Finite Group Databasebeta

← #11869498

Subgroups — #11869498

Order 1152.

933 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594969C211yesmaximal, characteristic
2#10594925C211yesmaximal, characteristic
3C3⋊D3×C22⋊C8C211yesmaximal, characteristic
4C3×#4723C212yesmaximal, complemented
5#10591102C212yesmaximal, complemented
6#10590715C212yesmaximal, complemented
7#10590713C212yesmaximal, complemented
8#10590687C211yesmaximal, characteristic, complemented
9#10590685C211yesmaximal, characteristic, complemented
10#10590672C211yesmaximal, characteristic, complemented
11#10590672C211yesmaximal, characteristic, complemented
12D3×#485—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×#3797C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C3×#926C2212yes—
18C3×#924C2212yes—
19#63982—21no—
20#63974—21no—
21#63974—21no—
22#63957—21no—
23#63900C2211yescharacteristic
24#63900C2211yescharacteristic
25#63900C2211yescharacteristic
26#63883—21no—
27C4×#624—21no—
28#63874—21no—
29#63871C2212yes—
30#63865—21no—
31#63849C2212yes—
32C32×C22⋊C8C2211yescharacteristic
33#63657C2211yescharacteristic
34#63647C2211yescharacteristic
35#63647C2211yescharacteristic
36C3×#818C2212yescomplemented
37C3×#817C2212yescomplemented
38C3×#816C2212yescomplemented
39C3×#816C2212yescomplemented
40#63576C2212yescomplemented
41#63574C2212yescomplemented
42#63565C2212yescomplemented
43#63565C2212yescomplemented
44D3×C22⋊Q8—32no—
45D3×#117—32no—
46C3×#485—32no—
47#5045—32no—
48#4996—32no—
49#4888—32no—
50D3×#107—32no—
51#4868—32no—
52D3×#106—32no—
53#4815—32no—
54#4814—32no—
55D3×#103—32no—
56D3×#103—32no—
57D3×C22⋊C8—32no—
58D3×C22⋊C8—61no—
59#4723D312yescomplemented
60C23×C3⋊D3D411yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C22×C3⋊Dic3D411yescharacteristic
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C3×Dic6C2312yes—
70C2×#627—21no—
71C2×#624—21no—
72C2×#624—21no—
73C2×#624—21no—
74C2×#624—21no—
75#3797—22no—
76#3797—22no—
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C8×C3⋊D3—22no—
82C8×C3⋊D3—22no—
83C3×#217—22no—
84C3×#217—22no—
85C3×C4⋊Dic3C2312yes—
86C3×C4⋊Dic3C2312yes—
87C3×C4⋊Dic3C2312yes—
88C3×Dic3⋊C4—22no—
89C3×C4×Dic3—22no—
90#3724—21no—
91#3724—21no—
92#3724—21no—
93Dic3⋊Dic3—22no—
94#3722—22no—
95#3722—22no—
96Dic32—22no—
97C2×#485—91noSylow
98C2×D3×Q8—32no—
99C22×C4×D3—32no—
100C22×C4×D3—61no—
101C3×C22⋊Q8—32no—
102C3×#117—32no—
103#946—32no—
104#926C2×D312yes—
105#924C2×D312yes—
106C2×D3×C8—32no—
107C2×D3×C8—32no—
108C2×D3×C8—61no—
109C2×D3×C8—61no—
110#897—32no—
111#896—62no—
112#892—32no—
113#892—32no—
114D3×C4⋊C4—32no—
115D3×C4⋊C4—32no—
116D3×C4⋊C4—32no—
117D3×C4⋊C4—62no—
118D3×C22⋊C4—62no—
119D3×C22⋊C4—62no—
120#878—62no—
121#877—62no—
122#872—62no—
123C42×D3—62no—
124C3×#107—32no—
125C3×#106—32no—
126C3×#103—32no—
127C3×#103—32no—
128C3×C22⋊C8—21no—
129C3×C22⋊C8C2×D312yes—
130#835—32no—
131#835—32no—
132#830—32no—
133#830—61no—
134(C2×D3)⋊C8—32no—
135(C2×D3)⋊C8—32no—
136(C2×D3)⋊C8—61no—
137(C2×D3)⋊C8—61no—
138#818C2×D312yescomplemented
139#817C2×D312yescomplemented
140#816C2×D312yescomplemented
141#816C2×D312yescomplemented
142#810—32no—
143#810—32no—
144#808—32no—
145#808—32no—
146#807—32no—
147#807—32no—
148C23×C32C2×D411yescharacteristic
149C22×C3⋊D3—22no—
150C22×C3⋊D3—22no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3C2×D411yescharacteristic
153C22×C3⋊D3C2×D411yescharacteristic
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3C2×D411yescharacteristic
160C2×C3⋊Dic3C2×D411yescharacteristic
161C4×C3⋊D3—22no—
162C4×C3⋊D3—21no—
163C4×C3⋊D3—21no—
164C4×C3⋊D3—22no—
165C4×C3⋊D3#4112yes—
166C4×C3⋊D3#4112yes—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C3×Dic6—22no—
172C3×Dic6—22no—
173#627—42no—
174#624—42no—
175#624—42no—
176#624—42no—
177#624—42no—
178C32×C8—21no—
179C32×C8—21no—
180C3⋊(C3⋊C8)—21no—
181C3⋊(C3⋊C8)—21no—
182C2×C22⋊Q8—91no—
183C2×#117—91no—
184#485—32no—
185#485—92no—
186#485—92no—
187#485—92no—
188C2×#107—91no—
189C2×#106—91no—
190C2×#103—91no—
191C2×#103—91no—
192C2×C22⋊C8—91no—
193C23×D3—32no—
194C23×D3—61no—
195C2×C3×Q8—32no—
196C22×C3×C4—21no—
197C22×C3×C4C22×D312yes—
198C22×Dic3—32no—
199C22×Dic3—61no—
200D3×Q8—64no—
201D3×Q8—64no—
202C2×C4×D3—32no—
203C2×C4×D3—32no—
204C2×C4×D3—32no—
205C2×C4×D3—32no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—64no—
211C2×C4×D3—64no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—122no—
217C2×C4×D3—122no—
218C2×Dic6—62no—
219C2×Dic6C22×D312yes—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8C22×D312yes—
223C2×C3×C8C22×D312yes—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—62no—
228C3×C22⋊C4—62no—
229C3×C22⋊C4—62no—
230C3×C42—62no—
231#217—22no—
232#217—22no—
233(C2×D3)⋊C4—62no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237C4⋊Dic3—62no—
238C4⋊Dic3C22×D312yes—
239C4⋊Dic3C22×D312yes—
240C4⋊Dic3C22×D312yes—
241Dic3⋊C4—22no—
242Dic3⋊C4—62no—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245Dic3⋊C4—62no—
246C4×Dic3—22no—
247C4×Dic3—62no—
248C4×Dic3—62no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—61no—
253D3×C8—64no—
254D3×C8—64no—
255D3×C8—122no—
256D3×C8—122no—
257C22×C32—21no—
258C22×C32—21no—
259C22×C32—21no—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—21no—
262C2×C3⋊D3—21no—
263C2×C3⋊D3—21no—
264C2×C3⋊D3—44no—
265C2×C3⋊D3#12312yes—
266C2×C3⋊D3#13512yes—
267C2×C3⋊D3#13712yes—
268C32×C4—21no—
269C32×C4C2×#4111yescharacteristic
270C32×C4C2×#4111yescharacteristic
271C3⋊Dic3—21no—
272C3⋊Dic3#12312yes—
273C3×Dic3—42no—
274C3×Dic3—42no—
275C3×Dic3—42no—
276C3×Dic3—42no—
277C22×Q8—91no—
278C23×C4—91no—
279C22×C8—91no—
280C22×C8—91no—
281C22⋊Q8—32no—
282C22⋊Q8—92no—
283C22⋊Q8—181no—
284C22⋊Q8—181no—
285#117—32no—
286#117—92no—
287#117—181no—
288#117—181no—
289C2×C4⋊C4—91no—
290C2×C4⋊C4—91no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4—181no—
293C2×C22⋊C4—181no—
294C2×C22⋊C4—181no—
295C2×C42—181no—
296#107—32no—
297#107—92no—
298#106—32no—
299#106—92no—
300#103—32no—
301#103—32no—
302#103—92no—
303#103—92no—
304C22⋊C8—91no—
305C22⋊C8—91no—
306C22⋊C8—91no—
307C22⋊C8D3211yescharacteristic
308C23×C3—21no—
309C23×C3D3×D412yes—
310C22×D3—32no—
311C22×D3—32no—
312C22×D3—61no—
313C22×D3—61no—
314C22×D3—64no—
315C22×D3—64no—
316C22×D3—64no—
317C22×D3—64no—
318C22×D3—122no—
319C22×D3—122no—
320C3×Q8—62no—
321C3×Q8—62no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4D3×D412yes—
333C2×C3×C4C23×D312yes—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—32no—
339C2×Dic3—32no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—64no—
343C2×Dic3—122no—
344C4×D3—34no—
345C4×D3—34no—
346C4×D3—62no—
347C4×D3—62no—
348C4×D3—64no—
349C4×D3—64no—
350C4×D3—62no—
351C4×D3—62no—
352C4×D3—122no—
353C4×D3—121no—
354C4×D3—121no—
355C4×D3—122no—
356C4×D3—124no—
357C4×D3—124no—
358C4×D3—124no—
359C4×D3—124no—
360Dic6—22no—
361Dic6—22no—
362Dic6—124no—
363C3×C8—22no—
364C3×C8—22no—
365C3×C8—41no—
366C3×C8—41no—
367C3⋊C8—62no—
368C3⋊C8—62no—
369C3⋊C8—121no—
370C3⋊C8—121no—
371C2×C32—41no—
372C2×C32C2×#12311yescharacteristic
373C2×C32C2×#13511yescharacteristic
374C2×C32C2×#13711yescharacteristic
375C3⋊D3—41no—
376C3⋊D3#48514yescomplemented
377C24—91no—
378C2×Q8—32no—
379C2×Q8—181no—
380C2×Q8—182no—
381C2×Q8—182no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4—91no—
386C22×C4—91no—
387C22×C4—182no—
388C22×C4—182no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4—181no—
392C22×C4—181no—
393C22×C4C2×D3211yescharacteristic
394C2×C8—91no—
395C2×C8—91no—
396C2×C8—182no—
397C2×C8—182no—
398C2×C8C2×D3211yescharacteristic
399C2×C8C2×D3211yescharacteristic
400C4⋊C4—32no—
401C4⋊C4—32no—
402C4⋊C4—32no—
403C4⋊C4—62no—
404C4⋊C4—181no—
405C4⋊C4—181no—
406C4⋊C4—181no—
407C4⋊C4—182no—
408C22⋊C4—62no—
409C22⋊C4—62no—
410C22⋊C4—182no—
411C22⋊C4—182no—
412C42—62no—
413C42—182no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—21no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3C2×D3×D412yes—
422C2×D3—34no—
423C2×D3—34no—
424C2×D3—34no—
425C2×D3—62no—
426C2×D3—62no—
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—62no—
431C2×D3—62no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—128no—
435C2×D3—128no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—41no—
440C3×C4—122no—
441C3×C4—122no—
442C3×C4—122no—
443C3×C4—122no—
444C3×C4D3×#4112yes—
445C3×C4D3×#4112yes—
446Dic3—34no—
447Dic3—42no—
448Dic3—42no—
449Dic3—42no—
450Dic3—42no—
451Dic3—62no—
452Dic3—62no—
453Dic3—121no—
454C32C2×#48511yescharacteristic, complemented, Sylow
455C23—91no—
456C23—91no—
457C23—182no—
458C23—182no—
459C23—182no—
460C23#380211yescharacteristic
461Q8—62no—
462Q8—62no—
463Q8—362no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—91no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—91no—
474C2×C4—182no—
475C2×C4—182no—
476C2×C4—182no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—362no—
480C2×C4—362no—
481C2×C4—362no—
482C2×C4—362no—
483C2×C4#380211yescharacteristic
484C2×C4C22×D3211yescharacteristic
485C8—21no—
486C8—21no—
487C8—181no—
488C8—181no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—42no—
493C2×C3—42no—
494C2×C3D3×#12312yes—
495C2×C3D3×#13512yes—
496C2×C3D3×#13712yes—
497D3—38no—
498D3—64no—
499D3—122no—
500D3—122no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—92no—
505C22—92no—
506C22—92no—
507C22—181no—
508C22—181no—
509C22—181no—
510C22—364no—
511C22C2×#380211yescharacteristic
512C4—21no—
513C4—92no—
514C4—122no—
515C4—122no—
516C4—122no—
517C4—122no—
518C4—181no—
519C4#6431211yescharacteristic
520C4#6431211yescharacteristic
521C3—21no—
522C3D3×#48512yescomplemented
523C2—41no—
524C2—94no—
525C2—361no—
526C2#1059429511yescharacteristic
527C2#1059468411yescharacteristic
528C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenterC22⋊C8D32
hypocenterC32C2×#485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4723C2semidirect
5. #10591102C2semidirect
6. #10590715C2semidirect
7. #10590713C2semidirect
8. #10590687C2semidirect
9. #10590685C2semidirect
10. #10590672C2semidirect
11. #10590672C2semidirect
36. C3×#818C22semidirect
37. C3×#817C22semidirect
38. C3×#816C22semidirect
39. C3×#816C22semidirect
40. #63576C22semidirect
41. #63574C22semidirect
42. #63565C22semidirect
43. #63565C22semidirect
59. #4723D3semidirect
138. #818C2×D3semidirect
139. #817C2×D3semidirect
140. #816C2×D3semidirect
141. #816C2×D3semidirect
376. C3⋊D3#485semidirect
454. C32C2×#485semidirect
522. C3D3×#485semidirect

Maximal subgroups

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

subgroupindex
#105949692
#105949252
C3⋊D3×C22⋊C82
C3×#47232
#105911022
#105907152
#105907132
#105906872
#105906852
#105906722
D3×#4853