Finite Group Databasebeta

← #10847436

Subgroups — #10847436

Order 768.

1226 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5624C211yesmaximal, characteristic, complemented
2C2×#5115C211yesmaximal, characteristic
3C2×#5048C211yesmaximal, characteristic, complemented
4#73999C211yesmaximal, characteristic, complemented
5C3×#1892C211yesmaximal, characteristic, complemented
6C2×#4550C211yesmaximal, characteristic, complemented
7#70277C211yesmaximal, characteristic, complemented
8#70245C211yesmaximal, characteristic, complemented
9#70240C211yesmaximal, characteristic, complemented
10#70236C211yesmaximal, characteristic, complemented
11#69515C211yesmaximal, characteristic, complemented
12#68899C211yesmaximal, characteristic, complemented
13#68897C211yesmaximal, characteristic, complemented
14#68895C211yesmaximal, characteristic, complemented
15#68829C211yesmaximal, characteristic, complemented
16#25500—31nomaximal, Sylow
17C23×C3×C8C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×#947C2211yescharacteristic
20C2×Q8×Dic3C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C22×C4×Dic3C2211yescharacteristic
25C23×C3⋊C8C2211yescharacteristic
26C22×D24C2211yescharacteristic
27#5624—24no—
28#5624—24no—
29C2×#898—21no—
30C2×#893C2211yescharacteristic
31C2×#892—21no—
32C2×#890C2211yescharacteristic
33C2×#886—21no—
34C2×#886—21no—
35C2×#67⋊C4—21no—
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C3×#380C2211yescharacteristic
39C2×#835C2211yescharacteristic
40#5115—24no—
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#818C2211yescharacteristic
44#5048—24no—
45#4988C2211yescharacteristic
46#4988C2211yescharacteristic
47#4984C2211yescharacteristic
48#4984C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#808C2211yescharacteristic
53#4958—21no—
54#4670—21no—
55#4670—21no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#529—31no—
65C2×#466—31no—
66C2×#465—31no—
67#2854—31no—
68#2059—31no—
69#2042—31no—
70#2025—31no—
71#2012—31no—
72#1893—31no—
73#1892D311yescharacteristic, complemented
74#1880—31no—
75#1879—31no—
76#1864—31no—
77#1863—31no—
78C2×#336—31no—
79C22×C3×Q8C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67—21no—
83C23×Dic3D411yescharacteristic
84C23×Dic3D411yescharacteristic
85C22×D12C2311yescharacteristic
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C22×C3×C8—22no—
89C22×C3×C8—22no—
90C22×C3×C8—41no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8D414yes—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101#947—22no—
102#947—22no—
103Q8×Dic3—22no—
104Q8×Dic3—22no—
105C2×#215—22no—
106C2×#215—22no—
107C2×#215—41no—
108#930—22no—
109#930—22no—
110#930—22no—
111#930D414yes—
112C2×(C2×D3)⋊C4—21no—
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×C4⋊Dic3—21no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×Dic3⋊C4—21no—
128C2×C4×Dic3—22no—
129C2×C4×Dic3—22no—
130C2×C4×Dic3—21no—
131C2×C4×Dic3D411yescharacteristic
132C2×C4×Dic3D411yescharacteristic
133C2×C4×Dic3C2311yescharacteristic
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8—22no—
136C22×C3⋊C8—22no—
137C22×C3⋊C8—41no—
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C2×D24—22no—
141C2×D24—22no—
142C2×D24—41no—
143#898—28no—
144#893—22no—
145#893—22no—
146#892—28no—
147#890—22no—
148#890—22no—
149#886—28no—
150#886—44no—
151#67⋊C4—28no—
152C3×#103—22no—
153C3×#103—41no—
154C3×#95—21no—
155#835—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158#821—22no—
159#821—22no—
160#818—22no—
161#809—22no—
162#809—22no—
163#809—41no—
164#808—22no—
165C22×SD16—31no—
166C22×D8—31no—
167C23×C8—31no—
168C23×C8C2×D311yescharacteristic
169#529—64no—
170#529—64no—
171C2×#126—61no—
172C2×#125—31no—
173C2×#124—31no—
174C2×#123—61no—
175C2×#123—61no—
176C2×C22⋊Q8C2×D311yescharacteristic
177C2×#121—31no—
178C2×#121—31no—
179C2×C4×Q8—31no—
180C2×C4×D4—31no—
181C2×C4×D4—61no—
182C2×#117—61no—
183C22×C42—31no—
184#466—64no—
185#465—64no—
186C2×#107—31no—
187C2×#106—31no—
188C2×#103—31no—
189C2×#103C2×D311yescharacteristic
190C2×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196#390—31no—
197#390—31no—
198#389—31no—
199#389—31no—
200#388—61no—
201#388—61no—
202#386—61no—
203#380C2×D311yescharacteristic
204#340—31no—
205#340—31no—
206#340C2×D311yescharacteristic
207#340C2×D311yescharacteristic
208#336—31no—
209#336—31no—
210#336—31no—
211#336—31no—
212C24×C3C2×D411yescharacteristic
213C23×D3—21no—
214C23×D3—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8C2×D412yes—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4C2×D412yes—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D412yes—
232C22×C3×C4C2411yescharacteristic
233C2×#67—24no—
234C2×#67—42no—
235C2×#67—42no—
236C2×#67—42no—
237C2×#67—42no—
238C2×#67—42no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—21no—
244C22×Dic3—22no—
245C22×Dic3—21no—
246C22×Dic3—41no—
247C22×Dic3C2×D411yescharacteristic
248C22×Dic3C2×D411yescharacteristic
249C22×Dic3C2×D411yescharacteristic
250C22×Dic3C2×D411yescharacteristic
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12C2×D412yes—
263C2×C4×D3—24no—
264C2×C4×D3—42no—
265C2×C4×D3—42no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—44no—
272C2×C3×C8#4112yes—
273C3×C4⋊C4—24no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4C2×D412yes—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—42no—
282#215—44no—
283(C2×D3)⋊C4—24no—
284(C2×D3)⋊C4—24no—
285(C2×D3)⋊C4—24no—
286(C2×D3)⋊C4—24no—
287(C2×D3)⋊C4—42no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4—42no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—42no—
292C4⋊Dic3—24no—
293C4⋊Dic3—24no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—42no—
298C4⋊Dic3—42no—
299C4⋊Dic3C2×D412yes—
300Dic3⋊C4—24no—
301C4×Dic3—24no—
302C4×Dic3—22no—
303C4×Dic3—22no—
304C4×Dic3—21no—
305C4×Dic3—21no—
306C4×Dic3—21no—
307C4×Dic3—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—44no—
314C2×C3⋊C8#4112yes—
315D24—44no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—31no—
318C22×D4—31no—
319C22×D4—61no—
320C22×D4—61no—
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—61no—
324C23×C4C22×D311yescharacteristic
325C2×SD16—62no—
326C2×SD16—62no—
327C2×SD16—121no—
328C2×D8—62no—
329C2×D8—62no—
330C2×D8—121no—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8—31no—
334C22×C8—31no—
335C22×C8—41no—
336C22×C8—62no—
337C22×C8—62no—
338C22×C8—121no—
339C22×C8C22×D311yescharacteristic
340C22×C8C22×D311yescharacteristic
341#126—68no—
342#125—62no—
343#125—62no—
344#124—62no—
345#124—62no—
346#123—68no—
347#123—124no—
348C22⋊Q8—22no—
349C22⋊Q8D1214yes—
350#121—34no—
351#121—62no—
352#121—62no—
353#121—62no—
354C4×Q8—62no—
355C4×Q8—62no—
356C4×D4—68no—
357C4×D4—62no—
358C4×D4—62no—
359#117—68no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4C22×D311yescharacteristic
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C42—31no—
383C2×C42—31no—
384C2×C42—31no—
385C2×C42—31no—
386C2×C42—61no—
387C2×C42—62no—
388C2×C42—62no—
389#107—62no—
390#106—62no—
391#103—22no—
392#103—41no—
393#103—62no—
394#102—62no—
395#102—62no—
396#102—62no—
397#102—62no—
398#102—121no—
399#95—21no—
400#95—61no—
401#95—61no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3#12012yes—
407C23×C3#13512yes—
408C23×C3AGL(1,ℤ/8)12yes—
409C23×C3C22×D411yescharacteristic
410C22×D3—22no—
411C22×D3—41no—
412C22×D3—41no—
413C22×D3—41no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C3×Q8—22no—
425C3×Q8—22no—
426C3×Q8—41no—
427C3×Q8—41no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4#12012yes—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C2×C3×C42−1+411yescharacteristic
453#67—48no—
454#67—84no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—22no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—44no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—44no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3#13512yes—
475D12—22no—
476D12—22no—
477D12—41no—
478D12—41no—
479D12—41no—
480D12—41no—
481D12—41no—
482D12—41no—
483C4×D3—48no—
484C3×C8—22no—
485C3×C8—41no—
486C3⋊C8—22no—
487C3⋊C8—41no—
488C24—61no—
489C24—61no—
490C24D3×D411yescharacteristic
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8C2×D1212yes—
497C2×D4—32no—
498C2×D4—64no—
499C2×D4—61no—
500C2×D4—61no—
501C2×D4—61no—
502C2×D4—61no—
503C2×D4—61no—
504C2×D4—61no—
505C2×D4—61no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—122no—
511C2×D4—122no—
512C2×D4—122no—
513C2×D4—122no—
514C2×D4—122no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—64no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—122no—
536C22×C4—122no—
537C22×C4—121no—
538C22×C4C2×D1212yes—
539C22×C4D3×D411yescharacteristic
540C22×C4D3×D412yes—
541C22×C4C23×D311yescharacteristic
542SD16—124no—
543D8—124no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—32no—
550C2×C8—44no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—124no—
557C2×C8#23712yes—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—32no—
565C4⋊C4—64no—
566C4⋊C4—64no—
567C4⋊C4—64no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—122no—
572C4⋊C4—122no—
573C4⋊C4C2×D1212yes—
574C22⋊C4—24no—
575C22⋊C4—42no—
576C22⋊C4—64no—
577C22⋊C4—64no—
578C22⋊C4—64no—
579C22⋊C4—64no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C42—64no—
586C42—62no—
587C42—62no—
588C42—61no—
589C42—61no—
590C42—61no—
591C42—61no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3#44914yes—
599C22×C3C2×#12011yescharacteristic
600C22×C3#53211yescharacteristic
601C22×C3#53711yescharacteristic
602C22×C3C2×#13511yescharacteristic
603C22×C3C2×#13511yescharacteristic
604C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
605C22×C3#57511yescharacteristic
606C2×D3—42no—
607C2×D3—42no—
608C2×D3—42no—
609C2×D3—81no—
610C2×D3—81no—
611C2×D3—81no—
612C2×D3—81no—
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C3×C4—22no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—81no—
624C3×C4—81no—
625C3×C4#54611yescharacteristic
626C3×C4#54611yescharacteristic
627C3×C4#54711yescharacteristic
628C3×C4#54711yescharacteristic
629Dic3—22no—
630Dic3—41no—
631Dic3—41no—
632Dic3—42no—
633Dic3—41no—
634Dic3—81no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—62no—
640C23—121no—
641C23—121no—
642C23—121no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23—121no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23#88212yes—
654C23#91412yes—
655C23#91912yes—
656C23C2×D3×D411yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661D4—62no—
662D4—62no—
663D4—128no—
664D4—121no—
665D4—121no—
666D4—121no—
667D4—121no—
668D4—121no—
669D4—121no—
670D4—244no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—32no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—62no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—128no—
703C2×C4—124no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—124no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4#88212yes—
711C2×C4C22×D1211yescharacteristic
712C2×C4C2×D3×D411yescharacteristic
713C2×C4C2×#23711yescharacteristic
714C2×C4#100411yescharacteristic
715C2×C4D3×#4111yescharacteristic
716C2×C4#101011yescharacteristic
717C8—22no—
718C8—41no—
719C8—62no—
720C8—121no—
721C2×C3—24no—
722C2×C3#243011yescharacteristic
723C2×C3C2×#44911yescharacteristic
724C2×C3#300211yescharacteristic
725C2×C3#316811yescharacteristic
726C2×C3#318011yescharacteristic
727C2×C3#324711yescharacteristic
728C2×C3#325011yescharacteristic
729D3—82no—
730D3—161no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—122no—
738C22—122no—
739C22—122no—
740C22—241no—
741C22—241no—
742C22—241no—
743C22—241no—
744C22—241no—
745C22—241no—
746C22—241no—
747C22—241no—
748C22—241no—
749C22—241no—
750C22—241no—
751C22#481014yes—
752C22C2×#88211yescharacteristic
753C22#559611yescharacteristic
754C22#559711yescharacteristic
755C22C2×#91411yescharacteristic
756C22C2×#91911yescharacteristic
757C22D3×#13511yescharacteristic
758C22#576811yescharacteristic
759C4—22no—
760C4—42no—
761C4—42no—
762C4—62no—
763C4—81no—
764C4—81no—
765C4—121no—
766C4—121no—
767C4—122no—
768C4—121no—
769C4—241no—
770C4#555411yescharacteristic
771C4#555511yescharacteristic
772C4#559111yescharacteristic
773C4#565511yescharacteristic
774C3#2550011yescharacteristic, complemented, Sylow
775C2—24no—
776C2—242no—
777C2—481no—
778C2#7469911yescharacteristic
779C2C2×#481011yescharacteristic
780C2#7883311yescharacteristic
781C2#8063811yescharacteristic
782C2#8064111yescharacteristic
783C2#8074011yescharacteristic
784C2#8074811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1892C2
socleC23×C3C22×D4
prime radicalC2×#5115C2
hypercenter#1892D3
hypocenterC3#25500
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
1. C2×#5624C2semidirect
3. C2×#5048C2semidirect
4. #73999C2semidirect
5. C3×#1892C2semidirect
6. C2×#4550C2semidirect
7. #70277C2semidirect
8. #70245C2semidirect
9. #70240C2semidirect
10. #70236C2semidirect
11. #69515C2semidirect
12. #68899C2semidirect
13. #68897C2semidirect
14. #68895C2semidirect
15. #68829C2semidirect
73. #1892D3semidirect
774. C3#25500semidirect

Maximal subgroups

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

subgroupindex
C2×#56242
C2×#51152
C2×#50482
#739992
C3×#18922
C2×#45502
#702772
#702452
#702402
#702362
#695152
#688992
#688972
#688952
#688292
#255003