Finite Group Databasebeta

← #11868642

Subgroups — #11868642

Order 1152.

1320 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2#10595988C211yesmaximal, characteristic, complemented
3C32×#418C211yesmaximal, characteristic
4#10592914C211yesmaximal, characteristic
5#10592820C211yesmaximal, characteristic, complemented
6#10592817C211yesmaximal, characteristic, complemented
7#10592694C211yesmaximal, characteristic, complemented
8#10592465C212yesmaximal, complemented
9#10592462C212yesmaximal, complemented
10#10592460C212yesmaximal, complemented
11#10592458C212yesmaximal, complemented
12#78917—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C23×C3⋊Dic3—21no—
15C2×C32×M16C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×#3757—21no—
18D4×C3⋊Dic3—21no—
19D4×C3⋊Dic3—21no—
20D4×C3⋊Dic3C2212yes—
21D4×C3⋊Dic3C2212yes—
22#64135C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26#64099C2211yescharacteristic, complemented
27#64099C2211yescharacteristic, complemented
28#64097C2211yescharacteristic, complemented
29#64097C2211yescharacteristic, complemented
30#64087—21no—
31#64087—21no—
32C4×#634—21no—
33C4×#634—21no—
34C32×#102C2212yes—
35C32×#102C2212yes—
36#63659C2212yes—
37#63659C2212yes—
38#63645C2212yescomplemented
39#63644C2212yescomplemented
40#63641C2212yescomplemented
41#63641C2212yescomplemented
42#63635C2212yescomplemented
43#63634C2212yescomplemented
44C2×D4×Dic3—34no—
45#5517—34no—
46C3×#418D314yes—
47#5215—34no—
48#5121—34no—
49#5118—34no—
50#4995—34no—
51#4766—38no—
52#4763—38no—
53#4761—38no—
54#4759—38no—
55C24×C32—21no—
56C2×C32×D4—21no—
57C2×C32×D4—22no—
58C2×C32×D4Q814yescomplemented
59C2×C32×D4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3—21no—
62C22×C3⋊Dic3—22no—
63C22×C3⋊Dic3—22no—
64C22×C3⋊Dic3—44no—
65C22×C3⋊Dic3D411yescharacteristic
66C22×C3⋊Dic3D411yescharacteristic
67C2×#634—21no—
68C2×#634—21no—
69C32×M16—22no—
70C2×C32×C8C2312yes—
71C32×C4⋊C4C2311yescharacteristic
72C32×C4⋊C4C2311yescharacteristic
73C32×C22⋊C4—21no—
74C32×C42—21no—
75#3757—21no—
76#3757—22no—
77#3757—22no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2312yes—
84#3750—21no—
85#3750—21no—
86#3750—21no—
87#3750—21no—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93#3748—22no—
94C2×C3⋊(C3⋊C8)C2312yes—
95#3077—91noSylow
96C22×C3×D4C2×D314yes—
97C23×Dic3—64no—
98C2×C3×M16C2×D314yes—
99C3×#117C2×D314yes—
100C2×#217—64no—
101D4×Dic3—38no—
102D4×Dic3—38no—
103D4×Dic3—64no—
104D4×Dic3—64no—
105#926—34no—
106C2×C4⋊Dic3—34no—
107C2×C4×Dic3—34no—
108C2×#208—34no—
109#890—34no—
110#890—34no—
111#888—34no—
112#888—34no—
113#878—64no—
114#878—64no—
115C4×Dic6—64no—
116C4×Dic6—64no—
117C3×#102C2×D318yes—
118C3×#102C2×D318yes—
119#832—38no—
120#832—38no—
121#818—38no—
122#817—38no—
123Dic3⋊C8—38no—
124Dic3⋊C8—38no—
125#808—38no—
126#807—38no—
127C23×C32—24no—
128C23×C32—22no—
129C23×C32—42no—
130C23×C32—42no—
131C23×C32C2×D411yescharacteristic
132C32×D4—24no—
133C32×D4—22no—
134C32×D4C2×Q814yes—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×Q812yes—
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—41no—
146C2×C3⋊Dic3—44no—
147C2×C3⋊Dic3—42no—
148C2×C3⋊Dic3—44no—
149C2×C3⋊Dic3C2×D411yescharacteristic
150C2×C3⋊Dic3C2×D411yescharacteristic
151C2×C3⋊Dic3C2×D411yescharacteristic
152C2×C3⋊Dic3C2×D411yescharacteristic
153#634—42no—
154#634—42no—
155C32×C8—22no—
156C3⋊(C3⋊C8)—22no—
157#533—91no—
158C2×C4×D4—91no—
159#478—92no—
160#478—92no—
161#476—92no—
162#474—92no—
163#428—91no—
164#428—91no—
165#423—91no—
166#418—91no—
167#418C3⋊D311yescharacteristic
168C24×C3—24no—
169C2×C3×D4—24no—
170C2×C3×D4—28no—
171C2×C3×D4Dic6116yescomplemented
172C2×C3×D4C22×D318yes—
173C22×C3×C4C22×D314yes—
174C22×Dic3—34no—
175C22×Dic3—34no—
176C22×Dic3—68no—
177C22×Dic3—68no—
178C22×Dic3—64no—
179C22×Dic3—1216no—
180C2×Dic6—64no—
181C2×Dic6—64no—
182C3×M16—28no—
183C2×C3×C8C22×D318yes—
184C3×C4⋊C4C22×D314yes—
185C3×C4⋊C4C22×D314yes—
186C3×C22⋊C4—24no—
187C3×C42—24no—
188#217—68no—
189#217—68no—
190#217—64no—
191C4⋊Dic3—38no—
192C4⋊Dic3—34no—
193C4⋊Dic3—34no—
194C4⋊Dic3—64no—
195C4⋊Dic3—64no—
196C4⋊Dic3—64no—
197Dic3⋊C4—64no—
198Dic3⋊C4—64no—
199Dic3⋊C4—64no—
200Dic3⋊C4—64no—
201C4×Dic3—34no—
202C4×Dic3—34no—
203C4×Dic3—34no—
204C4×Dic3—34no—
205C4×Dic3—64no—
206#208—68no—
207C2×C3⋊C8—38no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32—24no—
211C22×C32—48no—
212C22×C32—42no—
213C22×C32—42no—
214C22×C32C22⋊Q812yes—
215C22×C32C22×D411yescharacteristic
216C32×C4—41no—
217C32×C4—41no—
218C32×C4C22⋊Q812yes—
219C32×C4C22×Q811yescharacteristic
220C32×C4C2×#4111yescharacteristic
221C3⋊Dic3—21no—
222C3⋊Dic3—21no—
223C3⋊Dic3—21no—
224C3⋊Dic3—41no—
225C3⋊Dic3—42no—
226C3⋊Dic3—41no—
227C3⋊Dic3AGL(1,ℤ/8)12yes—
228C22×D4C2×C3⋊D311yescharacteristic
229C23×C4—181no—
230C2×M16—91no—
231C2×M16C2×C3⋊D311yescharacteristic
232C4⋊Q8—91no—
233C4⋊Q8—91no—
234#125—91no—
235#125—91no—
236C22⋊Q8—181no—
237C22⋊Q8—181no—
238C4×Q8—181no—
239C4×Q8—181no—
240C4×D4—92no—
241C4×D4—92no—
242C4×D4—181no—
243C4×D4—181no—
244#117—91no—
245#117C2×C3⋊D311yescharacteristic
246C2×C4⋊C4—91no—
247C2×C22⋊C4—181no—
248C2×C42—91no—
249#107—92no—
250#107—92no—
251#106—92no—
252#106—92no—
253C4⋊C8—92no—
254C4⋊C8—92no—
255#102—92no—
256#102—92no—
257#102C2×C3⋊D312yes—
258#102C2×C3⋊D312yes—
259C23×C3—216no—
260C23×C3—28no—
261C23×C3—48no—
262C23×C3—48no—
263C23×C3D3×D414yes—
264C3×D4—216no—
265C3×D4—28no—
266C3×D4C2×Dic6116yes—
267C2×C3×C4—24no—
268C2×C3×C4—24no—
269C2×C3×C4C2×Dic618yes—
270C2×C3×C4D3×D414yes—
271C2×C3×C4#23718yes—
272C2×C3×C4C23×D314yes—
273C2×Dic3—34no—
274C2×Dic3—34no—
275C2×Dic3—34no—
276C2×Dic3—34no—
277C2×Dic3—68no—
278C2×Dic3—64no—
279C2×Dic3—64no—
280C2×Dic3—68no—
281C2×Dic3—1216no—
282C2×Dic3—124no—
283C2×Dic3—1216no—
284C2×Dic3—128no—
285Dic6—128no—
286Dic6—128no—
287C3×C8—28no—
288C3⋊C8—68no—
289C2×C32—22no—
290C2×C32—44no—
291C2×C32C2×C22⋊Q811yescharacteristic
292C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
293C2×C32#57511yescharacteristic
294C24—21no—
295C2×Q8—181no—
296C2×Q8—181no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4#63414yescomplemented
300C2×D4C22×C3⋊D312yes—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—182no—
304C22×C4—182no—
305C22×C4—181no—
306C22×C4—364no—
307C22×C4C22×C3⋊D311yescharacteristic
308M16—22no—
309M16—182no—
310C2×C8—92no—
311C2×C8C22×C3⋊D312yes—
312C4⋊C4—91no—
313C4⋊C4—91no—
314C4⋊C4—92no—
315C4⋊C4—181no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4C22×C3⋊D311yescharacteristic
323C4⋊C4C22×C3⋊D311yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—182no—
326C22⋊C4—182no—
327C22⋊C4—181no—
328C42—21no—
329C42—91no—
330C42—91no—
331C42—91no—
332C42—91no—
333C42—181no—
334C22×C3—24no—
335C22×C3—24no—
336C22×C3—216no—
337C22×C3—432no—
338C22×C3—48no—
339C22×C3—48no—
340C22×C3#87818yes—
341C22×C3C2×D3×D414yes—
342C3×C4—44no—
343C3×C4—44no—
344C3×C4#87818yes—
345C3×C4C22×Dic614yes—
346C3×C4C2×#23714yes—
347Dic3—38no—
348Dic3—64no—
349Dic3—64no—
350Dic3—64no—
351Dic3—124no—
352Dic3—128no—
353Dic3—124no—
354C32#307711yescharacteristic, complemented, Sylow
355C23—24no—
356C23—22no—
357C23—42no—
358C23—42no—
359C23D4×C3⋊D311yescharacteristic
360Q8—362no—
361Q8—362no—
362D4—24no—
363D4—22no—
364D4C2×#63414yes—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—91no—
370C2×C4—91no—
371C2×C4—182no—
372C2×C4—181no—
373C2×C4—181no—
374C2×C4—182no—
375C2×C4—364no—
376C2×C4—361no—
377C2×C4—364no—
378C2×C4—362no—
379C2×C4C2×#63412yes—
380C2×C4D4×C3⋊D311yescharacteristic
381C2×C4#383012yes—
382C2×C4C23×C3⋊D311yescharacteristic
383C8—22no—
384C8—182no—
385C2×C3—28no—
386C2×C3—416no—
387C2×C3C2×#87814yes—
388C2×C3D3×AGL(1,ℤ/8)14yes—
389C2×C3#577314yes—
390C22—21no—
391C22—21no—
392C22—24no—
393C22—48no—
394C22—42no—
395C22—42no—
396C22#6408712yes—
397C22C2×D4×C3⋊D311yescharacteristic
398C4—41no—
399C4—41no—
400C4—92no—
401C4—181no—
402C4—181no—
403C4—181no—
404C4—362no—
405C4—361no—
406C4—361no—
407C4#6408712yes—
408C4C22×#63411yescharacteristic
409C4C2×#383011yescharacteristic
410C3#7891714yescomplemented
411C2—22no—
412C2—44no—
413C2C2×#6408711yescharacteristic
414C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
415C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#418C2
socleC22×C32C22×D4
prime radicalC22×C32×D4C22
hypercenter#418C3⋊D3
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #10595988C2semidirect
5. #10592820C2semidirect
6. #10592817C2semidirect
7. #10592694C2semidirect
8. #10592465C2semidirect
9. #10592462C2semidirect
10. #10592460C2semidirect
11. #10592458C2semidirect
26. #64099C22semidirect
27. #64099C22semidirect
28. #64097C22semidirect
29. #64097C22semidirect
38. #63645C22semidirect
39. #63644C22semidirect
40. #63641C22semidirect
41. #63641C22semidirect
42. #63635C22semidirect
43. #63634C22semidirect
58. C2×C32×D4Q8semidirect
171. C2×C3×D4Dic6semidirect
299. C2×D4#634semidirect
354. C32#3077semidirect
410. 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
#105959882
C32×#4182
#105929142
#105928202
#105928172
#105926942
#105924652
#105924622
#105924602
#105924582
#789173