Finite Group Databasebeta

← #10847383

Subgroups — #10847383

Order 768.

1474 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5548C211yesmaximal, characteristic, complemented
2C2×#4883C211yesmaximal, characteristic, complemented
3C2×#4775C211yesmaximal, characteristic, complemented
4#76286C211yesmaximal, characteristic, complemented
5C3×#1862C211yesmaximal, characteristic, complemented
6#71613C211yesmaximal, characteristic, complemented
7#70617C211yesmaximal, characteristic, complemented
8#70211C211yesmaximal, characteristic, complemented
9#70209C211yesmaximal, characteristic, complemented
10#70202C211yesmaximal, characteristic, complemented
11#69625C211yesmaximal, characteristic, complemented
12#68898C211yesmaximal, characteristic, complemented
13#68883C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15D3×#336C211yesmaximal, characteristic, complemented
16#25496—31nomaximal, Sylow
17C22×#235—21no—
18C2×C3×C4×D4C2211yescharacteristic
19C2×#940C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×C4×#67—21no—
23C22×D24C2211yescharacteristic
24C22×D3×C8C2211yescharacteristic
25C22×D3×C8C2211yescharacteristic
26#5548—24no—
27#5548—24no—
28C2×#895C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#894—21no—
31C2×#888C2211yescharacteristic
32C2×#885—21no—
33C2×#884—21no—
34C2×C4×D12C2211yescharacteristic
35C2×C42×D3C2211yescharacteristic
36C2×C3×#107C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C3×#389C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43#4990—21no—
44#4988C2211yescharacteristic
45#4987C2211yescharacteristic
46#4972C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4939C2211yescharacteristic
52#4883—24no—
53#4775—24no—
54#4669—21no—
55#4665—21no—
56C3×#340C2211yescharacteristic
57C3×#336C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#532—31no—
65C2×#466—31no—
66C2×#466—31no—
67#2854—31no—
68#2057—31no—
69#2041—31no—
70#2023—31no—
71#2011—31no—
72#1893—31no—
73#1893—31no—
74#1879—31no—
75#1879—31no—
76#1862—31no—
77#1862D311yescharacteristic, complemented
78C2×#336—31no—
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C22×#67—21no—
82C22×#67—21no—
83C22×#67—21no—
84C2×#235—28no—
85C2×#235—44no—
86C2×#235—44no—
87C22×D12—21no—
88C22×D12—21no—
89C22×D12C2311yescharacteristic
90C22×D12C2311yescharacteristic
91C22×C4×D3—21no—
92C22×C4×D3D411yescharacteristic
93C22×C4×D3D411yescharacteristic
94C22×C4×D3C2311yescharacteristic
95C22×Dic6—21no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×C4×D4—22no—
99C3×C4×D4—22no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C22⋊C4—21no—
105C2×C3×C42C2311yescharacteristic
106C2×#217—21no—
107#940—22no—
108#940—22no—
109#938—22no—
110#938D414yes—
111C2×#213—22no—
112C2×#213—22no—
113C2×#213—41no—
114C4×#67—28no—
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)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×C4×Dic3D411yescharacteristic
128C2×C4×Dic3D411yescharacteristic
129C2×C4×Dic3C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C2×D24—22no—
133C2×D24—22no—
134C2×D24—41no—
135C2×D3×C8—22no—
136C2×D3×C8—22no—
137C2×D3×C8—22no—
138C2×D3×C8—22no—
139C2×D3×C8—41no—
140C2×D3×C8—41no—
141#895—22no—
142#895—22no—
143#895—22no—
144#895D414yes—
145#894—44no—
146#888—22no—
147#888—22no—
148#885—28no—
149#884—28no—
150C4×D12—22no—
151C4×D12—22no—
152C42×D3—22no—
153C42×D3—22no—
154C3×#107—22no—
155C3×#102—22no—
156C3×#102—22no—
157C3×#95—21no—
158#832—41no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161#821—22no—
162#821—41no—
163#809—22no—
164#809—22no—
165#809—22no—
166#807—22no—
167C22×#41—61no—
168C22×D8—31no—
169C22×D8—31no—
170C23×C8—31no—
171C23×C8—31no—
172#532—64no—
173#532—64no—
174C2×C4⋊Q8—31no—
175C2×#127—31no—
176C2×#124—61no—
177C2×#123—61no—
178C2×#121—31no—
179C2×#121—31no—
180C2×#121—31no—
181C2×#121—61no—
182C2×C4×D4—31no—
183C2×C4×D4—61no—
184C2×C4×D4C2×D311yescharacteristic
185C22×C42—31no—
186#466—64no—
187#466—64no—
188C2×#107—31no—
189C2×#107C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102C2×D311yescharacteristic
197C2×#102C2×D311yescharacteristic
198#390—31no—
199#390—31no—
200#389—31no—
201#389C2×D311yescharacteristic
202#388—61no—
203#388—61no—
204#386—61no—
205#380—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340C2×D311yescharacteristic
210#336—31no—
211#336—31no—
212#336—31no—
213#336C2×D311yescharacteristic
214C24×C3—21no—
215C23×D3—21no—
216C23×D3—21no—
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×D4C2×D412yes—
224C22×C3×C4—24no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—42no—
229C22×C3×C4—42no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2411yescharacteristic
233C2×#67—24no—
234C2×#67—24no—
235C2×#67—24no—
236C2×#67—42no—
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—42no—
241C2×#67—42no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C22×Dic3C2×D411yescharacteristic
247#235—432no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—24no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—42no—
261C2×D12—42no—
262C2×D12—42no—
263C2×D12—42no—
264C2×D12—42no—
265C2×D12C2×D412yes—
266C2×C4×D3—22no—
267C2×C4×D3—22no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—24no—
273C2×C4×D3—22no—
274C2×C4×D3—22no—
275C2×C4×D3—41no—
276C2×C4×D3—42no—
277C2×C4×D3—42no—
278C2×C4×D3D814yescomplemented
279C2×C4×D3C2×D412yes—
280C2×C4×D3C2×D412yes—
281C2×Dic6—24no—
282C2×Dic6—42no—
283C2×Dic6—42no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8#4112yescomplemented
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—42no—
296C3×C4⋊C4C2×D412yes—
297C3×C22⋊C4—24no—
298C3×C42—21no—
299C3×C42—21no—
300#217—24no—
301#213—44no—
302(C2×D3)⋊C4—24no—
303(C2×D3)⋊C4—24no—
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—
309(C2×D3)⋊C4—42no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3C2×D412yes—
314Dic3⋊C4—24no—
315Dic3⋊C4—42no—
316C4×Dic3—21no—
317C4×Dic3—21no—
318C4×Dic3—22no—
319C4×Dic3—22no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8#4112yescomplemented
326D24—44no—
327D3×C8—44no—
328D3×C8—44no—
329C2×#41—68no—
330C2×#41—124no—
331C2×#41—124no—
332C22×Q8—61no—
333C22×D4—31no—
334C22×D4—31no—
335C22×D4—61no—
336C22×D4—61no—
337C22×D4—61no—
338C22×D4—61no—
339C22×D4—61no—
340C22×D4C22×D311yescharacteristic
341C23×C4—21no—
342C23×C4—31no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—61no—
346C2×D8—62no—
347C2×D8—62no—
348C2×D8—62no—
349C2×D8—62no—
350C2×D8—121no—
351C2×D8—121no—
352C22×C8—31no—
353C22×C8—31no—
354C22×C8—62no—
355C22×C8—62no—
356C22×C8—62no—
357C22×C8—62no—
358C22×C8—121no—
359C22×C8—121no—
360C22×C8C22×D311yescharacteristic
361C22×C8C22×D311yescharacteristic
362C4⋊Q8—62no—
363C4⋊Q8—62no—
364#127—62no—
365#127—62no—
366#124—68no—
367#123—124no—
368#121—34no—
369#121—34no—
370#121—68no—
371#121—62no—
372#121—62no—
373#121—62no—
374#121—62no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—62no—
378C4×D4—62no—
379C4×D4—68no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4C22×D311yescharacteristic
386C2×C4⋊C4C22×D311yescharacteristic
387C2×C4⋊C4C22×D311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C42—31no—
399C2×C42—31no—
400C2×C42—31no—
401C2×C42—62no—
402C2×C42—62no—
403C2×C42C22×D311yescharacteristic
404#107—22no—
405#107—62no—
406#102—22no—
407#102—22no—
408#102—62no—
409#102—62no—
410#102—62no—
411#102—62no—
412#102—121no—
413#102—121no—
414#95—21no—
415#95—61no—
416#95—61no—
417C23×C3—22no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3C22×D411yescharacteristic
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—22no—
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×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3#12012yes—
444C22×D3C2×D812yes—
445C22×D3AGL(1,ℤ/8)12yes—
446C3×D4—22no—
447C3×D4—22no—
448C3×D4—41no—
449C3×D4—41no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—48no—
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×C4C2×D812yes—
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4H(5,𝔽2)11yescharacteristic
471C2×C3×C42−1+411yescharacteristic
472#67—48no—
473#67—48no—
474#67—48no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—22no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3#12012yes—
488C2×Dic3C2×D812yes—
489C2×Dic3#13512yes—
490D12—22no—
491D12—22no—
492D12—48no—
493D12—41no—
494D12—41no—
495D12—41no—
496D12—41no—
497D12—41no—
498D12—41no—
499D12—84no—
500C4×D3—28no—
501C4×D3—22no—
502C4×D3—22no—
503C4×D3—22no—
504C4×D3—22no—
505C4×D3—44no—
506C4×D3—48no—
507Dic6—48no—
508C3×C8—22no—
509C3×C8—41no—
510C3⋊C8—22no—
511C3⋊C8—41no—
512C24—21no—
513C24—31no—
514C24—61no—
515C24—61no—
516#41—1232no—
517C2×Q8—64no—
518C2×Q8—122no—
519C2×Q8—122no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—32no—
526C2×D4—64no—
527C2×D4—64no—
528C2×D4—64no—
529C2×D4—64no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—61no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4—61no—
538C2×D4—61no—
539C2×D4—61no—
540C2×D4—61no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4—122no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4—122no—
549C2×D4—122no—
550C2×D4—122no—
551C2×D4—122no—
552C2×D4D3×D412yes—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—34no—
561C22×C4—32no—
562C22×C4—32no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—64no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—121no—
577C22×C4—122no—
578C22×C4—122no—
579C22×C4D3×D411yescharacteristic
580C22×C4D3×D411yescharacteristic
581C22×C4C23×D311yescharacteristic
582D8—124no—
583D8—124no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—32no—
590C2×C8—61no—
591C2×C8—61no—
592C2×C8—61no—
593C2×C8—61no—
594C2×C8—61no—
595C2×C8—124no—
596C2×C8—124no—
597C2×C8#23512yescomplemented
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—32no—
604C4⋊C4—42no—
605C4⋊C4—64no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—122no—
610C4⋊C4D3×D412yes—
611C22⋊C4—24no—
612C22⋊C4—64no—
613C22⋊C4—64no—
614C22⋊C4—64no—
615C22⋊C4—122no—
616C22⋊C4—122no—
617C22⋊C4—122no—
618C22⋊C4—122no—
619C22⋊C4—122no—
620C22⋊C4—122no—
621C42—21no—
622C42—21no—
623C42—62no—
624C42—62no—
625C42—61no—
626C42—61no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3C2×#12011yescharacteristic
635C22×C3#53211yescharacteristic
636C22×C3#53711yescharacteristic
637C22×C3C22×D811yescharacteristic
638C22×C3C2×#13511yescharacteristic
639C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
640C22×C3#57511yescharacteristic
641C2×D3—22no—
642C2×D3—22no—
643C2×D3—22no—
644C2×D3—22no—
645C2×D3—22no—
646C2×D3—22no—
647C2×D3—42no—
648C2×D3—42no—
649C2×D3—42no—
650C2×D3—81no—
651C2×D3—81no—
652C2×D3—81no—
653C2×D3—81no—
654C2×D3—81no—
655C2×D3—81no—
656C2×D3—81no—
657C2×D3—81no—
658C2×D3—81no—
659C2×D3—81no—
660C2×D3—81no—
661C2×D3#44714yes—
662C3×C4—22no—
663C3×C4—42no—
664C3×C4—41no—
665C3×C4—81no—
666C3×C4—81no—
667C3×C4#54611yescharacteristic
668C3×C4#54611yescharacteristic
669C3×C4#54711yescharacteristic
670C3×C4#54711yescharacteristic
671Dic3—22no—
672Dic3—22no—
673Dic3—22no—
674Dic3—42no—
675Dic3—81no—
676C23—22no—
677C23—32no—
678C23—32no—
679C23—32no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—62no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23—121no—
695C23—121no—
696C23—121no—
697C23—121no—
698C23—121no—
699C23—121no—
700C23—121no—
701C23—121no—
702C23—121no—
703C23—121no—
704C23C2×D3×D411yescharacteristic
705Q8—128no—
706D4—22no—
707D4—22no—
708D4—41no—
709D4—41no—
710D4—62no—
711D4—62no—
712D4—128no—
713D4—128no—
714D4—128no—
715D4—128no—
716D4—121no—
717D4—121no—
718D4—121no—
719D4—121no—
720D4—121no—
721D4—121no—
722D4—244no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—48no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—68no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—128no—
754C2×C4—124no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4D3×D812yes—
761C2×C4C2×#23511yescharacteristic
762C2×C4C2×D3×D411yescharacteristic
763C2×C4C2×D3×D411yescharacteristic
764C2×C4#100711yescharacteristic
765C2×C4D3×#4111yescharacteristic
766C2×C4#100911yescharacteristic
767C8—22no—
768C8—41no—
769C8—62no—
770C8—121no—
771C2×C3—82no—
772C2×C3#243011yescharacteristic
773C2×C3C2×#44711yescharacteristic
774C2×C3#300211yescharacteristic
775C2×C3#316911yescharacteristic
776C2×C3#318011yescharacteristic
777C2×C3#324511yescharacteristic
778C2×C3#324711yescharacteristic
779D3—24no—
780D3—82no—
781D3—161no—
782C22—34no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—62no—
787C22—62no—
788C22—62no—
789C22—62no—
790C22—62no—
791C22—62no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—122no—
797C22—122no—
798C22—122no—
799C22—241no—
800C22—241no—
801C22—241no—
802C22—241no—
803C22—241no—
804C22—241no—
805C22—241no—
806C22—241no—
807C22—241no—
808C22—241no—
809C22—241no—
810C22#554811yescharacteristic
811C22D3×#12011yescharacteristic
812C22#562911yescharacteristic
813C22C2×D3×D811yescharacteristic
814C22D3×#13511yescharacteristic
815C22D3×AGL(1,ℤ/8)11yescharacteristic
816C22#577711yescharacteristic
817C4—22no—
818C4—41no—
819C4—42no—
820C4—62no—
821C4—62no—
822C4—62no—
823C4—81no—
824C4—81no—
825C4—122no—
826C4—241no—
827C4#550711yescharacteristic
828C4#555011yescharacteristic
829C4#563111yescharacteristic
830C4#565411yescharacteristic
831C3#2549611yescharacteristic, complemented, Sylow
832C2—64no—
833C2—82no—
834C2—242no—
835C2—481no—
836C2#7460611yescharacteristic
837C2#7959811yescharacteristic
838C2#7979011yescharacteristic
839C2D3×#44711yescharacteristic
840C2#8022611yescharacteristic
841C2#8097511yescharacteristic
842C2#8114811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1862C2
socleC23×C3C22×D4
hypercenter#1862D3
hypocenterC3#25496
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
1. C2×#5548C2semidirect
2. C2×#4883C2semidirect
3. C2×#4775C2semidirect
4. #76286C2semidirect
5. C3×#1862C2semidirect
6. #71613C2semidirect
7. #70617C2semidirect
8. #70211C2semidirect
9. #70209C2semidirect
10. #70202C2semidirect
11. #69625C2semidirect
12. #68898C2semidirect
13. #68883C2semidirect
14. #68673C2semidirect
15. D3×#336C2semidirect
77. #1862D3semidirect
278. C2×C4×D3D8semidirect
289. C2×C3×C8#41semidirect
325. C2×C3⋊C8#41semidirect
597. C2×C8#235semidirect
831. C3#25496semidirect

Maximal subgroups

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

subgroupindex
C2×#55482
C2×#48832
C2×#47752
#762862
C3×#18622
#716132
#706172
#702112
#702092
#702022
#696252
#688982
#688832
#686732
D3×#3362
#254963