Finite Group Databasebeta

← #10846271

Subgroups — #10846271

Order 768.

1052 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#495C211yesmaximal, characteristic, complemented
2C2×#5171C211yesmaximal, characteristic, complemented
3C2×#5171C211yesmaximal, characteristic, complemented
4C2×Dic3×SD16C211yesmaximal, characteristic, complemented
5#82996C211yesmaximal, characteristic, complemented
6#82995C211yesmaximal, characteristic, complemented
7#72071C211yesmaximal, characteristic, complemented
8#72065C211yesmaximal, characteristic, complemented
9#72049C211yesmaximal, characteristic, complemented
10#72043C211yesmaximal, characteristic
11#72037C211yesmaximal, characteristic, complemented
12#71722C211yesmaximal, characteristic, complemented
13#71722C211yesmaximal, characteristic, complemented
14C8×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
15#69769C211yesmaximal, characteristic, complemented
16#25411—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×D8C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C2×#946C2211yescharacteristic
25C2×Q8×Dic3C2211yescharacteristic
26C2×#938C2211yescharacteristic
27C2×#938C2211yescharacteristic
28C2×D4×Dic3C2211yescharacteristic
29C22×D3×C8C2211yescharacteristic
30C3×#495—24no—
31C2×C3×C4×C8C2211yescharacteristic
32#5229C2211yescharacteristic
33C2×#835C2211yescharacteristic
34C2×#835C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37#5221C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42#5171—24no—
43#5171—24no—
44Dic3×SD16—24no—
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#817C2211yescharacteristic
47C2×#817C2211yescharacteristic
48C2×C8×Dic3C2211yescharacteristic
49#4961—21no—
50#4959—21no—
51#4958—21no—
52#4957—21no—
53#4952—21no—
54#4948—21no—
55#4945—21no—
56#4942—21no—
57C4×(C2×D3)⋊C4C2211yescharacteristic
58#4928C2211yescharacteristic
59#4928C2211yescharacteristic
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4550C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#495D311yescharacteristic, complemented
65C2×#465—31no—
66C2×#465—31no—
67C2×C4×SD16—31no—
68#2427—31no—
69#2426—31no—
70#2042—31no—
71#2042—31no—
72#2001—31no—
73#1999—31no—
74#1968—31no—
75#1941—31no—
76#1879—31no—
77#1878—31no—
78C8×C22⋊C4—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C23×Dic3—21no—
86C22×C4×D3C2311yescharacteristic
87C2×C3×Q16—22no—
88C2×C3×Q16—22no—
89C2×C3×Q16—41no—
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×SD16—22no—
93C2×C3×SD16—22no—
94C2×C3×SD16—22no—
95C2×C3×SD16D414yescomplemented
96C2×C3×D8—22no—
97C2×C3×D8—22no—
98C2×C3×D8—41no—
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×#124—22no—
102C3×#124—22no—
103C3×#124—41no—
104C3×#124—41no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊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#938—22no—
122#938—22no—
123#938—41no—
124#938—41no—
125D4×Dic3—22no—
126D4×Dic3—41no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4D411yescharacteristic
130C2×(C2×D3)⋊C4D411yescharacteristic
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×C4×Dic3—21no—
141C2×C4×Dic3C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C2×D3×C8—22no—
145C2×D3×C8—22no—
146C2×D3×C8—22no—
147C3×C4×C8—22no—
148#835—22no—
149#835—22no—
150#835—22no—
151#835—41no—
152#832—22no—
153#832—22no—
154#832—22no—
155#832—41no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95D411yescharacteristic
161C3⋊#95D411yescharacteristic
162(C2×D3)⋊C8—22no—
163#817—22no—
164#817D414yescomplemented
165C8×Dic3—22no—
166C22×Q16C2×D311yescharacteristic
167C22×SD16C2×D311yescharacteristic
168C22×SD16C2×D311yescharacteristic
169C22×D8C2×D311yescharacteristic
170C23×C8—31no—
171C2×#124C2×D311yescharacteristic
172C2×#124C2×D311yescharacteristic
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×Q8—31no—
178C2×C4×D4—31no—
179#495—24no—
180#465—64no—
181#465—64no—
182C4×SD16—64no—
183C2×#106—31no—
184C2×#106—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C4×C8—31no—
195C2×C4×C8C2×D311yescharacteristic
196#397—61no—
197#396—61no—
198#394—61no—
199#394—61no—
200#391—31no—
201#390—31no—
202#390—61no—
203#389—31no—
204#389—31no—
205#388—61no—
206#386—61no—
207#380—61no—
208C4×C22⋊C4—31no—
209#340—31no—
210#340—31no—
211#336—31no—
212#336—31no—
213C24×C3—21no—
214C24×C3—21no—
215C23×D3C2×D411yescharacteristic
216C2×C3×Q8—21no—
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×Q8C2×D412yes—
228C2×C3×D4—21no—
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×D4C2×D412yes—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2411yescharacteristic
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—81no—
250C2×#67—81no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—42no—
256C22×Dic3—42no—
257C22×Dic3—81no—
258C22×Dic3C2×D411yescharacteristic
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C3×Q16—44no—
268C3×SD16—28no—
269C3×SD16—44no—
270C3×D8—44no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8C2×D412yes—
274C2×C3×C8C2×D412yes—
275C2×C3×C8#4112yes—
276C2×C3×C8#4112yes—
277C3×C22⋊C4—42no—
278C3×C22⋊C4—42no—
279C3×C22⋊C4—42no—
280C3×C22⋊C4—42no—
281C3×C42—21no—
282C3×C42—21no—
283#217—42no—
284#217—42no—
285#217—42no—
286#217—42no—
287#217—81no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—42no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—42no—
299C4⋊Dic3C2×D412yes—
300C4⋊Dic3C2×D412yes—
301Dic3⋊C4—42no—
302Dic3⋊C4—42no—
303Dic3⋊C4—81no—
304Dic3⋊C4—81no—
305C4×Dic3—21no—
306C4×Dic3—21no—
307C4×Dic3—42no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314D3×C8—44no—
315C22×Q8C22×D311yescharacteristic
316C22×Q8C22×D311yescharacteristic
317C22×D4—61no—
318C22×D4—61no—
319C22×D4C22×D311yescharacteristic
320C22×D4C22×D311yescharacteristic
321C23×C4—31no—
322C23×C4—61no—
323C2×Q16—22no—
324C2×Q16—22no—
325C2×Q16—41no—
326C2×SD16—22no—
327C2×SD16—22no—
328C2×SD16—22no—
329C2×SD16—22no—
330C2×SD16—22no—
331C2×SD16#6714yescomplemented
332C2×D8—22no—
333C2×D8—22no—
334C2×D8—41no—
335C22×C8—31no—
336C22×C8—31no—
337C22×C8—62no—
338C22×C8—62no—
339C22×C8—62no—
340C22×C8C22×D311yescharacteristic
341C22×C8C22×D311yescharacteristic
342#124—22no—
343#124—22no—
344#124—41no—
345#124—41no—
346C22⋊Q8—62no—
347C22⋊Q8—62no—
348C22⋊Q8—121no—
349C22⋊Q8—121no—
350#121—62no—
351#121—62no—
352#121—121no—
353#121—121no—
354C4×Q8—62no—
355C4×Q8—121no—
356C4×D4—62no—
357C4×D4—121no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—31no—
372C2×C22⋊C4—31no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C42—31no—
381C2×C42—61no—
382C2×C42C22×D311yescharacteristic
383#106—34no—
384#106—62no—
385#103—62no—
386#103—62no—
387#103—62no—
388#103—121no—
389#102—62no—
390#102—62no—
391#102—62no—
392#102—121no—
393C22⋊C8—62no—
394C4×C8—22no—
395C4×C8—62no—
396#95—31no—
397#95—31no—
398#95—61no—
399#95—61no—
400#95—61no—
401#95—61no—
402C23×C3—22no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3C22×D411yescharacteristic
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3#13512yes—
424C3×Q8—22no—
425C3×Q8—22no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×Q8—41no—
429C3×Q8—41no—
430C3×Q8—41no—
431C3×Q8—41no—
432C3×D4—22no—
433C3×D4—22no—
434C3×D4—41no—
435C3×D4—41no—
436C3×D4—41no—
437C3×D4—41no—
438C3×D4—41no—
439C3×D4—41no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4H(5,𝔽2)11yescharacteristic
457C2×C3×C4H(5,𝔽2)11yescharacteristic
458#67—84no—
459#67—84no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—22no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—22no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—84no—
481C2×Dic3#13512yes—
482C4×D3—41no—
483C4×D3—41no—
484C4×D3—41no—
485C4×D3—41no—
486C3×C8—22no—
487C3×C8#12114yes—
488C3⋊C8—41no—
489C3⋊C8—41no—
490C24—21no—
491C24—21no—
492C24—31no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C2×#6712yes—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—122no—
517C2×D4—122no—
518C2×D4—122no—
519C2×D4—122no—
520C2×D4—241no—
521C2×D4—241no—
522C2×D4C2×#6712yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—122no—
539C22×C4—122no—
540C22×C4—241no—
541C22×C4D3×D411yescharacteristic
542C22×C4D3×D411yescharacteristic
543C22×C4C23×D311yescharacteristic
544Q16—44no—
545SD16—28no—
546SD16—44no—
547D8—44no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—61no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—124no—
557C2×C8D3×D412yes—
558C2×C8#23712yes—
559C2×C8#23712yes—
560C2×C8C2×#6712yes—
561C4⋊C4—32no—
562C4⋊C4—32no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—122no—
570C4⋊C4—122no—
571C4⋊C4—122no—
572C4⋊C4—241no—
573C4⋊C4—241no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—62no—
579C22⋊C4—62no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—241no—
587C42—21no—
588C42—21no—
589C42—61no—
590C42—61no—
591C42—122no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3#53211yescharacteristic
607C22×C3D4211yescharacteristic
608C22×C3D4211yescharacteristic
609C22×C3C2×#13511yescharacteristic
610C22×C3C2×#13511yescharacteristic
611C22×C3#57711yescharacteristic
612C22×C3#57711yescharacteristic
613C2×D3—22no—
614C2×D3—22no—
615C2×D3—22no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—41no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—81no—
624C3×C4C2×#12111yescharacteristic
625C3×C4#54011yescharacteristic
626C3×C4#54611yescharacteristic
627C3×C4#55011yescharacteristic
628Dic3—22no—
629Dic3—41no—
630Dic3—41no—
631Dic3—42no—
632Dic3—42no—
633Dic3—81no—
634Dic3—81no—
635C23—22no—
636C23—32no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23—61no—
656C23C2×D3×D411yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—244no—
674D4—244no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—32no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—244no—
713C2×C4C2×D3×D411yescharacteristic
714C2×C4C2×#23711yescharacteristic
715C2×C4C2×#23711yescharacteristic
716C2×C4#100411yescharacteristic
717C2×C4#100411yescharacteristic
718C2×C4C22×#6711yescharacteristic
719C8—22no—
720C8—121no—
721C8—121no—
722C8#93914yes—
723C2×C3—82no—
724C2×C3—161no—
725C2×C3#242811yescharacteristic
726C2×C3#316811yescharacteristic
727C2×C3#317311yescharacteristic
728C2×C3#328211yescharacteristic
729C2×C3#328211yescharacteristic
730C2×C3#328211yescharacteristic
731C2×C3#328411yescharacteristic
732D3—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—62no—
737C22—62no—
738C22—62no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22#571611yescharacteristic
755C22#571711yescharacteristic
756C22D3×#13511yescharacteristic
757C22D3×#13511yescharacteristic
758C22#577011yescharacteristic
759C22#577011yescharacteristic
760C22D4×#6711yescharacteristic
761C4—41no—
762C4—41no—
763C4—42no—
764C4—62no—
765C4—81no—
766C4—121no—
767C4—122no—
768C4—122no—
769C4—121no—
770C4—241no—
771C4—241no—
772C4#571811yescharacteristic
773C4#571911yescharacteristic
774C4C2×#93911yescharacteristic
775C4#580611yescharacteristic
776C3#2541111yescharacteristic, complemented, Sylow
777C2—82no—
778C2—122no—
779C2—161no—
780C2#8180911yescharacteristic
781C2#8181011yescharacteristic
782C2#8183211yescharacteristic
783C2#8183211yescharacteristic
784C2#8318611yescharacteristic
785C2#8391911yescharacteristic
786C2#8392711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#495C2
socleC23×C3C22×D4
prime radical#72043C2
hypercenterC2×#495D3
hypocenterC3#25411
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×C3×#495C2semidirect
2. C2×#5171C2semidirect
3. C2×#5171C2semidirect
4. C2×Dic3×SD16C2semidirect
5. #82996C2semidirect
6. #82995C2semidirect
7. #72071C2semidirect
8. #72065C2semidirect
9. #72049C2semidirect
11. #72037C2semidirect
12. #71722C2semidirect
13. #71722C2semidirect
14. C8×(C2×D3)⋊C4C2semidirect
15. #69769C2semidirect
64. C2×#495D3semidirect
95. C2×C3×SD16D4semidirect
164. #817D4semidirect
331. C2×SD16#67semidirect
776. C3#25411semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4952
C2×#51712
C2×Dic3×SD162
#829962
#829952
#720712
#720652
#720492
#720432
#720372
#717222
C8×(C2×D3)⋊C42
#697692
#254113