Finite Group Databasebeta

← #11865778

Subgroups — #11865778

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
1C2×C3×#916C211yesmaximal, characteristic, complemented
2#10595360C211yesmaximal, characteristic, complemented
3Dic3×#237C211yesmaximal, characteristic, complemented
4C2×#63935C211yesmaximal, characteristic, complemented
5#10592864C211yesmaximal, characteristic, complemented
6C3×#5162C211yesmaximal, characteristic, complemented
7#10591579C211yesmaximal, characteristic, complemented
8#10591574C211yesmaximal, characteristic, complemented
9#10591556C211yesmaximal, characteristic, complemented
10#10591481C211yesmaximal, characteristic, complemented
11#10591476C211yesmaximal, characteristic, complemented
12#10590799C211yesmaximal, characteristic, complemented
13#10590796C211yesmaximal, characteristic, complemented
14#10590690C211yesmaximal, characteristic, complemented
15D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
16#83900—31nomaximal
17#80427—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22#64156C2211yescharacteristic
23D4×C3⋊Dic3C2211yescharacteristic
24C2×#3753C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×#916—24no—
31C2×C3×#204C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33#67⋊Dic3—21no—
34Dic3×#67—21no—
35#63955—21no—
36C2×Dic32—21no—
37#63935—24no—
38#63911C2211yescharacteristic
39#63904—21no—
40#63904—21no—
41#63886—21no—
42#63886—21no—
43C4×D3×Dic3C2211yescharacteristic
44#63863C2211yescharacteristic
45#63843C2211yescharacteristic
46Dic3×Dic6C2211yescharacteristic
47#63841C2211yescharacteristic
48C2×#3718C2211yescharacteristic
49C2×#3717C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic
52#63648C2211yescharacteristic
53#63641C2211yescharacteristic
54C3×#835C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57#63572C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63566C2211yescharacteristic
60#63564C2211yescharacteristic
61#63563C2211yescharacteristic
62#63562C2211yescharacteristic
63C2×C3×#135—31no—
64#5832—31no—
65Dic3×#41—31no—
66C2×#950—31no—
67C2×#916—31no—
68C2×#916D311yescharacteristic, complemented
69#5725—31no—
70C4×#237—31no—
71C3×#461—31no—
72#5233—31no—
73#5185—31no—
74#5182—31no—
75#5166—31no—
76#5165—31no—
77#5165—31no—
78#5165—31no—
79#5165—61no—
80#5163—31no—
81#5162D311yescharacteristic, complemented
82#5153—31no—
83#5150—31no—
84#5113—31no—
85C2×Dic3⋊C8—31no—
86#5090—31no—
87#5015—31no—
88#4848—31no—
89D3×C4⋊C8—31no—
90#4804—31no—
91#4804—31no—
92#4798—31no—
93#4798—31no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C22×C3⋊Dic3—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×#239—22no—
102C3×#239—22no—
103C3×#237—22no—
104C3×#237D414yescomplemented
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#624—21no—
115C2×D3×Dic3D411yescharacteristic
116C2×D3×Dic3D411yescharacteristic
117#3799—22no—
118#3799—22no—
119C32×SD16—22no—
120C2×C32×C8C2311yescharacteristic
121#3757—21no—
122#3753—22no—
123#3752—21no—
124#3752—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C4×C3⋊Dic3C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#216—22no—
130C3×#214—22no—
131C3×#213—22no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×#204—22no—
139C3×D3×C8—22no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145Dic32—21no—
146Dic32—21no—
147Dic32—21no—
148Dic32D411yescharacteristic
149Dic32D411yescharacteristic
150#3718—22no—
151#3717—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—
160C3×#135—64no—
161C2×C3×Q16—31no—
162C2×C3×SD16—21no—
163C2×C3×SD16—31no—
164C2×C3×SD16—31no—
165C2×C3×SD16C2×D311yescharacteristic
166C2×C3×SD16C2×D311yescharacteristic
167C2×C3×D8—31no—
168C22×C3×C8—31no—
169C3×C4⋊Q8—31no—
170C3×C4×D4—31no—
171#950—64no—
172#947—31no—
173#947—31no—
174#947—31no—
175#947—61no—
176Q8×Dic3—31no—
177Q8×Dic3—31no—
178#944C2×D311yescharacteristic
179C2×#216—31no—
180C2×#216—31no—
181C2×#216C2×D311yescharacteristic
182C2×#215—31no—
183#940—31no—
184#939—61no—
185#939—61no—
186#936—31no—
187D4×Dic3—31no—
188D4×Dic3—31no—
189D4×Dic3—61no—
190D4×Dic3—61no—
191D4×Dic3—61no—
192D4×Dic3C2×D311yescharacteristic
193C2×#214C2×D311yescharacteristic
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—61no—
197C2×#213C2×D311yescharacteristic
198C4×#67—61no—
199C4×#67—61no—
200C4×#67—61no—
201#926—31no—
202#926—61no—
203C2×C4×Dic3—31no—
204C2×C4×Dic3—61no—
205C2×C4×Dic3—61no—
206C22×C3⋊C8—31no—
207#916—24no—
208#916—64no—
209C2×#204—31no—
210C2×#204C2×D311yescharacteristic
211C2×D3×C8—31no—
212C2×D3×C8C2×D311yescharacteristic
213#895—61no—
214#895—61no—
215#893—61no—
216#893—61no—
217#892—31no—
218#887—31no—
219#67⋊C4—61no—
220#877—61no—
221#874—31no—
222C42×D3—31no—
223C4×Dic6—31no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#103—31no—
227#835—31no—
228#835—31no—
229#835—31no—
230#835—61no—
231#835C2×D311yescharacteristic
232#832—31no—
233#832—31no—
234#821—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—61no—
239#816—31no—
240#816C2×D311yescharacteristic
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247Dic3⋊C8C2×D311yescharacteristic
248#809—31no—
249#809—31no—
250C4⋊(C3⋊C8)—31no—
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×D4C2×D412yes—
259C2×C32×C4—21no—
260C2×C32×C4C2411yescharacteristic
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—42no—
263C2×C3⋊Dic3C2×D411yescharacteristic
264C2×C3⋊Dic3C2×D411yescharacteristic
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—21no—
267C3×#67—24no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—24no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—42no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—42no—
279C3×C4×D3—42no—
280C3×C4×D3C2×D412yes—
281C3×C4×D3#4112yes—
282C3×Dic6—21no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6C2×D412yes—
286#626—42no—
287#626—42no—
288#626—42no—
289#624—42no—
290D3×Dic3—22no—
291D3×Dic3—41no—
292C32×C8—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#135—31no—
297C2×#135—91no—
298#532—91no—
299C4×#41—91no—
300#464—91no—
301#464—91no—
302#463—91no—
303#463—91no—
304#462—91no—
305#461—31no—
306#460—91no—
307#459—91no—
308C2×C4⋊C8—91no—
309#416—91no—
310#416—91no—
311C3×#41—34no—
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×D4C22×D311yescharacteristic
325C2×C3×D4C22×D311yescharacteristic
326C22×C3×C4—31no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C2×#67—21no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—31no—
337C22×Dic3—31no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—121no—
341#239—22no—
342#239—22no—
343#239—62no—
344#239—62no—
345#237—22no—
346#237#6714yescomplemented
347#235—62no—
348#235—62no—
349C2×D12—21no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12C22×D311yescharacteristic
357C2×C4×D3—21no—
358C2×C4×D3—31no—
359C2×C4×D3—31no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3C22×D311yescharacteristic
363C2×Dic6C22×D311yescharacteristic
364C2×Dic6C22×D311yescharacteristic
365C3×Q16—62no—
366C3×SD16—22no—
367C3×SD16—22no—
368C3×SD16—42no—
369C3×SD16—62no—
370C3×SD16—62no—
371C3×D8—62no—
372C2×C3×C8—21no—
373C2×C3×C8—31no—
374C2×C3×C8—31no—
375C2×C3×C8—62no—
376C2×C3×C8C22×D311yescharacteristic
377C2×C3×C8C22×D311yescharacteristic
378C3×C4⋊C4—31no—
379C3×C4⋊C4—61no—
380C3×C4⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C42—31no—
383#217—21no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—61no—
388#217—61no—
389#217—121no—
390#216—22no—
391#216—62no—
392#216—62no—
393#215—62no—
394#214—22no—
395#213—22no—
396#213—62no—
397#213—62no—
398#213—122no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—121no—
407(C2×D3)⋊C4—121no—
408C4⋊Dic3—31no—
409C4⋊Dic3—31no—
410C4⋊Dic3—61no—
411C4⋊Dic3—61no—
412C4⋊Dic3—61no—
413C4⋊Dic3C22×D311yescharacteristic
414Dic3⋊C4—21no—
415Dic3⋊C4—21no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418C4×Dic3—31no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—31no—
423C4×Dic3—31no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—61no—
429C4×Dic3—61no—
430C4×Dic3—61no—
431C4×Dic3C22×D311yescharacteristic
432C2×C3⋊C8—31no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—61no—
435C2×C3⋊C8—62no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438#204—22no—
439#204—62no—
440D3×C8—22no—
441D3×C8—62no—
442C22×C32—22no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
446C2×C3⋊D3—41no—
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—41no—
456C32×C4C22×D411yescharacteristic
457C32×C4C2×#4111yescharacteristic
458C3⋊Dic3—21no—
459C3⋊Dic3—21no—
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—64no—
471#135—184no—
472C2×Q16—31no—
473C2×Q16—91no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—91no—
477C2×SD16D3211yescharacteristic
478C2×D8—31no—
479C2×D8—91no—
480C22×C8—31no—
481C22×C8—91no—
482C4⋊Q8—31no—
483#127—91no—
484#124—91no—
485#124—91no—
486#121—181no—
487#121—181no—
488C4×Q8—91no—
489C4×Q8—91no—
490C4×D4—31no—
491C4×D4—91no—
492C4×D4—181no—
493C4×D4—181no—
494C4×D4—181no—
495C4×D4—181no—
496#117—91no—
497#117—181no—
498C2×C42—91no—
499C2×C42—181no—
500C4⋊C8—31no—
501C4⋊C8—91no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504#103—31no—
505#103—31no—
506#103—91no—
507#103—91no—
508#102—91no—
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×D3D3×D411yescharacteristic
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—22no—
535C3×D4—41no—
536C3×D4—64no—
537C3×D4—61no—
538C3×D4—61no—
539C3×D4—122no—
540C3×D4D3×D412yes—
541C3×D4C2×#6712yes—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—32no—
548C2×C3×C4—32no—
549C2×C3×C4—31no—
550C2×C3×C4—41no—
551C2×C3×C4—64no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—122no—
556C2×C3×C4—122no—
557C2×C3×C4C23×D311yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559#67—24no—
560#67—122no—
561#67—122no—
562#67—122no—
563C2×Dic3—21no—
564C2×Dic3—24no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—42no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—62no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—121no—
578C2×Dic3—121no—
579C2×Dic3—122no—
580C2×Dic3—122no—
581C2×Dic3—242no—
582C2×Dic3D3×D411yescharacteristic
583C2×Dic3D3×D411yescharacteristic
584C2×Dic3D3×D411yescharacteristic
585D12—21no—
586D12—21no—
587D12—42no—
588D12—61no—
589D12—61no—
590D12—61no—
591D12—61no—
592D12—121no—
593D12—121no—
594D12—122no—
595D12—122no—
596D12—122no—
597C4×D3—42no—
598C4×D3—62no—
599C4×D3—122no—
600C4×D3—121no—
601C4×D3—122no—
602C4×D3#23712yes—
603C4×D3C2×#6712yes—
604Dic6—21no—
605Dic6—21no—
606Dic6—21no—
607Dic6C2×#6712yes—
608C3×C8—21no—
609C3×C8—21no—
610C3×C8—41no—
611C3×C8—61no—
612C3×C8—61no—
613C3⋊C8—21no—
614C3⋊C8—21no—
615C3⋊C8—61no—
616C3⋊C8—61no—
617C3⋊C8—121no—
618C2×C32—42no—
619C2×C32C2×#12111yescharacteristic
620C2×C32C2×#13511yescharacteristic
621C2×C32#57511yescharacteristic
622C3⋊D3—81no—
623C3×D3—22no—
624C3×D3—81no—
625#41—34no—
626#41—62no—
627#41—62no—
628#41—62no—
629#41—182no—
630#41—182no—
631C2×Q8—31no—
632C2×Q8—31no—
633C2×Q8C2×D3211yescharacteristic
634C2×D4—31no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—91no—
638C2×D4—181no—
639C2×D4—181no—
640C2×D4—181no—
641C2×D4C2×D3211yescharacteristic
642C22×C4—31no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—91no—
647C22×C4—91no—
648C22×C4—181no—
649C22×C4—181no—
650Q16—62no—
651Q16—182no—
652SD16—22no—
653SD16—62no—
654SD16—62no—
655SD16—182no—
656D8—62no—
657D8—182no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—62no—
661C2×C8—91no—
662C2×C8—182no—
663C2×C8C2×D3211yescharacteristic
664C4⋊C4—31no—
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—91no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C22⋊C4—61no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C42—31no—
678C42—91no—
679C42—91no—
680C42—91no—
681C42—181no—
682C42—181no—
683C42—181no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—21no—
687C22×C3—32no—
688C22×C3—42no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3C2×D3×D411yescharacteristic
701C22×C3C2×D3×D411yescharacteristic
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—241no—
714C2×D3—241no—
715C2×D3—241no—
716C2×D3#93912yes—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—32no—
720C3×C4—32no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—61no—
724C3×C4—62no—
725C3×C4—81no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4C2×D3×D411yescharacteristic
729C3×C4C2×#23711yescharacteristic
730C3×C4D3×#4111yescharacteristic
731C3×C4C22×#6711yescharacteristic
732Dic3—21no—
733Dic3—22no—
734Dic3—41no—
735Dic3—41no—
736Dic3—61no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743Dic3—121no—
744Dic3—241no—
745Dic3#91612yescomplemented
746Dic3#93912yes—
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—64no—
760D4—61no—
761D4—61no—
762D4—122no—
763D4—181no—
764D4—181no—
765D4—362no—
766D4—362no—
767D4—362no—
768D4D3×#6712yes—
769C2×C4—21no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—31no—
775C2×C4—64no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—91no—
780C2×C4—91no—
781C2×C4—122no—
782C2×C4—122no—
783C2×C4—182no—
784C2×C4—181no—
785C2×C4—362no—
786C2×C4—361no—
787C2×C4—362no—
788C2×C4C22×D3211yescharacteristic
789C8—21no—
790C8—61no—
791C8—61no—
792C8—181no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—42no—
797C2×C3—42no—
798C2×C3—62no—
799C2×C3—82no—
800C2×C3—241no—
801C2×C3D3×#12111yescharacteristic
802C2×C3C2×#91611yescharacteristic
803C2×C3D3×#13511yescharacteristic
804C2×C3#576811yescharacteristic
805C2×C3#577711yescharacteristic
806C2×C3C2×#93911yescharacteristic
807D3—22no—
808D3—81no—
809D3—241no—
810D3—241no—
811D3—481no—
812C22—22no—
813C22—32no—
814C22—41no—
815C22—41no—
816C22—61no—
817C22—61no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—361no—
822C22—361no—
823C22—361no—
824C22D32×D411yescharacteristic
825C4—32no—
826C4—32no—
827C4—41no—
828C4—61no—
829C4—62no—
830C4—121no—
831C4—121no—
832C4—181no—
833C4—181no—
834C4—361no—
835C4D3×#23711yescharacteristic
836C4C2×D3×#6711yescharacteristic
837C3—21no—
838C3#8042711yescharacteristic, complemented
839C3#8390011yescharacteristic, complemented
840C2—42no—
841C2—62no—
842C2—241no—
843C2—721no—
844C2D3×#91611yescharacteristic
845C2#1059474611yescharacteristic
846C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#916C2semidirect
2. #10595360C2semidirect
3. Dic3×#237C2semidirect
4. C2×#63935C2semidirect
5. #10592864C2semidirect
6. C3×#5162C2semidirect
7. #10591579C2semidirect
8. #10591574C2semidirect
9. #10591556C2semidirect
10. #10591481C2semidirect
11. #10591476C2semidirect
12. #10590799C2semidirect
13. #10590796C2semidirect
14. #10590690C2semidirect
15. D3×Dic3⋊C8C2semidirect
68. C2×#916D3semidirect
81. #5162D3semidirect
104. C3×#237D4semidirect
346. #237#67semidirect
466. C3×Dic3#135semidirect
745. Dic3#916semidirect
747. C32#3035semidirect
838. C3#80427semidirect
839. C3#83900semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
#105953602
Dic3×#2372
C2×#639352
#105928642
C3×#51622
#105915792
#105915742
#105915562
#105914812
#105914762
#105907992
#105907962
#105906902
D3×Dic3⋊C82
#839003
#804273