Finite Group Databasebeta

← #11870849

Subgroups — #11870849

Order 1152.

1362 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2#10595950C211yesmaximal, characteristic, complemented
3#10592917C211yesmaximal, characteristic, complemented
4#10592916C211yesmaximal, characteristic
5C4×#3754C212yesmaximal, complemented
6#10592715C212yesmaximal, complemented
7C4×#3753C212yesmaximal, complemented
8#10592708C212yesmaximal, complemented
9#10592669C211yesmaximal, characteristic, complemented
10#10592667C211yesmaximal, characteristic, complemented
11#10592624C211yesmaximal, characteristic, complemented
12#82309—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C23×C32×C4—21no—
15C32×C4×D4—21no—
16C32×C4×D4—21no—
17C32×C4×D4C2212yes—
18C32×C4×D4C2212yes—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C22⋊C4—21no—
21C2×C32×C42C2211yescharacteristic
22C2×#3754C2212yes—
23C2×#3753C2212yes—
24#64139C2211yescharacteristic
25#64138—21no—
26C4×#638—21no—
27#64133C2211yescharacteristic
28#64085—21no—
29#64084C2211yescharacteristic, complemented
30C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
31#64081—21no—
32#64079C2211yescharacteristic, complemented
33C4×#634C2211yescharacteristic, complemented
34#63659C2212yes—
35#63659C2212yes—
36#63657C2211yescharacteristic
37#63657C2211yescharacteristic
38#63637C2212yescomplemented
39#63636C2212yescomplemented
40#63635C2212yescomplemented
41#63634C2212yescomplemented
42C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
43C4×C3⋊(C3⋊C8)C2212yescomplemented
44C2×C3×C4×D4D314yescomplemented
45#5479—34no—
46#5218—34no—
47#5217—34no—
48C4×#214—38no—
49#5016—38no—
50C4×#213—38no—
51#5009—38no—
52#4970—34no—
53#4968—34no—
54#4925—34no—
55C24×C32—21no—
56C2×C32×D4—24no—
57C2×C32×D4—21no—
58C2×C32×D4C2312yes—
59C22×C32×C4—21no—
60C22×C32×C4—22no—
61C22×C32×C4—22no—
62C22×C32×C4—44no—
63C22×C32×C4D411yescharacteristic
64C22×C32×C4D411yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C2×#638—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×#634C2311yescharacteristic
70C32×C4⋊C4—21no—
71C32×C4⋊C4C2312yes—
72C32×C22⋊C4—22no—
73C32×C22⋊C4—22no—
74C32×C42D411yescharacteristic
75C32×C42D411yescharacteristic
76C32×C42C2311yescharacteristic
77C32×C42C2311yescharacteristic
78#3757—21no—
79#3754—24no—
80#3753—24no—
81#3752—21no—
82#3752—21no—
83#3752—21no—
84#3752—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87#3750—21no—
88#3750—21no—
89#3750—21no—
90#3750—21no—
91C4×C3⋊Dic3—21no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C2×C3⋊(C3⋊C8)C2312yes—
94#3105—91noSylow
95C22×C3×D4C2×D314yes—
96C23×C3×C4—24no—
97C3×C4×D4—24no—
98C3×C4×D4—24no—
99C3×C4×D4C2×D318yes—
100C3×C4×D4C2×D318yes—
101C2×C3×C4⋊C4C2×D314yes—
102C2×C3×C22⋊C4—24no—
103C2×C3×C42C2×D314yes—
104C2×#214—38no—
105C2×#213—38no—
106#930—34no—
107#929—64no—
108C4×#67—64no—
109#924—34no—
110#876—64no—
111#875—34no—
112C4×D12—34no—
113#872—64no—
114#870—34no—
115C4×Dic6—34no—
116#832—38no—
117#832—38no—
118#830—34no—
119#830—34no—
120#810—38no—
121#809—38no—
122#808—38no—
123#807—38no—
124C4⋊(C3⋊C8)—38no—
125C4×C3⋊C8—38no—
126C23×C32—24no—
127C23×C32—22no—
128C23×C32—42no—
129C23×C32—42no—
130C23×C32C2×D411yescharacteristic
131C22×C3⋊D3—21no—
132C32×D4—24no—
133C32×D4—22no—
134C32×D4#4114yes—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4—44no—
140C2×C32×C4—42no—
141C2×C32×C4—44no—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2411yescharacteristic
148#638—42no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C4⋊(C3⋊D3)—22no—
153C4×C3⋊D3—42no—
154#634—22no—
155C3⋊(C3⋊C8)—22no—
156C3⋊(C3⋊C8)—22no—
157#529—91no—
158C2×C4×D4C3⋊D311yescharacteristic, complemented
159#484—91no—
160#481—91no—
161#478—92no—
162#463—92no—
163#450—91no—
164#447—91no—
165C4×SD16—92no—
166C4×D8—92no—
167#431—91no—
168C24×C3—24no—
169C2×C3×D4—216no—
170C2×C3×D4—24no—
171C2×C3×D4C22×D318yes—
172C22×C3×C4—24no—
173C22×C3×C4—28no—
174C22×C3×C4—28no—
175C22×C3×C4—416no—
176C22×C3×C4#6714yes—
177C22×C3×C4#6714yes—
178C22×C3×C4C22×D314yes—
179C2×#67—64no—
180C2×D12—34no—
181C2×C4×D3—64no—
182C2×Dic6—34no—
183C3×C4⋊C4—24no—
184C3×C4⋊C4C22×D318yes—
185C3×C22⋊C4—28no—
186C3×C22⋊C4—28no—
187C3×C42#6714yes—
188C3×C42#6714yes—
189C3×C42C22×D314yes—
190C3×C42C22×D314yes—
191#217—64no—
192#214—616no—
193#213—616no—
194(C2×D3)⋊C4—64no—
195(C2×D3)⋊C4—64no—
196(C2×D3)⋊C4—64no—
197(C2×D3)⋊C4—64no—
198C4⋊Dic3—34no—
199C4⋊Dic3—34no—
200Dic3⋊C4—64no—
201Dic3⋊C4—64no—
202Dic3⋊C4—64no—
203Dic3⋊C4—64no—
204C4×Dic3—64no—
205C2×C3⋊C8—38no—
206C2×C3⋊C8—38no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32—24no—
210C22×C32—48no—
211C22×C32—42no—
212C22×C32—42no—
213C22×C32#13512yes—
214C22×C32C22×D411yescharacteristic
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—42no—
223C32×C4AGL(1,ℤ/8)12yes—
224C32×C4C2×#4112yes—
225C3⋊Dic3—41no—
226C3⋊Dic3—41no—
227C3⋊Dic3—41no—
228C22×D4C2×C3⋊D311yescharacteristic
229C23×C4—21no—
230C2×SD16—92no—
231C2×D8—92no—
232#126—181no—
233#125—91no—
234#124—91no—
235#123—181no—
236C22⋊Q8—91no—
237#121—91no—
238C4×Q8—91no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—91no—
242C4×D4—181no—
243C4×D4C2×C3⋊D312yes—
244C4×D4C2×C3⋊D312yes—
245#117—181no—
246C2×C4⋊C4C2×C3⋊D311yescharacteristic
247C2×C22⋊C4—21no—
248C2×C42C2×C3⋊D311yescharacteristic
249#107—92no—
250#106—92no—
251C4⋊C8—92no—
252#103—92no—
253#102—92no—
254#102—92no—
255#102—92no—
256C22⋊C8—91no—
257C22⋊C8—91no—
258C4×C8—92no—
259C23×C3—216no—
260C23×C3—28no—
261C23×C3—48no—
262C23×C3—48no—
263C23×C3C2×#6714yes—
264C22×D3—64no—
265C3×D4—216no—
266C3×D4—28no—
267C3×D4#235116yes—
268C2×C3×C4—28no—
269C2×C3×C4—28no—
270C2×C3×C4—28no—
271C2×C3×C4—28no—
272C2×C3×C4—416no—
273C2×C3×C4—48no—
274C2×C3×C4—416no—
275C2×C3×C4C2×#6714yes—
276C2×C3×C4C2×#6714yes—
277C2×C3×C4C2×#6714yes—
278C2×C3×C4C2×#6714yes—
279C2×C3×C4C2×#6714yes—
280C2×C3×C4C23×D314yes—
281#67—128no—
282C2×Dic3—64no—
283C2×Dic3—64no—
284C2×Dic3—64no—
285D12—68no—
286C4×D3—128no—
287Dic6—68no—
288C3⋊C8—68no—
289C3⋊C8—68no—
290C2×C32—22no—
291C2×C32—44no—
292C2×C32#52511yescharacteristic
293C2×C32C2×#13511yescharacteristic
294C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
295C3⋊D3—81no—
296C24—21no—
297C2×Q8—91no—
298C2×D4—24no—
299C2×D4—21no—
300C2×D4—91no—
301C2×D4—181no—
302C2×D4C22×C3⋊D312yes—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—44no—
307C22×C4—181no—
308C22×C4#63811yescharacteristic
309C22×C4#63811yescharacteristic
310C22×C4C22×C3⋊D311yescharacteristic
311SD16—184no—
312D8—184no—
313C2×C8—92no—
314C2×C8—92no—
315C4⋊C4—21no—
316C4⋊C4—91no—
317C4⋊C4—91no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4C22×C3⋊D312yes—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—181no—
326C22⋊C4—181no—
327C22⋊C4—181no—
328C22⋊C4—181no—
329C22⋊C4—181no—
330C42—181no—
331C42#63811yescharacteristic
332C42#63811yescharacteristic
333C42C22×C3⋊D311yescharacteristic
334C42C22×C3⋊D311yescharacteristic
335C22×C3—24no—
336C22×C3—24no—
337C22×C3—216no—
338C22×C3—432no—
339C22×C3—48no—
340C22×C3—48no—
341C22×C3#95018yes—
342C22×C3C22×#6714yes—
343C2×D3—124no—
344C2×D3—124no—
345C2×D3—124no—
346C3×C4—24no—
347C3×C4—24no—
348C3×C4—24no—
349C3×C4—24no—
350C3×C4—48no—
351C3×C4#93218yes—
352C3×C4C2×#23518yes—
353Dic3—124no—
354Dic3—124no—
355Dic3—124no—
356C32#310511yescharacteristic, complemented, Sylow
357C23—24no—
358C23—22no—
359C23—42no—
360C23—42no—
361C23—181no—
362C23C2×#63811yescharacteristic
363Q8—182no—
364D4—24no—
365D4—22no—
366D4—182no—
367D4—362no—
368D4#382814yes—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—44no—
374C2×C4—42no—
375C2×C4—44no—
376C2×C4—181no—
377C2×C4—181no—
378C2×C4—181no—
379C2×C4—362no—
380C2×C4C2×#63811yescharacteristic
381C2×C4C2×#63811yescharacteristic
382C2×C4C2×#63811yescharacteristic
383C2×C4C2×#63811yescharacteristic
384C2×C4C2×#63811yescharacteristic
385C2×C4C23×C3⋊D311yescharacteristic
386C8—182no—
387C8—182no—
388C2×C3—28no—
389C2×C3—416no—
390C2×C3#579114yes—
391C2×C3C2×#93214yes—
392C2×C3C2×#95014yes—
393D3—244no—
394C22—21no—
395C22—21no—
396C22—24no—
397C22—48no—
398C22—42no—
399C22—42no—
400C22—361no—
401C22—361no—
402C22—361no—
403C22#6415912yes—
404C22C22×#63811yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—42no—
410C4—361no—
411C4—361no—
412C4—361no—
413C4#6414112yes—
414C4C2×#382812yes—
415C3#8230914yescomplemented
416C2—22no—
417C2—44no—
418C2—721no—
419C2#1059626211yescharacteristic
420C2C2×#6414111yescharacteristic
421C2C2×#6415911yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C4×D4C2
socleC22×C32C22×D4
prime radical#10592916C2
hypercenterC2×C4×D4C3⋊D3
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
2. #10595950C2semidirect
3. #10592917C2semidirect
5. C4×#3754C2semidirect
6. #10592715C2semidirect
7. C4×#3753C2semidirect
8. #10592708C2semidirect
9. #10592669C2semidirect
10. #10592667C2semidirect
11. #10592624C2semidirect
29. #64084C22semidirect
30. C4×C4⋊(C3⋊D3)C22semidirect
32. #64079C22semidirect
33. C4×#634C22semidirect
38. #63637C22semidirect
39. #63636C22semidirect
40. #63635C22semidirect
41. #63634C22semidirect
42. C4⋊(C3⋊(C3⋊C8))C22semidirect
43. C4×C3⋊(C3⋊C8)C22semidirect
44. C2×C3×C4×D4D3semidirect
158. C2×C4×D4C3⋊D3semidirect
356. C32#3105semidirect
415. C3#82309semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
#105959502
#105929172
#105929162
C4×#37542
#105927152
C4×#37532
#105927082
#105926692
#105926672
#105926242
#823093