Finite Group Databasebeta

← #10827602

Subgroups — #10827602

Order 768.

1300 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5730C211yesmaximal, characteristic, complemented
2C2×#4808C211yesmaximal, characteristic, complemented
3C2×#4803C211yesmaximal, characteristic, complemented
4#76618C211yesmaximal, characteristic
5C3×#2024C211yesmaximal, characteristic, complemented
6#71792C211yesmaximal, characteristic, complemented
7#70273C211yesmaximal, characteristic, complemented
8#70268C211yesmaximal, characteristic, complemented
9#69690C211yesmaximal, characteristic, complemented
10#68887C211yesmaximal, characteristic, complemented
11#68884C211yesmaximal, characteristic, complemented
12#68880C211yesmaximal, characteristic, complemented
13#68871C211yesmaximal, characteristic, complemented
14#68686C211yesmaximal, characteristic, complemented
15#68669C211yesmaximal, characteristic, complemented
16#23981—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic
19C2×#946—21no—
20C2×#946—21no—
21C2×#946C2211yescharacteristic
22C22×#216C2211yescharacteristic
23C22×#204C2211yescharacteristic
24C22×ΓL(1,𝔽25)C2211yescharacteristic
25#5730—24no—
26#5730—24no—
27C2×#897C2211yescharacteristic
28C2×#897C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#893—21no—
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#890—21no—
34C2×C4×D12C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C3×#391C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#816C2211yescharacteristic
45#4987C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49#4939C2211yescharacteristic
50#4808—24no—
51#4803—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×#554—31no—
65C2×#452—31no—
66C2×#417—31no—
67#2407—31no—
68#2024D311yescharacteristic, complemented
69#2023—31no—
70#2001—31no—
71#2000—31no—
72#1894—31no—
73#1880—31no—
74#1878—31no—
75#1874—31no—
76#1872—31no—
77#1870—31no—
78#1823—31no—
79C22×C3×Q8—21no—
80C22×C3×Q8C2311yescharacteristic
81C2×#239—22no—
82C2×#239—22no—
83C2×#239—22no—
84C2×#239—22no—
85C2×#239—41no—
86C2×#239—41no—
87C22×D12—21no—
88C22×D12—21no—
89C22×D12D411yescharacteristic
90C22×D12C2311yescharacteristic
91C22×C4×D3—21no—
92C22×C4×D3—21no—
93C22×C4×D3—21no—
94C22×C4×D3C2311yescharacteristic
95C22×C4×D3C2311yescharacteristic
96C22×Dic6C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×C4⋊Q8—22no—
100C3×C4⋊Q8—22no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C42C2311yescharacteristic
106#946—28no—
107#946—28no—
108#946—22no—
109#946—41no—
110C2×#216—22no—
111C2×#216—22no—
112C2×#216—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)⋊C4D411yescharacteristic
121C2×(C2×D3)⋊C4D411yescharacteristic
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3D411yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×C4×Dic3—21no—
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C2×#204—22no—
135C2×#204—22no—
136C2×#204—41no—
137C2×ΓL(1,𝔽25)—22no—
138C2×ΓL(1,𝔽25)—41no—
139C2×ΓL(1,𝔽25)—41no—
140#897—22no—
141#897—22no—
142#897—22no—
143#897D414yescomplemented
144#895—22no—
145#895—41no—
146#893—28no—
147D3×C4⋊C4—22no—
148D3×C4⋊C4—22no—
149D3×C4⋊C4—22no—
150D3×C4⋊C4D414yescomplemented
151#890—28no—
152C4×D12—22no—
153C4×D12—22no—
154C4×Dic6—22no—
155C4×Dic6—22no—
156C3×#103—22no—
157C3×#103—22no—
158C3×#95—21no—
159C3×#95—21no—
160#835—22no—
161C3⋊#95—21no—
162#821—22no—
163(C2×D3)⋊C8—22no—
164(C2×D3)⋊C8—41no—
165(C2×D3)⋊C8—41no—
166#816—41no—
167#810—41no—
168#809—22no—
169#809—22no—
170C22×#41—31no—
171C22×Q16—31no—
172C22×SD16—31no—
173C22×M16—31no—
174#554—64no—
175#554—64no—
176C2×C4⋊Q8C2×D311yescharacteristic
177C2×#125—61no—
178C2×C22⋊Q8—31no—
179C2×C22⋊Q8—31no—
180C2×C22⋊Q8—31no—
181C2×C22⋊Q8—61no—
182C2×C22⋊Q8—61no—
183C2×#121—31no—
184C2×C4×Q8—31no—
185C2×C4×D4—31no—
186C2×C4×D4—61no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189#452—64no—
190#417—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103C2×D311yescharacteristic
195C2×#103C2×D311yescharacteristic
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×D3C2×D411yescharacteristic
219C23×D3C2×D411yescharacteristic
220C2×C3×Q8—24no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—81no—
227C2×C3×Q8—81no—
228C2×C3×Q8#4112yes—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2411yescharacteristic
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3C2×D411yescharacteristic
240C22×Dic3C2×D411yescharacteristic
241#239—28no—
242#239—44no—
243#239—44no—
244#239—44no—
245C2×D12—22no—
246C2×D12—22no—
247C2×D12—22no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—42no—
254C2×D12—42no—
255C2×D12—42no—
256C2×D12—42no—
257C2×D12—42no—
258C2×D12—81no—
259C2×D12#4112yes—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—24no—
271C2×C4×D3—24no—
272C2×C4×D3—42no—
273C2×C4×D3—42no—
274C2×C4×D3—42no—
275C2×C4×D3—81no—
276C2×C4×D3—81no—
277C2×C4×D3—81no—
278C2×C4×D3—81no—
279C2×C4×D3C2×D412yes—
280C2×C4×D3C2×D412yes—
281C2×Dic6—21no—
282C2×Dic6—21no—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6C2×D412yes—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C3×C4⋊C4—24no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4C2×D412yes—
299C3×C4⋊C4C2×D412yes—
300C3×C42—21no—
301C3×C42—21no—
302#216—44no—
303(C2×D3)⋊C4—24no—
304(C2×D3)⋊C4—22no—
305(C2×D3)⋊C4—24no—
306(C2×D3)⋊C4—22no—
307(C2×D3)⋊C4—42no—
308(C2×D3)⋊C4—42no—
309(C2×D3)⋊C4—42no—
310(C2×D3)⋊C4—81no—
311(C2×D3)⋊C4—81no—
312C4⋊Dic3—24no—
313C4⋊Dic3—21no—
314C4⋊Dic3—22no—
315C4⋊Dic3—24no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3C2×D412yes—
319Dic3⋊C4—24no—
320Dic3⋊C4—24no—
321Dic3⋊C4—24no—
322Dic3⋊C4—42no—
323C4×Dic3—24no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330#204—44no—
331ΓL(1,𝔽25)—44no—
332C2×#41—62no—
333C2×#41—62no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—121no—
337C2×#41—121no—
338C22×Q8—21no—
339C22×Q8—31no—
340C22×Q8C22×D311yescharacteristic
341C22×D4—31no—
342C22×D4—31no—
343C22×D4—61no—
344C22×D4—61no—
345C23×C4—31no—
346C23×C4—31no—
347C23×C4—61no—
348C23×C4—61no—
349C23×C4—61no—
350C2×Q16—62no—
351C2×Q16—62no—
352C2×Q16—121no—
353C2×SD16—62no—
354C2×SD16—62no—
355C2×SD16—121no—
356C2×M16—62no—
357C2×M16—121no—
358C2×M16—121no—
359C22×C8—31no—
360C22×C8—31no—
361C22×C8C22×D311yescharacteristic
362C22×C8C22×D311yescharacteristic
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365#125—68no—
366C22⋊Q8—34no—
367C22⋊Q8—62no—
368C22⋊Q8—62no—
369C22⋊Q8—68no—
370C22⋊Q8—68no—
371C22⋊Q8—62no—
372C22⋊Q8—62no—
373C22⋊Q8—121no—
374#121—62no—
375#121—121no—
376C4×Q8—62no—
377C4×Q8—62no—
378C4×D4—62no—
379C4×D4—62no—
380C4×D4—68no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—62no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4—61no—
390C2×C4⋊C4—61no—
391C2×C4⋊C4—61no—
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×C42—61no—
408C2×C42C22×D311yescharacteristic
409#103—22no—
410#103—22no—
411#103—62no—
412#103—121no—
413#103—121no—
414#102—62no—
415#102—62no—
416#102—62no—
417C22⋊C8—62no—
418C22⋊C8—121no—
419C22⋊C8—121no—
420#95—21no—
421#95—21no—
422#95—61no—
423C23×C3C22×D411yescharacteristic
424C22×D3—21no—
425C22×D3—21no—
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—22no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3#12012yes—
444C22×D3#13712yes—
445C3×Q8—22no—
446C3×Q8—22no—
447C3×Q8—41no—
448C3×Q8—41no—
449C3×Q8—84no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4#13712yes—
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C22×D411yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×C3×C4H(5,𝔽2)11yescharacteristic
473C2×C3×C4H(5,𝔽2)11yescharacteristic
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3#12012yes—
489D12—28no—
490D12—22no—
491D12—22no—
492D12—48no—
493D12—41no—
494D12—41no—
495D12—84no—
496C4×D3—22no—
497C4×D3—22no—
498C4×D3—22no—
499C4×D3—22no—
500C4×D3—48no—
501C4×D3—41no—
502C4×D3—41no—
503C4×D3—41no—
504C4×D3—41no—
505C4×D3—84no—
506C4×D3—84no—
507Dic6—22no—
508Dic6—22no—
509Dic6—41no—
510Dic6—41no—
511C3×C8—41no—
512C3×C8—41no—
513C3⋊C8—41no—
514C3⋊C8—41no—
515C24—31no—
516C24—31no—
517C24—61no—
518#41—68no—
519#41—124no—
520#41—124no—
521#41—124no—
522C2×Q8—24no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—32no—
529C2×Q8—61no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—81no—
535C2×Q8—81no—
536C2×Q8#23912yes—
537C2×D4—32no—
538C2×D4—62no—
539C2×D4—62no—
540C2×D4—62no—
541C2×D4—61no—
542C2×D4—61no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4—122no—
549C2×D4—122no—
550C2×D4—122no—
551C2×D4—241no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—31no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—31no—
560C22×C4—64no—
561C22×C4—64no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—122no—
576C22×C4—122no—
577C22×C4—122no—
578C22×C4—241no—
579C22×C4—241no—
580C22×C4—241no—
581C22×C4—241no—
582C22×C4D3×D411yescharacteristic
583C22×C4D3×D411yescharacteristic
584C22×C4C23×D311yescharacteristic
585Q16—124no—
586SD16—124no—
587M16—124no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—61no—
595C2×C8—61no—
596C2×C8—61no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—32no—
606C4⋊C4—64no—
607C4⋊C4—62no—
608C4⋊C4—64no—
609C4⋊C4—64no—
610C4⋊C4—64no—
611C4⋊C4—64no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—122no—
616C4⋊C4D3×D412yes—
617C4⋊C4D3×D412yes—
618C22⋊C4—62no—
619C22⋊C4—62no—
620C22⋊C4—64no—
621C22⋊C4—64no—
622C22⋊C4—122no—
623C22⋊C4—122no—
624C22⋊C4—122no—
625C22⋊C4—241no—
626C22⋊C4—241no—
627C42—21no—
628C42—21no—
629C42—64no—
630C22×C3C2×#12011yescharacteristic
631C22×C3#54611yescharacteristic
632C22×C3#54611yescharacteristic
633C22×C3C2×#13711yescharacteristic
634C22×C3C2×#13711yescharacteristic
635C22×C3#57611yescharacteristic
636C22×C3#57711yescharacteristic
637C2×D3—22no—
638C2×D3—22no—
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—22no—
642C2×D3—22no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—81no—
655C2×D3—81no—
656C2×D3—81no—
657C2×D3—81no—
658C3×C4—22no—
659C3×C4—42no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4—41no—
663C3×C4—81no—
664C3×C4#52511yescharacteristic
665C3×C4#53511yescharacteristic
666C3×C4#54611yescharacteristic
667C3×C4#54611yescharacteristic
668Dic3—22no—
669Dic3—42no—
670Dic3—41no—
671Dic3—42no—
672Dic3—81no—
673C23—32no—
674C23—32no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—61no—
687C23—62no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23C2×D3×D411yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—41no—
698Q8—41no—
699Q8—62no—
700Q8—62no—
701Q8—84no—
702Q8—121no—
703Q8—121no—
704D4—68no—
705D4—62no—
706D4—62no—
707D4—128no—
708D4—121no—
709D4—121no—
710D4—244no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—32no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—61no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—128no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—244no—
753C2×C4—244no—
754C2×C4#91812yes—
755C2×C4C2×D3×D411yescharacteristic
756C2×C4C2×D3×D411yescharacteristic
757C2×C4C2×#23911yescharacteristic
758C2×C4D3×#4111yescharacteristic
759C2×C4#100911yescharacteristic
760C2×C4#100911yescharacteristic
761C8—41no—
762C8—41no—
763C8—121no—
764C8—121no—
765C2×C3#240411yescharacteristic
766C2×C3#300411yescharacteristic
767C2×C3#301211yescharacteristic
768C2×C3#331411yescharacteristic
769C2×C3#331611yescharacteristic
770C2×C3#333111yescharacteristic
771C2×C3#333311yescharacteristic
772D3—42no—
773D3—42no—
774D3—82no—
775C22—62no—
776C22—62no—
777C22—62no—
778C22—62no—
779C22—62no—
780C22—62no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—122no—
790C22—122no—
791C22—122no—
792C22—241no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22D3×#12011yescharacteristic
797C22#563011yescharacteristic
798C22#567611yescharacteristic
799C22#576211yescharacteristic
800C22C2×#91811yescharacteristic
801C22#577411yescharacteristic
802C22D3×#13711yescharacteristic
803C4—22no—
804C4—41no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—62no—
809C4—81no—
810C4—122no—
811C4—121no—
812C4—122no—
813C4—241no—
814C4#562711yescharacteristic
815C4#563011yescharacteristic
816C4#567411yescharacteristic
817C4#567611yescharacteristic
818C3#2398111yescharacteristic, complemented, Sylow
819C2—122no—
820C2—122no—
821C2—242no—
822C2#7686311yescharacteristic
823C2#8014911yescharacteristic
824C2#8018311yescharacteristic
825C2#8102411yescharacteristic
826C2#8112411yescharacteristic
827C2#8161911yescharacteristic
828C2#8170011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2024C2
socleC23×C3C22×D4
prime radical#76618C2
hypercenter#2024D3
hypocenterC3#23981
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
1. C2×#5730C2semidirect
2. C2×#4808C2semidirect
3. C2×#4803C2semidirect
5. C3×#2024C2semidirect
6. #71792C2semidirect
7. #70273C2semidirect
8. #70268C2semidirect
9. #69690C2semidirect
10. #68887C2semidirect
11. #68884C2semidirect
12. #68880C2semidirect
13. #68871C2semidirect
14. #68686C2semidirect
15. #68669C2semidirect
68. #2024D3semidirect
143. #897D4semidirect
150. D3×C4⋊C4D4semidirect
818. C3#23981semidirect

Maximal subgroups

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

subgroupindex
C2×#57302
C2×#48082
C2×#48032
#766182
C3×#20242
#717922
#702732
#702682
#696902
#688872
#688842
#688802
#688712
#686862
#686692
#239813