Finite Group Databasebeta

← #17948254

Subgroups — #17948254

Order 4352.

468 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544638C211yesmaximal, characteristic
2C4×C22⋊#3624C211yesmaximal, characteristic
3#14527009C211yesmaximal, characteristic
4C2×C4⋊#3624—21no—
5C2×C22⋊#3624—21no—
6C2×C22⋊#3624—21no—
7C2×C4×#3624C412yescomplemented
8#11763675—21no—
9#11763675C412yescomplemented
10C22×C4×Dic17C2211yescharacteristic
11C2×#10587502—21no—
12C2×#10587502—21no—
13C2×#10587502C411yescharacteristic
14C2×C17×#95C411yescharacteristic
15C23×C4×C17—21no—
16C23×C4×C17C2×C411yescharacteristic
17C23×Dic17—21no—
18C23×Dic17D411yescharacteristic
19C23×Dic17D411yescharacteristic
20C22×#3624—22no—
21C22×#3624—22no—
22C2×C4×Dic17—42no—
23C2×C4×Dic17C2×C411yescharacteristic
24C2×C4×Dic17C2×C411yescharacteristic
25C2×C4×Dic17D411yescharacteristic
26C2×C4×Dic17Q811yescharacteristic
27C22⋊#3624—22no—
28C22⋊#3624—22no—
29C22⋊#3624—41no—
30C22⋊#3624—41no—
31C4⋊#3624—42no—
32C4×#3624—42no—
33C17×#95—21no—
34C17×#95C812yescomplemented
35#10587502—21no—
36#10587502—42no—
37#10587502—41no—
38#10587502—41no—
39#10587502C812yescomplemented
40C24×C17C22⋊C411yescharacteristic
41C22×C4×C17—22no—
42C22×C4×C17—41no—
43C22×C4×C17—41no—
44C22×C4×C17—41no—
45C22×C4×C17—41no—
46C22×C4×C17—41no—
47C22×C4×C17—41no—
48C22×C4×C17—41no—
49C22×C4×C17—41no—
50C22×C4×C17C4211yescharacteristic
51C22×C4×C17C4⋊C411yescharacteristic
52C22×C4×C17C2×C811yescharacteristic
53C22×C4×C17C2×C811yescharacteristic
54C22×C4×C17M1611yescharacteristic
55C22×C4×C17M1611yescharacteristic
56C22×Dic17—21no—
57C22×Dic17—21no—
58C22×Dic17—22no—
59C22×Dic17—22no—
60C22×Dic17—41no—
61C22×Dic17—41no—
62C22×Dic17—41no—
63C22×Dic17—41no—
64C22×Dic17—41no—
65C22×Dic17—41no—
66C22×Dic17—41no—
67C22×Dic17—41no—
68C22×Dic17—41no—
69C22×Dic17C22⋊C411yescharacteristic
70C22×Dic17C22⋊C411yescharacteristic
71C22×Dic17C4⋊C411yescharacteristic
72C22×Dic17C4⋊C411yescharacteristic
73C22×Dic17D811yescharacteristic
74C22×Dic17SD1611yescharacteristic
75C22×Dic17SD1611yescharacteristic
76C22×Dic17Q1611yescharacteristic
77C2×#3624—24no—
78C2×#3624—42no—
79C2×#3624—42no—
80C2×#3624—42no—
81C2×#3624—42no—
82C2×#3624—42no—
83C4×Dic17—22no—
84C4×Dic17—22no—
85C4×Dic17—41no—
86C4×Dic17—41no—
87#7024—171nomaximal, Sylow
88C23×C17—21no—
89C23×C17—21no—
90C23×C17—21no—
91C23×C17—21no—
92C23×C17#9511yescharacteristic
93C23×C17C22⋊C811yescharacteristic
94C23×C17C22⋊C811yescharacteristic
95C23×C17#10211yescharacteristic
96C23×C17#10311yescharacteristic
97C23×C17#10411yescharacteristic
98C23×C17#10411yescharacteristic
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17—81no—
111C2×C4×C17—81no—
112C2×C4×C17—81no—
113C2×C4×C17—81no—
114C2×C4×C17C4×C811yescharacteristic
115C2×C4×C17#9711yescharacteristic
116C2×C4×C17C4⋊C811yescharacteristic
117C2×C4×C17C4⋊C811yescharacteristic
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17—21no—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—21no—
125C2×Dic17—21no—
126C2×Dic17—21no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—42no—
132C2×Dic17—42no—
133C2×Dic17—42no—
134C2×Dic17—42no—
135C2×Dic17—42no—
136C2×Dic17—81no—
137C2×Dic17—81no—
138C2×Dic17—81no—
139C2×Dic17—81no—
140C2×Dic17#9912yes—
141C2×Dic17#10211yescharacteristic
142C2×Dic17#10311yescharacteristic
143C2×Dic17#10611yescharacteristic
144C2×Dic17#10711yescharacteristic
145#3624—44no—
146#3624—82no—
147#1797—171no—
148C4×C22⋊C8—171no—
149#1434—171no—
150C22×C17—21no—
151C22×C17—21no—
152C22×C17—21no—
153C22×C17—21no—
154C22×C17—21no—
155C22×C17—21no—
156C22×C17—21no—
157C22×C17—21no—
158C22×C17—21no—
159C22×C17—21no—
160C22×C17—21no—
161C22×C17—21no—
162C22×C17D4⋊C811yescharacteristic
163C22×C17D4⋊C811yescharacteristic
164C22×C17Q8⋊C811yescharacteristic
165C22×C17Q8⋊C811yescharacteristic
166C22×C17#33611yescharacteristic
167C22×C17H(3,ℤ/4)11yescharacteristic
168C22×C17H(3,ℤ/4)11yescharacteristic
169C22×C17#33911yescharacteristic
170C22×C17#34011yescharacteristic
171C22×C17#34211yescharacteristic
172C22×C17#34411yescharacteristic
173C4×C17—21no—
174C4×C17—21no—
175C4×C17—21no—
176C4×C17—21no—
177C4×C17—82no—
178Dic17—22no—
179Dic17—21no—
180Dic17—21no—
181Dic17—21no—
182Dic17—21no—
183Dic17—41no—
184Dic17—82no—
185C22×C42—171no—
186C2×C4⋊C8—341no—
187C2×C22⋊C8—341no—
188C2×C22⋊C8—341no—
189C2×C4×C8—172no—
190C2×#95—171no—
191C2×#95—341no—
192C2×#95—341no—
193C2×#95#59511yescharacteristic
194#336—172no—
195#336—341no—
196C2×C17—21no—
197C2×C17—21no—
198C2×C17—21no—
199C2×C17—21no—
200C2×C17#127411yescharacteristic
201C2×C17#127911yescharacteristic
202C2×C17#128211yescharacteristic
203C2×C17#128411yescharacteristic
204C2×C17#128611yescharacteristic
205C2×C17#128811yescharacteristic
206C2×C17#128911yescharacteristic
207C23×C4—21no—
208C23×C4—171no—
209C23×C4—171no—
210C23×C4—341no—
211C23×C4C2×#59511yescharacteristic
212C22×C8—342no—
213C22×C8—342no—
214C2×C42—171no—
215C2×C42—171no—
216C2×C42—171no—
217C2×C42—171no—
218C2×C42—682no—
219C4⋊C8—682no—
220C22⋊C8—342no—
221C22⋊C8—342no—
222C22⋊C8—681no—
223C22⋊C8—681no—
224C4×C8—682no—
225#95—21no—
226#95—172no—
227#95—341no—
228#95—681no—
229#95—681no—
230#95—682no—
231#95#362412yescomplemented
232C17#702411yescharacteristic, complemented, Sylow
233C24C22⋊#59511yescharacteristic
234C22×C4—22no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—171no—
244C22×C4—171no—
245C22×C4—171no—
246C22×C4—171no—
247C22×C4—171no—
248C22×C4—171no—
249C22×C4—171no—
250C22×C4—171no—
251C22×C4—342no—
252C22×C4—341no—
253C22×C4—341no—
254C22×C4—342no—
255C22×C4—681no—
256C22×C4—681no—
257C22×C4—681no—
258C22×C4—681no—
259C22×C4—681no—
260C22×C4—681no—
261C22×C4—681no—
262C22×C4—681no—
263C22×C4—681no—
264C22×C4#6324211yescharacteristic
265C22×C4#6324311yescharacteristic
266C22×C4C4×#59511yescharacteristic
267C22×C4C4⋊#59511yescharacteristic
268C22×C4C2×#362411yescharacteristic
269C22×C4#6324711yescharacteristic
270C2×C8—344no—
271C2×C8—682no—
272C2×C8—682no—
273C2×C8—682no—
274C2×C8—682no—
275C2×C8—682no—
276C42—342no—
277C42—342no—
278C42—681no—
279C42—681no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23#1058754311yescharacteristic
285C23(C2×#595)⋊C411yescharacteristic
286C23#1058754711yescharacteristic
287C23#1058754811yescharacteristic
288C23#1058754911yescharacteristic
289C23#1058755011yescharacteristic
290C23C22⋊#362411yescharacteristic
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—171no—
307C2×C4—171no—
308C2×C4—171no—
309C2×C4—171no—
310C2×C4—172no—
311C2×C4—341no—
312C2×C4—341no—
313C2×C4—341no—
314C2×C4—341no—
315C2×C4—341no—
316C2×C4—341no—
317C2×C4—341no—
318C2×C4—341no—
319C2×C4—341no—
320C2×C4—681no—
321C2×C4—681no—
322C2×C4—681no—
323C2×C4—681no—
324C2×C4—682no—
325C2×C4—682no—
326C2×C4—682no—
327C2×C4—682no—
328C2×C4—682no—
329C2×C4—1361no—
330C2×C4—1361no—
331C2×C4—1361no—
332C2×C4—1361no—
333C2×C4C4×#362411yescharacteristic
334C2×C4C4⋊#362411yescharacteristic
335C2×C4#1058754211yescharacteristic
336C2×C4#1058754411yescharacteristic
337C8—684no—
338C8—1362no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22D4⋊#362411yescharacteristic
352C22#1176365711yescharacteristic
353C22Q8⋊#362411yescharacteristic
354C22#1176365911yescharacteristic
355C22#1176367511yescharacteristic
356C22#1176367611yescharacteristic
357C22#1176367611yescharacteristic
358C22#1176367911yescharacteristic
359C22#1176368211yescharacteristic
360C22#1176368611yescharacteristic
361C22#1176369011yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—342no—
368C4—341no—
369C4—341no—
370C4—341no—
371C4—341no—
372C4—681no—
373C4—1362no—
374C2—21no—
375C2—21no—
376C2—21no—
377C2—21no—
378C2#1454360811yescharacteristic
379C2#1454362011yescharacteristic
380C2#1454362711yescharacteristic
381C2#1454363111yescharacteristic
382C2#1454363711yescharacteristic
383C2#1454364311yescharacteristic
384C2#1454364611yescharacteristic
subgroupG/H
centerC23(C2×#595)⋊C4
commutatorC2×C4×C17C4×C8
FrattiniC23×C4C2×#595
FittingC2×C17×#95C4
socleC23×C17#95
prime radicalC24×C17C22⋊C4
cosocleC22×C4×Dic17C22
hypercenterC2×#95#595
hypocenterC17#7024
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
7. C2×C4×#3624C4semidirect
9. #11763675C4semidirect
34. C17×#95C8semidirect
39. #10587502C8semidirect
231. #95#3624semidirect
232. C17#7024semidirect

Maximal subgroups

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

subgroupindex
#145446382
C4×C22⋊#36242
#145270092
#702417