Finite Group Databasebeta

← #10827558

Subgroups — #10827558

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×#5642C211yesmaximal, characteristic, complemented
2C2×C3×#452C211yesmaximal, characteristic, complemented
3#84097C211yesmaximal, characteristic
4C2×#5232C211yesmaximal, characteristic, complemented
5#72071C211yesmaximal, characteristic, complemented
6#72065C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic, complemented
8#72048C211yesmaximal, characteristic, complemented
9#71697C211yesmaximal, characteristic, complemented
10#70269C211yesmaximal, characteristic, complemented
11#70232C211yesmaximal, characteristic, complemented
12#70201C211yesmaximal, characteristic, complemented
13#70164C211yesmaximal, characteristic, complemented
14#69953C211yesmaximal, characteristic, complemented
15#69925C211yesmaximal, characteristic, complemented
16#23978—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×Q8×Dic3C2211yescharacteristic
24C2×#938C2211yescharacteristic
25C2×C4×#67C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×#208C2211yescharacteristic
28#5642—24no—
29#5642—24no—
30C2×#898—21no—
31C2×#892C2211yescharacteristic
32C2×#890—21no—
33C2×#890C2211yescharacteristic
34C2×#886—21no—
35C2×#877—21no—
36C3×#452—24no—
37C2×C3×#103C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40#5232—24no—
41#5229C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44C2×#835C2211yescharacteristic
45C2×#835C2211yescharacteristic
46#5223—21no—
47#5222—21no—
48#5221C2211yescharacteristic
49C2×#832C2211yescharacteristic
50C2×#832C2211yescharacteristic
51#5213—21no—
52#5212C2211yescharacteristic
53#5210—21no—
54C2×(C2×D3)⋊C8C2211yescharacteristic
55C2×(C2×D3)⋊C8C2211yescharacteristic
56#4551C2211yescharacteristic
57#4551C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#552—31no—
65C2×#452D311yescharacteristic, complemented
66C2×#417—31no—
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×Q8C2311yescharacteristic
87C22×C3×D4—21no—
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4C2311yescharacteristic
91C22×#67—21no—
92C22×#67D411yescharacteristic
93C23×Dic3—21no—
94C22×C4×D3C2311yescharacteristic
95C2×C3×Q16—22no—
96C2×C3×Q16—22no—
97C2×C3×Q16—41no—
98C2×C3×SD16—22no—
99C2×C3×SD16—22no—
100C2×C3×SD16—41no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8D414yescomplemented
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217D411yescharacteristic
113#946—22no—
114#946—22no—
115#946—22no—
116#946—41no—
117Q8×Dic3—22no—
118Q8×Dic3—22no—
119#938—22no—
120#938—41no—
121C4×#67—22no—
122C4×#67—22no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4D411yescharacteristic
127C2×C4⋊Dic3—22no—
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3—21no—
131C2×C4⋊Dic3D414yescomplemented
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4D411yescharacteristic
140C2×C4×Dic3—21no—
141C2×C4×Dic3—21no—
142C2×C4×Dic3C2311yescharacteristic
143C2×#208—22no—
144C2×#208—41no—
145C2×#208—41no—
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148#898—28no—
149#892—22no—
150#892—22no—
151#890—28no—
152#890—22no—
153#890—22no—
154#886—28no—
155#877—28no—
156C3×#103—22no—
157C3×#102—22no—
158C3×C22⋊C8—22no—
159#835—22no—
160#835—22no—
161#835—41no—
162#835—41no—
163#832—22no—
164#832—22no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168(C2×D3)⋊C8—41no—
169(C2×D3)⋊C8—41no—
170C22×#41C2×D311yescharacteristic
171C22×Q16C2×D311yescharacteristic
172C22×SD16C2×D311yescharacteristic
173C22×M16—31no—
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⋊Q8C2×D311yescharacteristic
183C2×#121—31no—
184C2×C4×Q8—31no—
185C2×C4×D4—31no—
186C2×#117—31no—
187C2×#117—61no—
188C22×C4⋊C4—31no—
189#452—24no—
190#417—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103C2×D311yescharacteristic
196C2×#102—31no—
197C2×#102—31no—
198C2×#102C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8C2×D311yescharacteristic
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—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8C2×D412yes—
235C2×C3×Q8#4112yes—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—42no—
242C2×C3×D4—42no—
243C2×C3×D4—42no—
244C2×C3×D4#4112yes—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—42no—
253C22×C3×C4—42no—
254C22×C3×C4—42no—
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D412yes—
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2411yescharacteristic
259C2×#67—22no—
260C2×#67—41no—
261C2×#67—41no—
262C2×#67—42no—
263C2×#67—42no—
264C2×#67—81no—
265C22×Dic3—24no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—42no—
271C22×Dic3—42no—
272C22×Dic3C2×D411yescharacteristic
273C22×Dic3C2×D411yescharacteristic
274C22×Dic3C2×D411yescharacteristic
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C4×D3—21no—
281C3×Q16—44no—
282C3×SD16—44no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C3×C4⋊C4—24no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4C2×D412yes—
292C3×C22⋊C4—24no—
293#217—22no—
294#217—42no—
295#217—42no—
296#217—81no—
297#217—81no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—24no—
300(C2×D3)⋊C4—22no—
301(C2×D3)⋊C4—42no—
302C4⋊Dic3—24no—
303C4⋊Dic3—24no—
304C4⋊Dic3—24no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3C2×D412yes—
312C4⋊Dic3C2×D412yes—
313Dic3⋊C4—24no—
314Dic3⋊C4—24no—
315Dic3⋊C4—22no—
316Dic3⋊C4—42no—
317C4×Dic3—24no—
318C4×Dic3—24no—
319C4×Dic3—21no—
320C4×Dic3—21no—
321#208—44no—
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×Q8C22×D311yescharacteristic
335C22×Q8C22×D311yescharacteristic
336C22×D4—21no—
337C22×D4—31no—
338C22×D4—61no—
339C22×D4C22×D311yescharacteristic
340C23×C4—21no—
341C23×C4—31no—
342C23×C4—61no—
343C23×C4C22×D311yescharacteristic
344C2×Q16—22no—
345C2×Q16—22no—
346C2×Q16—41no—
347C2×SD16—22no—
348C2×SD16—22no—
349C2×SD16—41no—
350C2×M16—62no—
351C2×M16—121no—
352C2×M16—121no—
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—22no—
363C22⋊Q8—62no—
364C22⋊Q8—62no—
365C22⋊Q8—62no—
366C22⋊Q8—121no—
367C22⋊Q8#6714yescomplemented
368#121—62no—
369#121—121no—
370C4×Q8—62no—
371C4×Q8—62no—
372C4×D4—62no—
373C4×D4—62no—
374#117—68no—
375#117—62no—
376#117—62no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—34no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4—61no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4—61no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4—62no—
390C2×C4⋊C4—61no—
391C2×C4⋊C4C22×D311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—31no—
394C2×C22⋊C4—31no—
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—62no—
407#103—62no—
408#103—121no—
409#103—121no—
410#102—22no—
411#102—62no—
412#102—62no—
413C22⋊C8—22no—
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—22no—
444C3×Q8—22no—
445C3×Q8—41no—
446C3×Q8—41no—
447C3×Q8—41no—
448C3×Q8—41no—
449C3×D4—22no—
450C3×D4—22no—
451C3×D4—48no—
452C3×D4—41no—
453C3×D4—41no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—48no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4#12012yes—
471C2×C3×C4C22×D411yescharacteristic
472C2×C3×C4C22×D411yescharacteristic
473C2×C3×C4C2×#4111yescharacteristic
474C2×C3×C4C2×#4111yescharacteristic
475C2×C3×C4H(5,𝔽2)11yescharacteristic
476C2×C3×C4H(5,𝔽2)11yescharacteristic
477#67—44no—
478#67—84no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—22no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—48no—
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—
501C4×D3—41no—
502C4×D3—41no—
503C4×D3—41no—
504C4×D3—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—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8#23712yes—
527C2×Q8C2×#6712yes—
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#23712yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—64no—
557C22×C4—61no—
558C22×C4—61no—
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—122no—
568C22×C4—122no—
569C22×C4D3×D411yescharacteristic
570C22×C4D3×D412yes—
571C22×C4C2×#6712yes—
572C22×C4C23×D311yescharacteristic
573Q16—44no—
574SD16—44no—
575M16—124no—
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—32no—
591C4⋊C4—32no—
592C4⋊C4—64no—
593C4⋊C4—64no—
594C4⋊C4—64no—
595C4⋊C4—64no—
596C4⋊C4—64no—
597C4⋊C4—62no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—122no—
605C4⋊C4C2×#6712yes—
606C22⋊C4—24no—
607C22⋊C4—64no—
608C22⋊C4—64no—
609C22⋊C4—62no—
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—41no—
657Dic3—41no—
658Dic3—42no—
659Dic3—42no—
660Dic3—41no—
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—22no—
688Q8—22no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
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—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—62no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—62no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—128no—
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×D3×D411yescharacteristic
744C2×C4C2×#23711yescharacteristic
745C2×C4C2×#23711yescharacteristic
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#559111yescharacteristic
785C22#559111yescharacteristic
786C22#577011yescharacteristic
787C22#577111yescharacteristic
788C22#577711yescharacteristic
789C22#577711yescharacteristic
790C22C2×#93711yescharacteristic
791C4—22no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—121no—
796C4—122no—
797C4—122no—
798C4—121no—
799C4—121no—
800C4—241no—
801C4—241no—
802C4#558611yescharacteristic
803C4#559211yescharacteristic
804C4#580611yescharacteristic
805C4#580611yescharacteristic
806C3#2397811yescharacteristic, complemented, Sylow
807C2—42no—
808C2—82no—
809C2—241no—
810C2#8025411yescharacteristic
811C2#8025711yescharacteristic
812C2#8025811yescharacteristic
813C2#8025911yescharacteristic
814C2#8258111yescharacteristic
815C2#8391311yescharacteristic
816C2#8398011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#452C2
socleC23×C3C22×D4
prime radical#84097C2
hypercenterC2×#452D3
hypocenterC3#23978
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#5642C2semidirect
2. C2×C3×#452C2semidirect
4. C2×#5232C2semidirect
5. #72071C2semidirect
6. #72065C2semidirect
7. #72054C2semidirect
8. #72048C2semidirect
9. #71697C2semidirect
10. #70269C2semidirect
11. #70232C2semidirect
12. #70201C2semidirect
13. #70164C2semidirect
14. #69953C2semidirect
15. #69925C2semidirect
65. C2×#452D3semidirect
104. C3×C22⋊Q8D4semidirect
131. C2×C4⋊Dic3D4semidirect
367. C22⋊Q8#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×#56422
C2×C3×#4522
#840972
C2×#52322
#720712
#720652
#720542
#720482
#716972
#702692
#702322
#702012
#701642
#699532
#699252
#239783