Finite Group Databasebeta

← #11865800

Subgroups — #11865800

Order 1152.

1054 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5668C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3C2×#63935C211yesmaximal, characteristic, complemented
4C4×#3799C211yesmaximal, characteristic, complemented
5#10592756C211yesmaximal, characteristic, complemented
6C3×#5054C211yesmaximal, characteristic, complemented
7#10591574C211yesmaximal, characteristic, complemented
8#10591565C211yesmaximal, characteristic, complemented
9#10591556C211yesmaximal, characteristic, complemented
10#10591438C211yesmaximal, characteristic, complemented
11#10591429C211yesmaximal, characteristic, complemented
12#10591420C211yesmaximal, characteristic, complemented
13#10590356C211yesmaximal, characteristic, complemented
14D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#83296—31nomaximal
17#80597—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C32×#124C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C2×#3753C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#940C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C3×#884—21no—
30C3×#884—21no—
31C3×#67⋊C4—21no—
32C3×#67⋊C4—21no—
33C3×#875C2211yescharacteristic
34C3×C42×D3C2211yescharacteristic
35C3×C4×Dic6C2211yescharacteristic
36#63949—24no—
37#63935—24no—
38#63904—21no—
39C4×#626—21no—
40#63894C2211yescharacteristic
41C4×#624—21no—
42Dic3×Dic6C2211yescharacteristic
43#63841C2211yescharacteristic
44#63836—21no—
45C2×#3718C2211yescharacteristic
46C2×#3717C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic
52#63659C2211yescharacteristic
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
54C3×#835C2211yescharacteristic
55C3×#832C2211yescharacteristic
56C3×C4⋊(C3⋊C8)C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63566C2211yescharacteristic
60#63565C2211yescharacteristic
61#63563C2211yescharacteristic
62#63562C2211yescharacteristic
63C3×#532—31no—
64C2×#950—31no—
65C2×#950—31no—
66C2×#919—31no—
67C2×#916—31no—
68#5668D311yescharacteristic, complemented
69C4×#239—31no—
70C4×#235—31no—
71C3×#464—31no—
72#5233—31no—
73#5233—31no—
74#5182—31no—
75#5163—31no—
76#5090—31no—
77#5083—31no—
78#5075—31no—
79#5072—31no—
80#5057—31no—
81#5057—31no—
82#5057—31no—
83#5057—61no—
84#5054—31no—
85#5054D311yescharacteristic, complemented
86#5028—31no—
87C2×C4⋊(C3⋊C8)—31no—
88#4844—31no—
89D3×C4⋊C8—31no—
90#4818—31no—
91#4804—31no—
92#4786—31no—
93#4772—31no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×#239—22no—
103C3×#239—22no—
104C3×#237—22no—
105C3×#237—22no—
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3D411yescharacteristic
110C2×C3×C4×D3D411yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115C2×#624—21no—
116C2×#624—21no—
117#3799—22no—
118#3799D414yescomplemented
119C32×C22⋊C4—21no—
120C32×C22⋊C4—21no—
121C32×C42C2311yescharacteristic
122#3755—22no—
123#3753—22no—
124#3752—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#216—22no—
129C3×#214—22no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3D411yescharacteristic
138C3×C4×Dic3D411yescharacteristic
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142Dic3⋊Dic3—21no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145Dic32—21no—
146Dic32—21no—
147#3718—22no—
148#3717—22no—
149#3715—22no—
150#3714—22no—
151D3×C3⋊C8—22no—
152D3×C3⋊C8—22no—
153#3035—91noSylow
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C2×#239—31no—
157C2×#239C2×D311yescharacteristic
158C2×#237C2×D311yescharacteristic
159C2×#235—31no—
160C2×C3×Q16—31no—
161C2×C3×SD16—31no—
162C3×C4⋊Q8—31no—
163C3×#127—31no—
164C3×#124—21no—
165C3×#124—31no—
166C3×#124C2×D311yescharacteristic
167C3×#124C2×D311yescharacteristic
168C3×#121—61no—
169C3×#121—61no—
170C3×C4×Q8—31no—
171C3×C4×D4—61no—
172C3×C4×D4—61no—
173C2×C3×C42—31no—
174#950—64no—
175#950—64no—
176Q8×Dic3—31no—
177#944C2×D311yescharacteristic
178C2×#216—31no—
179C2×#216—31no—
180C2×#216C2×D311yescharacteristic
181C2×#215—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—61no—
186#940C2×D311yescharacteristic
187C2×#214—31no—
188C2×#214C2×D311yescharacteristic
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—61no—
193C4×#67—61no—
194C4×#67—61no—
195#926—31no—
196C22×C3⋊C8—31no—
197C22×C3⋊C8—31no—
198#919—64no—
199#916—64no—
200C2×D24—31no—
201C2×#204—31no—
202C2×D3×C8—31no—
203C2×D3×C8—31no—
204#893—31no—
205#893—61no—
206#892—31no—
207#892—61no—
208#884—21no—
209#884—21no—
210#67⋊C4—21no—
211#67⋊C4—21no—
212#875C2×D311yescharacteristic
213C4×D12—31no—
214C4×D12—31no—
215C4×D12—31no—
216C4×D12—61no—
217C4×D12—61no—
218#872—61no—
219C42×D3—61no—
220C42×D3—61no—
221C42×D3C2×D311yescharacteristic
222C4×Dic6—31no—
223C4×Dic6C2×D311yescharacteristic
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—31no—
227#835—31no—
228#835—31no—
229#835—31no—
230#835—31no—
231#835—61no—
232#835C2×D311yescharacteristic
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#832C2×D311yescharacteristic
239#821—31no—
240#816—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243#810—31no—
244#809—31no—
245C4⋊(C3⋊C8)—31no—
246C4⋊(C3⋊C8)—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic
251C23×C32—21no—
252C22×C3⋊D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C32×Q8—21no—
256C32×Q8—21no—
257C32×D4—21no—
258C32×D4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263C2×C3⋊Dic3—21no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)C2×D412yes—
266C4×C3⋊D3—42no—
267C3×#67—42no—
268C3×#67—42no—
269C3×#67—42no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—42no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—42no—
280C3×C4×D3—22no—
281C3×C4×D3—41no—
282C3×C4×D3—42no—
283C3×C4×D3C2×D412yes—
284C3×C4×D3#4112yes—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6C2×D412yes—
289#626—24no—
290#624—24no—
291#624—42no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#135—91no—
297C2×#135—91no—
298#532—31no—
299C4×#41—91no—
300#464—31no—
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—62no—
312C3×#41—62no—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—21no—
316C2×C3×Q8—31no—
317C2×C3×Q8—31no—
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×D4—21no—
321C2×C3×D4—31no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C2×#67—21no—
334C2×#67—21no—
335C2×#67—21no—
336C2×#67—61no—
337C22×Dic3—21no—
338#239—22no—
339#239—22no—
340#239—34no—
341#239—62no—
342#237—22no—
343#237—22no—
344#235—34no—
345#235—62no—
346C2×D12—21no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12C22×D311yescharacteristic
352C2×C4×D3—21no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C2×C4×D3—121no—
360C2×C4×D3#6711yescharacteristic
361C2×C4×D3#6711yescharacteristic
362C2×C4×D3C22×D311yescharacteristic
363C2×Dic6C22×D311yescharacteristic
364C2×Dic6C22×D311yescharacteristic
365C3×Q16—62no—
366C3×SD16—62no—
367C2×C3×C8—31no—
368C2×C3×C8—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—41no—
378C3×C22⋊C4—41no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C42—21no—
382C3×C42—31no—
383C3×C42—31no—
384C3×C42—31no—
385C3×C42—61no—
386C3×C42C22×D311yescharacteristic
387C3×C42C22×D311yescharacteristic
388#217—61no—
389#216—22no—
390#216—62no—
391#216—62no—
392#215—62no—
393#215—62no—
394#215—62no—
395#215—62no—
396#215—122no—
397#214—22no—
398#214—62no—
399#213—62no—
400#213—62no—
401#213—62no—
402#213—122no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—121no—
411C4⋊Dic3—31no—
412C4⋊Dic3—31no—
413C4⋊Dic3—61no—
414C4⋊Dic3—61no—
415C4⋊Dic3C22×D311yescharacteristic
416Dic3⋊C4—21no—
417Dic3⋊C4—21no—
418Dic3⋊C4—21no—
419Dic3⋊C4—61no—
420C4×Dic3—21no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3#6711yescharacteristic
426C4×Dic3#6711yescharacteristic
427C4×Dic3C22×D311yescharacteristic
428C2×C3⋊C8—31no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—31no—
432C2×C3⋊C8—61no—
433C2×C3⋊C8—61no—
434C2×C3⋊C8—62no—
435C2×C3⋊C8—62no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438D24—62no—
439#204—62no—
440D3×C8—62no—
441D3×C8—62no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
446C2×C3⋊D3—22no—
447C2×C3⋊D3—41no—
448C2×C3⋊D3—41no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3#12112yes—
455C32×C4—21no—
456C32×C4—21no—
457C32×C4—41no—
458C32×C4C22×D411yescharacteristic
459C32×C4C2×#4111yescharacteristic
460C3⋊Dic3—41no—
461C3×Dic3—22no—
462C3×Dic3—21no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3#12112yes—
466C3×Dic3#13512yescomplemented
467C2×#41—31no—
468C2×#41—31no—
469C2×#41—91no—
470#135—184no—
471#135—184no—
472C2×Q16—31no—
473C2×Q16—91no—
474C2×SD16—31no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×D8—91no—
479C2×D8—91no—
480C22×C8—91no—
481C22×C8—91no—
482C4⋊Q8—31no—
483#127—31no—
484#124—31no—
485#124D3211yescharacteristic
486#121—61no—
487#121—61no—
488C4×Q8—31no—
489C4×Q8—91no—
490C4×D4—61no—
491C4×D4—61no—
492C4×D4—91no—
493C4×D4—91no—
494C4×D4—181no—
495C4×D4—181no—
496#117—91no—
497#117—181no—
498C2×C42—31no—
499C2×C42—181no—
500C4⋊C8—31no—
501C4⋊C8—91no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504#103—31no—
505#103—91no—
506#103—91no—
507#103—91no—
508#102—31no—
509#102—91no—
510#102—91no—
511#102—91no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—31no—
515C23×C3—41no—
516C23×C3—61no—
517C22×D3—21no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—121no—
521C22×D3C2×#6711yescharacteristic
522C3×Q8—21no—
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×Q8—32no—
527C3×Q8—41no—
528C3×Q8—41no—
529C3×Q8—61no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×D4—21no—
533C3×D4—21no—
534C3×D4—21no—
535C3×D4—21no—
536C3×D4—41no—
537C3×D4—41no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—122no—
541C3×D4—122no—
542C3×D4—122no—
543C3×D4—122no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—32no—
552C2×C3×C4—32no—
553C2×C3×C4—31no—
554C2×C3×C4—41no—
555C2×C3×C4—62no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—121no—
560C2×C3×C4—122no—
561C2×C3×C4—122no—
562C2×C3×C4D3×D411yescharacteristic
563C2×C3×C4D3×D411yescharacteristic
564C2×C3×C4C2×#6711yescharacteristic
565C2×C3×C4C2×#6711yescharacteristic
566C2×C3×C4C23×D311yescharacteristic
567C2×C3×C4C23×D311yescharacteristic
568#67—42no—
569#67—42no—
570#67—42no—
571#67—64no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—42no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—121no—
579C2×Dic3C2×#6711yescharacteristic
580C2×Dic3C2×#6711yescharacteristic
581C2×Dic3C2×#6711yescharacteristic
582D12—21no—
583D12—21no—
584D12—32no—
585D12—32no—
586D12—42no—
587D12—62no—
588D12—64no—
589D12—61no—
590D12—61no—
591D12—121no—
592C4×D3—22no—
593C4×D3—41no—
594C4×D3—42no—
595C4×D3—64no—
596C4×D3—64no—
597C4×D3—122no—
598C4×D3—122no—
599C4×D3—122no—
600C4×D3—122no—
601C4×D3—242no—
602C4×D3D3×D412yes—
603C4×D3#23712yes—
604Dic6—21no—
605Dic6—21no—
606Dic6—21no—
607Dic6D3×D412yes—
608C3×C8—61no—
609C3×C8—61no—
610C3⋊C8—21no—
611C3⋊C8—21no—
612C3⋊C8—61no—
613C3⋊C8—61no—
614C3⋊C8—61no—
615C3⋊C8—61no—
616C3⋊C8—121no—
617C3⋊C8—121no—
618C2×C32—81no—
619C2×C32C2×#12111yescharacteristic
620C2×C32C2×#13511yescharacteristic
621C2×C32#57511yescharacteristic
622C3⋊D3—42no—
623C3×D3—22no—
624C3×D3—81no—
625#41—62no—
626#41—62no—
627#41—62no—
628#41—62no—
629#41—94no—
630#41—182no—
631C2×Q8—31no—
632C2×Q8—31no—
633C2×Q8C2×D3211yescharacteristic
634C2×D4—31no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4—61no—
639C2×D4—91no—
640C2×D4—181no—
641C2×D4C2×D3211yescharacteristic
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—181no—
648C22×C4—181no—
649C22×C4—181no—
650Q16—62no—
651Q16—182no—
652SD16—62no—
653SD16—182no—
654SD16—182no—
655SD16—182no—
656D8—182no—
657D8—182no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—91no—
661C2×C8—91no—
662C2×C8—182no—
663C2×C8—182no—
664C4⋊C4—31no—
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—91no—
669C4⋊C4—181no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C42—31no—
678C42—31no—
679C42—31no—
680C42—61no—
681C42—181no—
682C42—181no—
683C42C2×D3211yescharacteristic
684C22×C3—21no—
685C22×C3—32no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3C2×D3×D411yescharacteristic
701C22×C3C22×#6711yescharacteristic
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—122no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—241no—
715C2×D3—241no—
716C2×D3#93812yes—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—32no—
724C3×C4—32no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—61no—
730C3×C4—62no—
731C3×C4—81no—
732C3×C4—121no—
733C3×C4—121no—
734C3×C4C2×D3×D411yescharacteristic
735C3×C4C2×D3×D411yescharacteristic
736C3×C4C2×#23711yescharacteristic
737C3×C4D3×#4111yescharacteristic
738Dic3—21no—
739Dic3—22no—
740Dic3—41no—
741Dic3—41no—
742Dic3—121no—
743Dic3—121no—
744Dic3—241no—
745Dic3#93812yes—
746Dic3#95012yescomplemented
747C32#303511yescharacteristic, complemented, Sylow
748C23—21no—
749C23—31no—
750C23—61no—
751C23—181no—
752Q8—21no—
753Q8—21no—
754Q8—32no—
755Q8—61no—
756Q8—61no—
757Q8—61no—
758D4—21no—
759D4—21no—
760D4—61no—
761D4—61no—
762D4—92no—
763D4—122no—
764D4—122no—
765D4—122no—
766D4—122no—
767D4—184no—
768D4—181no—
769C2×C4—21no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—31no—
775C2×C4—62no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—121no—
780C2×C4—122no—
781C2×C4—122no—
782C2×C4—184no—
783C2×C4—181no—
784C2×C4—362no—
785C2×C4—362no—
786C2×C4D3×#6711yescharacteristic
787C2×C4D3×#6711yescharacteristic
788C2×C4C22×D3211yescharacteristic
789C8—61no—
790C8—61no—
791C8—181no—
792C8—181no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—62no—
797C2×C3—81no—
798C2×C3—81no—
799C2×C3—161no—
800C2×C3—241no—
801C2×C3D3×#12111yescharacteristic
802C2×C3D3×#13511yescharacteristic
803C2×C3#577711yescharacteristic
804C2×C3C2×#93811yescharacteristic
805C2×C3C2×#95011yescharacteristic
806C2×C3#582211yescharacteristic
807D3—22no—
808D3—81no—
809D3—122no—
810D3—122no—
811D3—242no—
812C22—32no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—61no—
817C22—61no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—182no—
822C22—361no—
823C22—361no—
824C22C2×D3×#6711yescharacteristic
825C4—21no—
826C4—21no—
827C4—32no—
828C4—32no—
829C4—41no—
830C4—61no—
831C4—62no—
832C4—121no—
833C4—121no—
834C4—361no—
835C4D32×D411yescharacteristic
836C4D3×#23711yescharacteristic
837C3—21no—
838C3#8059711yescharacteristic, complemented
839C3#8329611yescharacteristic, complemented
840C2—62no—
841C2—81no—
842C2—241no—
843C2—362no—
844C2D3×#93811yescharacteristic
845C2D3×#95011yescharacteristic
846C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
hypercenter#124D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#5668C2semidirect
2. C2×#63949C2semidirect
3. C2×#63935C2semidirect
4. C4×#3799C2semidirect
5. #10592756C2semidirect
6. C3×#5054C2semidirect
7. #10591574C2semidirect
8. #10591565C2semidirect
9. #10591556C2semidirect
10. #10591438C2semidirect
11. #10591429C2semidirect
12. #10591420C2semidirect
13. #10590356C2semidirect
14. D3×C4⋊(C3⋊C8)C2semidirect
15. #10590267C2semidirect
68. #5668D3semidirect
85. #5054D3semidirect
118. #3799D4semidirect
466. C3×Dic3#135semidirect
746. Dic3#950semidirect
747. C32#3035semidirect
838. C3#80597semidirect
839. C3#83296semidirect

Maximal subgroups

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

subgroupindex
C3×#56682
C2×#639492
C2×#639352
C4×#37992
#105927562
C3×#50542
#105915742
#105915652
#105915562
#105914382
#105914292
#105914202
#105903562
D3×C4⋊(C3⋊C8)2
#105902672
#832963
#805973