Finite Group Databasebeta

← C2×#10591205 #11808127

Subgroups — C2×#10591205 #11808127

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×#3752C211yesmaximal, characteristic
3C22×#3722C212yesmaximal
4C2×C3×C3⋊#95C212yesmaximal, complemented
5C2×#63579C211yesmaximal, characteristic, complemented
6#10591205C218yesmaximal, direct product factor
7C2×#4673—32nomaximal
8C24×C3⋊D3C2211yescharacteristic
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C22×#627—24no—
14C22×#627—28no—
15C22×#627C2214yescomplemented
16C2×#3752—24no—
17C2×#3752C2214yes—
18C2×#3722—28no—
19C2×#3722C2218yes—
20C3×C3⋊#95C2218yescomplemented
21#63579C2214yescomplemented
22C23×Dic6—32no—
23C22×(C2×D3)⋊C4—32no—
24C22×(C2×D3)⋊C4—32no—
25C22×(C2×D3)⋊C4—32no—
26C22×(C2×D3)⋊C4—61no—
27C2×C3×#95—32no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95D312yescomplemented
30#4673—316no—
31C24×C32C2311yescharacteristic
32C23×C3⋊D3—22no—
33C23×C3⋊D3—24no—
34C23×C3⋊D3—22no—
35C23×C3⋊D3—24no—
36C23×C3⋊D3Q814yescomplemented
37C23×C3⋊D3C2312yes—
38C22×C32×C4—22no—
39C22×C32×C4—24no—
40C22×C32×C4C2312yes—
41C22×C3⋊Dic3—24no—
42C22×C3⋊Dic3D414yes—
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#3752—28no—
56#3722—216no—
57C2×#393—91noSylow
58C24×D3—32no—
59C24×D3—61no—
60C23×C3×C4—21no—
61C23×C3×C4—32no—
62C23×C3×C4—32no—
63C23×C3×C4C2×D312yes—
64C23×Dic3—32no—
65C23×Dic3—61no—
66C23×Dic3C2×D312yes—
67C23×Dic3C2×D312yes—
68C22×Dic6—38no—
69C22×Dic6—68no—
70C22×Dic6—68no—
71C22×Dic6—68no—
72C2×(C2×D3)⋊C4—38no—
73C2×(C2×D3)⋊C4—38no—
74C2×(C2×D3)⋊C4—38no—
75C2×(C2×D3)⋊C4—64no—
76C2×(C2×D3)⋊C4—68no—
77C2×(C2×D3)⋊C4—68no—
78C2×(C2×D3)⋊C4—68no—
79C2×(C2×D3)⋊C4—68no—
80C3×#95—38no—
81C3⋊#95—38no—
82C3⋊#95C2×D318yescomplemented
83C23×C32C2×D414yes—
84C23×C32C2×D412yes—
85C23×C32C2×Q812yes—
86C23×C32#4112yes—
87C23×C32#4114yes—
88C23×C32C2411yescharacteristic
89C22×C3⋊D3—28no—
90C22×C3⋊D3—22no—
91C22×C3⋊D3—22no—
92C22×C3⋊D3—216no—
93C22×C3⋊D3—24no—
94C22×C3⋊D3—24no—
95C22×C3⋊D3—44no—
96C22×C3⋊D3—48no—
97C22×C3⋊D3—44no—
98C22×C3⋊D3C2×Q814yescomplemented
99C2×C32×C4—22no—
100C2×C32×C4—24no—
101C2×C32×C4—44no—
102C2×C3⋊Dic3—28no—
103C2×C3⋊Dic3—24no—
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—92no—
116C22×C22⋊C4—91no—
117#393—98no—
118C2×#95—32no—
119C2×#95—91no—
120C24×C3—21no—
121C24×C3C22×D312yes—
122C23×D3—38no—
123C23×D3—34no—
124C23×D3—64no—
125C23×D3—62no—
126C23×D3—64no—
127C23×D3—64no—
128C23×D3—64no—
129C23×D3—64no—
130C23×D3—64no—
131C23×D3—64no—
132C23×D3—64no—
133C23×D3—64no—
134C23×D3—124no—
135C23×D3—124no—
136C22×C3×C4—24no—
137C22×C3×C4—24no—
138C22×C3×C4—24no—
139C22×C3×C4—24no—
140C22×C3×C4—22no—
141C22×C3×C4—38no—
142C22×C3×C4—34no—
143C22×C3×C4—34no—
144C22×C3×C4—44no—
145C22×C3×C4—64no—
146C22×C3×C4—64no—
147C22×C3×C4—64no—
148C22×C3×C4—64no—
149C22×C3×C4—64no—
150C22×C3×C4C22×D314yes—
151C22×Dic3—24no—
152C22×Dic3—24no—
153C22×Dic3—24no—
154C22×Dic3—24no—
155C22×Dic3—24no—
156C22×Dic3—38no—
157C22×Dic3—34no—
158C22×Dic3—64no—
159C22×Dic3—62no—
160C22×Dic3—64no—
161C22×Dic3—64no—
162C22×Dic3—124no—
163C22×Dic3D1218yes—
164C22×Dic3C22×D314yes—
165C22×Dic3C22×D314yes—
166C2×Dic6—616no—
167C2×Dic6—616no—
168C2×Dic6—664no—
169C2×Dic6—616no—
170(C2×D3)⋊C4—616no—
171(C2×D3)⋊C4—616no—
172(C2×D3)⋊C4—616no—
173(C2×D3)⋊C4—616no—
174C22×C32#12014yes—
175C22×C32C22⋊Q814yes—
176C22×C32C22⋊Q818yes—
177C22×C32#12418yes—
178C22×C32#12414yes—
179C22×C32C22×D412yes—
180C22×C32C22×D411yescharacteristic
181C22×C32C22×Q811yescharacteristic
182C22×C32C2×#4111yescharacteristic
183C22×C32C2×#4112yes—
184C2×C3⋊D3—24no—
185C2×C3⋊D3—28no—
186C2×C3⋊D3—42no—
187C2×C3⋊D3—44no—
188C2×C3⋊D3—42no—
189C2×C3⋊D3—416no—
190C32×C4—42no—
191C3⋊Dic3—24no—
192C3×Dic3—28no—
193C3×Dic3—44no—
194C25—91no—
195C22×Q8—94no—
196C22×Q8—188no—
197C22×Q8—184no—
198C23×C4—32no—
199C23×C4—32no—
200C23×C4—91no—
201C23×C4D3211yescharacteristic
202C2×C22⋊C4—98no—
203C2×C22⋊C4—94no—
204C2×C22⋊C4—184no—
205C2×C22⋊C4—188no—
206#95—38no—
207#95—94no—
208C23×C3—21no—
209C23×C3—22no—
210C23×C3—22no—
211C23×C3—24no—
212C23×C3—24no—
213C23×C3—22no—
214C23×C3C2×D1214yes—
215C23×C3#23514yes—
216C23×C3#23514yes—
217C23×C3D3×D414yes—
218C23×C3D3×D414yes—
219C23×C3#23714yes—
220C23×C3D3×Q814yes—
221C23×C3C23×D312yes—
222C22×D3—38no—
223C22×D3—64no—
224C22×D3—64no—
225C22×D3—64no—
226C22×D3—616no—
227C22×D3—616no—
228C22×D3—616no—
229C22×D3—616no—
230C22×D3—64no—
231C22×D3—64no—
232C22×D3—64no—
233C22×D3—64no—
234C22×D3—64no—
235C22×D3—64no—
236C22×D3—124no—
237C22×D3—124no—
238C22×D3—1216no—
239C22×D3—1216no—
240C22×D3—128no—
241C22×D3—128no—
242C22×D3—128no—
243C22×D3—128no—
244C22×D3—128no—
245C22×D3—128no—
246C2×C3×C4—24no—
247C2×C3×C4—24no—
248C2×C3×C4—24no—
249C2×C3×C4—24no—
250C2×C3×C4—38no—
251C2×C3×C4—44no—
252C2×C3×C4—48no—
253C2×C3×C4—48no—
254C2×C3×C4—616no—
255C2×C3×C4—64no—
256C2×C3×C4—64no—
257C2×C3×C4—64no—
258C2×C3×C4—64no—
259C2×C3×C4—64no—
260C2×C3×C4—128no—
261C2×Dic3—216no—
262C2×Dic3—24no—
263C2×Dic3—24no—
264C2×Dic3—24no—
265C2×Dic3—24no—
266C2×Dic3—24no—
267C2×Dic3—38no—
268C2×Dic3—48no—
269C2×Dic3—64no—
270C2×Dic3—616no—
271C2×Dic3—64no—
272C2×Dic3—64no—
273C2×Dic3—124no—
274C2×Dic3—128no—
275C2×Dic3C2×D1218yes—
276Dic6—664no—
277C2×C32#39318yescomplemented
278C2×C32C2×#12011yescharacteristic
279C2×C32C2×C22⋊Q811yescharacteristic
280C2×C32C2×C22⋊Q812yes—
281C2×C32C2×#12412yes—
282C2×C32C2×#12411yescharacteristic
283C3⋊D3—44no—
284C24—92no—
285C24—94no—
286C24—182no—
287C24—184no—
288C24—184no—
289C24—182no—
290C24C2×D3211yescharacteristic
291C2×Q8—1816no—
292C2×Q8—188no—
293C2×Q8—1832no—
294C22×C4—24no—
295C22×C4—22no—
296C22×C4—34no—
297C22×C4—38no—
298C22×C4—34no—
299C22×C4—64no—
300C22×C4—64no—
301C22×C4—64no—
302C22×C4—64no—
303C22×C4—64no—
304C22×C4—92no—
305C22×C4—94no—
306C22×C4—184no—
307C22×C4C2×D3212yes—
308C22⋊C4—188no—
309C22⋊C4—1816no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—21no—
315C22×C3—28no—
316C22×C3—24no—
317C22×C3—28no—
318C22×C3—24no—
319C22×C3—24no—
320C22×C3#87518yes—
321C22×C3#88218yes—
322C22×C3#88518yes—
323C22×C3#88518yes—
324C22×C3#89618yes—
325C22×C3#89618yes—
326C22×C3#89718yes—
327C22×C3C22×D1212yes—
328C22×C3C2×#23512yes—
329C22×C3C2×#23512yes—
330C22×C3C2×D3×D412yes—
331C22×C3C2×D3×D412yes—
332C22×C3C2×#23712yes—
333C22×C3C2×D3×Q812yes—
334C2×D3—68no—
335C2×D3—68no—
336C2×D3—68no—
337C2×D3—68no—
338C2×D3—128no—
339C2×D3—128no—
340C2×D3—124no—
341C2×D3—1232no—
342C2×D3—124no—
343C2×D3—1232no—
344C2×D3—124no—
345C2×D3—124no—
346C2×D3—124no—
347C2×D3—124no—
348C3×C4—44no—
349C3×C4—44no—
350C3×C4—68no—
351C3×C4—124no—
352Dic3—28no—
353Dic3—44no—
354Dic3—68no—
355Dic3—124no—
356C32C2×#39311yescharacteristic, complemented, Sylow
357C23—94no—
358C23—182no—
359C23—184no—
360C23—184no—
361C23—182no—
362C23—188no—
363C23—1816no—
364C23—368no—
365C23—364no—
366C23—364no—
367C23#379712yes—
368C23#379812yes—
369C23D3×D1214yes—
370C23#380414yes—
371C23#381112yes—
372C23C22×D3211yescharacteristic
373Q8—1832no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—38no—
377C2×C4—44no—
378C2×C4—64no—
379C2×C4—64no—
380C2×C4—616no—
381C2×C4—64no—
382C2×C4—64no—
383C2×C4—64no—
384C2×C4—94no—
385C2×C4—128no—
386C2×C4—184no—
387C2×C4—188no—
388C2×C3—22no—
389C2×C3—21no—
390C2×C3—22no—
391C2×C3—21no—
392C2×C3—28no—
393C2×C3—21no—
394C2×C3#4673116yescomplemented
395C2×C3C2×#87512yes—
396C2×C3C2×#88212yes—
397C2×C3C2×#88512yes—
398C2×C3C2×#88512yes—
399C2×C3C2×#89612yes—
400C2×C3C2×#89612yes—
401C2×C3C2×#89712yes—
402D3—128no—
403D3—128no—
404C22—184no—
405C22—188no—
406C22—364no—
407C22—362no—
408C22—3616no—
409C22—362no—
410C22#6385218yes—
411C22#6386514yes—
412C22#6389518yes—
413C22#6392314yes—
414C22#6395314yes—
415C22C2×#379711yescharacteristic
416C22C2×#379811yescharacteristic
417C22C2×D3×D1212yes—
418C22C2×#380412yes—
419C22C2×#381111yescharacteristic
420C4—42no—
421C4—68no—
422C4—124no—
423C4—184no—
424C3—21no—
425C3C2×#467312yescomplemented
426C2—364no—
427C2#1059120518yesdirect product factor
428C2C2×#6385212yes—
429C2C2×#6386511yescharacteristic
430C2C2×#6389512yes—
431C2C2×#6392311yescharacteristic
432C2C2×#6395311yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32C2×#393
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×#627C2semidirect
4. C2×C3×C3⋊#95C2semidirect
5. C2×#63579C2semidirect
6. #10591205C2direct (N × H)
15. C22×#627C22semidirect
20. C3×C3⋊#95C22semidirect
21. #63579C22semidirect
29. C2×C3⋊#95D3semidirect
36. C23×C3⋊D3Q8semidirect
82. C3⋊#95C2×D3semidirect
98. C22×C3⋊D3C2×Q8semidirect
277. C2×C32#393semidirect
356. C32C2×#393semidirect
394. C2×C3#4673semidirect
425. C3C2×#4673semidirect
427. C2#10591205direct (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×#37522
C22×#37222
C2×C3×C3⋊#952
C2×#635792
#105912052
C2×#46733