Finite Group Databasebeta

← #10846139

Subgroups — #10846139

Order 768.

1120 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5171C211yesmaximal, characteristic, complemented
2C2×#5163C211yesmaximal, characteristic, complemented
3#82777C211yesmaximal, characteristic, complemented
4C2×#5049C211yesmaximal, characteristic, complemented
5#82669C211yesmaximal, characteristic
6C2×#4728C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8#71682C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#70220C211yesmaximal, characteristic, complemented
11#70206C211yesmaximal, characteristic, complemented
12#70160C211yesmaximal, characteristic, complemented
13#69935C211yesmaximal, characteristic, complemented
14#68883C211yesmaximal, characteristic, complemented
15#68797C211yesmaximal, characteristic, complemented
16#25402—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C2×#940—21no—
24C2×#940C2211yescharacteristic
25C2×#938C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×C4×#67C2211yescharacteristic
28C22×#208C2211yescharacteristic
29C22×D3×C8C2211yescharacteristic
30C2×#895C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×C22⋊C8C2211yescharacteristic
34C2×#835C2211yescharacteristic
35#5223—21no—
36C2×#832C2211yescharacteristic
37C2×#832C2211yescharacteristic
38#5212C2211yescharacteristic
39#5171—24no—
40#5163—24no—
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#817C2211yescharacteristic
45C2×#815C2211yescharacteristic
46C2×Dic3⋊C8C2211yescharacteristic
47#5049—24no—
48#4990—21no—
49#4987C2211yescharacteristic
50#4982—21no—
51#4977C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4961—21no—
56#4960—21no—
57#4957—21no—
58#4945—21no—
59#4728—24no—
60C3×#340C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#465—31no—
66C2×#460—31no—
67C2×#435—31no—
68#2541—31no—
69#2536—31no—
70#2034—31no—
71#2033—31no—
72#2000—31no—
73#2000D311yescharacteristic, complemented
74#1961—31no—
75#1949—31no—
76#1895—31no—
77#1893—31no—
78#1763—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C22×#67—21no—
87C22×#67D411yescharacteristic
88C22×D12—21no—
89C22×D12C2311yescharacteristic
90C22×C4×D3C2311yescharacteristic
91C2×C3×SD16—22no—
92C2×C3×SD16—22no—
93C2×C3×SD16—41no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C3×C22⋊Q8—22no—
97C3×C22⋊Q8—41no—
98C3×#121—22no—
99C3×#121—41no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217D411yescharacteristic
108#946—22no—
109#946—41no—
110Q8×Dic3—22no—
111Q8×Dic3—22no—
112C2×#215—22no—
113C2×#215—22no—
114C2×#215—41no—
115#940—22no—
116#940—22no—
117#940—44no—
118#938—22no—
119#938—41no—
120#930—22no—
121#930—41no—
122C4×#67—22no—
123C4×#67—22no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4D411yescharacteristic
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4D411yescharacteristic
135C2×C4×Dic3—21no—
136C2×C4×Dic3—21no—
137C2×C4×Dic3C2311yescharacteristic
138C2×#208—22no—
139C2×#208—22no—
140C2×#208—41no—
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×D3×C8—22no—
144C2×D3×C8—22no—
145C2×D3×C8—41no—
146#895—22no—
147#895—41no—
148C3×#103—22no—
149C3×#102—41no—
150C3×C22⋊C8—22no—
151#835D414yescomplemented
152#832—22no—
153#832—22no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#821—22no—
160#821—41no—
161(C2×D3)⋊C8—22no—
162#817—22no—
163#815—22no—
164Dic3⋊C8D414yescomplemented
165#809—22no—
166#807—22no—
167C22×SD16—31no—
168C22×SD16C2×D311yescharacteristic
169C22×M16—31no—
170C23×C8—31no—
171C2×#127—31no—
172C2×#127—61no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8C2×D311yescharacteristic
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121C2×D311yescharacteristic
179C2×C4×Q8—31no—
180C2×C4×D4—31no—
181#468—64no—
182#465—64no—
183#460—64no—
184#435—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×C4⋊C8—31no—
188C2×#103—31no—
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102C2×D311yescharacteristic
196C2×C22⋊C8—31no—
197C2×C22⋊C8C2×D311yescharacteristic
198C2×#97—31no—
199#398—61no—
200#394—61no—
201#392—61no—
202#392—61no—
203#390—61no—
204#388—61no—
205#388—61no—
206#382—31no—
207#380—31no—
208#380—31no—
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340C2×D311yescharacteristic
214C24×C3—21no—
215C24×C3C2×D411yescharacteristic
216C23×D3—21no—
217C23×D3C2×D411yescharacteristic
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8C2×D412yes—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—81no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2411yescharacteristic
244C2×#67—22no—
245C2×#67—22no—
246C2×#67—41no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—42no—
255C2×#67—81no—
256C2×#67—81no—
257C2×#67—81no—
258C2×#67—81no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—42no—
272C2×D12—42no—
273C2×D12—81no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C3×SD16—44no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8C2×D412yes—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—42no—
291C3×C4⋊C4#4112yes—
292C3×C22⋊C4—42no—
293C3×C22⋊C4—42no—
294#217—22no—
295#217—42no—
296#217—42no—
297#215—44no—
298(C2×D3)⋊C4—22no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—42no—
309C4⋊Dic3C2×D412yes—
310Dic3⋊C4—22no—
311Dic3⋊C4—42no—
312C4×Dic3—42no—
313C4×Dic3—42no—
314C4×Dic3C2×D412yes—
315C4×Dic3#4112yes—
316#208—44no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8C2×D412yes—
322C2×C3⋊C8C2×D412yes—
323D3×C8—44no—
324C22×Q8C22×D311yescharacteristic
325C22×D4—21no—
326C22×D4—31no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4—61no—
332C22×D4—61no—
333C22×D4C22×D311yescharacteristic
334C23×C4—31no—
335C23×C4C22×D311yescharacteristic
336C2×SD16—22no—
337C2×SD16—22no—
338C2×SD16—41no—
339C2×SD16—62no—
340C2×SD16—62no—
341C2×SD16—121no—
342C2×M16—62no—
343C2×M16—62no—
344C2×M16—121no—
345C22×C8—31no—
346C22×C8—31no—
347C22×C8—62no—
348C22×C8—62no—
349C22×C8—121no—
350C22×C8C22×D311yescharacteristic
351C22×C8C22×D311yescharacteristic
352#127—62no—
353#127—62no—
354#127—124no—
355C22⋊Q8—22no—
356C22⋊Q8—41no—
357C22⋊Q8—62no—
358C22⋊Q8—121no—
359#121—22no—
360#121—41no—
361#121—62no—
362#121—62no—
363#121—62no—
364#121—121no—
365#121—121no—
366#121—121no—
367C4×Q8—62no—
368C4×Q8—62no—
369C4×D4—62no—
370C4×D4—62no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C42—31no—
391C2×C42—61no—
392C2×C42—61no—
393#107—62no—
394#106—62no—
395C4⋊C8—34no—
396#103—22no—
397#103—34no—
398#102—41no—
399#102—62no—
400#102—62no—
401#102—62no—
402#102—62no—
403#102—121no—
404C22⋊C8—22no—
405C22⋊C8—62no—
406#97—62no—
407#95—61no—
408#95—61no—
409#95—61no—
410#95—61no—
411#95—61no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3C22×D411yescharacteristic
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3AGL(1,ℤ/8)12yes—
441C3×Q8—22no—
442C3×Q8—22no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—41no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—84no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
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×C4C22×D411yescharacteristic
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4H(5,𝔽2)11yescharacteristic
471C2×C3×C4H(5,𝔽2)11yescharacteristic
472#67—44no—
473#67—84no—
474#67—84no—
475#67—84no—
476#67—84no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—21no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3#12112yes—
494C2×Dic3#12112yes—
495D12—41no—
496D12—41no—
497D12—41no—
498D12—41no—
499D12—84no—
500C4×D3—41no—
501C4×D3—41no—
502C4×D3—41no—
503C4×D3—41no—
504C3×C8—22no—
505C3×C8—41no—
506C3⋊C8—22no—
507C3⋊C8—22no—
508C24—21no—
509C24—31no—
510C24—61no—
511C24D3×D411yescharacteristic
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8D3×D412yes—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—62no—
527C2×D4—62no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—81no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—121no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4—122no—
546C2×D4—241no—
547C2×D4—241no—
548C2×D4—241no—
549C2×D4—241no—
550C2×D4—241no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
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×C4D3×D411yescharacteristic
573C22×C4C23×D311yescharacteristic
574SD16—44no—
575SD16—124no—
576M16—124no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—32no—
583C2×C8—32no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—61no—
588C2×C8—124no—
589C2×C8D3×D412yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—32no—
594C4⋊C4—42no—
595C4⋊C4—62no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—122no—
602C4⋊C4—122no—
603C4⋊C4#23712yes—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—62no—
607C22⋊C4—62no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—32no—
615C42—32no—
616C42—122no—
617C42—122no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3C2×#12111yescharacteristic
633C22×C3D4211yescharacteristic
634C22×C3#54611yescharacteristic
635C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
636C22×C3#57511yescharacteristic
637C22×C3#57711yescharacteristic
638C22×C3#57711yescharacteristic
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—22no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—81no—
647C2×D3—81no—
648C2×D3—81no—
649C2×D3—81no—
650C2×D3—81no—
651C2×D3—81no—
652C2×D3—81no—
653C3×C4—41no—
654C3×C4—42no—
655C3×C4—42no—
656C3×C4—81no—
657C3×C4#53211yescharacteristic
658C3×C4#54011yescharacteristic
659C3×C4D4211yescharacteristic
660C3×C4#55011yescharacteristic
661Dic3—22no—
662Dic3—22no—
663Dic3—41no—
664Dic3—42no—
665Dic3—81no—
666Dic3—81no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—32no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23—121no—
695C23C2×D3×D411yescharacteristic
696Q8—22no—
697Q8—22no—
698Q8—41no—
699Q8—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—84no—
705D4—124no—
706D4—121no—
707D4—121no—
708D4—121no—
709D4—121no—
710D4—244no—
711D4—244no—
712D4—244no—
713D4—244no—
714D4—244no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—32no—
721C2×C4—32no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—62no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
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—121no—
753C2×C4C2×D3×D411yescharacteristic
754C2×C4C2×D3×D411yescharacteristic
755C2×C4C2×#23711yescharacteristic
756C2×C4#100411yescharacteristic
757C2×C4#100411yescharacteristic
758C2×C4D3×#4111yescharacteristic
759C8—22no—
760C8—41no—
761C8—62no—
762C8—62no—
763C2×C3—81no—
764C2×C3—161no—
765C2×C3#242811yescharacteristic
766C2×C3#305511yescharacteristic
767C2×C3#305711yescharacteristic
768C2×C3#326511yescharacteristic
769C2×C3#327111yescharacteristic
770C2×C3#331011yescharacteristic
771C2×C3#331711yescharacteristic
772D3—42no—
773D3—161no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—62no—
782C22—62no—
783C22—62no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22—241no—
801C22—241no—
802C22#559011yescharacteristic
803C22#559111yescharacteristic
804C22D3×#12111yescharacteristic
805C22#576211yescharacteristic
806C22#577011yescharacteristic
807C22D3×AGL(1,ℤ/8)11yescharacteristic
808C22#577711yescharacteristic
809C4—42no—
810C4—41no—
811C4—42no—
812C4—62no—
813C4—62no—
814C4—81no—
815C4—121no—
816C4—122no—
817C4—241no—
818C4—241no—
819C4#559011yescharacteristic
820C4#559611yescharacteristic
821C4#561511yescharacteristic
822C4#571811yescharacteristic
823C3#2540211yescharacteristic, complemented, Sylow
824C2—81no—
825C2—122no—
826C2—161no—
827C2—481no—
828C2#7667111yescharacteristic
829C2#8006511yescharacteristic
830C2#8012111yescharacteristic
831C2#8016111yescharacteristic
832C2#8025711yescharacteristic
833C2#8065911yescharacteristic
834C2#8080511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radical#82669C2
hypercenter#2000D3
hypocenterC3#25402
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#5171C2semidirect
2. C2×#5163C2semidirect
3. #82777C2semidirect
4. C2×#5049C2semidirect
6. C2×#4728C2semidirect
7. C3×#2000C2semidirect
8. #71682C2semidirect
9. #70272C2semidirect
10. #70220C2semidirect
11. #70206C2semidirect
12. #70160C2semidirect
13. #69935C2semidirect
14. #68883C2semidirect
15. #68797C2semidirect
73. #2000D3semidirect
151. #835D4semidirect
164. Dic3⋊C8D4semidirect
823. C3#25402semidirect

Maximal subgroups

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

subgroupindex
C2×#51712
C2×#51632
#827772
C2×#50492
#826692
C2×#47282
C3×#20002
#716822
#702722
#702202
#702062
#701602
#699352
#688832
#687972
#254023