Finite Group Databasebeta

← #11868617

Subgroups — #11868617

Order 1152.

931 conjugacy classes of subgroups.

The subgroup lattice has 623 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3832C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic, complemented
3C3×#5021C211yesmaximal, characteristic, complemented
4C3×#5020C211yesmaximal, characteristic, complemented
5#10591615C212yesmaximal, complemented
6#10591560C212yesmaximal
7#10590574C212yesmaximal, complemented
8#10590435C212yesmaximal, complemented
9#10590331C211yesmaximal, characteristic, complemented
10#10590313C211yesmaximal, characteristic, complemented
11#10590300C211yesmaximal, characteristic, complemented
12#81107—31nomaximal
13#81010—31nomaximal
14C2×#3832C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16Q8×C3⋊Dic3C2211yescharacteristic
17#64102—21no—
18#64102C2211yescharacteristic
19#64101—21no—
20#64101C2211yescharacteristic
21C4×C4⋊(C3⋊D3)—21no—
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C42×C3⋊D3—21no—
24C42×C3⋊D3C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C3×#869C2211yescharacteristic
27#63872C2212yes—
28#63871—21no—
29#63871—21no—
30#63849C2212yes—
31#63843—21no—
32#63843—21no—
33C2×#3710C2212yes—
34C3×#835C2212yes—
35C3×#835C2212yes—
36C3×#808C2212yes—
37C3×#807C2212yes—
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63573C2212yes—
42#63572C2212yes—
43#63564C2212yes—
44#63564C2212yes—
45#5728—31no—
46#5728—31no—
47C4×#239—31no—
48C4×#239—31no—
49C4×#239—61no—
50C3×#477—31no—
51C3×#475—31no—
52#5087—31no—
53#5084—31no—
54#5021D311yescharacteristic, complemented
55#5020D311yescharacteristic, complemented
56#4891—32no—
57#4880—32no—
58#4871—32no—
59#4860—32no—
60#4846—31no—
61#4842—31no—
62D3×C4⋊C8—31no—
63D3×C4⋊C8—31no—
64#4804—32no—
65#4804—32no—
66#4799—32no—
67#4796—32no—
68C2×C32×Q8C2311yescharacteristic
69#3832—22no—
70#3832Q814yescomplemented
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—21no—
75C2×C4×C3⋊D3—21no—
76C2×C4×C3⋊D3D411yescharacteristic
77C2×C4×C3⋊D3D411yescharacteristic
78C2×C4×C3⋊D3C2311yescharacteristic
79C2×C3×Dic6—21no—
80C2×C3×Dic6—21no—
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2311yescharacteristic
83C32×C42—21no—
84C32×C42C2311yescharacteristic
85#3752—21no—
86#3752—21no—
87#3752—21no—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C4×C3⋊Dic3—21no—
91C4×C3⋊Dic3—21no—
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2312yes—
98C3×C4⋊Dic3C2312yes—
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2312yes—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—22no—
103#3722—22no—
104Dic32—22no—
105#3710—24no—
106#3076—91noSylow
107C2×#239—31no—
108C2×#239—31no—
109C2×#239—61no—
110C3×C4⋊Q8—31no—
111C3×C4⋊Q8—31no—
112C3×C4×Q8—21no—
113C3×C4×Q8C2×D311yescharacteristic
114C3×C4×Q8C2×D311yescharacteristic
115#946—61no—
116#946—61no—
117Q8×Dic3—31no—
118Q8×Dic3—31no—
119Q8×Dic3—61no—
120Q8×Dic3—61no—
121Q8×Dic3—61no—
122C2×D3×C8—32no—
123C2×D3×C8—32no—
124#897—61no—
125#897—61no—
126#893—31no—
127#893—31no—
128#893—61no—
129#893—61no—
130#893—61no—
131#893—62no—
132#892—31no—
133#892—31no—
134#892—32no—
135#892—32no—
136#892—61no—
137#892—61no—
138#892—61no—
139#892—62no—
140#890—32no—
141#890—32no—
142#887—61no—
143#887—61no—
144C4×D12—31no—
145C4×D12—31no—
146C4×D12—61no—
147C4×D12—61no—
148C4×D12—61no—
149C4×D12—62no—
150C42×D3—31no—
151C42×D3—31no—
152C42×D3—61no—
153C42×D3—61no—
154C42×D3—61no—
155C42×D3—62no—
156#869C2×D311yescharacteristic
157#869C2×D311yescharacteristic
158C3×#107—32no—
159C3×#106—32no—
160C3×C4⋊C8—31no—
161C3×C4⋊C8—31no—
162C3×#103—32no—
163C3×#103—32no—
164#835C2×D312yes—
165#835C2×D312yes—
166#821—32no—
167#821—32no—
168#818—32no—
169#817—32no—
170Dic3⋊C8—32no—
171Dic3⋊C8—32no—
172#809—32no—
173#809—32no—
174#808—32no—
175#808C2×D312yes—
176#807—32no—
177#807C2×D312yes—
178C4⋊(C3⋊C8)C2×D311yescharacteristic
179C4⋊(C3⋊C8)C2×D311yescharacteristic
180C22×C3⋊D3—21no—
181C22×C3⋊D3C2×D411yescharacteristic
182C32×Q8—21no—
183C32×Q8C2×Q812yes—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C4⋊(C3⋊D3)—24no—
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)C2×Q812yes—
196C4×C3⋊D3—24no—
197C4×C3⋊D3—22no—
198C4×C3⋊D3—41no—
199C4×C3⋊D3—42no—
200C4×C3⋊D3—42no—
201C4×C3⋊D3C2×Q812yes—
202C4×C3⋊D3#4112yes—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C3×Dic6—42no—
206C3×Dic6—42no—
207C3×C3⋊C8—22no—
208C3×C3⋊C8—22no—
209#533—91no—
210C4×#41—91no—
211#479—92no—
212#478—92no—
213#477—31no—
214#476—91no—
215#475—31no—
216#474—91no—
217#427—92no—
218C2×C4⋊C8—91no—
219#416—92no—
220C2×C3×Q8—21no—
221C2×C3×Q8—61no—
222C2×C3×Q8—61no—
223C2×C3×Q8C22×D311yescharacteristic
224C2×C3×Q8C22×D311yescharacteristic
225#239—34no—
226#239—34no—
227#239—64no—
228#239—62no—
229#239—62no—
230#239—64no—
231C2×D12—31no—
232C2×D12—31no—
233C2×D12—61no—
234C2×D12—61no—
235C2×D12—61no—
236C2×D12—62no—
237C2×C4×D3—31no—
238C2×C4×D3—31no—
239C2×C4×D3—31no—
240C2×C4×D3—31no—
241C2×C4×D3—31no—
242C2×C4×D3—31no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×C4×D3—61no—
246C2×C4×D3—61no—
247C2×C4×D3—61no—
248C2×C4×D3—62no—
249C2×C4×D3—61no—
250C2×C4×D3—61no—
251C2×C4×D3—62no—
252C2×C4×D3—62no—
253C2×C4×D3—61no—
254C2×C4×D3—61no—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×C3×C8—32no—
258C2×C3×C8—32no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—32no—
264C3×C4⋊C4—32no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—61no—
267C3×C4⋊C4C22×D311yescharacteristic
268C3×C4⋊C4C22×D311yescharacteristic
269C3×C42—22no—
270C3×C42—21no—
271C3×C42—21no—
272C3×C42—21no—
273C3×C42C22×D311yescharacteristic
274C3×C42C22×D311yescharacteristic
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—61no—
278(C2×D3)⋊C4—61no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—61no—
281(C2×D3)⋊C4—62no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—61no—
285(C2×D3)⋊C4—61no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—31no—
289C4⋊Dic3—31no—
290C4⋊Dic3—61no—
291C4⋊Dic3—62no—
292C4⋊Dic3—62no—
293C4⋊Dic3—61no—
294C4⋊Dic3—61no—
295C4⋊Dic3—62no—
296C4⋊Dic3C22×D312yes—
297C4⋊Dic3C22×D312yes—
298Dic3⋊C4—62no—
299Dic3⋊C4—62no—
300C4×Dic3—31no—
301C4×Dic3—31no—
302C4×Dic3—31no—
303C4×Dic3—31no—
304C4×Dic3—31no—
305C4×Dic3—31no—
306C4×Dic3—61no—
307C4×Dic3—61no—
308C4×Dic3—61no—
309C4×Dic3—62no—
310C4×Dic3—62no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—62no—
316C4×Dic3—62no—
317C2×C3⋊C8C22×D312yes—
318C2×C3⋊C8C22×D312yes—
319D3×C8—64no—
320D3×C8—64no—
321C22×C32C22×D411yescharacteristic
322C2×C3⋊D3—22no—
323C2×C3⋊D3—21no—
324C2×C3⋊D3—21no—
325C2×C3⋊D3—41no—
326C2×C3⋊D3—41no—
327C2×C3⋊D3C22⋊Q812yes—
328C32×C4—22no—
329C32×C4—21no—
330C32×C4—41no—
331C32×C4#13512yes—
332C32×C4C22×Q811yescharacteristic
333C32×C4C2×#4111yescharacteristic
334C3⋊Dic3—21no—
335C3⋊Dic3—21no—
336C3⋊Dic3—41no—
337C3⋊Dic3C22⋊Q812yes—
338C3×Dic3—42no—
339C3×Dic3—42no—
340C2×#41—91no—
341C22×C8—92no—
342C4⋊Q8—31no—
343C4⋊Q8—31no—
344#125—92no—
345C22⋊Q8—181no—
346C22⋊Q8—181no—
347C4×Q8—91no—
348C4×Q8—181no—
349C4×Q8—181no—
350C4×Q8D3211yescharacteristic
351C4×D4—91no—
352C4×D4—91no—
353C4×D4—181no—
354C4×D4—181no—
355#117—92no—
356#117—91no—
357#117—181no—
358C2×C42—91no—
359C2×C42—181no—
360#107—32no—
361#107—92no—
362#106—32no—
363#106—92no—
364C4⋊C8—31no—
365C4⋊C8—31no—
366C4⋊C8—92no—
367#103—32no—
368#103—32no—
369#102—92no—
370#102—92no—
371C22×D3—31no—
372C22×D3—31no—
373C22×D3—61no—
374C22×D3—62no—
375C22×D3—61no—
376C22×D3—61no—
377C3×Q8—22no—
378C3×Q8—21no—
379C3×Q8—21no—
380C3×Q8—22no—
381C3×Q8—122no—
382C3×Q8—122no—
383C3×Q8D3×Q812yes—
384C3×Q8D3×Q812yes—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—62no—
395C2×C3×C4—62no—
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—31no—
405C2×Dic3—31no—
406C2×Dic3—31no—
407C2×Dic3—31no—
408C2×Dic3—31no—
409C2×Dic3—31no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—62no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416D12—32no—
417D12—32no—
418D12—62no—
419D12—64no—
420D12—64no—
421D12—68no—
422D12—62no—
423D12—61no—
424D12—61no—
425C4×D3—32no—
426C4×D3—32no—
427C4×D3—32no—
428C4×D3—32no—
429C4×D3—62no—
430C4×D3—62no—
431C4×D3—64no—
432C4×D3—64no—
433C4×D3—68no—
434C4×D3—62no—
435C4×D3—62no—
436C4×D3—122no—
437C4×D3—121no—
438C4×D3—121no—
439C4×D3—122no—
440C4×D3—124no—
441C4×D3—122no—
442C4×D3—122no—
443C4×D3—124no—
444C4×D3—122no—
445C4×D3—122no—
446Dic6—42no—
447Dic6—42no—
448C3×C8—62no—
449C3×C8—62no—
450C3⋊C8—22no—
451C3⋊C8—22no—
452C2×C32C2×C22⋊Q811yescharacteristic
453C2×C32C2×#13511yescharacteristic
454C2×C32#57511yescharacteristic
455C3⋊D3—22no—
456C3⋊D3—42no—
457#41—94no—
458#41—182no—
459C2×Q8—61no—
460C2×Q8—61no—
461C2×Q8C2×D3211yescharacteristic
462C2×D4—91no—
463C2×D4—181no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4—91no—
467C22×C4—181no—
468C22×C4—181no—
469C22×C4—181no—
470C2×C8—32no—
471C2×C8—32no—
472C2×C8—184no—
473C4⋊C4—21no—
474C4⋊C4—32no—
475C4⋊C4—32no—
476C4⋊C4—61no—
477C4⋊C4—61no—
478C4⋊C4—91no—
479C4⋊C4—181no—
480C4⋊C4—182no—
481C4⋊C4—182no—
482C4⋊C4C2×D3211yescharacteristic
483C22⋊C4—181no—
484C22⋊C4—181no—
485C22⋊C4—182no—
486C22⋊C4—181no—
487C42—21no—
488C42—91no—
489C42—91no—
490C42—91no—
491C42—181no—
492C42—181no—
493C42—182no—
494C42C2×D3211yescharacteristic
495C22×C3—21no—
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C2×D3×D411yescharacteristic
498C2×D3—32no—
499C2×D3—32no—
500C2×D3—62no—
501C2×D3—61no—
502C2×D3—61no—
503C2×D3—61no—
504C2×D3—61no—
505C2×D3—64no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—121no—
509C2×D3—121no—
510C2×D3—122no—
511C2×D3—122no—
512C2×D3—121no—
513C2×D3—121no—
514C2×D3—121no—
515C2×D3—121no—
516C3×C4—24no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—22no—
520C3×C4—22no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—22no—
524C3×C4—41no—
525C3×C4—42no—
526C3×C4—41no—
527C3×C4—41no—
528C3×C4—122no—
529C3×C4—122no—
530C3×C4#91612yes—
531C3×C4#91912yes—
532C3×C4C2×D3×Q811yescharacteristic
533C3×C4C2×D3×Q811yescharacteristic
534C3×C4D3×#4111yescharacteristic
535C3×C4D3×#4111yescharacteristic
536Dic3—32no—
537Dic3—32no—
538Dic3—42no—
539Dic3—42no—
540Dic3—62no—
541Dic3—62no—
542Dic3—61no—
543Dic3—61no—
544Dic3—61no—
545Dic3—61no—
546Dic3—121no—
547Dic3—122no—
548Dic3—121no—
549Dic3—121no—
550C32#307611yescharacteristic, complemented, Sylow
551C23—91no—
552C23—181no—
553Q8—21no—
554Q8—122no—
555Q8—122no—
556Q8#379712yes—
557D4—92no—
558D4—184no—
559D4—181no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—91no—
565C2×C4—92no—
566C2×C4—92no—
567C2×C4—91no—
568C2×C4—91no—
569C2×C4—184no—
570C2×C4—182no—
571C2×C4—181no—
572C2×C4—361no—
573C2×C4—362no—
574C2×C4—362no—
575C2×C4#381111yescharacteristic
576C2×C4#381111yescharacteristic
577C2×C4C22×D3211yescharacteristic
578C8—62no—
579C8—62no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3D3×C22⋊Q811yescharacteristic
584C2×C3D3×C22⋊Q811yescharacteristic
585C2×C3C2×#91611yescharacteristic
586C2×C3C2×#91911yescharacteristic
587C2×C3#577311yescharacteristic
588C2×C3#577711yescharacteristic
589D3—62no—
590D3—62no—
591D3—122no—
592D3—124no—
593D3—122no—
594D3—122no—
595C22—92no—
596C22—181no—
597C22—181no—
598C22—182no—
599C22—361no—
600C22—361no—
601C22C2×#381111yescharacteristic
602C4—22no—
603C4—21no—
604C4—41no—
605C4—92no—
606C4—122no—
607C4—122no—
608C4—181no—
609C4—181no—
610C4—361no—
611C4#6395012yes—
612C4C2×#379711yescharacteristic
613C4#6430611yescharacteristic
614C3—21no—
615C3#8101011yescharacteristic, complemented
616C3#8110711yescharacteristic, complemented
617C2—182no—
618C2—362no—
619C2#1059492511yescharacteristic
620C2C2×#6395011yescharacteristic
621C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3832C22
hypercenterC4×Q8D32
hypocenterC32#3076
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
2. #10593866C2semidirect
3. C3×#5021C2semidirect
4. C3×#5020C2semidirect
5. #10591615C2semidirect
7. #10590574C2semidirect
8. #10590435C2semidirect
9. #10590331C2semidirect
10. #10590313C2semidirect
11. #10590300C2semidirect
54. #5021D3semidirect
55. #5020D3semidirect
70. #3832Q8semidirect
550. C32#3076semidirect
615. C3#81010semidirect
616. C3#81107semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
#105938662
C3×#50212
C3×#50202
#105916152
#105915602
#105905742
#105904352
#105903312
#105903132
#105903002
#811073
#810103