Finite Group Databasebeta

← C2×#10591396 #11801732

Subgroups — C2×#10591396 #11801732

Order 1152.

2105 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#627C211yesmaximal, characteristic
2C22×C4×C3⋊Dic3C211yesmaximal, characteristic
3C22×#3724C211yesmaximal, characteristic
4C2×C3×C3⋊#95C212yesmaximal
5C2×#63579C212yesmaximal
6#10591396C218yesmaximal, direct product factor
7C2×#4646—32nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C22×#627—24no—
14C22×#627—24no—
15C22×#627C418yescomplemented
16C22×#627C2214yes—
17C2×C4×C3⋊Dic3—24no—
18C2×C4×C3⋊Dic3C2214yes—
19C2×#3724—24no—
20C2×#3724C2214yes—
21C3×C3⋊#95C2218yes—
22#63579C2218yes—
23C23×Dic6—32no—
24C22×Dic3⋊C4—32no—
25C22×C4×Dic3—32no—
26C22×C4×Dic3—61no—
27C2×C3×#95—32no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95—32no—
30C2×C3⋊#95D312yes—
31#4646—316no—
32C24×C32C2311yescharacteristic
33C22×C32×C4—22no—
34C22×C32×C4—22no—
35C22×C32×C4Q814yescomplemented
36C22×C32×C4C2312yes—
37C22×C3⋊Dic3—22no—
38C22×C3⋊Dic3—22no—
39C22×C3⋊Dic3C2×C414yes—
40C22×C3⋊Dic3D414yes—
41C22×C3⋊Dic3D414yes—
42C22×C3⋊Dic3Q814yescomplemented
43C22×C3⋊Dic3C2312yes—
44C22×C3⋊Dic3C2312yes—
45C22×C3×Dic3—24no—
46C22×C3×Dic3—24no—
47C22×C3×Dic3—24no—
48C22×C3×Dic3—24no—
49C22×C3×Dic3—24no—
50C22×C3×Dic3C2×C418yes—
51C22×C3×Dic3C2314yes—
52C22×C3×Dic3C2314yes—
53C2×#627—232no—
54C2×#627—28no—
55C2×#627—28no—
56C2×#627C2×C4116yescomplemented
57C4×C3⋊Dic3—28no—
58#3724—28no—
59C2×#391—91noSylow
60C23×C3×C4—21no—
61C23×C3×C4—32no—
62C23×C3×C4—32no—
63C23×C3×C4C2×D312yes—
64C23×Dic3—32no—
65C23×Dic3—32no—
66C23×Dic3—61no—
67C23×Dic3—61no—
68C23×Dic3C2×D312yes—
69C23×Dic3C2×D312yes—
70C22×Dic6—316no—
71C22×Dic6—38no—
72C22×Dic6—68no—
73C22×Dic6—68no—
74C2×Dic3⋊C4—38no—
75C2×Dic3⋊C4—68no—
76C2×C4×Dic3—38no—
77C2×C4×Dic3—64no—
78C2×C4×Dic3—68no—
79C2×C4×Dic3—68no—
80C3×#95—38no—
81C3⋊#95—38no—
82C3⋊#95—38no—
83C3⋊#95C2×D318yes—
84C23×C32C22×C412yes—
85C23×C32C2×D412yes—
86C23×C32C2×D412yes—
87C23×C32C2×Q812yes—
88C23×C32C2×Q812yes—
89C23×C32#4112yes—
90C23×C32#4112yes—
91C23×C32C2411yescharacteristic
92C2×C32×C4—28no—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4C2×Q814yescomplemented
96C2×C3⋊Dic3—28no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3C22⋊C4116yes—
100C2×C3⋊Dic3C22×C414yes—
101C2×C3⋊Dic3C2×D414yes—
102C2×C3⋊Dic3C2×D414yes—
103C2×C3⋊Dic3C2×Q814yescomplemented
104C2×C3×Dic3—216no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—48no—
111C2×C3×Dic3C22×C418yes—
112#627—232no—
113C23×Q8—91no—
114C22×C4⋊C4—91no—
115C22×C42—91no—
116#391—98no—
117C2×#95—32no—
118C2×#95—92no—
119C24×C3—21no—
120C24×C3C22×D312yes—
121C22×C3×C4—24no—
122C22×C3×C4—24no—
123C22×C3×C4—24no—
124C22×C3×C4—24no—
125C22×C3×C4—24no—
126C22×C3×C4—22no—
127C22×C3×C4—38no—
128C22×C3×C4—34no—
129C22×C3×C4—34no—
130C22×C3×C4—64no—
131C22×C3×C4—64no—
132C22×C3×C4—64no—
133C22×C3×C4—64no—
134C22×C3×C4—64no—
135C22×C3×C4Dic618yescomplemented
136C22×C3×C4C22×D314yes—
137C22×Dic3—24no—
138C22×Dic3—24no—
139C22×Dic3—24no—
140C22×Dic3—24no—
141C22×Dic3—24no—
142C22×Dic3—38no—
143C22×Dic3—38no—
144C22×Dic3—38no—
145C22×Dic3—34no—
146C22×Dic3—38no—
147C22×Dic3—34no—
148C22×Dic3—64no—
149C22×Dic3—62no—
150C22×Dic3—62no—
151C22×Dic3—64no—
152C22×Dic3—64no—
153C22×Dic3—64no—
154C22×Dic3—64no—
155C22×Dic3—64no—
156C22×Dic3—64no—
157C22×Dic3—64no—
158C22×Dic3C4×D318yes—
159C22×Dic3C22×D314yes—
160C22×Dic3C22×D314yes—
161C2×Dic6—332no—
162C2×Dic6—664no—
163C2×Dic6—616no—
164C2×Dic6—616no—
165Dic3⋊C4—616no—
166C4×Dic3—616no—
167C4×Dic3—616no—
168C22×C32C2×C22⋊C414yes—
169C22×C32C4×Q814yes—
170C22×C32C4×Q814yes—
171C22×C32C22⋊Q814yes—
172C22×C32C22⋊Q814yes—
173C22×C32#12414yes—
174C22×C32C4⋊Q814yes—
175C22×C32C23×C411yescharacteristic
176C22×C32C22×D411yescharacteristic
177C22×C32C22×D411yescharacteristic
178C22×C32C22×Q811yescharacteristic
179C22×C32C22×Q811yescharacteristic
180C22×C32C2×#4111yescharacteristic
181C22×C32C2×#4111yescharacteristic
182C32×C4—24no—
183C3⋊Dic3—24no—
184C3⋊Dic3C2×C22⋊C418yes—
185C3×Dic3—28no—
186C3×Dic3—44no—
187C22×Q8—94no—
188C22×Q8—98no—
189C22×Q8—184no—
190C22×Q8—184no—
191C23×C4—32no—
192C23×C4—32no—
193C23×C4—91no—
194C23×C4—91no—
195C23×C4D3211yescharacteristic
196C2×C4⋊C4—94no—
197C2×C4⋊C4—184no—
198C2×C42—94no—
199C2×C42—184no—
200#95—38no—
201#95—98no—
202C23×C3—21no—
203C23×C3—22no—
204C23×C3—22no—
205C23×C3—22no—
206C23×C3—22no—
207C23×C3—22no—
208C23×C3—22no—
209C23×C3—22no—
210C23×C3C2×Dic614yes—
211C23×C3C2×C4×D314yes—
212C23×C3#23514yes—
213C23×C3D3×D414yes—
214C23×C3D3×D414yes—
215C23×C3#23714yes—
216C23×C3D3×Q814yes—
217C23×C3C23×D312yes—
218C2×C3×C4—24no—
219C2×C3×C4—24no—
220C2×C3×C4—216no—
221C2×C3×C4—216no—
222C2×C3×C4—24no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—38no—
226C2×C3×C4—616no—
227C2×C3×C4—64no—
228C2×C3×C4—64no—
229C2×C3×C4—64no—
230C2×C3×C4—64no—
231C2×C3×C4—64no—
232C2×C3×C4—128no—
233C2×C3×C4C2×Dic618yescomplemented
234C2×Dic3—216no—
235C2×Dic3—24no—
236C2×Dic3—24no—
237C2×Dic3—24no—
238C2×Dic3—24no—
239C2×Dic3—24no—
240C2×Dic3—332no—
241C2×Dic3—38no—
242C2×Dic3—38no—
243C2×Dic3—38no—
244C2×Dic3—38no—
245C2×Dic3—48no—
246C2×Dic3—616no—
247C2×Dic3—64no—
248C2×Dic3—64no—
249C2×Dic3—64no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—64no—
253C2×Dic3—616no—
254C2×Dic3—616no—
255C2×Dic3—64no—
256C2×Dic3—64no—
257C2×Dic3C2×C4×D318yes—
258Dic6—664no—
259C2×C32#39118yescomplemented
260C2×C32C22×C22⋊C411yescharacteristic
261C2×C32C2×C4×Q811yescharacteristic
262C2×C32C2×C4×Q811yescharacteristic
263C2×C32C2×C22⋊Q811yescharacteristic
264C2×C32C2×C22⋊Q811yescharacteristic
265C2×C32C2×#12411yescharacteristic
266C2×C32C2×C4⋊Q811yescharacteristic
267C24C2×D3211yescharacteristic
268C2×Q8—916no—
269C2×Q8—188no—
270C2×Q8—188no—
271C2×Q8—1832no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—34no—
275C22×C4—38no—
276C22×C4—34no—
277C22×C4—64no—
278C22×C4—64no—
279C22×C4—64no—
280C22×C4—64no—
281C22×C4—64no—
282C22×C4—92no—
283C22×C4—94no—
284C22×C4—94no—
285C22×C4—94no—
286C22×C4—92no—
287C22×C4—94no—
288C22×C4—182no—
289C22×C4—182no—
290C22×C4#62714yescomplemented
291C22×C4C2×D3212yes—
292C4⋊C4—188no—
293C42—188no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—24no—
302C22×C3—24no—
303C22×C3—24no—
304C22×C3—24no—
305C22×C3—24no—
306C22×C3—24no—
307C22×C3—24no—
308C22×C3C4×Dic618yes—
309C22×C3#87818yes—
310C22×C3D3×C22⋊C418yes—
311C22×C3#88518yes—
312C22×C3#88718yes—
313C22×C3#88818yes—
314C22×C3#89618yes—
315C22×C3C22×Dic612yes—
316C22×C3C22×C4×D312yes—
317C22×C3C2×#23512yes—
318C22×C3C2×D3×D412yes—
319C22×C3C2×D3×D412yes—
320C22×C3C2×#23712yes—
321C22×C3C2×D3×Q812yes—
322C3×C4—28no—
323C3×C4—28no—
324C3×C4—68no—
325C3×C4—124no—
326Dic3—28no—
327Dic3—316no—
328Dic3—44no—
329Dic3—68no—
330Dic3—68no—
331Dic3—68no—
332C32C2×#39111yescharacteristic, complemented, Sylow
333C23#379712yes—
334C23#379812yes—
335C23C4×D3212yes—
336C23#380212yes—
337C23#380512yes—
338C23C2×#62712yes—
339C23#381112yes—
340C23C22×D3211yescharacteristic
341Q8—1832no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—28no—
345C2×C4—38no—
346C2×C4—64no—
347C2×C4—64no—
348C2×C4—616no—
349C2×C4—64no—
350C2×C4—64no—
351C2×C4—64no—
352C2×C4—94no—
353C2×C4—94no—
354C2×C4—94no—
355C2×C4—916no—
356C2×C4—94no—
357C2×C4—128no—
358C2×C4—182no—
359C2×C4—182no—
360C2×C4—188no—
361C2×C4C2×#62714yescomplemented
362C2×C3—21no—
363C2×C3—28no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3#4646116yescomplemented
371C2×C3C2×C4×Dic612yes—
372C2×C3C2×#87812yes—
373C2×C3C2×D3×C22⋊C412yes—
374C2×C3C2×#88512yes—
375C2×C3C2×#88712yes—
376C2×C3C2×#88812yes—
377C2×C3C2×#89612yes—
378C22#6383814yes—
379C22#6386514yes—
380C22#6391514yes—
381C22C4×#62714yes—
382C22#6391914yes—
383C22#6392114yes—
384C22#6398214yes—
385C22C2×#379711yescharacteristic
386C22C2×#379811yescharacteristic
387C22C2×C4×D3211yescharacteristic
388C22C2×#380211yescharacteristic
389C22C2×#380511yescharacteristic
390C22C22×#62711yescharacteristic
391C22C2×#381111yescharacteristic
392C4—24no—
393C4—68no—
394C4—98no—
395C4—124no—
396C4—184no—
397C3—21no—
398C3C2×#464612yescomplemented
399C2#1059139618yesdirect product factor
400C2C2×#6383811yescharacteristic
401C2C2×#6386511yescharacteristic
402C2C2×#6391511yescharacteristic
403C2C2×C4×#62711yescharacteristic
404C2C2×#6391911yescharacteristic
405C2C2×#6392111yescharacteristic
406C2C2×#6398211yescharacteristic
subgroupG/H
centerC24C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
cosocleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#391
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591396C2direct (N × H)
15. C22×#627C4semidirect
35. C22×C32×C4Q8semidirect
42. C22×C3⋊Dic3Q8semidirect
56. C2×#627C2×C4semidirect
95. C2×C32×C4C2×Q8semidirect
103. C2×C3⋊Dic3C2×Q8semidirect
135. C22×C3×C4Dic6semidirect
233. C2×C3×C4C2×Dic6semidirect
259. C2×C32#391semidirect
290. C22×C4#627semidirect
332. C32C2×#391semidirect
361. C2×C4C2×#627semidirect
370. C2×C3#4646semidirect
398. C3C2×#4646semidirect
399. C2#10591396direct (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×C4×C3⋊Dic32
C22×#37242
C2×C3×C3⋊#952
C2×#635792
#105913962
C2×#46463