Finite Group Databasebeta

← C2×#10591216 #11808314

Subgroups — C2×#10591216 #11808314

Order 1152.

1977 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic
2C22×#3724C211yesmaximal, characteristic, complemented
3C22×#3722C212yesmaximal
4C2×C3×C3⋊#95C212yesmaximal, complemented
5C2×#63579C211yesmaximal, characteristic, complemented
6#10591216C218yesmaximal, direct product factor
7C2×#4675—32nomaximal
8C24×C3⋊D3C2211yescharacteristic
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C2×#3752—24no—
14C2×#3752C2214yes—
15C2×#3724—24no—
16C2×#3724C2214yescomplemented
17C2×#3722—28no—
18C2×#3722C2218yes—
19C3×C3⋊#95C2218yescomplemented
20#63579C2214yescomplemented
21C22×(C2×D3)⋊C4—32no—
22C22×(C2×D3)⋊C4—32no—
23C22×(C2×D3)⋊C4—32no—
24C22×(C2×D3)⋊C4—61no—
25C22×Dic3⋊C4—32no—
26C2×C3×#95—32no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95D312yescomplemented
29#4675—316no—
30C24×C32C2311yescharacteristic
31C23×C3⋊D3—22no—
32C23×C3⋊D3—22no—
33C23×C3⋊D3—24no—
34C23×C3⋊D3—24no—
35C23×C3⋊D3D414yes—
36C23×C3⋊D3C2312yes—
37C22×C32×C4—22no—
38C22×C32×C4—24no—
39C22×C32×C4C2312yes—
40C22×C3⋊Dic3—24no—
41C22×C3⋊Dic3D414yes—
42C22×C3⋊Dic3C2312yes—
43C22×C3×Dic3—24no—
44C22×C3×Dic3—24no—
45C22×C3×Dic3—24no—
46C22×C3×Dic3—24no—
47C22×C3×Dic3—24no—
48C22×C3×Dic3—24no—
49C22×C3×Dic3C2314yes—
50C22×C3×Dic3C2314yes—
51#3752—28no—
52#3724—28no—
53#3722—216no—
54C2×#397—91noSylow
55C24×D3—32no—
56C24×D3—61no—
57C23×C3×C4—21no—
58C23×C3×C4—32no—
59C23×C3×C4—32no—
60C23×C3×C4C2×D312yes—
61C23×Dic3—32no—
62C23×Dic3—61no—
63C23×Dic3C2×D312yes—
64C23×Dic3C2×D312yes—
65C2×(C2×D3)⋊C4—38no—
66C2×(C2×D3)⋊C4—38no—
67C2×(C2×D3)⋊C4—38no—
68C2×(C2×D3)⋊C4—64no—
69C2×(C2×D3)⋊C4—68no—
70C2×(C2×D3)⋊C4—68no—
71C2×(C2×D3)⋊C4—68no—
72C2×(C2×D3)⋊C4—68no—
73C2×Dic3⋊C4—38no—
74C2×Dic3⋊C4—68no—
75C3×#95—38no—
76C3⋊#95—38no—
77C3⋊#95C2×D318yescomplemented
78C23×C32C2×D412yes—
79C23×C32C2×D412yes—
80C23×C32#4112yes—
81C23×C32#4114yes—
82C23×C32#4114yes—
83C23×C32C2411yescharacteristic
84C22×C3⋊D3—28no—
85C22×C3⋊D3—22no—
86C22×C3⋊D3—22no—
87C22×C3⋊D3—216no—
88C22×C3⋊D3—24no—
89C22×C3⋊D3—24no—
90C22×C3⋊D3—44no—
91C22×C3⋊D3—44no—
92C22×C3⋊D3—48no—
93C22×C3⋊D3C2×D414yes—
94C2×C32×C4—22no—
95C2×C32×C4—24no—
96C2×C32×C4—44no—
97C2×C3⋊Dic3—28no—
98C2×C3⋊Dic3—24no—
99C2×C3⋊Dic3C2×D414yes—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—24no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—48no—
107C2×C3×Dic3—48no—
108C22×C4⋊C4—91no—
109C22×C22⋊C4—92no—
110C22×C22⋊C4—91no—
111#397—98no—
112C2×#95—32no—
113C2×#95—91no—
114C24×C3—21no—
115C24×C3C22×D312yes—
116C23×D3—38no—
117C23×D3—34no—
118C23×D3—64no—
119C23×D3—62no—
120C23×D3—64no—
121C23×D3—64no—
122C23×D3—64no—
123C23×D3—64no—
124C23×D3—64no—
125C23×D3—64no—
126C23×D3—64no—
127C23×D3—64no—
128C23×D3—124no—
129C23×D3—124no—
130C22×C3×C4—24no—
131C22×C3×C4—24no—
132C22×C3×C4—24no—
133C22×C3×C4—24no—
134C22×C3×C4—22no—
135C22×C3×C4—34no—
136C22×C3×C4—34no—
137C22×C3×C4—44no—
138C22×C3×C4—64no—
139C22×C3×C4—64no—
140C22×C3×C4—64no—
141C22×C3×C4—64no—
142C22×C3×C4—64no—
143C22×C3×C4—64no—
144C22×C3×C4C22×D314yes—
145C22×Dic3—24no—
146C22×Dic3—24no—
147C22×Dic3—24no—
148C22×Dic3—24no—
149C22×Dic3—24no—
150C22×Dic3—24no—
151C22×Dic3—38no—
152C22×Dic3—34no—
153C22×Dic3—64no—
154C22×Dic3—62no—
155C22×Dic3—64no—
156C22×Dic3—64no—
157C22×Dic3—124no—
158C22×Dic3C22×D314yes—
159C22×Dic3C22×D314yes—
160(C2×D3)⋊C4—616no—
161(C2×D3)⋊C4—616no—
162(C2×D3)⋊C4—616no—
163(C2×D3)⋊C4—616no—
164Dic3⋊C4—616no—
165C22×C32#12114yes—
166C22×C32#12318yes—
167C22×C32#12314yes—
168C22×C32#12414yes—
169C22×C32#12618yes—
170C22×C32C22×D411yescharacteristic
171C22×C32C22×D411yescharacteristic
172C22×C32C2×#4111yescharacteristic
173C22×C32C2×#4112yes—
174C22×C32C2×#4112yes—
175C2×C3⋊D3—24no—
176C2×C3⋊D3—28no—
177C2×C3⋊D3—42no—
178C2×C3⋊D3—42no—
179C2×C3⋊D3—44no—
180C2×C3⋊D3—416no—
181C32×C4—42no—
182C3⋊Dic3—24no—
183C3×Dic3—44no—
184C3×Dic3—44no—
185C25—91no—
186C23×C4—32no—
187C23×C4—32no—
188C23×C4—91no—
189C23×C4D3211yescharacteristic
190C2×C4⋊C4—94no—
191C2×C4⋊C4—184no—
192C2×C22⋊C4—98no—
193C2×C22⋊C4—94no—
194C2×C22⋊C4—184no—
195C2×C22⋊C4—188no—
196#95—38no—
197#95—94no—
198C23×C3—21no—
199C23×C3—22no—
200C23×C3—24no—
201C23×C3—22no—
202C23×C3—24no—
203C23×C3—22no—
204C23×C3#23514yes—
205C23×C3#23514yes—
206C23×C3#23514yes—
207C23×C3D3×D414yes—
208C23×C3D3×D414yes—
209C23×C3#23714yes—
210C23×C3#23914yes—
211C23×C3C23×D312yes—
212C22×D3—38no—
213C22×D3—64no—
214C22×D3—64no—
215C22×D3—64no—
216C22×D3—616no—
217C22×D3—616no—
218C22×D3—616no—
219C22×D3—616no—
220C22×D3—64no—
221C22×D3—64no—
222C22×D3—64no—
223C22×D3—64no—
224C22×D3—64no—
225C22×D3—64no—
226C22×D3—124no—
227C22×D3—124no—
228C22×D3—1216no—
229C22×D3—1216no—
230C22×D3—128no—
231C22×D3—128no—
232C22×D3—128no—
233C22×D3—128no—
234C22×D3—128no—
235C22×D3—128no—
236C2×C3×C4—24no—
237C2×C3×C4—24no—
238C2×C3×C4—24no—
239C2×C3×C4—24no—
240C2×C3×C4—44no—
241C2×C3×C4—48no—
242C2×C3×C4—48no—
243C2×C3×C4—64no—
244C2×C3×C4—64no—
245C2×C3×C4—64no—
246C2×C3×C4—64no—
247C2×C3×C4—64no—
248C2×C3×C4—64no—
249C2×C3×C4—128no—
250C2×C3×C4—128no—
251C2×Dic3—24no—
252C2×Dic3—24no—
253C2×Dic3—24no—
254C2×Dic3—24no—
255C2×Dic3—24no—
256C2×Dic3—24no—
257C2×Dic3—38no—
258C2×Dic3—48no—
259C2×Dic3—48no—
260C2×Dic3—64no—
261C2×Dic3—616no—
262C2×Dic3—64no—
263C2×Dic3—64no—
264C2×Dic3—124no—
265C2×Dic3—128no—
266C2×C32#39718yescomplemented
267C2×C32C2×#12111yescharacteristic
268C2×C32C2×#12312yes—
269C2×C32C2×#12311yescharacteristic
270C2×C32C2×#12411yescharacteristic
271C2×C32C2×#12612yes—
272C3⋊D3—44no—
273C24—92no—
274C24—94no—
275C24—182no—
276C24—184no—
277C24—184no—
278C24—182no—
279C24C2×D3211yescharacteristic
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—34no—
283C22×C4—34no—
284C22×C4—64no—
285C22×C4—64no—
286C22×C4—64no—
287C22×C4—64no—
288C22×C4—64no—
289C22×C4—64no—
290C22×C4—92no—
291C22×C4—94no—
292C22×C4—184no—
293C22×C4C2×D3212yes—
294C4⋊C4—188no—
295C22⋊C4—188no—
296C22⋊C4—1816no—
297C22×C3—21no—
298C22×C3—22no—
299C22×C3—21no—
300C22×C3—22no—
301C22×C3—21no—
302C22×C3—28no—
303C22×C3—28no—
304C22×C3—24no—
305C22×C3—24no—
306C22×C3—24no—
307C22×C3#87618yes—
308C22×C3#88318yes—
309C22×C3#88418yes—
310C22×C3#88518yes—
311C22×C3#89418yes—
312C22×C3#89418yes—
313C22×C3#89818yes—
314C22×C3C2×#23512yes—
315C22×C3C2×#23512yes—
316C22×C3C2×#23512yes—
317C22×C3C2×D3×D412yes—
318C22×C3C2×D3×D412yes—
319C22×C3C2×#23712yes—
320C22×C3C2×#23912yes—
321C2×D3—68no—
322C2×D3—68no—
323C2×D3—68no—
324C2×D3—68no—
325C2×D3—128no—
326C2×D3—128no—
327C2×D3—124no—
328C2×D3—124no—
329C2×D3—1232no—
330C2×D3—1232no—
331C2×D3—124no—
332C2×D3—124no—
333C2×D3—124no—
334C2×D3—124no—
335C3×C4—44no—
336C3×C4—44no—
337C3×C4—124no—
338C3×C4—124no—
339Dic3—44no—
340Dic3—44no—
341Dic3—68no—
342Dic3—124no—
343C32C2×#39711yescharacteristic, complemented, Sylow
344C23—94no—
345C23—182no—
346C23—184no—
347C23—184no—
348C23—182no—
349C23—1816no—
350C23—188no—
351C23—368no—
352C23—364no—
353C23—364no—
354C23#379812yes—
355C23#379914yes—
356C23#380212yes—
357C23#380414yes—
358C23#381112yes—
359C23C22×D3211yescharacteristic
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—44no—
363C2×C4—64no—
364C2×C4—64no—
365C2×C4—64no—
366C2×C4—64no—
367C2×C4—64no—
368C2×C4—64no—
369C2×C4—94no—
370C2×C4—128no—
371C2×C4—128no—
372C2×C4—184no—
373C2×C4—188no—
374C2×C3—22no—
375C2×C3—22no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—28no—
380C2×C3#4675116yescomplemented
381C2×C3C2×#87612yes—
382C2×C3C2×#88312yes—
383C2×C3C2×#88412yes—
384C2×C3C2×#88512yes—
385C2×C3C2×#89412yes—
386C2×C3C2×#89412yes—
387C2×C3C2×#89812yes—
388D3—128no—
389D3—128no—
390C22—188no—
391C22—184no—
392C22—364no—
393C22—362no—
394C22—362no—
395C22—3616no—
396C22#6385418yes—
397C22#6386818yes—
398C22#6389714yes—
399C22#6391214yes—
400C22#6395314yes—
401C22C2×#379811yescharacteristic
402C22C2×#379912yes—
403C22C2×#380211yescharacteristic
404C22C2×#380412yes—
405C22C2×#381111yescharacteristic
406C4—42no—
407C4—124no—
408C4—124no—
409C4—184no—
410C3—21no—
411C3C2×#467512yescomplemented
412C2—364no—
413C2#1059121618yesdirect product factor
414C2C2×#6385412yes—
415C2C2×#6386812yes—
416C2C2×#6389711yescharacteristic
417C2C2×#6391211yescharacteristic
418C2C2×#6395311yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32C2×#397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3724C2semidirect
4. C2×C3×C3⋊#95C2semidirect
5. C2×#63579C2semidirect
6. #10591216C2direct (N × H)
16. C2×#3724C22semidirect
19. C3×C3⋊#95C22semidirect
20. #63579C22semidirect
28. C2×C3⋊#95D3semidirect
77. C3⋊#95C2×D3semidirect
266. C2×C32#397semidirect
343. C32C2×#397semidirect
380. C2×C3#4675semidirect
411. C3C2×#4675semidirect
413. C2#10591216direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37522
C22×#37242
C22×#37222
C2×C3×C3⋊#952
C2×#635792
#105912162
C2×#46753