Finite Group Databasebeta

← #16932676

Subgroups — #16932676

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
1#14529733C211yesmaximal, characteristic
2#14529545C211yesmaximal, characteristic
3C8×C4⋊Dic17C211yesmaximal, characteristic
4C2×#11762558C211yesmaximal, characteristic
5#14526667C211yesmaximal, characteristic
6#14526619C211yesmaximal, characteristic
7C17×#1990C211yesmaximal, characteristic
8C2×#10587479—21no—
9C2×C4⋊#3622C2211yescharacteristic
10C2×C4⋊#3622C2211yescharacteristic
11C2×C4⋊#3622C2211yescharacteristic
12C2×C8×Dic17—21no—
13C4×C4⋊Dic17C2211yescharacteristic
14#11762571—21no—
15#11762571—21no—
16#11762571—21no—
17#11762563—21no—
18#11762558C414yescomplemented
19C2×C17×C4⋊Q8C2211yescharacteristic
20C2×C4×C8×C17C2211yescharacteristic
21C17×#384C2211yescharacteristic
22C17×#340—21no—
23C17×#340—21no—
24C22×Q8×C17—21no—
25C22×C8×C17D411yescharacteristic
26C22×C8×C17D411yescharacteristic
27C17×C4⋊Q8—21no—
28C17×C4⋊Q8—21no—
29C17×C4⋊Q8—21no—
30C17×C4⋊Q8C2×C412yes—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17—21no—
36C2×C42×C17C2311yescharacteristic
37C2×C4⋊Dic17D411yescharacteristic
38C2×C4⋊Dic17D411yescharacteristic
39C2×C4×Dic17—21no—
40C22×#3622—21no—
41C22×#3622—21no—
42C22×#3622—21no—
43C4×C8×C17—21no—
44C4×C8×C17—21no—
45#10587502—21no—
46C8×Dic17—42no—
47#10587479—42no—
48C4⋊#3622—21no—
49C4⋊#3622—21no—
50C4⋊#3622—21no—
51C4⋊#3622—21no—
52C4⋊#3622C2×C412yes—
53C4⋊#3622C2×C412yes—
54C2×Q8×C17—22no—
55C2×Q8×C17—41no—
56C2×Q8×C17—81no—
57C2×Q8×C17—81no—
58C22×C4×C17—41no—
59C22×C4×C17—41no—
60C22×C4×C17C2×D411yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17#4111yescharacteristic
63C22×Dic17—21no—
64C22×Dic17—21no—
65C2×C8×C17—21no—
66C2×C8×C17—21no—
67C2×C8×C17—21no—
68C2×C8×C17—21no—
69C2×C8×C17—21no—
70C2×C8×C17SD1612yes—
71C4⋊C4×C17—22no—
72C4⋊C4×C17—22no—
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×C17C22×C411yescharacteristic
81C42×C17#4111yescharacteristic
82C42×C17#4111yescharacteristic
83C42×C17#4111yescharacteristic
84C4⋊Dic17—21no—
85C4⋊Dic17—21no—
86C4⋊Dic17SD1612yes—
87C4⋊Dic17Q1612yes—
88C4×Dic17—41no—
89C4×Dic17—41no—
90C2×#3622—22no—
91C2×#3622—22no—
92C2×#3622—41no—
93C2×#3622—41no—
94C2×#3622—41no—
95C2×#3622—41no—
96C2×#3622—41no—
97C2×#3622—41no—
98C2×#3622—41no—
99#9567—171nomaximal, Sylow
100C23×C17#12111yescharacteristic
101Q8×C17—82no—
102Q8×C17—82no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—42no—
106C2×C4×C17—81no—
107C2×C4×C17—81no—
108C2×C4×C17—81no—
109C2×C4×C17—81no—
110C2×C4×C17—81no—
111C2×C4×C17#11711yescharacteristic
112C2×C4×C17C4×D411yescharacteristic
113C2×C4×C17C4×D411yescharacteristic
114C2×C4×C17#12311yescharacteristic
115C2×C4×C17#12411yescharacteristic
116C2×C4×C17#12611yescharacteristic
117C2×C4×C17C2×SD1611yescharacteristic
118C2×C4×C17C2×SD1611yescharacteristic
119C2×C4×C17C2×Q1611yescharacteristic
120C2×C4×C17#13511yescharacteristic
121C2×C4×C17#13511yescharacteristic
122C2×C4×C17#13511yescharacteristic
123C2×C4×C17#13711yescharacteristic
124C2×C4×C17#13711yescharacteristic
125C2×Dic17—22no—
126C2×Dic17—22no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C8×C17—22no—
132C8×C17—41no—
133#3622—42no—
134#3622—42no—
135#3622—81no—
136#1990D1711yescharacteristic
137#1987—171no—
138#1948—171no—
139C8×C4⋊C4—171no—
140C2×#333—171no—
141#1296—171no—
142#1277—171no—
143C22×C17#38811yescharacteristic
144C22×C17#46111yescharacteristic
145C22×C17#46411yescharacteristic
146C22×C17#46511yescharacteristic
147C22×C17#46711yescharacteristic
148C22×C17#47111yescharacteristic
149C22×C17#47211yescharacteristic
150C4×C17—21no—
151C4×C17—21no—
152C4×C17—82no—
153C4×C17—161no—
154C4×C17C4×SD1611yescharacteristic
155C4×C17C4×SD1611yescharacteristic
156C4×C17C4×Q1611yescharacteristic
157C4×C17#44111yescharacteristic
158C4×C17#48311yescharacteristic
159C4×C17#48511yescharacteristic
160C4×C17#48711yescharacteristic
161C4×C17#48811yescharacteristic
162Dic17—42no—
163Dic17—42no—
164C2×C4⋊Q8C2×D1711yescharacteristic
165C2×#106—341no—
166C2×C4⋊C8—171no—
167C2×C4⋊C8—171no—
168C2×C4⋊C8—171no—
169C2×C4×C8—341no—
170C2×C4×C8C2×D1711yescharacteristic
171#384C2×D1711yescharacteristic
172C4×C4⋊C4—171no—
173#340—21no—
174#340—21no—
175#340—341no—
176#340—341no—
177#340—341no—
178#336—341no—
179#333—174no—
180C2×C17#167111yescharacteristic
181C2×C17#167511yescharacteristic
182C2×C17#167811yescharacteristic
183C2×C17#168411yescharacteristic
184C2×C17#192711yescharacteristic
185C2×C17#193111yescharacteristic
186C2×C17#193311yescharacteristic
187C22×Q8—21no—
188C22×C8—341no—
189C22×C8—341no—
190C22×C8—341no—
191C22×C8C22⋊D1711yescharacteristic
192C22×C8C22⋊D1711yescharacteristic
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8C4×D1712yes—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—171no—
203C2×C4⋊C4—171no—
204C2×C42—341no—
205C2×C42C22×D1711yescharacteristic
206#106—682no—
207C4⋊C8—172no—
208C4⋊C8—172no—
209C4⋊C8—341no—
210C4⋊C8—341no—
211C4⋊C8—341no—
212C4⋊C8—341no—
213C4×C8—21no—
214C4×C8—21no—
215C4×C8—682no—
216#95—341no—
217C17#956711yescharacteristic, complemented, Sylow
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—81no—
221C2×Q8—81no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—341no—
225C22×C4—341no—
226C22×C4D4×D1711yescharacteristic
227C22×C4#6325411yescharacteristic
228C22×C4C2×C22⋊D1711yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—342no—
235C2×C8—342no—
236C2×C8—681no—
237C2×C8—681no—
238C2×C8—681no—
239C2×C8—681no—
240C2×C8—681no—
241C2×C8—681no—
242C2×C8—681no—
243C2×C8#6323012yes—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—81no—
253C4⋊C4—172no—
254C4⋊C4—172no—
255C4⋊C4—341no—
256C4⋊C4—341no—
257C42—681no—
258C42—681no—
259C42C2×C4×D1711yescharacteristic
260C42#6325211yescharacteristic
261C42#6325411yescharacteristic
262C42#6325411yescharacteristic
263C23#1058762411yescharacteristic
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—342no—
275C2×C4—342no—
276C2×C4—681no—
277C2×C4—681no—
278C2×C4—681no—
279C2×C4—681no—
280C2×C4#1058756311yescharacteristic
281C2×C4#1058756511yescharacteristic
282C2×C4#1058756711yescharacteristic
283C2×C4#1058757111yescharacteristic
284C2×C4SD16×D1711yescharacteristic
285C2×C4#1058760211yescharacteristic
286C2×C4Q16×D1711yescharacteristic
287C2×C4#1058760511yescharacteristic
288C2×C4C4×C22⋊D1711yescharacteristic
289C2×C4#1058762111yescharacteristic
290C2×C4C2×#6323011yescharacteristic
291C2×C4#1058762811yescharacteristic
292C2×C4#1058763611yescharacteristic
293C2×C4#1058763711yescharacteristic
294C8—22no—
295C8—41no—
296C8—682no—
297C8—682no—
298C8—1361no—
299C22#1176269711yescharacteristic
300C22#1176301111yescharacteristic
301C22#1176302811yescharacteristic
302C22#1176303511yescharacteristic
303C22#1176304711yescharacteristic
304C22#1176306911yescharacteristic
305C22#1176307611yescharacteristic
306C4—21no—
307C4—21no—
308C4—82no—
309C4—161no—
310C4—682no—
311C4—682no—
312C4#1176289411yescharacteristic
313C4C4×#6323011yescharacteristic
314C4#1176290111yescharacteristic
315C4#1176291411yescharacteristic
316C4#1176313711yescharacteristic
317C4#1176314711yescharacteristic
318C4#1176315811yescharacteristic
319C4#1176316511yescharacteristic
320C2#1452815611yescharacteristic
321C2#1452818011yescharacteristic
322C2#1452819711yescharacteristic
323C2#1452823911yescharacteristic
324C2#1452941511yescharacteristic
325C2#1452944311yescharacteristic
326C2#1452945711yescharacteristic
subgroupG/H
centerC23#10587624
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1990C2
socle, prime radicalC23×C17#121
cosocleC2×C42×C17C23
hypercenter#1990D17
hypocenterC17#9567
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
18. #11762558C4semidirect
217. C17#9567semidirect

Maximal subgroups

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

subgroupindex
#145297332
#145295452
C8×C4⋊Dic172
C2×#117625582
#145266672
#145266192
C17×#19902
#956717