Finite Group Databasebeta

← C2×#10593419 #11860178

Subgroups — C2×#10593419 #11860178

Order 1152.

1034 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 167 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×#3774C211yesmaximal, characteristic
2C2×#63902C211yesmaximal, characteristic, complemented
3C2×C4×#625C211yesmaximal, characteristic, complemented
4C2×#63777C211yesmaximal, characteristic, complemented
5C2×#63742C211yesmaximal, characteristic, complemented
6C2×#63739C211yesmaximal, characteristic, complemented
7C2×#63739C211yesmaximal, characteristic, complemented
8#10593419C218yesmaximal, direct product factor
9C22×C3×C4×D3—21no—
10C22×#625C2211yescharacteristic
11C22×#625C2211yescharacteristic
12C22×D3×Dic3—21no—
13C22×#622C2211yescharacteristic
14C22×#622C2211yescharacteristic
15C2×#3774C418yescomplemented
16C2×#3774C2214yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4—21no—
19C2×#3724C2211yescharacteristic
20C2×#3724C2211yescharacteristic
21C2×(C2×D3)⋊Dic3—21no—
22#63902—22no—
23#63902C2214yescomplemented
24C4×#625—22no—
25C4×#625C2214yescomplemented
26#63777C2214yescomplemented
27#63742C2214yescomplemented
28#63739C2214yescomplemented
29#63739C2214yescomplemented
30C2×C4×#67—61no—
31C2×#67⋊C4—61no—
32C23×C3×D3—21no—
33C23×C3×D3—21no—
34C22×C32×C4D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C22×C3⋊Dic3C2311yescharacteristic
37C22×C3×Dic3—21no—
38C22×C3×Dic3—21no—
39C2×C3×C4×D3—24no—
40C2×C3×C4×D3—44no—
41C2×#625—21no—
42C2×#625—21no—
43C2×#625—22no—
44C2×#625—22no—
45C2×#625C2×C414yescomplemented
46C2×#625C2×C414yescomplemented
47C2×#625C2312yes—
48C2×#625C2312yes—
49C2×D3×Dic3—24no—
50C2×D3×Dic3—44no—
51C2×#622—22no—
52C2×#622C2×C414yescomplemented
53C2×#622C2312yes—
54C2×#622C2312yes—
55#3774C2×C4116yescomplemented
56C4×C3⋊Dic3D412yes—
57C4×C3⋊Dic3C2312yes—
58C3×(C2×D3)⋊C4—24no—
59#3724—21no—
60#3724—21no—
61#3724C2312yes—
62#3724C2312yes—
63(C2×D3)⋊Dic3—24no—
64C2×#442—91nomaximal, Sylow
65C23×C3×C4—61no—
66C22×#67—61no—
67C22×#67—61no—
68C23×Dic3—61no—
69C22×C4×D3—21no—
70C22×C4×D3—61no—
71C2×C3×C22⋊C4—61no—
72C2×#217—61no—
73C4×#67—64no—
74C4×#67—64no—
75C2×(C2×D3)⋊C4—21no—
76C2×(C2×D3)⋊C4—61no—
77C2×Dic3⋊C4—61no—
78C2×Dic3⋊C4—61no—
79C2×C4×Dic3—61no—
80C2×C4×Dic3—61no—
81#67⋊C4—64no—
82#67⋊C4—64no—
83C23×C32C2×D411yescharacteristic
84C22×C3×D3—24no—
85C22×C3×D3—24no—
86C22×C3×D3—22no—
87C22×C3×D3—22no—
88C22×C3×D3—42no—
89C22×C3×D3—42no—
90C22×C3×D3—42no—
91C22×C3×D3—42no—
92C2×C32×C4—22no—
93C2×C32×C4C2×D412yes—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3C22×C412yes—
96C2×C3⋊Dic3C2×D412yes—
97C2×C3⋊Dic3C2×D411yescharacteristic
98C2×C3⋊Dic3#4112yes—
99C2×C3⋊Dic3C2411yescharacteristic
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—42no—
103C2×C3×Dic3—42no—
104C3×C4×D3—48no—
105#625—24no—
106#625—24no—
107#625—22no—
108#625—22no—
109#625C22×C414yescomplemented
110#625C22×C414yescomplemented
111D3×Dic3—48no—
112#622—22no—
113#622C22×C414yescomplemented
114C22×D8—91no—
115C2×C4×D4—91no—
116C2×C4×D4—91no—
117#442—98no—
118C2×#106—91no—
119C2×#102—91no—
120C2×#102—91no—
121C2×#97—91no—
122C24×C3—61no—
123C24×C3—61no—
124C23×D3—21no—
125C23×D3—21no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—64no—
129C22×C3×C4—61no—
130C22×C3×C4—61no—
131C22×C3×C4—124no—
132C2×#67—62no—
133C2×#67—62no—
134C2×#67—64no—
135C2×#67—64no—
136C2×#67—62no—
137C2×#67—62no—
138C2×#67—64no—
139C2×#67—64no—
140C22×Dic3—21no—
141C22×Dic3—21no—
142C22×Dic3—61no—
143C22×Dic3—61no—
144C22×Dic3—61no—
145C22×Dic3—61no—
146C22×Dic3—64no—
147C22×Dic3—124no—
148C2×C4×D3—24no—
149C2×C4×D3—44no—
150C2×C4×D3—64no—
151C2×C4×D3—124no—
152C3×C22⋊C4—64no—
153#217—64no—
154(C2×D3)⋊C4—24no—
155(C2×D3)⋊C4—64no—
156Dic3⋊C4—62no—
157Dic3⋊C4—62no—
158Dic3⋊C4—62no—
159Dic3⋊C4—62no—
160C4×Dic3—62no—
161C4×Dic3—62no—
162C4×Dic3—62no—
163C4×Dic3—62no—
164C22×C32C4×D412yes—
165C22×C32AGL(1,ℤ/8)12yes—
166C22×C32AGL(1,ℤ/8)12yes—
167C22×C32C22×D411yescharacteristic
168C2×C3×D3—24no—
169C2×C3×D3—24no—
170C2×C3×D3—42no—
171C2×C3×D3—42no—
172C2×C3×D3—42no—
173C2×C3×D3—42no—
174C2×C3×D3—48no—
175C2×C3×D3—48no—
176C32×C4—22no—
177C3⋊Dic3—22no—
178C3⋊Dic3C4×D412yes—
179C3⋊Dic3C23×C411yescharacteristic
180C3⋊Dic3C2×#4111yescharacteristic
181C3×Dic3—42no—
182C3×Dic3—42no—
183C22×D4—91no—
184C22×D4—91no—
185C23×C4—61no—
186C23×C4—181no—
187C2×D8—94no—
188C2×D8—98no—
189C22×C8—91no—
190C22×C8—91no—
191C4×D4—94no—
192C4×D4—94no—
193C4×D4—182no—
194C4×D4—182no—
195C2×C4⋊C4—91no—
196C2×C4⋊C4—91no—
197C2×C22⋊C4—61no—
198C2×C22⋊C4—181no—
199C2×C42—91no—
200#106—94no—
201#102—94no—
202#102—94no—
203#97—94no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—62no—
207C23×C3—62no—
208C23×C3—64no—
209C23×C3—64no—
210C23×C3—122no—
211C23×C3—122no—
212C23×C3—122no—
213C23×C3—122no—
214C22×D3—22no—
215C22×D3—22no—
216C22×D3—24no—
217C22×D3—24no—
218C22×D3—42no—
219C22×D3—42no—
220C22×D3—42no—
221C22×D3—42no—
222C2×C3×C4—24no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—42no—
226C2×C3×C4—62no—
227C2×C3×C4—62no—
228C2×C3×C4—128no—
229C2×C3×C4—122no—
230C2×C3×C4—122no—
231#67—64no—
232#67—64no—
233#67—68no—
234#67—68no—
235#67—64no—
236#67—64no—
237C2×Dic3—22no—
238C2×Dic3—22no—
239C2×Dic3—42no—
240C2×Dic3—42no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250C2×Dic3—62no—
251C2×Dic3—64no—
252C2×Dic3—122no—
253C2×Dic3—128no—
254C4×D3—48no—
255C4×D3—128no—
256C2×C32#44214yescomplemented
257C2×C32C2×C4×D411yescharacteristic
258C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
259C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
260C3×D3—44no—
261C3×D3—44no—
262C24—61no—
263C24—61no—
264C2×D4—92no—
265C2×D4—92no—
266C2×D4—94no—
267C2×D4—94no—
268C2×D4—181no—
269C2×D4—181no—
270C2×D4—182no—
271C2×D4—182no—
272C22×C4—61no—
273C22×C4—61no—
274C22×C4—64no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—124no—
278C22×C4—184no—
279C22×C4—364no—
280C22×C4GO+(4,𝔽2)11yescharacteristic
281D8—916no—
282C2×C8—92no—
283C2×C8—94no—
284C2×C8—92no—
285C2×C8—182no—
286C4⋊C4—92no—
287C4⋊C4—92no—
288C4⋊C4—181no—
289C4⋊C4—181no—
290C22⋊C4—64no—
291C22⋊C4—184no—
292C42—92no—
293C42—92no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—22no—
297C22×C3—22no—
298C22×C3—22no—
299C22×C3—22no—
300C22×C3—22no—
301C22×C3—22no—
302C22×C3—64no—
303C22×C3—64no—
304C22×C3—122no—
305C22×C3—122no—
306C22×C3—128no—
307C22×C3—128no—
308C22×C3—122no—
309C22×C3—122no—
310C2×D3—24no—
311C2×D3—24no—
312C2×D3—42no—
313C2×D3—42no—
314C2×D3—48no—
315C2×D3—48no—
316C2×D3—42no—
317C2×D3—42no—
318C3×C4—24no—
319C3×C4—42no—
320C3×C4—122no—
321C3×C4—122no—
322Dic3—42no—
323Dic3—42no—
324Dic3—62no—
325Dic3—62no—
326Dic3—61no—
327Dic3—61no—
328Dic3—61no—
329Dic3—61no—
330Dic3—64no—
331Dic3—122no—
332C32C2×#44211yescharacteristic, complemented, Sylow
333C23—62no—
334C23—62no—
335C23—64no—
336C23—64no—
337C23—122no—
338C23—122no—
339C23—122no—
340C23—122no—
341C23C2×GO+(4,𝔽2)11yescharacteristic
342D4—94no—
343D4—94no—
344D4—182no—
345D4—182no—
346D4—184no—
347D4—184no—
348C2×C4—22no—
349C2×C4—62no—
350C2×C4—62no—
351C2×C4—91no—
352C2×C4—91no—
353C2×C4—92no—
354C2×C4—92no—
355C2×C4—92no—
356C2×C4—128no—
357C2×C4—122no—
358C2×C4—122no—
359C2×C4—182no—
360C2×C4—368no—
361C2×C4C2×GO+(4,𝔽2)12yes—
362C8—94no—
363C8—182no—
364C2×C3—24no—
365C2×C3—24no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—124no—
373C2×C3—124no—
374D3—44no—
375D3—44no—
376C22—64no—
377C22—64no—
378C22—128no—
379C22—128no—
380C22—122no—
381C22—122no—
382C22—122no—
383C22—122no—
384C22#6422412yes—
385C22C4×GO+(4,𝔽2)12yes—
386C22#6423612yes—
387C22C22×GO+(4,𝔽2)11yescharacteristic
388C4—22no—
389C4—91no—
390C4—91no—
391C4—92no—
392C4—122no—
393C4—122no—
394C4—182no—
395C3—21no—
396C3—21no—
397C2—124no—
398C2—124no—
399C2#1059341914yesdirect product factor
400C2C2×#6422411yescharacteristic
401C2C2×C4×GO+(4,𝔽2)11yescharacteristic
402C2C2×#6423611yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#3774C2
cosocleC2×C3⋊Dic3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#442
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63902C2semidirect
3. C2×C4×#625C2semidirect
4. C2×#63777C2semidirect
5. C2×#63742C2semidirect
6. C2×#63739C2semidirect
7. C2×#63739C2semidirect
8. #10593419C2direct (N × H)
15. C2×#3774C4semidirect
23. #63902C22semidirect
25. C4×#625C22semidirect
26. #63777C22semidirect
27. #63742C22semidirect
28. #63739C22semidirect
29. #63739C22semidirect
45. C2×#625C2×C4semidirect
46. C2×#625C2×C4semidirect
52. C2×#622C2×C4semidirect
55. #3774C2×C4semidirect
109. #625C22×C4semidirect
110. #625C22×C4semidirect
113. #622C22×C4semidirect
256. C2×C32#442semidirect
332. C32C2×#442semidirect
399. C2#10593419direct (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×#639022
C2×C4×#6252
C2×#637772
C2×#637422
C2×#637392
#105934192
C2×#4429