Finite Group Databasebeta

← C2×#10593426 #11865459

Subgroups — C2×#10593426 #11865459

Order 1152.

1110 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 135 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×#3774C212yesmaximal, complemented
2C2×#63914C211yesmaximal, characteristic, complemented
3C2×#63902C211yesmaximal, characteristic, complemented
4C2×#63779C211yesmaximal, characteristic, complemented
5C2×#63739C212yesmaximal, complemented
6#10593426C218yesmaximal, direct product factor
7C22×C3×D12—21no—
8C22×#625—21no—
9C22×#625C2212yes—
10C22×#625C2211yescharacteristic
11C22×D3×Dic3—21no—
12C22×#622C2212yes—
13C2×#3774—28no—
14C2×#3774C2218yescomplemented
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×#3724C2211yescharacteristic
18#63914—22no—
19#63914C2214yescomplemented
20#63902—22no—
21#63902C2214yescomplemented
22#63779C2214yescomplemented
23#63739C2218yescomplemented
24C2×#940—61no—
25C2×#67⋊C4—61no—
26C23×C3×D3—21no—
27C23×C3×D3—22no—
28C22×C32×C4D411yescharacteristic
29C22×C3⋊Dic3D411yescharacteristic
30C22×C3⋊Dic3C2311yescharacteristic
31C22×C3×Dic3—21no—
32C2×C3×D12—24no—
33C2×C3×D12—44no—
34C2×#625—21no—
35C2×#625—22no—
36C2×#625—24no—
37C2×#625—24no—
38C2×#625—24no—
39C2×#625—22no—
40C2×#625—44no—
41C2×#625D414yescomplemented
42C2×#625C2314yes—
43C2×#625C2312yes—
44C2×D3×Dic3—24no—
45C2×D3×Dic3—44no—
46C2×#622—24no—
47C2×#622C2314yes—
48#3774—216no—
49C4×C3⋊Dic3D412yes—
50C4×C3⋊Dic3C2312yes—
51C3×(C2×D3)⋊C4—24no—
52#3724—21no—
53#3724C2312yes—
54C2×#459—91nomaximal, Sylow
55C22×C3×D4—61no—
56C22×#67—61no—
57C22×#67—62no—
58C22×#67—62no—
59C23×Dic3—61no—
60C22×D12—21no—
61C22×C4×D3—61no—
62C2×C3×C22⋊C4—61no—
63#940—64no—
64#940—64no—
65C2×(C2×D3)⋊C4—21no—
66C2×Dic3⋊C4—61no—
67C2×C4×Dic3—61no—
68C2×C4×Dic3—61no—
69#67⋊C4—64no—
70#67⋊C4—64no—
71C23×C32C2×D411yescharacteristic
72C22×C3×D3—24no—
73C22×C3×D3—22no—
74C22×C3×D3—24no—
75C22×C3×D3—42no—
76C22×C3×D3—42no—
77C22×C3×D3—44no—
78C22×C3×D3—44no—
79C22×C3×D3—44no—
80C2×C32×C4—22no—
81C2×C32×C4C2×D412yes—
82C2×C3⋊Dic3D814yescomplemented
83C2×C3⋊Dic3C2×D411yescharacteristic
84C2×C3⋊Dic3C2×D412yes—
85C2×C3⋊Dic3C2×D412yes—
86C2×C3⋊Dic3#4112yes—
87C2×C3⋊Dic3C2411yescharacteristic
88C2×C3×Dic3—22no—
89C2×C3×Dic3—42no—
90C3×D12—48no—
91#625—24no—
92#625—22no—
93#625—24no—
94#625—24no—
95#625—44no—
96#625—48no—
97#625C2×D414yescomplemented
98D3×Dic3—48no—
99#622—24no—
100C22×D8—92no—
101C2×#127—91no—
102C2×C4×D4—91no—
103#459—98no—
104C2×C4⋊C8—91no—
105C2×#102—92no—
106C24×C3—61no—
107C24×C3—62no—
108C23×D3—21no—
109C23×D3—22no—
110C2×C3×D4—64no—
111C2×C3×D4—124no—
112C22×C3×C4—21no—
113C22×C3×C4—21no—
114C22×C3×C4—61no—
115C2×#67—62no—
116C2×#67—64no—
117C2×#67—64no—
118C2×#67—62no—
119C2×#67—64no—
120C2×#67—68no—
121C2×#67—64no—
122C2×#67—124no—
123C2×#67—124no—
124C2×#67—128no—
125C22×Dic3—21no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C22×Dic3—64no—
131C22×Dic3—124no—
132C2×D12—24no—
133C2×D12—44no—
134C2×C4×D3—64no—
135C2×C4×D3—124no—
136C3×C22⋊C4—64no—
137(C2×D3)⋊C4—24no—
138Dic3⋊C4—62no—
139Dic3⋊C4—62no—
140C4×Dic3—62no—
141C4×Dic3—62no—
142C4×Dic3—62no—
143C4×Dic3—62no—
144C22×C32#12112yes—
145C22×C32C2×D812yes—
146C22×C32AGL(1,ℤ/8)12yes—
147C22×C32C22×D411yescharacteristic
148C2×C3×D3—24no—
149C2×C3×D3—42no—
150C2×C3×D3—42no—
151C2×C3×D3—48no—
152C2×C3×D3—44no—
153C2×C3×D3—44no—
154C2×C3×D3—44no—
155C2×C3×D3—88no—
156C32×C4—22no—
157C3⋊Dic3#12112yes—
158C3⋊Dic3C2×D814yescomplemented
159C3⋊Dic3C22×D411yescharacteristic
160C3⋊Dic3C2×#4111yescharacteristic
161C3×Dic3—42no—
162C22×D4—61no—
163C22×D4—91no—
164C22×D4—92no—
165C22×D4—181no—
166C23×C4—181no—
167C2×D8—98no—
168C2×D8—188no—
169C22×C8—92no—
170#127—94no—
171#127—182no—
172C4×D4—94no—
173C4×D4—182no—
174C2×C4⋊C4—91no—
175C2×C22⋊C4—61no—
176C2×C42—91no—
177C4⋊C8—94no—
178#102—98no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—62no—
182C23×C3—64no—
183C23×C3—64no—
184C23×C3—122no—
185C23×C3—122no—
186C23×C3—124no—
187C23×C3—124no—
188C23×C3—124no—
189C22×D3—22no—
190C22×D3—24no—
191C22×D3—24no—
192C22×D3—42no—
193C22×D3—42no—
194C22×D3—44no—
195C22×D3—44no—
196C22×D3—44no—
197C3×D4—128no—
198C2×C3×C4—24no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—42no—
202C2×C3×C4—62no—
203C2×C3×C4—122no—
204#67—64no—
205#67—68no—
206#67—64no—
207#67—124no—
208#67—124no—
209#67—128no—
210#67—1216no—
211C2×Dic3—22no—
212C2×Dic3—42no—
213C2×Dic3—64no—
214C2×Dic3—64no—
215C2×Dic3—61no—
216C2×Dic3—62no—
217C2×Dic3—61no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—61no—
224C2×Dic3—61no—
225C2×Dic3—128no—
226D12—48no—
227C4×D3—128no—
228C2×C32#45914yescomplemented
229C2×C32C2×#12111yescharacteristic
230C2×C32C22×D811yescharacteristic
231C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
232C3×D3—44no—
233C3×D3—84no—
234C24—61no—
235C24—62no—
236C2×D4—64no—
237C2×D4—92no—
238C2×D4—94no—
239C2×D4—94no—
240C2×D4—124no—
241C2×D4—181no—
242C2×D4—182no—
243C2×D4—184no—
244C2×D4—184no—
245C2×D4—184no—
246C2×D4—182no—
247C2×D4—364no—
248C22×C4—61no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—184no—
252C22×C4—364no—
253C22×C4GO+(4,𝔽2)11yescharacteristic
254D8—1816no—
255C2×C8—94no—
256C2×C8—184no—
257C4⋊C4—92no—
258C4⋊C4—181no—
259C22⋊C4—64no—
260C42—92no—
261C42—92no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—64no—
271C22×C3—122no—
272C22×C3—128no—
273C22×C3—122no—
274C22×C3—124no—
275C22×C3—124no—
276C22×C3—124no—
277C22×C3—248no—
278C2×D3—24no—
279C2×D3—42no—
280C2×D3—48no—
281C2×D3—42no—
282C2×D3—44no—
283C2×D3—44no—
284C2×D3—44no—
285C2×D3—88no—
286C3×C4—24no—
287C3×C4—42no—
288C3×C4—122no—
289Dic3—42no—
290Dic3—64no—
291Dic3—62no—
292Dic3—61no—
293Dic3—61no—
294Dic3—62no—
295Dic3—64no—
296Dic3—61no—
297Dic3—61no—
298C32C2×#45911yescharacteristic, complemented, Sylow
299C23—62no—
300C23—64no—
301C23—64no—
302C23—122no—
303C23—122no—
304C23—124no—
305C23—124no—
306C23—124no—
307C23C2×GO+(4,𝔽2)11yescharacteristic
308D4—94no—
309D4—128no—
310D4—182no—
311D4—184no—
312D4—184no—
313D4—184no—
314D4—364no—
315D4—368no—
316C2×C4—22no—
317C2×C4—62no—
318C2×C4—91no—
319C2×C4—91no—
320C2×C4—92no—
321C2×C4—94no—
322C2×C4—92no—
323C2×C4—92no—
324C2×C4—122no—
325C2×C4—368no—
326C2×C4C2×GO+(4,𝔽2)12yes—
327C8—184no—
328C2×C3—24no—
329C2×C3—24no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—124no—
337C2×C3—244no—
338D3—44no—
339D3—84no—
340C22—64no—
341C22—128no—
342C22—122no—
343C22—122no—
344C22—124no—
345C22—124no—
346C22—124no—
347C22—248no—
348C22#6422512yes—
349C22#6423012yes—
350C22#6423612yes—
351C22C22×GO+(4,𝔽2)11yescharacteristic
352C4—22no—
353C4—94no—
354C4—91no—
355C4—91no—
356C4—92no—
357C4—122no—
358C3—21no—
359C3—21no—
360C2—124no—
361C2—244no—
362C2#1059342614yesdirect product factor
363C2C2×#6422511yescharacteristic
364C2C2×#6423011yescharacteristic
365C2C2×#6423611yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#459
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×#3774C2semidirect
2. C2×#63914C2semidirect
3. C2×#63902C2semidirect
4. C2×#63779C2semidirect
5. C2×#63739C2semidirect
6. #10593426C2direct (N × H)
14. C2×#3774C22semidirect
19. #63914C22semidirect
21. #63902C22semidirect
22. #63779C22semidirect
23. #63739C22semidirect
41. C2×#625D4semidirect
82. C2×C3⋊Dic3D8semidirect
97. #625C2×D4semidirect
158. C3⋊Dic3C2×D8semidirect
228. C2×C32#459semidirect
298. C32C2×#459semidirect
362. C2#10593426direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37742
C2×#639142
C2×#639022
C2×#637792
C2×#637392
#105934262
C2×#4599