Finite Group Databasebeta

← C2×#10591692 #11808125

Subgroups — C2×#10591692 #11808125

Order 1152.

2409 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#627C211yesmaximal, characteristic, complemented
2C22×#3757C211yesmaximal, characteristic
3C22×C3×#217C212yesmaximal
4C2×#63579C211yesmaximal, characteristic, complemented
5C2×#63579C212yesmaximal, complemented
6#10591692C218yesmaximal, direct product factor
7C2×#4947—32nomaximal
8C25×C32C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C22×#627—24no—
14C22×#627—28no—
15C22×#627C2214yescomplemented
16C2×#3757—24no—
17C2×#3757C2214yes—
18C2×C3×#217—28no—
19C2×C3×#217C2218yes—
20#63579C2214yescomplemented
21#63579C2218yescomplemented
22C23×Dic6—32no—
23C22×C3×C22⋊C4—32no—
24C22×#217—32no—
25C22×#217—61no—
26C22×#217D312yes—
27C2×C3⋊#95—32no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95—32no—
30#4947—316no—
31C24×C32—22no—
32C24×C32—24no—
33C24×C32—22no—
34C24×C32—24no—
35C24×C32Q814yescomplemented
36C24×C32C2312yes—
37C24×C32C2311yescharacteristic
38C22×C3⋊Dic3—24no—
39C22×C3⋊Dic3—22no—
40C22×C3⋊Dic3—24no—
41C22×C3⋊Dic3D414yes—
42C22×C3⋊Dic3C2312yes—
43C22×C3⋊Dic3C2312yes—
44C22×C3×Dic3—24no—
45C22×C3×Dic3—24no—
46C22×C3×Dic3—24no—
47C22×C3×Dic3—24no—
48C22×C3×Dic3—24no—
49C22×C3×Dic3D418yes—
50C22×C3×Dic3C2314yes—
51C22×C3×Dic3C2314yes—
52C2×#627—232no—
53C2×#627—28no—
54C2×#627—216no—
55#3757—28no—
56C3×#217—216no—
57C2×#393—91noSylow
58C25×C3—21no—
59C25×C3C2×D312yes—
60C23×C3×C4—32no—
61C23×C3×C4—32no—
62C23×Dic3—32no—
63C23×Dic3—32no—
64C23×Dic3—61no—
65C23×Dic3—61no—
66C23×Dic3C2×D312yes—
67C23×Dic3C2×D312yes—
68C22×Dic6—38no—
69C22×Dic6—68no—
70C22×Dic6—68no—
71C22×Dic6—68no—
72C2×C3×C22⋊C4—38no—
73C2×C3×C22⋊C4—68no—
74C2×#217—28no—
75C2×#217—38no—
76C2×#217—64no—
77C2×#217—68no—
78C2×#217—68no—
79C2×#217C2×D318yes—
80C3⋊#95—38no—
81C3⋊#95—38no—
82C3⋊#95—38no—
83C23×C32—28no—
84C23×C32—22no—
85C23×C32—22no—
86C23×C32—216no—
87C23×C32—24no—
88C23×C32—24no—
89C23×C32—44no—
90C23×C32—44no—
91C23×C32—48no—
92C23×C32C2×D412yes—
93C23×C32C2×D414yes—
94C23×C32C2×Q812yes—
95C23×C32C2×Q814yescomplemented
96C23×C32#4114yes—
97C23×C32#4112yes—
98C23×C32C2411yescharacteristic
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—28no—
101C2×C3⋊Dic3—24no—
102C2×C3⋊Dic3—24no—
103C2×C3⋊Dic3—44no—
104C2×C3⋊Dic3C2×D414yes—
105C2×C3×Dic3—216no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—48no—
112C2×C3×Dic3C2×D418yes—
113#627—232no—
114C23×Q8—91no—
115C22×C22⋊C4—32no—
116C22×C22⋊C4—91no—
117#393—98no—
118C2×#95—92no—
119C2×#95—91no—
120C24×C3—24no—
121C24×C3—24no—
122C24×C3—24no—
123C24×C3—24no—
124C24×C3—24no—
125C24×C3—24no—
126C24×C3—24no—
127C24×C3—24no—
128C24×C3—24no—
129C24×C3—22no—
130C24×C3—21no—
131C24×C3—44no—
132C24×C3—44no—
133C24×C3Dic618yescomplemented
134C24×C3C22×D314yes—
135C24×C3C22×D312yes—
136C22×C3×C4—38no—
137C22×C3×C4—34no—
138C22×C3×C4—34no—
139C22×C3×C4—64no—
140C22×C3×C4—64no—
141C22×C3×C4—64no—
142C22×C3×C4—64no—
143C22×C3×C4—64no—
144C22×Dic3—24no—
145C22×Dic3—24no—
146C22×Dic3—24no—
147C22×Dic3—24no—
148C22×Dic3—24no—
149C22×Dic3—38no—
150C22×Dic3—34no—
151C22×Dic3—34no—
152C22×Dic3—64no—
153C22×Dic3—62no—
154C22×Dic3—62no—
155C22×Dic3—64no—
156C22×Dic3—64no—
157C22×Dic3—64no—
158C22×Dic3—64no—
159C22×Dic3—64no—
160C22×Dic3—64no—
161C22×Dic3—124no—
162C22×Dic3—124no—
163C22×Dic3#6718yes—
164C22×Dic3C22×D314yes—
165C22×Dic3C22×D314yes—
166C2×Dic6—616no—
167C2×Dic6—616no—
168C2×Dic6—664no—
169C2×Dic6—616no—
170C3×C22⋊C4—616no—
171#217—216no—
172#217—616no—
173#217—616no—
174C22×C32—24no—
175C22×C32—28no—
176C22×C32—42no—
177C22×C32—42no—
178C22×C32—44no—
179C22×C32—416no—
180C22×C32#12014yes—
181C22×C32C22⋊Q814yes—
182C22×C32C22⋊Q818yes—
183C22×C32#12414yes—
184C22×C32#12418yes—
185C22×C32C22×D411yescharacteristic
186C22×C32C22×D412yes—
187C22×C32C22×Q811yescharacteristic
188C22×C32C2×#4112yes—
189C22×C32C2×#4111yescharacteristic
190C3⋊Dic3—24no—
191C3⋊Dic3—42no—
192C3×Dic3—28no—
193C3×Dic3—44no—
194C25D3211yescharacteristic
195C22×Q8—94no—
196C22×Q8—188no—
197C22×Q8—184no—
198C23×C4—32no—
199C23×C4—32no—
200C23×C4—91no—
201C23×C4—91no—
202C2×C22⋊C4—38no—
203C2×C22⋊C4—68no—
204C2×C22⋊C4—94no—
205C2×C22⋊C4—184no—
206#95—98no—
207#95—94no—
208C23×C3—24no—
209C23×C3—24no—
210C23×C3—216no—
211C23×C3—216no—
212C23×C3—216no—
213C23×C3—216no—
214C23×C3—24no—
215C23×C3—24no—
216C23×C3—24no—
217C23×C3—24no—
218C23×C3—24no—
219C23×C3—24no—
220C23×C3—21no—
221C23×C3—24no—
222C23×C3—22no—
223C23×C3—22no—
224C23×C3—24no—
225C23×C3—24no—
226C23×C3—22no—
227C23×C3—44no—
228C23×C3—44no—
229C23×C3—416no—
230C23×C3—48no—
231C23×C3—416no—
232C23×C3—48no—
233C23×C3—48no—
234C23×C3—48no—
235C23×C3—48no—
236C23×C3—48no—
237C23×C3C2×Dic614yes—
238C23×C3C2×Dic618yescomplemented
239C23×C3#23514yes—
240C23×C3D3×D414yes—
241C23×C3D3×D414yes—
242C23×C3#23714yes—
243C23×C3#23714yes—
244C23×C3C2×#6714yes—
245C23×C3C23×D312yes—
246C2×C3×C4—38no—
247C2×C3×C4—616no—
248C2×C3×C4—64no—
249C2×C3×C4—64no—
250C2×C3×C4—64no—
251C2×C3×C4—64no—
252C2×C3×C4—64no—
253C2×C3×C4—128no—
254C2×Dic3—216no—
255C2×Dic3—24no—
256C2×Dic3—24no—
257C2×Dic3—24no—
258C2×Dic3—24no—
259C2×Dic3—24no—
260C2×Dic3—38no—
261C2×Dic3—48no—
262C2×Dic3—64no—
263C2×Dic3—616no—
264C2×Dic3—64no—
265C2×Dic3—64no—
266C2×Dic3—64no—
267C2×Dic3—64no—
268C2×Dic3—64no—
269C2×Dic3—64no—
270C2×Dic3—124no—
271C2×Dic3—128no—
272C2×Dic3—124no—
273C2×Dic3—128no—
274C2×Dic3—128no—
275C2×Dic3C2×#6718yes—
276Dic6—664no—
277C2×C32—44no—
278C2×C32#39318yescomplemented
279C2×C32C2×#12011yescharacteristic
280C2×C32C2×C22⋊Q811yescharacteristic
281C2×C32C2×C22⋊Q812yes—
282C2×C32C2×#12411yescharacteristic
283C2×C32C2×#12412yes—
284C24—24no—
285C24—22no—
286C24—24no—
287C24—22no—
288C24#62714yescomplemented
289C24C2×D3212yes—
290C24C2×D3211yescharacteristic
291C2×Q8—1816no—
292C2×Q8—188no—
293C2×Q8—1832no—
294C22×C4—34no—
295C22×C4—38no—
296C22×C4—34no—
297C22×C4—64no—
298C22×C4—64no—
299C22×C4—64no—
300C22×C4—64no—
301C22×C4—64no—
302C22×C4—92no—
303C22×C4—94no—
304C22×C4—92no—
305C22×C4—184no—
306C22×C4—184no—
307C22×C4—182no—
308C22⋊C4—616no—
309C22⋊C4—188no—
310C22×C3—28no—
311C22×C3—28no—
312C22×C3—28no—
313C22×C3—28no—
314C22×C3—22no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—22no—
318C22×C3—21no—
319C22×C3—24no—
320C22×C3—28no—
321C22×C3—28no—
322C22×C3—24no—
323C22×C3—24no—
324C22×C3—48no—
325C22×C3—44no—
326C22×C3—48no—
327C22×C3—44no—
328C22×C3—432no—
329C22×C3—432no—
330C22×C3—44no—
331C22×C3—44no—
332C22×C3—44no—
333C22×C3—44no—
334C22×C3#87818yes—
335C22×C3#87818yes—
336C22×C3#88518yes—
337C22×C3#88518yes—
338C22×C3#92418yes—
339C22×C3#93618yes—
340C22×C3#93718yes—
341C22×C3C22×Dic612yes—
342C22×C3C2×#23512yes—
343C22×C3C2×D3×D412yes—
344C22×C3C2×D3×D412yes—
345C22×C3C2×#23712yes—
346C22×C3C2×#23712yes—
347C22×C3C22×#6712yes—
348C3×C4—68no—
349C3×C4—124no—
350Dic3—28no—
351Dic3—44no—
352Dic3—68no—
353Dic3—124no—
354Dic3—124no—
355Dic3—124no—
356C32C2×#39311yescharacteristic, complemented, Sylow
357C23—24no—
358C23—22no—
359C23—24no—
360C23—22no—
361C23—216no—
362C23—28no—
363C23—44no—
364C23—48no—
365C23—44no—
366C23#380414yes—
367C23#380512yes—
368C23C2×#62712yes—
369C23C2×#62714yescomplemented
370C23D3×#6714yes—
371C23#381112yes—
372C23C22×D3211yescharacteristic
373Q8—1832no—
374C2×C4—38no—
375C2×C4—64no—
376C2×C4—64no—
377C2×C4—616no—
378C2×C4—64no—
379C2×C4—64no—
380C2×C4—64no—
381C2×C4—94no—
382C2×C4—128no—
383C2×C4—184no—
384C2×C4—188no—
385C2×C4—184no—
386C2×C4—182no—
387C2×C4—364no—
388C2×C3—21no—
389C2×C3—22no—
390C2×C3—22no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—28no—
394C2×C3—48no—
395C2×C3—48no—
396C2×C3#4947116yescomplemented
397C2×C3C2×#87812yes—
398C2×C3C2×#87812yes—
399C2×C3C2×#88512yes—
400C2×C3C2×#88512yes—
401C2×C3C2×#92412yes—
402C2×C3C2×#93612yes—
403C2×C3C2×#93712yes—
404C22—28no—
405C22—24no—
406C22—42no—
407C22—44no—
408C22—42no—
409C22—416no—
410C22#6395314yes—
411C22#6395918yes—
412C22#6396418yes—
413C22#6398214yes—
414C22#6398314yes—
415C22C2×#380412yes—
416C22C2×#380511yescharacteristic
417C22C22×#62711yescharacteristic
418C22C2×D3×#6712yes—
419C22C2×#381111yescharacteristic
420C4—68no—
421C4—124no—
422C4—184no—
423C4—362no—
424C3—21no—
425C3C2×#494712yescomplemented
426C2—44no—
427C2#1059169218yesdirect product factor
428C2C2×#6395311yescharacteristic
429C2C2×#6395912yes—
430C2C2×#6396412yes—
431C2C2×#6398211yescharacteristic
432C2C2×#6398311yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
Fitting, prime radicalC25×C32C22
socleC24×C32C23
hypercenterC25D32
hypocenterC32C2×#393
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C23×#627C2semidirect
4. C2×#63579C2semidirect
5. C2×#63579C2semidirect
6. #10591692C2direct (N × H)
15. C22×#627C22semidirect
20. #63579C22semidirect
21. #63579C22semidirect
35. C24×C32Q8semidirect
95. C23×C32C2×Q8semidirect
133. C24×C3Dic6semidirect
238. C23×C3C2×Dic6semidirect
278. C2×C32#393semidirect
288. C24#627semidirect
356. C32C2×#393semidirect
369. C23C2×#627semidirect
396. C2×C3#4947semidirect
425. C3C2×#4947semidirect
427. C2#10591692direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6272
C22×#37572
C22×C3×#2172
C2×#635792
#105916922
C2×#49473