Finite Group Databasebeta

← #10827601

Subgroups — #10827601

Order 768.

1300 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5511C211yesmaximal, characteristic, complemented
2C2×#4966C211yesmaximal, characteristic, complemented
3C2×#4733C211yesmaximal, characteristic, complemented
4#74015C211yesmaximal, characteristic
5C3×#1823C211yesmaximal, characteristic, complemented
6#69953C211yesmaximal, characteristic, complemented
7#69516C211yesmaximal, characteristic, complemented
8#68910C211yesmaximal, characteristic, complemented
9#68909C211yesmaximal, characteristic, complemented
10#68908C211yesmaximal, characteristic, complemented
11#68898C211yesmaximal, characteristic, complemented
12#68888C211yesmaximal, characteristic, complemented
13#68887C211yesmaximal, characteristic, complemented
14#68880C211yesmaximal, characteristic, complemented
15#68878C211yesmaximal, characteristic, complemented
16#23981—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C2×C4×#67—21no—
20C2×C4×#67C2211yescharacteristic
21C2×#924—21no—
22C2×#924C2211yescharacteristic
23C22×#208C2211yescharacteristic
24C22×Dic12C2211yescharacteristic
25C22×#204C2211yescharacteristic
26#5511—24no—
27#5511—24no—
28C2×#897C2211yescharacteristic
29C2×#897C2211yescharacteristic
30C2×#896—21no—
31C2×#895C2211yescharacteristic
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#889—21no—
34C2×#888C2211yescharacteristic
35C2×#887C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C3×#380C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×#816C2211yescharacteristic
42#4988C2211yescharacteristic
43#4973C2211yescharacteristic
44C2×#810C2211yescharacteristic
45C2×#810C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48#4966—24no—
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51#4961—21no—
52#4960—21no—
53#4733—24no—
54#4668—21no—
55#4665—21no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#554—31no—
65C2×#452—31no—
66C2×#417—31no—
67#2407—31no—
68#2024—31no—
69#2023—31no—
70#2001—31no—
71#2000—31no—
72#1894—31no—
73#1880—31no—
74#1878—31no—
75#1874—31no—
76#1872—31no—
77#1870—31no—
78#1823D311yescharacteristic, complemented
79C23×C3×C4—21no—
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67D411yescharacteristic
83C2×#235—22no—
84C2×#235—22no—
85C2×#235—22no—
86C2×#235—22no—
87C2×#235—41no—
88C2×#235—41no—
89C22×D12—21no—
90C22×D12C2311yescharacteristic
91C22×C4×D3—21no—
92C22×C4×D3—21no—
93C22×C4×D3C2311yescharacteristic
94C22×Dic6—21no—
95C22×Dic6C2311yescharacteristic
96C22×Dic6C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4D414yescomplemented
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×#217—21no—
108C2×#217D411yescharacteristic
109C4×#67—28no—
110C4×#67—22no—
111C4×#67—22no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4D411yescharacteristic
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3C2311yescharacteristic
121#924—28no—
122#924—22no—
123#924D414yescomplemented
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4D411yescharacteristic
129C2×C4×Dic3—21no—
130C2×C4×Dic3C2311yescharacteristic
131C2×#208—22no—
132C2×#208—41no—
133C2×#208—41no—
134C22×C3⋊C8C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C2×Dic12—22no—
137C2×Dic12—22no—
138C2×Dic12—41no—
139C2×#204—22no—
140C2×#204—22no—
141C2×#204—41no—
142#897—22no—
143#897—22no—
144#897—22no—
145#897—41no—
146#896—28no—
147#895—22no—
148#895—41no—
149D3×C4⋊C4—22no—
150D3×C4⋊C4—22no—
151#889—28no—
152#888—22no—
153#888—22no—
154#887—22no—
155#887—22no—
156C3×C22⋊C8—22no—
157C3×#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160#821—22no—
161(C2×D3)⋊C8—41no—
162(C2×D3)⋊C8—41no—
163#816—22no—
164#810—22no—
165#810—22no—
166#810—41no—
167#810—41no—
168#809—22no—
169#809—22no—
170C22×#41—31no—
171C22×Q16—31no—
172C22×SD16—31no—
173C22×M16—31no—
174#554—64no—
175#554—64no—
176C2×C4⋊Q8—31no—
177C2×#125—61no—
178C2×C22⋊Q8—31no—
179C2×C22⋊Q8—31no—
180C2×C22⋊Q8—31no—
181C2×C22⋊Q8—61no—
182C2×C22⋊Q8—61no—
183C2×#121—31no—
184C2×C4×Q8—31no—
185C2×C4×D4—31no—
186C2×C4×D4—61no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4C2×D311yescharacteristic
189#452—64no—
190#417—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8C2×D311yescharacteristic
202#394—61no—
203#392—61no—
204#391—31no—
205#390—31no—
206#386—61no—
207#385—61no—
208#380C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#340C2×D311yescharacteristic
212#340C2×D311yescharacteristic
213#340C2×D311yescharacteristic
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3C2×D411yescharacteristic
218C23×D3—21no—
219C23×D3C2×D411yescharacteristic
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—24no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—81no—
230C22×C3×C4—81no—
231C22×C3×C4C2×D412yes—
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D412yes—
234C22×C3×C4C2411yescharacteristic
235C2×#67—22no—
236C2×#67—22no—
237C2×#67—22no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—42no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C22×Dic3C2×D411yescharacteristic
247#235—28no—
248#235—44no—
249#235—44no—
250#235—44no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—42no—
257C2×D12—42no—
258C2×D12—81no—
259C2×D12#4112yes—
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—24no—
267C2×C4×D3—42no—
268C2×C4×D3—42no—
269C2×C4×D3—42no—
270C2×C4×D3—81no—
271C2×C4×D3—81no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6—21no—
280C2×Dic6—21no—
281C2×Dic6—21no—
282C2×Dic6—24no—
283C2×Dic6—81no—
284C2×Dic6—81no—
285C2×Dic6C2×D412yes—
286C2×Dic6#4112yes—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C3×C4⋊C4—24no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4C2×D412yes—
301C3×C4⋊C4C2×D412yes—
302C3×C22⋊C4—81no—
303#217—22no—
304#217—24no—
305(C2×D3)⋊C4—24no—
306(C2×D3)⋊C4—22no—
307(C2×D3)⋊C4—42no—
308(C2×D3)⋊C4—42no—
309(C2×D3)⋊C4—42no—
310(C2×D3)⋊C4—81no—
311C4⋊Dic3—24no—
312C4⋊Dic3—21no—
313C4⋊Dic3—42no—
314C4⋊Dic3C2×D412yes—
315Dic3⋊C4—24no—
316Dic3⋊C4—24no—
317Dic3⋊C4—24no—
318Dic3⋊C4—22no—
319Dic3⋊C4—24no—
320C4×Dic3—24no—
321C4×Dic3—21no—
322C4×Dic3—21no—
323#208—44no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330Dic12—44no—
331#204—44no—
332C2×#41—62no—
333C2×#41—62no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—121no—
337C2×#41—121no—
338C22×Q8—31no—
339C22×Q8—31no—
340C22×Q8—61no—
341C22×D4—31no—
342C22×D4—31no—
343C22×D4—61no—
344C22×D4—61no—
345C23×C4—21no—
346C23×C4—31no—
347C23×C4—61no—
348C23×C4—61no—
349C23×C4C22×D311yescharacteristic
350C2×Q16—62no—
351C2×Q16—62no—
352C2×Q16—121no—
353C2×SD16—62no—
354C2×SD16—62no—
355C2×SD16—121no—
356C2×M16—62no—
357C2×M16—121no—
358C2×M16—121no—
359C22×C8—31no—
360C22×C8—31no—
361C22×C8C22×D311yescharacteristic
362C22×C8C22×D311yescharacteristic
363C4⋊Q8—62no—
364C4⋊Q8—62no—
365#125—68no—
366C22⋊Q8—34no—
367C22⋊Q8—62no—
368C22⋊Q8—68no—
369C22⋊Q8—68no—
370C22⋊Q8—62no—
371C22⋊Q8—62no—
372C22⋊Q8—62no—
373C22⋊Q8—121no—
374#121—62no—
375#121—121no—
376C4×Q8—62no—
377C4×Q8—62no—
378C4×D4—68no—
379C4×D4—62no—
380C4×D4—62no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4—61no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4—61no—
390C2×C4⋊C4—61no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4D1214yescomplemented
394C2×C4⋊C4C22×D311yescharacteristic
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—31no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—61no—
402C2×C22⋊C4—61no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C42—31no—
408C2×C42—61no—
409#103—62no—
410#103—62no—
411#103—62no—
412#103—121no—
413#103—121no—
414#102—62no—
415#102—62no—
416#102—62no—
417C22⋊C8—22no—
418C22⋊C8—121no—
419C22⋊C8—121no—
420#95—21no—
421#95—61no—
422#95—61no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3#12012yes—
430C23×C3C22×D411yescharacteristic
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—22no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3#13712yes—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
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—84no—
464C2×C3×C4#12012yes—
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4H(5,𝔽2)11yescharacteristic
470C2×C3×C4H(5,𝔽2)11yescharacteristic
471#67—28no—
472#67—48no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—22no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—22no—
479C2×Dic3—21no—
480C2×Dic3—22no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3#13712yes—
491D12—22no—
492D12—22no—
493D12—41no—
494D12—41no—
495D12—84no—
496C4×D3—48no—
497C4×D3—41no—
498C4×D3—41no—
499C4×D3—41no—
500C4×D3—41no—
501C4×D3—84no—
502Dic6—22no—
503Dic6—22no—
504Dic6—22no—
505Dic6—22no—
506Dic6—41no—
507Dic6—41no—
508Dic6—41no—
509Dic6—41no—
510Dic6—84no—
511C3×C8—41no—
512C3×C8—41no—
513C3⋊C8—41no—
514C3⋊C8—41no—
515C24—31no—
516C24—61no—
517C24D3×D411yescharacteristic
518#41—68no—
519#41—124no—
520#41—124no—
521#41—124no—
522C2×Q8—32no—
523C2×Q8—32no—
524C2×Q8—64no—
525C2×Q8—61no—
526C2×Q8—61no—
527C2×Q8—61no—
528C2×Q8—61no—
529C2×Q8—61no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—241no—
536C2×Q8—241no—
537C2×D4—32no—
538C2×D4—62no—
539C2×D4—62no—
540C2×D4—62no—
541C2×D4—61no—
542C2×D4—61no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4—122no—
549C2×D4—122no—
550C2×D4—122no—
551C2×D4—241no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—64no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—81no—
575C22×C4—81no—
576C22×C4—122no—
577C22×C4—122no—
578C22×C4—122no—
579C22×C4—241no—
580C22×C4—241no—
581C22×C4C2×D1212yes—
582C22×C4D3×D411yescharacteristic
583C22×C4D3×D412yes—
584C22×C4C23×D311yescharacteristic
585Q16—124no—
586SD16—124no—
587M16—124no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—61no—
595C2×C8—61no—
596C2×C8—61no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—32no—
608C4⋊C4—64no—
609C4⋊C4—64no—
610C4⋊C4—64no—
611C4⋊C4—64no—
612C4⋊C4—62no—
613C4⋊C4—64no—
614C4⋊C4—61no—
615C4⋊C4—122no—
616C4⋊C4C2×D1212yes—
617C4⋊C4C2×D1212yes—
618C22⋊C4—64no—
619C22⋊C4—62no—
620C22⋊C4—64no—
621C22⋊C4—62no—
622C22⋊C4—81no—
623C22⋊C4—122no—
624C22⋊C4—122no—
625C22⋊C4—122no—
626C22⋊C4—241no—
627C42—64no—
628C42—61no—
629C42—61no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3C2×#12011yescharacteristic
638C22×C3#54611yescharacteristic
639C22×C3#54611yescharacteristic
640C22×C3C2×#13711yescharacteristic
641C22×C3C2×#13711yescharacteristic
642C22×C3#57611yescharacteristic
643C22×C3#57711yescharacteristic
644C2×D3—22no—
645C2×D3—22no—
646C2×D3—22no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—81no—
655C2×D3—81no—
656C2×D3—81no—
657C2×D3—81no—
658C3×C4—22no—
659C3×C4—42no—
660C3×C4—42no—
661C3×C4—81no—
662C3×C4—81no—
663C3×C4#52511yescharacteristic
664C3×C4#53511yescharacteristic
665C3×C4#54611yescharacteristic
666C3×C4#54611yescharacteristic
667Dic3—22no—
668Dic3—42no—
669Dic3—42no—
670Dic3—41no—
671Dic3—41no—
672Dic3—42no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—32no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—62no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23#88212yes—
694C23C2×D3×D411yescharacteristic
695Q8—62no—
696Q8—62no—
697Q8—62no—
698Q8—62no—
699Q8—121no—
700Q8—121no—
701Q8—121no—
702Q8—121no—
703Q8—244no—
704D4—68no—
705D4—62no—
706D4—62no—
707D4—128no—
708D4—121no—
709D4—121no—
710D4—244no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—32no—
720C2×C4—41no—
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—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—62no—
734C2×C4—61no—
735C2×C4—62no—
736C2×C4—61no—
737C2×C4—62no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—84no—
742C2×C4—128no—
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—121no—
752C2×C4—121no—
753C2×C4—244no—
754C2×C4#88212yes—
755C2×C4C22×D1211yescharacteristic
756C2×C4C2×D3×D411yescharacteristic
757C2×C4D3×#4111yescharacteristic
758C2×C4D3×#4111yescharacteristic
759C2×C4#100911yescharacteristic
760C2×C4#100911yescharacteristic
761C8—41no—
762C8—41no—
763C8—121no—
764C8—121no—
765C2×C3—42no—
766C2×C3#240411yescharacteristic
767C2×C3#300411yescharacteristic
768C2×C3#301211yescharacteristic
769C2×C3#331411yescharacteristic
770C2×C3#331611yescharacteristic
771C2×C3#333111yescharacteristic
772C2×C3#333311yescharacteristic
773D3—42no—
774D3—82no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—62no—
783C22—62no—
784C22—62no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—122no—
790C22—122no—
791C22—122no—
792C22—241no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22C2×#88211yescharacteristic
797C22#565411yescharacteristic
798C22#565411yescharacteristic
799C22#575711yescharacteristic
800C22#576211yescharacteristic
801C22D3×#13711yescharacteristic
802C22D3×#13711yescharacteristic
803C4—22no—
804C4—42no—
805C4—42no—
806C4—62no—
807C4—81no—
808C4—81no—
809C4—121no—
810C4—122no—
811C4—122no—
812C4—121no—
813C4—122no—
814C4#552411yescharacteristic
815C4#552511yescharacteristic
816C4#565411yescharacteristic
817C4#565411yescharacteristic
818C3#2398111yescharacteristic, complemented, Sylow
819C2—42no—
820C2—122no—
821C2—242no—
822C2#7412511yescharacteristic
823C2#7874711yescharacteristic
824C2#7895811yescharacteristic
825C2#8128911yescharacteristic
826C2#8130711yescharacteristic
827C2#8143311yescharacteristic
828C2#8144711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1823C2
socleC23×C3C22×D4
prime radical#74015C2
hypercenter#1823D3
hypocenterC3#23981
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
1. C2×#5511C2semidirect
2. C2×#4966C2semidirect
3. C2×#4733C2semidirect
5. C3×#1823C2semidirect
6. #69953C2semidirect
7. #69516C2semidirect
8. #68910C2semidirect
9. #68909C2semidirect
10. #68908C2semidirect
11. #68898C2semidirect
12. #68888C2semidirect
13. #68887C2semidirect
14. #68880C2semidirect
15. #68878C2semidirect
78. #1823D3semidirect
101. C2×C3×C4⋊C4D4semidirect
123. #924D4semidirect
393. C2×C4⋊C4D12semidirect
818. C3#23981semidirect

Maximal subgroups

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

subgroupindex
C2×#55112
C2×#49662
C2×#47332
#740152
C3×#18232
#699532
#695162
#689102
#689092
#689082
#688982
#688882
#688872
#688802
#688782
#239813