Finite Group Databasebeta

← #10827365

Subgroups — #10827365

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×#5695C211yesmaximal, characteristic, complemented
2C2×#4810C211yesmaximal, characteristic, complemented
3C2×#4804C211yesmaximal, characteristic, complemented
4#76618C211yesmaximal, characteristic, complemented
5C3×#2026C211yesmaximal, characteristic, complemented
6#71743C211yesmaximal, characteristic, complemented
7#70272C211yesmaximal, characteristic, complemented
8#70268C211yesmaximal, characteristic, complemented
9#69687C211yesmaximal, characteristic, complemented
10#68886C211yesmaximal, characteristic, complemented
11#68883C211yesmaximal, characteristic, complemented
12#68880C211yesmaximal, characteristic, complemented
13#68873C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68668C211yesmaximal, characteristic, complemented
16#23962—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C2×C3×#125C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C22×D24C2211yescharacteristic
22C22×D3×C8C2211yescharacteristic
23#5695—24no—
24#5695—24no—
25C2×#898—21no—
26C2×#895—21no—
27C2×#895C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#894—21no—
31C2×#893—21no—
32C2×#892C2211yescharacteristic
33C2×D3×C4⋊C4C2211yescharacteristic
34C2×C4×D12C2211yescharacteristic
35C2×C4×D12C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C3×#391C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45#4987C2211yescharacteristic
46C2×#809C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49#4939C2211yescharacteristic
50#4810—24no—
51#4804—24no—
52#4672—21no—
53#4671—21no—
54#4668—21no—
55#4665—21no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#336C2211yescharacteristic
59#4551C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#553—31no—
65C2×#449—31no—
66C2×#416—31no—
67#2407—31no—
68#2026D311yescharacteristic, complemented
69#2025—31no—
70#2000—31no—
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1877—31no—
75#1874—31no—
76#1872—31no—
77#1869—31no—
78#1825—31no—
79C22×C3×Q8C2311yescharacteristic
80C2×#239—22no—
81C2×#239—22no—
82C2×#239—22no—
83C2×#239—22no—
84C2×#239—41no—
85C2×#239—41no—
86C22×D12—21no—
87C22×D12—21no—
88C22×D12—21no—
89C22×D12—21no—
90C22×D12D411yescharacteristic
91C22×D12C2311yescharacteristic
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×C4×D3C2311yescharacteristic
97C22×C4×D3C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×#125—22no—
101C3×#125—22no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C42C2311yescharacteristic
108#946—22no—
109#946—41no—
110C2×#215—22no—
111C2×#215—22no—
112C2×#215—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)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4D411yescharacteristic
123C2×(C2×D3)⋊C4D411yescharacteristic
124C2×C4⋊Dic3D411yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×C4×Dic3—21no—
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C2×D24—22no—
133C2×D24—22no—
134C2×D24—41no—
135C2×D3×C8—22no—
136C2×D3×C8—41no—
137C2×D3×C8—41no—
138#898—28no—
139#895—28no—
140#895—22no—
141#895—22no—
142#895—22no—
143#895—22no—
144#895—41no—
145#895D414yescomplemented
146#894—28no—
147#893—28no—
148#892—22no—
149#892D414yescomplemented
150D3×C4⋊C4—22no—
151D3×C4⋊C4—22no—
152C4×D12—22no—
153C4×D12—22no—
154C4×D12—22no—
155C4×D12—22no—
156C3×#103—22no—
157C3×#103—22no—
158C3×#95—21no—
159C3×#95—21no—
160#835—22no—
161C3⋊#95—21no—
162#821—22no—
163#821—41no—
164(C2×D3)⋊C8—22no—
165(C2×D3)⋊C8—41no—
166(C2×D3)⋊C8—41no—
167#809—22no—
168#809—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×#125C2×D311yescharacteristic
178C2×#123—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×C4×D4—61no—
187C2×#117—31no—
188C22×C4⋊C4—31no—
189#449—64no—
190#416—64no—
191C2×#103—31no—
192C2×#103C2×D311yescharacteristic
193C2×#103C2×D311yescharacteristic
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202#394—61no—
203#392—61no—
204#391C2×D311yescharacteristic
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#336C2×D311yescharacteristic
217C23×D3—21no—
218C23×D3—21no—
219C23×D3C2×D411yescharacteristic
220C23×D3C2×D411yescharacteristic
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8#4112yes—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2411yescharacteristic
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3C2×D411yescharacteristic
237C22×Dic3C2×D411yescharacteristic
238#239—28no—
239#239—44no—
240#239—44no—
241#239—44no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—24no—
251C2×D12—22no—
252C2×D12—22no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—24no—
256C2×D12—41no—
257C2×D12—42no—
258C2×D12—42no—
259C2×D12—42no—
260C2×D12—42no—
261C2×D12—42no—
262C2×D12—42no—
263C2×D12—42no—
264C2×D12—81no—
265C2×D12—81no—
266C2×D12—81no—
267C2×D12C2×D412yes—
268C2×D12#4112yes—
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×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—24no—
280C2×C4×D3—24no—
281C2×C4×D3—42no—
282C2×C4×D3—42no—
283C2×C4×D3—42no—
284C2×C4×D3—81no—
285C2×C4×D3—81no—
286C2×C4×D3—81no—
287C2×C4×D3—81no—
288C2×C4×D3C2×D412yes—
289C2×C4×D3C2×D412yes—
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—24no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4C2×D412yes—
303C3×C4⋊C4C2×D412yes—
304C3×C42—21no—
305C3×C42—21no—
306#215—44no—
307(C2×D3)⋊C4—24no—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—22no—
310(C2×D3)⋊C4—24no—
311(C2×D3)⋊C4—22no—
312(C2×D3)⋊C4—24no—
313(C2×D3)⋊C4—42no—
314(C2×D3)⋊C4—42no—
315(C2×D3)⋊C4—42no—
316(C2×D3)⋊C4—81no—
317(C2×D3)⋊C4—81no—
318C4⋊Dic3—21no—
319C4⋊Dic3—22no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3C2×D412yes—
323Dic3⋊C4—24no—
324Dic3⋊C4—42no—
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—
332D24—44no—
333D3×C8—44no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—62no—
337C2×#41—62no—
338C2×#41—121no—
339C2×#41—121no—
340C22×Q8C22×D311yescharacteristic
341C22×D4—31no—
342C22×D4—31no—
343C22×D4—31no—
344C22×D4—61no—
345C22×D4—61no—
346C22×D4—61no—
347C22×D4—61no—
348C23×C4—31no—
349C23×C4—31no—
350C23×C4—61no—
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
366#126—68no—
367#125—22no—
368#125—22no—
369#123—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—
383C4×D4—68no—
384#117—34no—
385#117—62no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—62no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
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×C22⋊C4—61no—
409C2×C42—61no—
410C2×C42C22×D311yescharacteristic
411#103—22no—
412#103—22no—
413#103—62no—
414#102—62no—
415#102—62no—
416#102—62no—
417#102—121no—
418#102—121no—
419C22⋊C8—62no—
420C22⋊C8—121no—
421C22⋊C8—121no—
422#95—21no—
423#95—21no—
424#95—61no—
425C23×C3C22×D411yescharacteristic
426C22×D3—21no—
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—22no—
439C22×D3—22no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3#12012yes—
453C22×D3#13512yes—
454C3×Q8—22no—
455C3×Q8—22no—
456C3×Q8—41no—
457C3×Q8—41no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
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—41no—
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
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—22no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3#12012yes—
494D12—22no—
495D12—22no—
496D12—22no—
497D12—22no—
498D12—44no—
499D12—48no—
500D12—48no—
501D12—41no—
502D12—41no—
503D12—41no—
504D12—41no—
505D12—84no—
506D12—84no—
507C4×D3—22no—
508C4×D3—22no—
509C4×D3—22no—
510C4×D3—22no—
511C4×D3—48no—
512C4×D3—41no—
513C4×D3—41no—
514C4×D3—41no—
515C4×D3—41no—
516C4×D3—84no—
517C4×D3—84no—
518C3×C8—41no—
519C3×C8—41no—
520C3⋊C8—41no—
521C3⋊C8—41no—
522C24—31no—
523C24—31no—
524C24—61no—
525C24—61no—
526#41—68no—
527#41—124no—
528#41—124no—
529#41—124no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8#23912yes—
536C2×D4—32no—
537C2×D4—32no—
538C2×D4—62no—
539C2×D4—62no—
540C2×D4—64no—
541C2×D4—64no—
542C2×D4—61no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—121no—
553C2×D4—122no—
554C2×D4—122no—
555C2×D4—122no—
556C2×D4—122no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—122no—
560C2×D4—241no—
561C2×D4—241no—
562C2×D4—241no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—31no—
568C22×C4—32no—
569C22×C4—32no—
570C22×C4—31no—
571C22×C4—64no—
572C22×C4—64no—
573C22×C4—61no—
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—122no—
586C22×C4—122no—
587C22×C4—122no—
588C22×C4—241no—
589C22×C4—241no—
590C22×C4—241no—
591C22×C4—241no—
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—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—32no—
617C4⋊C4—62no—
618C4⋊C4—64no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—122no—
623C4⋊C4D3×D412yes—
624C4⋊C4D3×D412yes—
625C22⋊C4—62no—
626C22⋊C4—64no—
627C22⋊C4—62no—
628C22⋊C4—64no—
629C22⋊C4—64no—
630C22⋊C4—64no—
631C22⋊C4—122no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—241no—
635C22⋊C4—241no—
636C42—21no—
637C42—21no—
638C42—64no—
639C22×C3C2×#12011yescharacteristic
640C22×C3#54611yescharacteristic
641C22×C3#54611yescharacteristic
642C22×C3C2×#13511yescharacteristic
643C22×C3#57511yescharacteristic
644C22×C3#57611yescharacteristic
645C22×C3#57711yescharacteristic
646C2×D3—22no—
647C2×D3—22no—
648C2×D3—22no—
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—42no—
661C2×D3—42no—
662C2×D3—42no—
663C2×D3—42no—
664C2×D3—42no—
665C2×D3—42no—
666C2×D3—81no—
667C2×D3—81no—
668C2×D3—81no—
669C2×D3—81no—
670C2×D3—81no—
671C2×D3—81no—
672C2×D3—81no—
673C2×D3—81no—
674C3×C4—42no—
675C3×C4—41no—
676C3×C4—42no—
677C3×C4—41no—
678C3×C4—42no—
679C3×C4—81no—
680C3×C4#52511yescharacteristic
681C3×C4#53511yescharacteristic
682C3×C4#54611yescharacteristic
683C3×C4#54611yescharacteristic
684Dic3—22no—
685Dic3—41no—
686Dic3—42no—
687Dic3—81no—
688C23—32no—
689C23—32no—
690C23—61no—
691C23—61no—
692C23—61no—
693C23—61no—
694C23—61no—
695C23—61no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—62no—
703C23—62no—
704C23—121no—
705C23—121no—
706C23—121no—
707C23—121no—
708C23—121no—
709C23—121no—
710C23—121no—
711C23—121no—
712C23—121no—
713C23—121no—
714C23—121no—
715C23—121no—
716C23C2×D3×D411yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—41no—
720Q8—41no—
721D4—62no—
722D4—62no—
723D4—62no—
724D4—62no—
725D4—124no—
726D4—128no—
727D4—128no—
728D4—121no—
729D4—121no—
730D4—121no—
731D4—121no—
732D4—244no—
733D4—244no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—32no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—61no—
760C2×C4—62no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—128no—
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—244no—
774C2×C4—244no—
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#240411yescharacteristic
786C2×C3#300211yescharacteristic
787C2×C3#301211yescharacteristic
788C2×C3#329711yescharacteristic
789C2×C3#330111yescharacteristic
790C2×C3#330711yescharacteristic
791C2×C3#330911yescharacteristic
792D3—42no—
793D3—42no—
794D3—82no—
795D3—82no—
796C22—62no—
797C22—62no—
798C22—62no—
799C22—62no—
800C22—62no—
801C22—62no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—122no—
811C22—122no—
812C22—122no—
813C22—122no—
814C22—122no—
815C22—122no—
816C22—241no—
817C22—241no—
818C22—241no—
819C22—241no—
820C22—241no—
821C22—241no—
822C22—241no—
823C22—241no—
824C22D3×#12011yescharacteristic
825C22#563011yescharacteristic
826C22#567611yescharacteristic
827C22D3×#13511yescharacteristic
828C22#576911yescharacteristic
829C22#577711yescharacteristic
830C22#577811yescharacteristic
831C4—42no—
832C4—41no—
833C4—42no—
834C4—41no—
835C4—42no—
836C4—62no—
837C4—81no—
838C4—121no—
839C4—122no—
840C4—241no—
841C4#562711yescharacteristic
842C4#563011yescharacteristic
843C4#567411yescharacteristic
844C4#567611yescharacteristic
845C3#2396211yescharacteristic, complemented, Sylow
846C2—122no—
847C2—122no—
848C2—242no—
849C2—242no—
850C2#7686311yescharacteristic
851C2#8022611yescharacteristic
852C2#8023111yescharacteristic
853C2#8124611yescharacteristic
854C2#8124711yescharacteristic
855C2#8165311yescharacteristic
856C2#8174811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2026C2
socleC23×C3C22×D4
hypercenter#2026D3
hypocenterC3#23962
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2026

Complements

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

NH ≅ G/Ntype
1. C2×#5695C2semidirect
2. C2×#4810C2semidirect
3. C2×#4804C2semidirect
4. #76618C2semidirect
5. C3×#2026C2semidirect
6. #71743C2semidirect
7. #70272C2semidirect
8. #70268C2semidirect
9. #69687C2semidirect
10. #68886C2semidirect
11. #68883C2semidirect
12. #68880C2semidirect
13. #68873C2semidirect
14. #68673C2semidirect
15. #68668C2semidirect
68. #2026D3semidirect
145. #895D4semidirect
149. #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×#56952
C2×#48102
C2×#48042
#766182
C3×#20262
#717432
#702722
#702682
#696872
#688862
#688832
#688802
#688732
#686732
#686682
#239623