Finite Group Databasebeta

← #11864610

Subgroups — #11864610

Order 1152.

1977 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3#10595043C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5232C211yesmaximal, characteristic, complemented
6#10591602C212yesmaximal, complemented
7#10591593C212yesmaximal, complemented
8#10591467C212yesmaximal, complemented
9#10591456C212yesmaximal, complemented
10C2×#63564C211yesmaximal, characteristic, complemented
11#10591073C211yesmaximal, characteristic, complemented
12#83912—31nomaximal
13#78886—31nomaximal
14C2×C32×#41C2211yescharacteristic
15#64366—24no—
16#64366—24no—
17C2×#3832C2212yes—
18C2×D4×C3⋊D3—22no—
19C2×D4×C3⋊D3C2212yes—
20C2×#3828—21no—
21C2×#3828C2211yescharacteristic
22C22×C4⋊(C3⋊D3)—21no—
23C22×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×#235C2211yescharacteristic, complemented
25C3×#950—24no—
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C2×C3×#214C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
31C2×C3×#208C2211yescharacteristic, complemented
32C22×C3×C3⋊C8C2211yescharacteristic, complemented
33#63978—22no—
34#63916C2212yescomplemented
35#63909—21no—
36#63871C2212yescomplemented
37#63857—21no—
38C2×#3717C2212yescomplemented
39#63825—24no—
40C2×#3714C2212yescomplemented
41C3×#835C2212yescomplemented
42C3×#832C2212yescomplemented
43#63564C2212yescomplemented
44#63564C2212yescomplemented
45#63557C2212yescomplemented
46#63557C2212yescomplemented
47C2×#1009—31no—
48C2×#1009—31no—
49C2×#1009—61no—
50C2×C3×#135—31no—
51#5833—31no—
52C2×#950D311yescharacteristic, complemented
53C2×#949—31no—
54C2×#908—31no—
55#5510—31no—
56C3×#417—31no—
57#5232D311yescharacteristic, complemented
58#5187—32no—
59#5172—32no—
60#5169—32no—
61#5156—32no—
62#5129—31no—
63C2×#821—31no—
64#5110—31no—
65C2×#809—31no—
66#4810—32no—
67#4808—32no—
68#4776—32no—
69#4773—32no—
70C23×C3⋊D3—21no—
71C23×C3⋊D3—22no—
72C32×#41—22no—
73C32×#41D414yescomplemented
74C2×C32×Q8C2311yescharacteristic
75C2×C32×D4—21no—
76C2×C32×D4C2311yescharacteristic
77C22×C32×C4—21no—
78C22×C32×C4C2311yescharacteristic
79C2×#638—22no—
80C2×#638D412yes—
81#3832—24no—
82#3832—24no—
83D4×C3⋊D3—216no—
84D4×C3⋊D3—24no—
85D4×C3⋊D3—24no—
86#3828—28no—
87#3828—22no—
88#3828—22no—
89C2×C4⋊(C3⋊D3)—28no—
90C2×C4⋊(C3⋊D3)—22no—
91C2×C4⋊(C3⋊D3)—21no—
92C2×C4⋊(C3⋊D3)—22no—
93C2×C4⋊(C3⋊D3)D411yescharacteristic
94C2×C4⋊(C3⋊D3)D414yescomplemented
95C2×C4⋊(C3⋊D3)C2312yes—
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3C2312yes—
98C2×#634D411yescharacteristic
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×#235—22no—
102C3×#235—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—22no—
107C3×#216—22no—
108C3×#215—22no—
109C3×#214—22no—
110C3×#213—22no—
111C3×C4⋊Dic3—21no—
112C3×C4⋊Dic3C2312yes—
113C3×#208—22no—
114C2×C3×C3⋊C8—22no—
115C2×C3×C3⋊C8C2311yescharacteristic
116C2×C3×C3⋊C8C2311yescharacteristic
117C2×C3×C3⋊C8C2312yes—
118Dic3⋊Dic3—22no—
119#3722—22no—
120(C2×D3)⋊Dic3—22no—
121#3717—24no—
122#3714—24no—
123#3012—91noSylow
124C2×C3×#41—21no—
125C2×C3×#41—31no—
126C2×C3×#41C2×D311yescharacteristic
127C2×C3×#41C2×D311yescharacteristic
128#1009—64no—
129#1009—64no—
130#1009—68no—
131#1009—68no—
132#1009—64no—
133#1009—64no—
134C2×#239—32no—
135C2×#239—32no—
136C2×#239—62no—
137C2×D3×D4—32no—
138C2×D3×D4—32no—
139C2×D3×D4—62no—
140C2×D3×D4—62no—
141C2×D3×D4—62no—
142C2×D3×D4—64no—
143C2×#235—31no—
144C2×#235—31no—
145C2×#235—61no—
146C2×#235—61no—
147C2×#235—61no—
148C2×#235—62no—
149C2×#235C2×D311yescharacteristic, complemented
150C22×D12—31no—
151C22×D12—31no—
152C22×D12—61no—
153C22×D12—61no—
154C22×D12—61no—
155C22×D12—62no—
156C3×#135—64no—
157C2×C3×Q16—31no—
158C2×C3×SD16—31no—
159C2×C3×SD16—31no—
160C2×C3×D8—31no—
161C2×C3×M16—31no—
162C22×C3×C8—31no—
163C2×C3×C4⋊C4—31no—
164#950—24no—
165#949—64no—
166#946—32no—
167C2×#216C2×D311yescharacteristic, complemented
168C2×#215—32no—
169C2×#215C2×D311yescharacteristic, complemented
170#939—62no—
171#938—32no—
172C2×#214C2×D311yescharacteristic, complemented
173C2×#213—32no—
174C2×#213C2×D311yescharacteristic, complemented
175#930—61no—
176#930—62no—
177C2×C4⋊Dic3C2×D311yescharacteristic, complemented
178#924—61no—
179C2×#208C2×D311yescharacteristic, complemented
180C22×C3⋊C8C2×D311yescharacteristic, complemented
181#908—64no—
182C2×D24—32no—
183C2×#204—32no—
184#897—32no—
185#897—61no—
186#895—32no—
187#895—61no—
188C3×#103—32no—
189C3×#102—32no—
190#835C2×D312yescomplemented
191#832C2×D312yescomplemented
192#821—32no—
193#821—32no—
194(C2×D3)⋊C8—32no—
195(C2×D3)⋊C8—32no—
196(C2×D3)⋊C8—32no—
197(C2×D3)⋊C8—32no—
198#809—32no—
199#809—32no—
200C23×C32—21no—
201C23×C32C2×D411yescharacteristic
202C22×C3⋊D3—22no—
203C22×C3⋊D3—28no—
204C22×C3⋊D3—24no—
205C22×C3⋊D3—82no—
206C22×C3⋊D3—82no—
207C22×C3⋊D3—81no—
208C22×C3⋊D3—81no—
209C22×C3⋊D3C2×D412yes—
210C22×C3×D3—21no—
211C32×Q8—21no—
212C32×Q8C2×D412yes—
213C32×D4—24no—
214C32×D4—21no—
215C32×D4C2×D412yes—
216C2×C32×C4—21no—
217C2×C32×C4—24no—
218C2×C32×C4C2×D412yes—
219C2×C32×C4C2×D411yescharacteristic
220C2×C32×C4C2×D412yes—
221C2×C32×C4C2411yescharacteristic
222#638—28no—
223#638—24no—
224C2×C3⋊Dic3C2×D412yes—
225C4⋊(C3⋊D3)—28no—
226C4⋊(C3⋊D3)—22no—
227C4⋊(C3⋊D3)—24no—
228C4⋊(C3⋊D3)—22no—
229C4⋊(C3⋊D3)C2×D414yes—
230C4×C3⋊D3—28no—
231C4×C3⋊D3—22no—
232C4×C3⋊D3—22no—
233#634—22no—
234C3×#67—42no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—81no—
238C3×D12—21no—
239C3×D12—21no—
240C3×C4×D3—42no—
241C3×Dic6—21no—
242C3×Dic6—21no—
243#626—82no—
244C3×C3⋊C8—22no—
245C3×C3⋊C8—21no—
246C3×C3⋊C8—21no—
247C2×H(5,𝔽2)—91no—
248C2×AGL(1,ℤ/8)—91no—
249C2×#135—31no—
250#537—91no—
251#452—92no—
252#450—92no—
253#449—92no—
254#447—92no—
255#417—31no—
256C2×#102—91no—
257#408—91no—
258C23×D3—62no—
259C23×D3—62no—
260C23×D3—64no—
261C23×D3—62no—
262C23×D3—61no—
263C23×D3—61no—
264C3×#41—24no—
265C3×#41—22no—
266C3×#41—22no—
267C3×#41—24no—
268C3×#41—62no—
269C3×#41—62no—
270C3×#41D1214yescomplemented
271C3×#41#6714yescomplemented
272C2×C3×Q8—21no—
273C2×C3×Q8—31no—
274C2×C3×Q8C22×D311yescharacteristic
275C2×C3×Q8C22×D311yescharacteristic
276C2×C3×D4—22no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—31no—
281C2×C3×D4—61no—
282C2×C3×D4C22×D311yescharacteristic
283C2×C3×D4C22×D311yescharacteristic
284C22×C3×C4—22no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—61no—
289C22×C3×C4—61no—
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C2×#67—21no—
293C2×#67—32no—
294C2×#67—32no—
295C2×#67—62no—
296C2×#67—62no—
297C2×#67—62no—
298C2×#67—62no—
299C2×#67—64no—
300C22×Dic3—21no—
301#239—64no—
302#239—64no—
303#239—68no—
304#239—68no—
305#239—64no—
306#239—64no—
307D3×D4—64no—
308D3×D4—64no—
309D3×D4—68no—
310D3×D4—632no—
311D3×D4—616no—
312D3×D4—616no—
313D3×D4—68no—
314D3×D4—64no—
315D3×D4—64no—
316#235—22no—
317#235—22no—
318#235—616no—
319#235—68no—
320#235—68no—
321#235—64no—
322#235—64no—
323#235—62no—
324#235—62no—
325#235—62no—
326#235—62no—
327C2×D12—34no—
328C2×D12—34no—
329C2×D12—32no—
330C2×D12—32no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—61no—
334C2×D12—62no—
335C2×D12—64no—
336C2×D12—62no—
337C2×D12—62no—
338C2×D12—62no—
339C2×D12—64no—
340C2×D12—616no—
341C2×D12—68no—
342C2×D12—68no—
343C2×D12—64no—
344C2×D12—62no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12—62no—
348C2×D12—62no—
349C2×D12C22×D311yescharacteristic
350C2×C4×D3—21no—
351C2×C4×D3—32no—
352C2×C4×D3—32no—
353C2×C4×D3—62no—
354C2×C4×D3—62no—
355C2×C4×D3—62no—
356C2×C4×D3—64no—
357C2×Dic6—31no—
358C2×Dic6—31no—
359C2×Dic6—61no—
360C2×Dic6C22×D311yescharacteristic
361C3×Q16—62no—
362C3×SD16—62no—
363C3×SD16—62no—
364C3×D8—62no—
365C3×M16—62no—
366C2×C3×C8—31no—
367C2×C3×C8—31no—
368C2×C3×C8—32no—
369C2×C3×C8—62no—
370C3×C4⋊C4—32no—
371C3×C4⋊C4—61no—
372#217—62no—
373#216—22no—
374#215—22no—
375#215—64no—
376#214—22no—
377#213—22no—
378#213—64no—
379(C2×D3)⋊C4—62no—
380(C2×D3)⋊C4—62no—
381(C2×D3)⋊C4—62no—
382C4⋊Dic3—21no—
383C4⋊Dic3—62no—
384C4⋊Dic3C22×D312yes—
385Dic3⋊C4—62no—
386#208—22no—
387C2×C3⋊C8—22no—
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390C2×C3⋊C8C22×D312yes—
391D24—64no—
392#204—64no—
393C22×C32—22no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32#12012yes—
399C22×C32C22×D411yescharacteristic
400C2×C3⋊D3—22no—
401C2×C3⋊D3—24no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—22no—
404C2×C3⋊D3—42no—
405C2×C3⋊D3—42no—
406C2×C3⋊D3—84no—
407C2×C3⋊D3—88no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C32×C4—22no—
412C32×C4#12012yes—
413C32×C4C22×D411yescharacteristic
414C32×C4C22×D411yescharacteristic
415C3⋊Dic3—22no—
416C3×Dic3—41no—
417C3×Dic3—42no—
418H(5,𝔽2)—184no—
419H(5,𝔽2)—184no—
420C2×#41—31no—
421C2×#41—91no—
422C2×#41—92no—
423C2×#41—181no—
424C2×#41D3211yescharacteristic
425C22×D4—92no—
426C22×D4—91no—
427C22×D4—181no—
428C22×D4—182no—
429AGL(1,ℤ/8)—184no—
430#135—64no—
431C2×Q16—31no—
432C2×SD16—31no—
433C2×SD16—31no—
434C2×SD16—92no—
435C2×D8—31no—
436C2×D8—92no—
437C2×M16—31no—
438C22×C8—31no—
439C22⋊Q8—92no—
440C22⋊Q8—181no—
441#121—92no—
442#121—181no—
443#121—182no—
444C2×C4⋊C4—31no—
445#103—32no—
446#102—32no—
447#102—92no—
448#102—92no—
449C22⋊C8—92no—
450C22⋊C8—92no—
451C23×C3—22no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—61no—
456C23×C3D3×D411yescharacteristic
457C23×C3D3×D411yescharacteristic
458C22×D3—21no—
459C22×D3—32no—
460C22×D3—32no—
461C22×D3—62no—
462C22×D3—64no—
463C22×D3—62no—
464C22×D3—62no—
465C22×D3—616no—
466C22×D3—68no—
467C22×D3—68no—
468C22×D3—68no—
469C22×D3—64no—
470C22×D3—64no—
471C22×D3—242no—
472C22×D3—242no—
473C22×D3—242no—
474C22×D3—242no—
475C22×D3—241no—
476C22×D3—241no—
477C22×D3—241no—
478C22×D3—241no—
479C22×D3—242no—
480C22×D3—242no—
481C22×D3—244no—
482C22×D3—244no—
483C3×Q8—22no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—22no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8C2×D1212yes—
490C3×Q8C2×#6712yes—
491C3×D4—28no—
492C3×D4—22no—
493C3×D4—24no—
494C3×D4—24no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—22no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—122no—
501C3×D4C2×D1212yes—
502C3×D4C2×#6712yes—
503C2×C3×C4—22no—
504C2×C3×C4—28no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—24no—
508C2×C3×C4—24no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—21no—
512C2×C3×C4—22no—
513C2×C3×C4—61no—
514C2×C3×C4—62no—
515C2×C3×C4—122no—
516C2×C3×C4—241no—
517C2×C3×C4C2×D1212yes—
518C2×C3×C4D3×D411yescharacteristic
519C2×C3×C4D3×D412yes—
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D412yes—
522C2×C3×C4C2×#6712yes—
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525#67—42no—
526#67—616no—
527#67—68no—
528#67—68no—
529#67—68no—
530#67—64no—
531#67—64no—
532#67—242no—
533C2×Dic3—22no—
534C2×Dic3—21no—
535C2×Dic3—32no—
536C2×Dic3—32no—
537C2×Dic3—62no—
538C2×Dic3—81no—
539D12—21no—
540D12—21no—
541D12—34no—
542D12—34no—
543D12—64no—
544D12—64no—
545D12—68no—
546D12—616no—
547D12—68no—
548D12—68no—
549D12—64no—
550D12—64no—
551D12—62no—
552D12—64no—
553D12—62no—
554D12—62no—
555D12—62no—
556D12—242no—
557C4×D3—42no—
558C4×D3—616no—
559C4×D3—68no—
560C4×D3—68no—
561C4×D3—64no—
562C4×D3—64no—
563C4×D3—62no—
564C4×D3—62no—
565C4×D3—62no—
566C4×D3—62no—
567Dic6—21no—
568Dic6—21no—
569Dic6—64no—
570Dic6—62no—
571Dic6—62no—
572C3×C8—61no—
573C3×C8—61no—
574C3×C8—62no—
575C3⋊C8—22no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C2×C32—22no—
579C2×C32—42no—
580C2×C32C2×#12011yescharacteristic
581C2×C32#57611yescharacteristic
582C2×C32#57711yescharacteristic
583C3⋊D3—42no—
584C3⋊D3—44no—
585C3×D3—81no—
586C24—182no—
587C24—181no—
588#41—22no—
589#41—62no—
590#41—62no—
591#41—188no—
592#41—184no—
593#41—184no—
594#41—182no—
595#41—182no—
596#41#62614yescomplemented
597C2×Q8—31no—
598C2×Q8—91no—
599C2×Q8C2×D3211yescharacteristic
600C2×D4—21no—
601C2×D4—31no—
602C2×D4—61no—
603C2×D4—92no—
604C2×D4—92no—
605C2×D4—94no—
606C2×D4—91no—
607C2×D4—182no—
608C2×D4—188no—
609C2×D4—182no—
610C2×D4—182no—
611C2×D4—184no—
612C2×D4—1816no—
613C2×D4—184no—
614C2×D4—182no—
615C2×D4—181no—
616C2×D4C2×D3211yescharacteristic
617C22×C4—21no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—92no—
621C22×C4—182no—
622C22×C4C2×D3211yescharacteristic
623Q16—62no—
624SD16—62no—
625SD16—62no—
626SD16—184no—
627D8—62no—
628D8—184no—
629M16—62no—
630C2×C8—32no—
631C2×C8—31no—
632C2×C8—31no—
633C2×C8—62no—
634C4⋊C4—32no—
635C4⋊C4—61no—
636C4⋊C4—182no—
637C22⋊C4—182no—
638C22⋊C4—182no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—24no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—21no—
647C22×C3—22no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3#88212yes—
660C22×C3#93712yes—
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C2×D3×D411yescharacteristic
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—68no—
667C2×D3—64no—
668C2×D3—64no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—62no—
672C2×D3—62no—
673C2×D3—62no—
674C2×D3—64no—
675C2×D3—62no—
676C2×D3—122no—
677C2×D3—122no—
678C2×D3—124no—
679C2×D3—124no—
680C2×D3—122no—
681C2×D3—122no—
682C2×D3—122no—
683C2×D3—122no—
684C2×D3—244no—
685C2×D3—244no—
686C2×D3—248no—
687C2×D3—2416no—
688C2×D3—248no—
689C2×D3—248no—
690C3×C4—24no—
691C3×C4—22no—
692C3×C4—22no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—22no—
696C3×C4—121no—
697C3×C4—122no—
698C3×C4#88212yes—
699C3×C4#93712yes—
700C3×C4C22×D1211yescharacteristic
701C3×C4C2×D3×D411yescharacteristic
702C3×C4C2×D3×D411yescharacteristic
703C3×C4C22×#6711yescharacteristic
704Dic3—42no—
705Dic3—41no—
706Dic3—64no—
707Dic3—62no—
708Dic3—62no—
709C32#301211yescharacteristic, complemented, Sylow
710C23—21no—
711C23—61no—
712C23—92no—
713C23—188no—
714C23—182no—
715C23—184no—
716C23—721no—
717C23—721no—
718C23—722no—
719C23—722no—
720C23#381111yescharacteristic
721Q8—21no—
722Q8—61no—
723Q8—61no—
724Q8—182no—
725Q8C2×#62612yes—
726D4—24no—
727D4—21no—
728D4—61no—
729D4—61no—
730D4—94no—
731D4—122no—
732D4—188no—
733D4—188no—
734D4—184no—
735D4—182no—
736D4—184no—
737D4—182no—
738D4—722no—
739D4C2×#62612yes—
740C2×C4—21no—
741C2×C4—24no—
742C2×C4—62no—
743C2×C4—61no—
744C2×C4—92no—
745C2×C4—122no—
746C2×C4—188no—
747C2×C4—182no—
748C2×C4—182no—
749C2×C4—241no—
750C2×C4C2×#62612yes—
751C2×C4#381112yes—
752C2×C4#381111yescharacteristic
753C2×C4C22×D3211yescharacteristic
754C8—61no—
755C8—61no—
756C8—62no—
757C2×C3—22no—
758C2×C3—22no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—42no—
763C2×C3—44no—
764C2×C3—42no—
765C2×C3—42no—
766C2×C3—241no—
767C2×C3C2×#88211yescharacteristic
768C2×C3#576911yescharacteristic
769C2×C3#577011yescharacteristic
770C2×C3#577411yescharacteristic
771C2×C3#577811yescharacteristic
772C2×C3C2×#93711yescharacteristic
773D3—81no—
774D3—124no—
775D3—128no—
776D3—122no—
777D3—124no—
778D3—122no—
779D3—124no—
780C22—21no—
781C22—21no—
782C22—22no—
783C22—41no—
784C22—41no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—182no—
789C22—182no—
790C22—184no—
791C22—182no—
792C22—362no—
793C22—362no—
794C22—724no—
795C22—728no—
796C22#6398112yes—
797C22C2×#381111yescharacteristic
798C4—22no—
799C4—122no—
800C4—121no—
801C4—182no—
802C4#6398112yes—
803C4C22×#62611yescharacteristic
804C4C2×#381111yescharacteristic
805C3—21no—
806C3#7888611yescharacteristic, complemented
807C3#8391211yescharacteristic, complemented
808C2—22no—
809C2—42no—
810C2—241no—
811C2—362no—
812C2—364no—
813C2#1059546111yescharacteristic
814C2#1059547311yescharacteristic
815C2C2×#6398111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64366C2semidirect
2. C2×C3×#950C2semidirect
3. #10595043C2semidirect
4. C2×#63825C2semidirect
5. C3×#5232C2semidirect
6. #10591602C2semidirect
7. #10591593C2semidirect
8. #10591467C2semidirect
9. #10591456C2semidirect
10. C2×#63564C2semidirect
11. #10591073C2semidirect
24. C2×C3×#235C22semidirect
26. C2×C3×#216C22semidirect
27. C2×C3×#215C22semidirect
28. C2×C3×#214C22semidirect
29. C2×C3×#213C22semidirect
30. C2×C3×C4⋊Dic3C22semidirect
31. C2×C3×#208C22semidirect
32. C22×C3×C3⋊C8C22semidirect
34. #63916C22semidirect
36. #63871C22semidirect
38. C2×#3717C22semidirect
40. C2×#3714C22semidirect
41. C3×#835C22semidirect
42. C3×#832C22semidirect
43. #63564C22semidirect
44. #63564C22semidirect
45. #63557C22semidirect
46. #63557C22semidirect
52. C2×#950D3semidirect
57. #5232D3semidirect
73. C32×#41D4semidirect
94. C2×C4⋊(C3⋊D3)D4semidirect
149. C2×#235C2×D3semidirect
167. C2×#216C2×D3semidirect
169. C2×#215C2×D3semidirect
172. C2×#214C2×D3semidirect
174. C2×#213C2×D3semidirect
177. C2×C4⋊Dic3C2×D3semidirect
179. C2×#208C2×D3semidirect
180. C22×C3⋊C8C2×D3semidirect
190. #835C2×D3semidirect
191. #832C2×D3semidirect
270. C3×#41D12semidirect
271. C3×#41#67semidirect
596. #41#626semidirect
709. C32#3012semidirect
806. C3#78886semidirect
807. C3#83912semidirect

Maximal subgroups

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

subgroupindex
C2×#643662
C2×C3×#9502
#105950432
C2×#638252
C3×#52322
#105916022
#105915932
#105914672
#105914562
C2×#635642
#105910732
#839123
#788863