Finite Group Databasebeta

← #10701974

Subgroups — #10701974

Order 768.

1406 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#949C211yesmaximal, characteristic
2C2×C3×#417C211yesmaximal, characteristic, complemented
3C2×#5234C211yesmaximal, characteristic, complemented
4C22×#823C211yesmaximal, characteristic, complemented
5C22×#809C211yesmaximal, characteristic, complemented
6C2×#4558C211yesmaximal, characteristic, complemented
7C2×#4530C211yesmaximal, characteristic, complemented
8#11020—31nomaximal, Sylow
9C22×C3×#41C2211yescharacteristic
10C23×D12C2211yescharacteristic
11C22×C3×M16C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C2×#949—22no—
14C2×#949—22no—
15C2×#949—22no—
16C2×#949—22no—
17C2×#949—22no—
18C2×#949C414yescomplemented
19C22×#215—21no—
20C22×#213—21no—
21C22×#208C2211yescharacteristic
22C22×#208C2211yescharacteristic
23C23×C3⋊C8C2211yescharacteristic
24C3×#417—22no—
25C3×#417—22no—
26C2×C3×#103—21no—
27C2×C3×#102—21no—
28#5234—22no—
29#5234—22no—
30C2×#830—22no—
31C2×#823—22no—
32C2×#823—22no—
33C2×#823—22no—
34C2×#809—22no—
35C2×#809—22no—
36C2×#809—22no—
37#4558—22no—
38#4530—22no—
39C22×AGL(1,ℤ/8)—31no—
40C2×#417D311yescharacteristic, complemented
41C22×#102—31no—
42C22×#100—31no—
43C2×#408—31no—
44C2×#343—31no—
45C2×#341—31no—
46C24×D3—21no—
47C2×C3×#41—21no—
48C2×C3×#41—21no—
49C2×C3×#41—21no—
50C2×C3×#41—21no—
51C2×C3×#41—21no—
52C2×C3×#41—21no—
53C2×C3×#41—21no—
54C2×C3×#41—21no—
55C2×C3×#41—21no—
56C2×C3×#41—21no—
57C2×C3×#41C2×C412yes—
58C2×C3×#41D412yes—
59C22×C3×Q8D411yescharacteristic
60C22×C3×D4—21no—
61C22×C3×D4D411yescharacteristic
62C23×C3×C4—21no—
63C23×C3×C4—21no—
64C23×C3×C4C2311yescharacteristic
65C22×D12—21no—
66C22×D12—21no—
67C22×D12—21no—
68C22×D12—21no—
69C22×D12—21no—
70C22×D12—21no—
71C22×D12—21no—
72C22×D12—21no—
73C22×D12—21no—
74C22×D12—21no—
75C22×D12—21no—
76C22×D12C2×C412yes—
77C22×D12D412yes—
78C22×D12D412yes—
79C2×C3×M16—21no—
80C2×C3×M16—21no—
81C2×C3×M16—21no—
82C2×C3×M16—21no—
83C2×C3×M16—21no—
84C2×C3×M16D412yes—
85C22×C3×C8—21no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4D412yes—
92#949—28no—
93#949—28no—
94#949—28no—
95#949—28no—
96C2×#215—24no—
97C2×#215—24no—
98C2×#215—24no—
99C2×#213—24no—
100C2×#213—24no—
101C2×#213—24no—
102C2×#208—21no—
103C2×#208—21no—
104C2×#208—21no—
105C2×#208—21no—
106C2×#208—21no—
107C2×#208—21no—
108C2×#208—21no—
109C2×#208—21no—
110C2×#208C2×C412yes—
111C2×#208D412yes—
112C2×#208D412yes—
113C2×#208D412yes—
114C22×C3⋊C8—21no—
115C22×C3⋊C8—21no—
116C22×C3⋊C8—21no—
117C22×C3⋊C8—21no—
118C22×C3⋊C8—21no—
119C22×C3⋊C8—21no—
120C22×C3⋊C8—21no—
121C22×C3⋊C8—21no—
122C22×C3⋊C8D412yes—
123C3×#103—24no—
124C3×#102—24no—
125#830—28no—
126#823—28no—
127#809—28no—
128C22×#41C2×D311yescharacteristic
129C23×D4—31no—
130C2×AGL(1,ℤ/8)—34no—
131C2×AGL(1,ℤ/8)—62no—
132C2×AGL(1,ℤ/8)—62no—
133C2×AGL(1,ℤ/8)—62no—
134C2×AGL(1,ℤ/8)—62no—
135C2×AGL(1,ℤ/8)—62no—
136C22×SD16—61no—
137C22×D8—61no—
138C22×M16—31no—
139C22×M16—31no—
140C22×M16C2×D311yescharacteristic
141C23×C8—31no—
142C22×C4⋊C4C2×D311yescharacteristic
143#417—22no—
144#417—22no—
145C2×#103—21no—
146C2×#102—21no—
147C2×#102—62no—
148C2×#102—62no—
149C2×#102—62no—
150C2×#100—62no—
151C2×#100—62no—
152C2×#100—62no—
153#408—62no—
154#408—62no—
155C2×C22⋊C8—62no—
156#343—62no—
157#341—62no—
158C24×C3—21no—
159C24×C3#4111yescharacteristic
160C23×D3—22no—
161C23×D3—22no—
162C23×D3—22no—
163C23×D3—41no—
164C23×D3—41no—
165C23×D3—41no—
166C23×D3—41no—
167C23×D3—82no—
168C23×D3—82no—
169C3×#41—22no—
170C3×#41—22no—
171C3×#41—22no—
172C3×#41—22no—
173C3×#41—22no—
174C3×#41—22no—
175C3×#41—22no—
176C3×#41—22no—
177C3×#41—41no—
178C3×#41—41no—
179C3×#41—41no—
180C3×#41—41no—
181C3×#41—41no—
182C3×#41—41no—
183C3×#41—41no—
184C3×#41—41no—
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8C22⋊C412yes—
191C2×C3×D4—22no—
192C2×C3×D4—22no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—41no—
199C2×C3×D4—41no—
200C2×C3×D4—41no—
201C2×C3×D4—41no—
202C2×C3×D4C22⋊C412yes—
203C22×C3×C4—21no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—41no—
208C22×C3×C4—41no—
209C22×C3×C4—41no—
210C22×C3×C4—41no—
211C22×C3×C4—41no—
212C22×C3×C4—41no—
213C22×C3×C4—82no—
214C22×C3×C4C22×C411yescharacteristic
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4#4111yescharacteristic
226C22×C3×C4#4111yescharacteristic
227C22×C3×C4#4111yescharacteristic
228C2×D12—22no—
229C2×D12—22no—
230C2×D12—22no—
231C2×D12—22no—
232C2×D12—22no—
233C2×D12—22no—
234C2×D12—22no—
235C2×D12—22no—
236C2×D12—22no—
237C2×D12—22no—
238C2×D12—22no—
239C2×D12—22no—
240C2×D12—22no—
241C2×D12—22no—
242C2×D12—22no—
243C2×D12—41no—
244C2×D12—41no—
245C2×D12—41no—
246C2×D12—41no—
247C2×D12—41no—
248C2×D12—41no—
249C2×D12—41no—
250C2×D12—41no—
251C2×D12—41no—
252C2×D12—41no—
253C2×D12—41no—
254C2×D12—41no—
255C2×D12C22⋊C414yes—
256C3×M16—22no—
257C3×M16—22no—
258C3×M16—41no—
259C3×M16—41no—
260C2×C3×C8—22no—
261C2×C3×C8—41no—
262C2×C3×C8—41no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—22no—
265C3×C4⋊C4—41no—
266C3×C4⋊C4—41no—
267#215—216no—
268#213—216no—
269#208—22no—
270#208—22no—
271#208—22no—
272#208—22no—
273#208—22no—
274#208—41no—
275#208—41no—
276#208C22⋊C414yes—
277C2×C3⋊C8—22no—
278C2×C3⋊C8—22no—
279C2×C3⋊C8—22no—
280C2×C3⋊C8—22no—
281C2×C3⋊C8—22no—
282C2×C3⋊C8—22no—
283C2×C3⋊C8—22no—
284C2×C3⋊C8—41no—
285C2×C3⋊C8—41no—
286C2×C3⋊C8—41no—
287C2×C3⋊C8—41no—
288C2×C3⋊C8—41no—
289C2×C3⋊C8—41no—
290C25—61no—
291C2×#41—21no—
292C2×#41—21no—
293C2×#41—21no—
294C2×#41—21no—
295C2×#41—21no—
296C2×#41—21no—
297C2×#41—21no—
298C2×#41—21no—
299C2×#41—21no—
300C2×#41—21no—
301C2×#41C4×D312yes—
302C2×#41D1212yes—
303C22×Q8#6711yescharacteristic
304C22×D4—21no—
305C22×D4—32no—
306C22×D4—32no—
307C22×D4—32no—
308C22×D4—61no—
309C22×D4—61no—
310C22×D4—61no—
311C22×D4—61no—
312C22×D4—61no—
313C22×D4—61no—
314C22×D4—61no—
315C22×D4—61no—
316C22×D4—61no—
317C22×D4—61no—
318C22×D4—61no—
319C22×D4#6711yescharacteristic
320C23×C4—21no—
321C23×C4—21no—
322C23×C4C22×D311yescharacteristic
323AGL(1,ℤ/8)—68no—
324AGL(1,ℤ/8)—68no—
325AGL(1,ℤ/8)—68no—
326AGL(1,ℤ/8)—68no—
327C2×SD16—64no—
328C2×SD16—64no—
329C2×SD16—64no—
330C2×D8—64no—
331C2×D8—64no—
332C2×D8—64no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—32no—
339C2×M16—32no—
340C2×M16—32no—
341C2×M16—32no—
342C2×M16—61no—
343C2×M16—61no—
344C2×M16—61no—
345C2×M16—61no—
346C2×M16—61no—
347C2×M16—61no—
348C2×M16—61no—
349C2×M16—61no—
350C2×M16#6712yes—
351C22×C8—21no—
352C22×C8—32no—
353C22×C8—61no—
354C22×C8—61no—
355C22×C8—61no—
356C22×C8—61no—
357C22×C8—61no—
358C22×C8—61no—
359C22×C8—61no—
360C22×C8—61no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4#6712yes—
367#103—24no—
368#102—24no—
369#102—68no—
370#100—68no—
371C22⋊C8—68no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3C4×D411yescharacteristic
380C23×C3#12111yescharacteristic
381C23×C3#12111yescharacteristic
382C23×C3#12111yescharacteristic
383C23×C3#12311yescharacteristic
384C23×C3#12311yescharacteristic
385C23×C3#12411yescharacteristic
386C22×D3—24no—
387C22×D3—42no—
388C22×D3—42no—
389C22×D3—42no—
390C22×D3—42no—
391C22×D3—42no—
392C22×D3—42no—
393C22×D3—84no—
394C22×D3—84no—
395C22×D3—82no—
396C22×D3—82no—
397C22×D3—82no—
398C22×D3—82no—
399C22×D3—84no—
400C22×D3—84no—
401C22×D3—82no—
402C22×D3—82no—
403C3×Q8—22no—
404C3×Q8—22no—
405C3×Q8—41no—
406C3×Q8—41no—
407C3×D4—22no—
408C3×D4—22no—
409C3×D4—42no—
410C3×D4—42no—
411C3×D4—42no—
412C3×D4—42no—
413C3×D4—41no—
414C3×D4—41no—
415C2×C3×C4—22no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—82no—
424C2×C3×C4—82no—
425C2×C3×C4—82no—
426C2×C3×C4C2×C22⋊C411yescharacteristic
427C2×C3×C4C2×C22⋊C411yescharacteristic
428C2×C3×C4C2×C22⋊C411yescharacteristic
429C2×C3×C4C4×D411yescharacteristic
430C2×C3×C4C4×D411yescharacteristic
431C2×C3×C4C4×D411yescharacteristic
432C2×C3×C4#12011yescharacteristic
433C2×C3×C4#12011yescharacteristic
434C2×C3×C4#12011yescharacteristic
435C2×C3×C4#12011yescharacteristic
436C2×C3×C4#12011yescharacteristic
437C2×C3×C4#12011yescharacteristic
438C2×C3×C4#12011yescharacteristic
439C2×C3×C4#12011yescharacteristic
440C2×C3×C4#12111yescharacteristic
441C2×C3×C4#12111yescharacteristic
442C2×C3×C4#12111yescharacteristic
443C2×C3×C4#12111yescharacteristic
444C2×C3×C4#12111yescharacteristic
445C2×C3×C4#12111yescharacteristic
446C2×C3×C4#12111yescharacteristic
447C2×C3×C4#12111yescharacteristic
448C2×C3×C4#12111yescharacteristic
449C2×C3×C4#12311yescharacteristic
450C2×C3×C4#12311yescharacteristic
451C2×C3×C4#12411yescharacteristic
452C2×C3×C4#12711yescharacteristic
453C2×C3×C4#12711yescharacteristic
454D12—24no—
455D12—24no—
456D12—42no—
457D12—42no—
458D12—42no—
459D12—42no—
460D12—42no—
461D12—42no—
462C3×C8—42no—
463C3⋊C8—24no—
464C3⋊C8—42no—
465C3⋊C8—42no—
466C24—21no—
467C24—62no—
468C24—62no—
469C24—62no—
470C24—121no—
471C24—121no—
472C24—121no—
473C24—121no—
474C24—242no—
475C24—242no—
476C24#23711yescharacteristic
477#41—22no—
478#41—22no—
479#41—22no—
480#41—22no—
481#41—22no—
482#41—22no—
483#41—22no—
484#41—22no—
485#41—41no—
486#41—41no—
487#41—41no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8(C2×D3)⋊C412yes—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—34no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—41no—
511C2×D4—62no—
512C2×D4—62no—
513C2×D4—62no—
514C2×D4—62no—
515C2×D4—62no—
516C2×D4—62no—
517C2×D4—62no—
518C2×D4—62no—
519C2×D4—62no—
520C2×D4—62no—
521C2×D4—62no—
522C2×D4—62no—
523C2×D4—62no—
524C2×D4—62no—
525C2×D4—62no—
526C2×D4—121no—
527C2×D4—121no—
528C2×D4—121no—
529C2×D4—121no—
530C2×D4—121no—
531C2×D4—121no—
532C2×D4—121no—
533C2×D4—121no—
534C2×D4—121no—
535C2×D4—121no—
536C2×D4—121no—
537C2×D4—121no—
538C2×D4(C2×D3)⋊C412yes—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—82no—
550C22×C4C2×C4×D311yescharacteristic
551C22×C4C2×D1211yescharacteristic
552C22×C4#23511yescharacteristic
553C22×C4#23511yescharacteristic
554C22×C4D3×D411yescharacteristic
555C22×C4D3×D411yescharacteristic
556C22×C4D3×D411yescharacteristic
557C22×C4D3×D411yescharacteristic
558C22×C4D3×D411yescharacteristic
559C22×C4D3×D411yescharacteristic
560C22×C4#23711yescharacteristic
561C22×C4C2×#6711yescharacteristic
562C22×C4C2×#6711yescharacteristic
563C22×C4C2×#6711yescharacteristic
564SD16—616no—
565D8—616no—
566M16—22no—
567M16—22no—
568M16—34no—
569M16—41no—
570M16—41no—
571M16—62no—
572M16—62no—
573M16—62no—
574M16—62no—
575M16—62no—
576M16—121no—
577M16—121no—
578C2×C8—22no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—62no—
582C2×C8—62no—
583C2×C8—62no—
584C2×C8—62no—
585C2×C8—62no—
586C2×C8—62no—
587C2×C8—62no—
588C2×C8—121no—
589C2×C8—121no—
590C2×C8—121no—
591C2×C8—121no—
592C2×C8—121no—
593C2×C8—121no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—44no—
607C22×C3—42no—
608C22×C3—82no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3#38611yescharacteristic
612C22×C3#38611yescharacteristic
613C22×C3#39011yescharacteristic
614C22×C3#39211yescharacteristic
615C22×C3#39411yescharacteristic
616C22×C3#39411yescharacteristic
617C22×C3#39411yescharacteristic
618C22×C3#47112yes—
619C22×C3#47212yes—
620C2×D3—44no—
621C2×D3—84no—
622C2×D3—84no—
623C2×D3—84no—
624C2×D3—84no—
625C2×D3—84no—
626C2×D3—82no—
627C2×D3—82no—
628C2×D3—84no—
629C3×C4—42no—
630C3×C4—82no—
631C3×C4#37911yescharacteristic
632C3×C4#38611yescharacteristic
633C3×C4#38611yescharacteristic
634C3×C4#39011yescharacteristic
635C3×C4#39211yescharacteristic
636C3×C4#39211yescharacteristic
637C3×C4#39211yescharacteristic
638C3×C4#39411yescharacteristic
639C23—22no—
640C23—22no—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—41no—
645C23—41no—
646C23—64no—
647C23—122no—
648C23—122no—
649C23—122no—
650C23—122no—
651C23—122no—
652C23—122no—
653C23—244no—
654C23—242no—
655C23—244no—
656C23—242no—
657C23—244no—
658C23—242no—
659C23—244no—
660C23—242no—
661C23—242no—
662C23—242no—
663C23#67⋊C411yescharacteristic
664C23#88311yescharacteristic
665C23#88511yescharacteristic
666C23#88611yescharacteristic
667C23#93811yescharacteristic
668C23#93911yescharacteristic
669C23#93911yescharacteristic
670Q8—22no—
671Q8—22no—
672Q8—41no—
673Q8—41no—
674D4—22no—
675D4—22no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—41no—
681D4—41no—
682D4—64no—
683D4—64no—
684D4—122no—
685D4—122no—
686D4—122no—
687D4—122no—
688D4—122no—
689D4—122no—
690C2×C4—22no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4D3×C22⋊C411yescharacteristic
702C2×C4D3×C22⋊C411yescharacteristic
703C2×C4#67⋊C411yescharacteristic
704C2×C4#88211yescharacteristic
705C2×C4#88211yescharacteristic
706C2×C4#88211yescharacteristic
707C2×C4#88311yescharacteristic
708C2×C4#88411yescharacteristic
709C2×C4#88411yescharacteristic
710C2×C4#88411yescharacteristic
711C2×C4#88411yescharacteristic
712C2×C4#88511yescharacteristic
713C2×C4C2×(C2×D3)⋊C411yescharacteristic
714C2×C4C4×#6711yescharacteristic
715C2×C4C4×#6711yescharacteristic
716C2×C4#92911yescharacteristic
717C2×C4#93011yescharacteristic
718C2×C4#93011yescharacteristic
719C2×C4#93711yescharacteristic
720C2×C4#93711yescharacteristic
721C2×C4#93711yescharacteristic
722C2×C4#93711yescharacteristic
723C2×C4#93811yescharacteristic
724C2×C4#93911yescharacteristic
725C2×C4#93911yescharacteristic
726C2×C4#94011yescharacteristic
727C2×C4#94011yescharacteristic
728C2×C4#95311yescharacteristic
729C8—42no—
730C8—64no—
731C8—122no—
732C8—122no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—82no—
738C2×C3#143811yescharacteristic
739C2×C3#190712yes—
740C2×C3#201811yescharacteristic
741C2×C3#201911yescharacteristic
742C2×C3#205112yes—
743D3—84no—
744C22—22no—
745C22—22no—
746C22—21no—
747C22—21no—
748C22—22no—
749C22—22no—
750C22—21no—
751C22—21no—
752C22—42no—
753C22—44no—
754C22—81no—
755C22—82no—
756C22—81no—
757C22—124no—
758C22—244no—
759C22—244no—
760C22—244no—
761C22—244no—
762C22—244no—
763C22—242no—
764C22—244no—
765C22—242no—
766C22#495611yescharacteristic
767C22#495711yescharacteristic
768C22#495811yescharacteristic
769C22#495911yescharacteristic
770C22#496111yescharacteristic
771C22#496111yescharacteristic
772C22#519912yes—
773C22#520312yes—
774C22#522311yescharacteristic
775C4—42no—
776C4—82no—
777C4#495511yescharacteristic
778C4#495611yescharacteristic
779C4#495711yescharacteristic
780C4#495911yescharacteristic
781C4#496011yescharacteristic
782C4#496011yescharacteristic
783C4#521311yescharacteristic
784C4#522311yescharacteristic
785C3#1102011yescharacteristic, complemented, Sylow
786C2—21no—
787C2—21no—
788C2—21no—
789C2—21no—
790C2—82no—
791C2—244no—
792C2#7030312yes—
793C2#7030712yes—
794C2#7155011yescharacteristic
795C2#7209511yescharacteristic
796C2#7210711yescharacteristic
subgroupG/H
centerC23#939
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#417C2
socleC23×C3#121
prime radicalC22×#949C2
cosocleC23×C3×C4C23
hypercenterC2×#417D3
hypocenterC3#11020
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×C3×#417C2semidirect
3. C2×#5234C2semidirect
4. C22×#823C2semidirect
5. C22×#809C2semidirect
6. C2×#4558C2semidirect
7. C2×#4530C2semidirect
18. C2×#949C4semidirect
40. C2×#417D3semidirect
785. C3#11020semidirect

Maximal subgroups

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

subgroupindex
C22×#9492
C2×C3×#4172
C2×#52342
C22×#8232
C22×#8092
C2×#45582
C2×#45302
#110203