Finite Group Databasebeta

← C2×#10593436 #11863634

Subgroups — C2×#10593436 #11863634

Order 1152.

1430 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 1430 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×#3797C211yesmaximal, characteristic, complemented
2C22×#3775C212yesmaximal, complemented
3C2×#63912C211yesmaximal, characteristic
4C2×#63778C211yesmaximal, characteristic, complemented
5C2×#63740C212yesmaximal, complemented
6#10593436C218yesmaximal, direct product factor
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C3×Dic6—21no—
9C22×#627C2212yes—
10C22×#626—21no—
11C22×#625C2211yescharacteristic
12C22×#624—21no—
13C2×#3797—22no—
14C2×#3797—28no—
15C2×#3797C2214yescomplemented
16C22×#622C2212yes—
17C2×#3775—28no—
18C2×#3775C2218yescomplemented
19C2×C3×(C2×D3)⋊C4—21no—
20C2×#3724C2211yescharacteristic
21#63912—22no—
22#63912C2214yes—
23#63778C2214yescomplemented
24#63740C2218yescomplemented
25C22×D3×Q8—61no—
26C2×#884—61no—
27C23×C3⋊D3D411yescharacteristic
28C23×C3×D3—21no—
29C22×C32×C4D411yescharacteristic
30C22×C3⋊Dic3C2311yescharacteristic
31C2×C4×C3⋊D3—24no—
32C2×C4×C3⋊D3D412yes—
33C2×C4×C3⋊D3C2312yes—
34C22×C3×Dic3—22no—
35C22×C3×Dic3—21no—
36C2×C3×Dic6—28no—
37C2×C3×Dic6—24no—
38C2×#627—22no—
39C2×#627—24no—
40C2×#627D418yescomplemented
41C2×#627C2314yes—
42C2×#626—24no—
43C2×#626—44no—
44C2×#625—24no—
45C2×#625—21no—
46C2×#625C2312yes—
47C2×#624—28no—
48C2×#624—24no—
49#3797—216no—
50#3797—216no—
51C2×#622—24no—
52C2×#622C2314yes—
53#3775—216no—
54C3×(C2×D3)⋊C4—24no—
55#3724—21no—
56#3724C2312yes—
57C2×#448—91nomaximal, Sylow
58C22×C3×Q8—61no—
59C22×#67—61no—
60C22×#67—61no—
61C2×D3×Q8—64no—
62C2×D3×Q8—64no—
63C2×D3×Q8—616no—
64C22×D12—61no—
65C22×C4×D3—61no—
66C22×C4×D3—61no—
67C22×C4×D3—62no—
68C22×Dic6—21no—
69C22×Dic6—62no—
70C2×C3×C22⋊C4—61no—
71C2×(C2×D3)⋊C4—21no—
72C2×Dic3⋊C4—61no—
73#884—64no—
74#884—64no—
75C23×C32C2×D411yescharacteristic
76C22×C3⋊D3—22no—
77C22×C3⋊D3—22no—
78C22×C3⋊D3SD1614yescomplemented
79C22×C3⋊D3C2×D412yes—
80C22×C3×D3—22no—
81C22×C3×D3—42no—
82C22×C3×D3—42no—
83C22×C3×D3—42no—
84C2×C32×C4—22no—
85C2×C32×C4C2×D412yes—
86C2×C3⋊Dic3C2×D411yescharacteristic
87C2×C3⋊Dic3C2×D414yes—
88C2×C3⋊Dic3C2411yescharacteristic
89C4×C3⋊D3—24no—
90C4×C3⋊D3—24no—
91C2×C3×Dic3—28no—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—22no—
94C2×C3×Dic3—42no—
95C3×Dic6—216no—
96#627—28no—
97#627—24no—
98#627C2×D418yescomplemented
99#626—48no—
100#625—24no—
101#625—42no—
102#624—216no—
103#622—24no—
104C23×Q8—91no—
105C22×SD16—92no—
106C2×#121—91no—
107#448—98no—
108C2×#103—92no—
109C2×C22⋊C8—91no—
110C24×C3—61no—
111C23×D3—21no—
112C23×D3—61no—
113C23×D3—61no—
114C2×C3×Q8—68no—
115C2×C3×Q8—64no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—62no—
119C22×C3×C4—61no—
120C2×#67—62no—
121C2×#67—64no—
122C2×#67—62no—
123C2×#67—124no—
124C2×#67—124no—
125C22×Dic3—22no—
126C22×Dic3—21no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129D3×Q8—632no—
130D3×Q8—632no—
131C2×D12—64no—
132C2×D12—124no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×C4×D3—62no—
136C2×C4×D3—62no—
137C2×C4×D3—68no—
138C2×C4×D3—616no—
139C2×C4×D3—68no—
140C2×C4×D3—124no—
141C2×Dic6—28no—
142C2×Dic6—24no—
143C2×Dic6—68no—
144C2×Dic6—64no—
145C2×Dic6—64no—
146C2×Dic6—68no—
147C3×C22⋊C4—64no—
148(C2×D3)⋊C4—24no—
149Dic3⋊C4—62no—
150Dic3⋊C4—62no—
151C22×C32#12012yes—
152C22×C32C2×SD1612yes—
153C22×C32#13712yes—
154C22×C32C22×D411yescharacteristic
155C2×C3⋊D3—22no—
156C2×C3⋊D3—22no—
157C2×C3⋊D3—28no—
158C2×C3⋊D3C2×SD1614yescomplemented
159C2×C3×D3—42no—
160C2×C3×D3—42no—
161C2×C3×D3—42no—
162C2×C3×D3—84no—
163C32×C4—22no—
164C3⋊Dic3#12012yes—
165C3⋊Dic3C22×D412yes—
166C3×Dic3—28no—
167C3×Dic3—42no—
168C22×Q8—61no—
169C22×Q8—92no—
170C22×Q8—94no—
171C22×Q8—182no—
172C22×Q8—188no—
173C22×D4—91no—
174C22×D4—181no—
175C23×C4—91no—
176C23×C4—181no—
177C2×SD16—98no—
178C2×SD16—188no—
179C22×C8—92no—
180#121—94no—
181#121—182no—
182C2×C4⋊C4—91no—
183C2×C22⋊C4—61no—
184#103—98no—
185C22⋊C8—94no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—62no—
189C23×C3—122no—
190C23×C3—122no—
191C23×C3—122no—
192C22×D3—22no—
193C22×D3—42no—
194C22×D3—42no—
195C22×D3—42no—
196C22×D3—64no—
197C22×D3—62no—
198C22×D3—64no—
199C22×D3—62no—
200C22×D3—64no—
201C22×D3—64no—
202C22×D3—122no—
203C22×D3—122no—
204C3×Q8—616no—
205C2×C3×C4—24no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—42no—
209C2×C3×C4—64no—
210C2×C3×C4—68no—
211C2×C3×C4—62no—
212C2×C3×C4—122no—
213#67—124no—
214#67—128no—
215#67—124no—
216C2×Dic3—24no—
217C2×Dic3—28no—
218C2×Dic3—22no—
219C2×Dic3—42no—
220C2×Dic3—61no—
221C2×Dic3—61no—
222C2×Dic3—64no—
223C2×Dic3—64no—
224C2×Dic3—61no—
225C2×Dic3—61no—
226D12—128no—
227C4×D3—632no—
228C4×D3—68no—
229C4×D3—68no—
230C4×D3—124no—
231C4×D3—124no—
232Dic6—216no—
233Dic6—68no—
234Dic6—616no—
235Dic6—68no—
236C2×C32#44814yescomplemented
237C2×C32C2×#12011yescharacteristic
238C2×C32C22×SD1611yescharacteristic
239C2×C32C2×#13711yescharacteristic
240C3⋊D3—24no—
241C3×D3—82no—
242C24—61no—
243C24—91no—
244C2×Q8—68no—
245C2×Q8—64no—
246C2×Q8—94no—
247C2×Q8—98no—
248C2×Q8—182no—
249C2×Q8—184no—
250C2×Q8—1816no—
251C2×Q8—1816no—
252C2×D4—92no—
253C2×D4—184no—
254C2×D4—184no—
255C2×D4—181no—
256C2×D4—364no—
257C22×C4—62no—
258C22×C4—61no—
259C22×C4—91no—
260C22×C4—92no—
261C22×C4—92no—
262C22×C4—184no—
263C22×C4—184no—
264C22×C4—188no—
265C22×C4GO+(4,𝔽2)11yescharacteristic
266SD16—1816no—
267C2×C8—94no—
268C2×C8—184no—
269C4⋊C4—92no—
270C4⋊C4—181no—
271C22⋊C4—64no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—22no—
275C22×C3—22no—
276C22×C3—22no—
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3—122no—
281C22×C3—122no—
282C22×C3—122no—
283C22×C3—244no—
284C2×D3—42no—
285C2×D3—42no—
286C2×D3—42no—
287C2×D3—64no—
288C2×D3—64no—
289C2×D3—64no—
290C2×D3—64no—
291C2×D3—616no—
292C2×D3—84no—
293C2×D3—122no—
294C2×D3—122no—
295C2×D3—128no—
296C3×C4—24no—
297C3×C4—42no—
298C3×C4—68no—
299C3×C4—122no—
300Dic3—28no—
301Dic3—42no—
302Dic3—62no—
303Dic3—62no—
304Dic3—62no—
305Dic3—62no—
306C32C2×#44811yescharacteristic, complemented, Sylow
307C23—62no—
308C23—92no—
309C23—94no—
310C23—122no—
311C23—122no—
312C23—122no—
313C23—182no—
314C23—182no—
315C23C2×GO+(4,𝔽2)11yescharacteristic
316Q8—616no—
317Q8—98no—
318Q8—184no—
319Q8—188no—
320D4—184no—
321D4—362no—
322D4—368no—
323C2×C4—22no—
324C2×C4—64no—
325C2×C4—68no—
326C2×C4—62no—
327C2×C4—91no—
328C2×C4—91no—
329C2×C4—94no—
330C2×C4—122no—
331C2×C4—184no—
332C2×C4—184no—
333C2×C4—1816no—
334C2×C4C2×GO+(4,𝔽2)12yes—
335C8—184no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—24no—
341C2×C3—24no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—242no—
345D3—68no—
346D3—82no—
347D3—124no—
348C22—94no—
349C22—122no—
350C22—122no—
351C22—122no—
352C22—182no—
353C22—188no—
354C22—182no—
355C22—244no—
356C22#6422612yes—
357C22#6422712yes—
358C22#6424112yes—
359C22C22×GO+(4,𝔽2)11yescharacteristic
360C4—22no—
361C4—68no—
362C4—92no—
363C4—92no—
364C4—122no—
365C3—21no—
366C3—21no—
367C2—184no—
368C2—242no—
369C2#1059343614yesdirect product factor
370C2C2×#6422611yescharacteristic
371C2C2×#6422711yescharacteristic
372C2C2×#6424111yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC2×#63912C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#448
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
1. C22×#3797C2semidirect
2. C22×#3775C2semidirect
4. C2×#63778C2semidirect
5. C2×#63740C2semidirect
6. #10593436C2direct (N × H)
15. C2×#3797C22semidirect
18. C2×#3775C22semidirect
23. #63778C22semidirect
24. #63740C22semidirect
40. C2×#627D4semidirect
78. C22×C3⋊D3SD16semidirect
98. #627C2×D4semidirect
158. C2×C3⋊D3C2×SD16semidirect
236. C2×C32#448semidirect
306. C32C2×#448semidirect
369. C2#10593436direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C22×#37752
C2×#639122
C2×#637782
C2×#637402
#105934362
C2×#4489