Finite Group Databasebeta

← #10847381

Subgroups — #10847381

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×#5157C211yesmaximal, characteristic, complemented
3C2×#4775C211yesmaximal, characteristic, complemented
4#76475C211yesmaximal, characteristic, complemented
5C3×#1879C211yesmaximal, characteristic, complemented
6#72044C211yesmaximal, characteristic, complemented
7#71606C211yesmaximal, characteristic, complemented
8#70202C211yesmaximal, characteristic, complemented
9#70177C211yesmaximal, characteristic, complemented
10#70163C211yesmaximal, characteristic, complemented
11#69657C211yesmaximal, characteristic, complemented
12#68883C211yesmaximal, characteristic, complemented
13#68826C211yesmaximal, characteristic, complemented
14#68670C211yesmaximal, characteristic, complemented
15D3×#336C211yesmaximal, characteristic, complemented
16#25496—31nomaximal, Sylow
17C22×#235—21no—
18C22×C3×D8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#940C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×C4×#67—21no—
25C22×D3×C8C2211yescharacteristic
26C22×D3×C8C2211yescharacteristic
27#5548—24no—
28#5548—24no—
29C2×#895C2211yescharacteristic
30C2×#888C2211yescharacteristic
31C2×#885—21no—
32C2×#884—21no—
33C2×#883—21no—
34C2×C4×D12C2211yescharacteristic
35C2×C42×D3C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C3×#390C2211yescharacteristic
39#5221C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43#5157—24no—
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×#818C2211yescharacteristic
47#4987C2211yescharacteristic
48#4984C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4956—21no—
52#4951—21no—
53#4945—21no—
54#4928C2211yescharacteristic
55#4775—24no—
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#1879D311yescharacteristic, complemented
76#1862—31no—
77#1862—31no—
78C2×#336—31no—
79C22×C3×D4C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C22×#67—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C2×#235—28no—
87C2×#235—44no—
88C2×#235—44no—
89C22×D12—21no—
90C22×D12C2311yescharacteristic
91C22×C4×D3—21no—
92C22×C4×D3D411yescharacteristic
93C22×C4×D3D411yescharacteristic
94C22×C4×D3C2311yescharacteristic
95C22×Dic6—21no—
96C2×C3×D8—22no—
97C2×C3×D8—22no—
98C2×C3×D8—41no—
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×C4×D4—22no—
102C3×C4×D4—22no—
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C22⋊C4—21no—
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#940—22no—
114#940—22no—
115#938—22no—
116#938—22no—
117#938—22no—
118#938D414yes—
119C2×#213—22no—
120C2×#213—22no—
121C2×#213—41no—
122C4×#67—28no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×C4⋊Dic3—21no—
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×C4×Dic3D411yescharacteristic
133C2×C4×Dic3D411yescharacteristic
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C2×D3×C8—22no—
138C2×D3×C8—22no—
139C2×D3×C8—22no—
140C2×D3×C8—22no—
141C2×D3×C8—41no—
142C2×D3×C8—41no—
143#895—22no—
144#895D414yes—
145#888—22no—
146#888—22no—
147#885—28no—
148#884—28no—
149#883—44no—
150C4×D12—22no—
151C4×D12—22no—
152C42×D3—22no—
153C42×D3—22no—
154C3×#102—22no—
155C3×#102—41no—
156#832—22no—
157#832—22no—
158#832—22no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#821—22no—
163#821—22no—
164#818—22no—
165#809—41no—
166#807—22no—
167C22×#41—61no—
168C22×D8—31no—
169C22×D8C2×D311yescharacteristic
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×#107—31no—
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#390C2×D311yescharacteristic
200#389—31no—
201#389—31no—
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—
215C24×C3—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×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4C2×D412yes—
230C22×C3×C4—24no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—42no—
234C22×C3×C4—42no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2411yescharacteristic
238C2×#67—24no—
239C2×#67—24no—
240C2×#67—24no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256#235—432no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—24no—
262C2×D12—21no—
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—
284C3×D8—44no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8#4112yescomplemented
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4C2×D412yes—
295C3×C22⋊C4—24no—
296C3×C22⋊C4—42no—
297C3×C22⋊C4—42no—
298C3×C42—21no—
299C3×C42—21no—
300#217—24no—
301#217—42no—
302#217—42no—
303#217—42no—
304#213—44no—
305(C2×D3)⋊C4—24no—
306(C2×D3)⋊C4—24no—
307(C2×D3)⋊C4—42no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—42no—
314C4⋊Dic3C2×D412yes—
315Dic3⋊C4—24no—
316Dic3⋊C4—42no—
317C4×Dic3—21no—
318C4×Dic3—21no—
319C4×Dic3—22no—
320C4×Dic3—22no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8#4112yescomplemented
327D3×C8—44no—
328D3×C8—44no—
329C2×#41—68no—
330C2×#41—124no—
331C2×#41—124no—
332C22×Q8—61no—
333C22×D4—31no—
334C22×D4—61no—
335C22×D4—61no—
336C22×D4—61no—
337C22×D4—61no—
338C22×D4—61no—
339C22×D4C22×D311yescharacteristic
340C22×D4C22×D311yescharacteristic
341C23×C4—21no—
342C23×C4—31no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—61no—
346C2×D8—22no—
347C2×D8—22no—
348C2×D8—41no—
349C2×D8—62no—
350C2×D8—62no—
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—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4—61no—
386C2×C4⋊C4C22×D311yescharacteristic
387C2×C4⋊C4C22×D311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
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—62no—
405#107—62no—
406#102—22no—
407#102—41no—
408#102—62no—
409#102—62no—
410#102—62no—
411#102—62no—
412#102—62no—
413#102—121no—
414#95—61no—
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×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3C22×D411yescharacteristic
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—22no—
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—
450C3×D4—41no—
451C3×D4—41no—
452C3×D4—41no—
453C3×D4—41no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—22no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—48no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4C2×D812yes—
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4H(5,𝔽2)11yescharacteristic
472C2×C3×C42−1+411yescharacteristic
473#67—48no—
474#67—48no—
475#67—48no—
476#67—84no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3#12012yes—
493C2×Dic3C2×D812yes—
494C2×Dic3#13512yes—
495D12—22no—
496D12—22no—
497D12—48no—
498D12—41no—
499D12—41no—
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—21no—
514C24—31no—
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—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—32no—
532C2×D4—64no—
533C2×D4—64no—
534C2×D4—64no—
535C2×D4—64no—
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—31no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—34no—
560C22×C4—32no—
561C22×C4—32no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—64no—
569C22×C4—61no—
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—44no—
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—32no—
602C4⋊C4—64no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—122no—
609C4⋊C4—122no—
610C4⋊C4D3×D412yes—
611C22⋊C4—24no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—64no—
615C22⋊C4—64no—
616C22⋊C4—64no—
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×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3C2×#12011yescharacteristic
642C22×C3#53211yescharacteristic
643C22×C3#53711yescharacteristic
644C22×C3C22×D811yescharacteristic
645C22×C3C2×#13511yescharacteristic
646C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
647C22×C3#57511yescharacteristic
648C2×D3—22no—
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—42no—
655C2×D3—42no—
656C2×D3—42no—
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#54611yescharacteristic
667C3×C4#54611yescharacteristic
668C3×C4#54711yescharacteristic
669C3×C4#54711yescharacteristic
670Dic3—22no—
671Dic3—22no—
672Dic3—22no—
673Dic3—42no—
674Dic3—81no—
675Dic3—81no—
676C23—22no—
677C23—32no—
678C23—32no—
679C23—32no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—61no—
694C23—61no—
695C23—61no—
696C23—61no—
697C23—62no—
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—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—62no—
715D4—62no—
716D4—128no—
717D4—128no—
718D4—128no—
719D4—128no—
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—68no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—128no—
751C2×C4—124no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—121no—
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#100411yescharacteristic
765C2×C4D3×#4111yescharacteristic
766C2×C4#101011yescharacteristic
767C8—22no—
768C8—41no—
769C8—62no—
770C8—121no—
771C2×C3—82no—
772C2×C3—161no—
773C2×C3#243011yescharacteristic
774C2×C3C2×#44711yescharacteristic
775C2×C3#300211yescharacteristic
776C2×C3#316911yescharacteristic
777C2×C3#318011yescharacteristic
778C2×C3#324511yescharacteristic
779C2×C3#324711yescharacteristic
780D3—24no—
781D3—82no—
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—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—122no—
804C22—122no—
805C22—122no—
806C22—241no—
807C22—241no—
808C22—241no—
809C22—241no—
810C22#554811yescharacteristic
811C22D3×#12011yescharacteristic
812C22#560811yescharacteristic
813C22C2×D3×D811yescharacteristic
814C22D3×#13511yescharacteristic
815C22D3×AGL(1,ℤ/8)11yescharacteristic
816C22#577311yescharacteristic
817C4—22no—
818C4—42no—
819C4—41no—
820C4—62no—
821C4—62no—
822C4—62no—
823C4—81no—
824C4—122no—
825C4—241no—
826C4—241no—
827C4#549011yescharacteristic
828C4#555111yescharacteristic
829C4#561211yescharacteristic
830C4#565511yescharacteristic
831C3#2549611yescharacteristic, complemented, Sylow
832C2—64no—
833C2—82no—
834C2—161no—
835C2—242no—
836C2#7489611yescharacteristic
837C2#7959811yescharacteristic
838C2#7987611yescharacteristic
839C2D3×#44711yescharacteristic
840C2#8008211yescharacteristic
841C2#8034211yescharacteristic
842C2#8051211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1879C2
socleC23×C3C22×D4
hypercenter#1879D3
hypocenterC3#25496
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. C2×#5548C2semidirect
2. C2×#5157C2semidirect
3. C2×#4775C2semidirect
4. #76475C2semidirect
5. C3×#1879C2semidirect
6. #72044C2semidirect
7. #71606C2semidirect
8. #70202C2semidirect
9. #70177C2semidirect
10. #70163C2semidirect
11. #69657C2semidirect
12. #68883C2semidirect
13. #68826C2semidirect
14. #68670C2semidirect
15. D3×#336C2semidirect
75. #1879D3semidirect
278. C2×C4×D3D8semidirect
290. C2×C3×C8#41semidirect
326. 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×#51572
C2×#47752
#764752
C3×#18792
#720442
#716062
#702022
#701772
#701632
#696572
#688832
#688262
#686702
D3×#3362
#254963