Finite Group Databasebeta

← #10830986

Subgroups — #10830986

Order 768.

1412 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#137C211yesmaximal, characteristic, complemented
2#84097C211yesmaximal, characteristic
3#84068C211yesmaximal, characteristic, complemented
4C2×#5189C211yesmaximal, characteristic, complemented
5C2×#5174C211yesmaximal, characteristic, complemented
6C2×#5128C211yesmaximal, characteristic, complemented
7#72135C211yesmaximal, characteristic, complemented
8#72132C211yesmaximal, characteristic, complemented
9#72071C211yesmaximal, characteristic, complemented
10#72068C211yesmaximal, characteristic, complemented
11#72066C211yesmaximal, characteristic, complemented
12#72054C211yesmaximal, characteristic, complemented
13#72051C211yesmaximal, characteristic, complemented
14#72049C211yesmaximal, characteristic, complemented
15#71988C211yesmaximal, characteristic, complemented
16#24276—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C2×C3×#137—24no—
20C2×C3×#137—24no—
21C2×C3×#137—24no—
22C22×C3×Q16C2211yescharacteristic
23C22×C3×Q16C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic
25C22×C3×SD16C2211yescharacteristic
26C22×C3×M16C2211yescharacteristic
27C2×#946C2211yescharacteristic
28C2×#946C2211yescharacteristic
29C2×#946C2211yescharacteristic
30C2×#938C2211yescharacteristic
31C2×C4×#67C2211yescharacteristic
32C22×ΓL(1,𝔽25)C2211yescharacteristic
33#5231—21no—
34#5230—21no—
35#5229C2211yescharacteristic
36#5229C2211yescharacteristic
37#5229C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44#5223—21no—
45#5222—21no—
46#5221C2211yescharacteristic
47C2×#832C2211yescharacteristic
48C2×#832C2211yescharacteristic
49#5213—21no—
50#5213—21no—
51#5212C2211yescharacteristic
52#5212C2211yescharacteristic
53#5210—21no—
54#5210—21no—
55C2×#830C2211yescharacteristic
56#5189—24no—
57#5174—24no—
58#5128—24no—
59C2×(C2×D3)⋊C8C2211yescharacteristic
60C2×#818C2211yescharacteristic
61C2×#817C2211yescharacteristic
62C2×Dic3⋊C8C2211yescharacteristic
63C2×C8×Dic3C2211yescharacteristic
64#4551C2211yescharacteristic
65#4551C2211yescharacteristic
66C22×#137D311yescharacteristic, complemented
67C2×#470—31no—
68C2×#468—31no—
69C2×#436—31no—
70#2409—31no—
71#2407—31no—
72#2056—31no—
73#2055—31no—
74#2001—31no—
75#2000—31no—
76#1969—31no—
77#1968—31no—
78#1809—31no—
79#1788—31no—
80#1787—31no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—41no—
86C2×C3×#41—41no—
87C22×C3×Q8—21no—
88C22×C3×Q8—22no—
89C22×C3×Q8—22no—
90C22×C3×Q8—22no—
91C22×C3×Q8—22no—
92C22×C3×Q8—41no—
93C22×C3×Q8—41no—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×C3×Q8C2311yescharacteristic
97C22×C3×D4—21no—
98C22×C3×D4C2311yescharacteristic
99C23×C3×C4—21no—
100C23×C3×C4—21no—
101C23×C3×C4C2311yescharacteristic
102C22×#67—21no—
103C22×#67D411yescharacteristic
104C22×C4×D3C2311yescharacteristic
105C3×#137—232no—
106C2×C3×Q16—22no—
107C2×C3×Q16—22no—
108C2×C3×Q16—22no—
109C2×C3×Q16—22no—
110C2×C3×Q16—22no—
111C2×C3×Q16D414yescomplemented
112C2×C3×SD16—22no—
113C2×C3×SD16—22no—
114C2×C3×SD16—22no—
115C2×C3×SD16—22no—
116C2×C3×SD16—22no—
117C2×C3×SD16D414yescomplemented
118C2×C3×M16—22no—
119C2×C3×M16—22no—
120C2×C3×M16D414yescomplemented
121C22×C3×C8C2311yescharacteristic
122C22×C3×C8C2311yescharacteristic
123C2×#217—21no—
124C2×#217—21no—
125C2×#217—21no—
126C2×#217—21no—
127C2×#217—21no—
128C2×#217D411yescharacteristic
129#946—22no—
130#946—22no—
131#946—22no—
132#946—41no—
133#946—41no—
134#946—41no—
135#938—22no—
136#938—41no—
137C4×#67—22no—
138C4×#67—22no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4D411yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4—21no—
149C2×Dic3⋊C4—21no—
150C2×Dic3⋊C4D411yescharacteristic
151C2×C4×Dic3C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C2×ΓL(1,𝔽25)—22no—
155C2×ΓL(1,𝔽25)—22no—
156C2×ΓL(1,𝔽25)—22no—
157#835—22no—
158#835—22no—
159#835—22no—
160#835—41no—
161#835—41no—
162#835—41no—
163#832—22no—
164#832—41no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172C3⋊#95—21no—
173#830—22no—
174(C2×D3)⋊C8—22no—
175#818—22no—
176#817—22no—
177Dic3⋊C8—22no—
178C8×Dic3—22no—
179C22×#41C2×D311yescharacteristic
180C23×Q8C2×D311yescharacteristic
181C2×#137—24no—
182C2×#137—24no—
183C2×#137—24no—
184C22×Q16C2×D311yescharacteristic
185C22×Q16C2×D311yescharacteristic
186C22×SD16C2×D311yescharacteristic
187C22×SD16C2×D311yescharacteristic
188C22×M16—31no—
189C22×M16C2×D311yescharacteristic
190C2×C22⋊Q8—31no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×#121—31no—
194C2×C4×D4—31no—
195#470—64no—
196#468—64no—
197#436—64no—
198C2×#107—31no—
199C2×#106—31no—
200C2×C4⋊C8—31no—
201C2×#103—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#103—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×C22⋊C8—31no—
210C2×C22⋊C8—31no—
211C2×C4×C8—31no—
212#395—61no—
213#394—61no—
214#393—61no—
215#392—61no—
216#391—31no—
217#391—31no—
218#391—31no—
219#390—31no—
220#386—61no—
221#386—61no—
222#385—61no—
223#385—61no—
224#380—31no—
225#380—31no—
226#340—31no—
227#340—31no—
228C24×C3—21no—
229C24×C3C2×D411yescharacteristic
230C23×D3C2×D411yescharacteristic
231C3×#41—28no—
232C3×#41—44no—
233C3×#41—44no—
234C3×#41—44no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—28no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—42no—
252C2×C3×Q8—42no—
253C2×C3×Q8—44no—
254C2×C3×Q8—44no—
255C2×C3×Q8—44no—
256C2×C3×Q8—42no—
257C2×C3×Q8C2×D412yes—
258C2×C3×Q8C2×D412yes—
259C2×C3×Q8C2×D412yes—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—42no—
266C2×C3×D4—42no—
267C2×C3×D4—42no—
268C2×C3×D4C2×D412yes—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—42no—
277C22×C3×C4—42no—
278C22×C3×C4—42no—
279C22×C3×C4—42no—
280C22×C3×C4—42no—
281C22×C3×C4—42no—
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2×D412yes—
284C22×C3×C4#4112yes—
285C22×C3×C4C2411yescharacteristic
286C2×#67—22no—
287C2×#67—22no—
288C2×#67—41no—
289C2×#67—42no—
290C2×#67—42no—
291C2×#67—81no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3C2×D411yescharacteristic
297C22×Dic3C2×D411yescharacteristic
298C22×Dic3C2×D411yescharacteristic
299C2×C4×D3—21no—
300C2×C4×D3—21no—
301C2×C4×D3—21no—
302C2×C4×D3—21no—
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C3×Q16—28no—
306C3×Q16—28no—
307C3×SD16—28no—
308C3×SD16—28no—
309C3×M16—28no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8C2×D412yes—
313C2×C3×C8C2×D412yes—
314C2×C3×C8C2×D412yes—
315C2×C3×C8C2×D412yes—
316#217—22no—
317#217—42no—
318#217—42no—
319#217—42no—
320#217—81no—
321#217—81no—
322(C2×D3)⋊C4—22no—
323(C2×D3)⋊C4—42no—
324(C2×D3)⋊C4—42no—
325(C2×D3)⋊C4—42no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330C4⋊Dic3—21no—
331C4⋊Dic3—21no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334Dic3⋊C4—22no—
335Dic3⋊C4—42no—
336Dic3⋊C4—42no—
337Dic3⋊C4—42no—
338C4×Dic3—21no—
339C4×Dic3—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346ΓL(1,𝔽25)—44no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41—41no—
352C2×#41—41no—
353C22×Q8—21no—
354C22×Q8—22no—
355C22×Q8—22no—
356C22×Q8—22no—
357C22×Q8—22no—
358C22×Q8—41no—
359C22×Q8—41no—
360C22×Q8C22×D311yescharacteristic
361C22×Q8C22×D311yescharacteristic
362C22×Q8C22×D311yescharacteristic
363C22×D4—21no—
364C22×D4—31no—
365C22×D4—61no—
366C22×D4C22×D311yescharacteristic
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—31no—
370C23×C4C22×D311yescharacteristic
371#137—232no—
372C2×Q16—22no—
373C2×Q16—22no—
374C2×Q16—22no—
375C2×Q16—22no—
376C2×Q16—22no—
377C2×Q16#6714yescomplemented
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16#6714yescomplemented
384C2×M16—22no—
385C2×M16—22no—
386C2×M16—62no—
387C2×M16—62no—
388C2×M16—62no—
389C2×M16#6714yescomplemented
390C22×C8—31no—
391C22×C8—31no—
392C22×C8C22×D311yescharacteristic
393C22×C8C22×D311yescharacteristic
394C22⋊Q8—62no—
395C22⋊Q8—62no—
396C22⋊Q8—62no—
397C22⋊Q8—121no—
398C22⋊Q8—121no—
399C22⋊Q8—121no—
400#121—62no—
401#121—121no—
402C4×D4—62no—
403C4×D4—62no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—31no—
409C2×C4⋊C4—61no—
410C2×C4⋊C4—61no—
411C2×C4⋊C4—61no—
412C2×C22⋊C4—31no—
413C2×C22⋊C4—31no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4—61no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—61no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C42—31no—
423#107—62no—
424#106—62no—
425C4⋊C8—62no—
426#103—62no—
427#103—62no—
428#103—62no—
429#103—121no—
430#103—121no—
431#103—121no—
432#102—62no—
433#102—121no—
434C22⋊C8—62no—
435C22⋊C8—62no—
436C4×C8—62no—
437#95—61no—
438#95—61no—
439#95—61no—
440#95—61no—
441#95—61no—
442#95—61no—
443#95—61no—
444#95—61no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—22no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3#12112yes—
459C23×C3C22×D411yescharacteristic
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—21no—
467C3×Q8—22no—
468C3×Q8—22no—
469C3×Q8—22no—
470C3×Q8—22no—
471C3×Q8—22no—
472C3×Q8—22no—
473C3×Q8—48no—
474C3×Q8—41no—
475C3×Q8—41no—
476C3×Q8—41no—
477C3×Q8—41no—
478C3×Q8—41no—
479C3×Q8—41no—
480C3×D4—22no—
481C3×D4—22no—
482C3×D4—48no—
483C3×D4—41no—
484C3×D4—41no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—48no—
495C2×C3×C4—48no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4#12112yes—
503C2×C3×C4C22×D411yescharacteristic
504C2×C3×C4C22×D411yescharacteristic
505C2×C3×C4C22×D411yescharacteristic
506C2×C3×C4C2×#4111yescharacteristic
507C2×C3×C4H(5,𝔽2)11yescharacteristic
508C2×C3×C4H(5,𝔽2)11yescharacteristic
509#67—44no—
510#67—84no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3#13712yescomplemented
532C4×D3—41no—
533C4×D3—41no—
534C4×D3—41no—
535C4×D3—41no—
536C3×C8—22no—
537C3×C8#12014yes—
538C3⋊C8—41no—
539C3⋊C8—41no—
540C24—21no—
541C24—31no—
542C24D3×D411yescharacteristic
543#41—28no—
544#41—44no—
545#41—44no—
546#41—44no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—28no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—42no—
564C2×Q8—42no—
565C2×Q8—44no—
566C2×Q8—44no—
567C2×Q8—44no—
568C2×Q8—42no—
569C2×Q8C2×#6712yes—
570C2×Q8C2×#6712yes—
571C2×Q8C2×#6712yes—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—62no—
581C2×D4—62no—
582C2×D4—121no—
583C2×D4—122no—
584C2×D4—122no—
585C2×D4—241no—
586C2×D4C2×#6712yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4D3×D411yescharacteristic
614C22×C4#23712yes—
615C22×C4C2×#6712yes—
616C22×C4C23×D311yescharacteristic
617Q16—28no—
618Q16—28no—
619SD16—28no—
620SD16—28no—
621M16—28no—
622M16—124no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—61no—
626C2×C8—61no—
627C2×C8—61no—
628C2×C8—61no—
629C2×C8—61no—
630C2×C8—61no—
631C2×C8C2×#6712yes—
632C2×C8C2×#6712yes—
633C2×C8C2×#6712yes—
634C2×C8C2×#6712yes—
635C4⋊C4—62no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—122no—
645C4⋊C4—122no—
646C4⋊C4—122no—
647C22⋊C4—62no—
648C22⋊C4—62no—
649C22⋊C4—122no—
650C22⋊C4—122no—
651C22⋊C4—122no—
652C22⋊C4—122no—
653C22⋊C4—122no—
654C22⋊C4—122no—
655C22⋊C4—241no—
656C22⋊C4—241no—
657C42—61no—
658C42—61no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3C2×#12111yescharacteristic
674C22×C3D4211yescharacteristic
675C22×C3D4211yescharacteristic
676C22×C3C2×#13711yescharacteristic
677C22×C3#57511yescharacteristic
678C22×C3#57711yescharacteristic
679C22×C3#57811yescharacteristic
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C3×C4—22no—
688C3×C4—42no—
689C3×C4—42no—
690C3×C4—42no—
691C3×C4C2×#12011yescharacteristic
692C3×C4#53511yescharacteristic
693C3×C4#54611yescharacteristic
694C3×C4#54611yescharacteristic
695Dic3—22no—
696Dic3—41no—
697Dic3—41no—
698Dic3—81no—
699Dic3—81no—
700Dic3—81no—
701Dic3—81no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—61no—
716C23—61no—
717C23—61no—
718C23—61no—
719C23—61no—
720C23—61no—
721C23—61no—
722C23#93812yes—
723C23C2×D3×D411yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—48no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—124no—
743D4—244no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—32no—
754C2×C4—48no—
755C2×C4—48no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—121no—
774C2×C4—121no—
775C2×C4—121no—
776C2×C4—121no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4#93812yes—
787C2×C4C2×#23711yescharacteristic
788C2×C4#100411yescharacteristic
789C2×C4#100411yescharacteristic
790C2×C4C22×#6711yescharacteristic
791C2×C4C22×#6711yescharacteristic
792C2×C4C22×#6711yescharacteristic
793C8—22no—
794C8—121no—
795C8—121no—
796C8#95314yes—
797C2×C3—42no—
798C2×C3—82no—
799C2×C3#240811yescharacteristic
800C2×C3#305611yescharacteristic
801C2×C3#306311yescharacteristic
802C2×C3#327511yescharacteristic
803C2×C3#327611yescharacteristic
804C2×C3#327711yescharacteristic
805C2×C3#327811yescharacteristic
806D3—81no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22D3×#13711yescharacteristic
829C22#577711yescharacteristic
830C22#577811yescharacteristic
831C22#577911yescharacteristic
832C22C2×#93811yescharacteristic
833C22D4×#6711yescharacteristic
834C22D4×#6711yescharacteristic
835C4—22no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—62no—
840C4—121no—
841C4—121no—
842C4—241no—
843C4—241no—
844C4—241no—
845C4—241no—
846C4#580511yescharacteristic
847C4#580611yescharacteristic
848C4#580611yescharacteristic
849C4C2×#95311yescharacteristic
850C3#2427611yescharacteristic, complemented, Sylow
851C2—42no—
852C2—82no—
853C2—241no—
854C2#8398511yescharacteristic
855C2#8398611yescharacteristic
856C2#8399111yescharacteristic
857C2#8399411yescharacteristic
858C2#8399611yescharacteristic
859C2#8399711yescharacteristic
860C2#8405311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC22×C3×#137C2
socleC23×C3C22×D4
prime radical#84097C2
hypercenterC22×#137D3
hypocenterC3#24276
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×C3×#137C2semidirect
3. #84068C2semidirect
4. C2×#5189C2semidirect
5. C2×#5174C2semidirect
6. C2×#5128C2semidirect
7. #72135C2semidirect
8. #72132C2semidirect
9. #72071C2semidirect
10. #72068C2semidirect
11. #72066C2semidirect
12. #72054C2semidirect
13. #72051C2semidirect
14. #72049C2semidirect
15. #71988C2semidirect
66. C22×#137D3semidirect
111. C2×C3×Q16D4semidirect
117. C2×C3×SD16D4semidirect
120. C2×C3×M16D4semidirect
377. C2×Q16#67semidirect
383. C2×SD16#67semidirect
389. C2×M16#67semidirect
531. C2×Dic3#137semidirect
850. C3#24276semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1372
#840972
#840682
C2×#51892
C2×#51742
C2×#51282
#721352
#721322
#720712
#720682
#720662
#720542
#720512
#720492
#719882
#242763