Finite Group Databasebeta

← #10827562

Subgroups — #10827562

Order 768.

1262 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5513C211yesmaximal, characteristic, complemented
2C2×C3×#417C211yesmaximal, characteristic, complemented
3#84097C211yesmaximal, characteristic
4C2×#5239C211yesmaximal, characteristic, complemented
5#71996C211yesmaximal, characteristic, complemented
6#71989C211yesmaximal, characteristic, complemented
7#71554C211yesmaximal, characteristic, complemented
8#70281C211yesmaximal, characteristic, complemented
9#70273C211yesmaximal, characteristic, complemented
10#70269C211yesmaximal, characteristic, complemented
11#70232C211yesmaximal, characteristic, complemented
12#70213C211yesmaximal, characteristic, complemented
13#70205C211yesmaximal, characteristic, complemented
14#70201C211yesmaximal, characteristic, complemented
15#70164C211yesmaximal, characteristic, complemented
16#23978—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C2×#929—21no—
25C2×C4×#67C2211yescharacteristic
26C2×#926—21no—
27C2×#924C2211yescharacteristic
28#5513—24no—
29#5513—24no—
30C2×#898—21no—
31C2×#897C2211yescharacteristic
32C2×#892C2211yescharacteristic
33C2×#890C2211yescharacteristic
34C2×#889—21no—
35C2×#887C2211yescharacteristic
36C3×#417—24no—
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41#5239—24no—
42#5229C2211yescharacteristic
43C2×#835C2211yescharacteristic
44#5223—21no—
45#5222—21no—
46#5221C2211yescharacteristic
47C2×#832C2211yescharacteristic
48#5213—21no—
49#5212C2211yescharacteristic
50#5210—21no—
51C2×#830C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×(C2×D3)⋊C8C2211yescharacteristic
54C2×#816C2211yescharacteristic
55C2×#816C2211yescharacteristic
56#4551C2211yescharacteristic
57#4551C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#552—31no—
65C2×#452—31no—
66C2×#417D311yescharacteristic, complemented
67#2407—31no—
68#2026—31no—
69#2025—31no—
70#2001—31no—
71#2000—31no—
72#1894—31no—
73#1880—31no—
74#1878—31no—
75#1875—31no—
76#1873—31no—
77#1870—31no—
78#1824—31no—
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4C2311yescharacteristic
88C23×C3×C4—21no—
89C23×C3×C4—21no—
90C23×C3×C4C2311yescharacteristic
91C22×#67—21no—
92C22×#67D411yescharacteristic
93C22×C4×D3C2311yescharacteristic
94C22×Dic6C2311yescharacteristic
95C2×C3×M16—22no—
96C2×C3×M16—41no—
97C2×C3×M16—41no—
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4D414yescomplemented
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217D411yescharacteristic
111#946—22no—
112#946—41no—
113C2×#216—22no—
114C2×#216—22no—
115C2×#216—41no—
116#938—22no—
117#938—41no—
118C2×#214—22no—
119C2×#214—22no—
120C2×#214—41no—
121#929—28no—
122C4×#67—22no—
123C4×#67—22no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4D411yescharacteristic
128#926—28no—
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3—21no—
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134#924—22no—
135#924D414yescomplemented
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4D411yescharacteristic
141C2×C4×Dic3—21no—
142C2×C4×Dic3—21no—
143C2×C4×Dic3C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146#898—28no—
147#897—22no—
148#897—22no—
149#892—22no—
150#892—22no—
151#890—22no—
152#890—22no—
153#889—28no—
154#887—22no—
155#887—22no—
156C3×#103—22no—
157C3×#103—22no—
158C3×#102—22no—
159C3×#102—22no—
160#835—22no—
161#832—22no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165#830—22no—
166(C2×D3)⋊C8—41no—
167(C2×D3)⋊C8—41no—
168#816—41no—
169#816—41no—
170C22×#41C2×D311yescharacteristic
171C22×Q16—31no—
172C22×SD16—31no—
173C22×M16C2×D311yescharacteristic
174#552—64no—
175#552—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#125—61no—
179C2×#123—61no—
180C2×C22⋊Q8—31no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×#121—31no—
184C2×C4×Q8—31no—
185C2×C4×D4—31no—
186C2×#117—31no—
187C2×#117—61no—
188C22×C4⋊C4C2×D311yescharacteristic
189#452—64no—
190#417—24no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103C2×D311yescharacteristic
195C2×#103C2×D311yescharacteristic
196C2×#102—31no—
197C2×#102C2×D311yescharacteristic
198C2×#102C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202#394—61no—
203#392—61no—
204#391—31no—
205#390—31no—
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C23×D3C2×D411yescharacteristic
220C3×#41—28no—
221C3×#41—44no—
222C3×#41—44no—
223C3×#41—44no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8#4112yes—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4#4112yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—24no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—42no—
248C22×C3×C4—42no—
249C22×C3×C4—42no—
250C22×C3×C4—42no—
251C22×C3×C4—42no—
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D412yes—
254C22×C3×C4C2×D412yes—
255C22×C3×C4C2411yescharacteristic
256C2×#67—22no—
257C2×#67—41no—
258C2×#67—41no—
259C2×#67—42no—
260C2×#67—42no—
261C2×#67—81no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3C2×D411yescharacteristic
267C22×Dic3C2×D411yescharacteristic
268C22×Dic3C2×D411yescharacteristic
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×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6—21no—
280C2×Dic6C2×D412yes—
281C3×M16—44no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C3×C4⋊C4—24no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4C2×D412yes—
292C3×C4⋊C4C2×D412yes—
293#217—24no—
294#217—22no—
295#217—42no—
296#217—42no—
297#217—81no—
298#217—81no—
299#216—44no—
300#214—44no—
301(C2×D3)⋊C4—24no—
302(C2×D3)⋊C4—24no—
303(C2×D3)⋊C4—22no—
304(C2×D3)⋊C4—42no—
305C4⋊Dic3—24no—
306C4⋊Dic3—24no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3C2×D412yes—
313Dic3⋊C4—24no—
314Dic3⋊C4—24no—
315Dic3⋊C4—22no—
316Dic3⋊C4—24no—
317Dic3⋊C4—42no—
318C4×Dic3—24no—
319C4×Dic3—24no—
320C4×Dic3—21no—
321C4×Dic3—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—41no—
333C2×#41—41no—
334C22×Q8—31no—
335C22×Q8C22×D311yescharacteristic
336C22×D4—21no—
337C22×D4—31no—
338C22×D4—61no—
339C22×D4C22×D311yescharacteristic
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—31no—
343C23×C4C22×D311yescharacteristic
344C2×Q16—62no—
345C2×Q16—62no—
346C2×Q16—121no—
347C2×SD16—62no—
348C2×SD16—62no—
349C2×SD16—121no—
350C2×M16—22no—
351C2×M16—41no—
352C2×M16—41no—
353C22×C8—31no—
354C22×C8—31no—
355C22×C8C22×D311yescharacteristic
356C22×C8C22×D311yescharacteristic
357#126—68no—
358#125—62no—
359#125—68no—
360#125—62no—
361#123—68no—
362C22⋊Q8—34no—
363C22⋊Q8—62no—
364C22⋊Q8—62no—
365C22⋊Q8—62no—
366C22⋊Q8—62no—
367C22⋊Q8—121no—
368#121—62no—
369#121—121no—
370C4×Q8—62no—
371C4×Q8—62no—
372C4×D4—62no—
373C4×D4—62no—
374#117—62no—
375#117—68no—
376#117—62no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4—61no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4—61no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4#6714yescomplemented
390C2×C4⋊C4C22×D311yescharacteristic
391C2×C4⋊C4C22×D311yescharacteristic
392C2×C22⋊C4—31no—
393C2×C22⋊C4—31no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4—61no—
401C2×C22⋊C4—61no—
402C2×C42—31no—
403C2×C42—61no—
404C2×C42—61no—
405#103—22no—
406#103—22no—
407#103—62no—
408#103—121no—
409#103—121no—
410#102—22no—
411#102—22no—
412#102—62no—
413C22⋊C8—62no—
414C22⋊C8—121no—
415C22⋊C8—121no—
416#95—61no—
417#95—61no—
418#95—61no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—22no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3#12012yes—
433C23×C3C22×D411yescharacteristic
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C3×Q8—22no—
442C3×Q8—22no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—22no—
446C3×D4—22no—
447C3×D4—48no—
448C3×D4—41no—
449C3×D4—41no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—48no—
460C2×C3×C4—48no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4#12012yes—
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C22×D411yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×C3×C4H(5,𝔽2)11yescharacteristic
473C2×C3×C4H(5,𝔽2)11yescharacteristic
474#67—44no—
475#67—84no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C4×D3—41no—
498C4×D3—41no—
499C4×D3—41no—
500C4×D3—41no—
501Dic6—22no—
502Dic6—22no—
503Dic6—41no—
504Dic6—41no—
505C3×C8—41no—
506C3×C8—41no—
507C3⋊C8—41no—
508C3⋊C8—41no—
509C24—21no—
510C24—31no—
511C24D3×D411yescharacteristic
512#41—28no—
513#41—44no—
514#41—44no—
515#41—44no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—32no—
522C2×Q8—61no—
523C2×Q8—61no—
524C2×Q8—61no—
525C2×Q8—61no—
526C2×Q8—61no—
527C2×Q8#23512yes—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—62no—
537C2×D4—121no—
538C2×D4—121no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—241no—
542C2×D4#23512yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4D3×D411yescharacteristic
570C22×C4D3×D412yes—
571C22×C4C2×#6712yes—
572C22×C4C23×D311yescharacteristic
573Q16—124no—
574SD16—124no—
575M16—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—61no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—32no—
592C4⋊C4—64no—
593C4⋊C4—64no—
594C4⋊C4—64no—
595C4⋊C4—64no—
596C4⋊C4—62no—
597C4⋊C4—64no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—122no—
604C4⋊C4C2×#6712yes—
605C4⋊C4C2×#6712yes—
606C22⋊C4—64no—
607C22⋊C4—64no—
608C22⋊C4—62no—
609C22⋊C4—64no—
610C22⋊C4—62no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C22⋊C4—241no—
615C22⋊C4—241no—
616C42—64no—
617C42—64no—
618C42—61no—
619C42—61no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3C2×#12011yescharacteristic
635C22×C3#54611yescharacteristic
636C22×C3#54611yescharacteristic
637C22×C3#57511yescharacteristic
638C22×C3#57511yescharacteristic
639C22×C3#57711yescharacteristic
640C22×C3#57811yescharacteristic
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C3×C4—22no—
649C3×C4—42no—
650C3×C4—42no—
651C3×C4—42no—
652C3×C4#52511yescharacteristic
653C3×C4#53511yescharacteristic
654C3×C4#54611yescharacteristic
655C3×C4#54611yescharacteristic
656Dic3—42no—
657Dic3—41no—
658Dic3—41no—
659Dic3—41no—
660Dic3—42no—
661Dic3—81no—
662Dic3—81no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23#93712yes—
684C23C2×D3×D411yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—41no—
688Q8—41no—
689Q8—62no—
690Q8—62no—
691Q8—121no—
692Q8—121no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—124no—
699D4—244no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—48no—
710C2×C4—48no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—61no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4#93712yes—
743C2×C4C2×#23511yescharacteristic
744C2×C4C2×#23511yescharacteristic
745C2×C4C2×D3×D411yescharacteristic
746C2×C4#100411yescharacteristic
747C2×C4#100411yescharacteristic
748C2×C4C22×#6711yescharacteristic
749C8—41no—
750C8—41no—
751C8—121no—
752C8—121no—
753C2×C3—42no—
754C2×C3—82no—
755C2×C3#240411yescharacteristic
756C2×C3#300511yescharacteristic
757C2×C3#301311yescharacteristic
758C2×C3#331511yescharacteristic
759C2×C3#331711yescharacteristic
760C2×C3#332311yescharacteristic
761C2×C3#332711yescharacteristic
762D3—81no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22#549011yescharacteristic
785C22#549011yescharacteristic
786C22#577311yescharacteristic
787C22#577311yescharacteristic
788C22#577811yescharacteristic
789C22#577911yescharacteristic
790C22C2×#93711yescharacteristic
791C4—22no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—121no—
796C4—122no—
797C4—121no—
798C4—122no—
799C4—121no—
800C4—241no—
801C4—241no—
802C4#549011yescharacteristic
803C4#549011yescharacteristic
804C4#579111yescharacteristic
805C4#580511yescharacteristic
806C3#2397811yescharacteristic, complemented, Sylow
807C2—42no—
808C2—82no—
809C2—241no—
810C2#7889911yescharacteristic
811C2#7890111yescharacteristic
812C2#7890311yescharacteristic
813C2#7890511yescharacteristic
814C2#8212511yescharacteristic
815C2#8394511yescharacteristic
816C2#8398411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#417C2
socleC23×C3C22×D4
prime radical#84097C2
hypercenterC2×#417D3
hypocenterC3#23978
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#5513C2semidirect
2. C2×C3×#417C2semidirect
4. C2×#5239C2semidirect
5. #71996C2semidirect
6. #71989C2semidirect
7. #71554C2semidirect
8. #70281C2semidirect
9. #70273C2semidirect
10. #70269C2semidirect
11. #70232C2semidirect
12. #70213C2semidirect
13. #70205C2semidirect
14. #70201C2semidirect
15. #70164C2semidirect
66. C2×#417D3semidirect
102. C2×C3×C4⋊C4D4semidirect
135. #924D4semidirect
389. C2×C4⋊C4#67semidirect
806. C3#23978semidirect

Maximal subgroups

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

subgroupindex
C2×#55132
C2×C3×#4172
#840972
C2×#52392
#719962
#719892
#715542
#702812
#702732
#702692
#702322
#702132
#702052
#702012
#701642
#239783