Finite Group Databasebeta

← #11865783

Subgroups — #11865783

Order 1152.

1071 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5832C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3Dic3×#235C211yesmaximal, characteristic, complemented
4C2×#63822C211yesmaximal, characteristic, complemented
5#10592932C211yesmaximal, characteristic, complemented
6#10591578C211yesmaximal, characteristic, complemented
7#10591574C211yesmaximal, characteristic, complemented
8#10591567C211yesmaximal, characteristic, complemented
9#10591564C211yesmaximal, characteristic, complemented
10#10591442C211yesmaximal, characteristic, complemented
11#10591438C211yesmaximal, characteristic, complemented
12#10591431C211yesmaximal, characteristic, complemented
13#10591428C211yesmaximal, characteristic, complemented
14C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
15#10591084C211yesmaximal, characteristic, complemented
16#83900—31nomaximal
17#83296—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21#64135C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#950—24no—
24C3×#947C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C3×#940C2211yescharacteristic
29C3×#939—21no—
30C3×#939—21no—
31C3×#936C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C2×C3×#213C2211yescharacteristic
34C3×C4×#67—21no—
35C3×C4×#67—21no—
36C2×C3×C4×Dic3C2211yescharacteristic
37C22×C3×C3⋊C8C2211yescharacteristic
38Dic3×#67—21no—
39Dic3×#67—21no—
40Dic3×D12C2211yescharacteristic
41Dic3×D12C2211yescharacteristic
42C4×D3×Dic3—21no—
43#63855—21no—
44Dic3×Dic6C2211yescharacteristic
45Dic3×Dic6C2211yescharacteristic
46C2×#3718C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49#63822—24no—
50C2×#3713C2211yescharacteristic
51#63662C2211yescharacteristic
52#63662C2211yescharacteristic
53#63659C2211yescharacteristic
54#63659C2211yescharacteristic
55Dic3⋊(C3⋊C8)C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61#63563C2211yescharacteristic
62#63563C2211yescharacteristic
63C2×C3×#135—31no—
64C3×#532—31no—
65#5832D311yescharacteristic, complemented
66Dic3×#41—31no—
67C2×#950—31no—
68C2×#950—31no—
69C2×#950D311yescharacteristic, complemented
70C4×#235—31no—
71#5233—31no—
72#5233—31no—
73#5233—31no—
74#5233—61no—
75#5185—31no—
76#5182—31no—
77#5166—31no—
78#5165—31no—
79#5163—31no—
80#5162—31no—
81#5153—31no—
82#5150—31no—
83#5113—31no—
84C2×Dic3⋊C8—31no—
85#5090—31no—
86#5083—31no—
87#5075—31no—
88#5072—31no—
89#5057—31no—
90#5057—31no—
91#5054—31no—
92#5054—31no—
93C2×C4⋊(C3⋊C8)—31no—
94C32×#41—22no—
95C32×#41—22no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4—21no—
100C22×C32×C4C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C22×C3×Dic3D411yescharacteristic
106C22×C3×Dic3D411yescharacteristic
107C3×#235—22no—
108C3×#235—22no—
109C3×#235—22no—
110C3×#235D414yescomplemented
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119#3757—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C4×C3⋊Dic3—21no—
123C2×C3⋊(C3⋊C8)—22no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#217—21no—
128C3×#216—22no—
129C3×#215—22no—
130C3×#214—22no—
131C3×#213—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3D411yescharacteristic
137C3×C4×Dic3D411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8—22no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32—21no—
148Dic32—21no—
149#3718—22no—
150#3715—22no—
151#3715—22no—
152#3713—22no—
153#3035—91noSylow
154C2×C3×#41—21no—
155C2×C3×#41—31no—
156C2×C3×#41—31no—
157C2×C3×#41C2×D311yescharacteristic
158C2×C3×#41C2×D311yescharacteristic
159C2×#235C2×D311yescharacteristic
160C2×#235C2×D311yescharacteristic
161C3×#135—64no—
162C2×C3×Q16—31no—
163C2×C3×SD16—31no—
164C2×C3×SD16—31no—
165C2×C3×D8—31no—
166C22×C3×C8—31no—
167C3×C4⋊Q8—31no—
168C3×#127—31no—
169C3×#124—31no—
170C3×#124—31no—
171C3×#121—61no—
172C3×#121—61no—
173C3×C4×D4—61no—
174C3×C4×D4—61no—
175C2×C3×C42—31no—
176#950—24no—
177#950—64no—
178#950—64no—
179#947C2×D311yescharacteristic
180Q8×Dic3—31no—
181Q8×Dic3—31no—
182#944C2×D311yescharacteristic
183C2×#216—31no—
184C2×#216—31no—
185C2×#216C2×D311yescharacteristic
186C2×#215—31no—
187C2×#215—31no—
188C2×#215C2×D311yescharacteristic
189#940C2×D311yescharacteristic
190#939—21no—
191#939—21no—
192#936C2×D311yescharacteristic
193D4×Dic3—31no—
194D4×Dic3—31no—
195D4×Dic3—61no—
196D4×Dic3—61no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214C2×D311yescharacteristic
200C2×#213—31no—
201C2×#213—31no—
202C2×#213C2×D311yescharacteristic
203C4×#67—21no—
204C4×#67—21no—
205C4×#67—61no—
206C4×#67—61no—
207#926—31no—
208#926—31no—
209#926—61no—
210#926—61no—
211C2×C4×Dic3—61no—
212C2×C4×Dic3C2×D311yescharacteristic
213C22×C3⋊C8—31no—
214C22×C3⋊C8—31no—
215C22×C3⋊C8—61no—
216C22×C3⋊C8C2×D311yescharacteristic
217C4×D12—31no—
218C4×D12—31no—
219#872—61no—
220C42×D3—61no—
221C4×Dic6—31no—
222C4×Dic6—31no—
223#835—31no—
224#835—31no—
225#835—31no—
226#835—31no—
227#835—31no—
228#835—31no—
229#835—61no—
230#835—61no—
231#832—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#832—61no—
239#821—31no—
240#821—31no—
241#816—31no—
242#816—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C23×C32C2×D411yescharacteristic
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C32×Q8—21no—
256C32×Q8—21no—
257C32×D4—21no—
258C32×D4—21no—
259C32×D4—42no—
260C2×C32×C4—21no—
261C2×C32×C4—42no—
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2×D412yes—
264C2×C32×C4#4112yes—
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C3×#67—24no—
269C3×#67—42no—
270C3×#67—42no—
271C3×#67—42no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—41no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12C2×D412yes—
284C3×C4×D3—24no—
285C3×C4×D3—42no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6C2×D412yes—
290D3×Dic3—42no—
291D3×Dic3—42no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#135—31no—
297C2×#135—91no—
298#532—31no—
299C4×#41—91no—
300#464—91no—
301#464—91no—
302#463—91no—
303#463—91no—
304#462—91no—
305#461—91no—
306#460—91no—
307#459—91no—
308C2×C4⋊C8—91no—
309#416—91no—
310#416—91no—
311C3×#41—24no—
312C3×#41—22no—
313C3×#41—22no—
314C3×#41—22no—
315C3×#41—22no—
316C3×#41—34no—
317C3×#41—42no—
318C3×#41—62no—
319C3×#41—62no—
320C3×#41—62no—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—21no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—41no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—41no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C2×#67—21no—
349C2×#67—21no—
350C2×#67—21no—
351C2×#67—21no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3#6711yescharacteristic
355C22×Dic3#6711yescharacteristic
356#235—22no—
357#235—22no—
358#235—22no—
359#235#6714yescomplemented
360C2×D12C22×D311yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×C4×D3—21no—
363C2×C4×D3—21no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×Dic6C22×D311yescharacteristic
367C2×Dic6C22×D311yescharacteristic
368C3×Q16—62no—
369C3×SD16—62no—
370C3×SD16—62no—
371C3×D8—62no—
372C2×C3×C8—31no—
373C2×C3×C8—31no—
374C2×C3×C8—62no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C42—31no—
382C3×C42—31no—
383C3×C42—31no—
384C3×C42—31no—
385#217—21no—
386#217—21no—
387#217—61no—
388#217—61no—
389#217—61no—
390#217—61no—
391#217—121no—
392#216—22no—
393#216—62no—
394#216—62no—
395#215—22no—
396#215—62no—
397#215—62no—
398#214—22no—
399#214—62no—
400#214—62no—
401#213—22no—
402#213—62no—
403#213—62no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408C4⋊Dic3—31no—
409C4⋊Dic3—31no—
410C4⋊Dic3—31no—
411C4⋊Dic3—31no—
412C4⋊Dic3—61no—
413C4⋊Dic3—61no—
414C4⋊Dic3—61no—
415C4⋊Dic3—61no—
416Dic3⋊C4—21no—
417Dic3⋊C4—21no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—121no—
427C4×Dic3#6711yescharacteristic
428C4×Dic3#6711yescharacteristic
429C4×Dic3C22×D311yescharacteristic
430C4×Dic3C22×D311yescharacteristic
431C2×C3⋊C8—22no—
432C2×C3⋊C8—31no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—31no—
435C2×C3⋊C8—31no—
436C2×C3⋊C8—61no—
437C2×C3⋊C8—61no—
438C2×C3⋊C8—62no—
439C2×C3⋊C8—62no—
440C2×C3⋊C8—122no—
441C2×C3⋊C8C22×D311yescharacteristic
442C2×C3⋊C8C22×D311yescharacteristic
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32#12112yes—
449C22×C32C22×D411yescharacteristic
450C2×C3×D3—22no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C32×C4—41no—
457C32×C4#12112yes—
458C32×C4C22×D411yescharacteristic
459C32×C4C2×#4111yescharacteristic
460C3⋊Dic3—41no—
461C3⋊Dic3—41no—
462C3×Dic3—22no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—21no—
466C3×Dic3—41no—
467C3×Dic3#13512yescomplemented
468C2×#41—31no—
469C2×#41—31no—
470C2×#41D3211yescharacteristic
471#135—64no—
472#135—184no—
473C2×Q16—31no—
474C2×Q16—91no—
475C2×SD16—31no—
476C2×SD16—31no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×D8—31no—
480C2×D8—91no—
481C22×C8—31no—
482C22×C8—91no—
483C4⋊Q8—31no—
484#127—31no—
485#124—31no—
486#124—31no—
487#121—61no—
488#121—61no—
489C4×Q8—91no—
490C4×Q8—91no—
491C4×D4—61no—
492C4×D4—61no—
493C4×D4—91no—
494C4×D4—91no—
495C4×D4—181no—
496C4×D4—181no—
497#117—91no—
498#117—181no—
499C2×C42—31no—
500C2×C42—181no—
501C4⋊C8—91no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505#103—91no—
506#103—91no—
507#103—91no—
508#103—91no—
509#102—91no—
510#102—91no—
511#102—91no—
512#102—91no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—41no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3D3×D411yescharacteristic
520C23×C3C2×#6711yescharacteristic
521C22×D3—21no—
522C22×D3—21no—
523C3×Q8—22no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×Q8—21no—
527C3×Q8—21no—
528C3×Q8—32no—
529C3×Q8—41no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8—61no—
533C3×D4—22no—
534C3×D4—21no—
535C3×D4—21no—
536C3×D4—21no—
537C3×D4—21no—
538C3×D4—32no—
539C3×D4—41no—
540C3×D4—44no—
541C3×D4—42no—
542C3×D4—42no—
543C3×D4—64no—
544C3×D4—61no—
545C3×D4—61no—
546C3×D4—61no—
547C3×D4—122no—
548C3×D4—122no—
549C3×D4—122no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—21no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—41no—
561C2×C3×C4—44no—
562C2×C3×C4—42no—
563C2×C3×C4—42no—
564C2×C3×C4—62no—
565C2×C3×C4—61no—
566C2×C3×C4—64no—
567C2×C3×C4—61no—
568C2×C3×C4—121no—
569C2×C3×C4—122no—
570C2×C3×C4D3×D412yes—
571C2×C3×C4D3×D411yescharacteristic
572C2×C3×C4#23712yes—
573C2×C3×C4#23712yes—
574C2×C3×C4C2×#6712yes—
575C2×C3×C4C2×#6711yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—24no—
579#67—42no—
580#67—42no—
581#67—42no—
582C2×Dic3—21no—
583C2×Dic3—22no—
584C2×Dic3—21no—
585C2×Dic3—41no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—121no—
591C2×Dic3—121no—
592C2×Dic3—122no—
593C2×Dic3—122no—
594C2×Dic3C2×#6711yescharacteristic
595C2×Dic3C2×#6711yescharacteristic
596C2×Dic3C2×#6711yescharacteristic
597C2×Dic3C2×#6711yescharacteristic
598D12—21no—
599D12—21no—
600D12—21no—
601D12C2×#6712yes—
602C4×D3—24no—
603C4×D3—42no—
604C4×D3—122no—
605C4×D3—122no—
606Dic6—21no—
607Dic6—21no—
608Dic6—21no—
609Dic6C2×#6712yes—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—61no—
615C3⋊C8—61no—
616C3⋊C8—61no—
617C3⋊C8—61no—
618C3⋊C8—121no—
619C3⋊C8—121no—
620C2×C32—22no—
621C2×C32—81no—
622C2×C32C2×#12111yescharacteristic
623C2×C32C2×#13511yescharacteristic
624C2×C32#57511yescharacteristic
625C3×D3—42no—
626C3×D3—81no—
627#41—22no—
628#41—22no—
629#41—34no—
630#41—62no—
631#41—62no—
632#41—62no—
633C2×Q8—31no—
634C2×Q8—31no—
635C2×Q8C2×D3211yescharacteristic
636C2×D4—21no—
637C2×D4—31no—
638C2×D4—31no—
639C2×D4—61no—
640C2×D4—61no—
641C2×D4—61no—
642C2×D4—61no—
643C2×D4C2×D3211yescharacteristic
644C22×C4—21no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—181no—
650C22×C4—181no—
651C22×C4C2×D3211yescharacteristic
652Q16—62no—
653Q16—182no—
654SD16—62no—
655SD16—62no—
656SD16—182no—
657SD16—182no—
658D8—62no—
659D8—182no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—62no—
663C2×C8—91no—
664C2×C8—91no—
665C2×C8—182no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—91no—
669C4⋊C4—91no—
670C4⋊C4—181no—
671C4⋊C4—181no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—31no—
680C42—31no—
681C42—31no—
682C42—31no—
683C42—181no—
684C42—181no—
685C42—181no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—22no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—42no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—62no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3—121no—
705C22×C3—121no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3—121no—
709C22×C3#93812yes—
710C22×C3#93912yes—
711C22×C3C2×D3×D411yescharacteristic
712C22×C3C22×#6711yescharacteristic
713C2×D3—22no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—41no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—22no—
722C3×C4—32no—
723C3×C4—42no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—61no—
727C3×C4—61no—
728C3×C4—61no—
729C3×C4—62no—
730C3×C4—121no—
731C3×C4#93812yes—
732C3×C4#93912yes—
733C3×C4C2×D3×D411yescharacteristic
734C3×C4C2×#23711yescharacteristic
735C3×C4C2×#23711yescharacteristic
736C3×C4C22×#6711yescharacteristic
737Dic3—22no—
738Dic3—21no—
739Dic3—21no—
740Dic3—21no—
741Dic3—41no—
742Dic3—121no—
743Dic3—121no—
744Dic3—121no—
745Dic3—121no—
746Dic3—241no—
747Dic3—241no—
748Dic3#95012yescomplemented
749C32#303511yescharacteristic, complemented, Sylow
750C23—21no—
751C23—61no—
752C23—61no—
753C23D3×#6711yescharacteristic
754Q8—21no—
755Q8—21no—
756Q8—32no—
757Q8—61no—
758Q8—61no—
759Q8—61no—
760D4—21no—
761D4—21no—
762D4—32no—
763D4—42no—
764D4—64no—
765D4—61no—
766D4—61no—
767D4—61no—
768D4—122no—
769D4—122no—
770D4—122no—
771C2×C4—21no—
772C2×C4—31no—
773C2×C4—31no—
774C2×C4—31no—
775C2×C4—31no—
776C2×C4—42no—
777C2×C4—62no—
778C2×C4—61no—
779C2×C4—64no—
780C2×C4—61no—
781C2×C4—121no—
782C2×C4—122no—
783C2×C4—181no—
784C2×C4—181no—
785C2×C4—362no—
786C2×C4—362no—
787C2×C4#380512yes—
788C2×C4D3×#6712yes—
789C2×C4D3×#6711yescharacteristic
790C2×C4C22×D3211yescharacteristic
791C8—61no—
792C8—61no—
793C8—181no—
794C8—181no—
795C2×C3—22no—
796C2×C3—22no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—42no—
801C2×C3—82no—
802C2×C3—81no—
803C2×C3—81no—
804C2×C3—122no—
805C2×C3—241no—
806C2×C3D3×#13511yescharacteristic
807C2×C3#576811yescharacteristic
808C2×C3C2×#93811yescharacteristic
809C2×C3C2×#93911yescharacteristic
810C2×C3C2×#95011yescharacteristic
811C2×C3#582211yescharacteristic
812D3—42no—
813D3—81no—
814C22—21no—
815C22—21no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—62no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22#6397012yes—
826C22C2×D3×#6711yescharacteristic
827C4—32no—
828C4—41no—
829C4—61no—
830C4—61no—
831C4—61no—
832C4—62no—
833C4—121no—
834C4—361no—
835C4—361no—
836C4#6397012yes—
837C4C2×#380511yescharacteristic
838C4C2×D3×#6711yescharacteristic
839C3—21no—
840C3#8329611yescharacteristic, complemented
841C3#8390011yescharacteristic, complemented
842C2—22no—
843C2—81no—
844C2—122no—
845C2—241no—
846C2D3×#95011yescharacteristic
847C2#1059545311yescharacteristic
848C2C2×#6397011yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5832C2semidirect
2. C2×C3×#950C2semidirect
3. Dic3×#235C2semidirect
4. C2×#63822C2semidirect
5. #10592932C2semidirect
6. #10591578C2semidirect
7. #10591574C2semidirect
8. #10591567C2semidirect
9. #10591564C2semidirect
10. #10591442C2semidirect
11. #10591438C2semidirect
12. #10591431C2semidirect
13. #10591428C2semidirect
14. C2×Dic3⋊(C3⋊C8)C2semidirect
15. #10591084C2semidirect
65. #5832D3semidirect
69. C2×#950D3semidirect
110. C3×#235D4semidirect
359. #235#67semidirect
467. C3×Dic3#135semidirect
748. Dic3#950semidirect
749. C32#3035semidirect
840. C3#83296semidirect
841. C3#83900semidirect

Maximal subgroups

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

subgroupindex
C3×#58322
C2×C3×#9502
Dic3×#2352
C2×#638222
#105929322
#105915782
#105915742
#105915672
#105915642
#105914422
#105914382
#105914312
#105914282
C2×Dic3⋊(C3⋊C8)2
#105910842
#839003
#832963