Finite Group Databasebeta

← #10827367

Subgroups — #10827367

Order 768.

1338 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5514C211yesmaximal, characteristic, complemented
2#82701C211yesmaximal, characteristic, complemented
3C2×#4781C211yesmaximal, characteristic, complemented
4C2×#4772C211yesmaximal, characteristic, complemented
5C3×#1874C211yesmaximal, characteristic, complemented
6#71684C211yesmaximal, characteristic, complemented
7#71559C211yesmaximal, characteristic, complemented
8#70208C211yesmaximal, characteristic, complemented
9#70164C211yesmaximal, characteristic, complemented
10#69962C211yesmaximal, characteristic, complemented
11#69957C211yesmaximal, characteristic, complemented
12#68911C211yesmaximal, characteristic, complemented
13#68896C211yesmaximal, characteristic, complemented
14#68883C211yesmaximal, characteristic, complemented
15#68813C211yesmaximal, characteristic, complemented
16#23962—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×#213C2211yescharacteristic
21C2×#930—21no—
22C2×#930C2211yescharacteristic
23C2×C4×#67—21no—
24C2×C4×#67C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C22×#204C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28#5514—24no—
29#5514—24no—
30C2×#898—21no—
31C2×#895C2211yescharacteristic
32C2×#894—21no—
33C2×#893C2211yescharacteristic
34C2×#892C2211yescharacteristic
35C2×#890C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39#5223—21no—
40#5221C2211yescharacteristic
41#5220—21no—
42C2×#832C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#816C2211yescharacteristic
47#4987C2211yescharacteristic
48#4973C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#809C2211yescharacteristic
52#4959—21no—
53#4946—21no—
54#4781—24no—
55#4772—24no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#553—31no—
65C2×#449—31no—
66C2×#416—31no—
67#2407—31no—
68#2026—31no—
69#2025—31no—
70#2000—31no—
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1877—31no—
75#1874D311yescharacteristic, complemented
76#1872—31no—
77#1869—31no—
78#1825—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67D411yescharacteristic
86C23×Dic3—21no—
87C2×#237—22no—
88C2×#237—22no—
89C2×#237—22no—
90C2×#237—22no—
91C2×#237—41no—
92C2×#237—41no—
93C22×D12—21no—
94C22×D12C2311yescharacteristic
95C22×C4×D3—21no—
96C22×C4×D3C2311yescharacteristic
97C22×Dic6C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×#121—22no—
101C3×#121—41no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217D411yescharacteristic
113C2×#213—22no—
114C2×#213—22no—
115C2×#213—41no—
116#930—28no—
117#930—22no—
118#930—22no—
119C4×#67—28no—
120C4×#67—22no—
121C4×#67—22no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4D411yescharacteristic
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131#924—22no—
132#924—41no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4D411yescharacteristic
136C2×C4×Dic3—21no—
137C2×C4×Dic3C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C2×#204—22no—
141C2×#204—22no—
142C2×#204—41no—
143C2×D3×C8—22no—
144C2×D3×C8—41no—
145C2×D3×C8—41no—
146#898—28no—
147#895—22no—
148#895D414yescomplemented
149#894—28no—
150#893—22no—
151#893—22no—
152#892—22no—
153#892D414yescomplemented
154#890—22no—
155#890—22no—
156C3×#102—22no—
157C3×#102—22no—
158C3×C22⋊C8—41no—
159#832—22no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163#830—41no—
164#821—41no—
165(C2×D3)⋊C8—22no—
166#816—22no—
167#810—22no—
168#810—22no—
169#809—41no—
170C22×#41—31no—
171C22×SD16—31no—
172C22×D8—31no—
173C23×C8—31no—
174#553—64no—
175#553—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#123—61no—
179C2×C22⋊Q8—31no—
180C2×#121—31no—
181C2×#121—31no—
182C2×#121—61no—
183C2×#121C2×D311yescharacteristic
184C2×C4×D4—31no—
185C2×C4×D4—31no—
186C2×C4×D4—61no—
187C2×#117—31no—
188C22×C4⋊C4C2×D311yescharacteristic
189#449—64no—
190#416—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102C2×D311yescharacteristic
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#340C2×D311yescharacteristic
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C23×D3C2×D411yescharacteristic
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—42no—
227C2×C3×D4—42no—
228C2×C3×D4—81no—
229C2×C3×D4#4112yes—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—24no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—81no—
241C22×C3×C4—81no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2411yescharacteristic
244C2×#67—24no—
245C2×#67—22no—
246C2×#67—22no—
247C2×#67—41no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—42no—
257C22×Dic3—42no—
258C22×Dic3—42no—
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262#237—28no—
263#237—44no—
264#237—44no—
265#237—44no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—24no—
272C2×D12—81no—
273C2×D12—81no—
274C2×D12C2×D412yes—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—24no—
280C2×C4×D3—81no—
281C2×C4×D3—81no—
282C2×C4×D3C2×D412yes—
283C2×C4×D3C2×D412yes—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6#4112yes—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C3×C4⋊C4—24no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4C2×D412yes—
302C3×C4⋊C4C2×D412yes—
303C3×C22⋊C4—42no—
304#217—22no—
305#217—42no—
306#217—42no—
307#217—81no—
308#213—44no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—24no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—22no—
313(C2×D3)⋊C4—24no—
314(C2×D3)⋊C4—81no—
315C4⋊Dic3—24no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3C2×D412yes—
320Dic3⋊C4—24no—
321Dic3⋊C4—22no—
322Dic3⋊C4—42no—
323C4×Dic3—21no—
324C4×Dic3—21no—
325C4×Dic3—24no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332#204—44no—
333D3×C8—44no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—62no—
337C2×#41—62no—
338C2×#41—121no—
339C2×#41—121no—
340C22×Q8—31no—
341C22×D4—21no—
342C22×D4—31no—
343C22×D4—31no—
344C22×D4—61no—
345C22×D4—61no—
346C22×D4—61no—
347C22×D4C22×D311yescharacteristic
348C23×C4—21no—
349C23×C4—31no—
350C23×C4—61no—
351C23×C4—61no—
352C23×C4C22×D311yescharacteristic
353C2×SD16—62no—
354C2×SD16—62no—
355C2×SD16—121no—
356C2×D8—62no—
357C2×D8—62no—
358C2×D8—121no—
359C22×C8—31no—
360C22×C8—31no—
361C22×C8—62no—
362C22×C8—121no—
363C22×C8—121no—
364C22×C8C22×D311yescharacteristic
365C22×C8C22×D311yescharacteristic
366#126—68no—
367#125—62no—
368#125—62no—
369#123—68no—
370C22⋊Q8—62no—
371C22⋊Q8—121no—
372#121—22no—
373#121—34no—
374#121—41no—
375#121—62no—
376#121—62no—
377#121—62no—
378#121—68no—
379C4×D4—62no—
380C4×D4—62no—
381C4×D4—62no—
382C4×D4—68no—
383C4×D4—62no—
384#117—34no—
385#117—62no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—31no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—61no—
402C2×C22⋊C4—61no—
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×C42—31no—
410C2×C42—61no—
411#103—62no—
412#103—62no—
413#103—62no—
414#102—22no—
415#102—22no—
416#102—62no—
417#102—121no—
418#102—121no—
419C22⋊C8—41no—
420C22⋊C8—62no—
421C22⋊C8—121no—
422#95—61no—
423#95—61no—
424#95—61no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—22no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3#13512yes—
439C23×C3C22×D411yescharacteristic
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—22no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3#12012yes—
454C3×D4—22no—
455C3×D4—22no—
456C3×D4—41no—
457C3×D4—41no—
458C3×D4—84no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
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—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—84no—
476C2×C3×C4C22×D411yescharacteristic
477C2×C3×C4C22×D411yescharacteristic
478C2×C3×C4C2×#4111yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480C2×C3×C4H(5,𝔽2)11yescharacteristic
481C2×C3×C4H(5,𝔽2)11yescharacteristic
482#67—44no—
483#67—48no—
484#67—48no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—48no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3#12012yes—
504D12—22no—
505D12—22no—
506D12—41no—
507D12—41no—
508D12—84no—
509C4×D3—22no—
510C4×D3—22no—
511C4×D3—22no—
512C4×D3—22no—
513C4×D3—84no—
514Dic6—22no—
515Dic6—22no—
516Dic6—41no—
517Dic6—41no—
518C3×C8—41no—
519C3×C8—41no—
520C3⋊C8—41no—
521C3⋊C8—41no—
522C24—21no—
523C24—31no—
524C24—61no—
525C24D3×D411yescharacteristic
526#41—68no—
527#41—124no—
528#41—124no—
529#41—124no—
530C2×Q8—32no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—61no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—32no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—64no—
545C2×D4—62no—
546C2×D4—64no—
547C2×D4—62no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—81no—
554C2×D4—121no—
555C2×D4—122no—
556C2×D4—122no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—122no—
560C2×D4—241no—
561C2×D4—241no—
562C2×D4#23512yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—31no—
574C22×C4—32no—
575C22×C4—32no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—64no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—122no—
589C22×C4—122no—
590C22×C4—122no—
591C22×C4—241no—
592C22×C4—241no—
593C22×C4D3×D411yescharacteristic
594C22×C4C23×D311yescharacteristic
595SD16—124no—
596D8—124no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C2×C8—124no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—32no—
616C4⋊C4—62no—
617C4⋊C4—64no—
618C4⋊C4—64no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—122no—
623C4⋊C4D3×D412yes—
624C4⋊C4D3×D412yes—
625C22⋊C4—42no—
626C22⋊C4—64no—
627C22⋊C4—62no—
628C22⋊C4—64no—
629C22⋊C4—64no—
630C22⋊C4—64no—
631C22⋊C4—62no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—241no—
635C22⋊C4—241no—
636C42—64no—
637C42—61no—
638C42—61no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—42no—
647C22×C3—42no—
648C22×C3—42no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3C2×#12011yescharacteristic
654C22×C3#54611yescharacteristic
655C22×C3#54611yescharacteristic
656C22×C3C2×#13511yescharacteristic
657C22×C3#57511yescharacteristic
658C22×C3#57611yescharacteristic
659C22×C3#57711yescharacteristic
660C2×D3—22no—
661C2×D3—22no—
662C2×D3—22no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—42no—
668C2×D3—42no—
669C2×D3—42no—
670C2×D3—81no—
671C2×D3—81no—
672C2×D3—81no—
673C2×D3—81no—
674C3×C4—41no—
675C3×C4—42no—
676C3×C4—42no—
677C3×C4—81no—
678C3×C4#52511yescharacteristic
679C3×C4#53511yescharacteristic
680C3×C4#54611yescharacteristic
681C3×C4#54611yescharacteristic
682Dic3—22no—
683Dic3—42no—
684Dic3—41no—
685Dic3—42no—
686Dic3—41no—
687Dic3—81no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—22no—
695C23—32no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23—61no—
708C23—62no—
709C23—121no—
710C23—121no—
711C23—121no—
712C23—121no—
713C23—121no—
714C23—121no—
715C23#91612yes—
716C23C2×D3×D411yescharacteristic
717Q8—62no—
718Q8—62no—
719Q8—121no—
720Q8—121no—
721D4—22no—
722D4—22no—
723D4—41no—
724D4—41no—
725D4—62no—
726D4—62no—
727D4—84no—
728D4—124no—
729D4—128no—
730D4—128no—
731D4—121no—
732D4—121no—
733D4—244no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—32no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—62no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—84no—
766C2×C4—128no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—121no—
774C2×C4—244no—
775C2×C4C2×#23511yescharacteristic
776C2×C4C2×D3×D411yescharacteristic
777C2×C4C2×D3×D411yescharacteristic
778C2×C4#100411yescharacteristic
779C2×C4D3×#4111yescharacteristic
780C2×C4#100911yescharacteristic
781C8—41no—
782C8—41no—
783C8—121no—
784C8—121no—
785C2×C3—42no—
786C2×C3—82no—
787C2×C3#240411yescharacteristic
788C2×C3#300211yescharacteristic
789C2×C3#301211yescharacteristic
790C2×C3#329711yescharacteristic
791C2×C3#330111yescharacteristic
792C2×C3#330711yescharacteristic
793C2×C3#330911yescharacteristic
794D3—42no—
795D3—82no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—62no—
807C22—62no—
808C22—62no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—122no—
818C22—122no—
819C22—122no—
820C22—241no—
821C22—241no—
822C22—241no—
823C22—241no—
824C22#549011yescharacteristic
825C22D3×#12011yescharacteristic
826C22#565411yescharacteristic
827C22#575711yescharacteristic
828C22C2×#91611yescharacteristic
829C22#577511yescharacteristic
830C22#577711yescharacteristic
831C4—42no—
832C4—42no—
833C4—41no—
834C4—62no—
835C4—81no—
836C4—121no—
837C4—122no—
838C4—121no—
839C4—122no—
840C4—241no—
841C4#554711yescharacteristic
842C4#555011yescharacteristic
843C4#560711yescharacteristic
844C4#561211yescharacteristic
845C3#2396211yescharacteristic, complemented, Sylow
846C2—42no—
847C2—82no—
848C2—122no—
849C2—242no—
850C2#7488611yescharacteristic
851C2#7876011yescharacteristic
852C2#7889511yescharacteristic
853C2#8000511yescharacteristic
854C2#8003811yescharacteristic
855C2#8128811yescharacteristic
856C2#8134511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1874C2
socleC23×C3C22×D4
hypercenter#1874D3
hypocenterC3#23962
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C2×#5514C2semidirect
2. #82701C2semidirect
3. C2×#4781C2semidirect
4. C2×#4772C2semidirect
5. C3×#1874C2semidirect
6. #71684C2semidirect
7. #71559C2semidirect
8. #70208C2semidirect
9. #70164C2semidirect
10. #69962C2semidirect
11. #69957C2semidirect
12. #68911C2semidirect
13. #68896C2semidirect
14. #68883C2semidirect
15. #68813C2semidirect
75. #1874D3semidirect
148. #895D4semidirect
153. #892D4semidirect
845. C3#23962semidirect

Maximal subgroups

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

subgroupindex
C2×#55142
#827012
C2×#47812
C2×#47722
C3×#18742
#716842
#715592
#702082
#701642
#699622
#699572
#689112
#688962
#688832
#688132
#239623