Finite Group Databasebeta

← #10944285

Subgroups — #10944285

Order 768.

1502 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×M16C211yesmaximal, characteristic
2#82834C211yesmaximal, characteristic
3C2×#5052C211yesmaximal, characteristic, complemented
4C2×#4816C211yesmaximal, characteristic, complemented
5C2×#4813C211yesmaximal, characteristic, complemented
6#74049C211yesmaximal, characteristic
7C3×#1894C211yesmaximal, characteristic, complemented
8#71989C211yesmaximal, characteristic, complemented
9#70271C211yesmaximal, characteristic, complemented
10#70270C211yesmaximal, characteristic, complemented
11#69513C211yesmaximal, characteristic, complemented
12#68884C211yesmaximal, characteristic, complemented
13#68882C211yesmaximal, characteristic, complemented
14#68870C211yesmaximal, characteristic, complemented
15#68868C211yesmaximal, characteristic, complemented
16#32937—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C22×#216C2211yescharacteristic, complemented
23C2×#924C2211yescharacteristic
24C22×#208C2211yescharacteristic
25C2×D3×M16—24no—
26C2×D3×M16—24no—
27C2×D3×M16—24no—
28C22×ΓL(1,𝔽25)C2211yescharacteristic
29C22×ΓL(1,𝔽25)C2211yescharacteristic
30C22×D3×C8C2211yescharacteristic
31C22×D3×C8C2211yescharacteristic
32C2×#897C2211yescharacteristic
33C2×#897C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic, complemented
35C2×C3×#103C2211yescharacteristic, complemented
36C3×#380C2211yescharacteristic
37C2×#835C2211yescharacteristic, complemented
38#5212C2211yescharacteristic
39C2×#816C2211yescharacteristic, complemented
40C2×#816C2211yescharacteristic, complemented
41#5052—24no—
42#4989—21no—
43#4989—21no—
44#4987C2211yescharacteristic
45#4987C2211yescharacteristic
46#4987C2211yescharacteristic
47#4987C2211yescharacteristic
48C2×#810C2211yescharacteristic, complemented
49C2×#808C2211yescharacteristic, complemented
50C2×#808C2211yescharacteristic, complemented
51C2×#807C2211yescharacteristic, complemented
52#4955—21no—
53#4955—21no—
54#4950—21no—
55#4946—21no—
56#4816—24no—
57#4813—24no—
58#4668—21no—
59#4668—21no—
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62#4551C2211yescharacteristic, complemented
63#4551C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C23×M16—31no—
67C2×#470—31no—
68C2×#470—31no—
69C2×#467—31no—
70#2848—31no—
71#2848—31no—
72#1894—31no—
73#1894—31no—
74#1894—31no—
75#1894D311yescharacteristic, complemented
76#1892—31no—
77#1892—31no—
78#1809—31no—
79#1809—31no—
80#1807—31no—
81C24×D3D411yescharacteristic
82C22×C3×Q8C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×Dic3D411yescharacteristic
85C22×C4×D3—22no—
86C22×C4×D3—22no—
87C22×C4×D3—22no—
88C22×C4×D3—22no—
89C22×C4×D3—22no—
90C22×C4×D3—22no—
91C22×C4×D3D411yescharacteristic
92C22×C4×D3D411yescharacteristic
93C22×C4×D3C2311yescharacteristic
94C22×C4×D3C2311yescharacteristic
95C22×Dic6C2311yescharacteristic
96C2×C3×M16—22no—
97C2×C3×M16—22no—
98C2×C3×M16—22no—
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×C22⋊Q8—22no—
102C3×C22⋊Q8—22no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×#217—21no—
110C2×#217—21no—
111#946—22no—
112#946—22no—
113#946—22no—
114#946—22no—
115C2×#216—22no—
116C2×#216—22no—
117C2×#216—22no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×C4⋊Dic3—21no—
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131#924—22no—
132#924—22no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×#208—22no—
137C2×#208—22no—
138C2×#208D414yes—
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141D3×M16—232no—
142C2×ΓL(1,𝔽25)—22no—
143C2×ΓL(1,𝔽25)—22no—
144C2×ΓL(1,𝔽25)—22no—
145C2×ΓL(1,𝔽25)—22no—
146C2×ΓL(1,𝔽25)—22no—
147C2×ΓL(1,𝔽25)D414yes—
148C2×D3×C8—22no—
149C2×D3×C8—22no—
150C2×D3×C8—22no—
151C2×D3×C8—22no—
152C2×D3×C8—22no—
153C2×D3×C8D414yes—
154#897—22no—
155#897—22no—
156#897—22no—
157#897—22no—
158C3×#103—22no—
159C3×#103—22no—
160C3×#95—21no—
161#835—22no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167#816—22no—
168#816—22no—
169#810—22no—
170#808—22no—
171#808—22no—
172#807—22no—
173C24×C4—31no—
174C22×Q16—31no—
175C22×M16—31no—
176C22×M16—31no—
177C22×M16—31no—
178C22×M16—64no—
179C22×M16—64no—
180C22×M16—64no—
181C22×M16C2×D311yescharacteristic
182C23×C8—31no—
183C23×C8—31no—
184C2×C22⋊Q8—31no—
185C2×C22⋊Q8—31no—
186C2×C22⋊Q8—31no—
187C2×C22⋊Q8—31no—
188C2×C22⋊Q8—31no—
189C2×C22⋊Q8C2×D311yescharacteristic
190#470—64no—
191#470—64no—
192#467—64no—
193C2×#107—31no—
194C2×#106—31no—
195C2×#106—31no—
196C2×#103—31no—
197C2×#103—31no—
198C2×#103—31no—
199C2×#103—31no—
200C2×#103C2×D311yescharacteristic, complemented
201C2×#103C2×D311yescharacteristic, complemented
202#385—61no—
203#385—61no—
204#385—61no—
205#385—61no—
206#385—61no—
207#385—61no—
208#380—31no—
209#380—31no—
210#380—31no—
211#380—31no—
212#380—31no—
213#380C2×D311yescharacteristic
214#379—61no—
215#379—61no—
216#340—31no—
217#340—31no—
218#340—31no—
219#340—31no—
220#340C2×D311yescharacteristic, complemented
221#340C2×D311yescharacteristic, complemented
222C24×C3C2×D411yescharacteristic
223C23×D3—22no—
224C23×D3—22no—
225C23×D3—22no—
226C23×D3—22no—
227C23×D3—22no—
228C23×D3—41no—
229C23×D3—41no—
230C23×D3C2×D411yescharacteristic
231C23×D3C2×D411yescharacteristic
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D412yes—
248C22×C3×C4#4112yes—
249C22×C3×C4C2411yescharacteristic
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3C2×D411yescharacteristic
258C22×Dic3C2×D411yescharacteristic
259C2×C4×D3—28no—
260C2×C4×D3—28no—
261C2×C4×D3—28no—
262C2×C4×D3—28no—
263C2×C4×D3—22no—
264C2×C4×D3—22no—
265C2×C4×D3—22no—
266C2×C4×D3—22no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—22no—
276C2×C4×D3—22no—
277C2×C4×D3C2×D412yes—
278C2×C4×D3C2×D412yes—
279C2×C4×D3#4112yes—
280C2×C4×D3#4112yes—
281C2×Dic6—21no—
282C2×Dic6—21no—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C3×M16—28no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8C2×D412yes—
293C2×C3×C8C2×D412yes—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—42no—
301C3×C22⋊C4—42no—
302C3×C22⋊C4—42no—
303#217—42no—
304#217—42no—
305#216—44no—
306(C2×D3)⋊C4—42no—
307(C2×D3)⋊C4—42no—
308(C2×D3)⋊C4—42no—
309(C2×D3)⋊C4—42no—
310(C2×D3)⋊C4—42no—
311(C2×D3)⋊C4—42no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4—42no—
314C4⋊Dic3—21no—
315C4⋊Dic3—21no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—42no—
321C4⋊Dic3—42no—
322Dic3⋊C4—42no—
323Dic3⋊C4—42no—
324Dic3⋊C4—42no—
325#208—28no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8C2×D412yes—
329C2×C3⋊C8C2×D412yes—
330C2×C3⋊C8C2×D412yes—
331C2×C3⋊C8C2×D412yes—
332ΓL(1,𝔽25)—28no—
333ΓL(1,𝔽25)—28no—
334D3×C8—28no—
335D3×C8—28no—
336C25—31no—
337C22×Q8—31no—
338C22×Q8C22×D311yescharacteristic
339C23×C4—31no—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—31no—
344C23×C4—62no—
345C23×C4—62no—
346C23×C4—62no—
347C23×C4—62no—
348C23×C4—62no—
349C23×C4—62no—
350C23×C4C22×D311yescharacteristic
351C2×Q16—62no—
352C2×Q16—62no—
353C2×Q16—62no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—34no—
358C2×M16—34no—
359C2×M16—62no—
360C2×M16—62no—
361C2×M16—62no—
362C2×M16—62no—
363C2×M16—62no—
364C2×M16—62no—
365C2×M16—632no—
366C2×M16—62no—
367C22×C8—31no—
368C22×C8—31no—
369C22×C8—34no—
370C22×C8—62no—
371C22×C8—62no—
372C22×C8—62no—
373C22×C8—62no—
374C22×C8—62no—
375C22×C8C22×D311yescharacteristic
376C22×C8C22×D311yescharacteristic
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—62no—
380C22⋊Q8—62no—
381C22⋊Q8—62no—
382C22⋊Q8—62no—
383C22⋊Q8—62no—
384C22⋊Q8—62no—
385C22⋊Q8—62no—
386C22⋊Q8—62no—
387C22⋊Q8—62no—
388C22⋊Q8—62no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4C22×D311yescharacteristic
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4—61no—
408C2×C22⋊C4—61no—
409C2×C22⋊C4—61no—
410C2×C22⋊C4—61no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413#107—62no—
414#106—62no—
415#106—62no—
416#103—22no—
417#103—22no—
418#103—62no—
419#103—62no—
420#103—62no—
421#103—62no—
422#95—21no—
423#95—61no—
424#95—61no—
425#95—61no—
426#95—61no—
427#95—61no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3#12112yes—
435C23×C3C22×D411yescharacteristic
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—28no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—44no—
448C22×D3—44no—
449C22×D3—44no—
450C22×D3—44no—
451C22×D3—44no—
452C22×D3—44no—
453C22×D3#12112yes—
454C22×D3#12112yes—
455C22×D3#13712yes—
456C22×D3#13712yes—
457C3×Q8—41no—
458C3×Q8—41no—
459C3×Q8—41no—
460C3×Q8—41no—
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—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4#12112yes—
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C22×D411yescharacteristic
482C2×C3×C4C22×D411yescharacteristic
483C2×C3×C4C2×#4111yescharacteristic
484C2×C3×C4C2×#4111yescharacteristic
485C2×C3×C4C2×#4111yescharacteristic
486C2×Dic3—28no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
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—41no—
503C2×Dic3#12112yes—
504C2×Dic3#12112yes—
505C4×D3—28no—
506C4×D3—28no—
507C4×D3—22no—
508C4×D3—22no—
509C4×D3—22no—
510C4×D3—22no—
511C4×D3—22no—
512C4×D3—22no—
513C4×D3—22no—
514C4×D3—22no—
515Dic6—41no—
516Dic6—41no—
517Dic6—41no—
518Dic6—41no—
519C3×C8—22no—
520C3×C8—22no—
521C3⋊C8—22no—
522C3⋊C8#12014yes—
523C24—31no—
524C24—31no—
525C24—62no—
526C24—62no—
527C24—62no—
528C24—62no—
529C24—62no—
530C24—121no—
531C24—121no—
532C24D3×D411yescharacteristic
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—61no—
540C2×Q8—61no—
541C2×Q8—61no—
542C2×Q8—61no—
543C2×Q8—61no—
544C2×Q8—61no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—68no—
564C22×C4—68no—
565C22×C4—68no—
566C22×C4—68no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4#23512yes—
585C22×C4D3×D411yescharacteristic
586C22×C4D3×D412yes—
587C22×C4C23×D311yescharacteristic
588Q16—124no—
589M16—28no—
590M16—68no—
591M16—68no—
592M16—68no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—32no—
598C2×C8—32no—
599C2×C8—32no—
600C2×C8—32no—
601C2×C8—68no—
602C2×C8—68no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8D3×D412yes—
606C2×C8D3×D412yes—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—42no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—122no—
621C4⋊C4—122no—
622C4⋊C4—122no—
623C4⋊C4—122no—
624C4⋊C4—122no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—122no—
628C22⋊C4—122no—
629C22⋊C4—122no—
630C22⋊C4—122no—
631C22⋊C4—122no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—122no—
635C22⋊C4—122no—
636C22⋊C4—122no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3C2×#12111yescharacteristic
645C22×C3C2×#12111yescharacteristic
646C22×C3C2×#12111yescharacteristic
647C22×C3C2×#13711yescharacteristic
648C22×C3C2×#13711yescharacteristic
649C22×C3#57511yescharacteristic
650C22×C3#57511yescharacteristic
651C2×D3—22no—
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—22no—
657C2×D3—22no—
658C2×D3—22no—
659C2×D3—22no—
660C2×D3—416no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3#47014yescomplemented
666C3×C4—22no—
667C3×C4—81no—
668C3×C4—81no—
669C3×C4—81no—
670C3×C4—81no—
671C3×C4C2×#12011yescharacteristic
672C3×C4#52511yescharacteristic
673C3×C4#52511yescharacteristic
674C3×C4#52511yescharacteristic
675Dic3—22no—
676Dic3—22no—
677Dic3—81no—
678Dic3—81no—
679Dic3—81no—
680Dic3—81no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—32no—
688C23—32no—
689C23—32no—
690C23—32no—
691C23—68no—
692C23—61no—
693C23—61no—
694C23—61no—
695C23—61no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—124no—
703C23—124no—
704C23—124no—
705C23—124no—
706C23—124no—
707C23—124no—
708C23#88412yes—
709C23C2×D3×D411yescharacteristic
710Q8—41no—
711Q8—41no—
712Q8—41no—
713Q8—41no—
714Q8—121no—
715Q8—121no—
716Q8—121no—
717Q8—121no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—68no—
739C2×C4—68no—
740C2×C4—68no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4—121no—
762C2×C4—121no—
763C2×C4—121no—
764C2×C4—121no—
765C2×C4#88412yes—
766C2×C4C2×#23511yescharacteristic
767C2×C4C2×D3×D411yescharacteristic
768C2×C4C2×D3×D411yescharacteristic
769C2×C4C2×D3×D411yescharacteristic
770C2×C4D3×#4111yescharacteristic
771C2×C4D3×#4111yescharacteristic
772C8—22no—
773C8—22no—
774C8—34no—
775C8—62no—
776C2×C3—42no—
777C2×C3#284711yescharacteristic
778C2×C3C2×#47011yescharacteristic
779C2×C3#305411yescharacteristic
780C2×C3#305611yescharacteristic
781C2×C3#305611yescharacteristic
782C2×C3#305611yescharacteristic
783C2×C3#305611yescharacteristic
784D3—24no—
785D3—42no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—34no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—62no—
795C22—62no—
796C22—62no—
797C22—62no—
798C22—62no—
799C22—62no—
800C22—62no—
801C22—62no—
802C22—62no—
803C22—1216no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22C2×#88411yescharacteristic
809C22D3×#12111yescharacteristic
810C22D3×#12111yescharacteristic
811C22#577311yescharacteristic
812C22D3×#13711yescharacteristic
813C22D3×#13711yescharacteristic
814C22#577711yescharacteristic
815C4—22no—
816C4—62no—
817C4—62no—
818C4—81no—
819C4—81no—
820C4—81no—
821C4—81no—
822C4—241no—
823C4—241no—
824C4—241no—
825C4—241no—
826C4#554711yescharacteristic
827C4#554711yescharacteristic
828C4D3×#12011yescharacteristic
829C4#565611yescharacteristic
830C3#3293711yescharacteristic, complemented, Sylow
831C2—42no—
832C2—64no—
833C2—122no—
834C2#7493511yescharacteristic
835C2#7888911yescharacteristic
836C2#7896211yescharacteristic
837C2#8080411yescharacteristic
838C2#8080611yescharacteristic
839C2D3×#47011yescharacteristic
840C2#8090411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1894C2
socleC23×C3C22×D4
prime radicalC24×D3D4
hypercenter#1894D3
hypocenterC3#32937
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
3. C2×#5052C2semidirect
4. C2×#4816C2semidirect
5. C2×#4813C2semidirect
7. C3×#1894C2semidirect
8. #71989C2semidirect
9. #70271C2semidirect
10. #70270C2semidirect
11. #69513C2semidirect
12. #68884C2semidirect
13. #68882C2semidirect
14. #68870C2semidirect
15. #68868C2semidirect
22. C22×#216C22semidirect
34. C2×C3×#103C22semidirect
35. C2×C3×#103C22semidirect
37. C2×#835C22semidirect
39. C2×#816C22semidirect
40. C2×#816C22semidirect
48. C2×#810C22semidirect
49. C2×#808C22semidirect
50. C2×#808C22semidirect
51. C2×#807C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. #4551C22semidirect
63. #4551C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
75. #1894D3semidirect
200. C2×#103C2×D3semidirect
201. C2×#103C2×D3semidirect
220. #340C2×D3semidirect
221. #340C2×D3semidirect
665. C2×D3#470semidirect
830. C3#32937semidirect

Maximal subgroups

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

subgroupindex
C22×D3×M162
#828342
C2×#50522
C2×#48162
C2×#48132
#740492
C3×#18942
#719892
#702712
#702702
#695132
#688842
#688822
#688702
#688682
#329373