Finite Group Databasebeta

← #11873537

Subgroups — #11873537

Order 1152.

953 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595432C211yesmaximal, characteristic
2#10594374C211yesmaximal, characteristic, complemented
3C3⋊D3×#103C211yesmaximal, characteristic, complemented
4C3×#4794C212yesmaximal, complemented
5#10591624C212yesmaximal, complemented
6#10591552C211yesmaximal, characteristic, complemented
7#10590940C211yesmaximal, characteristic
8#10590895C212yesmaximal, complemented
9#10590668C211yesmaximal, characteristic, complemented
10#10590593C211yesmaximal, characteristic
11#10590531C212yesmaximal, complemented
12D3×#489—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×#3802C2211yescharacteristic
15C2×#3797—21no—
16C2×C8×C3⋊D3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2211yescharacteristic
18C3×#947C2212yes—
19C3×#888C2212yescomplemented
20#63921—21no—
21#63921—21no—
22#63918C2212yescomplemented
23#63913—22no—
24#63900C2211yescharacteristic
25#63883—21no—
26C4×#624C2211yescharacteristic
27#63860C2212yes—
28#63839—22no—
29C2×#3710C2211yescharacteristic
30C32×#103C2211yescharacteristic, complemented
31#63662C2211yescharacteristic, complemented
32#63643C2211yescharacteristic, complemented
33#63637C2211yescharacteristic, complemented
34C3×#835C2212yescomplemented
35C3×#821C2212yes—
36C3×#815C2212yescomplemented
37C3×#809C2212yes—
38#63567C2212yescomplemented
39#63563C2212yes—
40#63562C2212yes—
41#63554C2212yescomplemented
42D3×C4⋊Q8—32no—
43D3×#124—32no—
44C3×#489—32no—
45#5089—32no—
46#5055—32no—
47D3×#103—32no—
48D3×#103—32no—
49D3×#103—61no—
50#4794—32no—
51#4794D312yescomplemented
52D3×#102—32no—
53D3×#102—32no—
54#4765—32no—
55#4765—32no—
56#4714—32no—
57D3×#97—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×C3×Dic6—22no—
69C2×#627—22no—
70C2×#625—21no—
71C2×#624—21no—
72C2×#624D411yescharacteristic
73C2×#624D411yescharacteristic
74#3802—22no—
75#3802—22no—
76#3797—44no—
77C2×C32×C8C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—21no—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C8×C3⋊D3—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3C2312yes—
86C3×Dic3⋊C4—22no—
87C3×C4×Dic3C2312yes—
88C2×C3×C3⋊C8C2312yes—
89#3724—21no—
90Dic3⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93Dic32D412yes—
94#3710—22no—
95C2×#489—91noSylow
96C2×D3×Q8—32no—
97C2×D3×Q8—61no—
98C2×D3×Q8—62no—
99C2×D3×D4—32no—
100C3×C4⋊Q8—32no—
101C3×#124—32no—
102#947C2×D312yes—
103#944—62no—
104#936—32no—
105C2×D3×C8—32no—
106C2×D3×C8—32no—
107C2×D3×C8—61no—
108D3×C4⋊C4—32no—
109D3×C4⋊C4—32no—
110D3×C4⋊C4—61no—
111D3×C4⋊C4—62no—
112#888—32no—
113#888—62no—
114#888C2×D312yescomplemented
115#885—62no—
116#885—62no—
117D3×C22⋊C4—62no—
118D3×C22⋊C4—62no—
119#875—32no—
120C42×D3—32no—
121#869—32no—
122C3×#103—21no—
123C3×#103—32no—
124C3×#103C2×D312yescomplemented
125C3×#102—32no—
126C3×#102—32no—
127C3×#97—32no—
128#835—32no—
129#835—61no—
130#835C2×D312yescomplemented
131#832—32no—
132#832—32no—
133#821—32no—
134#821C2×D312yes—
135#816—32no—
136#816—32no—
137#816—61no—
138#815—32no—
139#815C2×D312yescomplemented
140#810—32no—
141#810—32no—
142#810—61no—
143#809—32no—
144#809C2×D312yes—
145#803—32no—
146C22×C3⋊D3C2×D411yescharacteristic
147C22×C3×D3—22no—
148C2×D32—42no—
149C2×D32—42no—
150C2×D32—42no—
151C32×Q8—21no—
152C32×Q8—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3C2×D411yescharacteristic
159C4×C3⋊D3—42no—
160C4×C3⋊D3—42no—
161C4×C3⋊D3#4112yes—
162C4×C3⋊D3#4112yes—
163#634—21no—
164#634—21no—
165#634—42no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3C2×D412yes—
168C2×C3×Dic3C2×D412yes—
169C3×D12—22no—
170C3×D12—22no—
171C3×Dic6—44no—
172#627—44no—
173#625—42no—
174#624—22no—
175#624—22no—
176#624—42no—
177C32×C8—21no—
178C3⋊(C3⋊C8)—21no—
179C3×C3⋊C8—22no—
180C2×C4⋊Q8—91no—
181C2×#124—91no—
182#489—32no—
183#489—92no—
184#489—92no—
185#489—92no—
186C2×#103—91no—
187C2×#103—91no—
188C2×#102—91no—
189C2×#102—91no—
190C2×#97—91no—
191C23×D3—62no—
192C2×C3×Q8—21no—
193C2×C3×Q8—62no—
194C2×C3×Q8C22×D312yes—
195C2×C3×D4—32no—
196C2×#67—62no—
197D3×Q8—64no—
198D3×Q8—64no—
199D3×Q8—64no—
200D3×Q8—122no—
201D3×Q8—128no—
202D3×D4—64no—
203D3×D4—64no—
204C2×D12C22×D312yes—
205C2×C4×D3—32no—
206C2×C4×D3—32no—
207C2×C4×D3—32no—
208C2×C4×D3—61no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—121no—
213C2×C4×D3—121no—
214C2×Dic6—22no—
215C2×Dic6—32no—
216C2×Dic6—61no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C2×Dic6—121no—
221C2×C3×C8—21no—
222C2×C3×C8—32no—
223C2×C3×C8C22×D312yes—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4C22×D312yes—
228C3×C22⋊C4—62no—
229C3×C22⋊C4—62no—
230C3×C42—32no—
231#217—62no—
232#217—62no—
233(C2×D3)⋊C4—22no—
234(C2×D3)⋊C4—22no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237C4⋊Dic3—32no—
238C4⋊Dic3—61no—
239C4⋊Dic3—62no—
240C4⋊Dic3C22×D312yes—
241Dic3⋊C4—22no—
242Dic3⋊C4—62no—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245Dic3⋊C4—121no—
246C4×Dic3—32no—
247C4×Dic3—32no—
248C4×Dic3C22×D312yes—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8C22×D312yes—
252D3×C8—64no—
253D3×C8—64no—
254D3×C8—122no—
255C22×C32C22×D411yescharacteristic
256C2×C3⋊D3#12412yes—
257C2×C3⋊D3AGL(1,ℤ/8)12yes—
258C2×C3⋊D3#13712yes—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262D32—84no—
263C32×C4—41no—
264C32×C4—41no—
265C32×C4C2×#4111yescharacteristic
266C32×C4C2×#4111yescharacteristic
267C3⋊Dic3—41no—
268C3⋊Dic3—41no—
269C3⋊Dic3#12412yes—
270C3×Dic3—22no—
271C3×Dic3—22no—
272C3×Dic3—42no—
273C22×Q8—91no—
274C22×Q8—181no—
275C22×D4—91no—
276C22×C8—91no—
277C22×C8—91no—
278C4⋊Q8—32no—
279C4⋊Q8—92no—
280C4⋊Q8—182no—
281#124—32no—
282#124—92no—
283#124—182no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—181no—
287C2×C22⋊C4—181no—
288C2×C22⋊C4—181no—
289C2×C42—91no—
290#103—32no—
291#103—92no—
292#103—91no—
293#103—91no—
294#103—91no—
295#103D3211yescharacteristic, complemented
296#102—32no—
297#102—32no—
298#102—92no—
299#102—92no—
300#97—32no—
301#97—92no—
302C23×C3—62no—
303C22×D3—22no—
304C22×D3—32no—
305C22×D3—61no—
306C22×D3—124no—
307C22×D3—124no—
308C22×D3—124no—
309C3×Q8—22no—
310C3×Q8—22no—
311C3×Q8—22no—
312C3×Q8—41no—
313C3×Q8—124no—
314C3×D4—62no—
315C3×D4—62no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—32no—
320C2×C3×C4—32no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—62no—
324C2×C3×C4C23×D312yes—
325#67—124no—
326C2×Dic3—22no—
327C2×Dic3—32no—
328C2×Dic3—61no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3D3×D412yes—
334C2×Dic3D3×D412yes—
335D12—22no—
336D12—22no—
337C4×D3—34no—
338C4×D3—34no—
339C4×D3—62no—
340C4×D3—62no—
341C4×D3—64no—
342C4×D3—64no—
343C4×D3—124no—
344C4×D3—124no—
345C4×D3—124no—
346C4×D3—124no—
347C4×D3—242no—
348Dic6—44no—
349Dic6—62no—
350Dic6—62no—
351Dic6—62no—
352Dic6—121no—
353Dic6—124no—
354Dic6—124no—
355Dic6—124no—
356Dic6—124no—
357C3×C8—22no—
358C3×C8—41no—
359C3×C8—62no—
360C3⋊C8—22no—
361C3⋊C8—62no—
362C3⋊C8—121no—
363C2×C32C2×#12411yescharacteristic
364C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
365C2×C32C2×#13711yescharacteristic
366C3⋊D3#48914yescomplemented
367C3×D3—82no—
368C24—181no—
369C2×Q8—62no—
370C2×Q8—91no—
371C2×Q8—181no—
372C2×Q8—182no—
373C2×Q8—182no—
374C2×Q8—182no—
375C2×Q8—364no—
376C2×Q8C2×D3211yescharacteristic
377C2×D4—32no—
378C2×D4—182no—
379C2×D4—182no—
380C2×D4—181no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—181no—
385C22×C4—181no—
386C22×C4—181no—
387C2×C8—32no—
388C2×C8—91no—
389C2×C8—182no—
390C2×C8—182no—
391C2×C8C2×D3211yescharacteristic
392C4⋊C4—32no—
393C4⋊C4—62no—
394C4⋊C4—91no—
395C4⋊C4—181no—
396C4⋊C4—182no—
397C4⋊C4—181no—
398C4⋊C4C2×D3211yescharacteristic
399C22⋊C4—62no—
400C22⋊C4—62no—
401C22⋊C4—182no—
402C22⋊C4—182no—
403C42—32no—
404C42—92no—
405C22×C3—21no—
406C22×C3—122no—
407C22×C3—122no—
408C22×C3—122no—
409C22×C3C2×D3×D412yes—
410C2×D3—34no—
411C2×D3—34no—
412C2×D3—34no—
413C2×D3—42no—
414C2×D3—42no—
415C2×D3—42no—
416C2×D3—62no—
417C2×D3—62no—
418C2×D3—62no—
419C2×D3—248no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—42no—
423C3×C4—42no—
424C3×C4—42no—
425C3×C4—62no—
426C3×C4—62no—
427C3×C4—81no—
428C3×C4—122no—
429C3×C4D3×#4112yes—
430C3×C4D3×#4112yes—
431Dic3—22no—
432Dic3—22no—
433Dic3—34no—
434Dic3—42no—
435Dic3—62no—
436Dic3—122no—
437Dic3—122no—
438Dic3—122no—
439Dic3—241no—
440C32C2×#48911yescharacteristic, complemented, Sylow
441C23—62no—
442C23—91no—
443C23—362no—
444C23—362no—
445C23—362no—
446Q8—21no—
447Q8—21no—
448Q8—124no—
449Q8—181no—
450Q8—181no—
451Q8—362no—
452Q8—364no—
453D4—62no—
454D4—62no—
455D4—362no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—32no—
459C2×C4—32no—
460C2×C4—62no—
461C2×C4—91no—
462C2×C4—92no—
463C2×C4—92no—
464C2×C4—182no—
465C2×C4—182no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—362no—
469C2×C4—362no—
470C2×C4—362no—
471C2×C4C22×D3211yescharacteristic
472C8—21no—
473C8—62no—
474C8—181no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—242no—
479C2×C3D3×#12412yes—
480C2×C3D3×AGL(1,ℤ/8)12yes—
481C2×C3D3×#13712yes—
482D3—38no—
483D3—64no—
484D3—82no—
485C22—92no—
486C22—92no—
487C22—92no—
488C22—122no—
489C22—122no—
490C22—122no—
491C22—724no—
492C22D32×D411yescharacteristic
493C4—41no—
494C4—41no—
495C4—62no—
496C4—62no—
497C4—92no—
498C4—122no—
499C4—361no—
500C4—361no—
501C4#6430611yescharacteristic
502C4#6431211yescharacteristic
503C3—21no—
504C3D3×#48912yescomplemented
505C2—94no—
506C2—242no—
507C2#1059428811yescharacteristic
508C2#1059474011yescharacteristic
509C2#1059476011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenter#103D32
hypocenterC32C2×#489
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. #10594374C2semidirect
3. C3⋊D3×#103C2semidirect
4. C3×#4794C2semidirect
5. #10591624C2semidirect
6. #10591552C2semidirect
8. #10590895C2semidirect
9. #10590668C2semidirect
11. #10590531C2semidirect
19. C3×#888C22semidirect
22. #63918C22semidirect
30. C32×#103C22semidirect
31. #63662C22semidirect
32. #63643C22semidirect
33. #63637C22semidirect
34. C3×#835C22semidirect
36. C3×#815C22semidirect
38. #63567C22semidirect
41. #63554C22semidirect
51. #4794D3semidirect
114. #888C2×D3semidirect
124. C3×#103C2×D3semidirect
130. #835C2×D3semidirect
139. #815C2×D3semidirect
295. #103D32semidirect
366. C3⋊D3#489semidirect
440. C32C2×#489semidirect
504. C3D3×#489semidirect

Maximal subgroups

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

subgroupindex
#105954322
#105943742
C3⋊D3×#1032
C3×#47942
#105916242
#105915522
#105909402
#105908952
#105906682
#105905932
#105905312
D3×#4893