Finite Group Databasebeta

← C2×#14530224 #17063214

Subgroups — C2×#14530224 #17063214

Order 4352.

950 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587489C211yesmaximal, characteristic, complemented
2C2×#11762810C212yesmaximal
3#14530224C218yesmaximal, direct product factor
4C2×#11762577C212yesmaximal, complemented
5C2×#11762574C211yesmaximal, characteristic, complemented
6C2×C17×#408C211yesmaximal, characteristic
7C22×#63223C2212yes—
8C22×C4⋊Dic17C2212yes—
9C2×#10587489—22no—
10C2×#10587489—22no—
11C2×#10587489C2214yescomplemented
12#11762810—24no—
13#11762810C2218yes—
14C2×#10587506—22no—
15C2×#10587503—22no—
16#11762577C2218yescomplemented
17#11762574C2214yescomplemented
18C22×#41×C17C2211yescharacteristic
19C22×M16×C17C2211yescharacteristic
20C23×C8×C17C2211yescharacteristic
21C17×#408—22no—
22C17×#408C2214yes—
23C2×C17×C22⋊C8—22no—
24C2×#41×C17—21no—
25C2×#41×C17—21no—
26C2×#41×C17—24no—
27C2×#41×C17—24no—
28C2×#41×C17D412yes—
29C2×#41×C17C2312yes—
30C22×Q8×C17D411yescharacteristic
31C22×D4×C17—21no—
32C22×D4×C17D411yescharacteristic
33C23×C4×C17—21no—
34C23×C4×C17C2311yescharacteristic
35C23×Dic17—22no—
36C2×M16×C17—21no—
37C2×M16×C17—24no—
38C2×M16×C17C2312yes—
39C22×C8×C17—24no—
40C22×C8×C17—21no—
41C22×C8×C17D412yes—
42C22×C8×C17D412yes—
43C22×C8×C17C2312yes—
44C2×C4⋊Dic17—22no—
45C2×C4⋊Dic17—22no—
46C2×C4⋊Dic17—22no—
47C2×C4⋊Dic17—22no—
48C2×C4⋊Dic17—22no—
49C2×C4⋊Dic17C2314yes—
50C2×#63223—22no—
51C2×#63223—24no—
52C2×#63223—24no—
53C2×#63223C2314yes—
54C22×#3622—22no—
55C17×C22⋊C8—28no—
56#10587506—28no—
57#10587503—28no—
58#10587489—28no—
59C24×C17—21no—
60C24×C17#4111yescharacteristic
61#41×C17—28no—
62#41×C17—24no—
63#41×C17—24no—
64#41×C17—42no—
65#41×C17—42no—
66#41×C17—44no—
67C2×Q8×C17—21no—
68C2×Q8×C17—24no—
69C2×Q8×C17C2×D412yes—
70C2×D4×C17—22no—
71C2×D4×C17—22no—
72C2×D4×C17—21no—
73C2×D4×C17—24no—
74C2×D4×C17—44no—
75C2×D4×C17C2×D412yes—
76C22×C4×C17—21no—
77C22×C4×C17—22no—
78C22×C4×C17—22no—
79C22×C4×C17—42no—
80C22×C4×C17—42no—
81C22×C4×C17C2×D411yescharacteristic
82C22×C4×C17C2×D411yescharacteristic
83C22×C4×C17C2×D411yescharacteristic
84C22×C4×C17C2×D411yescharacteristic
85C22×C4×C17#4111yescharacteristic
86C22×C4×C17#4114yes—
87C22×C4×C17#4114yes—
88C22×C4×C17C2411yescharacteristic
89C22×Dic17—24no—
90C22×Dic17—42no—
91C22×Dic17—42no—
92C22×Dic17—84no—
93M16×C17—24no—
94M16×C17—42no—
95C2×C8×C17—24no—
96C2×C8×C17—24no—
97C2×C8×C17—24no—
98C2×C8×C17—22no—
99C2×C8×C17—42no—
100C2×C8×C17C2×D414yes—
101C4⋊Dic17—24no—
102C4⋊Dic17—24no—
103C4⋊Dic17—42no—
104C4⋊Dic17—42no—
105#63223—24no—
106#63223—24no—
107#63223—44no—
108C2×#3622—24no—
109C2×#3622—44no—
110C2×#2078—171nomaximal, Sylow
111C23×C17—22no—
112C23×C17—22no—
113C23×C17—22no—
114C23×C17—42no—
115C23×C17—42no—
116C23×C17—42no—
117C23×C17#12111yescharacteristic
118C23×C17#12111yescharacteristic
119C23×C17#12614yes—
120C23×C17C2×#4111yescharacteristic
121Q8×C17—24no—
122Q8×C17—42no—
123D4×C17—24no—
124D4×C17—44no—
125D4×C17—44no—
126D4×C17—42no—
127C2×C4×C17—22no—
128C2×C4×C17—42no—
129C2×C4×C17—42no—
130C2×C4×C17—42no—
131C2×C4×C17—44no—
132C2×C4×C17#12111yescharacteristic
133C2×C4×C17#12111yescharacteristic
134C2×C4×C17#12314yes—
135C2×C4×C17#12314yes—
136C2×C4×C17#12312yes—
137C2×C4×C17#12312yes—
138C2×C4×C17#12412yes—
139C2×C4×C17#12412yes—
140C2×C4×C17#12614yes—
141C2×C4×C17C22×D411yescharacteristic
142C2×C4×C17C22×D411yescharacteristic
143C2×C4×C17C2×#4112yes—
144C2×C4×C17C2×#4112yes—
145C2×Dic17—44no—
146C2×Dic17—84no—
147C2×Dic17—84no—
148C2×Dic17—84no—
149C8×C17—24no—
150C8×C17—42no—
151#3622—44no—
152C22×#107—171no—
153C2×#417—172no—
154C2×#408D1711yescharacteristic
155#2078—178no—
156C2×#343—172no—
157C2×#341—171no—
158C22×C17—28no—
159C22×C17—21no—
160C22×C17—21no—
161C22×C17—21no—
162C22×C17—21no—
163C22×C17—42no—
164C22×C17—42no—
165C22×C17—42no—
166C22×C17—84no—
167C22×C17#39712yes—
168C22×C17#39712yes—
169C22×C17#47212yes—
170C22×C17#47312yes—
171C22×C17C2×#12111yescharacteristic
172C22×C17C2×#12612yes—
173C4×C17—42no—
174C4×C17#39712yes—
175C4×C17#39712yes—
176C4×C17C2×#12311yescharacteristic
177C4×C17C2×#12312yes—
178C4×C17C2×#12411yescharacteristic
179Dic17—84no—
180C22×#41C2×D1711yescharacteristic
181C22×M16—172no—
182C22×M16C2×D1711yescharacteristic
183C23×C8C2×D1711yescharacteristic
184C22×C4⋊C4—172no—
185C2×#107—174no—
186C2×#107—342no—
187C2×#107—342no—
188#417—178no—
189#417—344no—
190C2×#103—342no—
191C2×#102—342no—
192#408—22no—
193#408C2×D1714yes—
194C2×C22⋊C8—22no—
195#343—178no—
196#341—174no—
197C2×C17—22no—
198C2×C17—22no—
199C2×C17—82no—
200C2×C17#207814yescomplemented
201C2×C17C2×#39711yescharacteristic
202C2×C17C2×#47211yescharacteristic
203C2×C17C2×#47311yescharacteristic
204C2×#41—21no—
205C2×#41—21no—
206C2×#41—24no—
207C2×#41—24no—
208C2×#41D6812yes—
209C2×#41C22×D1712yes—
210C22×Q8D6811yescharacteristic
211C22×D4—21no—
212C22×D4D6811yescharacteristic
213C23×C4—21no—
214C23×C4—342no—
215C23×C4C22×D1711yescharacteristic
216C2×M16—21no—
217C2×M16—24no—
218C2×M16—174no—
219C2×M16—342no—
220C2×M16—344no—
221C2×M16—344no—
222C2×M16C22×D1712yes—
223C22×C8—24no—
224C22×C8—21no—
225C22×C8—342no—
226C22×C8C22⋊D1712yes—
227C22×C8C22⋊D1712yes—
228C22×C8C22×D1712yes—
229C2×C4⋊C4—174no—
230C2×C4⋊C4—342no—
231C2×C4⋊C4—342no—
232C2×C4⋊C4—342no—
233C2×C4⋊C4—342no—
234C2×C4⋊C4—342no—
235#107—348no—
236#103—348no—
237#102—348no—
238C22⋊C8—28no—
239C17C2×#207811yescharacteristic, complemented, Sylow
240C24—21no—
241C24#6325211yescharacteristic
242#41—24no—
243#41—24no—
244#41—28no—
245#41—44no—
246#41—42no—
247#41—42no—
248C2×Q8—21no—
249C2×Q8—24no—
250C2×Q8C2×D6812yes—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—24no—
254C2×D4—21no—
255C2×D4—44no—
256C2×D4C2×D6812yes—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—344no—
263C22×C4—682no—
264C22×C4—682no—
265C22×C4—1364no—
266C22×C4C2×D6811yescharacteristic
267C22×C4C2×D6811yescharacteristic
268C22×C4#6325211yescharacteristic
269C22×C4#6325414yes—
270C22×C4#6325414yes—
271C22×C4C2×C22⋊D1711yescharacteristic
272C22×C4C2×C22⋊D1711yescharacteristic
273C22×C4C23×D1711yescharacteristic
274M16—24no—
275M16—42no—
276M16—344no—
277M16—344no—
278M16—684no—
279C2×C8—24no—
280C2×C8—24no—
281C2×C8—24no—
282C2×C8—22no—
283C2×C8—42no—
284C2×C8—344no—
285C2×C8—684no—
286C2×C8C2×C22⋊D1714yes—
287C4⋊C4—344no—
288C4⋊C4—344no—
289C4⋊C4—682no—
290C4⋊C4—682no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—42no—
295C23—42no—
296C23—42no—
297C23#1058756514yes—
298C23#1058761611yescharacteristic
299C23#1058761611yescharacteristic
300C23C2×#6325211yescharacteristic
301Q8—24no—
302Q8—42no—
303D4—24no—
304D4—44no—
305D4—44no—
306D4—42no—
307C2×C4—22no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—684no—
313C2×C4—1364no—
314C2×C4—1364no—
315C2×C4—1364no—
316C2×C4#1058756514yes—
317C2×C4#1058757214yes—
318C2×C4#1058757214yes—
319C2×C4#1058761611yescharacteristic
320C2×C4#1058761611yescharacteristic
321C2×C4#1058762112yes—
322C2×C4#1058762112yes—
323C2×C4#1058762212yes—
324C2×C4#1058762212yes—
325C2×C4C22×D6811yescharacteristic
326C2×C4C2×#6325412yes—
327C2×C4C2×#6325412yes—
328C2×C4C22×C22⋊D1711yescharacteristic
329C8—24no—
330C8—42no—
331C8—684no—
332C22—21no—
333C22—21no—
334C22—28no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—84no—
341C22#1176273412yes—
342C22#1176273412yes—
343C22#1176307912yes—
344C22#1176308412yes—
345C22C2×#1058761611yescharacteristic
346C22C2×#1058756512yes—
347C4—42no—
348C4—1364no—
349C4#1176273412yes—
350C4#1176273412yes—
351C4C2×#1058762111yescharacteristic
352C4C2×#1058757212yes—
353C4C2×#1058762211yescharacteristic
354C2—22no—
355C2—22no—
356C2—82no—
357C2#1453022414yesdirect product factor
358C2C2×#1176273411yescharacteristic
359C2C2×#1176307911yescharacteristic
360C2C2×#1176308411yescharacteristic
subgroupG/H
centerC23#10587616
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#408C2
socleC23×C17#121
prime radicalC22×#41×C17C22
hypercenterC2×#408D17
hypocenterC17C2×#2078
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C22×#10587489C2semidirect
3. #14530224C2direct (N × H)
4. C2×#11762577C2semidirect
5. C2×#11762574C2semidirect
11. C2×#10587489C22semidirect
16. #11762577C22semidirect
17. #11762574C22semidirect
200. C2×C17#2078semidirect
239. C17C2×#2078semidirect
357. C2#14530224direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105874892
C2×#117628102
#145302242
C2×#117625772
C2×#117625742
C2×C17×#4082
C2×#207817