Finite Group Databasebeta

← #11895872

Subgroups — #11895872

Order 1152.

804 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic, complemented
2#10593903C211yesmaximal, characteristic, complemented
3#10592782C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591624C212yesmaximal, complemented
6#10591568C212yesmaximal
7#10591546C212yesmaximal, complemented
8#10591540C212yesmaximal, complemented
9C4×#3714C211yesmaximal, characteristic
10#10590269C211yesmaximal, characteristic, complemented
11#10590258C211yesmaximal, characteristic, complemented
12#83668—31nomaximal
13#81622—31nomaximal
14C2×#3797—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C2×#3755C2212yes—
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#947C2212yes—
19C3×Q8×Dic3C2212yes—
20C3×#898—22no—
21C3×#897—21no—
22C3×#892—21no—
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63918C2212yes—
27#63895—22no—
28#63894C2212yes—
29#63871—21no—
30C2×#3714C2211yescharacteristic
31#63662C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#835C2212yes—
34C3×#835C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63576C2212yes—
37#63575C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63564C2211yescharacteristic
40#63563C2211yescharacteristic
41#63562C2212yes—
42#63554C2212yes—
43C3×#556—31no—
44#5732D311yescharacteristic, complemented
45#5727—31no—
46Q8×D12—31no—
47C3×#487—31no—
48#5087—31no—
49#5083—31no—
50#5083—31no—
51#5083—61no—
52#5079D311yescharacteristic, complemented
53#5057—32no—
54#5055—32no—
55#5026—32no—
56#5024—31no—
57#5021—32no—
58C4×#213—31no—
59#5007—31no—
60#4819—32no—
61#4817—32no—
62#4794—32no—
63#4793—32no—
64C4×D24—31no—
65#4679—31no—
66C2×C32×Q8C2312yes—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×#627—22no—
74C2×#624—22no—
75#3797—44no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4—21no—
78C32×C42C2311yescharacteristic
79#3755—24no—
80#3752—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×(C2×D3)⋊C4—21no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3—22no—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96Dic3⋊Dic3—22no—
97#3722—22no—
98#3714—22no—
99#3367—91noSylow
100C2×D3×Q8—61no—
101C2×D3×Q8—61no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×#126—62no—
107C3×#124—32no—
108C3×C22⋊Q8—61no—
109C3×C4×Q8—31no—
110C3×C4×Q8—32no—
111C3×C4×D4—31no—
112C3×#117—61no—
113#947C2×D312yes—
114#946—61no—
115Q8×Dic3C2×D312yes—
116C2×#215—32no—
117C2×#215—32no—
118C2×#215—62no—
119C2×#213—31no—
120C2×D24—31no—
121#898—22no—
122#897—21no—
123#897—62no—
124#897—61no—
125#896—62no—
126#893—32no—
127#892—21no—
128#888—32no—
129C4×D12—31no—
130C4×D12—31no—
131C4×D12—32no—
132C4×D12—61no—
133C4×D12C2×D311yescharacteristic
134#869—32no—
135#869C2×D311yescharacteristic
136C4×Dic6C2×D311yescharacteristic
137C3×#103—32no—
138C3×#103—32no—
139C3×C4×C8—31no—
140#835—32no—
141#835—32no—
142#835—62no—
143#835C2×D312yes—
144#835C2×D312yes—
145#832—32no—
146#832—31no—
147#821—31no—
148#821—31no—
149#818—31no—
150#815—32no—
151Dic3⋊C8—32no—
152#809—32no—
153#809—31no—
154#807—32no—
155#807—32no—
156#807—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161#803—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—21no—
164C22×C3×D3—21no—
165C32×Q8—22no—
166C32×Q8—22no—
167C2×C32×C4—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—21no—
172C4⋊(C3⋊D3)—21no—
173C4⋊(C3⋊D3)#4112yes—
174C4×C3⋊D3—42no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×D12—21no—
180C3×D12—21no—
181C3×C4×D3—42no—
182C3×Dic6—22no—
183C3×Dic6—42no—
184#627—44no—
185#624—44no—
186C3⋊(C3⋊C8)—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189#556—31no—
190D4×Q8—91no—
191#489—92no—
192#487—31no—
193#477—92no—
194#474—91no—
195#463—92no—
196#461—91no—
197#446—91no—
198#440—92no—
199C4×D8—91no—
200C2×C3×Q8—22no—
201C2×C3×Q8—31no—
202C2×C3×Q8—61no—
203C2×C3×Q8C22×D312yes—
204C2×C3×Q8C22×D312yes—
205C2×C3×D4—31no—
206C22×C3×C4—61no—
207D3×Q8—124no—
208D3×Q8—124no—
209C2×D12—31no—
210C2×D12—31no—
211C2×D12—61no—
212C2×D12C22×D311yescharacteristic
213C2×C4×D3—21no—
214C2×C4×D3—62no—
215C2×C4×D3—61no—
216C2×C4×D3—61no—
217C2×C4×D3—62no—
218C2×C4×D3—121no—
219C2×Dic6—21no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6#6711yescharacteristic
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—41no—
234C3×C4⋊C4—41no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—61no—
237C3×C22⋊C4—62no—
238C3×C22⋊C4—62no—
239C3×C22⋊C4—61no—
240C3×C42—21no—
241C3×C42—32no—
242C3×C42—62no—
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D311yescharacteristic
245#215—64no—
246#215—64no—
247#215—124no—
248#213—62no—
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—22no—
251(C2×D3)⋊C4—22no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—61no—
254(C2×D3)⋊C4—61no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—121no—
257C4⋊Dic3—21no—
258C4⋊Dic3—22no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—61no—
262C4⋊Dic3—62no—
263C4⋊Dic3#6711yescharacteristic
264C4⋊Dic3C22×D311yescharacteristic
265C4⋊Dic3C22×D312yes—
266Dic3⋊C4—62no—
267Dic3⋊C4#6712yes—
268C4×Dic3—22no—
269C4×Dic3C22×D312yes—
270C2×C3⋊C8—32no—
271C2×C3⋊C8—32no—
272C2×C3⋊C8—62no—
273C2×C3⋊C8C22×D311yescharacteristic
274C2×C3⋊C8C22×D311yescharacteristic
275D24—62no—
276C22×C32C22×D411yescharacteristic
277C2×C3⋊D3—22no—
278C2×C3⋊D3—41no—
279C2×C3⋊D3—41no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C32×C4—21no—
284C32×C4—42no—
285C32×C4AGL(1,ℤ/8)12yes—
286C32×C4C2×#4111yescharacteristic
287C32×C42−1+411yescharacteristic
288C3⋊Dic3—41no—
289C3×Dic3—22no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3—41no—
293C22×Q8—181no—
294C2×SD16—92no—
295C2×D8—91no—
296C4⋊Q8—31no—
297C4⋊Q8—92no—
298C4⋊Q8D3211yescharacteristic
299#126—62no—
300#124—32no—
301C22⋊Q8—61no—
302C22⋊Q8—182no—
303C22⋊Q8—181no—
304C4×Q8—31no—
305C4×Q8—32no—
306C4×D4—31no—
307C4×D4—92no—
308C4×D4—91no—
309#117—61no—
310#107—92no—
311#107—91no—
312C4⋊C8—92no—
313C4⋊C8—91no—
314#103—32no—
315#103—32no—
316#103—92no—
317#102—91no—
318#102—92no—
319#102—91no—
320#97—92no—
321C4×C8—31no—
322C23×C3—61no—
323C22×D3—21no—
324C22×D3—61no—
325C22×D3—61no—
326C22×D3—121no—
327C3×Q8—22no—
328C3×Q8—22no—
329C3×Q8—22no—
330C3×Q8—22no—
331C3×Q8—42no—
332C3×Q8—42no—
333C3×Q8—62no—
334C3×Q8—122no—
335C3×D4—61no—
336C3×D4—61no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—32no—
343C2×C3×C4—32no—
344C2×C3×C4—42no—
345C2×C3×C4—61no—
346C2×C3×C4—62no—
347C2×C3×C4—122no—
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×Dic3—22no—
355C2×Dic3—21no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—121no—
359C2×Dic3C2×#6712yes—
360C2×Dic3C2×#6712yes—
361D12—21no—
362D12—21no—
363D12—32no—
364D12—32no—
365D12—62no—
366D12—61no—
367D12—61no—
368D12—121no—
369C4×D3—42no—
370C4×D3—124no—
371C4×D3—124no—
372C4×D3—122no—
373C4×D3—122no—
374C4×D3—242no—
375Dic6—22no—
376Dic6—42no—
377Dic6—124no—
378Dic6—124no—
379C3×C8—61no—
380C3×C8—61no—
381C3⋊C8—21no—
382C3⋊C8—21no—
383C3⋊C8—62no—
384C3⋊C8—62no—
385C3⋊C8—122no—
386C2×C32#54811yescharacteristic
387C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
388C2×C32#57811yescharacteristic
389C3⋊D3—42no—
390C3×D3—81no—
391C2×Q8—31no—
392C2×Q8—61no—
393C2×Q8—182no—
394C2×Q8—364no—
395C2×Q8C2×D3212yes—
396C2×D4—31no—
397C2×D4—91no—
398C22×C4—61no—
399C22×C4—182no—
400C22×C4—181no—
401SD16—184no—
402D8—182no—
403C2×C8—31no—
404C2×C8—31no—
405C2×C8—92no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—31no—
409C4⋊C4—32no—
410C4⋊C4—32no—
411C4⋊C4—31no—
412C4⋊C4—62no—
413C4⋊C4—61no—
414C4⋊C4—91no—
415C4⋊C4—182no—
416C22⋊C4—62no—
417C22⋊C4—62no—
418C22⋊C4—61no—
419C22⋊C4—182no—
420C22⋊C4—181no—
421C42—32no—
422C42—62no—
423C42C2×D3211yescharacteristic
424C22×C3—21no—
425C22×C3—121no—
426C22×C3—121no—
427C22×C3—121no—
428C22×C3C2×D3×D411yescharacteristic
429C22×C3C22×#6711yescharacteristic
430C2×D3—41no—
431C2×D3—41no—
432C2×D3—41no—
433C2×D3—62no—
434C2×D3—62no—
435C2×D3—122no—
436C2×D3—121no—
437C2×D3—121no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—241no—
441C2×D3—241no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—22no—
447C3×C4—41no—
448C3×C4—42no—
449C3×C4—42no—
450C3×C4—62no—
451C3×C4—62no—
452C3×C4—82no—
453C3×C4—121no—
454C3×C4—122no—
455C3×C4#91412yes—
456C3×C4#94912yes—
457C3×C4D3×#4111yescharacteristic
458C3×C4D3×#4111yescharacteristic
459C3×C4#101011yescharacteristic
460C3×C4#101011yescharacteristic
461Dic3—22no—
462Dic3—22no—
463Dic3—42no—
464Dic3—41no—
465Dic3—121no—
466Dic3—121no—
467Dic3—241no—
468C32#336711yescharacteristic, complemented, Sylow
469C23—61no—
470C23—181no—
471Q8—22no—
472Q8—22no—
473Q8—62no—
474Q8—122no—
475Q8—364no—
476D4—61no—
477D4—61no—
478D4—92no—
479D4—181no—
480C2×C4—22no—
481C2×C4—32no—
482C2×C4—32no—
483C2×C4—61no—
484C2×C4—62no—
485C2×C4—122no—
486C2×C4—181no—
487C2×C4—364no—
488C2×C4—362no—
489C2×C4D3×#6711yescharacteristic
490C2×C4D3×#6711yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—61no—
493C8—61no—
494C8—182no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—241no—
499C2×C3#567711yescharacteristic
500C2×C3C2×#91411yescharacteristic
501C2×C3#576611yescharacteristic
502C2×C3C2×#94911yescharacteristic
503C2×C3#583111yescharacteristic
504C2×C3#583811yescharacteristic
505D3—81no—
506D3—122no—
507D3—122no—
508D3—242no—
509C22—121no—
510C22—121no—
511C22—121no—
512C22—182no—
513C22—361no—
514C22—361no—
515C22C2×D3×#6711yescharacteristic
516C4—21no—
517C4—42no—
518C4—62no—
519C4—62no—
520C4—121no—
521C4—122no—
522C4—361no—
523C4#6393912yes—
524C4#6430911yescharacteristic
525C4#6431211yescharacteristic
526C3—21no—
527C3#8162211yescharacteristic, complemented
528C3#8366811yescharacteristic, complemented
529C2—241no—
530C2—362no—
531C2#1059523711yescharacteristic
532C2C2×#6393911yescharacteristic
533C2#1059532711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4⋊Q8D32
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5732C2semidirect
2. #10593903C2semidirect
3. #10592782C2semidirect
4. C3×#5079C2semidirect
5. #10591624C2semidirect
7. #10591546C2semidirect
8. #10591540C2semidirect
10. #10590269C2semidirect
11. #10590258C2semidirect
44. #5732D3semidirect
52. #5079D3semidirect
468. C32#3367semidirect
527. C3#81622semidirect
528. C3#83668semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
#105939032
#105927822
C3×#50792
#105916242
#105915682
#105915462
#105915402
C4×#37142
#105902692
#105902582
#836683
#816223