Finite Group Databasebeta

← #10833979

Subgroups — #10833979

Order 768.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5156C211yesmaximal, characteristic
2C2×#4709C211yesmaximal, characteristic, complemented
3#76458C211yesmaximal, characteristic, complemented
4#76428C211yesmaximal, characteristic, complemented
5C3×#1972C211yesmaximal, characteristic, complemented
6#72040C211yesmaximal, characteristic, complemented
7#70585C211yesmaximal, characteristic, complemented
8#70580C211yesmaximal, characteristic, complemented
9#70212C211yesmaximal, characteristic, complemented
10#70201C211yesmaximal, characteristic, complemented
11#70198C211yesmaximal, characteristic, complemented
12#70194C211yesmaximal, characteristic, complemented
13#69818C211yesmaximal, characteristic, complemented
14#69647C211yesmaximal, characteristic, complemented
15#69644C211yesmaximal, characteristic, complemented
16#24512—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×#938C2211yescharacteristic
20C22×#213C2211yescharacteristic
21C2×#892C2211yescharacteristic
22C2×#872C2211yescharacteristic
23C2×C3×#106C2211yescharacteristic, complemented
24C2×C3×#102C2211yescharacteristic
25C2×C3×#102C2211yescharacteristic, complemented
26C2×C3×#97C2211yescharacteristic, complemented
27C3×#390C2211yescharacteristic
28C3×#390C2211yescharacteristic, complemented
29#5221C2211yescharacteristic
30#5221C2211yescharacteristic, complemented
31C2×#832C2211yescharacteristic
32C2×#832C2211yescharacteristic
33C2×#832C2211yescharacteristic, complemented
34#5156—24no—
35C2×#821C2211yescharacteristic
36C2×#821C2211yescharacteristic
37C2×(C2×D3)⋊C8C2211yescharacteristic
38C2×(C2×D3)⋊C8C2211yescharacteristic
39C2×Dic3⋊C8C2211yescharacteristic, complemented
40C2×Dic3⋊C8C2211yescharacteristic, complemented
41#4988C2211yescharacteristic
42#4987C2211yescharacteristic
43#4984C2211yescharacteristic, complemented
44C2×#809C2211yescharacteristic
45C2×#807C2211yescharacteristic, complemented
46#4961—21no—
47#4959—21no—
48#4957—21no—
49#4957—21no—
50#4955—21no—
51#4955—21no—
52#4952—21no—
53#4949—21no—
54#4939C2211yescharacteristic
55#4928C2211yescharacteristic, complemented
56C2×C4×C3⋊C8C2211yescharacteristic, complemented
57#4709—24no—
58#4551C2211yescharacteristic, complemented
59#4551C2211yescharacteristic, complemented
60#4529C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62C2×#447—31no—
63C2×#433—31no—
64#2624—31no—
65#2309—31no—
66#2067—31no—
67#2065—31no—
68#2054—31no—
69#2054—31no—
70#1972D311yescharacteristic, complemented
71#1970—31no—
72#1936—31no—
73#1934—31no—
74#1875—31no—
75#1854—31no—
76#1786—31no—
77C24×D3—21no—
78C22×C3×D4C2311yescharacteristic
79C22×C3×D4C2311yescharacteristic
80C22×#67—21no—
81C22×#67—21no—
82C2×D3×D4—22no—
83C2×D3×D4—22no—
84C2×D3×D4—22no—
85C2×D3×D4—22no—
86C2×D3×D4—41no—
87C2×D3×D4—41no—
88C22×D12C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C2×C3×D8—22no—
91C2×C3×D8—22no—
92C2×C3×D8—41no—
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C22⋊C4—21no—
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C42C2311yescharacteristic
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107#938—22no—
108#938—22no—
109C2×#213—22no—
110C2×#213—22no—
111C2×#213—41no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4D411yescharacteristic
119C2×(C2×D3)⋊C4D411yescharacteristic
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3C2311yescharacteristic
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4D411yescharacteristic
126C2×Dic3⋊C4D411yescharacteristic
127C2×C4×Dic3—21no—
128C2×C4×Dic3C2311yescharacteristic
129C22×C3⋊C8C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131#892—41no—
132#892—41no—
133#872—22no—
134#872—22no—
135C3×#106—41no—
136C3×#102—41no—
137C3×#102—41no—
138C3×#97—22no—
139#832—22no—
140#832—22no—
141#832—41no—
142C3⋊#95—21no—
143C3⋊#95—21no—
144C3⋊#95—21no—
145#821—22no—
146#821—22no—
147(C2×D3)⋊C8—22no—
148(C2×D3)⋊C8D414yes—
149Dic3⋊C8—22no—
150Dic3⋊C8—22no—
151#809—41no—
152#807—41no—
153C4×C3⋊C8—22no—
154C23×D4—31no—
155C22×D8—31no—
156C22×D8C2×D311yescharacteristic
157C2×#121—31no—
158C2×#117—31no—
159C2×#117—31no—
160#447—64no—
161#433—64no—
162C2×#107—31no—
163C2×#106C2×D311yescharacteristic, complemented
164C2×C4⋊C8—31no—
165C2×C4⋊C8—31no—
166C2×#102—31no—
167C2×#102—31no—
168C2×#102—31no—
169C2×#102—31no—
170C2×#102—31no—
171C2×#102—31no—
172C2×#102C2×D311yescharacteristic
173C2×#102C2×D311yescharacteristic, complemented
174C2×C22⋊C8—31no—
175C2×C22⋊C8—31no—
176C2×#97C2×D311yescharacteristic, complemented
177C2×C4×C8—31no—
178#399—61no—
179#397—61no—
180#394—61no—
181#394—61no—
182#390—31no—
183#390—31no—
184#390—31no—
185#390—31no—
186#390—61no—
187#390—61no—
188#390C2×D311yescharacteristic
189#390C2×D311yescharacteristic, complemented
190#389—31no—
191#389—31no—
192#380—31no—
193#379—61no—
194#379—61no—
195#340—31no—
196#340—31no—
197#340—31no—
198#340—31no—
199C24×C3—21no—
200C24×C3—21no—
201C23×D3—21no—
202C23×D3—24no—
203C23×D3—42no—
204C23×D3—42no—
205C23×D3—81no—
206C23×D3—81no—
207C23×D3—81no—
208C23×D3—81no—
209C23×D3C2×D411yescharacteristic
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4#4112yes—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2411yescharacteristic
227C2×#67—24no—
228C2×#67—42no—
229C2×#67—42no—
230C2×#67—42no—
231C2×#67—81no—
232C2×#67—81no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3C2×D411yescharacteristic
237C22×Dic3C2×D411yescharacteristic
238C22×Dic3C2×D411yescharacteristic
239D3×D4—44no—
240D3×D4—44no—
241D3×D4—44no—
242D3×D4—44no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12#4112yes—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3C2×D412yes—
254C2×C4×D3#4112yes—
255C3×D8—44no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8C2×D412yes—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C22⋊C4—81no—
267C3×C22⋊C4—81no—
268C3×C22⋊C4—81no—
269C3×C22⋊C4—81no—
270C3×C42—21no—
271C3×C42—21no—
272#217—42no—
273#217—81no—
274#217—81no—
275#217—81no—
276#217—81no—
277#213—44no—
278(C2×D3)⋊C4—22no—
279(C2×D3)⋊C4—22no—
280(C2×D3)⋊C4—42no—
281(C2×D3)⋊C4—81no—
282(C2×D3)⋊C4—81no—
283(C2×D3)⋊C4—81no—
284(C2×D3)⋊C4—81no—
285(C2×D3)⋊C4—81no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—81no—
293Dic3⋊C4—22no—
294Dic3⋊C4—22no—
295Dic3⋊C4—81no—
296C4×Dic3—21no—
297C4×Dic3—21no—
298C4×Dic3—42no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8C2×D412yes—
305C25—61no—
306C22×D4—31no—
307C22×D4—62no—
308C22×D4—62no—
309C22×D4—61no—
310C22×D4—62no—
311C22×D4—62no—
312C22×D4—61no—
313C22×D4—121no—
314C22×D4—121no—
315C22×D4C22×D311yescharacteristic
316C22×D4C22×D311yescharacteristic
317C23×C4—31no—
318C2×D8—22no—
319C2×D8—22no—
320C2×D8—41no—
321C2×D8—62no—
322C2×D8—62no—
323C2×D8—121no—
324C22×C8—31no—
325C22×C8—31no—
326C22×C8C22×D311yescharacteristic
327C22×C8C22×D311yescharacteristic
328#121—62no—
329#121—62no—
330#117—62no—
331#117—62no—
332#117—121no—
333#117—121no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—61no—
340C2×C4⋊C4—61no—
341C2×C4⋊C4C22×D311yescharacteristic
342C2×C4⋊C4C22×D311yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—31no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—61no—
350C2×C22⋊C4—61no—
351C2×C22⋊C4—61no—
352C2×C22⋊C4—61no—
353C2×C22⋊C4—61no—
354C2×C22⋊C4—61no—
355C2×C22⋊C4—61no—
356C2×C22⋊C4—61no—
357C2×C22⋊C4—61no—
358C2×C22⋊C4—61no—
359C2×C22⋊C4—61no—
360C2×C42—31no—
361C2×C42—61no—
362C2×C42C22×D311yescharacteristic
363#107—121no—
364#106—41no—
365C4⋊C8—62no—
366C4⋊C8—62no—
367#102—41no—
368#102—41no—
369#102—62no—
370#102—62no—
371#102—62no—
372#102—62no—
373#102—121no—
374#102—121no—
375C22⋊C8—34no—
376C22⋊C8—62no—
377#97—22no—
378C4×C8—62no—
379#95—61no—
380#95—61no—
381#95—61no—
382C23×C3—22no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3C22×D411yescharacteristic
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—21no—
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—22no—
404C22×D3—48no—
405C22×D3—41no—
406C22×D3—41no—
407C22×D3—41no—
408C22×D3—41no—
409C22×D3—41no—
410C22×D3—41no—
411C22×D3—84no—
412C22×D3—84no—
413C22×D3—84no—
414C22×D3—84no—
415C22×D3—84no—
416C22×D3—84no—
417C22×D3#12112yes—
418C3×D4—22no—
419C3×D4—22no—
420C3×D4—41no—
421C3×D4—41no—
422C3×D4—41no—
423C3×D4—41no—
424C3×D4—41no—
425C3×D4—41no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4C22×D411yescharacteristic
439C2×C3×C4C2×#4111yescharacteristic
440C2×C3×C4C2×#4111yescharacteristic
441C2×C3×C4C2×#4111yescharacteristic
442C2×C3×C4H(5,𝔽2)11yescharacteristic
443C2×C3×C4H(5,𝔽2)11yescharacteristic
444#67—48no—
445#67—84no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3#12112yes—
464D12—22no—
465D12—22no—
466D12—41no—
467D12—41no—
468C4×D3—22no—
469C4×D3—22no—
470C4×D3—22no—
471C4×D3—22no—
472C3×C8—22no—
473C3×C8—41no—
474C3⋊C8—22no—
475C3⋊C8—41no—
476C24—21no—
477C24—21no—
478C24—31no—
479C24—64no—
480C24—61no—
481C24—122no—
482C24—122no—
483C24—241no—
484C24—241no—
485C24—241no—
486C24—241no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—32no—
499C2×D4—64no—
500C2×D4—61no—
501C2×D4—61no—
502C2×D4—61no—
503C2×D4—61no—
504C2×D4—61no—
505C2×D4—122no—
506C2×D4—124no—
507C2×D4—124no—
508C2×D4—124no—
509C2×D4—124no—
510C2×D4—122no—
511C2×D4—122no—
512C2×D4—241no—
513C2×D4—241no—
514C2×D4#23512yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—31no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—31no—
521C22×C4—31no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4D3×D411yescharacteristic
530C22×C4D3×D411yescharacteristic
531C22×C4C23×D311yescharacteristic
532D8—44no—
533D8—124no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—32no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8D3×D412yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—62no—
551C4⋊C4—62no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—241no—
559C4⋊C4—241no—
560C22⋊C4—62no—
561C22⋊C4—62no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C22⋊C4—81no—
565C22⋊C4—81no—
566C22⋊C4—122no—
567C22⋊C4—122no—
568C22⋊C4—241no—
569C22⋊C4—241no—
570C22⋊C4—241no—
571C22⋊C4—241no—
572C22⋊C4—241no—
573C22⋊C4—241no—
574C22⋊C4—241no—
575C22⋊C4—241no—
576C22⋊C4—241no—
577C42—21no—
578C42—21no—
579C42—61no—
580C42—61no—
581C42—122no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3—81no—
588C22×C3—81no—
589C22×C3—81no—
590C22×C3—81no—
591C22×C3—81no—
592C22×C3—81no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3C2×#12111yescharacteristic
597C22×C3#52511yescharacteristic
598C22×C3#53511yescharacteristic
599C22×C3#57611yescharacteristic
600C22×C3#57611yescharacteristic
601C22×C3#57611yescharacteristic
602C22×C3#57711yescharacteristic
603C2×D3—22no—
604C2×D3—22no—
605C2×D3—22no—
606C2×D3—41no—
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—41no—
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—816no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C2×D3—81no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—81no—
621C3×C4—81no—
622C3×C4#54611yescharacteristic
623C3×C4#54611yescharacteristic
624C3×C4#55111yescharacteristic
625C3×C4#55111yescharacteristic
626Dic3—22no—
627Dic3—41no—
628Dic3—41no—
629Dic3—81no—
630Dic3—81no—
631Dic3—81no—
632C23—22no—
633C23—32no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—62no—
654C23—128no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23—121no—
660C23—121no—
661C23—244no—
662C23—244no—
663C23—244no—
664C23—244no—
665C23—244no—
666C23—244no—
667C23C2×D3×D411yescharacteristic
668D4—22no—
669D4—22no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—62no—
677D4—62no—
678D4—128no—
679D4—121no—
680D4—121no—
681D4—244no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—32no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4C2×#23511yescharacteristic
717C2×C4C2×D3×D411yescharacteristic
718C2×C4#100411yescharacteristic
719C2×C4#100411yescharacteristic
720C2×C4D3×#4111yescharacteristic
721C2×C4D3×#4111yescharacteristic
722C8—22no—
723C8—41no—
724C8—62no—
725C8—121no—
726C2×C3—82no—
727C2×C3—161no—
728C2×C3#241111yescharacteristic
729C2×C3#305811yescharacteristic
730C2×C3#306211yescharacteristic
731C2×C3#311811yescharacteristic
732C2×C3#312211yescharacteristic
733C2×C3#322011yescharacteristic
734C2×C3#322411yescharacteristic
735D3—42no—
736D3—82no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—62no—
741C22—62no—
742C22—62no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—121no—
755C22—121no—
756C22—121no—
757C22—121no—
758C22—122no—
759C22—122no—
760C22—122no—
761C22—2416no—
762C22—241no—
763C22—241no—
764C22—241no—
765C22—241no—
766C22#554711yescharacteristic
767C22D3×#12111yescharacteristic
768C22#571511yescharacteristic
769C22#577411yescharacteristic
770C22#577411yescharacteristic
771C22#577411yescharacteristic
772C22#577511yescharacteristic
773C4—41no—
774C4—41no—
775C4—62no—
776C4—81no—
777C4—81no—
778C4—121no—
779C4—121no—
780C4—241no—
781C4—241no—
782C4—241no—
783C4#549011yescharacteristic
784C4#555611yescharacteristic
785C4#561211yescharacteristic
786C4#567911yescharacteristic
787C3#2451211yescharacteristic, complemented, Sylow
788C2—82no—
789C2—122no—
790C2—161no—
791C2—242no—
792C2#7643711yescharacteristic
793C2#7987411yescharacteristic
794C2#7988611yescharacteristic
795C2#8086511yescharacteristic
796C2#8086711yescharacteristic
797C2#8185311yescharacteristic
798C2#8185511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1972C2
socleC23×C3C22×D4
prime radicalC2×#5156C2
hypercenter#1972D3
hypocenterC3#24512
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1972

Complements

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

NH ≅ G/Ntype
2. C2×#4709C2semidirect
3. #76458C2semidirect
4. #76428C2semidirect
5. C3×#1972C2semidirect
6. #72040C2semidirect
7. #70585C2semidirect
8. #70580C2semidirect
9. #70212C2semidirect
10. #70201C2semidirect
11. #70198C2semidirect
12. #70194C2semidirect
13. #69818C2semidirect
14. #69647C2semidirect
15. #69644C2semidirect
23. C2×C3×#106C22semidirect
25. C2×C3×#102C22semidirect
26. C2×C3×#97C22semidirect
28. C3×#390C22semidirect
30. #5221C22semidirect
33. C2×#832C22semidirect
39. C2×Dic3⋊C8C22semidirect
40. C2×Dic3⋊C8C22semidirect
43. #4984C22semidirect
45. C2×#807C22semidirect
55. #4928C22semidirect
56. C2×C4×C3⋊C8C22semidirect
58. #4551C22semidirect
59. #4551C22semidirect
60. #4529C22semidirect
61. #4529C22semidirect
70. #1972D3semidirect
163. C2×#106C2×D3semidirect
173. C2×#102C2×D3semidirect
176. C2×#97C2×D3semidirect
189. #390C2×D3semidirect
787. C3#24512semidirect

Maximal subgroups

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

subgroupindex
C2×#51562
C2×#47092
#764582
#764282
C3×#19722
#720402
#705852
#705802
#702122
#702012
#701982
#701942
#698182
#696472
#696442
#245123