Finite Group Databasebeta

← #11868684

Subgroups — #11868684

Order 1152.

1093 conjugacy classes of subgroups.

The subgroup lattice has 445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2#10595050C211yesmaximal, characteristic, complemented
3C3×#5215C212yesmaximal
4#10591495C212yesmaximal, complemented
5#10591494C212yesmaximal, complemented
6#10591479C214yesmaximal, complemented
7#10591131C212yesmaximal, complemented
8#10591120C211yesmaximal, characteristic, complemented
9#78917—32nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3⋊Dic3—21no—
12C2×#3757—21no—
13D4×C3⋊Dic3—21no—
14D4×C3⋊Dic3—21no—
15D4×C3⋊Dic3C2212yes—
16D4×C3⋊Dic3C2212yes—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C3×#926C2212yes—
20C2×C3×#208C2212yes—
21#63982—21no—
22#63982—21no—
23#63919C2211yescharacteristic, complemented
24#63919C2211yescharacteristic, complemented
25C4×#627—21no—
26C4×#627—21no—
27#63872C2212yescomplemented
28C3×#832C2214yes—
29C3×#832C2214yes—
30#63575C2214yescomplemented
31#63573C2214yescomplemented
32#63572C2212yescomplemented
33#63572C2212yescomplemented
34C2×D4×Dic3—32no—
35C2×D4×Dic3—61no—
36#5517—32no—
37C3×#418—32no—
38#5215D312yes—
39#5121—32no—
40#5118—32no—
41#4995—32no—
42#4766—34no—
43#4763—34no—
44#4761—34no—
45#4759—34no—
46C24×C32—21no—
47C2×C32×D4—21no—
48C2×C32×D4—22no—
49C2×C32×D4Q814yescomplemented
50C2×C32×D4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3—22no—
54C22×C3⋊Dic3—22no—
55C22×C3⋊Dic3—44no—
56C22×C3⋊Dic3D411yescharacteristic
57C22×C3⋊Dic3D411yescharacteristic
58C2×#627—21no—
59C2×#627—21no—
60#3757—22no—
61#3757—22no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)C2312yes—
64C4×C3⋊Dic3D411yescharacteristic
65C4×C3⋊Dic3D411yescharacteristic
66C4×C3⋊Dic3C2311yescharacteristic
67C4×C3⋊Dic3C2311yescharacteristic
68C3×#217—22no—
69C3×C4⋊Dic3C2312yes—
70C3×C4⋊Dic3C2312yes—
71C3×C4×Dic3—22no—
72C3×#208—24no—
73C2×C3×C3⋊C8C2314yes—
74#3724—21no—
75#3724—21no—
76Dic3⋊Dic3—22no—
77Dic3⋊Dic3—22no—
78#3077—91noSylow
79C22×C3×D4—21no—
80C22×C3×D4C2×D312yes—
81C23×Dic3—62no—
82C23×Dic3—62no—
83C2×C3×M16—32no—
84C3×#117—32no—
85C2×#217—62no—
86C2×#217—62no—
87D4×Dic3—34no—
88D4×Dic3—34no—
89D4×Dic3—62no—
90D4×Dic3—62no—
91D4×Dic3—62no—
92D4×Dic3—62no—
93D4×Dic3—62no—
94D4×Dic3—62no—
95#926C2×D312yes—
96C2×C4⋊Dic3—32no—
97C2×C4⋊Dic3—61no—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—61no—
100C2×#208C2×D312yes—
101#890—32no—
102#890—32no—
103#888—32no—
104#888—32no—
105#878—62no—
106#878—62no—
107C4×Dic6—62no—
108C4×Dic6—62no—
109C3×#102—34no—
110C3×#102—34no—
111#832C2×D314yes—
112#832C2×D314yes—
113#818—34no—
114#817—34no—
115Dic3⋊C8—34no—
116Dic3⋊C8—34no—
117#808—34no—
118#807—34no—
119C23×C32—24no—
120C23×C32—22no—
121C23×C32—42no—
122C23×C32—42no—
123C23×C32C2×D411yescharacteristic
124C32×D4—24no—
125C32×D4—22no—
126C32×D4C2×Q814yes—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×Q812yes—
129C2×C32×C4#4112yes—
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—44no—
135C2×C3⋊Dic3—42no—
136C2×C3⋊Dic3—44no—
137C2×C3⋊Dic3C2×D411yescharacteristic
138C2×C3⋊Dic3C2×D411yescharacteristic
139C2×C3⋊Dic3C2×D411yescharacteristic
140C2×C3⋊Dic3C2×D411yescharacteristic
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143#627—42no—
144#627—42no—
145C3×C3⋊C8—24no—
146#533—91no—
147C2×C4×D4—91no—
148#478—94no—
149#476—92no—
150#474—92no—
151#428—92no—
152#423—91no—
153#418—32no—
154C24×C3—22no—
155C24×C3—22no—
156C2×C3×D4—22no—
157C2×C3×D4—24no—
158C2×C3×D4—22no—
159C2×C3×D4—24no—
160C2×C3×D4—24no—
161C2×C3×D4—22no—
162C2×C3×D4Dic618yescomplemented
163C2×C3×D4C22×D314yes—
164C22×C3×C4—21no—
165C22×C3×C4C22×D312yes—
166C22×Dic3—32no—
167C22×Dic3—32no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—64no—
171C22×Dic3—64no—
172C22×Dic3—62no—
173C22×Dic3—64no—
174C22×Dic3—64no—
175C22×Dic3—62no—
176C22×Dic3—128no—
177C22×Dic3—128no—
178C2×Dic6—62no—
179C2×Dic6—62no—
180C3×M16—64no—
181C2×C3×C8—34no—
182C3×C4⋊C4—32no—
183C3×C4⋊C4—32no—
184C3×C22⋊C4—62no—
185C3×C42—62no—
186#217—22no—
187#217—64no—
188#217—64no—
189#217—64no—
190#217—64no—
191C4⋊Dic3—34no—
192C4⋊Dic3—62no—
193C4⋊Dic3—62no—
194C4⋊Dic3—62no—
195C4⋊Dic3—62no—
196C4⋊Dic3—62no—
197C4⋊Dic3C22×D312yes—
198C4⋊Dic3C22×D312yes—
199Dic3⋊C4—62no—
200Dic3⋊C4—62no—
201Dic3⋊C4—62no—
202Dic3⋊C4—62no—
203C4×Dic3—22no—
204C4×Dic3—32no—
205C4×Dic3—32no—
206C4×Dic3—32no—
207C4×Dic3—32no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212#208—24no—
213C2×C3⋊C8C22×D314yes—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32—24no—
217C22×C32—48no—
218C22×C32—42no—
219C22×C32—42no—
220C22×C32C22⋊Q812yes—
221C22×C32C22×D411yescharacteristic
222C32×C4C22⋊Q812yes—
223C32×C4C22×Q811yescharacteristic
224C32×C4C2×#4111yescharacteristic
225C3⋊Dic3—21no—
226C3⋊Dic3—21no—
227C3⋊Dic3—21no—
228C3⋊Dic3—42no—
229C3⋊Dic3AGL(1,ℤ/8)12yes—
230C3×Dic3—42no—
231C3×Dic3—42no—
232C22×D4D3211yescharacteristic
233C23×C4—181no—
234C2×M16—32no—
235C4⋊Q8—91no—
236C4⋊Q8—91no—
237#125—92no—
238C22⋊Q8—181no—
239C22⋊Q8—181no—
240C4×Q8—181no—
241C4×Q8—181no—
242C4×D4—92no—
243C4×D4—92no—
244C4×D4—181no—
245C4×D4—181no—
246#117—32no—
247C2×C4⋊C4—91no—
248C2×C22⋊C4—181no—
249C2×C42—91no—
250#107—94no—
251#106—94no—
252C4⋊C8—92no—
253C4⋊C8—92no—
254#102—34no—
255#102—34no—
256C23×C3—24no—
257C23×C3—28no—
258C23×C3—28no—
259C23×C3—24no—
260C23×C3—21no—
261C23×C3—44no—
262C23×C3—44no—
263C23×C3—44no—
264C23×C3—44no—
265C23×C3D3×D412yes—
266C3×D4—24no—
267C3×D4—28no—
268C3×D4—28no—
269C3×D4—24no—
270C3×D4—24no—
271C3×D4C2×Dic618yes—
272C2×C3×C4—21no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×C3×C4C2×Dic614yes—
279C2×C3×C4D3×D412yes—
280C2×C3×C4#23714yes—
281C2×C3×C4C23×D312yes—
282C2×Dic3—22no—
283C2×Dic3—22no—
284C2×Dic3—32no—
285C2×Dic3—32no—
286C2×Dic3—32no—
287C2×Dic3—32no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—64no—
293C2×Dic3—64no—
294C2×Dic3—64no—
295C2×Dic3—64no—
296C2×Dic3—128no—
297C2×Dic3—122no—
298C2×Dic3—128no—
299C2×Dic3—128no—
300C2×Dic3—128no—
301C2×Dic3—122no—
302C2×Dic3—124no—
303C2×Dic3—124no—
304Dic6—124no—
305Dic6—124no—
306C3×C8—64no—
307C3⋊C8—24no—
308C2×C32—22no—
309C2×C32—44no—
310C2×C32C2×C22⋊Q811yescharacteristic
311C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
312C2×C32#57511yescharacteristic
313C24—21no—
314C2×Q8—181no—
315C2×Q8—181no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4#62714yescomplemented
319C2×D4C2×D3212yes—
320C22×C4—91no—
321C22×C4—91no—
322C22×C4—182no—
323C22×C4—182no—
324C22×C4—181no—
325C22×C4—364no—
326C22×C4C2×D3211yescharacteristic
327M16—64no—
328C2×C8—34no—
329C4⋊C4—32no—
330C4⋊C4—32no—
331C4⋊C4—92no—
332C4⋊C4—182no—
333C4⋊C4—182no—
334C4⋊C4—181no—
335C4⋊C4—181no—
336C4⋊C4—181no—
337C22⋊C4—62no—
338C22⋊C4—182no—
339C22⋊C4—182no—
340C42—62no—
341C42—91no—
342C42—91no—
343C42—91no—
344C42—91no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—28no—
350C22×C3—28no—
351C22×C3—21no—
352C22×C3—22no—
353C22×C3—44no—
354C22×C3—416no—
355C22×C3—416no—
356C22×C3—44no—
357C22×C3—44no—
358C22×C3—44no—
359C22×C3#87814yes—
360C22×C3C2×D3×D412yes—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—22no—
364C3×C4—122no—
365C3×C4—122no—
366C3×C4#87814yes—
367C3×C4C22×Dic612yes—
368C3×C4C2×#23712yes—
369Dic3—34no—
370Dic3—42no—
371Dic3—42no—
372Dic3—62no—
373Dic3—62no—
374Dic3—62no—
375Dic3—62no—
376Dic3—62no—
377Dic3—121no—
378Dic3—121no—
379Dic3—124no—
380Dic3—124no—
381C32#307711yescharacteristic, complemented, Sylow
382C23—22no—
383C23—24no—
384C23—42no—
385C23—42no—
386C23#381111yescharacteristic
387Q8—362no—
388Q8—362no—
389D4—22no—
390D4—24no—
391D4C2×#62714yes—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—91no—
395C2×C4—91no—
396C2×C4—91no—
397C2×C4—91no—
398C2×C4—182no—
399C2×C4—182no—
400C2×C4—364no—
401C2×C4—361no—
402C2×C4—364no—
403C2×C4—362no—
404C2×C4#380512yes—
405C2×C4C2×#62712yes—
406C2×C4#381111yescharacteristic
407C2×C4C22×D3211yescharacteristic
408C8—64no—
409C2×C3—24no—
410C2×C3—24no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—48no—
415C2×C3—48no—
416C2×C3C2×#87812yes—
417C2×C3D3×AGL(1,ℤ/8)12yes—
418C2×C3#577312yes—
419C22—21no—
420C22—21no—
421C22—24no—
422C22—48no—
423C22—42no—
424C22—42no—
425C22#6398212yes—
426C22C2×#381111yescharacteristic
427C4—92no—
428C4—122no—
429C4—122no—
430C4—181no—
431C4—181no—
432C4—181no—
433C4—362no—
434C4#6398212yes—
435C4C2×#380511yescharacteristic
436C4C22×#62711yescharacteristic
437C3—21no—
438C3#7891712yescomplemented
439C2—22no—
440C2—44no—
441C2#1059510011yescharacteristic
442C2#1059510111yescharacteristic
443C2C2×#6398211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10595050C2semidirect
4. #10591495C2semidirect
5. #10591494C2semidirect
6. #10591479C2semidirect
7. #10591131C2semidirect
8. #10591120C2semidirect
23. #63919C22semidirect
24. #63919C22semidirect
27. #63872C22semidirect
30. #63575C22semidirect
31. #63573C22semidirect
32. #63572C22semidirect
33. #63572C22semidirect
49. C2×C32×D4Q8semidirect
162. C2×C3×D4Dic6semidirect
318. C2×D4#627semidirect
381. C32#3077semidirect
438. C3#78917semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
#105950502
C3×#52152
#105914952
#105914942
#105914792
#105911312
#105911202
#789173