Finite Group Databasebeta

← #10827400

Subgroups — #10827400

Order 768.

1332 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×#5734C211yesmaximal, characteristic, complemented
2C2×#4781C211yesmaximal, characteristic, complemented
3C2×#4772C211yesmaximal, characteristic, complemented
4#76435C211yesmaximal, characteristic, complemented
5C3×#2023C211yesmaximal, characteristic, complemented
6#71794C211yesmaximal, characteristic, complemented
7#70204C211yesmaximal, characteristic, complemented
8#70201C211yesmaximal, characteristic, complemented
9#69657C211yesmaximal, characteristic, complemented
10#68887C211yesmaximal, characteristic, complemented
11#68883C211yesmaximal, characteristic, complemented
12#68879C211yesmaximal, characteristic, complemented
13#68813C211yesmaximal, characteristic, complemented
14#68672C211yesmaximal, characteristic, complemented
15#68668C211yesmaximal, characteristic, complemented
16#23965—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic
19C2×#947—21no—
20C2×#947—21no—
21C2×#938C2211yescharacteristic
22C22×#213C2211yescharacteristic
23C22×#204C2211yescharacteristic
24C22×D3×C8C2211yescharacteristic
25#5734—24no—
26#5734—24no—
27C2×#897C2211yescharacteristic
28C2×#895—21no—
29C2×#895C2211yescharacteristic
30C2×#895C2211yescharacteristic
31C2×#892—21no—
32C2×#892C2211yescharacteristic
33C2×#892C2211yescharacteristic
34C2×C4×D12C2211yescharacteristic
35C2×C4×D12C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C3×#390C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#816C2211yescharacteristic
45#4987C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#809C2211yescharacteristic
49#4961—21no—
50#4960—21no—
51#4958—21no—
52#4950—21no—
53#4929C2211yescharacteristic
54#4781—24no—
55#4772—24no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#336C2211yescharacteristic
59#4551C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#555—31no—
65C2×#449—31no—
66C2×#416—31no—
67#2407—31no—
68#2024—31no—
69#2023D311yescharacteristic, complemented
70#2000—31no—
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1877—31no—
75#1875—31no—
76#1873—31no—
77#1869—31no—
78#1825—31no—
79C22×C3×Q8—21no—
80C22×C3×D4C2311yescharacteristic
81C22×#67—21no—
82C22×#67—21no—
83C23×Dic3—21no—
84C2×#237—22no—
85C2×#237—22no—
86C2×#237—22no—
87C2×#237—22no—
88C2×#237—41no—
89C2×#237—41no—
90C22×D12—21no—
91C22×D12—21no—
92C22×D12D411yescharacteristic
93C22×D12C2311yescharacteristic
94C22×C4×D3—21no—
95C22×C4×D3C2311yescharacteristic
96C22×C4×D3C2311yescharacteristic
97C22×Dic6C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C4⋊Q8—22no—
101C3×C4⋊Q8—22no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C42C2311yescharacteristic
109C2×#217—21no—
110#947—28no—
111#947—28no—
112#938—22no—
113#938—41no—
114C2×#213—22no—
115C2×#213—22no—
116C2×#213—41no—
117C2×(C2×D3)⋊C4—21no—
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)⋊C4D411yescharacteristic
125C2×(C2×D3)⋊C4D411yescharacteristic
126C2×C4⋊Dic3—21no—
127C2×C4⋊Dic3D411yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4×Dic3—21no—
131C2×C4×Dic3—21no—
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C2×#204—22no—
135C2×#204—22no—
136C2×#204—41no—
137C2×D3×C8—22no—
138C2×D3×C8—41no—
139C2×D3×C8—41no—
140#897—22no—
141#897—41no—
142#895—28no—
143#895—22no—
144#895—22no—
145#895—22no—
146#895D414yescomplemented
147#892—28no—
148#892—22no—
149#892—22no—
150#892—22no—
151#892D414yescomplemented
152C4×D12—22no—
153C4×D12—22no—
154C4×D12—22no—
155C4×D12—22no—
156C3×#102—22no—
157C3×#102—22no—
158#832—22no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#821—41no—
163(C2×D3)⋊C8—22no—
164(C2×D3)⋊C8—41no—
165(C2×D3)⋊C8—41no—
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#555—64no—
175#555—64no—
176C2×C4⋊Q8C2×D311yescharacteristic
177C2×#124—61no—
178C2×#124—61no—
179C2×C22⋊Q8—31no—
180C2×#121—31no—
181C2×#121—31no—
182C2×#121—31no—
183C2×#121—61no—
184C2×C4×D4—31no—
185C2×C4×D4—31no—
186C2×#117—31no—
187C2×#117—31no—
188C2×#117—61no—
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⋊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×D3—21no—
219C23×D3C2×D411yescharacteristic
220C23×D3C2×D411yescharacteristic
221C2×C3×Q8—24no—
222C2×C3×Q8—81no—
223C2×C3×Q8—81no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4#4112yes—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2411yescharacteristic
236C2×#67—42no—
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—42no—
241C2×#67—81no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—42no—
246C22×Dic3—42no—
247C22×Dic3—42no—
248C22×Dic3C2×D411yescharacteristic
249C22×Dic3C2×D411yescharacteristic
250#237—28no—
251#237—44no—
252#237—44no—
253#237—44no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—22no—
259C2×D12—22no—
260C2×D12—21no—
261C2×D12—24no—
262C2×D12—24no—
263C2×D12—41no—
264C2×D12—81no—
265C2×D12—81no—
266C2×D12—81no—
267C2×D12—81no—
268C2×D12C2×D412yes—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—24no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C4×D3—42no—
281C2×C4×D3—42no—
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—
304C3×C22⋊C4—81no—
305C3×C42—21no—
306C3×C42—21no—
307#217—42no—
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—22no—
315(C2×D3)⋊C4—24no—
316(C2×D3)⋊C4—42no—
317(C2×D3)⋊C4—81no—
318C4⋊Dic3—21no—
319C4⋊Dic3—22no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3—42no—
323C4⋊Dic3C2×D412yes—
324C4×Dic3—24no—
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—21no—
341C22×Q8—31no—
342C22×D4—31no—
343C22×D4—31no—
344C22×D4—61no—
345C22×D4—61no—
346C22×D4—61no—
347C22×D4—61no—
348C22×D4C22×D311yescharacteristic
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—61no—
352C23×C4—61no—
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
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368#124—68no—
369#124—68no—
370C22⋊Q8—62no—
371C22⋊Q8—121no—
372#121—34no—
373#121—62no—
374#121—62no—
375#121—68no—
376#121—62no—
377#121—62no—
378#121—121no—
379C4×D4—62no—
380C4×D4—62no—
381C4×D4—62no—
382C4×D4—62no—
383#117—34no—
384#117—62no—
385#117—62no—
386#117—68no—
387#117—62no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4C22×D311yescharacteristic
394C2×C4⋊C4C22×D311yescharacteristic
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—31no—
399C2×C22⋊C4—31no—
400C2×C22⋊C4—61no—
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×C42—61no—
409C2×C42—61no—
410C2×C42C22×D311yescharacteristic
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—62no—
420C22⋊C8—121no—
421C22⋊C8—121no—
422#95—61no—
423#95—61no—
424#95—61no—
425C23×C3—22no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3C22×D411yescharacteristic
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—22no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3#12012yes—
454C3×Q8—84no—
455C3×D4—22no—
456C3×D4—22no—
457C3×D4—41no—
458C3×D4—41no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
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#13512yes—
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C22×D411yescharacteristic
476C2×C3×C4C2×#4111yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478C2×C3×C4H(5,𝔽2)11yescharacteristic
479C2×C3×C4H(5,𝔽2)11yescharacteristic
480#67—48no—
481#67—84no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—22no—
486C2×Dic3—21no—
487C2×Dic3—22no—
488C2×Dic3—21no—
489C2×Dic3—48no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3#12012yes—
498D12—22no—
499D12—22no—
500D12—44no—
501D12—41no—
502D12—41no—
503D12—84no—
504D12—84no—
505C4×D3—22no—
506C4×D3—22no—
507C4×D3—22no—
508C4×D3—22no—
509C4×D3—48no—
510C4×D3—41no—
511C4×D3—41no—
512C4×D3—41no—
513C4×D3—41no—
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—31no—
525C24—61no—
526#41—68no—
527#41—124no—
528#41—124no—
529#41—124no—
530C2×Q8—24no—
531C2×Q8—32no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—61no—
536C2×Q8—61no—
537C2×Q8—81no—
538C2×Q8—81no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—32no—
545C2×D4—62no—
546C2×D4—64no—
547C2×D4—64no—
548C2×D4—62no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
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—241no—
563C2×D4—241no—
564C2×D4—241no—
565C2×D4#23912yes—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—31no—
570C22×C4—32no—
571C22×C4—32no—
572C22×C4—31no—
573C22×C4—64no—
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—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—122no—
588C22×C4—122no—
589C22×C4—122no—
590C22×C4—122no—
591C22×C4—122no—
592C22×C4D3×D411yescharacteristic
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—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—122no—
621C4⋊C4D3×D412yes—
622C4⋊C4D3×D412yes—
623C22⋊C4—42no—
624C22⋊C4—62no—
625C22⋊C4—64no—
626C22⋊C4—62no—
627C22⋊C4—64no—
628C22⋊C4—64no—
629C22⋊C4—64no—
630C22⋊C4—64no—
631C22⋊C4—81no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—241no—
635C42—21no—
636C42—21no—
637C42—64no—
638C42—64no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3C2×#12011yescharacteristic
647C22×C3#54611yescharacteristic
648C22×C3#54611yescharacteristic
649C22×C3C2×#13511yescharacteristic
650C22×C3#57511yescharacteristic
651C22×C3#57611yescharacteristic
652C22×C3#57711yescharacteristic
653C2×D3—22no—
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—42no—
662C2×D3—42no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—42no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—81no—
671C2×D3—81no—
672C2×D3—81no—
673C2×D3—81no—
674C3×C4—22no—
675C3×C4—42no—
676C3×C4—42no—
677C3×C4—41no—
678C3×C4—81no—
679C3×C4#52511yescharacteristic
680C3×C4#53511yescharacteristic
681C3×C4#54611yescharacteristic
682C3×C4#54611yescharacteristic
683Dic3—22no—
684Dic3—42no—
685Dic3—41no—
686Dic3—42no—
687Dic3—81no—
688C23—22no—
689C23—32no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23—62no—
708C23—61no—
709C23—61no—
710C23—121no—
711C23—121no—
712C23—121no—
713C23—121no—
714C23—121no—
715C23—121no—
716C23C2×D3×D411yescharacteristic
717Q8—62no—
718Q8—62no—
719Q8—84no—
720Q8—121no—
721Q8—121no—
722D4—22no—
723D4—22no—
724D4—41no—
725D4—41no—
726D4—62no—
727D4—62no—
728D4—124no—
729D4—128no—
730D4—121no—
731D4—121no—
732D4—244no—
733D4—244no—
734D4—244no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—32no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—61no—
758C2×C4—62no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—128no—
762C2×C4—128no—
763C2×C4—121no—
764C2×C4—121no—
765C2×C4—121no—
766C2×C4—121no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—121no—
774C2×C4#91612yes—
775C2×C4C2×D3×D411yescharacteristic
776C2×C4C2×D3×D411yescharacteristic
777C2×C4C2×#23911yescharacteristic
778C2×C4D3×#4111yescharacteristic
779C2×C4#100911yescharacteristic
780C2×C4#100911yescharacteristic
781C8—41no—
782C8—41no—
783C8—121no—
784C8—121no—
785C2×C3—82no—
786C2×C3#240411yescharacteristic
787C2×C3#300211yescharacteristic
788C2×C3#301211yescharacteristic
789C2×C3#330311yescharacteristic
790C2×C3#330511yescharacteristic
791C2×C3#331911yescharacteristic
792C2×C3#332111yescharacteristic
793D3—42no—
794D3—81no—
795D3—82no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—62no—
800C22—62no—
801C22—62no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—121no—
811C22—121no—
812C22—122no—
813C22—121no—
814C22—121no—
815C22—122no—
816C22—122no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—241no—
821C22—241no—
822C22—241no—
823C22—241no—
824C22D3×#12011yescharacteristic
825C22#563011yescharacteristic
826C22#567611yescharacteristic
827C22#575711yescharacteristic
828C22C2×#91611yescharacteristic
829C22#577511yescharacteristic
830C22#577711yescharacteristic
831C4—22no—
832C4—41no—
833C4—42no—
834C4—42no—
835C4—62no—
836C4—81no—
837C4—121no—
838C4—122no—
839C4—122no—
840C4—241no—
841C4#562711yescharacteristic
842C4#563011yescharacteristic
843C4#567411yescharacteristic
844C4#567611yescharacteristic
845C3#2396511yescharacteristic, complemented, Sylow
846C2—82no—
847C2—122no—
848C2—241no—
849C2—242no—
850C2#7686311yescharacteristic
851C2#8000511yescharacteristic
852C2#8003811yescharacteristic
853C2#8098311yescharacteristic
854C2#8107611yescharacteristic
855C2#8157911yescharacteristic
856C2#8170311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2023C2
socleC23×C3C22×D4
hypercenter#2023D3
hypocenterC3#23965
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. C2×#5734C2semidirect
2. C2×#4781C2semidirect
3. C2×#4772C2semidirect
4. #76435C2semidirect
5. C3×#2023C2semidirect
6. #71794C2semidirect
7. #70204C2semidirect
8. #70201C2semidirect
9. #69657C2semidirect
10. #68887C2semidirect
11. #68883C2semidirect
12. #68879C2semidirect
13. #68813C2semidirect
14. #68672C2semidirect
15. #68668C2semidirect
69. #2023D3semidirect
146. #895D4semidirect
151. #892D4semidirect
845. C3#23965semidirect

Maximal subgroups

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

subgroupindex
C2×#57342
C2×#47812
C2×#47722
#764352
C3×#20232
#717942
#702042
#702012
#696572
#688872
#688832
#688792
#688132
#686722
#686682
#239653