8×C17C22⋊Q811yescharacteristic
131C8×C17#12611yescharacteristic
132#3622—41no—
133C2×#367—171no—
134C2×C4⋊C16—171no—
135C2×#357—171no—
136C2×#357—171no—
137#1970—171no—
138#1942—171no—
139#1380D1711yescharacteristic, complemented
140C22×C17#45911yescharacteristic
141C22×C17#46611yescharacteristic
142C22×C17#47411yescharacteristic
143C22×C17C2×SD3211yescharacteristic
144C22×C17#50811yescharacteristic
145C22×C17#50911yescharacteristic
146C22×C17#50911yescharacteristic
147C2×D17—82no—
148C2×D17—82no—
149C2×D17—82no—
150C2×D17—161no—
151C2×D17—161no—
152C2×D17—161no—
153C2×D17—161no—
154C4×C17—161no—
155C4×C17—161no—
156C4×C17#39611yescharacteristic
157C4×C17#46411yescharacteristic
158C4×C17#46811yescharacteristic
159C4×C17#47811yescharacteristic
160Dic17—22no—
161Dic17—41no—
162Dic17—82no—
163C22×D8—171no—
164C22×C16—171no—
165C22×C16C2×D1711yescharacteristic
166C2×#107—171no—
167C2×#107C2×D1711yescharacteristic
168C2×#107C2×D1711yescharacteristic
169C2×#102—341no—
170C2×C4×C8—171no—
171#390—341no—
172#389—341no—
173#367—342no—
174C4⋊C16—342no—
175#357—342no—
176#357—342no—
177#340—341no—
178C2×C17#206711yescharacteristic
179C2×C17#220711yescharacteristic
180C2×C17#221011yescharacteristic
181C2×C17#221711yescharacteristic
182C2×C17#221811yescharacteristic
183C2×C17#222611yescharacteristic
184C2×C17#222811yescharacteristic
185D17—162no—
186C22×D4—341no—
187C2×D8—172no—
188C2×D8—341no—
189C2×D8—341no—
190C2×D8—341no—
191C2×D8—341no—
192C2×D8—341no—
193C22×C8—171no—
194C22×C8C22×D1711yescharacteristic
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—341no—
198C2×C4⋊C4—681no—
199C2×C22⋊C4—681no—
200C2×C22⋊C4—681no—
201C2×C42—171no—
202C2×C16—21no—
203C2×C16—21no—
204C2×C16—21no—
205C2×C16—172no—
206C2×C16—341no—
207C2×C16—341no—
208#107—21no—
209#107—21no—
210#107—21no—
211#107—21no—
212#107—172no—
213#107—341no—
214#102—682no—
215C4×C8—341no—
216C4×C8—341no—
217#95—681no—
218C17#1347611yescharacteristic, complemented, Sylow
219C24—681no—
220C2×D4—342no—
221C2×D4—681no—
222C2×D4—681no—
223C2×D4—681no—
224C2×D4—681no—
225C2×D4—681no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—171no—
229C22×C4—171no—
230C22×C4—681no—
231C22×C4D4×D1711yescharacteristic
232D8—342no—
233D8—342no—
234D8—681no—
235D8—681no—
236C2×C8—341no—
237C2×C8—341no—
238C2×C8—341no—
239C2×C8#6325211yescharacteristic
240C2×C8#6325211yescharacteristic
241C2×C8#6325211yescharacteristic
242C2×C8D4×D1711yescharacteristic
243C2×C8D4×D1711yescharacteristic
244C2×C8Q8×D1711yescharacteristic
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—342no—
250C4⋊C4—681no—
251C4⋊C4—1362no—
252C22⋊C4—1362no—
253C22⋊C4—1362no—
254C42—341no—
255C42—341no—
256C16—41no—
257C16—342no—
258C23—682no—
259C23—1361no—
260C23—1361no—
261C23—1361no—
262C23—1361no—
263C23—1361no—
264C23—1361no—
265C23D8×D1711yescharacteristic
266D4—682no—
267D4—682no—
268D4—1361no—
269D4—1361no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—172no—
277C2×C4—341no—
278C2×C4—341no—
279C2×C4—341no—
280C2×C4—341no—
281C2×C4—341no—
282C2×C4—682no—
283C2×C4—1361no—
284C2×C4—1361no—
285C2×C4#1058757011yescharacteristic
286C2×C4#1058757011yescharacteristic
287C2×C4#1058758211yescharacteristic
288C2×C4#1058760011yescharacteristic
289C2×C4#1058760211yescharacteristic
290C2×C4#1058760411yescharacteristic
291C8—681no—
292C8#1058756211yescharacteristic
293C8#1058757011yescharacteristic
294C8#1058758211yescharacteristic
295C8#1058758211yescharacteristic
296C22—2721no—
297C22—2721no—
298C22—2721no—
299C22—2721no—
300C22—1362no—
301C22—1362no—
302C22—1362no—
303C22#1176300311yescharacteristic
304C22#1176304411yescharacteristic
305C22#1176308811yescharacteristic
306C22SD32×D1711yescharacteristic
307C22#1176324211yescharacteristic
308C22#1176324311yescharacteristic
309C22#1176324611yescharacteristic
310C4—161no—
311C4—161no—
312C4—342no—
313C4—681no—
314C4—1362no—
315C4#1176273311yescharacteristic
316C4#1176303411yescharacteristic
317C4#1176305811yescharacteristic
318C4#1176310811yescharacteristic
319C2—2722no—
320C2#1453017311yescharacteristic
321C2#1453082311yescharacteristic
322C2#1453084211yescharacteristic
323C2#1453088311yescharacteristic
324C2#1453088611yescharacteristic
325C2#1453093011yescharacteristic
326C2#1453094411yescharacteristic
subgroupG/H
centerC23D8×D17
commutator, cosocleC22×C8×C17C23
FrattiniC22×C8C22×D17
FittingC17×#1380C2
socleC23×C17C2×D8
prime radicalC22×D136C22
hypercenter#1380D17
hypocenterC17#13476
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
1. C2×#11762636C2semidirect
2. C2×#11762627C2semidirect
6. #14529515C2semidirect
7. C17×#1380C2semidirect
139. #1380D17semidirect
218. C17#13476semidirect

Maximal subgroups

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

subgroupindex
C2×#117626362
C2×#117626272
C2×#117626112
C2×#117626092
#145296482
#145295152
C17×#13802
#1347617