Finite Group Databasebeta

← #10944152

Subgroups — #10944152

Order 768.

1448 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5523C211yesmaximal, characteristic, complemented
2#82287C211yesmaximal, characteristic, complemented
3C2×#4845C211yesmaximal, characteristic, complemented
4C2×#4844C211yesmaximal, characteristic, complemented
5C2×#4733C211yesmaximal, characteristic, complemented
6C2×#4734C211yesmaximal, characteristic
7C3×#1798C211yesmaximal, characteristic, complemented
8#70485C211yesmaximal, characteristic, complemented
9#70479C211yesmaximal, characteristic, complemented
10#69932C211yesmaximal, characteristic, complemented
11#69930C211yesmaximal, characteristic, complemented
12#68686C211yesmaximal, characteristic, complemented
13#68685C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68672C211yesmaximal, characteristic, complemented
16#32919—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C2×C3×#117C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C22×C4⋊Dic3C2211yescharacteristic
21C2×#924C2211yescharacteristic
22C22×Dic12C2211yescharacteristic
23C22×D24C2211yescharacteristic
24C22×#204C2211yescharacteristic
25C22×#204C2211yescharacteristic
26#5523—24no—
27#5523—24no—
28C2×#892—21no—
29C2×D3×C4⋊C4—21no—
30C2×#67⋊C4—21no—
31C2×#67⋊C4—21no—
32C2×#875C2211yescharacteristic
33C2×C4×D12C2211yescharacteristic
34C2×C4×D12C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C2×C4×Dic6C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×C4⋊C8C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#816C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49#4994—21no—
50#4994—21no—
51#4961—21no—
52#4961—21no—
53#4939C2211yescharacteristic
54#4935C2211yescharacteristic
55#4929C2211yescharacteristic
56#4845—24no—
57#4844—24no—
58#4734—24no—
59#4733—24no—
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64#4551C2211yescharacteristic
65#4551C2211yescharacteristic
66C2×#520—31no—
67C2×#464—31no—
68C2×#463—31no—
69C2×#452—31no—
70C2×#449—31no—
71#2620—31no—
72#1880—31no—
73#1879—31no—
74#1878—31no—
75#1877—31no—
76#1874—31no—
77#1872—31no—
78#1803—31no—
79#1802—31no—
80#1798D311yescharacteristic, complemented
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C23×Dic3—21no—
85C2×#235—22no—
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235D414yes—
91C22×D12C2311yescharacteristic
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×Dic6C2311yescharacteristic
97C22×Dic6C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C3×#117—22no—
103C3×#117—22no—
104C2×C3×C4⋊C4D411yescharacteristic
105C2×C3×C4⋊C4D411yescharacteristic
106C2×C3×C22⋊C4D411yescharacteristic
107C2×C3×C22⋊C4D411yescharacteristic
108C2×C3×C42C2311yescharacteristic
109C2×C3×C42C2311yescharacteristic
110C2×#217—21no—
111#930—22no—
112#930—22no—
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)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3—22no—
122C2×C4⋊Dic3—22no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129#924—22no—
130#924—22no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3—21no—
136C2×Dic12—22no—
137C2×Dic12—22no—
138C2×Dic12—22no—
139C2×D24—22no—
140C2×D24—22no—
141C2×D24—22no—
142C2×#204—22no—
143C2×#204—22no—
144C2×#204—22no—
145C2×#204—22no—
146C2×#204—22no—
147C2×#204—22no—
148#892—28no—
149D3×C4⋊C4—28no—
150#67⋊C4—28no—
151#67⋊C4—28no—
152#875—22no—
153#875—22no—
154C4×D12—22no—
155C4×D12—22no—
156C4×D12—22no—
157C4×D12D414yescomplemented
158C4×Dic6—22no—
159C4×Dic6—22no—
160C4×Dic6—22no—
161C4×Dic6D414yescomplemented
162C3×C4⋊C8—22no—
163C3×C4⋊C8—22no—
164C3×C22⋊C8—22no—
165C3×C22⋊C8—22no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168#821—22no—
169#821—22no—
170#821—22no—
171#821—22no—
172#816—22no—
173#816—22no—
174#816—22no—
175#816—22no—
176C22×#41—31no—
177C22×Q16—31no—
178C22×SD16—31no—
179C22×SD16—31no—
180C22×D8—31no—
181C2×#124—31no—
182C2×C22⋊Q8—31no—
183C2×#121—31no—
184#520—64no—
185#520—64no—
186C2×C4×Q8—31no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×C4×D4—31no—
190C2×C4×D4—61no—
191C2×C4×D4—61no—
192C2×#117—61no—
193C2×#117C2×D311yescharacteristic
194C22×C4⋊C4—31no—
195C22×C4⋊C4—61no—
196#464—64no—
197#463—64no—
198#452—64no—
199#449—64no—
200C2×C4⋊C8C2×D311yescharacteristic
201C2×C4⋊C8C2×D311yescharacteristic
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102—31no—
210C2×C22⋊C8C2×D311yescharacteristic
211C2×C22⋊C8C2×D311yescharacteristic
212#396—61no—
213#396—61no—
214#394—61no—
215#394—61no—
216#391—31no—
217#390—31no—
218#384—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340—31no—
223#336C2×D311yescharacteristic
224#336C2×D311yescharacteristic
225C24×C3C2×D411yescharacteristic
226C23×D3—21no—
227C23×D3—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D412yes—
238C22×C3×C4#4112yes—
239C22×C3×C4C2411yescharacteristic
240C2×#67—24no—
241C2×#67—24no—
242C2×#67—24no—
243C2×#67—42no—
244C2×#67—81no—
245C2×#67—81no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—24no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—81no—
254C22×Dic3—81no—
255#235—28no—
256#235—28no—
257#235—28no—
258#235—28no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12C2×D412yes—
269C2×D12C2×D412yes—
270C2×D12#4112yes—
271C2×C4×D3—24no—
272C2×C4×D3—24no—
273C2×C4×D3—24no—
274C2×C4×D3—24no—
275C2×C4×D3—24no—
276C2×C4×D3—81no—
277C2×C4×D3—81no—
278C2×C4×D3—81no—
279C2×C4×D3—81no—
280C2×Dic6—21no—
281C2×Dic6—21no—
282C2×Dic6—21no—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6C2×D412yes—
290C2×Dic6C2×D412yes—
291C2×Dic6#4112yes—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—22no—
306C3×C22⋊C4—22no—
307C3×C22⋊C4—22no—
308C3×C42—21no—
309C3×C42—21no—
310C3×C42C2×D412yes—
311C3×C42C2×D412yes—
312#217—42no—
313(C2×D3)⋊C4—24no—
314(C2×D3)⋊C4—24no—
315(C2×D3)⋊C4—42no—
316(C2×D3)⋊C4—42no—
317(C2×D3)⋊C4—42no—
318(C2×D3)⋊C4—81no—
319(C2×D3)⋊C4—81no—
320C4⋊Dic3—24no—
321C4⋊Dic3—21no—
322C4⋊Dic3—21no—
323C4⋊Dic3—21no—
324C4⋊Dic3—21no—
325C4⋊Dic3—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3—81no—
328C4⋊Dic3—81no—
329C4⋊Dic3C2×D412yes—
330C4⋊Dic3C2×D412yes—
331Dic3⋊C4—24no—
332Dic3⋊C4—24no—
333Dic3⋊C4—42no—
334C4×Dic3—24no—
335C4×Dic3—24no—
336Dic12—44no—
337D24—44no—
338#204—44no—
339#204—44no—
340C2×#41—34no—
341C2×#41—62no—
342C2×#41—62no—
343C2×#41—62no—
344C2×#41—62no—
345C2×#41—62no—
346C22×Q8—31no—
347C22×Q8—31no—
348C22×D4—31no—
349C22×D4—31no—
350C22×D4—61no—
351C22×D4—61no—
352C23×C4—61no—
353C23×C4—61no—
354C23×C4—61no—
355C23×C4—61no—
356C23×C4C22×D311yescharacteristic
357C2×Q16—62no—
358C2×Q16—62no—
359C2×Q16—62no—
360C2×SD16—62no—
361C2×SD16—62no—
362C2×SD16—62no—
363C2×SD16—62no—
364C2×SD16—62no—
365C2×SD16—62no—
366C2×D8—62no—
367C2×D8—62no—
368C2×D8—62no—
369C22×C8C22×D311yescharacteristic
370C22×C8C22×D311yescharacteristic
371C22×C8C22×D311yescharacteristic
372C22×C8C22×D311yescharacteristic
373#124—62no—
374#124—62no—
375C22⋊Q8—62no—
376C22⋊Q8—62no—
377#121—62no—
378#121—62no—
379C4×Q8—34no—
380C4×Q8—62no—
381C4×Q8—62no—
382C4×Q8—62no—
383C4×D4—34no—
384C4×D4—62no—
385C4×D4—62no—
386C4×D4—68no—
387C4×D4—68no—
388C4×D4—62no—
389#117—22no—
390#117—22no—
391#117—68no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—68no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4—61no—
401C2×C4⋊C4—61no—
402C2×C4⋊C4—61no—
403C2×C4⋊C4—61no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4D1211yescharacteristic
406C2×C4⋊C4D1211yescharacteristic
407C2×C22⋊C4—61no—
408C2×C22⋊C4—61no—
409C2×C22⋊C4—61no—
410C2×C22⋊C4—61no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413C2×C22⋊C4—61no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4D1211yescharacteristic
416C2×C22⋊C4D1211yescharacteristic
417C2×C42—61no—
418C2×C42—61no—
419C2×C42C22×D311yescharacteristic
420C2×C42C22×D311yescharacteristic
421C4⋊C8—22no—
422C4⋊C8—22no—
423#103—62no—
424#103—62no—
425#103—62no—
426#103—62no—
427#102—62no—
428#102—62no—
429#102—62no—
430#102—62no—
431C22⋊C8—22no—
432C22⋊C8—22no—
433#95—61no—
434#95—61no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3#12112yes—
442C23×C3C22×D411yescharacteristic
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3—41no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4#12012yes—
474C2×C3×C4#12012yes—
475C2×C3×C4#12112yes—
476C2×C3×C4C22×D411yescharacteristic
477C2×C3×C4C22×D411yescharacteristic
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480C2×C3×C4C2×#4111yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482#67—216no—
483#67—84no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—41no—
490C2×Dic3—41no—
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×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—84no—
503D12—22no—
504D12—22no—
505D12—22no—
506D12—41no—
507D12—41no—
508D12—41no—
509D12—41no—
510D12#12114yes—
511C4×D3—216no—
512C4×D3—84no—
513C4×D3—84no—
514Dic6—22no—
515Dic6—22no—
516Dic6—22no—
517Dic6—41no—
518Dic6—41no—
519Dic6—41no—
520Dic6—41no—
521Dic6#12114yes—
522C3×C8—41no—
523C3×C8—41no—
524C3×C8—41no—
525C3×C8—41no—
526C24—61no—
527C24—61no—
528C24C2×D1211yescharacteristic
529#41—68no—
530#41—68no—
531#41—68no—
532#41—68no—
533C2×Q8—32no—
534C2×Q8—32no—
535C2×Q8—32no—
536C2×Q8—61no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—61no—
540C2×Q8—61no—
541C2×Q8—61no—
542C2×Q8—61no—
543C2×Q8—61no—
544C2×Q8—61no—
545C2×D4—32no—
546C2×D4—32no—
547C2×D4—32no—
548C2×D4—64no—
549C2×D4—64no—
550C2×D4—64no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—61no—
555C2×D4—61no—
556C2×D4—61no—
557C2×D4—61no—
558C2×D4—61no—
559C2×D4—61no—
560C2×D4—122no—
561C2×D4—241no—
562C2×D4—241no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—64no—
568C22×C4—64no—
569C22×C4—64no—
570C22×C4—61no—
571C22×C4—64no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—64no—
575C22×C4—64no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—241no—
580C22×C4—241no—
581C22×C4—241no—
582C22×C4—241no—
583C22×C4—241no—
584C22×C4—241no—
585C22×C4C2×D1211yescharacteristic
586C22×C4C2×D1211yescharacteristic
587C22×C4C2×D1211yescharacteristic
588C22×C4C2×D1211yescharacteristic
589C22×C4C2×D1211yescharacteristic
590C22×C4D3×D412yes—
591C22×C4#23912yes—
592C22×C4C23×D311yescharacteristic
593Q16—124no—
594SD16—124no—
595SD16—124no—
596D8—124no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—32no—
612C4⋊C4—32no—
613C4⋊C4—64no—
614C4⋊C4—64no—
615C4⋊C4—64no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—122no—
623C4⋊C4—241no—
624C4⋊C4—241no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—64no—
628C22⋊C4—64no—
629C22⋊C4—122no—
630C22⋊C4—122no—
631C22⋊C4—122no—
632C22⋊C4—122no—
633C22⋊C4—241no—
634C22⋊C4—241no—
635C42—21no—
636C42—21no—
637C42—64no—
638C42—64no—
639C42D3×D412yes—
640C42D3×D412yes—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3C2×#12011yescharacteristic
649C22×C3C2×#12111yescharacteristic
650C22×C3#52511yescharacteristic
651C22×C3#57611yescharacteristic
652C22×C3#57711yescharacteristic
653C22×C3#57711yescharacteristic
654C22×C3#57811yescharacteristic
655C2×D3—24no—
656C2×D3—42no—
657C2×D3—42no—
658C2×D3—42no—
659C2×D3—42no—
660C2×D3—42no—
661C2×D3—42no—
662C2×D3—81no—
663C2×D3—81no—
664C2×D3—81no—
665C2×D3—81no—
666C2×D3—81no—
667C2×D3—81no—
668C2×D3—81no—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—22no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4C2×#12111yescharacteristic
675C3×C4C2×#12111yescharacteristic
676C3×C4#52511yescharacteristic
677C3×C4#52511yescharacteristic
678Dic3—24no—
679Dic3—42no—
680Dic3—42no—
681Dic3—81no—
682Dic3—81no—
683Dic3—81no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—62no—
691C23—62no—
692C23—62no—
693C23—121no—
694C23—121no—
695C23—121no—
696C23—121no—
697C23—121no—
698C23—121no—
699C23—121no—
700C23—121no—
701C23—121no—
702C23—121no—
703C23—121no—
704C23#89512yes—
705C23C22×D1211yescharacteristic
706Q8—34no—
707Q8—62no—
708Q8—62no—
709Q8—62no—
710Q8—121no—
711Q8—121no—
712Q8—121no—
713Q8—121no—
714D4—34no—
715D4—616no—
716D4—62no—
717D4—62no—
718D4—62no—
719D4—121no—
720D4—121no—
721D4—121no—
722D4—121no—
723D4—244no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—616no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—244no—
760C2×C4—244no—
761C2×C4—244no—
762C2×C4#88212yes—
763C2×C4#88212yes—
764C2×C4#89512yes—
765C2×C4C2×D3×D411yescharacteristic
766C2×C4C2×D3×D411yescharacteristic
767C2×C4C2×D3×D411yescharacteristic
768C2×C4C2×#23911yescharacteristic
769C2×C4D3×#4111yescharacteristic
770C2×C4D3×#4111yescharacteristic
771C8—41no—
772C8—41no—
773C8—41no—
774C8—41no—
775C2×C3—42no—
776C2×C3#284711yescharacteristic
777C2×C3#301211yescharacteristic
778C2×C3#301311yescharacteristic
779C2×C3#304511yescharacteristic
780C2×C3#304611yescharacteristic
781C2×C3#312411yescharacteristic
782C2×C3#312511yescharacteristic
783D3—44no—
784D3—161no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—64no—
793C22—122no—
794C22—122no—
795C22—122no—
796C22—122no—
797C22—122no—
798C22—122no—
799C22—241no—
800C22—241no—
801C22—241no—
802C22—241no—
803C22—241no—
804C22—241no—
805C22—241no—
806C22C2×#88211yescharacteristic
807C22C2×#89511yescharacteristic
808C22#552411yescharacteristic
809C22#575111yescharacteristic
810C22#575111yescharacteristic
811C22#575211yescharacteristic
812C22#575311yescharacteristic
813C4—22no—
814C4—22no—
815C4—22no—
816C4—41no—
817C4—41no—
818C4—64no—
819C4—122no—
820C4—122no—
821C4—241no—
822C4—241no—
823C4—241no—
824C4D3×#12111yescharacteristic
825C4D3×#12111yescharacteristic
826C4#562711yescharacteristic
827C4#562711yescharacteristic
828C3#3291911yescharacteristic, complemented, Sylow
829C2—42no—
830C2—124no—
831C2—481no—
832C2#7404811yescharacteristic
833C2#7867211yescharacteristic
834C2#7868011yescharacteristic
835C2#7908811yescharacteristic
836C2#7908911yescharacteristic
837C2#7938811yescharacteristic
838C2#7938911yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1798C2
socleC23×C3C22×D4
prime radicalC2×#4734C2
hypercenter#1798D3
hypocenterC3#32919
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1798

Complements

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

NH ≅ G/Ntype
1. C2×#5523C2semidirect
2. #82287C2semidirect
3. C2×#4845C2semidirect
4. C2×#4844C2semidirect
5. C2×#4733C2semidirect
7. C3×#1798C2semidirect
8. #70485C2semidirect
9. #70479C2semidirect
10. #69932C2semidirect
11. #69930C2semidirect
12. #68686C2semidirect
13. #68685C2semidirect
14. #68673C2semidirect
15. #68672C2semidirect
80. #1798D3semidirect
157. C4×D12D4semidirect
161. C4×Dic6D4semidirect
828. C3#32919semidirect

Maximal subgroups

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

subgroupindex
C2×#55232
#822872
C2×#48452
C2×#48442
C2×#47332
C2×#47342
C3×#17982
#704852
#704792
#699322
#699302
#686862
#686852
#686732
#686722
#329193