Finite Group Databasebeta

← #10846144

Subgroups — #10846144

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×#4886C211yesmaximal, characteristic, complemented
2C2×#4864C211yesmaximal, characteristic, complemented
3C2×#4848C211yesmaximal, characteristic, complemented
4C2×#4836C211yesmaximal, characteristic, complemented
5#74240C211yesmaximal, characteristic, complemented
6#73799C211yesmaximal, characteristic
7C3×#1949C211yesmaximal, characteristic, complemented
8#70634C211yesmaximal, characteristic, complemented
9#70581C211yesmaximal, characteristic, complemented
10#69553C211yesmaximal, characteristic, complemented
11#69475C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68887C211yesmaximal, characteristic, complemented
14#68885C211yesmaximal, characteristic, complemented
15#68883C211yesmaximal, characteristic, complemented
16#25402—31nomaximal, Sylow
17C22×#204C2211yescharacteristic
18C22×#204C2211yescharacteristic
19C22×ΓL(1,𝔽25)C2211yescharacteristic
20C22×D3×C8C2211yescharacteristic
21C2×#897C2211yescharacteristic
22C2×#897C2211yescharacteristic
23C2×#895C2211yescharacteristic
24C2×#895C2211yescharacteristic
25C2×#895C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#874—21no—
28C2×#874C2211yescharacteristic
29C2×C4×D12C2211yescharacteristic
30C2×C4×Dic6C2211yescharacteristic
31C2×C3×#107C2211yescharacteristic
32C2×C3×#106C2211yescharacteristic
33C2×C3×C4⋊C8C2211yescharacteristic
34C3×#382C2211yescharacteristic
35C3×C4×C4⋊C4C2211yescharacteristic
36C2×#821C2211yescharacteristic
37C2×#821C2211yescharacteristic
38C2×(C2×D3)⋊C8C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40#4987C2211yescharacteristic
41#4987C2211yescharacteristic
42C2×#810C2211yescharacteristic
43C2×#810C2211yescharacteristic
44C2×#809C2211yescharacteristic
45C2×#809C2211yescharacteristic
46C2×#809C2211yescharacteristic
47C2×#809C2211yescharacteristic
48#4939—21no—
49C2×#803C2211yescharacteristic
50#4886—24no—
51#4864—24no—
52#4848—24no—
53#4836—24no—
54#4672—21no—
55#4671—21no—
56#4671—21no—
57#4670—21no—
58#4670—21no—
59#4661—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#1949D311yescharacteristic, complemented
76#1895—31no—
77#1893—31no—
78#1763—31no—
79C22×D12—21no—
80C22×D12—21no—
81C22×D12—21no—
82C22×D12—21no—
83C22×D12—21no—
84C22×D12—21no—
85C22×D12D411yescharacteristic
86C22×D12C2311yescharacteristic
87C22×D12C2311yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C22×Dic6C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C42—21no—
98C2×C3×C42C2311yescharacteristic
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—21no—
101C2×(C2×D3)⋊C4—21no—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4D411yescharacteristic
108C2×(C2×D3)⋊C4D411yescharacteristic
109C2×C4⋊Dic3—21no—
110C2×C4⋊Dic3—21no—
111C2×C4⋊Dic3D411yescharacteristic
112C2×C4⋊Dic3C2311yescharacteristic
113C2×Dic3⋊C4—21no—
114C2×C4×Dic3—21no—
115C22×C3⋊C8C2311yescharacteristic
116C22×C3⋊C8C2311yescharacteristic
117C2×#204—22no—
118C2×#204—22no—
119C2×#204—22no—
120C2×#204—22no—
121C2×#204—41no—
122C2×#204—41no—
123C2×ΓL(1,𝔽25)—22no—
124C2×ΓL(1,𝔽25)—22no—
125C2×ΓL(1,𝔽25)—41no—
126C2×D3×C8—22no—
127C2×D3×C8—22no—
128C2×D3×C8—41no—
129#897—22no—
130#897—22no—
131#897—41no—
132#897—41no—
133#895—22no—
134#895—22no—
135#895—22no—
136#895—22no—
137#895—41no—
138#895—41no—
139#895—41no—
140#895—41no—
141#874—22no—
142#874—22no—
143#874—44no—
144C4×D12—22no—
145C4×D12—22no—
146C4×Dic6—22no—
147C4×Dic6—22no—
148C3×#107—22no—
149C3×#106—22no—
150C3×C4⋊C8D414yescomplemented
151C3×#95—21no—
152C3×#95—21no—
153C3×#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#821—22no—
157#821—22no—
158(C2×D3)⋊C8—22no—
159(C2×D3)⋊C8—22no—
160#810—22no—
161#810D414yescomplemented
162#809—22no—
163#809—22no—
164#809—41no—
165#809—41no—
166#803—22no—
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×Q8—31no—
180C2×C4×D4—31no—
181#468—64no—
182#465—64no—
183#460—64no—
184#435—64no—
185C2×#107C2×D311yescharacteristic
186C2×#106C2×D311yescharacteristic
187C2×C4⋊C8C2×D311yescharacteristic
188C2×#103—31no—
189C2×#103—31no—
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×#97—31no—
199#398—61no—
200#394—61no—
201#392—61no—
202#392—61no—
203#390—61no—
204#388—61no—
205#388—61no—
206#382C2×D311yescharacteristic
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
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2411yescharacteristic
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3C2×D411yescharacteristic
228C22×Dic3C2×D411yescharacteristic
229C2×D12—22no—
230C2×D12—22no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—41no—
244C2×D12—42no—
245C2×D12—42no—
246C2×D12—42no—
247C2×D12—42no—
248C2×D12—42no—
249C2×D12—42no—
250C2×D12—42no—
251C2×D12—42no—
252C2×D12—42no—
253C2×D12—42no—
254C2×D12—42no—
255C2×D12—42no—
256C2×D12—81no—
257C2×D12—81no—
258C2×D12—81no—
259C2×D12—81no—
260C2×D12—81no—
261C2×D12—81no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
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—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6C2×D412yes—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8C2×D412yes—
285C2×C3×C8C2×D412yes—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4C2×D412yes—
293C3×C4⋊C4#4112yes—
294C3×C42—42no—
295C3×C42C2×D412yes—
296C3×C42#4112yes—
297(C2×D3)⋊C4—22no—
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—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—42no—
306(C2×D3)⋊C4—42no—
307C4⋊Dic3—22no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—42no—
311C4⋊Dic3—42no—
312Dic3⋊C4—42no—
313C4×Dic3—42no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8C2×D412yes—
320#204—44no—
321#204—44no—
322ΓL(1,𝔽25)—44no—
323D3×C8—44no—
324C22×Q8—31no—
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—62no—
368C4×Q8—62no—
369C4×D4—62no—
370C4×D4—62no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4C22×D311yescharacteristic
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—61no—
392C2×C42C22×D311yescharacteristic
393#107—22no—
394#106—22no—
395C4⋊C8D1214yescomplemented
396#103—34no—
397#103—62no—
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—62no—
407#95—21no—
408#95—21no—
409#95—21no—
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—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
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×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4#12112yes—
458C2×C3×C4#12112yes—
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4H(5,𝔽2)11yescharacteristic
464C2×C3×C4H(5,𝔽2)11yescharacteristic
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—22no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477D12—44no—
478D12—41no—
479D12—41no—
480D12—41no—
481D12—41no—
482D12—41no—
483D12—41no—
484D12—41no—
485D12—41no—
486D12—84no—
487D12—84no—
488D12—84no—
489D12—84no—
490D12—84no—
491D12—84no—
492C4×D3—41no—
493C4×D3—41no—
494C4×D3—41no—
495C4×D3—41no—
496C4×D3—41no—
497C4×D3—41no—
498C4×D3—41no—
499C4×D3—41no—
500Dic6—22no—
501Dic6—22no—
502Dic6—41no—
503Dic6—41no—
504C3×C8—22no—
505C3×C8—22no—
506C3⋊C8—22no—
507C3⋊C8—41no—
508C24—31no—
509C24—31no—
510C24—61no—
511C24—61no—
512C2×Q8—32no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
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—32no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—124no—
588C2×C8C2×D1212yes—
589C2×C8C2×D1212yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—62no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—122no—
600C4⋊C4—122no—
601C4⋊C4—122no—
602C4⋊C4D3×D412yes—
603C4⋊C4#23912yes—
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—122no—
616C42C2×D1212yes—
617C42#23912yes—
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—81no—
658C3×C4—81no—
659C3×C4#53211yescharacteristic
660C3×C4#54011yescharacteristic
661C3×C4D4211yescharacteristic
662C3×C4#55011yescharacteristic
663Dic3—42no—
664Dic3—41no—
665Dic3—41no—
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—62no—
697Q8—62no—
698Q8—121no—
699Q8—121no—
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—41no—
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—62no—
736C2×C4—61no—
737C2×C4—61no—
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#89512yes—
752C2×C4#89512yes—
753C2×C4C22×D1211yescharacteristic
754C2×C4C2×D3×D411yescharacteristic
755C2×C4C2×#23911yescharacteristic
756C2×C4C2×#23911yescharacteristic
757C2×C4#100911yescharacteristic
758C2×C4#100911yescharacteristic
759C8—22no—
760C8—22no—
761C8—62no—
762C8—121no—
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×#89511yescharacteristic
803C22#560911yescharacteristic
804C22#563011yescharacteristic
805C22#577011yescharacteristic
806C22#577011yescharacteristic
807C22D3×AGL(1,ℤ/8)11yescharacteristic
808C22#577711yescharacteristic
809C4—22no—
810C4—22no—
811C4—42no—
812C4—42no—
813C4—81no—
814C4—81no—
815C4—121no—
816C4—121no—
817C4—122no—
818C4—241no—
819C4D4×D1211yescharacteristic
820C4#557711yescharacteristic
821C4#569711yescharacteristic
822C4#572511yescharacteristic
823C3#2540211yescharacteristic, complemented, Sylow
824C2—122no—
825C2—241no—
826C2—481no—
827C2—481no—
828C2#7622011yescharacteristic
829C2#7918211yescharacteristic
830C2#7921111yescharacteristic
831C2#8055311yescharacteristic
832C2#8061211yescharacteristic
833C2#8118911yescharacteristic
834C2#8124911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1949C2
socleC23×C3C22×D4
prime radical#73799C2
hypercenter#1949D3
hypocenterC3#25402
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
1. C2×#4886C2semidirect
2. C2×#4864C2semidirect
3. C2×#4848C2semidirect
4. C2×#4836C2semidirect
5. #74240C2semidirect
7. C3×#1949C2semidirect
8. #70634C2semidirect
9. #70581C2semidirect
10. #69553C2semidirect
11. #69475C2semidirect
12. #68887C2semidirect
13. #68887C2semidirect
14. #68885C2semidirect
15. #68883C2semidirect
75. #1949D3semidirect
150. C3×C4⋊C8D4semidirect
161. #810D4semidirect
395. C4⋊C8D12semidirect
823. C3#25402semidirect

Maximal subgroups

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

subgroupindex
C2×#48862
C2×#48642
C2×#48482
C2×#48362
#742402
#737992
C3×#19492
#706342
#705812
#695532
#694752
#688872
#688852
#688832
#254023