Finite Group Databasebeta

← #10846256

Subgroups — #10846256

Order 768.

1104 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#492C211yesmaximal, characteristic, complemented
2C2×#5171C211yesmaximal, characteristic, complemented
3C2×#5171C211yesmaximal, characteristic, complemented
4C2×Dic3×SD16C211yesmaximal, characteristic, complemented
5#83254C211yesmaximal, characteristic, complemented
6#83186C211yesmaximal, characteristic
7#72054C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#72049C211yesmaximal, characteristic, complemented
10#72048C211yesmaximal, characteristic, complemented
11#72047C211yesmaximal, characteristic, complemented
12#71781C211yesmaximal, characteristic, complemented
13#71762C211yesmaximal, characteristic, complemented
14C8×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
15#69769C211yesmaximal, characteristic, complemented
16#25410—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#127C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C2×#946C2211yescharacteristic
25C2×Q8×Dic3C2211yescharacteristic
26C2×#939—21no—
27C2×#938C2211yescharacteristic
28C2×#938C2211yescharacteristic
29C2×D4×Dic3C2211yescharacteristic
30C22×D3×C8C2211yescharacteristic
31C3×#492—24no—
32C2×C3×C4×C8C2211yescharacteristic
33#5229C2211yescharacteristic
34C2×#835C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38#5223—21no—
39#5222—21no—
40#5221C2211yescharacteristic
41#5220—21no—
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45C2×#832C2211yescharacteristic
46#5171—24no—
47#5171—24no—
48Dic3×SD16—24no—
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×#817C2211yescharacteristic
51C2×#817C2211yescharacteristic
52C2×C8×Dic3C2211yescharacteristic
53#4994—21no—
54#4990—21no—
55#4982—21no—
56#4976—21no—
57C4×(C2×D3)⋊C4C2211yescharacteristic
58#4928C2211yescharacteristic
59#4928C2211yescharacteristic
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4550C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#492D311yescharacteristic, complemented
65C2×#465—31no—
66C2×#465—31no—
67C2×C4×SD16—31no—
68#2429—31no—
69#2428—31no—
70#2043—31no—
71#2041—31no—
72#2000—31no—
73#2000—31no—
74#1968—31no—
75#1941—31no—
76#1880—31no—
77#1877—31no—
78C8×C22⋊C4—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C23×Dic3—21no—
88C22×C4×D3C2311yescharacteristic
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×SD16—22no—
93C2×C3×SD16—22no—
94C2×C3×SD16—22no—
95C2×C3×SD16—22no—
96C2×C3×SD16—22no—
97C2×C3×SD16—22no—
98C2×C3×SD16—41no—
99C2×C3×SD16—41no—
100C2×C3×SD16D414yescomplemented
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C3×C4⋊Q8—22no—
104C3×C4⋊Q8—41no—
105C3×#127—22no—
106C3×#127—41no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C42C2311yescharacteristic
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115#946—22no—
116#946—22no—
117#946—41no—
118#946—41no—
119Q8×Dic3—22no—
120Q8×Dic3—41no—
121#939—44no—
122#938—22no—
123#938—22no—
124#938—41no—
125#938—41no—
126D4×Dic3—22no—
127D4×Dic3—41no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4D411yescharacteristic
131C2×(C2×D3)⋊C4D411yescharacteristic
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×C4×Dic3—21no—
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×D3×C8—22no—
146C2×D3×C8—22no—
147C2×D3×C8—22no—
148C3×C4×C8—22no—
149#835—22no—
150#835—22no—
151#835—22no—
152#835—41no—
153#832—22no—
154#832—22no—
155#832—22no—
156#832—41no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95D411yescharacteristic
162C3⋊#95D411yescharacteristic
163(C2×D3)⋊C8—22no—
164#817—22no—
165#817D414yescomplemented
166C8×Dic3—22no—
167C22×SD16C2×D311yescharacteristic
168C22×SD16C2×D311yescharacteristic
169C22×SD16C2×D311yescharacteristic
170C22×SD16C2×D311yescharacteristic
171C23×C8—31no—
172C2×C4⋊Q8C2×D311yescharacteristic
173C2×#127C2×D311yescharacteristic
174C2×C22⋊Q8—31no—
175C2×C22⋊Q8—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121—61no—
179C2×C4×Q8—31no—
180C2×C4×D4—31no—
181#492—24no—
182#465—64no—
183#465—64no—
184C4×SD16—64no—
185C2×#106—31no—
186C2×#106—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8—31no—
197C2×C4×C8C2×D311yescharacteristic
198#398—61no—
199#396—61no—
200#394—61no—
201#392—61no—
202#391—31no—
203#390—31no—
204#389—31no—
205#389—31no—
206#389—61no—
207#388—61no—
208#386—61no—
209C4×C22⋊C4—31no—
210#340—31no—
211#340—31no—
212#336—31no—
213#336—31no—
214C24×C3—21no—
215C24×C3—21no—
216C23×D3C2×D411yescharacteristic
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8C2×D412yes—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—42no—
241C2×C3×D4—42no—
242C2×C3×D4—42no—
243C2×C3×D4—42no—
244C2×C3×D4—81no—
245C2×C3×D4—81no—
246C2×C3×D4C2×D412yes—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2411yescharacteristic
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—42no—
255C2×#67—42no—
256C2×#67—81no—
257C2×#67—81no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—42no—
263C22×Dic3—42no—
264C22×Dic3—81no—
265C22×Dic3C2×D411yescharacteristic
266C22×Dic3C2×D411yescharacteristic
267C22×Dic3C2×D411yescharacteristic
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C3×SD16—28no—
275C3×SD16—44no—
276C3×SD16—44no—
277C3×SD16—44no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8C2×D412yes—
281C2×C3×C8C2×D412yes—
282C2×C3×C8#4112yes—
283C2×C3×C8#4112yes—
284C3×C4⋊C4—42no—
285C3×C4⋊C4—42no—
286C3×C42—21no—
287C3×C42—21no—
288#217—42no—
289#217—42no—
290#217—42no—
291#217—42no—
292#217—81no—
293(C2×D3)⋊C4—22no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4SD1614yescomplemented
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—42no—
304C4⋊Dic3C2×D412yes—
305C4⋊Dic3C2×D412yes—
306Dic3⋊C4—42no—
307Dic3⋊C4—42no—
308Dic3⋊C4—42no—
309Dic3⋊C4—42no—
310C4×Dic3—21no—
311C4×Dic3—21no—
312C4×Dic3—42no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319D3×C8—44no—
320C22×Q8C22×D311yescharacteristic
321C22×Q8C22×D311yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4C22×D311yescharacteristic
327C22×D4C22×D311yescharacteristic
328C23×C4—31no—
329C23×C4—61no—
330C2×SD16—22no—
331C2×SD16—22no—
332C2×SD16—22no—
333C2×SD16—22no—
334C2×SD16—22no—
335C2×SD16—22no—
336C2×SD16—22no—
337C2×SD16—22no—
338C2×SD16—22no—
339C2×SD16—41no—
340C2×SD16—41no—
341C2×SD16#6714yescomplemented
342C22×C8—31no—
343C22×C8—31no—
344C22×C8—62no—
345C22×C8—62no—
346C22×C8—62no—
347C22×C8C22×D311yescharacteristic
348C22×C8C22×D311yescharacteristic
349C4⋊Q8—22no—
350C4⋊Q8—41no—
351#127—22no—
352#127—41no—
353C22⋊Q8—62no—
354C22⋊Q8—62no—
355C22⋊Q8—121no—
356C22⋊Q8—121no—
357#121—62no—
358#121—62no—
359#121—124no—
360#121—121no—
361#121—121no—
362C4×Q8—62no—
363C4×Q8—121no—
364C4×D4—62no—
365C4×D4—121no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C22⋊C4—31no—
378C2×C22⋊C4—31no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C42—31no—
387C2×C42—61no—
388C2×C42C22×D311yescharacteristic
389#106—34no—
390#106—62no—
391#103—62no—
392#103—62no—
393#103—62no—
394#103—121no—
395#102—62no—
396#102—62no—
397#102—62no—
398#102—121no—
399C22⋊C8—62no—
400C4×C8—22no—
401C4×C8—62no—
402#95—31no—
403#95—31no—
404#95—61no—
405#95—61no—
406#95—61no—
407#95—61no—
408C23×C3—22no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3C22×D411yescharacteristic
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3C2×SD1612yes—
430C3×Q8—22no—
431C3×Q8—22no—
432C3×Q8—41no—
433C3×Q8—41no—
434C3×Q8—41no—
435C3×Q8—41no—
436C3×Q8—41no—
437C3×Q8—41no—
438C3×D4—22no—
439C3×D4—22no—
440C3×D4—41no—
441C3×D4—41no—
442C3×D4—41no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—84no—
447C3×D4—84no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4C2×SD1612yes—
459C2×C3×C4#13512yes—
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4H(5,𝔽2)11yescharacteristic
465C2×C3×C4H(5,𝔽2)11yescharacteristic
466#67—84no—
467#67—84no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—22no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—22no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—84no—
489C2×Dic3C2×SD1612yes—
490C4×D3—41no—
491C4×D3—41no—
492C4×D3—41no—
493C4×D3—41no—
494C3×C8—22no—
495C3×C8#12114yescomplemented
496C3⋊C8—41no—
497C3⋊C8—41no—
498C24—21no—
499C24—21no—
500C24—31no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8C2×#6712yes—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—81no—
529C2×D4—81no—
530C2×D4—122no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—241no—
535C2×D4—241no—
536C2×D4C2×#6712yes—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—122no—
553C22×C4—122no—
554C22×C4—241no—
555C22×C4D3×D411yescharacteristic
556C22×C4D3×D411yescharacteristic
557C22×C4C23×D311yescharacteristic
558SD16—28no—
559SD16—44no—
560SD16—44no—
561SD16—44no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—61no—
565C2×C8—61no—
566C2×C8—61no—
567C2×C8—61no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—124no—
571C2×C8D3×D412yes—
572C2×C8#23712yes—
573C2×C8#23712yes—
574C2×C8C2×#6712yes—
575C4⋊C4—32no—
576C4⋊C4—32no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—61no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—122no—
586C4⋊C4—122no—
587C4⋊C4—122no—
588C4⋊C4—122no—
589C4⋊C4—122no—
590C22⋊C4—34no—
591C22⋊C4—62no—
592C22⋊C4—122no—
593C22⋊C4—122no—
594C22⋊C4—122no—
595C22⋊C4—122no—
596C22⋊C4—122no—
597C22⋊C4—122no—
598C22⋊C4—241no—
599C42—21no—
600C42—21no—
601C42—61no—
602C42—61no—
603C42—122no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3#53211yescharacteristic
619C22×C3D4211yescharacteristic
620C22×C3D4211yescharacteristic
621C22×C3C22×SD1611yescharacteristic
622C22×C3C2×#13511yescharacteristic
623C22×C3#57711yescharacteristic
624C22×C3#57711yescharacteristic
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—41no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—42no—
635C3×C4—81no—
636C3×C4C2×#12111yescharacteristic
637C3×C4#54011yescharacteristic
638C3×C4#54611yescharacteristic
639C3×C4#55011yescharacteristic
640Dic3—22no—
641Dic3—41no—
642Dic3—42no—
643Dic3—41no—
644Dic3—42no—
645Dic3—81no—
646Dic3—81no—
647C23—22no—
648C23—32no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—61no—
663C23—61no—
664C23—61no—
665C23—61no—
666C23—61no—
667C23—61no—
668C23C2×D3×D411yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677D4—22no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—84no—
686D4—84no—
687D4—244no—
688D4—244no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—32no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—244no—
725C2×C4D3×SD1612yes—
726C2×C4#91612yes—
727C2×C4C2×D3×D411yescharacteristic
728C2×C4C2×#23711yescharacteristic
729C2×C4C2×#23711yescharacteristic
730C2×C4#100411yescharacteristic
731C2×C4#100411yescharacteristic
732C2×C4C22×#6711yescharacteristic
733C8—22no—
734C8—121no—
735C8—121no—
736C8#93914yescomplemented
737C2×C3—82no—
738C2×C3—161no—
739C2×C3#242811yescharacteristic
740C2×C3#316711yescharacteristic
741C2×C3#317411yescharacteristic
742C2×C3D4×SD1611yescharacteristic
743C2×C3D4×SD1611yescharacteristic
744C2×C3#328211yescharacteristic
745C2×C3#328411yescharacteristic
746D3—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—62no—
751C22—62no—
752C22—62no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22#571611yescharacteristic
769C22#571711yescharacteristic
770C22C2×D3×SD1611yescharacteristic
771C22C2×#91611yescharacteristic
772C22#576211yescharacteristic
773C22#576211yescharacteristic
774C22D4×#6711yescharacteristic
775C4—22no—
776C4—22no—
777C4—42no—
778C4—62no—
779C4—81no—
780C4—122no—
781C4—121no—
782C4—122no—
783C4—121no—
784C4—241no—
785C4—241no—
786C4#571811yescharacteristic
787C4#571911yescharacteristic
788C4C2×#93911yescharacteristic
789C4#580611yescharacteristic
790C3#2541011yescharacteristic, complemented, Sylow
791C2—82no—
792C2—122no—
793C2—161no—
794C2#8175211yescharacteristic
795C2#8175311yescharacteristic
796C2#8177111yescharacteristic
797C2#8177211yescharacteristic
798C2#8318611yescharacteristic
799C2SD16×#6711yescharacteristic
800C2#8386711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#492C2
socleC23×C3C22×D4
prime radical#83186C2
hypercenterC2×#492D3
hypocenterC3#25410
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
1. C2×C3×#492C2semidirect
2. C2×#5171C2semidirect
3. C2×#5171C2semidirect
4. C2×Dic3×SD16C2semidirect
5. #83254C2semidirect
7. #72054C2semidirect
8. #72054C2semidirect
9. #72049C2semidirect
10. #72048C2semidirect
11. #72047C2semidirect
12. #71781C2semidirect
13. #71762C2semidirect
14. C8×(C2×D3)⋊C4C2semidirect
15. #69769C2semidirect
64. C2×#492D3semidirect
100. C2×C3×SD16D4semidirect
165. #817D4semidirect
296. (C2×D3)⋊C4SD16semidirect
341. C2×SD16#67semidirect
495. C3×C8#121semidirect
736. C8#939semidirect
790. C3#25410semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4922
C2×#51712
C2×Dic3×SD162
#832542
#831862
#720542
#720492
#720482
#720472
#717812
#717622
C8×(C2×D3)⋊C42
#697692
#254103