Finite Group Databasebeta

← C2×#10593354 #11863588

Subgroups — C2×#10593354 #11863588

Order 1152.

1838 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 1838 conjugacy classes of subgroups — too many to draw. Only its 143 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
2C22×#3775C212yesmaximal, complemented
3C2×#63865C211yesmaximal, characteristic, complemented
4C2×#63778C211yesmaximal, characteristic, complemented
5C2×#63739C212yesmaximal, complemented
6#10593354C218yesmaximal, direct product factor
7C23×D32—21no—
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×C3×D12—21no—
10C22×#627C2211yescharacteristic, complemented
11C22×#625C2212yes—
12C2×#3802—22no—
13C2×#3802—28no—
14C2×#3802C2214yes—
15C22×#622C2212yescomplemented
16C2×#3775—28no—
17C2×#3775C2218yescomplemented
18C2×C3×Dic3⋊C4—21no—
19C2×#3724C2211yescharacteristic, complemented
20C2×#3722—21no—
21#63865—22no—
22#63865C2214yescomplemented
23#63778C2214yescomplemented
24#63739C2218yescomplemented
25C22×D3×D4—61no—
26C2×#896—61no—
27C23×C3⋊D3D411yescharacteristic
28C23×C3×D3—22no—
29C22×D32—28no—
30C22×D32—24no—
31C22×D32—44no—
32C22×D32—44no—
33C22×C32×C4D411yescharacteristic
34C22×C3⋊Dic3C2311yescharacteristic
35C2×C4×C3⋊D3—24no—
36C2×C4×C3⋊D3D412yes—
37C2×C4×C3⋊D3C2312yes—
38C22×C3×Dic3—21no—
39C22×C3×Dic3—21no—
40C2×C3×D12—28no—
41C2×C3×D12—24no—
42C2×#627—24no—
43C2×#627—21no—
44C2×#627C2312yescomplemented
45C2×#625—22no—
46C2×#625—24no—
47C2×#625D418yes—
48C2×#625C2314yes—
49#3802—216no—
50#3802—216no—
51C2×#622—24no—
52C2×#622C2314yescomplemented
53#3775—216no—
54C3×Dic3⋊C4—24no—
55#3724—21no—
56#3724C2312yescomplemented
57#3722—24no—
58C2×#450—91nomaximal, Sylow
59C24×D3—62no—
60C22×C3×D4—61no—
61C22×#67—62no—
62C2×D3×D4—64no—
63C2×D3×D4—64no—
64C2×D3×D4—616no—
65C22×D12—21no—
66C22×C4×D3—61no—
67C22×C4×D3—61no—
68C22×Dic6—61no—
69C2×C3×C4⋊C4—61no—
70C2×(C2×D3)⋊C4—61no—
71C2×(C2×D3)⋊C4—61no—
72C2×Dic3⋊C4—21no—
73C2×Dic3⋊C4—61no—
74#896—64no—
75#896—64no—
76C23×C32C2×D411yescharacteristic
77C22×C3⋊D3—22no—
78C22×C3⋊D3—22no—
79C22×C3⋊D3SD1614yescomplemented
80C22×C3⋊D3C2×D412yes—
81C22×C3×D3—28no—
82C22×C3×D3—24no—
83C22×C3×D3—44no—
84C22×C3×D3—44no—
85C2×D32—216no—
86C2×D32—48no—
87C2×D32—432no—
88C2×D32—48no—
89C2×C32×C4—22no—
90C2×C32×C4C2×D412yes—
91C2×C3⋊Dic3C2×D411yescharacteristic
92C2×C3⋊Dic3C2×D414yes—
93C2×C3⋊Dic3C2411yescharacteristic
94C4×C3⋊D3—24no—
95C4×C3⋊D3—24no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—42no—
99C2×C3×Dic3—42no—
100C3×D12—216no—
101#627—24no—
102#627—42no—
103#625—28no—
104#625—24no—
105#625C2×D418yes—
106#622—24no—
107C23×D4—91no—
108C22×SD16—92no—
109C2×C22⋊Q8—91no—
110#450—98no—
111C2×#102—92no—
112C2×C22⋊C8—91no—
113C24×C3—62no—
114C23×D3—22no—
115C23×D3—61no—
116C23×D3—61no—
117C23×D3—68no—
118C23×D3—616no—
119C23×D3—128no—
120C23×D3—128no—
121C2×C3×D4—68no—
122C2×C3×D4—64no—
123C22×C3×C4—21no—
124C22×C3×C4—21no—
125C22×C3×C4—61no—
126C22×C3×C4—61no—
127C2×#67—68no—
128C2×#67—64no—
129C2×#67—64no—
130C2×#67—68no—
131C22×Dic3—21no—
132C22×Dic3—21no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135D3×D4—632no—
136D3×D4—632no—
137C2×D12—28no—
138C2×D12—24no—
139C2×C4×D3—62no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×C4×D3—68no—
144C2×C4×D3—124no—
145C2×Dic6—62no—
146C2×Dic6—62no—
147C2×Dic6—124no—
148C3×C4⋊C4—64no—
149(C2×D3)⋊C4—64no—
150(C2×D3)⋊C4—64no—
151Dic3⋊C4—24no—
152Dic3⋊C4—62no—
153Dic3⋊C4—62no—
154C22×C32#12012yes—
155C22×C32C2×SD1612yes—
156C22×C32AGL(1,ℤ/8)12yes—
157C22×C32C22×D411yescharacteristic
158C2×C3⋊D3—22no—
159C2×C3⋊D3—22no—
160C2×C3⋊D3—28no—
161C2×C3⋊D3C2×SD1614yescomplemented
162C2×C3×D3—28no—
163C2×C3×D3—44no—
164C2×C3×D3—44no—
165C2×C3×D3—416no—
166D32—432no—
167C32×C4—22no—
168C3⋊Dic3#12012yes—
169C3⋊Dic3C22×D412yes—
170C3×Dic3—42no—
171C3×Dic3—42no—
172C25—181no—
173C22×Q8—91no—
174C22×D4—61no—
175C22×D4—94no—
176C22×D4—92no—
177C22×D4—182no—
178C22×D4—188no—
179C23×C4—91no—
180C2×SD16—98no—
181C2×SD16—188no—
182C22×C8—92no—
183C22⋊Q8—94no—
184C22⋊Q8—182no—
185C2×C4⋊C4—61no—
186C2×C4⋊C4—91no—
187C2×C22⋊C4—181no—
188#102—98no—
189C22⋊C8—94no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—64no—
193C23×C3—68no—
194C23×C3—124no—
195C23×C3—124no—
196C22×D3—24no—
197C22×D3—28no—
198C22×D3—44no—
199C22×D3—44no—
200C22×D3—64no—
201C22×D3—62no—
202C22×D3—64no—
203C22×D3—62no—
204C22×D3—632no—
205C22×D3—64no—
206C22×D3—64no—
207C22×D3—122no—
208C22×D3—122no—
209C22×D3—1216no—
210C22×D3—1264no—
211C22×D3—1216no—
212C3×D4—616no—
213C2×C3×C4—24no—
214C2×C3×C4—22no—
215C2×C3×C4—22no—
216C2×C3×C4—42no—
217C2×C3×C4—62no—
218C2×C3×C4—62no—
219C2×C3×C4—122no—
220C2×C3×C4—122no—
221#67—68no—
222#67—616no—
223#67—68no—
224C2×Dic3—22no—
225C2×Dic3—22no—
226C2×Dic3—42no—
227C2×Dic3—42no—
228C2×Dic3—61no—
229C2×Dic3—64no—
230C2×Dic3—61no—
231C2×Dic3—64no—
232C2×Dic3—61no—
233C2×Dic3—61no—
234D12—216no—
235C4×D3—68no—
236C4×D3—68no—
237C4×D3—124no—
238C4×D3—124no—
239Dic6—124no—
240Dic6—124no—
241C2×C32#45014yescomplemented
242C2×C32C2×#12011yescharacteristic
243C2×C32C22×SD1611yescharacteristic
244C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
245C3⋊D3—24no—
246C3×D3—48no—
247C24—62no—
248C24—91no—
249C24—184no—
250C24—188no—
251C24—364no—
252C24—364no—
253C2×Q8—92no—
254C2×Q8—181no—
255C2×Q8—184no—
256C2×D4—68no—
257C2×D4—64no—
258C2×D4—94no—
259C2×D4—98no—
260C2×D4—182no—
261C2×D4—184no—
262C2×D4—1816no—
263C2×D4—1816no—
264C22×C4—61no—
265C22×C4—61no—
266C22×C4—91no—
267C22×C4—92no—
268C22×C4—92no—
269C22×C4—184no—
270C22×C4GO+(4,𝔽2)11yescharacteristic
271SD16—1816no—
272C2×C8—94no—
273C2×C8—184no—
274C4⋊C4—64no—
275C4⋊C4—92no—
276C4⋊C4—181no—
277C22⋊C4—184no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—22no—
281C22×C3—22no—
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—22no—
285C22×C3—22no—
286C22×C3—68no—
287C22×C3—1216no—
288C22×C3—124no—
289C22×C3—124no—
290C2×D3—28no—
291C2×D3—416no—
292C2×D3—44no—
293C2×D3—44no—
294C2×D3—64no—
295C2×D3—64no—
296C2×D3—64no—
297C2×D3—616no—
298C2×D3—64no—
299C2×D3—122no—
300C2×D3—128no—
301C2×D3—122no—
302C2×D3—1264no—
303C3×C4—24no—
304C3×C4—42no—
305C3×C4—122no—
306C3×C4—122no—
307Dic3—42no—
308Dic3—42no—
309Dic3—62no—
310Dic3—62no—
311Dic3—62no—
312Dic3—62no—
313C32C2×#45011yescharacteristic, complemented, Sylow
314C23—64no—
315C23—68no—
316C23—92no—
317C23—94no—
318C23—124no—
319C23—124no—
320C23—1816no—
321C23—182no—
322C23—182no—
323C23—368no—
324C23—3632no—
325C23—368no—
326C23C2×GO+(4,𝔽2)11yescharacteristic
327Q8—184no—
328Q8—362no—
329D4—616no—
330D4—98no—
331D4—184no—
332D4—188no—
333C2×C4—22no—
334C2×C4—62no—
335C2×C4—62no—
336C2×C4—91no—
337C2×C4—91no—
338C2×C4—94no—
339C2×C4—122no—
340C2×C4—122no—
341C2×C4—184no—
342C2×C4—184no—
343C2×C4C2×GO+(4,𝔽2)12yes—
344C8—184no—
345C2×C3—24no—
346C2×C3—24no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—128no—
354D3—48no—
355D3—68no—
356D3—124no—
357C22—68no—
358C22—94no—
359C22—1216no—
360C22—124no—
361C22—124no—
362C22—188no—
363C22—182no—
364C22—182no—
365C22—3632no—
366C22#6422412yes—
367C22#6422712yes—
368C22#6424112yes—
369C22C22×GO+(4,𝔽2)11yescharacteristic
370C4—22no—
371C4—92no—
372C4—92no—
373C4—122no—
374C4—122no—
375C3—21no—
376C3—21no—
377C2—128no—
378C2—184no—
379C2#1059335414yesdirect product factor
380C2C2×#6422411yescharacteristic
381C2C2×#6422711yescharacteristic
382C2C2×#6424111yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#3802C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#450
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3775C2semidirect
3. C2×#63865C2semidirect
4. C2×#63778C2semidirect
5. C2×#63739C2semidirect
6. #10593354C2direct (N × H)
10. C22×#627C22semidirect
15. C22×#622C22semidirect
17. C2×#3775C22semidirect
19. C2×#3724C22semidirect
22. #63865C22semidirect
23. #63778C22semidirect
24. #63739C22semidirect
44. C2×#627C23semidirect
52. C2×#622C23semidirect
56. #3724C23semidirect
79. C22×C3⋊D3SD16semidirect
161. C2×C3⋊D3C2×SD16semidirect
241. C2×C32#450semidirect
313. C32C2×#450semidirect
379. C2#10593354direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38022
C22×#37752
C2×#638652
C2×#637782
C2×#637392
#105933542
C2×#4509