Finite Group Databasebeta

← #11873440

Subgroups — #11873440

Order 1152.

905 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595432C211yesmaximal, characteristic
2#10594482C211yesmaximal, characteristic, complemented
3C3⋊D3×#103C211yesmaximal, characteristic, complemented
4C3×#4800C212yesmaximal, complemented
5#10591614C212yesmaximal, complemented
6#10591552C211yesmaximal, characteristic, complemented
7#10590940C211yesmaximal, characteristic
8#10590863C212yesmaximal, complemented
9C8×#624C211yesmaximal, characteristic, complemented
10#10590593C211yesmaximal, characteristic
11#10590533C212yesmaximal, complemented
12D3×#488—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×#3802C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C4⋊C4×C3⋊D3C2211yescharacteristic
17C3×#947C2212yes—
18C3×#890C2212yescomplemented
19#63921—21no—
20#63921—21no—
21#63913—22no—
22#63900—21no—
23#63900C2211yescharacteristic
24#63883—21no—
25C4×#624C2211yescharacteristic
26#63869C2212yescomplemented
27#63860C2212yes—
28#63847—22no—
29C2×#3710C2211yescharacteristic
30C32×#103C2211yescharacteristic, complemented
31#63662C2211yescharacteristic, complemented
32#63643C2211yescharacteristic, complemented
33#63637C2211yescharacteristic, complemented
34C3×#835C2212yescomplemented
35C3×#821C2212yes—
36C3×C8×Dic3C2212yescomplemented
37C3×#809C2212yes—
38#63567C2212yescomplemented
39#63563C2212yes—
40#63562C2212yes—
41Dic3×C3⋊C8C2212yescomplemented
42D3×#125—32no—
43D3×#124—32no—
44C3×#488—32no—
45#5068—32no—
46#5056—32no—
47D3×#103—32no—
48D3×#103—32no—
49D3×#103—61no—
50#4800—32no—
51#4800D312yescomplemented
52D3×#102—32no—
53D3×#102—32no—
54#4768—32no—
55#4768—32no—
56#4697—32no—
57C4×D3×C8—32no—
58C22×D32—21no—
59C2×C32×Q8C2311yescharacteristic
60Q8×C3⋊D3—22no—
61Q8×C3⋊D3—22no—
62C2×C4×C3⋊D3—21no—
63C2×C4×C3⋊D3—21no—
64C2×C4×C3⋊D3C2311yescharacteristic
65C2×#634—21no—
66C2×#634C2311yescharacteristic
67C2×C3×D12C2312yes—
68C2×#625—21no—
69C2×#624—21no—
70C2×#624D411yescharacteristic
71C2×#624D411yescharacteristic
72#3802—22no—
73#3802—22no—
74C2×C32×C8C2311yescharacteristic
75C32×C4⋊C4C2311yescharacteristic
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77#3750—21no—
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C8×C3⋊D3—22no—
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4—22no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3C2312yes—
86C2×C3×C3⋊C8C2312yes—
87#3724—21no—
88#3724—22no—
89Dic3⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92Dic32D412yes—
93#3710—22no—
94C2×#488—91noSylow
95C2×D3×Q8—32no—
96C2×D3×Q8—61no—
97C2×D3×D4—32no—
98C3×#125—32no—
99C3×#124—32no—
100#947C2×D312yes—
101#936—32no—
102C2×D3×C8—32no—
103C2×D3×C8—32no—
104C2×D3×C8—61no—
105D3×C4⋊C4—32no—
106D3×C4⋊C4—32no—
107D3×C4⋊C4—61no—
108D3×C4⋊C4—62no—
109D3×C4⋊C4—62no—
110#890—32no—
111#890C2×D312yescomplemented
112#889—62no—
113#889—62no—
114#885—62no—
115#885—62no—
116D3×C22⋊C4—62no—
117D3×C22⋊C4—62no—
118#875—32no—
119C42×D3—32no—
120#870—32no—
121C3×#103—21no—
122C3×#103—32no—
123C3×#103C2×D312yescomplemented
124C3×#102—32no—
125C3×#102—32no—
126C3×C4×C8—32no—
127#835—32no—
128#835—61no—
129#835C2×D312yescomplemented
130#832—32no—
131#832—32no—
132#821—32no—
133#821C2×D312yes—
134#816—32no—
135#816—32no—
136#816—61no—
137C8×Dic3—32no—
138C8×Dic3C2×D312yescomplemented
139#810—32no—
140#810—32no—
141#810—61no—
142#809—32no—
143#809C2×D312yes—
144C4×C3⋊C8—32no—
145C22×C3⋊D3C2×D411yescharacteristic
146C22×C3×D3—22no—
147C2×D32—42no—
148C2×D32—42no—
149C2×D32—42no—
150C32×Q8—21no—
151C32×Q8—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4C2411yescharacteristic
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3C2×D411yescharacteristic
158C4×C3⋊D3—42no—
159C4×C3⋊D3—42no—
160C4×C3⋊D3#4112yes—
161C4×C3⋊D3#4112yes—
162#634—21no—
163#634—21no—
164#634—42no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3C2×D412yes—
167C2×C3×Dic3C2×D412yes—
168C3×D12—22no—
169C3×D12—22no—
170#625—42no—
171#624—22no—
172#624—22no—
173#624—42no—
174C32×C8—21no—
175C3⋊(C3⋊C8)—21no—
176C3×C3⋊C8—22no—
177C2×#125—91no—
178C2×#124—91no—
179#488—32no—
180#488—92no—
181#488—92no—
182#488—92no—
183C2×#103—91no—
184C2×#103—91no—
185C2×#102—91no—
186C2×#102—91no—
187C2×C4×C8—91no—
188C23×D3—62no—
189C2×C3×Q8—21no—
190C2×C3×Q8C22×D312yes—
191C2×C3×D4—32no—
192C2×#67—62no—
193D3×Q8—64no—
194D3×Q8—64no—
195D3×Q8—64no—
196D3×Q8—122no—
197D3×D4—64no—
198D3×D4—64no—
199C2×D12C22×D312yes—
200C2×C4×D3—32no—
201C2×C4×D3—32no—
202C2×C4×D3—32no—
203C2×C4×D3—61no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C4×D3—121no—
208C2×C4×D3—121no—
209C2×Dic6—32no—
210C2×Dic6—61no—
211C2×Dic6—62no—
212C2×Dic6—121no—
213C2×C3×C8—21no—
214C2×C3×C8—32no—
215C2×C3×C8C22×D312yes—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—32no—
218C3×C4⋊C4—62no—
219C3×C4⋊C4—62no—
220C3×C4⋊C4C22×D312yes—
221C3×C22⋊C4—62no—
222C3×C22⋊C4—62no—
223C3×C42—32no—
224#217—62no—
225#217—62no—
226(C2×D3)⋊C4—22no—
227(C2×D3)⋊C4—22no—
228(C2×D3)⋊C4—62no—
229(C2×D3)⋊C4—62no—
230C4⋊Dic3—22no—
231C4⋊Dic3—32no—
232C4⋊Dic3—61no—
233C4⋊Dic3—62no—
234C4⋊Dic3C22×D312yes—
235Dic3⋊C4—22no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—121no—
242C4×Dic3—32no—
243C4×Dic3—32no—
244C4×Dic3C22×D312yes—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8C22×D312yes—
248D3×C8—64no—
249D3×C8—64no—
250D3×C8—122no—
251C22×C32C22×D411yescharacteristic
252C2×C3⋊D3#12412yes—
253C2×C3⋊D3#13512yes—
254C2×C3⋊D3#13512yes—
255C2×C3×D3—42no—
256C2×C3×D3—42no—
257C2×C3×D3—42no—
258D32—84no—
259C32×C4—41no—
260C32×C4—41no—
261C32×C4C2×#4111yescharacteristic
262C32×C4C2×#4111yescharacteristic
263C3⋊Dic3—41no—
264C3⋊Dic3—41no—
265C3⋊Dic3#12412yes—
266C3×Dic3—22no—
267C3×Dic3—22no—
268C3×Dic3—42no—
269C22×Q8—91no—
270C22×D4—91no—
271C22×C8—91no—
272C22×C8—91no—
273#125—32no—
274#125—92no—
275#125—182no—
276#124—32no—
277#124—92no—
278#124—182no—
279C2×C4⋊C4—91no—
280C2×C4⋊C4—91no—
281C2×C4⋊C4—181no—
282C2×C4⋊C4—181no—
283C2×C22⋊C4—181no—
284C2×C22⋊C4—181no—
285C2×C42—91no—
286#103—32no—
287#103—92no—
288#103—91no—
289#103—91no—
290#103—91no—
291#103D3211yescharacteristic, complemented
292#102—32no—
293#102—32no—
294#102—92no—
295#102—92no—
296C4×C8—32no—
297C4×C8—92no—
298C23×C3—62no—
299C22×D3—22no—
300C22×D3—32no—
301C22×D3—61no—
302C22×D3—124no—
303C22×D3—124no—
304C22×D3—124no—
305C3×Q8—22no—
306C3×Q8—22no—
307C3×Q8—22no—
308C3×Q8—41no—
309C3×D4—62no—
310C3×D4—62no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—21no—
314C2×C3×C4—32no—
315C2×C3×C4—32no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—62no—
319C2×C3×C4C23×D312yes—
320#67—124no—
321C2×Dic3—22no—
322C2×Dic3—32no—
323C2×Dic3—61no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3D3×D412yes—
329C2×Dic3D3×D412yes—
330D12—22no—
331D12—22no—
332C4×D3—34no—
333C4×D3—34no—
334C4×D3—62no—
335C4×D3—62no—
336C4×D3—64no—
337C4×D3—64no—
338C4×D3—124no—
339C4×D3—124no—
340C4×D3—124no—
341C4×D3—124no—
342C4×D3—242no—
343Dic6—62no—
344Dic6—62no—
345Dic6—62no—
346Dic6—121no—
347Dic6—124no—
348Dic6—124no—
349C3×C8—22no—
350C3×C8—41no—
351C3×C8—62no—
352C3⋊C8—22no—
353C3⋊C8—62no—
354C3⋊C8—121no—
355C2×C32C2×#12411yescharacteristic
356C2×C32C2×#13511yescharacteristic
357C2×C32C2×#13511yescharacteristic
358C3⋊D3#48814yescomplemented
359C3×D3—82no—
360C24—181no—
361C2×Q8—91no—
362C2×Q8—181no—
363C2×Q8—182no—
364C2×Q8—182no—
365C2×Q8C2×D3211yescharacteristic
366C2×D4—32no—
367C2×D4—182no—
368C2×D4—182no—
369C2×D4—181no—
370C22×C4—91no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—181no—
374C22×C4—181no—
375C22×C4—181no—
376C2×C8—32no—
377C2×C8—91no—
378C2×C8—182no—
379C2×C8—182no—
380C2×C8C2×D3211yescharacteristic
381C4⋊C4—32no—
382C4⋊C4—62no—
383C4⋊C4—62no—
384C4⋊C4—91no—
385C4⋊C4—181no—
386C4⋊C4—182no—
387C4⋊C4—182no—
388C4⋊C4—181no—
389C4⋊C4C2×D3211yescharacteristic
390C22⋊C4—62no—
391C22⋊C4—62no—
392C22⋊C4—182no—
393C22⋊C4—182no—
394C42—32no—
395C42—92no—
396C22×C3—21no—
397C22×C3—122no—
398C22×C3—122no—
399C22×C3—122no—
400C22×C3C2×D3×D412yes—
401C2×D3—34no—
402C2×D3—34no—
403C2×D3—34no—
404C2×D3—42no—
405C2×D3—42no—
406C2×D3—42no—
407C2×D3—62no—
408C2×D3—62no—
409C2×D3—62no—
410C2×D3—248no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—42no—
414C3×C4—42no—
415C3×C4—42no—
416C3×C4—62no—
417C3×C4—62no—
418C3×C4—81no—
419C3×C4—122no—
420C3×C4D3×#4112yes—
421C3×C4D3×#4112yes—
422Dic3—22no—
423Dic3—22no—
424Dic3—34no—
425Dic3—42no—
426Dic3—62no—
427Dic3—122no—
428Dic3—122no—
429Dic3—122no—
430Dic3—241no—
431C32C2×#48811yescharacteristic, complemented, Sylow
432C23—62no—
433C23—91no—
434C23—362no—
435C23—362no—
436C23—362no—
437Q8—21no—
438Q8—21no—
439Q8—181no—
440Q8—181no—
441Q8—362no—
442D4—62no—
443D4—62no—
444D4—362no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—62no—
450C2×C4—91no—
451C2×C4—92no—
452C2×C4—92no—
453C2×C4—182no—
454C2×C4—182no—
455C2×C4—181no—
456C2×C4—181no—
457C2×C4—362no—
458C2×C4—362no—
459C2×C4—362no—
460C2×C4C22×D3211yescharacteristic
461C8—21no—
462C8—62no—
463C8—181no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—242no—
468C2×C3D3×#12412yes—
469C2×C3D3×#13512yes—
470C2×C3D3×#13512yes—
471D3—38no—
472D3—64no—
473D3—82no—
474C22—92no—
475C22—92no—
476C22—92no—
477C22—122no—
478C22—122no—
479C22—122no—
480C22—724no—
481C22D32×D411yescharacteristic
482C4—41no—
483C4—41no—
484C4—62no—
485C4—62no—
486C4—92no—
487C4—122no—
488C4—361no—
489C4—361no—
490C4#6430611yescharacteristic
491C4#6431211yescharacteristic
492C3—21no—
493C3D3×#48812yescomplemented
494C2—94no—
495C2—242no—
496C2#1059428811yescharacteristic
497C2#1059474711yescharacteristic
498C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenter#103D32
hypocenterC32C2×#488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594482C2semidirect
3. C3⋊D3×#103C2semidirect
4. C3×#4800C2semidirect
5. #10591614C2semidirect
6. #10591552C2semidirect
8. #10590863C2semidirect
9. C8×#624C2semidirect
11. #10590533C2semidirect
18. C3×#890C22semidirect
26. #63869C22semidirect
30. C32×#103C22semidirect
31. #63662C22semidirect
32. #63643C22semidirect
33. #63637C22semidirect
34. C3×#835C22semidirect
36. C3×C8×Dic3C22semidirect
38. #63567C22semidirect
41. Dic3×C3⋊C8C22semidirect
51. #4800D3semidirect
111. #890C2×D3semidirect
123. C3×#103C2×D3semidirect
129. #835C2×D3semidirect
138. C8×Dic3C2×D3semidirect
291. #103D32semidirect
358. C3⋊D3#488semidirect
431. C32C2×#488semidirect
493. C3D3×#488semidirect

Maximal subgroups

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

subgroupindex
#105954322
#105944822
C3⋊D3×#1032
C3×#48002
#105916142
#105915522
#105909402
#105908632
C8×#6242
#105905932
#105905332
D3×#4883