Finite Group Databasebeta

← #10815498

Subgroups — #10815498

Order 768.

1386 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×C3×#442C211yesmaximal, characteristic, complemented
2C2×#5156C211yesmaximal, characteristic
3#82399C211yesmaximal, characteristic, complemented
4D4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×D3×#102C211yesmaximal, characteristic, complemented
6#72037C211yesmaximal, characteristic, complemented
7#71613C211yesmaximal, characteristic, complemented
8#71607C211yesmaximal, characteristic, complemented
9#70579C211yesmaximal, characteristic, complemented
10#70569C211yesmaximal, characteristic, complemented
11#70202C211yesmaximal, characteristic, complemented
12#70191C211yesmaximal, characteristic, complemented
13#70152C211yesmaximal, characteristic, complemented
14#69831C211yesmaximal, characteristic, complemented
15#69818C211yesmaximal, characteristic, complemented
16#22858—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic, complemented
21C2×#938C2211yescharacteristic
22C2×D4×Dic3C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×C4×#67—21no—
25C22×(C2×D3)⋊C4—21no—
26C22×D3×C8C2211yescharacteristic
27C2×D3×C4⋊C4C2211yescharacteristic
28C3×#442—24no—
29C2×C3×#106C2211yescharacteristic, complemented
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic, complemented
32C2×C3×#97C2211yescharacteristic, complemented
33#5221C2211yescharacteristic, complemented
34C2×#832C2211yescharacteristic
35C2×#832C2211yescharacteristic
36C2×#832C2211yescharacteristic, complemented
37#5213—21no—
38#5210—21no—
39#5156C418yescomplemented
40C2×#821C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#815C2211yescharacteristic, complemented
44#4988C2211yescharacteristic
45#4987C2211yescharacteristic
46Dic3×C4⋊C4C2211yescharacteristic, complemented
47C2×#809C2211yescharacteristic
48C2×#808C2211yescharacteristic, complemented
49#4958—21no—
50#4956—21no—
51#4955—21no—
52#4945—21no—
53#4939C2211yescharacteristic
54C4×(C2×D3)⋊C4C2211yescharacteristic
55#4928C2211yescharacteristic, complemented
56D3×#102—24no—
57#4551C2211yescharacteristic, complemented
58#4551C2211yescharacteristic, complemented
59#4550C2211yescharacteristic, complemented
60#4529C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62#4524C2211yescharacteristic, complemented
63C2×#447—31no—
64C2×#442D311yescharacteristic, complemented
65C22×#102—31no—
66#2361—31no—
67D4×C22⋊C4—31no—
68#1972—31no—
69#1936—31no—
70#1926—31no—
71#1893—31no—
72#1879—31no—
73#1879—31no—
74#1864—31no—
75#1853—31no—
76#1762—31no—
77#1752—31no—
78C24×D3—21no—
79C22×C3×D4C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4—21no—
83C22×#67—21no—
84C22×#67—21no—
85C23×Dic3—21no—
86C2×D3×D4—22no—
87C2×D3×D4—22no—
88C2×D3×D4—22no—
89C2×D3×D4—41no—
90C2×D3×D4—41no—
91C2×D3×D4C2×C414yescomplemented
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C22×C4×D3C2311yescharacteristic
95C2×C3×D8—22no—
96C2×C3×D8—22no—
97C2×C3×D8C2×C414yescomplemented
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C4×D4—22no—
101C3×C4×D4—22no—
102C3×C4×D4—41no—
103C3×C4×D4—41no—
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C42C2311yescharacteristic
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113#938—22no—
114#938C2×C414yescomplemented
115D4×Dic3—22no—
116D4×Dic3—41no—
117C2×#213—41no—
118C2×#213—41no—
119C2×#213C2×C414yescomplemented
120C4×#67—44no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—44no—
127C2×(C2×D3)⋊C4D411yescharacteristic
128C2×(C2×D3)⋊C4D411yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138C2×D3×C8—22no—
139C2×D3×C8—22no—
140C2×D3×C8—41no—
141D3×C4⋊C4—22no—
142D3×C4⋊C4—41no—
143C3×#106—22no—
144C3×#102—22no—
145C3×#102D414yescomplemented
146C3×#97—22no—
147#832—22no—
148#832—41no—
149#832C2×C414yescomplemented
150C3⋊#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95D411yescharacteristic
154C3⋊#95D411yescharacteristic
155#821—22no—
156#821C2×C414yescomplemented
157(C2×D3)⋊C8C2×C414yescomplemented
158#815—41no—
159#809—22no—
160#808—41no—
161C23×D4—31no—
162C22×D8—31no—
163C22×D8C2×D311yescharacteristic
164C23×C8—31no—
165C2×#121—31no—
166C2×C4×D4—31no—
167C2×C4×D4—61no—
168C2×C4×D4C2×D311yescharacteristic
169C2×C4×D4C2×D311yescharacteristic, complemented
170C22×C4⋊C4—31no—
171C22×C22⋊C4—61no—
172#447—38no—
173#442—24no—
174C2×#106—31no—
175C2×#106C2×D311yescharacteristic, complemented
176C2×#102—31no—
177C2×#102—31no—
178C2×#102—31no—
179C2×#102—31no—
180C2×#102—31no—
181C2×#102—31no—
182C2×#102—64no—
183C2×#102C2×D311yescharacteristic
184C2×#102C2×D311yescharacteristic, complemented
185C2×C22⋊C8—31no—
186C2×#97—31no—
187C2×#97C2×D311yescharacteristic, complemented
188#390—31no—
189#390—31no—
190#390—31no—
191#389—31no—
192#388—61no—
193#386—61no—
194#386—61no—
195#386—61no—
196#385—61no—
197#380—31no—
198#379—61no—
199C4×C4⋊C4—31no—
200C4×C22⋊C4—31no—
201#340—31no—
202#340—31no—
203#340—31no—
204#340—31no—
205#336—31no—
206#336—31no—
207C24×C3—21no—
208C24×C3—21no—
209C23×D3—21no—
210C23×D3—24no—
211C23×D3—42no—
212C23×D3—42no—
213C23×D3—42no—
214C23×D3—42no—
215C23×D3—81no—
216C23×D3—81no—
217C23×D3C2×D411yescharacteristic
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4C22×C412yes—
227C2×C3×D4C22×C412yes—
228C2×C3×D4C2×D412yes—
229C2×C3×D4#4112yes—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—42no—
233C22×C3×C4—42no—
234C22×C3×C4—42no—
235C22×C3×C4—42no—
236C22×C3×C4—81no—
237C22×C3×C4—81no—
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2411yescharacteristic
241C2×#67—24no—
242C2×#67—24no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—42no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—42no—
251C22×Dic3—42no—
252C22×Dic3—81no—
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256D3×D4—28no—
257D3×D4—44no—
258D3×D4—44no—
259D3×D4—44no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12C22×C412yes—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—42no—
271C2×C4×D3—42no—
272C2×C4×D3—81no—
273C2×C4×D3C22×C412yes—
274C2×C4×D3#4112yes—
275C3×D8—28no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8C22×C412yes—
281C2×C3×C8C2×D412yes—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4C2×D412yes—
286C3×C22⋊C4—42no—
287C3×C22⋊C4—42no—
288C3×C42—21no—
289C3×C42—21no—
290#217—24no—
291#217—42no—
292#217—42no—
293#217—81no—
294#213—44no—
295(C2×D3)⋊C4—22no—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—81no—
301(C2×D3)⋊C4—81no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3C22×C412yes—
308Dic3⋊C4—42no—
309Dic3⋊C4—42no—
310C4×Dic3—21no—
311C4×Dic3—21no—
312C4×Dic3—42no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8C22×C412yes—
319D3×C8—44no—
320C25—61no—
321C22×D4—34no—
322C22×D4—31no—
323C22×D4—62no—
324C22×D4—61no—
325C22×D4—62no—
326C22×D4—62no—
327C22×D4—61no—
328C22×D4—121no—
329C22×D4—121no—
330C22×D4C22×D311yescharacteristic
331C22×D4C22×D311yescharacteristic
332C23×C4—21no—
333C23×C4—21no—
334C23×C4—31no—
335C23×C4—61no—
336C23×C4—61no—
337C2×D8—22no—
338C2×D8—22no—
339C2×D8—34no—
340C2×D8—121no—
341C2×D8—121no—
342C2×D8C4×D314yescomplemented
343C22×C8—31no—
344C22×C8—31no—
345C22×C8—62no—
346C22×C8—62no—
347C22×C8—121no—
348C22×C8C22×D311yescharacteristic
349C22×C8C22×D311yescharacteristic
350#121—34no—
351#121—62no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—41no—
355C4×D4—41no—
356C4×D4—62no—
357C4×D4—121no—
358C4×D4—124no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—62no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—121no—
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C4⋊C4C22×D311yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—31no—
371C2×C22⋊C4—31no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—124no—
382C2×C42—31no—
383C2×C42—61no—
384C2×C42C22×D311yescharacteristic
385#106—22no—
386#106—121no—
387#102—22no—
388#102—34no—
389#102—34no—
390#102—62no—
391#102—62no—
392#102—62no—
393#102—121no—
394#102#6714yescomplemented
395C22⋊C8—34no—
396#97—22no—
397#97—121no—
398#95—31no—
399#95—31no—
400#95—61no—
401#95—61no—
402#95—61no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3C22×D411yescharacteristic
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—22no—
423C22×D3—48no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—48no—
431C22×D3—84no—
432C22×D3—84no—
433C22×D3—84no—
434C22×D3—84no—
435C22×D3—84no—
436C22×D3C4×D412yes—
437C22×D3AGL(1,ℤ/8)12yes—
438C22×D3AGL(1,ℤ/8)12yes—
439C3×D4—22no—
440C3×D4—22no—
441C3×D4—22no—
442C3×D4—22no—
443C3×D4—22no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4C4×D414yescomplemented
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—84no—
460C2×C3×C4—84no—
461C2×C3×C4C23×C411yescharacteristic
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4H(5,𝔽2)11yescharacteristic
466C2×C3×C4H(5,𝔽2)11yescharacteristic
467#67—48no—
468#67—48no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—84no—
487C2×Dic3C4×D412yes—
488D12—22no—
489D12—22no—
490D12—41no—
491D12—41no—
492C4×D3—22no—
493C4×D3—22no—
494C4×D3—22no—
495C4×D3—22no—
496C4×D3—84no—
497C3×C8—22no—
498C3×C8—22no—
499C3⋊C8—22no—
500C3⋊C8—41no—
501C24—21no—
502C24—21no—
503C24—31no—
504C24—64no—
505C24—61no—
506C24—122no—
507C24—122no—
508C24—122no—
509C24—122no—
510C24—241no—
511C24—241no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—32no—
521C2×D4—64no—
522C2×D4—68no—
523C2×D4—64no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—124no—
530C2×D4—124no—
531C2×D4—124no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4C2×C4×D312yes—
537C2×D4C2×C4×D312yes—
538C2×D4#23512yes—
539C2×D4C2×#6712yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—31no—
543C22×C4—32no—
544C22×C4—32no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—122no—
561C22×C4—122no—
562C22×C4—122no—
563C22×C4—122no—
564C22×C4—241no—
565C22×C4—241no—
566C22×C4D3×D411yescharacteristic
567C22×C4D3×D411yescharacteristic
568C22×C4C23×D311yescharacteristic
569D8—28no—
570D8—124no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—32no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—124no—
582C2×C8C2×C4×D312yes—
583C2×C8C2×#6712yes—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—32no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—122no—
594C4⋊C4—122no—
595C4⋊C4C2×#6712yes—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—62no—
599C22⋊C4—62no—
600C22⋊C4—64no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—122no—
606C22⋊C4—241no—
607C22⋊C4—241no—
608C22⋊C4—241no—
609C42—21no—
610C42—21no—
611C42—61no—
612C42—61no—
613C42—122no—
614C22×C3—24no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3C2×C4×D411yescharacteristic
629C22×C3D4211yescharacteristic
630C22×C3#54611yescharacteristic
631C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
632C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
633C22×C3#57611yescharacteristic
634C22×C3#57711yescharacteristic
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—22no—
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—42no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—816no—
645C2×D3—81no—
646C2×D3—81no—
647C2×D3—81no—
648C2×D3—81no—
649C2×D3#44214yescomplemented
650C3×C4—42no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—81no—
654C3×C4C2×C4×D411yescharacteristic
655C3×C4#51811yescharacteristic
656C3×C4#54611yescharacteristic
657C3×C4#55111yescharacteristic
658Dic3—22no—
659Dic3—42no—
660Dic3—41no—
661Dic3—41no—
662Dic3—81no—
663Dic3—81no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—32no—
669C23—32no—
670C23—32no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—62no—
686C23—128no—
687C23—128no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23—244no—
695C23—244no—
696C23—244no—
697C23—244no—
698C23—244no—
699C23C2×D3×D411yescharacteristic
700D4—22no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—41no—
706D4—41no—
707D4—62no—
708D4—62no—
709D4—128no—
710D4—128no—
711D4—121no—
712D4—121no—
713D4C4×#6714yescomplemented
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—32no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—62no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—84no—
741C2×C4—84no—
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—244no—
751C2×C4—244no—
752C2×C4C22×C4×D311yescharacteristic
753C2×C4C2×#23511yescharacteristic
754C2×C4#100411yescharacteristic
755C2×C4D3×#4111yescharacteristic
756C2×C4#100911yescharacteristic
757C2×C4C22×#6711yescharacteristic
758C8—22no—
759C8—22no—
760C8—62no—
761C8—121no—
762C2×C3—44no—
763C2×C3—82no—
764C2×C3#235811yescharacteristic
765C2×C3C2×#44211yescharacteristic
766C2×C3#294611yescharacteristic
767C2×C3#326411yescharacteristic
768C2×C3#326511yescharacteristic
769C2×C3#330611yescharacteristic
770C2×C3#331811yescharacteristic
771D3—24no—
772D3—82no—
773C22—24no—
774C22—34no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—62no—
785C22—62no—
786C22—62no—
787C22—62no—
788C22—62no—
789C22—62no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—122no—
795C22—122no—
796C22—122no—
797C22—2416no—
798C22—241no—
799C22—241no—
800C22—241no—
801C22—241no—
802C22C4×D3×D411yescharacteristic
803C22#555011yescharacteristic
804C22D3×AGL(1,ℤ/8)11yescharacteristic
805C22D3×AGL(1,ℤ/8)11yescharacteristic
806C22#577411yescharacteristic
807C22#577511yescharacteristic
808C22D4×#6711yescharacteristic
809C4—41no—
810C4—42no—
811C4—41no—
812C4—62no—
813C4—81no—
814C4—121no—
815C4—121no—
816C4—122no—
817C4—241no—
818C4—241no—
819C4#554511yescharacteristic
820C4#555611yescharacteristic
821C4C2×C4×#6711yescharacteristic
822C4#582911yescharacteristic
823C3#2285811yescharacteristic, complemented, Sylow
824C2—44no—
825C2—64no—
826C2—82no—
827C2—242no—
828C2D3×#44211yescharacteristic
829C2#7986611yescharacteristic
830C2#7988011yescharacteristic
831C2#7988211yescharacteristic
832C2#8239811yescharacteristic
833C2#8395211yescharacteristic
834C2#8395311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC2×C3×#442C2
socleC23×C3C22×D4
prime radicalC2×#5156C2
cosocleC22×C3×C4C24
hypercenterC2×#442D3
hypocenterC3#22858
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×C3×#442C2semidirect
3. #82399C2semidirect
4. D4×(C2×D3)⋊C4C2semidirect
5. C2×D3×#102C2semidirect
6. #72037C2semidirect
7. #71613C2semidirect
8. #71607C2semidirect
9. #70579C2semidirect
10. #70569C2semidirect
11. #70202C2semidirect
12. #70191C2semidirect
13. #70152C2semidirect
14. #69831C2semidirect
15. #69818C2semidirect
20. C2×C3×C4×D4C22semidirect
29. C2×C3×#106C22semidirect
31. C2×C3×#102C22semidirect
32. C2×C3×#97C22semidirect
33. #5221C22semidirect
36. C2×#832C22semidirect
39. #5156C4semidirect
43. C2×#815C22semidirect
46. Dic3×C4⋊C4C22semidirect
48. C2×#808C22semidirect
55. #4928C22semidirect
57. #4551C22semidirect
58. #4551C22semidirect
59. #4550C22semidirect
60. #4529C22semidirect
61. #4529C22semidirect
62. #4524C22semidirect
64. C2×#442D3semidirect
91. C2×D3×D4C2×C4semidirect
97. C2×C3×D8C2×C4semidirect
114. #938C2×C4semidirect
119. C2×#213C2×C4semidirect
145. C3×#102D4semidirect
149. #832C2×C4semidirect
156. #821C2×C4semidirect
157. (C2×D3)⋊C8C2×C4semidirect
169. C2×C4×D4C2×D3semidirect
175. C2×#106C2×D3semidirect
184. C2×#102C2×D3semidirect
187. C2×#97C2×D3semidirect
342. C2×D8C4×D3semidirect
394. #102#67semidirect
446. C3×D4C4×D4semidirect
649. C2×D3#442semidirect
713. D4C4×#67semidirect
823. C3#22858semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4422
C2×#51562
#823992
D4×(C2×D3)⋊C42
C2×D3×#1022
#720372
#716132
#716072
#705792
#705692
#702022
#701912
#701522
#698312
#698182
#228583