Finite Group Databasebeta

← #11870414

Subgroups — #11870414

Order 1152.

1476 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596187C211yesmaximal, characteristic, complemented
2C4×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×#459C211yesmaximal, characteristic, complemented
4#10592855C212yesmaximal, complemented
5D8×C3⋊Dic3C212yesmaximal, complemented
6#10592771C211yesmaximal, characteristic, complemented
7#10592706C211yesmaximal, characteristic, complemented
8#10592545C211yesmaximal, characteristic, complemented
9#10592532C211yesmaximal, characteristic, complemented
10#10592473C212yesmaximal, complemented
11#10592455C212yesmaximal, complemented
12#80312—34nomaximal
13C2×#3830—21no—
14C2×D4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3—21no—
16C2×C32×D8C2212yes—
17C32×#127C2211yescharacteristic, complemented
18C32×C4×D4C2211yescharacteristic
19#64147—21no—
20#64147C2212yes—
21#64145—21no—
22D4×C3⋊Dic3—21no—
23D4×C3⋊Dic3C2211yescharacteristic
24D4×C3⋊Dic3C2212yescomplemented
25C2×#3753C2212yes—
26C4×#638—21no—
27#64102C2211yescharacteristic
28C4⋊C4×C3⋊D3C2211yescharacteristic
29#64090—21no—
30C22⋊C4×C3⋊D3—21no—
31C4×C4⋊(C3⋊D3)C2211yescharacteristic
32C42×C3⋊D3C2211yescharacteristic
33#64078C2211yescharacteristic, complemented
34C32×C4⋊C8C2211yescharacteristic, complemented
35C32×#102C2212yescomplemented
36#63659C2212yes—
37#63659C2212yescomplemented
38#63648C2212yes—
39#63647C2212yes—
40#63645C2212yescomplemented
41C8×C3⋊Dic3C2212yescomplemented
42#63634C2212yescomplemented
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
44#5716—34no—
45C4×D3×D4—34no—
46C3×#459D314yescomplemented
47#5156—38no—
48Dic3×D8—38no—
49#5072—34no—
50#5007—34no—
51#4846—34no—
52#4833—34no—
53#4774—38no—
54#4756—38no—
55C23×C3⋊D3—21no—
56C2×C32×D4—21no—
57C2×C32×D4—21no—
58C2×C32×D4C2312yes—
59C2×C32×D4C2311yescharacteristic
60C22×C32×C4—21no—
61C2×#638—22no—
62C2×#638—21no—
63C22×C3⋊Dic3—21no—
64C22×C3⋊Dic3—22no—
65#3830—44no—
66D4×C3⋊D3—22no—
67D4×C3⋊D3—22no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3—21no—
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3—44no—
73C2×C4×C3⋊D3D411yescharacteristic
74C2×C4×C3⋊D3D411yescharacteristic
75C2×C4×C3⋊D3C2311yescharacteristic
76C2×#634—21no—
77C32×D8—24no—
78C2×C32×C8C2312yes—
79C32×C4⋊C4C2311yescharacteristic
80C32×C22⋊C4—21no—
81C32×C42C2311yescharacteristic
82#3757—21no—
83#3757—22no—
84#3757—22no—
85#3753—24no—
86#3752—21no—
87#3752—21no—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91#3750—21no—
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3C2311yescharacteristic
95C2×C3⋊(C3⋊C8)C2312yes—
96#3100—91noSylow
97C2×#237—64no—
98C2×D3×D4—34no—
99C22×C4×D3—64no—
100C2×C3×D8C2×D318yes—
101C3×#127C2×D314yescomplemented
102C3×C4×D4C2×D314yes—
103#938—38no—
104#938—64no—
105#936—64no—
106D4×Dic3—34no—
107D4×Dic3—38no—
108D4×Dic3—64no—
109C2×#213—38no—
110C4×#67—64no—
111#893—34no—
112D3×C4⋊C4—34no—
113#67⋊C4—64no—
114D3×C22⋊C4—64no—
115C4×D12—34no—
116C42×D3—34no—
117#869—34no—
118C3×C4⋊C8C2×D314yescomplemented
119C3×#102C2×D318yescomplemented
120#832—38no—
121#832—38no—
122#821—38no—
123(C2×D3)⋊C8—38no—
124#818—38no—
125C8×Dic3—38no—
126#807—38no—
127C4⋊(C3⋊C8)—34no—
128C23×C32—21no—
129C23×C32—22no—
130C22×C3⋊D3—24no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3—42no—
133C22×C3⋊D3—42no—
134C22×C3⋊D3C2×D411yescharacteristic
135C32×D4—21no—
136C32×D4—22no—
137C32×D4—22no—
138C32×D4—42no—
139C32×D4—42no—
140C32×D4#4112yescomplemented
141C2×C32×C4—21no—
142C2×C32×C4—42no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2411yescharacteristic
146#638—24no—
147#638—44no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—42no—
151C2×C3⋊Dic3—44no—
152C2×C3⋊Dic3C2×D411yescharacteristic
153C2×C3⋊Dic3C2×D411yescharacteristic
154C2×C3⋊Dic3C2×D411yescharacteristic
155C4⋊(C3⋊D3)—21no—
156C4⋊(C3⋊D3)#4112yescomplemented
157C4×C3⋊D3—21no—
158C4×C3⋊D3—21no—
159C4×C3⋊D3—41no—
160C4×C3⋊D3—42no—
161C4×C3⋊D3—42no—
162C4×C3⋊D3—42no—
163C4×C3⋊D3D814yescomplemented
164#634—42no—
165C32×C8—22no—
166C3⋊(C3⋊C8)—22no—
167#532—91no—
168C2×C4×D4—91no—
169#480—92no—
170#474—91no—
171#474—91no—
172#459—91no—
173#459C3⋊D311yescharacteristic, complemented
174#447—92no—
175C4×D8—92no—
176C4×D8—92no—
177#431—91no—
178C23×D3—64no—
179C2×C3×D4—24no—
180C2×C3×D4—24no—
181C2×C3×D4C22×D318yes—
182C2×C3×D4C22×D314yes—
183C22×C3×C4—24no—
184C2×#67—64no—
185C2×#67—68no—
186C22×Dic3—64no—
187C22×Dic3—68no—
188#237—1216no—
189D3×D4—68no—
190D3×D4—68no—
191C2×D12—34no—
192C2×C4×D3—34no—
193C2×C4×D3—34no—
194C2×C4×D3—34no—
195C2×C4×D3—64no—
196C2×C4×D3—64no—
197C2×C4×D3—64no—
198C2×C4×D3—1216no—
199C2×Dic6—64no—
200C3×D8—216no—
201C2×C3×C8C22×D318yes—
202C3×C4⋊C4C22×D314yes—
203C3×C22⋊C4—24no—
204C3×C42C22×D314yes—
205#217—64no—
206#217—68no—
207#217—68no—
208#213—616no—
209(C2×D3)⋊C4—64no—
210(C2×D3)⋊C4—64no—
211C4⋊Dic3—38no—
212C4⋊Dic3—34no—
213C4⋊Dic3—64no—
214Dic3⋊C4—64no—
215C4×Dic3—34no—
216C4×Dic3—34no—
217C4×Dic3—34no—
218C2×C3⋊C8—38no—
219C22×C32—22no—
220C22×C32—41no—
221C22×C32—41no—
222C22×C32—42no—
223C22×C32—42no—
224C22×C32—42no—
225C22×C32C22×D411yescharacteristic
226C2×C3⋊D3—21no—
227C2×C3⋊D3—21no—
228C2×C3⋊D3—22no—
229C2×C3⋊D3—48no—
230C2×C3⋊D3—41no—
231C2×C3⋊D3—41no—
232C2×C3⋊D3C2×D812yes—
233C32×C4—21no—
234C32×C4—41no—
235C32×C4C2×D812yes—
236C32×C4C2×#4111yescharacteristic
237C32×C4C2×#4111yescharacteristic
238C3⋊Dic3—21no—
239C3⋊Dic3—21no—
240C3⋊Dic3—42no—
241C3⋊Dic3—41no—
242C3⋊Dic3C2×D812yes—
243C2×#41—181no—
244C22×D4—91no—
245C23×C4—181no—
246C2×D8—92no—
247C2×D8C2×C3⋊D312yes—
248C4⋊Q8—91no—
249#127C2×C3⋊D311yescharacteristic, complemented
250#124—181no—
251#121—92no—
252#121—181no—
253C4×D4—91no—
254C4×D4—92no—
255C4×D4—91no—
256C4×D4—91no—
257C4×D4—181no—
258C4×D4—181no—
259C4×D4—181no—
260C4×D4C2×C3⋊D311yescharacteristic
261C2×C4⋊C4—91no—
262C2×C22⋊C4—181no—
263C2×C42—91no—
264#107—92no—
265#107—92no—
266C4⋊C8—91no—
267C4⋊C8C2×C3⋊D311yescharacteristic, complemented
268#102—92no—
269#102—92no—
270#102—92no—
271#102C2×C3⋊D312yescomplemented
272C22⋊C8—92no—
273C4×C8—92no—
274C23×C3—24no—
275C23×C3—28no—
276C22×D3—34no—
277C22×D3—616no—
278C22×D3—64no—
279C22×D3—128no—
280C22×D3—128no—
281C3×D4—28no—
282C3×D4—24no—
283C3×D4—28no—
284C3×D4—48no—
285C3×D4—48no—
286C3×D4#23718yescomplemented
287C2×C3×C4—24no—
288C2×C3×C4—48no—
289C2×C3×C4D3×D414yes—
290C2×C3×C4D3×D414yes—
291C2×C3×C4C23×D314yes—
292#67—616no—
293#67—1216no—
294C2×Dic3—34no—
295C2×Dic3—34no—
296C2×Dic3—34no—
297C2×Dic3—64no—
298C2×Dic3—68no—
299C2×Dic3—128no—
300C2×Dic3—1216no—
301D12—38no—
302D12—64no—
303C4×D3—316no—
304C4×D3—64no—
305C4×D3—64no—
306C4×D3—128no—
307C4×D3—124no—
308C4×D3—128no—
309C4×D3—128no—
310Dic6—128no—
311C3×C8—28no—
312C3⋊C8—68no—
313C2×C32—42no—
314C2×C32—82no—
315C2×C32#52511yescharacteristic
316C2×C32C22×D811yescharacteristic
317C2×C32#57511yescharacteristic
318C3⋊D3—22no—
319C3⋊D3—42no—
320C24—181no—
321#41—364no—
322C2×Q8—181no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—91no—
326C2×D4—181no—
327C2×D4—182no—
328C2×D4—182no—
329C2×D4—182no—
330C2×D4C22×C3⋊D312yes—
331C2×D4C22×C3⋊D311yescharacteristic
332C22×C4—21no—
333C22×C4—91no—
334C22×C4—91no—
335C22×C4—91no—
336C22×C4—181no—
337C22×C4—181no—
338C22×C4—181no—
339C22×C4—182no—
340C22×C4—181no—
341C22×C4—364no—
342D8—24no—
343D8—184no—
344C2×C8—92no—
345C2×C8C22×C3⋊D312yes—
346C4⋊C4—91no—
347C4⋊C4—92no—
348C4⋊C4—181no—
349C4⋊C4—181no—
350C4⋊C4C22×C3⋊D311yescharacteristic
351C22⋊C4—21no—
352C22⋊C4—181no—
353C22⋊C4—181no—
354C22⋊C4—182no—
355C22⋊C4—182no—
356C22⋊C4—181no—
357C42—91no—
358C42—91no—
359C42—91no—
360C42C22×C3⋊D311yescharacteristic
361C22×C3—28no—
362C22×C3—44no—
363C22×C3—44no—
364C22×C3—48no—
365C22×C3—48no—
366C22×C3—48no—
367C22×C3C2×D3×D414yes—
368C2×D3—38no—
369C2×D3—64no—
370C2×D3—64no—
371C2×D3—68no—
372C2×D3—1232no—
373C2×D3—124no—
374C2×D3—124no—
375C3×C4—24no—
376C3×C4—44no—
377C3×C4D3×D818yes—
378C3×C4C2×#23714yes—
379C3×C4D3×#4114yes—
380Dic3—38no—
381Dic3—64no—
382Dic3—64no—
383Dic3—128no—
384Dic3—124no—
385C32#310011yescharacteristic, complemented, Sylow
386C23—21no—
387C23—22no—
388C23—91no—
389C23—184no—
390C23—181no—
391C23—362no—
392C23—362no—
393Q8—362no—
394D4—22no—
395D4—21no—
396D4—22no—
397D4—42no—
398D4—42no—
399D4—92no—
400D4—184no—
401D4—181no—
402D4—364no—
403D4#383012yescomplemented
404C2×C4—21no—
405C2×C4—42no—
406C2×C4—91no—
407C2×C4—94no—
408C2×C4—91no—
409C2×C4—91no—
410C2×C4—181no—
411C2×C4—181no—
412C2×C4—181no—
413C2×C4—182no—
414C2×C4—361no—
415C2×C4—362no—
416C2×C4—362no—
417C2×C4—362no—
418C2×C4—364no—
419C2×C4—362no—
420C2×C4D4×C3⋊D311yescharacteristic
421C2×C4D4×C3⋊D311yescharacteristic
422C2×C4C23×C3⋊D311yescharacteristic
423C8—22no—
424C8—182no—
425C2×C3—48no—
426C2×C3—88no—
427C2×C3#560614yes—
428C2×C3C2×D3×D814yes—
429C2×C3#577314yes—
430D3—68no—
431D3—128no—
432C22—22no—
433C22—41no—
434C22—41no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—92no—
439C22—181no—
440C22—181no—
441C22—182no—
442C22—368no—
443C22—361no—
444C22—361no—
445C22C2×D4×C3⋊D311yescharacteristic
446C4—21no—
447C4—41no—
448C4—92no—
449C4—181no—
450C4—181no—
451C4—361no—
452C4—362no—
453C4D8×C3⋊D312yes—
454C4C2×#383011yescharacteristic
455C4#41×C3⋊D311yescharacteristic
456C3#8031214yescomplemented
457C2—42no—
458C2—82no—
459C2—182no—
460C2—362no—
461C2#1059607711yescharacteristic
462C2C2×D8×C3⋊D311yescharacteristic
463C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#459C2
socleC22×C32C22×D4
hypercenter#459C3⋊D3
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #10596187C2semidirect
2. C4×D4×C3⋊D3C2semidirect
3. C32×#459C2semidirect
4. #10592855C2semidirect
5. D8×C3⋊Dic3C2semidirect
6. #10592771C2semidirect
7. #10592706C2semidirect
8. #10592545C2semidirect
9. #10592532C2semidirect
10. #10592473C2semidirect
11. #10592455C2semidirect
17. C32×#127C22semidirect
24. D4×C3⋊Dic3C22semidirect
33. #64078C22semidirect
34. C32×C4⋊C8C22semidirect
35. C32×#102C22semidirect
37. #63659C22semidirect
40. #63645C22semidirect
41. C8×C3⋊Dic3C22semidirect
42. #63634C22semidirect
43. C4⋊(C3⋊(C3⋊C8))C22semidirect
46. C3×#459D3semidirect
101. C3×#127C2×D3semidirect
118. C3×C4⋊C8C2×D3semidirect
119. C3×#102C2×D3semidirect
140. C32×D4#41semidirect
156. C4⋊(C3⋊D3)#41semidirect
163. C4×C3⋊D3D8semidirect
173. #459C3⋊D3semidirect
249. #127C2×C3⋊D3semidirect
267. C4⋊C8C2×C3⋊D3semidirect
271. #102C2×C3⋊D3semidirect
286. C3×D4#237semidirect
385. C32#3100semidirect
403. D4#3830semidirect
456. C3#80312semidirect

Maximal subgroups

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

subgroupindex
#105961872
C4×D4×C3⋊D32
C32×#4592
#105928552
D8×C3⋊Dic32
#105927712
#105927062
#105925452
#105925322
#105924732
#105924552
#803123