Finite Group Databasebeta

← C2×#10591652 #11863574

Subgroups — C2×#10591652 #11863574

Order 1152.

2153 conjugacy classes of subgroups; only the 252 normal subgroups are shown.

normal subgroups only

This group has 2153 conjugacy classes of subgroups — too many to draw. Only its 252 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3802C211yesmaximal, characteristic
2C2×#64155C211yesmaximal, characteristic, complemented
3C22×C3×#215C212yesmaximal, complemented
4#10591652C218yesmaximal, direct product factor
5C2×#63563C212yesmaximal, complemented
6C2×#63557C211yesmaximal, characteristic, complemented
7C2×#5169—32nomaximal
8C23×D32—21no—
9C22×C32×Q8C2211yescharacteristic, complemented
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×D12C2212yes—
12C22×#625—21no—
13C2×#3802—22no—
14C2×#3802—28no—
15C2×#3802C2214yes—
16#64155—22no—
17#64155C2214yescomplemented
18C2×#3752—21no—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
20C2×#3750—21no—
21C2×C3×#215—28no—
22C2×C3×#215C2218yescomplemented
23C22×C3×C3⋊C8C2212yescomplemented
24#63563C2218yescomplemented
25#63557C2214yescomplemented
26C22×D3×D4—32no—
27C22×C3×SD16—32no—
28C2×#946—32no—
29C2×#946—61no—
30C22×#215D312yescomplemented
31C2×#832—32no—
32#5169—316no—
33C2×#821—32no—
34C2×(C2×D3)⋊C8—32no—
35C23×C3⋊D3D411yescharacteristic
36C23×C3×D3—22no—
37C22×D32—28no—
38C22×D32—24no—
39C22×D32—44no—
40C22×D32—44no—
41C2×C32×Q8—21no—
42C2×C32×Q8—24no—
43C2×C32×Q8C2312yescomplemented
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3D411yescharacteristic
48C2×C4×C3⋊D3—24no—
49C2×C4×C3⋊D3D412yes—
50C2×C4×C3⋊D3C2312yes—
51C2×C3×D12—22no—
52C2×C3×D12—24no—
53C2×C3×D12D418yes—
54C2×C3×D12C2314yes—
55C2×#625—28no—
56C2×#625—24no—
57#3802—216no—
58#3802—216no—
59#3752—24no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)C2312yescomplemented
62#3750—24no—
63C3×#215—216no—
64C2×C3×C3⋊C8—24no—
65C2×C3×C3⋊C8C2314yescomplemented
66C2×#450—91noSylow
67C24×D3—62no—
68C22×C3×Q8—21no—
69C22×C3×Q8C2×D312yescomplemented
70C22×C3×D4—32no—
71C22×#67—62no—
72C2×D3×D4—38no—
73C2×D3×D4—64no—
74C2×D3×D4—68no—
75C2×D3×D4—68no—
76C22×D12C2×D312yes—
77C22×C4×D3—32no—
78C22×C4×D3—61no—
79C2×C3×SD16—38no—
80C2×C3×SD16—68no—
81C22×C3×C8—32no—
82#946—38no—
83#946—64no—
84#946—64no—
85#946—64no—
86C2×#215—28no—
87C2×#215C2×D318yescomplemented
88C2×(C2×D3)⋊C4—62no—
89C2×(C2×D3)⋊C4—62no—
90C2×C4⋊Dic3—32no—
91C2×C4⋊Dic3—61no—
92C2×Dic3⋊C4—62no—
93C2×Dic3⋊C4—62no—
94C22×C3⋊C8C2×D312yescomplemented
95#832—38no—
96#821—38no—
97(C2×D3)⋊C8—38no—
98C23×C32C2×D411yescharacteristic
99C22×C3⋊D3—22no—
100C22×C3⋊D3—22no—
101C22×C3⋊D3SD1614yescomplemented
102C22×C3⋊D3C2×D412yes—
103C22×C3×D3—28no—
104C22×C3×D3—24no—
105C22×C3×D3—44no—
106C22×C3×D3—44no—
107C2×D32—216no—
108C2×D32—48no—
109C2×D32—432no—
110C2×D32—48no—
111C32×Q8—24no—
112C32×Q8—42no—
113C2×C32×C4—22no—
114C2×C32×C4—42no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D414yes—
117C2×C32×C4C2411yescharacteristic
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—42no—
121C2×C3⋊Dic3C2×D412yes—
122C4×C3⋊D3—24no—
123C4×C3⋊D3—24no—
124C3×D12—28no—
125C3×D12—24no—
126C3×D12C2×D418yes—
127#625—216no—
128C3×C3⋊C8—24no—
129C23×D4—91no—
130C22×SD16—32no—
131C2×C22⋊Q8—91no—
132#450—98no—
133C2×#102—92no—
134C2×C22⋊C8—91no—
135C24×C3—62no—
136C23×D3—22no—
137C23×D3—32no—
138C23×D3—61no—
139C23×D3—68no—
140C23×D3—616no—
141C23×D3—128no—
142C23×D3—128no—
143C2×C3×Q8—22no—
144C2×C3×Q8—22no—
145C2×C3×Q8—24no—
146C2×C3×Q8—24no—
147C2×C3×Q8—22no—
148C2×C3×Q8—44no—
149C2×C3×Q8C22×D314yescomplemented
150C2×C3×D4—38no—
151C2×C3×D4—34no—
152C2×C3×D4—62no—
153C2×C3×D4—64no—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—21no—
157C22×C3×C4C22×D312yes—
158C2×#67—68no—
159C2×#67—616no—
160C22×Dic3—32no—
161C22×Dic3—61no—
162C22×Dic3—62no—
163C22×Dic3—62no—
164D3×D4—616no—
165D3×D4—632no—
166D3×D4—616no—
167C2×D12—24no—
168C2×D12—22no—
169C2×D12#6718yes—
170C2×D12C22×D314yes—
171C2×C4×D3—34no—
172C2×C4×D3—34no—
173C2×C4×D3—62no—
174C2×C4×D3—62no—
175C2×C4×D3—64no—
176C2×C4×D3—64no—
177C2×C4×D3—124no—
178C3×SD16—616no—
179C2×C3×C8—34no—
180C2×C3×C8—64no—
181#215—216no—
182(C2×D3)⋊C4—68no—
183(C2×D3)⋊C4—68no—
184C4⋊Dic3—34no—
185C4⋊Dic3—62no—
186C4⋊Dic3—62no—
187C4⋊Dic3—62no—
188Dic3⋊C4—68no—
189Dic3⋊C4—68no—
190C2×C3⋊C8—24no—
191C2×C3⋊C8C22×D314yescomplemented
192C22×C32#12012yes—
193C22×C32C2×SD1612yes—
194C22×C32AGL(1,ℤ/8)12yes—
195C22×C32C22×D411yescharacteristic
196C2×C3⋊D3—22no—
197C2×C3⋊D3—22no—
198C2×C3⋊D3—28no—
199C2×C3⋊D3C2×SD1614yescomplemented
200C2×C3×D3—28no—
201C2×C3×D3—44no—
202C2×C3×D3—44no—
203C2×C3×D3—416no—
204D32—432no—
205C32×C4—42no—
206C32×C4#12012yes—
207C32×C4C22×D412yes—
208C3⋊Dic3—22no—
209C3⋊Dic3—42no—
210C25—181no—
211C22×Q8D3211yescharacteristic, complemented
212C22×D4—32no—
213C22×D4—94no—
214C22×D4—182no—
215C22×D4—181no—
216C22×D4—188no—
217C23×C4—91no—
218C2×SD16—38no—
219C2×SD16—68no—
220C22×C8—32no—
221C22⋊Q8—94no—
222C22⋊Q8—182no—
223C2×C4⋊C4—91no—
224C2×C4⋊C4—181no—
225C2×C22⋊C4—181no—
226#102—98no—
227C22⋊C8—94no—
228C23×C3—21no—
229C23×C3—68no—
230C23×C3—64no—
231C23×C3—124no—
232C23×C3—124no—
233C23×C3D3×D412yes—
234C22×D3—28no—
235C22×D3—24no—
236C22×D3—38no—
237C22×D3—34no—
238C22×D3—44no—
239C22×D3—44no—
240C22×D3—64no—
241C22×D3—62no—
242C22×D3—632no—
243C22×D3—64no—
244C22×D3—64no—
245C22×D3—122no—
246C22×D3—122no—
247C22×D3—1216no—
248C22×D3—1264no—
249C22×D3—1216no—
250C3×Q8—24no—
251C3×Q8—24no—
252C3×Q8—44no—
253C3×Q8—44no—
254C3×Q8—44no—
255C3×D4—38no—
256C3×D4—68no—
257C3×D4—64no—
258C2×C3×C4—24no—
259C2×C3×C4—24no—
260C2×C3×C4—21no—
261C2×C3×C4—24no—
262C2×C3×C4—21no—
263C2×C3×C4—44no—
264C2×C3×C4—44no—
265C2×C3×C4D3×D414yes—
266C2×C3×C4D3×D412yes—
267C2×C3×C4C2×#6714yes—
268C2×C3×C4C23×D312yes—
269#67—632no—
270C2×Dic3—34no—
271C2×Dic3—62no—
272C2×Dic3—64no—
273C2×Dic3—64no—
274C2×Dic3—64no—
275C2×Dic3—122no—
276C2×Dic3—124no—
277C2×Dic3—124no—
278D12—28no—
279D12—24no—
280D12C2×#6718yes—
281C4×D3—68no—
282C4×D3—64no—
283C4×D3—64no—
284C4×D3—124no—
285C4×D3—124no—
286C3×C8—64no—
287C3⋊C8—24no—
288C2×C32#45014yescomplemented
289C2×C32C2×#12011yescharacteristic
290C2×C32C22×SD1611yescharacteristic
291C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
292C3⋊D3—24no—
293C3×D3—48no—
294C24—62no—
295C24—91no—
296C24—184no—
297C24—188no—
298C24—364no—
299C24—364no—
300C2×Q8—21no—
301C2×Q8—24no—
302C2×Q8C2×D3212yescomplemented
303C2×D4—34no—
304C2×D4—38no—
305C2×D4—64no—
306C2×D4—62no—
307C2×D4—184no—
308C2×D4—1816no—
309C2×D4—1816no—
310C2×D4—188no—
311C22×C4—21no—
312C22×C4—91no—
313C22×C4—92no—
314C22×C4—92no—
315C22×C4—184no—
316C22×C4—181no—
317C22×C4C2×D3211yescharacteristic
318SD16—616no—
319C2×C8—34no—
320C2×C8—64no—
321C4⋊C4—92no—
322C4⋊C4—184no—
323C4⋊C4—181no—
324C22⋊C4—184no—
325C22×C3—21no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—68no—
330C22×C3—1216no—
331C22×C3—124no—
332C22×C3—124no—
333C22×C3D3×SD1614yes—
334C22×C3#91414yes—
335C22×C3#93714yes—
336C22×C3C2×D3×D412yes—
337C2×D3—28no—
338C2×D3—38no—
339C2×D3—416no—
340C2×D3—44no—
341C2×D3—44no—
342C2×D3—64no—
343C2×D3—616no—
344C2×D3—64no—
345C2×D3—64no—
346C2×D3—122no—
347C2×D3—128no—
348C2×D3—122no—
349C2×D3—1264no—
350C3×C4—22no—
351C3×C4—22no—
352C3×C4—44no—
353C3×C4—44no—
354C3×C4#93714yes—
355C3×C4C2×D3×D412yes—
356C3×C4C22×#6712yes—
357Dic3—64no—
358Dic3—122no—
359Dic3—124no—
360Dic3—124no—
361C32C2×#45011yescharacteristic, complemented, Sylow
362C23—64no—
363C23—68no—
364C23—92no—
365C23—94no—
366C23—124no—
367C23—124no—
368C23—1816no—
369C23—182no—
370C23—182no—
371C23—368no—
372C23—3632no—
373C23—368no—
374C23#381111yescharacteristic
375Q8—24no—
376Q8—42no—
377D4—38no—
378D4—64no—
379D4—68no—
380D4—1816no—
381C2×C4—22no—
382C2×C4—42no—
383C2×C4—92no—
384C2×C4—182no—
385C2×C4—184no—
386C2×C4—184no—
387C2×C4—182no—
388C2×C4—362no—
389C2×C4D3×#6714yes—
390C2×C4#381111yescharacteristic
391C2×C4C22×D3211yescharacteristic
392C8—64no—
393C2×C3—24no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—128no—
398C2×C3#516918yescomplemented
399C2×C3C2×D3×SD1612yes—
400C2×C3C2×#91412yes—
401C2×C3C2×#93712yes—
402D3—48no—
403D3—68no—
404D3—124no—
405C22—68no—
406C22—94no—
407C22—1216no—
408C22—124no—
409C22—124no—
410C22—188no—
411C22—182no—
412C22—182no—
413C22—3632no—
414C22#6394012yes—
415C22#6394112yes—
416C22#6398312yes—
417C22C2×#381111yescharacteristic
418C4—42no—
419C4—182no—
420C4—362no—
421C4#6398312yes—
422C4C2×D3×#6712yes—
423C3—21no—
424C3C2×#516912yescomplemented
425C2—128no—
426C2—184no—
427C2#1059165214yesdirect product factor
428C2C2×#6394011yescharacteristic
429C2C2×#6394111yescharacteristic
430C2C2×#6398311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×#3802C2
hypercenterC22×Q8D32
hypocenterC32C2×#450
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#64155C2semidirect
3. C22×C3×#215C2semidirect
4. #10591652C2direct (N × H)
5. C2×#63563C2semidirect
6. C2×#63557C2semidirect
9. C22×C32×Q8C22semidirect
17. #64155C22semidirect
19. C2×C4⋊(C3⋊Dic3)C22semidirect
22. C2×C3×#215C22semidirect
23. C22×C3×C3⋊C8C22semidirect
24. #63563C22semidirect
25. #63557C22semidirect
30. C22×#215D3semidirect
43. C2×C32×Q8C23semidirect
61. C4⋊(C3⋊Dic3)C23semidirect
65. C2×C3×C3⋊C8C23semidirect
69. C22×C3×Q8C2×D3semidirect
87. C2×#215C2×D3semidirect
94. C22×C3⋊C8C2×D3semidirect
101. C22×C3⋊D3SD16semidirect
149. C2×C3×Q8C22×D3semidirect
191. C2×C3⋊C8C22×D3semidirect
199. C2×C3⋊D3C2×SD16semidirect
211. C22×Q8D32semidirect
288. C2×C32#450semidirect
302. C2×Q8C2×D32semidirect
361. C32C2×#450semidirect
398. C2×C3#5169semidirect
424. C3C2×#5169semidirect
427. C2#10591652direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38022
C2×#641552
C22×C3×#2152
#105916522
C2×#635632
C2×#635572
C2×#51693