Finite Group Databasebeta

← #10846288

Subgroups — #10846288

Order 768.

1066 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2427C211yesmaximal, characteristic, complemented
2C2×#5059C211yesmaximal, characteristic, complemented
3C2×#5051C211yesmaximal, characteristic, complemented
4C2×#5038C211yesmaximal, characteristic
5C2×C4×#213C211yesmaximal, characteristic, complemented
6#73486C211yesmaximal, characteristic, complemented
7#71722C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#71685C211yesmaximal, characteristic, complemented
10#71612C211yesmaximal, characteristic, complemented
11#69687C211yesmaximal, characteristic, complemented
12#69677C211yesmaximal, characteristic, complemented
13#69628C211yesmaximal, characteristic, complemented
14#69619C211yesmaximal, characteristic, complemented
15C22⋊C4×C3⋊C8C211yesmaximal, characteristic, complemented
16#25413—31nomaximal, Sylow
17C2×C3×#124C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C22×#213C2211yescharacteristic
25C2×#930C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C23×C3⋊C8C2211yescharacteristic
28C2×#875C2211yescharacteristic
29C2×C4×D12C2211yescharacteristic
30C3×#397—21no—
31C3×#394—21no—
32C3×#391C2211yescharacteristic
33C3×#389C2211yescharacteristic
34C3×#386—21no—
35C3×#380—21no—
36C3×C4×C22⋊C4C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#830C2211yescharacteristic
42#5059—24no—
43#5051—24no—
44#5038—24no—
45C4×#213—24no—
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#807C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4959—21no—
53#4956—21no—
54#4929C2211yescharacteristic
55#4928C2211yescharacteristic
56C2×C4×C3⋊C8C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4675—21no—
59#4667—21no—
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#495—31no—
65C2×#467—31no—
66C2×#466—31no—
67C2×C4×D8—31no—
68#2427—31no—
69#2427D311yescharacteristic, complemented
70#2042—31no—
71#2042—31no—
72#2000—31no—
73#2000—31no—
74#1969—31no—
75#1942—31no—
76#1877—31no—
77#1877—31no—
78C8×C22⋊C4—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×D12C2311yescharacteristic
86C22×C4×D3—21no—
87C22×Dic6C2311yescharacteristic
88C3×#124—22no—
89C3×#124—41no—
90C3×C22⋊Q8—22no—
91C3×C22⋊Q8—41no—
92C3×#121—22no—
93C3×#121—41no—
94C3×C4×D4—22no—
95C3×C4×D4—41no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4D411yescharacteristic
106C2×C3×C22⋊C4D411yescharacteristic
107C2×C3×C42C2311yescharacteristic
108C2×C3×C42C2311yescharacteristic
109C2×#217—21no—
110C2×#216—22no—
111C2×#216—22no—
112C2×#216—22no—
113C2×#215—22no—
114C2×#215—22no—
115C2×#215—41no—
116C2×#214—22no—
117C2×#214—22no—
118C2×#214—41no—
119C2×#213—22no—
120C2×#213—22no—
121C2×#213D414yes—
122#930—22no—
123#930—41no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130#924—22no—
131#924—41no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C22×C3⋊C8—22no—
135C22×C3⋊C8—22no—
136C22×C3⋊C8—22no—
137C22×C3⋊C8C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141#875—22no—
142#875—41no—
143C4×D12—22no—
144C4×D12—41no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95—21no—
148C3×#95D411yescharacteristic
149C3×#95D411yescharacteristic
150#835—22no—
151#835—41no—
152#832—22no—
153#832—22no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#830—22no—
158#810—22no—
159#810—41no—
160#809—22no—
161#809—22no—
162#807—22no—
163#807D414yescomplemented
164C4×C3⋊C8—22no—
165C4×C3⋊C8—22no—
166C22×Q16—31no—
167C22×SD16—31no—
168C22×SD16—31no—
169C22×D8—31no—
170C23×C8—31no—
171C2×#124—31no—
172C2×#124C2×D311yescharacteristic
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8C2×D311yescharacteristic
175C2×#121—31no—
176C2×#121C2×D311yescharacteristic
177C2×C4×D4—31no—
178C2×C4×D4C2×D311yescharacteristic
179#495—64no—
180#467—64no—
181#466—64no—
182C4×D8—64no—
183C2×#107—31no—
184C2×#107—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×C8—31no—
196#397—21no—
197#397—61no—
198#394—21no—
199#394—61no—
200#391—31no—
201#391C2×D311yescharacteristic
202#389—31no—
203#389C2×D311yescharacteristic
204#386—21no—
205#386—61no—
206#380—21no—
207#380—61no—
208C4×C22⋊C4C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#336—31no—
212#336—31no—
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C23×D3—21no—
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×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—42no—
228C2×C3×D4—42no—
229C2×C3×D4—81no—
230C2×C3×D4C2×D412yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—42no—
241C22×C3×C4—42no—
242C22×C3×C4—81no—
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2411yescharacteristic
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—81no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12C2×D412yes—
261C2×C4×D3—42no—
262C2×C4×D3—42no—
263C2×C4×D3—81no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—42no—
274C3×C4⋊C4—81no—
275C3×C4⋊C4C2×D412yes—
276C3×C22⋊C4—22no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—42no—
279C3×C22⋊C4—42no—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—42no—
282C3×C22⋊C4—42no—
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—21no—
286C3×C42—21no—
287#217—42no—
288#216—44no—
289#215—44no—
290#214—44no—
291#213—28no—
292(C2×D3)⋊C4—42no—
293(C2×D3)⋊C4—42no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—42no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3C2×D412yes—
300Dic3⋊C4—42no—
301Dic3⋊C4—81no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—44no—
311C2×C3⋊C8C2×D412yes—
312C2×C3⋊C8C2×D412yes—
313C2×C3⋊C8#4112yes—
314C2×C3⋊C8#4112yes—
315C22×Q8—31no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—21no—
318C22×D4—31no—
319C22×D4—61no—
320C22×D4C22×D311yescharacteristic
321C23×C4—21no—
322C23×C4—61no—
323C23×C4C22×D311yescharacteristic
324C2×Q16—62no—
325C2×Q16—62no—
326C2×Q16—62no—
327C2×SD16—62no—
328C2×SD16—62no—
329C2×SD16—62no—
330C2×SD16—62no—
331C2×SD16—121no—
332C2×SD16—121no—
333C2×D8—34no—
334C2×D8—62no—
335C2×D8—62no—
336C22×C8—31no—
337C22×C8—31no—
338C22×C8—31no—
339C22×C8—31no—
340C22×C8—62no—
341C22×C8—62no—
342C22×C8—62no—
343#124—22no—
344#124—41no—
345#124—62no—
346#124—121no—
347C22⋊Q8—22no—
348C22⋊Q8—41no—
349C22⋊Q8—62no—
350C22⋊Q8—121no—
351#121—22no—
352#121—41no—
353#121—62no—
354#121—121no—
355C4×D4—22no—
356C4×D4—41no—
357C4×D4—62no—
358C4×D4—121no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4#6711yescharacteristic
378C2×C22⋊C4#6711yescharacteristic
379C2×C42C22×D311yescharacteristic
380C2×C42C22×D311yescharacteristic
381#107—34no—
382#107—62no—
383#103—62no—
384#103—62no—
385#103—121no—
386#103—121no—
387#102—62no—
388#102—62no—
389#102—62no—
390#102—62no—
391C22⋊C8—62no—
392C4×C8—62no—
393C4×C8—62no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—61no—
398#95—61no—
399#95—61no—
400#95#6711yescharacteristic
401#95#6711yescharacteristic
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—22no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3#13512yes—
416C23×C3C22×D411yescharacteristic
417C22×D3—22no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C3×Q8—41no—
425C3×Q8—41no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×D4—22no—
429C3×D4—22no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—84no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—84no—
461C2×C3×C4#13512yes—
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×C3×C4H(5,𝔽2)11yescharacteristic
467C2×C3×C4H(5,𝔽2)11yescharacteristic
468#67—84no—
469C2×Dic3—22no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478D12—22no—
479D12—22no—
480D12—41no—
481D12—41no—
482C4×D3—84no—
483Dic6—41no—
484Dic6—41no—
485Dic6—41no—
486Dic6—41no—
487C3⋊C8—22no—
488C3⋊C8—41no—
489C3⋊C8—41no—
490C3⋊C8#12114yes—
491C24—21no—
492C24—61no—
493C24C2×#6711yescharacteristic
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—61no—
501C2×Q8—61no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×Q8—61no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—32no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—81no—
520C2×D4—122no—
521C2×D4—122no—
522C2×D4—241no—
523C2×D4D3×D412yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—81no—
539C22×C4—122no—
540C22×C4—122no—
541C22×C4—241no—
542C22×C4C2×#6711yescharacteristic
543C22×C4C2×#6711yescharacteristic
544C22×C4C2×#6711yescharacteristic
545C22×C4C2×#6711yescharacteristic
546C22×C4C2×#6711yescharacteristic
547C22×C4C23×D311yescharacteristic
548Q16—124no—
549SD16—124no—
550SD16—124no—
551D8—68no—
552C2×C8—32no—
553C2×C8—32no—
554C2×C8—32no—
555C2×C8—32no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8—61no—
563C2×C8—61no—
564C2×C8—124no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—32no—
569C4⋊C4—42no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—81no—
574C4⋊C4—122no—
575C4⋊C4—241no—
576C4⋊C4D3×D412yes—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—122no—
587C22⋊C4—122no—
588C22⋊C4—122no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3#53211yescharacteristic
608C22×C3D4211yescharacteristic
609C22×C3D4211yescharacteristic
610C22×C3C2×#13511yescharacteristic
611C22×C3C2×#13511yescharacteristic
612C22×C3#57611yescharacteristic
613C22×C3#57811yescharacteristic
614C2×D3—42no—
615C2×D3—42no—
616C2×D3—42no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C2×D3—81no—
621C3×C4—22no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—42no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—81no—
628C3×C4—81no—
629C3×C4C2×#12111yescharacteristic
630C3×C4#54011yescharacteristic
631C3×C4#54611yescharacteristic
632C3×C4#55011yescharacteristic
633Dic3—42no—
634Dic3—81no—
635Dic3—81no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—62no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23#95012yes—
657C23C22×#6711yescharacteristic
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—121no—
663Q8—121no—
664Q8—121no—
665Q8—121no—
666D4—22no—
667D4—22no—
668D4—41no—
669D4—41no—
670D4—62no—
671D4—62no—
672D4—84no—
673D4—121no—
674D4—121no—
675D4—244no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—62no—
704C2×C4—84no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—244no—
714C2×C4#95012yes—
715C2×C4C2×D3×D411yescharacteristic
716C2×C4C2×D3×D411yescharacteristic
717C2×C4#100411yescharacteristic
718C2×C4#100411yescharacteristic
719C2×C4D3×#4111yescharacteristic
720C2×C4D3×#4111yescharacteristic
721C8—34no—
722C8—62no—
723C8—121no—
724C8—121no—
725C2×C3—42no—
726C2×C3—82no—
727C2×C3#242811yescharacteristic
728C2×C3#316811yescharacteristic
729C2×C3#317511yescharacteristic
730C2×C3#328011yescharacteristic
731C2×C3#328011yescharacteristic
732C2×C3#328311yescharacteristic
733C2×C3#328511yescharacteristic
734D3—82no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—122no—
750C22—122no—
751C22—122no—
752C22—241no—
753C22—241no—
754C22—241no—
755C22—241no—
756C22D4×#6711yescharacteristic
757C22D4×#6711yescharacteristic
758C22C2×#95011yescharacteristic
759C22C2×#95011yescharacteristic
760C22#583211yescharacteristic
761C22#583511yescharacteristic
762C22#583811yescharacteristic
763C4—22no—
764C4—41no—
765C4—42no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—81no—
770C4—81no—
771C4—122no—
772C4—241no—
773C4—241no—
774C4#559911yescharacteristic
775C4D3×#12111yescharacteristic
776C4#561011yescharacteristic
777C4#561511yescharacteristic
778C3#2541311yescharacteristic, complemented, Sylow
779C2—42no—
780C2—82no—
781C2—242no—
782C2#8265011yescharacteristic
783C2#8313411yescharacteristic
784C2#8345711yescharacteristic
785C2#8350511yescharacteristic
786C2#8350511yescharacteristic
787C2#8352411yescharacteristic
788C2#8354911yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2427C2
socleC23×C3C22×D4
prime radicalC2×#5038C2
hypercenter#2427D3
hypocenterC3#25413
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2427

Complements

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

NH ≅ G/Ntype
1. C3×#2427C2semidirect
2. C2×#5059C2semidirect
3. C2×#5051C2semidirect
5. C2×C4×#213C2semidirect
6. #73486C2semidirect
7. #71722C2semidirect
8. #71699C2semidirect
9. #71685C2semidirect
10. #71612C2semidirect
11. #69687C2semidirect
12. #69677C2semidirect
13. #69628C2semidirect
14. #69619C2semidirect
15. C22⋊C4×C3⋊C8C2semidirect
69. #2427D3semidirect
163. #807D4semidirect
778. C3#25413semidirect

Maximal subgroups

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

subgroupindex
C3×#24272
C2×#50592
C2×#50512
C2×#50382
C2×C4×#2132
#734862
#717222
#716992
#716852
#716122
#696872
#696772
#696282
#696192
C22⋊C4×C3⋊C82
#254133