Finite Group Databasebeta

← #10846245

Subgroups — #10846245

Order 768.

1104 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#83254C211yesmaximal, characteristic, complemented
2C2×#5085C211yesmaximal, characteristic, complemented
3C2×#4807C211yesmaximal, characteristic, complemented
4C2×#4807C211yesmaximal, characteristic, complemented
5C2×#4788C211yesmaximal, characteristic, complemented
6#76220C211yesmaximal, characteristic
7C3×#2043C211yesmaximal, characteristic, complemented
8#70276C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#70272C211yesmaximal, characteristic, complemented
11#70257C211yesmaximal, characteristic, complemented
12#70240C211yesmaximal, characteristic, complemented
13#69618C211yesmaximal, characteristic, complemented
14#68647C211yesmaximal, characteristic, complemented
15#68629C211yesmaximal, characteristic, complemented
16#25410—31nomaximal, Sylow
17C2×C3×C4⋊Q8C2211yescharacteristic
18C2×#946C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C2×Q8×Dic3C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C22×#215C2211yescharacteristic
25C22×D3×C8C2211yescharacteristic
26C2×#895—21no—
27C2×#895C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#893C2211yescharacteristic
30C2×#874C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C3×#389C2211yescharacteristic
36#5229C2211yescharacteristic
37C2×#821C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×C8×Dic3C2211yescharacteristic
43#5085—24no—
44#4994—21no—
45#4991—21no—
46#4990—21no—
47#4988C2211yescharacteristic
48#4982—21no—
49#4976—21no—
50C2×#808C2211yescharacteristic
51C2×#808C2211yescharacteristic
52C4×(C2×D3)⋊C4C2211yescharacteristic
53#4928C2211yescharacteristic
54C2×C4×C3⋊C8C2211yescharacteristic
55#4807—24no—
56#4807—24no—
57#4788—24no—
58#4671—21no—
59#4665—21no—
60C3×#336C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#492—31no—
65C2×#465—31no—
66C2×#465—31no—
67C2×C4×SD16—31no—
68#2429—31no—
69#2428—31no—
70#2043D311yescharacteristic, complemented
71#2041—31no—
72#2000—31no—
73#2000—31no—
74#1968—31no—
75#1941—31no—
76#1880—31no—
77#1877—31no—
78C8×C22⋊C4—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×D12—21no—
82C22×D12—21no—
83C22×D12—21no—
84C22×D12—21no—
85C22×D12C2311yescharacteristic
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C22×C4×D3C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C3×C4⋊Q8—22no—
92C3×C4⋊Q8—41no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C42C2311yescharacteristic
99#946—22no—
100#946—22no—
101#946—41no—
102#946—41no—
103Q8×Dic3—22no—
104Q8×Dic3—41no—
105C2×#215—22no—
106C2×#215—22no—
107C2×#215—22no—
108C2×#215—22no—
109C2×#215—22no—
110C2×#215—22no—
111C2×#215—22no—
112C2×#215—22no—
113C2×#215—22no—
114C2×#215—41no—
115C2×#215—41no—
116C2×#215D414yescomplemented
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⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×C4×Dic3—21no—
133C2×C4×Dic3C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C2×D3×C8—22no—
137C2×D3×C8—22no—
138C2×D3×C8—22no—
139#895—22no—
140#895—22no—
141#895—41no—
142#895—41no—
143#895—44no—
144#893—22no—
145#893—41no—
146#874—22no—
147#874—41no—
148C3×#103—22no—
149C3×#103—22no—
150C3×#103—22no—
151C3×#103—41no—
152C3×#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95D411yescharacteristic
157C3⋊#95D411yescharacteristic
158#821—22no—
159#821—22no—
160#821—22no—
161#821—41no—
162(C2×D3)⋊C8—22no—
163C8×Dic3—22no—
164#808—22no—
165#808D414yescomplemented
166C4×C3⋊C8—22no—
167C22×SD16—31no—
168C22×SD16—31no—
169C22×SD16—31no—
170C22×SD16—31no—
171C23×C8—31no—
172C2×C4⋊Q8C2×D311yescharacteristic
173C2×#127—31no—
174C2×C22⋊Q8—31no—
175C2×C22⋊Q8—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121—61no—
179C2×C4×Q8—31no—
180C2×C4×D4—31no—
181#492—64no—
182#465—64no—
183#465—64no—
184C4×SD16—64no—
185C2×#106—31no—
186C2×#106—31no—
187C2×#103C2×D311yescharacteristic
188C2×#103C2×D311yescharacteristic
189C2×#103C2×D311yescharacteristic
190C2×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8—31no—
197C2×C4×C8—31no—
198#398—61no—
199#396—61no—
200#394—61no—
201#392—61no—
202#391—31no—
203#390—31no—
204#389—31no—
205#389—61no—
206#389C2×D311yescharacteristic
207#388—61no—
208#386—61no—
209C4×C22⋊C4—31no—
210#340—31no—
211#340—31no—
212#336—31no—
213#336C2×D311yescharacteristic
214C23×D3—21no—
215C23×D3—21no—
216C23×D3C2×D411yescharacteristic
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8C2×D412yes—
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×Dic3C2×D411yescharacteristic
239C22×Dic3C2×D411yescharacteristic
240C22×Dic3C2×D411yescharacteristic
241C2×D12—21no—
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—21no—
251C2×D12—21no—
252C2×D12—42no—
253C2×D12—42no—
254C2×D12—42no—
255C2×D12—42no—
256C2×D12—42no—
257C2×D12—42no—
258C2×D12—42no—
259C2×D12—42no—
260C2×D12—81no—
261C2×D12—81no—
262C2×D12—81no—
263C2×D12—81no—
264C2×D12C2×D412yes—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—42no—
272C2×C4×D3—42no—
273C2×C4×D3—81no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—42no—
284C3×C4⋊C4—42no—
285C3×C4⋊C4—42no—
286C3×C4⋊C4C2×D412yes—
287C3×C42—21no—
288C3×C42—21no—
289#215—28no—
290#215—44no—
291#215—44no—
292#215—44no—
293(C2×D3)⋊C4—22no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—81no—
301(C2×D3)⋊C4SD1614yescomplemented
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—42no—
306C4⋊Dic3C2×D412yes—
307Dic3⋊C4—42no—
308Dic3⋊C4—42no—
309Dic3⋊C4—42no—
310C4×Dic3—21no—
311C4×Dic3—21no—
312C4×Dic3—42no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8C2×D412yes—
316C2×C3⋊C8C2×D412yes—
317C2×C3⋊C8#4112yes—
318C2×C3⋊C8#4112yes—
319D3×C8—44no—
320C22×Q8C22×D311yescharacteristic
321C22×Q8C22×D311yescharacteristic
322C22×D4—31no—
323C22×D4—31no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4—61no—
328C23×C4—31no—
329C23×C4—61no—
330C2×SD16—34no—
331C2×SD16—62no—
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—62no—
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—121no—
341C2×SD16—121no—
342C22×C8—31no—
343C22×C8—31no—
344C22×C8—62no—
345C22×C8—62no—
346C22×C8—62no—
347C22×C8C22×D311yescharacteristic
348C22×C8C22×D311yescharacteristic
349C4⋊Q8—22no—
350C4⋊Q8—41no—
351#127—62no—
352#127—121no—
353C22⋊Q8—62no—
354C22⋊Q8—62no—
355C22⋊Q8—121no—
356C22⋊Q8—121no—
357#121—62no—
358#121—62no—
359#121—124no—
360#121—121no—
361#121—121no—
362C4×Q8—62no—
363C4×Q8—121no—
364C4×D4—62no—
365C4×D4—121no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4C22×D311yescharacteristic
376C2×C4⋊C4C22×D311yescharacteristic
377C2×C22⋊C4—31no—
378C2×C22⋊C4—31no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C42—31no—
387C2×C42—61no—
388C2×C42C22×D311yescharacteristic
389#106—34no—
390#106—62no—
391#103—22no—
392#103—22no—
393#103—22no—
394#103—41no—
395#102—62no—
396#102—62no—
397#102—62no—
398#102—121no—
399C22⋊C8—62no—
400C4×C8—62no—
401C4×C8—62no—
402#95—21no—
403#95—31no—
404#95—31no—
405#95—61no—
406#95—61no—
407#95—61no—
408C23×C3C22×D411yescharacteristic
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—22no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3C2×SD1612yes—
430C3×Q8—22no—
431C3×Q8—22no—
432C3×Q8—41no—
433C3×Q8—41no—
434C3×Q8—41no—
435C3×Q8—41no—
436C3×Q8—41no—
437C3×Q8—41no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4C2×SD1612yes—
455C2×C3×C4#13512yes—
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C22×D411yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4H(5,𝔽2)11yescharacteristic
461C2×C3×C4H(5,𝔽2)11yescharacteristic
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—22no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3C2×SD1612yes—
477D12—22no—
478D12—22no—
479D12—41no—
480D12—41no—
481D12—41no—
482D12—41no—
483D12—41no—
484D12—41no—
485D12—84no—
486D12—84no—
487D12—84no—
488D12—84no—
489C4×D3—41no—
490C4×D3—41no—
491C4×D3—41no—
492C4×D3—41no—
493C4×D3—84no—
494C3×C8—41no—
495C3×C8—41no—
496C3⋊C8—22no—
497C3⋊C8#12114yescomplemented
498C24—31no—
499C24—61no—
500C24—61no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8D3×D412yes—
513C2×D4—32no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—122no—
526C2×D4—122no—
527C2×D4—122no—
528C2×D4—122no—
529C2×D4—122no—
530C2×D4—122no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—241no—
534C2×D4—241no—
535C2×D4—241no—
536C2×D4—241no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—122no—
553C22×C4—122no—
554C22×C4—241no—
555C22×C4D3×D411yescharacteristic
556C22×C4D3×D411yescharacteristic
557C22×C4C23×D311yescharacteristic
558SD16—68no—
559SD16—124no—
560SD16—124no—
561SD16—124no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—32no—
569C2×C8—32no—
570C2×C8—32no—
571C2×C8—32no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—124no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—32no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—122no—
586C4⋊C4—122no—
587C4⋊C4—122no—
588C4⋊C4—122no—
589C4⋊C4D3×D412yes—
590C22⋊C4—34no—
591C22⋊C4—62no—
592C22⋊C4—122no—
593C22⋊C4—122no—
594C22⋊C4—122no—
595C22⋊C4—122no—
596C22⋊C4—122no—
597C22⋊C4—122no—
598C22⋊C4—241no—
599C42—21no—
600C42—21no—
601C42—61no—
602C42—61no—
603C42—122no—
604C22×C3#53211yescharacteristic
605C22×C3D4211yescharacteristic
606C22×C3D4211yescharacteristic
607C22×C3C22×SD1611yescharacteristic
608C22×C3C2×#13511yescharacteristic
609C22×C3#57711yescharacteristic
610C22×C3#57711yescharacteristic
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—22no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—42no—
619C2×D3—42no—
620C2×D3—42no—
621C2×D3—81no—
622C2×D3—81no—
623C2×D3—81no—
624C2×D3—81no—
625C2×D3—81no—
626C2×D3—81no—
627C2×D3—81no—
628C2×D3—81no—
629C2×D3—81no—
630C2×D3—81no—
631C2×D3—81no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—81no—
637C3×C4—81no—
638C3×C4C2×#12111yescharacteristic
639C3×C4#54011yescharacteristic
640C3×C4#54611yescharacteristic
641C3×C4#55011yescharacteristic
642Dic3—22no—
643Dic3—41no—
644Dic3—41no—
645Dic3—42no—
646Dic3—81no—
647C23—32no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—62no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23—121no—
660C23—121no—
661C23—121no—
662C23—121no—
663C23—121no—
664C23—121no—
665C23—121no—
666C23—121no—
667C23—121no—
668C23C2×D3×D411yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677D4—62no—
678D4—62no—
679D4—121no—
680D4—121no—
681D4—121no—
682D4—121no—
683D4—121no—
684D4—121no—
685D4—244no—
686D4—244no—
687D4—244no—
688D4—244no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—32no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—62no—
714C2×C4—61no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—244no—
725C2×C4D3×SD1612yes—
726C2×C4#91912yes—
727C2×C4C2×D3×D411yescharacteristic
728C2×C4C2×D3×D411yescharacteristic
729C2×C4#100411yescharacteristic
730C2×C4D3×#4111yescharacteristic
731C2×C4D3×#4111yescharacteristic
732C2×C4#100911yescharacteristic
733C8—34no—
734C8—41no—
735C8—41no—
736C8—62no—
737C2×C3#242811yescharacteristic
738C2×C3#316711yescharacteristic
739C2×C3#317411yescharacteristic
740C2×C3D4×SD1611yescharacteristic
741C2×C3D4×SD1611yescharacteristic
742C2×C3#328211yescharacteristic
743C2×C3#328411yescharacteristic
744D3—42no—
745D3—82no—
746D3—161no—
747C22—62no—
748C22—62no—
749C22—62no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—122no—
755C22—122no—
756C22—122no—
757C22—241no—
758C22—241no—
759C22—241no—
760C22—241no—
761C22—241no—
762C22—241no—
763C22—241no—
764C22—241no—
765C22—241no—
766C22—241no—
767C22—241no—
768C22#559011yescharacteristic
769C22#560911yescharacteristic
770C22#566811yescharacteristic
771C22C2×D3×SD1611yescharacteristic
772C22C2×#91911yescharacteristic
773C22#577811yescharacteristic
774C22#577811yescharacteristic
775C4—22no—
776C4—22no—
777C4—42no—
778C4—42no—
779C4—62no—
780C4—81no—
781C4—81no—
782C4—121no—
783C4—121no—
784C4—122no—
785C4—241no—
786C4#559911yescharacteristic
787C4D3×#12111yescharacteristic
788C4#565411yescharacteristic
789C4#566311yescharacteristic
790C3#2541011yescharacteristic, complemented, Sylow
791C2—122no—
792C2—242no—
793C2—481no—
794C2#7690311yescharacteristic
795C2#8006311yescharacteristic
796C2#8020711yescharacteristic
797C2#8044811yescharacteristic
798C2#8050211yescharacteristic
799C2#8159211yescharacteristic
800C2#8172911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2043C2
socleC23×C3C22×D4
prime radical#76220C2
hypercenter#2043D3
hypocenterC3#25410
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
1. #83254C2semidirect
2. C2×#5085C2semidirect
3. C2×#4807C2semidirect
4. C2×#4807C2semidirect
5. C2×#4788C2semidirect
7. C3×#2043C2semidirect
8. #70276C2semidirect
9. #70272C2semidirect
10. #70272C2semidirect
11. #70257C2semidirect
12. #70240C2semidirect
13. #69618C2semidirect
14. #68647C2semidirect
15. #68629C2semidirect
70. #2043D3semidirect
116. C2×#215D4semidirect
165. #808D4semidirect
301. (C2×D3)⋊C4SD16semidirect
497. C3⋊C8#121semidirect
790. C3#25410semidirect

Maximal subgroups

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

subgroupindex
#832542
C2×#50852
C2×#48072
C2×#47882
#762202
C3×#20432
#702762
#702722
#702572
#702402
#696182
#686472
#686292
#254103