Finite Group Databasebeta

← #10845950

Subgroups — #10845950

Order 768.

1116 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4883C211yesmaximal, characteristic, complemented
2C2×#4864C211yesmaximal, characteristic, complemented
3C2×#4844C211yesmaximal, characteristic, complemented
4C2×#4834C211yesmaximal, characteristic, complemented
5#74239C211yesmaximal, characteristic, complemented
6#73798C211yesmaximal, characteristic, complemented
7C3×#1949C211yesmaximal, characteristic, complemented
8#70635C211yesmaximal, characteristic, complemented
9#70581C211yesmaximal, characteristic, complemented
10#69551C211yesmaximal, characteristic, complemented
11C4×#809C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68886C211yesmaximal, characteristic, complemented
14#68883C211yesmaximal, characteristic, complemented
15#68882C211yesmaximal, characteristic, complemented
16#25388—31nomaximal, Sylow
17C22×D24C2211yescharacteristic
18C22×#204C2211yescharacteristic
19C22×D3×C8C2211yescharacteristic
20C22×D3×C8C2211yescharacteristic
21C2×#897C2211yescharacteristic
22C2×#897C2211yescharacteristic
23C2×#895C2211yescharacteristic
24C2×#895C2211yescharacteristic
25C2×#895C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#875C2211yescharacteristic
28C2×C4×D12C2211yescharacteristic
29C2×C4×D12C2211yescharacteristic
30C2×C3×#107C2211yescharacteristic
31C2×C3×#106C2211yescharacteristic
32C2×C3×C4⋊C8C2211yescharacteristic
33C3×#382C2211yescharacteristic
34C3×C4×C4⋊C4C2211yescharacteristic
35C2×#821C2211yescharacteristic
36C2×(C2×D3)⋊C8C2211yescharacteristic
37C2×(C2×D3)⋊C8C2211yescharacteristic
38C2×#816C2211yescharacteristic
39#4987C2211yescharacteristic
40#4987C2211yescharacteristic
41C2×#810C2211yescharacteristic
42C2×#810C2211yescharacteristic
43C2×#809C2211yescharacteristic
44C2×#809C2211yescharacteristic
45C2×#809C2211yescharacteristic
46C2×#809C2211yescharacteristic
47#4939—21no—
48#4939—21no—
49C2×C4×C3⋊C8C2211yescharacteristic
50#4883—24no—
51#4864—24no—
52#4844—24no—
53#4834—24no—
54#4677—21no—
55#4674—21no—
56#4671—21no—
57#4671—21no—
58#4665—21no—
59#4665—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#466—31no—
65C2×#465—31no—
66C2×#463—31no—
67C2×C8×D4—31no—
68#2540—31no—
69#2535—31no—
70#2036—31no—
71#2034—31no—
72#2000—31no—
73#1999—31no—
74#1958—31no—
75#1949D311yescharacteristic, complemented
76#1893—31no—
77#1892—31no—
78C4×#102—31no—
79C22×D12—21no—
80C22×D12—21no—
81C22×D12—21no—
82C22×D12—21no—
83C22×D12D411yescharacteristic
84C22×D12C2311yescharacteristic
85C22×D12C2311yescharacteristic
86C22×C4×D3—21no—
87C22×C4×D3C2311yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C22×Dic6C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C42—21no—
97C2×C3×C42C2311yescharacteristic
98C2×(C2×D3)⋊C4—21no—
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)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4D411yescharacteristic
110C2×(C2×D3)⋊C4D411yescharacteristic
111C2×C4⋊Dic3—21no—
112C2×C4⋊Dic3—21no—
113C2×C4⋊Dic3D411yescharacteristic
114C2×C4⋊Dic3C2311yescharacteristic
115C22×C3⋊C8C2311yescharacteristic
116C22×C3⋊C8C2311yescharacteristic
117C2×D24—22no—
118C2×D24—22no—
119C2×D24—41no—
120C2×#204—22no—
121C2×#204—22no—
122C2×#204—41no—
123C2×D3×C8—22no—
124C2×D3×C8—22no—
125C2×D3×C8—22no—
126C2×D3×C8—22no—
127C2×D3×C8—41no—
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#875—22no—
142#875—22no—
143C4×D12—22no—
144C4×D12—22no—
145C4×D12—22no—
146C4×D12—22no—
147C3×#107—22no—
148C3×#106—22no—
149C3×C4⋊C8D414yescomplemented
150C3×#95—21no—
151C3×#95—21no—
152C3×#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155#821—22no—
156(C2×D3)⋊C8—22no—
157(C2×D3)⋊C8—22no—
158#816—22no—
159#810—22no—
160#810—41no—
161#809—22no—
162#809—22no—
163#809—41no—
164#809D414yescomplemented
165C4×C3⋊C8—22no—
166C22×SD16—31no—
167C22×D8—31no—
168C23×C8—31no—
169C23×C8—31no—
170C2×#124—31no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×#121—31no—
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179#466—64no—
180#465—64no—
181#463—64no—
182C8×D4—64no—
183C2×#107C2×D311yescharacteristic
184C2×#106C2×D311yescharacteristic
185C2×C4⋊C8C2×D311yescharacteristic
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8—31no—
197#399—61no—
198#397—61no—
199#392—61no—
200#392—61no—
201#390—61no—
202#390—61no—
203#386—61no—
204#386—61no—
205#382C2×D311yescharacteristic
206#380—31no—
207#380—31no—
208C4×C4⋊C4C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#340C2×D311yescharacteristic
212#340C2×D311yescharacteristic
213C23×D3—21no—
214C23×D3—21no—
215C23×D3C2×D411yescharacteristic
216C23×D3C2×D411yescharacteristic
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2411yescharacteristic
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3C2×D411yescharacteristic
227C22×Dic3C2×D411yescharacteristic
228C2×D12—22no—
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—42no—
243C2×D12—42no—
244C2×D12—42no—
245C2×D12—42no—
246C2×D12—42no—
247C2×D12—42no—
248C2×D12—42no—
249C2×D12—42no—
250C2×D12—81no—
251C2×D12—81no—
252C2×D12—81no—
253C2×D12—81no—
254C2×D12C2×D412yes—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—42no—
268C2×C4×D3—81no—
269C2×C4×D3—81no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8C2×D412yes—
281C2×C3×C8C2×D412yes—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4C2×D412yes—
289C3×C4⋊C4#4112yes—
290C3×C42—81no—
291C3×C42C2×D412yes—
292C3×C42#4112yes—
293(C2×D3)⋊C4—22no—
294(C2×D3)⋊C4—22no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
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—81no—
305(C2×D3)⋊C4—81no—
306C4⋊Dic3—22no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—42no—
310C4⋊Dic3—42no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8C2×D412yes—
317D24—44no—
318#204—44no—
319D3×C8—44no—
320D3×C8—44no—
321C22×Q8—31no—
322C22×D4—31no—
323C22×D4—31no—
324C22×D4—31no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4—61no—
328C22×D4—61no—
329C23×C4—31no—
330C23×C4—31no—
331C23×C4—61no—
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—121no—
335C2×D8—62no—
336C2×D8—62no—
337C2×D8—121no—
338C22×C8—31no—
339C22×C8—31no—
340C22×C8—62no—
341C22×C8—62no—
342C22×C8—62no—
343C22×C8—62no—
344C22×C8—121no—
345C22×C8—121no—
346C22×C8C22×D311yescharacteristic
347C22×C8C22×D311yescharacteristic
348#124—62no—
349#124—62no—
350C22⋊Q8—62no—
351C22⋊Q8—62no—
352C22⋊Q8—121no—
353C22⋊Q8—121no—
354#121—62no—
355#121—62no—
356#121—62no—
357#121—62no—
358#121—121no—
359#121—121no—
360#121—121no—
361#121—121no—
362C4×D4—62no—
363C4×D4—62no—
364C4×D4—62no—
365C4×D4—62no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C22⋊C4—31no—
375C2×C22⋊C4—31no—
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×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C42—21no—
388C2×C42C22×D311yescharacteristic
389#107—22no—
390#106—22no—
391C4⋊C8D1214yescomplemented
392#103—62no—
393#103—62no—
394#103—121no—
395#102—34no—
396#102—62no—
397#102—62no—
398#102—62no—
399#102—121no—
400C22⋊C8—62no—
401C22⋊C8—62no—
402C4×C8—62no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—61no—
407#95—61no—
408C23×C3C22×D411yescharacteristic
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
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—22no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
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#13512yes—
436C22×D3#13512yes—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
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#12112yes—
454C2×C3×C4#12112yes—
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4H(5,𝔽2)11yescharacteristic
460C2×C3×C4H(5,𝔽2)11yescharacteristic
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473D12—28no—
474D12—22no—
475D12—22no—
476D12—41no—
477D12—41no—
478D12—41no—
479D12—41no—
480D12—41no—
481D12—41no—
482D12—84no—
483D12—84no—
484D12—84no—
485D12—84no—
486C4×D3—41no—
487C4×D3—41no—
488C4×D3—41no—
489C4×D3—41no—
490C4×D3—41no—
491C4×D3—41no—
492C4×D3—41no—
493C4×D3—41no—
494C4×D3—84no—
495Dic6—41no—
496Dic6—41no—
497Dic6—41no—
498Dic6—41no—
499C3×C8—22no—
500C3×C8—22no—
501C3⋊C8—22no—
502C3⋊C8—41no—
503C24—31no—
504C24—31no—
505C24—61no—
506C24—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×D4—32no—
514C2×D4—62no—
515C2×D4—62no—
516C2×D4—62no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
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—122no—
529C2×D4—122no—
530C2×D4—122no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—241no—
537C2×D4—241no—
538C2×D4—241no—
539C2×D4—241no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—122no—
561C22×C4—241no—
562C22×C4—241no—
563C22×C4D3×D411yescharacteristic
564C22×C4D3×D411yescharacteristic
565C22×C4C23×D311yescharacteristic
566SD16—124no—
567D8—124no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—32no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—124no—
579C2×C8—124no—
580C2×C8C2×D1212yes—
581C2×C8C2×D1212yes—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—62no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—122no—
592C4⋊C4—122no—
593C4⋊C4D3×D412yes—
594C4⋊C4#23912yes—
595C22⋊C4—62no—
596C22⋊C4—62no—
597C22⋊C4—122no—
598C22⋊C4—122no—
599C22⋊C4—122no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—122no—
606C22⋊C4—241no—
607C22⋊C4—241no—
608C42—81no—
609C42C2×D1212yes—
610C42#23912yes—
611C22×C3C2×#12111yescharacteristic
612C22×C3D4211yescharacteristic
613C22×C3#54611yescharacteristic
614C22×C3C2×#13511yescharacteristic
615C22×C3C2×#13511yescharacteristic
616C22×C3#57611yescharacteristic
617C22×C3#57711yescharacteristic
618C2×D3—22no—
619C2×D3—22no—
620C2×D3—22no—
621C2×D3—22no—
622C2×D3—22no—
623C2×D3—22no—
624C2×D3—41no—
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—81no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C2×D3—81no—
643C2×D3—81no—
644C2×D3—81no—
645C2×D3—81no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—42no—
649C3×C4—42no—
650C3×C4—81no—
651C3×C4—81no—
652C3×C4#53211yescharacteristic
653C3×C4#54011yescharacteristic
654C3×C4D4211yescharacteristic
655C3×C4#55011yescharacteristic
656Dic3—41no—
657Dic3—41no—
658Dic3—81no—
659Dic3—81no—
660C23—32no—
661C23—32no—
662C23—61no—
663C23—61no—
664C23—61no—
665C23—61no—
666C23—61no—
667C23—61no—
668C23—61no—
669C23—61no—
670C23—61no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—62no—
675C23—121no—
676C23—121no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—121no—
688C23C2×D3×D411yescharacteristic
689Q8—121no—
690Q8—121no—
691Q8—121no—
692Q8—121no—
693D4—68no—
694D4—62no—
695D4—62no—
696D4—121no—
697D4—121no—
698D4—121no—
699D4—121no—
700D4—121no—
701D4—121no—
702D4—244no—
703D4—244no—
704D4—244no—
705D4—244no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—244no—
743C2×C4#89512yes—
744C2×C4#89512yes—
745C2×C4C22×D1211yescharacteristic
746C2×C4C2×D3×D411yescharacteristic
747C2×C4C2×#23911yescharacteristic
748C2×C4C2×#23911yescharacteristic
749C2×C4#100911yescharacteristic
750C2×C4#100911yescharacteristic
751C8—22no—
752C8—22no—
753C8—62no—
754C8—121no—
755C2×C3#242811yescharacteristic
756C2×C3#305011yescharacteristic
757C2×C3#306211yescharacteristic
758C2×C3#328011yescharacteristic
759C2×C3#328211yescharacteristic
760C2×C3#329711yescharacteristic
761C2×C3#330111yescharacteristic
762D3—42no—
763D3—42no—
764D3—82no—
765D3—161no—
766C22—62no—
767C22—62no—
768C22—62no—
769C22—62no—
770C22—62no—
771C22—62no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—122no—
781C22—122no—
782C22—122no—
783C22—241no—
784C22—241no—
785C22—241no—
786C22—241no—
787C22—241no—
788C22—241no—
789C22—241no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22C2×#89511yescharacteristic
795C22#560911yescharacteristic
796C22#563011yescharacteristic
797C22D3×#13511yescharacteristic
798C22D3×#13511yescharacteristic
799C22#577411yescharacteristic
800C22#577811yescharacteristic
801C4—22no—
802C4—22no—
803C4—42no—
804C4—42no—
805C4—81no—
806C4—81no—
807C4—121no—
808C4—121no—
809C4—241no—
810C4—241no—
811C4D4×D1211yescharacteristic
812C4#557711yescharacteristic
813C4#569711yescharacteristic
814C4#572511yescharacteristic
815C3#2538811yescharacteristic, complemented, Sylow
816C2—122no—
817C2—122no—
818C2—242no—
819C2—481no—
820C2#7622011yescharacteristic
821C2#7918011yescharacteristic
822C2#7921311yescharacteristic
823C2#8055711yescharacteristic
824C2#8063011yescharacteristic
825C2#8118711yescharacteristic
826C2#8124611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1949C2
socleC23×C3C22×D4
hypercenter#1949D3
hypocenterC3#25388
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×#4883C2semidirect
2. C2×#4864C2semidirect
3. C2×#4844C2semidirect
4. C2×#4834C2semidirect
5. #74239C2semidirect
6. #73798C2semidirect
7. C3×#1949C2semidirect
8. #70635C2semidirect
9. #70581C2semidirect
10. #69551C2semidirect
11. C4×#809C2semidirect
12. #68887C2semidirect
13. #68886C2semidirect
14. #68883C2semidirect
15. #68882C2semidirect
75. #1949D3semidirect
149. C3×C4⋊C8D4semidirect
164. #809D4semidirect
391. C4⋊C8D12semidirect
815. C3#25388semidirect

Maximal subgroups

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

subgroupindex
C2×#48832
C2×#48642
C2×#48442
C2×#48342
#742392
#737982
C3×#19492
#706352
#705812
#695512
C4×#8092
#688872
#688862
#688832
#688822
#253883