Finite Group Databasebeta

← #10846146

Subgroups — #10846146

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
1#82499C211yesmaximal, characteristic, complemented
2C2×#5027C211yesmaximal, characteristic, complemented
3C2×#4812C211yesmaximal, characteristic, complemented
4C2×#4807C211yesmaximal, characteristic, complemented
5C2×#4706C211yesmaximal, characteristic, complemented
6#73799C211yesmaximal, characteristic
7C3×#1763C211yesmaximal, characteristic, complemented
8#70272C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#69823C211yesmaximal, characteristic, complemented
11#69468C211yesmaximal, characteristic, complemented
12#68885C211yesmaximal, characteristic, complemented
13#68883C211yesmaximal, characteristic, complemented
14#68823C211yesmaximal, characteristic, complemented
15#68822C211yesmaximal, characteristic, complemented
16#25402—31nomaximal, Sylow
17C2×C3×C4×Q8C2211yescharacteristic
18C2×#946C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C22×ΓL(1,𝔽25)C2211yescharacteristic
23C22×D3×C8C2211yescharacteristic
24C2×#895C2211yescharacteristic
25C2×#895C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#895C2211yescharacteristic
28C2×#874—21no—
29C2×#874C2211yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#97C2211yescharacteristic
34C3×C4×C4⋊C4C2211yescharacteristic
35C2×#821C2211yescharacteristic
36C2×#821C2211yescharacteristic
37C2×#821C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41#5027—24no—
42#4991—21no—
43#4987C2211yescharacteristic
44#4987C2211yescharacteristic
45#4981—21no—
46C2×#809C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#808C2211yescharacteristic
49C2×#807C2211yescharacteristic
50#4940—21no—
51#4940—21no—
52#4939—21no—
53#4936C2211yescharacteristic
54C2×C4⋊(C3⋊C8)C2211yescharacteristic
55#4812—24no—
56#4807—24no—
57#4706—24no—
58#4671—21no—
59#4671—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
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#2000—31no—
74#1961—31no—
75#1949—31no—
76#1895—31no—
77#1893—31no—
78#1763D311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×D12—21no—
81C22×D12—21no—
82C22×D12—21no—
83C22×D12—21no—
84C22×D12—21no—
85C22×D12—21no—
86C22×D12D411yescharacteristic
87C22×D12C2311yescharacteristic
88C22×D12C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C22×C4×D3C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C4×Q8—22no—
94C3×C4×Q8—22no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C42—21no—
100C2×C3×C42—21no—
101C2×C3×C42C2311yescharacteristic
102#946—22no—
103#946—22no—
104#946—41no—
105#946—41no—
106C2×#215—22no—
107C2×#215—22no—
108C2×#215—22no—
109C2×#215—22no—
110C2×#215—41no—
111C2×#215—41no—
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)⋊C4D411yescharacteristic
121C2×(C2×D3)⋊C4D411yescharacteristic
122C2×C4⋊Dic3D411yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C22×C3⋊C8C2311yescharacteristic
128C22×C3⋊C8C2311yescharacteristic
129C2×ΓL(1,𝔽25)—22no—
130C2×ΓL(1,𝔽25)—22no—
131C2×ΓL(1,𝔽25)—41no—
132C2×D3×C8—22no—
133C2×D3×C8—22no—
134C2×D3×C8—41no—
135#895—22no—
136#895—22no—
137#895—22no—
138#895—22no—
139#895—41no—
140#895—41no—
141#895—41no—
142#895—41no—
143#874—22no—
144#874—22no—
145#874—44no—
146C4×D12—22no—
147C4×D12—22no—
148C3×#103—22no—
149C3×#103D414yescomplemented
150C3×#97—22no—
151C3×#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#821—22no—
157#821—22no—
158#821—41no—
159#821—41no—
160(C2×D3)⋊C8—22no—
161(C2×D3)⋊C8—22no—
162#809—22no—
163#809—22no—
164#808—22no—
165#807—22no—
166C4⋊(C3⋊C8)D414yescomplemented
167C22×SD16—31no—
168C22×SD16—31no—
169C22×M16—31no—
170C23×C8—31no—
171C2×#127—31no—
172C2×#127—61no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121—31no—
179C2×C4×Q8C2×D311yescharacteristic
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×#103C2×D311yescharacteristic
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×#97C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
210#340—31no—
211#340—31no—
212#340C2×D311yescharacteristic
213#340C2×D311yescharacteristic
214C23×D3—21no—
215C23×D3—21no—
216C23×D3C2×D411yescharacteristic
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—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2411yescharacteristic
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3C2×D411yescharacteristic
234C22×Dic3C2×D411yescharacteristic
235C2×D12—22no—
236C2×D12—22no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
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—41no—
250C2×D12—42no—
251C2×D12—42no—
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—42no—
261C2×D12—42no—
262C2×D12—81no—
263C2×D12—81no—
264C2×D12—81no—
265C2×D12—81no—
266C2×D12—81no—
267C2×D12—81no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8C2×D412yes—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—42no—
291C3×C4⋊C4C2×D412yes—
292C3×C4⋊C4#4112yes—
293C3×C42—42no—
294C3×C42—42no—
295C3×C42C2×D412yes—
296C3×C42#4112yes—
297#215—44no—
298#215—44no—
299(C2×D3)⋊C4—22no—
300(C2×D3)⋊C4—22no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—42no—
306(C2×D3)⋊C4—42no—
307(C2×D3)⋊C4—42no—
308(C2×D3)⋊C4—42no—
309C4⋊Dic3—22no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314Dic3⋊C4—42no—
315Dic3⋊C4—42no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8C2×D412yes—
321C2×C3⋊C8C2×D412yes—
322ΓL(1,𝔽25)—44no—
323D3×C8—44no—
324C22×Q8C22×D311yescharacteristic
325C22×D4—31no—
326C22×D4—31no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4—61no—
332C22×D4—61no—
333C22×D4—61no—
334C23×C4—31no—
335C23×C4—31no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—121no—
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—62no—
356C22⋊Q8—62no—
357C22⋊Q8—121no—
358C22⋊Q8—121no—
359#121—62no—
360#121—62no—
361#121—62no—
362#121—62no—
363#121—121no—
364#121—121no—
365#121—121no—
366#121—121no—
367C4×Q8—22no—
368C4×Q8—22no—
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—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C22⋊C4—31no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
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—21no—
391C2×C42—21no—
392C2×C42C22×D311yescharacteristic
393#107—62no—
394#106—62no—
395C4⋊C8—34no—
396#103—22no—
397#103D1214yescomplemented
398#102—62no—
399#102—62no—
400#102—62no—
401#102—62no—
402#102—121no—
403#102—121no—
404C22⋊C8—62no—
405C22⋊C8—62no—
406#97—22no—
407#95—21no—
408#95—61no—
409#95—61no—
410#95—61no—
411#95—61no—
412C23×C3C22×D411yescharacteristic
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
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—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
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#12112yes—
462C2×C3×C4#12112yes—
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C22×D411yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467C2×C3×C4H(5,𝔽2)11yescharacteristic
468C2×C3×C4H(5,𝔽2)11yescharacteristic
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481D12—44no—
482D12—41no—
483D12—41no—
484D12—41no—
485D12—41no—
486D12—41no—
487D12—41no—
488D12—41no—
489D12—41no—
490D12—84no—
491D12—84no—
492D12—84no—
493D12—84no—
494D12—84no—
495D12—84no—
496C4×D3—41no—
497C4×D3—41no—
498C4×D3—41no—
499C4×D3—41no—
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—31no—
509C24—31no—
510C24—61no—
511C24—61no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8C2×D1212yes—
518C2×D4—62no—
519C2×D4—62no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—121no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4—241no—
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—31no—
556C22×C4—31no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
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×C4D3×D411yescharacteristic
572C22×C4D3×D411yescharacteristic
573C22×C4C23×D311yescharacteristic
574SD16—124no—
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×C8C2×D1212yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—62no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—122no—
601C4⋊C4—122no—
602C4⋊C4C2×D1212yes—
603C4⋊C4#23512yes—
604C22⋊C4—62no—
605C22⋊C4—62no—
606C22⋊C4—122no—
607C22⋊C4—122no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—42no—
615C42—42no—
616C42#23512yes—
617C42D3×D412yes—
618C22×C3C2×#12111yescharacteristic
619C22×C3D4211yescharacteristic
620C22×C3#54611yescharacteristic
621C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
622C22×C3#57511yescharacteristic
623C22×C3#57711yescharacteristic
624C22×C3#57711yescharacteristic
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C2×D3—81no—
643C2×D3—81no—
644C2×D3—81no—
645C2×D3—81no—
646C2×D3—81no—
647C2×D3—81no—
648C2×D3—81no—
649C2×D3—81no—
650C2×D3—81no—
651C2×D3—81no—
652C2×D3—81no—
653C3×C4—22no—
654C3×C4—22no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4—81no—
659C3×C4#53211yescharacteristic
660C3×C4#54011yescharacteristic
661C3×C4D4211yescharacteristic
662C3×C4#55011yescharacteristic
663Dic3—41no—
664Dic3—41no—
665Dic3—81no—
666Dic3—81no—
667C23—32no—
668C23—61no—
669C23—61no—
670C23—61no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—121no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—121no—
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—124no—
701D4—121no—
702D4—121no—
703D4—121no—
704D4—121no—
705D4—121no—
706D4—121no—
707D4—121no—
708D4—121no—
709D4—244no—
710D4—244no—
711D4—244no—
712D4—244no—
713D4—244no—
714D4—244no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
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—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
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#88412yes—
752C2×C4#88412yes—
753C2×C4C22×D1211yescharacteristic
754C2×C4C2×#23511yescharacteristic
755C2×C4C2×#23511yescharacteristic
756C2×C4C2×D3×D411yescharacteristic
757C2×C4#100911yescharacteristic
758C2×C4#100911yescharacteristic
759C8—22no—
760C8—41no—
761C8—62no—
762C8—62no—
763C2×C3#242811yescharacteristic
764C2×C3#305511yescharacteristic
765C2×C3#305711yescharacteristic
766C2×C3#326511yescharacteristic
767C2×C3#327111yescharacteristic
768C2×C3#331011yescharacteristic
769C2×C3#331711yescharacteristic
770D3—42no—
771D3—81no—
772D3—161no—
773D3—161no—
774C22—62no—
775C22—62no—
776C22—62no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—241no—
789C22—241no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22—241no—
801C22—241no—
802C22C2×#88411yescharacteristic
803C22D4×D1211yescharacteristic
804C22#555011yescharacteristic
805C22D3×AGL(1,ℤ/8)11yescharacteristic
806C22#577711yescharacteristic
807C22#577811yescharacteristic
808C22#577811yescharacteristic
809C4—22no—
810C4—22no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—81no—
815C4—121no—
816C4—121no—
817C4—241no—
818C4—241no—
819C4#547711yescharacteristic
820C4#553511yescharacteristic
821C4D4×D1211yescharacteristic
822C4#555311yescharacteristic
823C3#2540211yescharacteristic, complemented, Sylow
824C2—122no—
825C2—241no—
826C2—481no—
827C2—481no—
828C2#7348711yescharacteristic
829C2#7888811yescharacteristic
830C2#7896311yescharacteristic
831C2#7979411yescharacteristic
832C2#7980011yescharacteristic
833C2#7984011yescharacteristic
834C2#7984411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1763C2
socleC23×C3C22×D4
prime radical#73799C2
hypercenter#1763D3
hypocenterC3#25402
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
1. #82499C2semidirect
2. C2×#5027C2semidirect
3. C2×#4812C2semidirect
4. C2×#4807C2semidirect
5. C2×#4706C2semidirect
7. C3×#1763C2semidirect
8. #70272C2semidirect
9. #70272C2semidirect
10. #69823C2semidirect
11. #69468C2semidirect
12. #68885C2semidirect
13. #68883C2semidirect
14. #68823C2semidirect
15. #68822C2semidirect
78. #1763D3semidirect
149. C3×#103D4semidirect
166. C4⋊(C3⋊C8)D4semidirect
397. #103D12semidirect
823. C3#25402semidirect

Maximal subgroups

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

subgroupindex
#824992
C2×#50272
C2×#48122
C2×#48072
C2×#47062
#737992
C3×#17632
#702722
#698232
#694682
#688852
#688832
#688232
#688222
#254023