Finite Group Databasebeta

← C2×#10588893 #11801299

Subgroups — C2×#10588893 #11801299

Order 1152.

2364 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×C9C211yesmaximal, characteristic, complemented
2C23×#611C211yesmaximal, characteristic
3C22×#3676C211yesmaximal, characteristic, complemented
4C22×(C2×D9)⋊C4C212yesmaximal, complemented
5#10588893C218yesmaximal, direct product factor
6C2×C9⋊#95C212yesmaximal, complemented
7C2×#5213—31nomaximal
8C25×C9C2211yescharacteristic
9C24×D9C2211yescharacteristic
10C23×C4×C9—24no—
11C23×C4×C9—28no—
12C23×C4×C9C2212yes—
13C23×C4×C9C2214yescomplemented
14C22×#611—24no—
15C22×#611—24no—
16C22×#611C418yescomplemented
17C22×#611C2214yes—
18C23×Dic9C2212yes—
19C23×Dic9C2211yescharacteristic
20C2×#3676—24no—
21C2×#3676C2214yescomplemented
22C2×(C2×D9)⋊C4—28no—
23C2×(C2×D9)⋊C4C2218yescomplemented
24C9⋊#95C2218yescomplemented
25C24×C3×C4D311yescharacteristic
26C23×#67—31no—
27C22×#217—31no—
28C22×(C2×D3)⋊C4—32no—
29#5213—38no—
30C2×C3⋊#95—32no—
31C24×C9—24no—
32C24×C9—24no—
33C24×C9C2×C414yes—
34C24×C9D414yes—
35C24×C9D414yes—
36C24×C9C2312yes—
37C24×C9C2311yescharacteristic
38C23×D9—24no—
39C23×D9—22no—
40C23×D9—22no—
41C23×D9—24no—
42C23×D9C2×C414yescomplemented
43C23×D9C2312yes—
44C22×C4×C9—232no—
45C22×C4×C9—24no—
46C22×C4×C9—24no—
47C22×C4×C9—28no—
48C22×C4×C9—216no—
49C22×C4×C9D418yescomplemented
50C22×C4×C9C2314yes—
51C2×#611—232no—
52C2×#611—28no—
53C2×#611—28no—
54C2×#611C2×C4116yescomplemented
55C22×Dic9—22no—
56C22×Dic9—22no—
57C22×Dic9—24no—
58C22×Dic9—24no—
59C22×Dic9—24no—
60C22×Dic9C2×C414yescomplemented
61C22×Dic9C2314yes—
62C22×Dic9C2312yes—
63#3676—28no—
64(C2×D9)⋊C4—216no—
65C2×#386—91noSylow
66C25×C3C2×D311yescharacteristic
67C24×D3—31no—
68C23×C3×C4—24no—
69C23×C3×C4—28no—
70C23×C3×C4C2×D312yes—
71C23×C3×C4C2×D314yes—
72C22×#67—38no—
73C22×#67—34no—
74C22×#67—64no—
75C22×#67—64no—
76C23×Dic3—31no—
77C23×Dic3—32no—
78C2×#217—34no—
79C2×#217—64no—
80C2×(C2×D3)⋊C4—38no—
81C2×(C2×D3)⋊C4—68no—
82C3⋊#95—38no—
83C23×C9—216no—
84C23×C9—28no—
85C23×C9—216no—
86C23×C9—28no—
87C23×C9—24no—
88C23×C9—24no—
89C23×C9C22⋊C4116yescomplemented
90C23×C9C22×C414yes—
91C23×C9C22×C412yes—
92C23×C9C2×D414yes—
93C23×C9C2×D412yes—
94C23×C9C2×D414yes—
95C23×C9C2×D412yes—
96C23×C9C2×D414yes—
97C23×C9#4114yes—
98C23×C9C2411yescharacteristic
99C22×D9—28no—
100C22×D9—216no—
101C22×D9—24no—
102C22×D9—22no—
103C22×D9—22no—
104C22×D9—24no—
105C22×D9—44no—
106C22×D9—48no—
107C22×D9—44no—
108C22×D9C22×C414yescomplemented
109C2×C4×C9—232no—
110C2×C4×C9—216no—
111C2×C4×C9—24no—
112C2×C4×C9—24no—
113C2×C4×C9C2×D418yescomplemented
114#611—232no—
115C2×Dic9—28no—
116C2×Dic9—22no—
117C2×Dic9—22no—
118C2×Dic9—24no—
119C2×Dic9—24no—
120C2×Dic9—24no—
121C2×Dic9—48no—
122C2×Dic9C22×C414yescomplemented
123C23×D4—91no—
124C24×C4D911yescharacteristic, complemented
125C22×C22⋊C4—91no—
126C22×C22⋊C4—92no—
127#386—98no—
128C2×#95—92no—
129C24×C3—24no—
130C24×C3—24no—
131C24×C3C4×D314yes—
132C24×C3D1214yes—
133C24×C3#6714yes—
134C24×C3C22×D312yes—
135C24×C3C22×D311yescharacteristic
136C23×D3—34no—
137C23×D3—32no—
138C23×D3—62no—
139C23×D3—64no—
140C23×D3—64no—
141C23×D3—62no—
142C22×C3×C4—232no—
143C22×C3×C4—24no—
144C22×C3×C4—24no—
145C22×C3×C4—28no—
146C22×C3×C4—216no—
147C22×C3×C4#6718yes—
148C22×C3×C4C22×D314yes—
149C2×#67—316no—
150C2×#67—632no—
151C2×#67—68no—
152C2×#67—68no—
153C22×Dic3—34no—
154C22×Dic3—32no—
155C22×Dic3—34no—
156C22×Dic3—62no—
157C22×Dic3—62no—
158C22×Dic3—64no—
159C22×Dic3—64no—
160C22×Dic3—64no—
161#217—68no—
162(C2×D3)⋊C4—616no—
163C22×C9—28no—
164C22×C9—24no—
165C22×C9—28no—
166C22×C9—24no—
167C22×C9—232no—
168C22×C9C2×C22⋊C414yes—
169C22×C9C2×C22⋊C418yescomplemented
170C22×C9C4×D418yes—
171C22×C9#12014yes—
172C22×C9#12118yes—
173C22×C9#12314yes—
174C22×C9C23×C411yescharacteristic
175C22×C9C22×D411yescharacteristic
176C22×C9C22×D411yescharacteristic
177C22×C9C22×D412yes—
178C22×C9C2×#4112yes—
179C2×D9—24no—
180C2×D9—28no—
181C2×D9—42no—
182C2×D9—44no—
183C2×D9—42no—
184C2×D9—416no—
185C4×C9—28no—
186Dic9—24no—
187Dic9—44no—
188C25—91no—
189C25C2×D911yescharacteristic
190C22×D4—98no—
191C22×D4—94no—
192C22×D4—184no—
193C22×D4—184no—
194C23×C4—24no—
195C23×C4—28no—
196C23×C4—91no—
197C23×C4—92no—
198C23×C4C2×D912yes—
199C23×C4C2×D914yescomplemented
200C2×C22⋊C4—94no—
201C2×C22⋊C4—98no—
202C2×C22⋊C4—184no—
203C2×C22⋊C4—188no—
204#95—98no—
205C23×C3—216no—
206C23×C3—28no—
207C23×C3—216no—
208C23×C3—28no—
209C23×C3—24no—
210C23×C3—24no—
211C23×C3(C2×D3)⋊C4116yes—
212C23×C3C2×C4×D314yes—
213C23×C3C2×C4×D312yes—
214C23×C3C2×D1214yes—
215C23×C3C2×D1212yes—
216C23×C3#23514yes—
217C23×C3C2×#6714yes—
218C23×C3C2×#6712yes—
219C23×C3C2×#6714yes—
220C23×C3C23×D311yescharacteristic
221C22×D3—34no—
222C22×D3—68no—
223C22×D3—616no—
224C22×D3—62no—
225C22×D3—64no—
226C22×D3—64no—
227C22×D3—62no—
228C22×D3—124no—
229C22×D3—128no—
230C22×D3—124no—
231C2×C3×C4—232no—
232C2×C3×C4—216no—
233C2×C3×C4—24no—
234C2×C3×C4—24no—
235C2×C3×C4C2×#6718yes—
236#67—632no—
237C2×Dic3—34no—
238C2×Dic3—68no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—64no—
244C2×Dic3—128no—
245C2×C9—28no—
246C2×C9#38618yescomplemented
247C2×C9C22×C22⋊C411yescharacteristic
248C2×C9C2×C4×D412yes—
249C2×C9C2×#12011yescharacteristic
250C2×C9C2×#12112yes—
251C2×C9C2×#12311yescharacteristic
252D9—44no—
253C24—24no—
254C24—24no—
255C24—94no—
256C24—92no—
257C24—182no—
258C24—184no—
259C24—184no—
260C24—182no—
261C24C4×D914yes—
262C24D3614yes—
263C24#61114yes—
264C24C22×D912yes—
265C24C22×D911yescharacteristic
266C2×D4—916no—
267C2×D4—1832no—
268C2×D4—188no—
269C2×D4—188no—
270C22×C4—232no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—28no—
274C22×C4—216no—
275C22×C4—94no—
276C22×C4—92no—
277C22×C4—94no—
278C22×C4—182no—
279C22×C4—182no—
280C22×C4—184no—
281C22×C4—184no—
282C22×C4—184no—
283C22×C4#61118yescomplemented
284C22×C4C22×D914yes—
285C22⋊C4—188no—
286C22⋊C4—1816no—
287C22×C3—232no—
288C22×C3—28no—
289C22×C3—24no—
290C22×C3—28no—
291C22×C3—24no—
292C22×C3C2×(C2×D3)⋊C414yes—
293C22×C3C2×(C2×D3)⋊C418yes—
294C22×C3C4×#6718yes—
295C22×C3#92914yes—
296C22×C3#93018yes—
297C22×C3#95314yes—
298C22×C3C22×C4×D311yescharacteristic
299C22×C3C22×D1211yescharacteristic
300C22×C3C2×#23512yes—
301C22×C3C22×#6711yescharacteristic
302C22×C3C22×#6712yes—
303C2×D3—64no—
304C2×D3—68no—
305C2×D3—1216no—
306C2×D3—122no—
307C2×D3—124no—
308C2×D3—122no—
309C3×C4—28no—
310Dic3—64no—
311Dic3—124no—
312C9C2×#38611yescharacteristic, complemented, Sylow
313C23—216no—
314C23—28no—
315C23—216no—
316C23—28no—
317C23—24no—
318C23—24no—
319C23—94no—
320C23—188no—
321C23—1816no—
322C23—182no—
323C23—184no—
324C23—184no—
325C23—182no—
326C23—364no—
327C23—368no—
328C23—364no—
329C23(C2×D9)⋊C4116yescomplemented
330C23C2×C4×D914yes—
331C23C2×C4×D912yes—
332C23C2×D3614yes—
333C23C2×D3612yes—
334C23#369714yes—
335C23C2×#61114yes—
336C23C2×#61112yes—
337C23C2×#61114yes—
338C23C23×D911yescharacteristic
339D4—1832no—
340C2×C4—232no—
341C2×C4—216no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—94no—
345C2×C4—188no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4—184no—
349C2×C4—184no—
350C2×C4—184no—
351C2×C4—368no—
352C2×C4C2×#61118yescomplemented
353C2×C3—28no—
354C2×C3#521318yes—
355C2×C3C22×(C2×D3)⋊C411yescharacteristic
356C2×C3C2×C4×#6712yes—
357C2×C3C2×#92911yescharacteristic
358C2×C3C2×#93012yes—
359C2×C3C2×#95311yescharacteristic
360D3—124no—
361C22—28no—
362C22—24no—
363C22—28no—
364C22—232no—
365C22—24no—
366C22—184no—
367C22—188no—
368C22—362no—
369C22—364no—
370C22—3616no—
371C22—362no—
372C22C2×(C2×D9)⋊C414yes—
373C22C2×(C2×D9)⋊C418yescomplemented
374C22C4×#61118yes—
375C22#6349114yes—
376C22#6349218yes—
377C22#6351514yes—
378C22C22×C4×D911yescharacteristic
379C22C22×D3611yescharacteristic
380C22C2×#369712yes—
381C22C22×#61111yescharacteristic
382C22C22×#61112yes—
383C4—28no—
384C4—184no—
385C4—364no—
386C3C2×#521311yescharacteristic
387C2—28no—
388C2—364no—
389C2#1058889318yesdirect product factor
390C2C22×(C2×D9)⋊C411yescharacteristic
391C2C2×C4×#61112yes—
392C2C2×#6349111yescharacteristic
393C2C2×#6349212yes—
394C2C2×#6351511yescharacteristic
subgroupG/H
centerC24C22×D9
commutatorC22×C9C23×C4
FrattiniC23×C3C23×D3
FittingC24×C4×C9C2
socleC24×C3C22×D3
prime radicalC23×#611C2
cosocleC23×C9C24
hypercenterC24×C4D9
hypocenterC9C2×#386
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C24 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. C24×C4×C9C2semidirect
3. C22×#3676C2semidirect
4. C22×(C2×D9)⋊C4C2semidirect
5. #10588893C2direct (N × H)
6. C2×C9⋊#95C2semidirect
13. C23×C4×C9C22semidirect
16. C22×#611C4semidirect
21. C2×#3676C22semidirect
23. C2×(C2×D9)⋊C4C22semidirect
24. C9⋊#95C22semidirect
42. C23×D9C2×C4semidirect
49. C22×C4×C9D4semidirect
54. C2×#611C2×C4semidirect
60. C22×Dic9C2×C4semidirect
89. C23×C9C22⋊C4semidirect
108. C22×D9C22×C4semidirect
113. C2×C4×C9C2×D4semidirect
122. C2×Dic9C22×C4semidirect
124. C24×C4D9semidirect
169. C22×C9C2×C22⋊C4semidirect
199. C23×C4C2×D9semidirect
246. C2×C9#386semidirect
283. C22×C4#611semidirect
312. C9C2×#386semidirect
329. C23(C2×D9)⋊C4semidirect
352. C2×C4C2×#611semidirect
373. C22C2×(C2×D9)⋊C4semidirect
389. C2#10588893direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×C92
C23×#6112
C22×#36762
C22×(C2×D9)⋊C42
#105888932
C2×C9⋊#952
C2×#52133