Finite Group Databasebeta

← #11873438

Subgroups — #11873438

Order 1152.

925 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595170C211yesmaximal, characteristic
2#10594482C211yesmaximal, characteristic, complemented
3C3⋊D3×#102C211yesmaximal, characteristic
4C3×#4768C212yesmaximal, complemented
5#10591478C212yesmaximal, complemented
6#10591416C211yesmaximal, characteristic
7#10590872C212yesmaximal, complemented
8#10590672C211yesmaximal, characteristic, complemented
9C8×#624C211yesmaximal, characteristic, complemented
10#10590601C211yesmaximal, characteristic, complemented
11#10590537C212yesmaximal, complemented
12D3×#488—32nomaximal
13C2×D4×C3⋊D3C2211yescharacteristic
14C2×#3797C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C4⋊C4×C3⋊D3C2211yescharacteristic
17C3×#936C2212yes—
18C3×#890C2212yescomplemented
19#63974—21no—
20#63974—21no—
21#63953—22no—
22#63900—21no—
23#63900C2211yescharacteristic
24#63883—21no—
25C4×#624C2211yescharacteristic
26#63869C2212yescomplemented
27#63864C2212yes—
28#63847—22no—
29C2×#3710C2211yescharacteristic
30C32×#102C2211yescharacteristic
31#63659C2211yescharacteristic
32#63648C2211yescharacteristic
33#63636C2211yescharacteristic
34C3×#832C2212yes—
35C3×#816C2212yescomplemented
36C3×C8×Dic3C2212yescomplemented
37C3×#810C2212yescomplemented
38#63566C2212yescomplemented
39#63565C2212yescomplemented
40#63564C2212yes—
41Dic3×C3⋊C8C2212yescomplemented
42D3×#125—32no—
43D3×#124—32no—
44C3×#488—32no—
45#5068—32no—
46#5056—32no—
47D3×#103—32no—
48D3×#103—32no—
49#4800—32no—
50#4800—32no—
51D3×#102—32no—
52D3×#102—32no—
53D3×#102—61no—
54#4768—32no—
55#4768D312yescomplemented
56#4697—32no—
57C4×D3×C8—32no—
58C23×C3⋊D3—21no—
59C2×C32×D4C2311yescharacteristic
60C2×#638—21no—
61D4×C3⋊D3—22no—
62D4×C3⋊D3—22no—
63C2×C4⋊(C3⋊D3)C2311yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×C3×Dic6C2312yes—
67C2×#627—21no—
68C2×#624—21no—
69C2×#624—21no—
70C2×#624D411yescharacteristic
71C2×#624D411yescharacteristic
72#3797—22no—
73#3797—22no—
74C2×C32×C8C2311yescharacteristic
75C32×C4⋊C4C2311yescharacteristic
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77#3750—21no—
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C8×C3⋊D3—22no—
80C3×#217—22no—
81C3×#217—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#3722—22no—
91#3722—22no—
92Dic32D412yes—
93#3710—22no—
94C2×#488—91noSylow
95C2×D3×Q8—32no—
96C2×D3×D4—32no—
97C2×D3×D4—61no—
98C3×#125—32no—
99C3×#124—32no—
100#947—32no—
101#936C2×D312yes—
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—32no—
122C3×#103—32no—
123C3×#102—21no—
124C3×#102—32no—
125C3×#102C2×D312yes—
126C3×C4×C8—32no—
127#835—32no—
128#835—32no—
129#832—32no—
130#832—61no—
131#832C2×D312yes—
132#821—32no—
133#821—32no—
134#821—61no—
135#816—32no—
136#816C2×D312yescomplemented
137C8×Dic3—32no—
138C8×Dic3C2×D312yescomplemented
139#810—32no—
140#810C2×D312yescomplemented
141#809—32no—
142#809—32no—
143#809—61no—
144C4×C3⋊C8—32no—
145C23×C32—21no—
146C22×C3⋊D3—21no—
147C22×C3⋊D3—42no—
148C22×C3⋊D3—42no—
149C22×C3⋊D3—42no—
150C22×C3⋊D3C2×D411yescharacteristic
151C32×D4—21no—
152C32×D4—21no—
153C2×C32×C4—21no—
154C2×C32×C4C2411yescharacteristic
155#638—42no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3C2×D411yescharacteristic
158C4⋊(C3⋊D3)—21no—
159C4⋊(C3⋊D3)—21no—
160C4×C3⋊D3—42no—
161C4×C3⋊D3#4112yes—
162C4×C3⋊D3#4112yes—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C2×D412yes—
166C2×C3×Dic3C2×D412yes—
167C3×Dic6—22no—
168C3×Dic6—22no—
169#627—42no—
170#624—22no—
171#624—22no—
172#624—42no—
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—
189C23×D3—121no—
190C2×C3×Q8—32no—
191C2×C3×D4—21no—
192C2×C3×D4C22×D312yes—
193C2×#67—62no—
194C2×#67—121no—
195D3×Q8—64no—
196D3×Q8—64no—
197D3×D4—64no—
198D3×D4—64no—
199D3×D4—64no—
200D3×D4—122no—
201C2×D12—32no—
202C2×D12—61no—
203C2×C4×D3—32no—
204C2×C4×D3—32no—
205C2×C4×D3—32no—
206C2×C4×D3—61no—
207C2×C4×D3—62no—
208C2×C4×D3—62no—
209C2×C4×D3—62no—
210C2×C4×D3—121no—
211C2×Dic6—62no—
212C2×Dic6C22×D312yes—
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—22no—
225#217—22no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—62no—
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×C32—41no—
252C22×C32—41no—
253C22×C32—41no—
254C22×C32C22×D411yescharacteristic
255C2×C3⋊D3—41no—
256C2×C3⋊D3—41no—
257C2×C3⋊D3—41no—
258C2×C3⋊D3—84no—
259C2×C3⋊D3#12412yes—
260C2×C3⋊D3#13512yes—
261C2×C3⋊D3#13512yes—
262C32×C4—41no—
263C32×C4C2×#4111yescharacteristic
264C32×C4C2×#4111yescharacteristic
265C3⋊Dic3—41no—
266C3⋊Dic3#12412yes—
267C3×Dic3—22no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C3×Dic3—42no—
271C22×Q8—91no—
272C22×D4—91no—
273C22×C8—91no—
274C22×C8—91no—
275#125—32no—
276#125—92no—
277#125—182no—
278#124—32no—
279#124—92no—
280#124—182no—
281C2×C4⋊C4—91no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—181no—
284C2×C4⋊C4—181no—
285C2×C22⋊C4—181no—
286C2×C22⋊C4—181no—
287C2×C42—91no—
288#103—32no—
289#103—32no—
290#103—92no—
291#103—92no—
292#102—32no—
293#102—92no—
294#102—91no—
295#102—91no—
296#102—91no—
297#102D3211yescharacteristic
298C4×C8—32no—
299C4×C8—92no—
300C23×C3—22no—
301C23×C3—41no—
302C22×D3—32no—
303C22×D3—61no—
304C22×D3—62no—
305C22×D3—121no—
306C22×D3—124no—
307C22×D3—124no—
308C22×D3—124no—
309C22×D3—124no—
310C22×D3—242no—
311C22×D3—242no—
312C3×Q8—62no—
313C3×Q8—62no—
314C3×D4—22no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—41no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—32no—
321C2×C3×C4—32no—
322C2×C3×C4—41no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4C23×D312yes—
326#67—124no—
327#67—124no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—32no—
331C2×Dic3—61no—
332C2×Dic3—62no—
333C2×Dic3—121no—
334C2×Dic3D3×D412yes—
335C2×Dic3D3×D412yes—
336D12—62no—
337D12—62no—
338D12—62no—
339D12—121no—
340C4×D3—34no—
341C4×D3—34no—
342C4×D3—62no—
343C4×D3—62no—
344C4×D3—64no—
345C4×D3—64no—
346C4×D3—124no—
347C4×D3—124no—
348C4×D3—124no—
349C4×D3—242no—
350Dic6—22no—
351Dic6—22no—
352Dic6—124no—
353C3×C8—22no—
354C3×C8—41no—
355C3×C8—62no—
356C3⋊C8—22no—
357C3⋊C8—62no—
358C3⋊C8—121no—
359C2×C32—81no—
360C2×C32C2×#12411yescharacteristic
361C2×C32C2×#13511yescharacteristic
362C2×C32C2×#13511yescharacteristic
363C3⋊D3—81no—
364C3⋊D3#48814yescomplemented
365C24—181no—
366C2×Q8—32no—
367C2×Q8—181no—
368C2×Q8—182no—
369C2×Q8—182no—
370C2×D4—91no—
371C2×D4—182no—
372C2×D4—182no—
373C2×D4—181no—
374C2×D4C2×D3211yescharacteristic
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—181no—
379C22×C4—181no—
380C22×C4—181no—
381C2×C8—32no—
382C2×C8—91no—
383C2×C8—182no—
384C2×C8—182no—
385C2×C8C2×D3211yescharacteristic
386C4⋊C4—32no—
387C4⋊C4—62no—
388C4⋊C4—62no—
389C4⋊C4—91no—
390C4⋊C4—181no—
391C4⋊C4—182no—
392C4⋊C4—182no—
393C4⋊C4—181no—
394C4⋊C4C2×D3211yescharacteristic
395C22⋊C4—62no—
396C22⋊C4—62no—
397C22⋊C4—182no—
398C22⋊C4—182no—
399C42—32no—
400C42—92no—
401C22×C3—21no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—81no—
407C22×C3—81no—
408C22×C3C2×D3×D412yes—
409C2×D3—34no—
410C2×D3—34no—
411C2×D3—34no—
412C2×D3—62no—
413C2×D3—62no—
414C2×D3—62no—
415C2×D3—122no—
416C2×D3—122no—
417C2×D3—122no—
418C2×D3—122no—
419C2×D3—241no—
420C2×D3—241no—
421C2×D3—248no—
422C2×D3—248no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—42no—
426C3×C4—62no—
427C3×C4—62no—
428C3×C4—81no—
429C3×C4—122no—
430C3×C4—122no—
431C3×C4D3×#4112yes—
432C3×C4D3×#4112yes—
433Dic3—22no—
434Dic3—22no—
435Dic3—34no—
436Dic3—42no—
437Dic3—42no—
438Dic3—62no—
439Dic3—122no—
440Dic3—241no—
441C32C2×#48811yescharacteristic, complemented, Sylow
442C23—21no—
443C23—91no—
444C23—181no—
445C23—362no—
446C23—362no—
447C23—362no—
448Q8—62no—
449Q8—62no—
450Q8—362no—
451D4—21no—
452D4—21no—
453D4—181no—
454D4—181no—
455D4—362no—
456C2×C4—21no—
457C2×C4—32no—
458C2×C4—32no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—91no—
462C2×C4—92no—
463C2×C4—92no—
464C2×C4—182no—
465C2×C4—182no—
466C2×C4—181no—
467C2×C4—362no—
468C2×C4—362no—
469C2×C4—362no—
470C2×C4C22×D3211yescharacteristic
471C8—21no—
472C8—62no—
473C8—181no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—82no—
478C2×C3—82no—
479C2×C3D3×#12412yes—
480C2×C3D3×#13512yes—
481C2×C3D3×#13512yes—
482D3—38no—
483D3—64no—
484D3—242no—
485D3—242no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—92no—
490C22—92no—
491C22—92no—
492C22—361no—
493C22—361no—
494C22—361no—
495C22—724no—
496C22D32×D411yescharacteristic
497C4—41no—
498C4—62no—
499C4—62no—
500C4—92no—
501C4—122no—
502C4—122no—
503C4—361no—
504C4#6430611yescharacteristic
505C4#6431211yescharacteristic
506C3—21no—
507C3D3×#48812yescomplemented
508C2—81no—
509C2—94no—
510C2—721no—
511C2#1059428811yescharacteristic
512C2#1059473011yescharacteristic
513C2#1059474711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#102D32
hypocenterC32C2×#488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594482C2semidirect
4. C3×#4768C2semidirect
5. #10591478C2semidirect
7. #10590872C2semidirect
8. #10590672C2semidirect
9. C8×#624C2semidirect
10. #10590601C2semidirect
11. #10590537C2semidirect
18. C3×#890C22semidirect
26. #63869C22semidirect
35. C3×#816C22semidirect
36. C3×C8×Dic3C22semidirect
37. C3×#810C22semidirect
38. #63566C22semidirect
39. #63565C22semidirect
41. Dic3×C3⋊C8C22semidirect
55. #4768D3semidirect
111. #890C2×D3semidirect
136. #816C2×D3semidirect
138. C8×Dic3C2×D3semidirect
140. #810C2×D3semidirect
364. C3⋊D3#488semidirect
441. C32C2×#488semidirect
507. C3D3×#488semidirect

Maximal subgroups

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

subgroupindex
#105951702
#105944822
C3⋊D3×#1022
C3×#47682
#105914782
#105914162
#105908722
#105906722
C8×#6242
#105906012
#105905372
D3×#4883