Finite Group Databasebeta

← #10827563

Subgroups — #10827563

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×#5694C211yesmaximal, characteristic, complemented
2C2×#4783C211yesmaximal, characteristic, complemented
3C2×#4771C211yesmaximal, characteristic, complemented
4#76435C211yesmaximal, characteristic
5C3×#2025C211yesmaximal, characteristic, complemented
6#71744C211yesmaximal, characteristic, complemented
7#70205C211yesmaximal, characteristic, complemented
8#70201C211yesmaximal, characteristic, complemented
9#69660C211yesmaximal, characteristic, complemented
10#68888C211yesmaximal, characteristic, complemented
11#68884C211yesmaximal, characteristic, complemented
12#68879C211yesmaximal, characteristic, complemented
13#68872C211yesmaximal, characteristic, complemented
14#68685C211yesmaximal, characteristic, complemented
15#68669C211yesmaximal, characteristic, complemented
16#23978—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C2×C3×#125C2211yescharacteristic
19C2×#938C2211yescharacteristic
20C22×#214C2211yescharacteristic
21C22×Dic12C2211yescharacteristic
22C22×ΓL(1,𝔽25)C2211yescharacteristic
23#5694—24no—
24#5694—24no—
25C2×#898—21no—
26C2×#897C2211yescharacteristic
27C2×#897C2211yescharacteristic
28C2×#897C2211yescharacteristic
29C2×#894—21no—
30C2×#892—21no—
31C2×#892C2211yescharacteristic
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#890—21no—
34C2×C4×D12C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C3×#390C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#816C2211yescharacteristic
44C2×#816C2211yescharacteristic
45#4987C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49#4961—21no—
50#4960—21no—
51#4958—21no—
52#4950—21no—
53#4929C2211yescharacteristic
54#4783—24no—
55#4771—24no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#336C2211yescharacteristic
59#4551C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#552—31no—
65C2×#452—31no—
66C2×#417—31no—
67#2407—31no—
68#2026—31no—
69#2025D311yescharacteristic, complemented
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—
79C22×C3×D4C2311yescharacteristic
80C22×#67—21no—
81C22×#67—21no—
82C23×Dic3—21no—
83C2×#237—22no—
84C2×#237—22no—
85C2×#237—22no—
86C2×#237—22no—
87C2×#237—41no—
88C2×#237—41no—
89C22×D12D411yescharacteristic
90C22×C4×D3—21no—
91C22×C4×D3C2311yescharacteristic
92C22×C4×D3C2311yescharacteristic
93C22×Dic6C2311yescharacteristic
94C22×Dic6C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C3×#125—22no—
98C3×#125—22no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C42C2311yescharacteristic
107C2×#217—21no—
108#938—22no—
109#938—41no—
110C2×#214—22no—
111C2×#214—22no—
112C2×#214—41no—
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)⋊C4D411yescharacteristic
119C2×(C2×D3)⋊C4D411yescharacteristic
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3D411yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×C4×Dic3—21no—
129C2×C4×Dic3—21no—
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C2×Dic12—22no—
133C2×Dic12—22no—
134C2×Dic12—41no—
135C2×ΓL(1,𝔽25)—22no—
136C2×ΓL(1,𝔽25)—41no—
137C2×ΓL(1,𝔽25)—41no—
138#898—28no—
139#897—22no—
140#897—22no—
141#897—22no—
142#897—22no—
143#897—41no—
144#897D414yescomplemented
145#894—28no—
146#892—28no—
147#892—22no—
148#892—22no—
149D3×C4⋊C4—22no—
150D3×C4⋊C4D414yescomplemented
151#890—28no—
152C4×D12—22no—
153C4×D12—22no—
154C4×Dic6—22no—
155C4×Dic6—22no—
156C3×#102—22no—
157C3×#102—22no—
158#832—22no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162(C2×D3)⋊C8—22no—
163(C2×D3)⋊C8—41no—
164(C2×D3)⋊C8—41no—
165#816—22no—
166#816—41no—
167#810—22no—
168#810—22no—
169#810—41no—
170C22×#41—31no—
171C22×Q16—31no—
172C22×SD16—31no—
173C22×M16—31no—
174#552—64no—
175#552—64no—
176C2×#126—61no—
177C2×#125—61no—
178C2×#125C2×D311yescharacteristic
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⋊C4—31no—
189#452—64no—
190#417—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
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#390C2×D311yescharacteristic
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340C2×D311yescharacteristic
214#340C2×D311yescharacteristic
215#336—31no—
216#336C2×D311yescharacteristic
217C24×C3—21no—
218C23×D3C2×D411yescharacteristic
219C23×D3C2×D411yescharacteristic
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4#4112yes—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2411yescharacteristic
232C2×#67—42no—
233C2×#67—42no—
234C2×#67—42no—
235C2×#67—42no—
236C2×#67—42no—
237C2×#67—81no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—42no—
243C22×Dic3—42no—
244C22×Dic3—42no—
245C22×Dic3C2×D411yescharacteristic
246C22×Dic3C2×D411yescharacteristic
247#237—28no—
248#237—44no—
249#237—44no—
250#237—44no—
251C2×D12—22no—
252C2×D12—41no—
253C2×D12—41no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—24no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—42no—
266C2×C4×D3—42no—
267C2×C4×D3C2×D412yes—
268C2×C4×D3C2×D412yes—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6C2×D412yes—
280C2×Dic6#4112yes—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—24no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4C2×D412yes—
294C3×C4⋊C4C2×D412yes—
295C3×C22⋊C4—42no—
296C3×C22⋊C4—81no—
297C3×C42—21no—
298C3×C42—21no—
299#217—42no—
300#214—44no—
301(C2×D3)⋊C4—24no—
302(C2×D3)⋊C4—24no—
303(C2×D3)⋊C4—22no—
304(C2×D3)⋊C4—24no—
305(C2×D3)⋊C4—22no—
306(C2×D3)⋊C4—42no—
307(C2×D3)⋊C4—81no—
308C4⋊Dic3—24no—
309C4⋊Dic3—21no—
310C4⋊Dic3—22no—
311C4⋊Dic3—24no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3—42no—
315C4⋊Dic3C2×D412yes—
316Dic3⋊C4—24no—
317Dic3⋊C4—24no—
318C4×Dic3—24no—
319C4×Dic3—24no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326Dic12—44no—
327ΓL(1,𝔽25)—44no—
328C2×#41—62no—
329C2×#41—62no—
330C2×#41—62no—
331C2×#41—62no—
332C2×#41—121no—
333C2×#41—121no—
334C22×Q8—31no—
335C22×Q8—31no—
336C22×D4—31no—
337C22×D4—61no—
338C22×D4—61no—
339C22×D4C22×D311yescharacteristic
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—61no—
343C23×C4—61no—
344C2×Q16—62no—
345C2×Q16—62no—
346C2×Q16—121no—
347C2×SD16—62no—
348C2×SD16—62no—
349C2×SD16—121no—
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—22no—
359#125—22no—
360#125—68no—
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—21no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—34no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4—61no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4—61no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4C22×D311yescharacteristic
390C2×C4⋊C4C22×D311yescharacteristic
391C2×C4⋊C4C22×D311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—31no—
395C2×C22⋊C4—31no—
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—61no—
403C2×C42—61no—
404C2×C42C22×D311yescharacteristic
405#103—62no—
406#103—62no—
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—22no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3C22×D411yescharacteristic
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3#12012yes—
441C3×D4—22no—
442C3×D4—22no—
443C3×D4—41no—
444C3×D4—41no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—21no—
448C2×C3×C4—22no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4H(5,𝔽2)11yescharacteristic
465C2×C3×C4H(5,𝔽2)11yescharacteristic
466#67—48no—
467#67—84no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—22no—
471C2×Dic3—21no—
472C2×Dic3—22no—
473C2×Dic3—21no—
474C2×Dic3—22no—
475C2×Dic3—21no—
476C2×Dic3—48no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3#12012yes—
487D12—44no—
488C4×D3—22no—
489C4×D3—22no—
490C4×D3—22no—
491C4×D3—22no—
492C4×D3—48no—
493C4×D3—41no—
494C4×D3—41no—
495C4×D3—41no—
496C4×D3—41no—
497Dic6—22no—
498Dic6—22no—
499Dic6—22no—
500Dic6—22no—
501Dic6—41no—
502Dic6—41no—
503Dic6—41no—
504Dic6—41no—
505C3×C8—41no—
506C3×C8—41no—
507C3⋊C8—41no—
508C3⋊C8—41no—
509C24—21no—
510C24—31no—
511C24—31no—
512#41—68no—
513#41—124no—
514#41—124no—
515#41—124no—
516C2×Q8—32no—
517C2×Q8—32no—
518C2×Q8—61no—
519C2×Q8—61no—
520C2×Q8—61no—
521C2×Q8—61no—
522C2×Q8—61no—
523C2×Q8—61no—
524C2×Q8—61no—
525C2×Q8—61no—
526C2×Q8—61no—
527C2×Q8—61no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—62no—
534C2×D4—121no—
535C2×D4—121no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—241no—
542C2×D4#23912yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—31no—
547C22×C4—32no—
548C22×C4—32no—
549C22×C4—31no—
550C22×C4—64no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
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—122no—
566C22×C4—122no—
567C22×C4—122no—
568C22×C4—122no—
569C22×C4—122no—
570C22×C4D3×D411yescharacteristic
571C22×C4D3×D411yescharacteristic
572C22×C4C23×D311yescharacteristic
573Q16—124no—
574SD16—124no—
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—24no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—32no—
595C4⋊C4—64no—
596C4⋊C4—62no—
597C4⋊C4—64no—
598C4⋊C4—64no—
599C4⋊C4—64no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—122no—
604C4⋊C4D3×D412yes—
605C4⋊C4D3×D412yes—
606C22⋊C4—42no—
607C22⋊C4—62no—
608C22⋊C4—62no—
609C22⋊C4—64no—
610C22⋊C4—64no—
611C22⋊C4—64no—
612C22⋊C4—81no—
613C22⋊C4—122no—
614C22⋊C4—122no—
615C22⋊C4—241no—
616C42—21no—
617C42—21no—
618C42—64no—
619C42—64no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3C2×#12011yescharacteristic
628C22×C3#54611yescharacteristic
629C22×C3#54611yescharacteristic
630C22×C3#57511yescharacteristic
631C22×C3#57511yescharacteristic
632C22×C3#57711yescharacteristic
633C22×C3#57811yescharacteristic
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C3×C4—42no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—42no—
652C3×C4—81no—
653C3×C4#52511yescharacteristic
654C3×C4#53511yescharacteristic
655C3×C4#54611yescharacteristic
656C3×C4#54611yescharacteristic
657Dic3—22no—
658Dic3—42no—
659Dic3—42no—
660Dic3—41no—
661Dic3—42no—
662Dic3—81no—
663C23—22no—
664C23—32no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23C2×D3×D411yescharacteristic
685Q8—62no—
686Q8—62no—
687Q8—62no—
688Q8—62no—
689Q8—121no—
690Q8—121no—
691Q8—121no—
692Q8—121no—
693D4—22no—
694D4—22no—
695D4—41no—
696D4—41no—
697D4—124no—
698D4—128no—
699D4—244no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—32no—
709C2×C4—41no—
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—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—61no—
724C2×C4—62no—
725C2×C4—61no—
726C2×C4—62no—
727C2×C4—61no—
728C2×C4—128no—
729C2×C4—128no—
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—121no—
743C2×C4C2×D3×D411yescharacteristic
744C2×C4C2×D3×D411yescharacteristic
745C2×C4C2×#23911yescharacteristic
746C2×C4D3×#4111yescharacteristic
747C2×C4#100911yescharacteristic
748C2×C4#100911yescharacteristic
749C8—41no—
750C8—41no—
751C8—121no—
752C8—121no—
753C2×C3—82no—
754C2×C3#240411yescharacteristic
755C2×C3#300511yescharacteristic
756C2×C3#301311yescharacteristic
757C2×C3#331511yescharacteristic
758C2×C3#331711yescharacteristic
759C2×C3#332311yescharacteristic
760C2×C3#332711yescharacteristic
761D3—42no—
762D3—81no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—62no—
767C22—62no—
768C22—62no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22D3×#12011yescharacteristic
785C22#563011yescharacteristic
786C22#567611yescharacteristic
787C22#576811yescharacteristic
788C22#577111yescharacteristic
789C22#577311yescharacteristic
790C22#577511yescharacteristic
791C4—41no—
792C4—42no—
793C4—41no—
794C4—42no—
795C4—62no—
796C4—81no—
797C4—121no—
798C4—122no—
799C4—122no—
800C4—122no—
801C4—241no—
802C4#562711yescharacteristic
803C4#563011yescharacteristic
804C4#567411yescharacteristic
805C4#567611yescharacteristic
806C3#2397811yescharacteristic, complemented, Sylow
807C2—82no—
808C2—122no—
809C2—241no—
810C2#7686311yescharacteristic
811C2#8008311yescharacteristic
812C2#8008811yescharacteristic
813C2#8119011yescharacteristic
814C2#8119311yescharacteristic
815C2#8165911yescharacteristic
816C2#8172611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2025C2
socleC23×C3C22×D4
prime radical#76435C2
hypercenter#2025D3
hypocenterC3#23978
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

Complements

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

NH ≅ G/Ntype
1. C2×#5694C2semidirect
2. C2×#4783C2semidirect
3. C2×#4771C2semidirect
5. C3×#2025C2semidirect
6. #71744C2semidirect
7. #70205C2semidirect
8. #70201C2semidirect
9. #69660C2semidirect
10. #68888C2semidirect
11. #68884C2semidirect
12. #68879C2semidirect
13. #68872C2semidirect
14. #68685C2semidirect
15. #68669C2semidirect
69. #2025D3semidirect
144. #897D4semidirect
150. D3×C4⋊C4D4semidirect
806. C3#23978semidirect

Maximal subgroups

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

subgroupindex
C2×#56942
C2×#47832
C2×#47712
#764352
C3×#20252
#717442
#702052
#702012
#696602
#688882
#688842
#688792
#688722
#686852
#686692
#239783