Finite Group Databasebeta

← #10847380

Subgroups — #10847380

Order 768.

1474 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5596C211yesmaximal, characteristic, complemented
2C2×C3×#466C211yesmaximal, characteristic, complemented
3#82699C211yesmaximal, characteristic, complemented
4C2×#5038C211yesmaximal, characteristic, complemented
5#72044C211yesmaximal, characteristic, complemented
6#72037C211yesmaximal, characteristic, complemented
7#71973C211yesmaximal, characteristic, complemented
8C2×#4550C211yesmaximal, characteristic, complemented
9#71681C211yesmaximal, characteristic, complemented
10#70638C211yesmaximal, characteristic, complemented
11#70617C211yesmaximal, characteristic, complemented
12#70211C211yesmaximal, characteristic, complemented
13#70208C211yesmaximal, characteristic, complemented
14#70167C211yesmaximal, characteristic, complemented
15#70163C211yesmaximal, characteristic, complemented
16#25496—31nomaximal, Sylow
17C22×#237—21no—
18C22×C3×D8C2211yescharacteristic
19C23×C3×C8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×#940C2211yescharacteristic
23C2×#939—21no—
24C2×#935—21no—
25C2×D4×Dic3C2211yescharacteristic
26C22×#213C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C23×C3⋊C8C2211yescharacteristic
30#5596—24no—
31#5596—24no—
32C2×#893C2211yescharacteristic
33C2×#888C2211yescharacteristic
34C2×#885—21no—
35C2×#67⋊C4—21no—
36C3×#466—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40#5221C2211yescharacteristic
41#5221C2211yescharacteristic
42#5220—21no—
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45C2×#832C2211yescharacteristic
46#5212C2211yescharacteristic
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic
49#5038—24no—
50#4972C2211yescharacteristic
51#4972C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#807C2211yescharacteristic
54#4944—21no—
55#4944—21no—
56#4551C2211yescharacteristic
57#4551C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#532—31no—
65C2×#466—31no—
66C2×#466D311yescharacteristic, complemented
67#2854—31no—
68#2057—31no—
69#2041—31no—
70#2023—31no—
71#2011—31no—
72#1893—31no—
73#1893—31no—
74#1879—31no—
75#1879—31no—
76#1862—31no—
77#1862—31no—
78C2×#336—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C22×#67—21no—
87C23×Dic3—21no—
88C23×Dic3D411yescharacteristic
89C23×Dic3D411yescharacteristic
90C2×#237—28no—
91C2×#237—44no—
92C2×#237—44no—
93C22×D12C2311yescharacteristic
94C22×C4×D3—21no—
95C22×Dic6—21no—
96C2×C3×D8—22no—
97C2×C3×D8—22no—
98C2×C3×D8—41no—
99C22×C3×C8—22no—
100C22×C3×C8—22no—
101C22×C3×C8—41no—
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C3×#121—22no—
105C3×#121—22no—
106C3×#121—22no—
107C3×#121D414yes—
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115C2×#217—21no—
116C2×#217—21no—
117C2×#217—21no—
118#940—22no—
119#940—22no—
120#939—28no—
121#935—44no—
122D4×Dic3—22no—
123D4×Dic3—22no—
124C2×#213—22no—
125C2×#213—22no—
126C2×#213—41no—
127#930—22no—
128#930D414yes—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×C4×Dic3—22no—
138C2×C4×Dic3—22no—
139C2×C4×Dic3D411yescharacteristic
140C2×C4×Dic3D411yescharacteristic
141C2×C4×Dic3C2311yescharacteristic
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8—22no—
144C22×C3⋊C8—22no—
145C22×C3⋊C8—41no—
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148#893—22no—
149#893—22no—
150#888—22no—
151#888—22no—
152#885—28no—
153#67⋊C4—28no—
154C3×#107—22no—
155C3×#102—22no—
156C3×#102—22no—
157#832—22no—
158#832—22no—
159#832—41no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163#821—22no—
164#821—41no—
165#809—22no—
166#807—22no—
167C22×#41—61no—
168C22×D8—31no—
169C22×D8C2×D311yescharacteristic
170C23×C8—31no—
171C23×C8C2×D311yescharacteristic
172#532—64no—
173#532—64no—
174C2×C4⋊Q8—31no—
175C2×#127—31no—
176C2×#124—61no—
177C2×#123—61no—
178C2×#121—31no—
179C2×#121—61no—
180C2×#121C2×D311yescharacteristic
181C2×#121C2×D311yescharacteristic
182C2×C4×D4—31no—
183C2×C4×D4—31no—
184C2×C4×D4—61no—
185C22×C42—31no—
186#466—24no—
187#466—64no—
188C2×#107—31no—
189C2×#107C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102C2×D311yescharacteristic
197C2×#102C2×D311yescharacteristic
198#390—31no—
199#390—31no—
200#389—31no—
201#389—31no—
202#388—61no—
203#388—61no—
204#386—61no—
205#380—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#336—31no—
211#336—31no—
212#336—31no—
213#336—31no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3C2×D411yescharacteristic
217C23×D3—21no—
218C2×C3×D4—24no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4C2×D412yes—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D412yes—
244C22×C3×C4C2×D412yes—
245C22×C3×C4C2411yescharacteristic
246C2×#67—24no—
247C2×#67—24no—
248C2×#67—24no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—42no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—24no—
258C22×Dic3—22no—
259C22×Dic3—21no—
260C22×Dic3—22no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—41no—
264C22×Dic3—42no—
265C22×Dic3—42no—
266C22×Dic3D814yescomplemented
267C22×Dic3C2×D411yescharacteristic
268C22×Dic3C2×D411yescharacteristic
269C22×Dic3C2×D411yescharacteristic
270C22×Dic3C2×D411yescharacteristic
271#237—432no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12C2×D412yes—
278C2×C4×D3—24no—
279C2×C4×D3—42no—
280C2×C4×D3—42no—
281C2×Dic6—24no—
282C2×Dic6—42no—
283C2×Dic6—42no—
284C3×D8—44no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—44no—
291C2×C3×C8#4112yescomplemented
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4C2×D412yes—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—42no—
298#217—24no—
299#217—42no—
300#217—42no—
301#217—42no—
302#217—42no—
303#217—42no—
304#213—44no—
305(C2×D3)⋊C4—24no—
306(C2×D3)⋊C4—24no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3C2×D412yes—
313Dic3⋊C4—24no—
314Dic3⋊C4—42no—
315Dic3⋊C4—42no—
316C4×Dic3—22no—
317C4×Dic3—22no—
318C4×Dic3—21no—
319C4×Dic3—21no—
320C4×Dic3—21no—
321C4×Dic3—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—44no—
328C2×C3⋊C8#4112yescomplemented
329C2×#41—68no—
330C2×#41—124no—
331C2×#41—124no—
332C22×Q8—61no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—31no—
336C22×D4—61no—
337C22×D4—61no—
338C22×D4—61no—
339C22×D4C22×D311yescharacteristic
340C22×D4C22×D311yescharacteristic
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—61no—
344C23×C4—61no—
345C23×C4C22×D311yescharacteristic
346C2×D8—22no—
347C2×D8—22no—
348C2×D8—41no—
349C2×D8—62no—
350C2×D8—62no—
351C2×D8—121no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—31no—
355C22×C8—31no—
356C22×C8—41no—
357C22×C8—62no—
358C22×C8—62no—
359C22×C8—121no—
360C22×C8C22×D311yescharacteristic
361C22×C8C22×D311yescharacteristic
362C4⋊Q8—62no—
363C4⋊Q8—62no—
364#127—62no—
365#127—62no—
366#124—68no—
367#123—124no—
368#121—22no—
369#121—22no—
370#121—22no—
371#121—34no—
372#121—68no—
373#121—62no—
374#121#6714yes—
375C4×D4—68no—
376C4×D4—62no—
377C4×D4—62no—
378C4×D4—62no—
379C4×D4—62no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4—61no—
386C2×C4⋊C4C22×D311yescharacteristic
387C2×C4⋊C4C22×D311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C42—31no—
399C2×C42—31no—
400C2×C42—31no—
401C2×C42—31no—
402C2×C42—62no—
403C2×C42—62no—
404#107—22no—
405#107—62no—
406#102—22no—
407#102—22no—
408#102—62no—
409#102—62no—
410#102—62no—
411#102—62no—
412#102—121no—
413#102—121no—
414#95—61no—
415#95—61no—
416#95—61no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—22no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3#12012yes—
436C23×C3C2×D812yes—
437C23×C3AGL(1,ℤ/8)12yes—
438C23×C3C22×D411yescharacteristic
439C22×D3—22no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C3×D4—22no—
447C3×D4—22no—
448C3×D4—48no—
449C3×D4—41no—
450C3×D4—41no—
451C3×D4—41no—
452C3×D4—41no—
453C3×D4—41no—
454C3×D4—41no—
455C3×D4—84no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4#12012yes—
469C2×C3×C4C22×D411yescharacteristic
470C2×C3×C4C22×D411yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×C3×C4C2×#4111yescharacteristic
473C2×C3×C4H(5,𝔽2)11yescharacteristic
474C2×C3×C42−1+411yescharacteristic
475#67—48no—
476#67—48no—
477#67—48no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—28no—
485C2×Dic3—21no—
486C2×Dic3—22no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—44no—
490C2×Dic3—48no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3C2×D812yes—
500C2×Dic3C2×D812yes—
501C2×Dic3#13512yes—
502D12—22no—
503D12—22no—
504D12—41no—
505D12—41no—
506C4×D3—48no—
507Dic6—48no—
508C3×C8—22no—
509C3×C8—41no—
510C3⋊C8—22no—
511C3⋊C8—41no—
512C24—21no—
513C24—21no—
514C24—61no—
515C24D3×D411yescharacteristic
516#41—1232no—
517C2×Q8—64no—
518C2×Q8—122no—
519C2×Q8—122no—
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—32no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—64no—
539C2×D4—64no—
540C2×D4—64no—
541C2×D4—61no—
542C2×D4—61no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4—122no—
549C2×D4—122no—
550C2×D4—122no—
551C2×D4—122no—
552C2×D4C2×#6712yes—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—34no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—64no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—64no—
569C22×C4—62no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—122no—
574C22×C4—122no—
575C22×C4—122no—
576C22×C4—121no—
577C22×C4—122no—
578C22×C4D3×D411yescharacteristic
579C22×C4D3×D412yes—
580C22×C4C2×#6712yes—
581C22×C4C23×D311yescharacteristic
582D8—44no—
583D8—124no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—32no—
590C2×C8—44no—
591C2×C8—61no—
592C2×C8—61no—
593C2×C8—61no—
594C2×C8—61no—
595C2×C8—61no—
596C2×C8—124no—
597C2×C8#23712yescomplemented
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—32no—
602C4⋊C4—64no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—122no—
609C4⋊C4—122no—
610C4⋊C4C2×#6712yes—
611C22⋊C4—24no—
612C22⋊C4—42no—
613C22⋊C4—64no—
614C22⋊C4—64no—
615C22⋊C4—64no—
616C22⋊C4—122no—
617C22⋊C4—122no—
618C22⋊C4—122no—
619C22⋊C4—122no—
620C22⋊C4—122no—
621C42—62no—
622C42—62no—
623C42—61no—
624C42—61no—
625C42—61no—
626C42—61no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3#44714yes—
648C22×C3C2×#12011yescharacteristic
649C22×C3#53211yescharacteristic
650C22×C3#53711yescharacteristic
651C22×C3C22×D811yescharacteristic
652C22×C3C2×#13511yescharacteristic
653C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
654C22×C3#57511yescharacteristic
655C2×D3—42no—
656C2×D3—42no—
657C2×D3—42no—
658C2×D3—81no—
659C2×D3—81no—
660C2×D3—81no—
661C2×D3—81no—
662C3×C4—22no—
663C3×C4—42no—
664C3×C4—81no—
665C3×C4#54611yescharacteristic
666C3×C4#54611yescharacteristic
667C3×C4#54711yescharacteristic
668C3×C4#54711yescharacteristic
669Dic3—22no—
670Dic3—22no—
671Dic3—22no—
672Dic3—42no—
673Dic3—41no—
674Dic3—81no—
675Dic3—81no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—62no—
695C23—121no—
696C23—121no—
697C23—121no—
698C23—121no—
699C23—121no—
700C23—121no—
701C23D3×D812yes—
702C23#91112yes—
703C23#93712yes—
704C23C2×D3×D411yescharacteristic
705Q8—128no—
706D4—22no—
707D4—22no—
708D4—48no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—62no—
716D4—62no—
717D4—84no—
718D4—128no—
719D4—128no—
720D4—128no—
721D4—121no—
722D4—121no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—68no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—62no—
749C2×C4—128no—
750C2×C4—124no—
751C2×C4—128no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4#93712yes—
761C2×C4C2×D3×D411yescharacteristic
762C2×C4C2×#23711yescharacteristic
763C2×C4#100411yescharacteristic
764C2×C4D3×#4111yescharacteristic
765C2×C4#101011yescharacteristic
766C2×C4C22×#6711yescharacteristic
767C8—22no—
768C8—41no—
769C8—62no—
770C8—121no—
771C2×C3—24no—
772C2×C3—82no—
773C2×C3—161no—
774C2×C3#243011yescharacteristic
775C2×C3C2×#44711yescharacteristic
776C2×C3#300211yescharacteristic
777C2×C3#316911yescharacteristic
778C2×C3#318011yescharacteristic
779C2×C3#324511yescharacteristic
780C2×C3#324711yescharacteristic
781D3—82no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—122no—
803C22—122no—
804C22—122no—
805C22—241no—
806C22—241no—
807C22—241no—
808C22—241no—
809C22#515614yes—
810C22#559611yescharacteristic
811C22#559711yescharacteristic
812C22C2×D3×D811yescharacteristic
813C22C2×#91111yescharacteristic
814C22D3×#13511yescharacteristic
815C22#576811yescharacteristic
816C22C2×#93711yescharacteristic
817C4—22no—
818C4—42no—
819C4—62no—
820C4—62no—
821C4—62no—
822C4—81no—
823C4—122no—
824C4—121no—
825C4—241no—
826C4—241no—
827C4#561011yescharacteristic
828C4#561111yescharacteristic
829C4#580611yescharacteristic
830C4#582411yescharacteristic
831C3#2549611yescharacteristic, complemented, Sylow
832C2—24no—
833C2—82no—
834C2—161no—
835C2—242no—
836C2#8069711yescharacteristic
837C2#8070111yescharacteristic
838C2#8070211yescharacteristic
839C2#8070311yescharacteristic
840C2#8265111yescharacteristic
841C2C2×#515611yescharacteristic
842C2#8391111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#466C2
socleC23×C3C22×D4
hypercenterC2×#466D3
hypocenterC3#25496
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#5596C2semidirect
2. C2×C3×#466C2semidirect
3. #82699C2semidirect
4. C2×#5038C2semidirect
5. #72044C2semidirect
6. #72037C2semidirect
7. #71973C2semidirect
8. C2×#4550C2semidirect
9. #71681C2semidirect
10. #70638C2semidirect
11. #70617C2semidirect
12. #70211C2semidirect
13. #70208C2semidirect
14. #70167C2semidirect
15. #70163C2semidirect
66. C2×#466D3semidirect
266. C22×Dic3D8semidirect
291. C2×C3×C8#41semidirect
328. C2×C3⋊C8#41semidirect
597. C2×C8#237semidirect
831. C3#25496semidirect

Maximal subgroups

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

subgroupindex
C2×#55962
C2×C3×#4662
#826992
C2×#50382
#720442
#720372
#719732
C2×#45502
#716812
#706382
#706172
#702112
#702082
#701672
#701632
#254963