Finite Group Databasebeta

← #10811316

Subgroups — #10811316

Order 768.

1696 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5490C211yesmaximal, characteristic
2C22⋊C4×#67C212yesmaximal, complemented
3C2×C3×#342C211yesmaximal, characteristic, complemented
4#71543C212yesmaximal, complemented
5#71542C211yesmaximal, characteristic, complemented
6#68970C212yesmaximal, complemented
7#68969C211yesmaximal, characteristic, complemented
8D3×#342C211yesmaximal, characteristic, complemented
9#68959C211yesmaximal, characteristic, complemented
10#68955C212yesmaximal, complemented
11#68952C211yesmaximal, characteristic, complemented
12#22476—31nomaximal, Sylow
13C23×#67C2211yescharacteristic
14C22×#235C411yescharacteristic, complemented
15C22×C3×C22⋊C4C2211yescharacteristic
16C22×C3×C22⋊C4C2212yes—
17C2×#953C2211yescharacteristic
18C2×#930C411yescharacteristic, complemented
19C2×#929C411yescharacteristic, complemented
20C2×C4×#67—22no—
21C2×C4×#67C411yescharacteristic, complemented
22C2×#885C411yescharacteristic, complemented
23#5490—22no—
24#5490—22no—
25#5490—22no—
26#5490—22no—
27C2×#884C411yescharacteristic, complemented
28C2×#884C411yescharacteristic, complemented
29C2×#883C411yescharacteristic, complemented
30C2×#882C2211yescharacteristic
31C2×#67⋊C4C2211yescharacteristic
32C2×D3×C22⋊C4C2211yescharacteristic
33C2×D3×C22⋊C4C2212yes—
34C2×#878C2211yescharacteristic
35#5247C2212yes—
36#5213—22no—
37#4957—22no—
38#4956—22no—
39#4955C2212yes—
40C2×#806C2212yes—
41C2×#806C2212yes—
42#4942C2212yes—
43Dic3×C22⋊C4C2212yes—
44C3×#342C2211yescharacteristic
45C3×#342C2212yes—
46C3×#342C2211yescharacteristic
47#4527C2212yes—
48#4527C2212yes—
49#4526C2211yescharacteristic
50#4526C2212yes—
51#4526C2211yescharacteristic
52C2×#546—31no—
53D4×C22⋊C4—32no—
54#1996—32no—
55#1898—32no—
56#1898—32no—
57#1819—31no—
58#1819—31no—
59#1799—31no—
60C4×#99—31no—
61C2×#342—31no—
62C2×#342D311yescharacteristic, complemented
63C25×C3C2311yescharacteristic
64C24×D3C2311yescharacteristic
65C23×C3×C4—22no—
66C23×C3×C4C2×C411yescharacteristic, complemented
67C23×C3×C4C2×C411yescharacteristic, complemented
68C22×#67—44no—
69C22×#67C2×C411yescharacteristic
70C22×#67C2×C411yescharacteristic
71C22×#67C2×C411yescharacteristic
72C22×#67C2×C411yescharacteristic
73C22×#67C2×C411yescharacteristic, complemented
74C22×#67C2×C411yescharacteristic, complemented
75C22×#67D412yes—
76C22×#67D412yes—
77C22×#67D412yes—
78C22×#67D412yes—
79C22×#67C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C2×#235—21no—
82C2×#235—21no—
83C2×#235—21no—
84C2×#235—21no—
85C2×#235—44no—
86C22×D12C2×C411yescharacteristic, complemented
87C22×D12C2×C411yescharacteristic, complemented
88C22×C4×D3—22no—
89C22×C4×D3C2×C411yescharacteristic, complemented
90C22×C4×D3C2×C411yescharacteristic, complemented
91C22×C4×D3C2×C411yescharacteristic, complemented
92C22×Dic6C2×C411yescharacteristic, complemented
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—42no—
98C2×C3×C22⋊C4C2×C411yescharacteristic, complemented
99C2×C3×C22⋊C4C2×C411yescharacteristic, complemented
100C2×C3×C22⋊C4C2312yes—
101C2×C3×C22⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4C2312yes—
104#953—22no—
105#953—22no—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217C2×C411yescharacteristic, complemented
109C2×#217C2×C411yescharacteristic, complemented
110C2×#217C2312yes—
111C2×#217C2312yes—
112C2×#217C2311yescharacteristic
113#930—22no—
114#930—22no—
115#929—22no—
116#929—22no—
117C4×#67—21no—
118C4×#67—21no—
119C4×#67—21no—
120C4×#67—21no—
121C4×#67—48no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
126C2×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
127C2×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
128C2×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
129C2×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
130C2×C4⋊Dic3C2×C411yescharacteristic, complemented
131C2×Dic3⋊C4—22no—
132C2×Dic3⋊C4C2×C411yescharacteristic, complemented
133C2×Dic3⋊C4C2×C411yescharacteristic, complemented
134C2×Dic3⋊C4C2×C411yescharacteristic, complemented
135C2×C4×Dic3—22no—
136C2×C4×Dic3C2×C411yescharacteristic, complemented
137#885—22no—
138#885—22no—
139#884—22no—
140#884—22no—
141#884—22no—
142#884—22no—
143#883—22no—
144#883—22no—
145#882—22no—
146#882—22no—
147#67⋊C4—22no—
148#67⋊C4—22no—
149D3×C22⋊C4—22no—
150D3×C22⋊C4—22no—
151D3×C22⋊C4—24no—
152D3×C22⋊C4—42no—
153#878—22no—
154#878—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157#806—24no—
158#806—42no—
159C22×#41—31no—
160C23×D4—31no—
161#546—62no—
162#546—62no—
163#546—62no—
164#546—62no—
165C2×#124—31no—
166C2×#123—31no—
167C2×#123—31no—
168C2×C22⋊Q8—31no—
169C2×#121—31no—
170C2×#121—31no—
171C2×#121—31no—
172C2×#120—31no—
173C2×#120—31no—
174C2×C4×D4—31no—
175C2×C4×D4—31no—
176C2×C4×D4—62no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—32no—
179C22×C22⋊C4C2×D311yescharacteristic
180C22×C22⋊C4C2×D312yes—
181C2×#99—32no—
182C2×#99—32no—
183#390—62no—
184#386—62no—
185#386—62no—
186#380—32no—
187#379—32no—
188#379—32no—
189C4×C22⋊C4—32no—
190#342—31no—
191#342—31no—
192#342—32no—
193#342—32no—
194#342—32no—
195#342C2×D311yescharacteristic
196#342C2×D312yes—
197#342C2×D311yescharacteristic
198C24×C3—22no—
199C24×C3—21no—
200C24×C3—21no—
201C24×C3—42no—
202C24×C3—81no—
203C24×C3C22×C411yescharacteristic
204C24×C3C22×C411yescharacteristic
205C24×C3C2×D412yes—
206C24×C3C2×D412yes—
207C24×C3C2411yescharacteristic
208C23×D3—22no—
209C23×D3—21no—
210C23×D3—21no—
211C23×D3—42no—
212C23×D3—81no—
213C23×D3C22×C411yescharacteristic
214C23×D3C22×C411yescharacteristic
215C23×D3C22×C411yescharacteristic
216C23×D3C2×D412yes—
217C23×D3C2×D412yes—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—22no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—22no—
224C22×C3×C4—44no—
225C22×C3×C4—42no—
226C22×C3×C4—44no—
227C22×C3×C4—82no—
228C22×C3×C4—81no—
229C22×C3×C4C22×C411yescharacteristic
230C22×C3×C4C22×C411yescharacteristic
231C22×C3×C4C22×C411yescharacteristic
232C22×C3×C4C22×C411yescharacteristic
233C2×#67—28no—
234C2×#67—24no—
235C2×#67—21no—
236C2×#67—21no—
237C2×#67—22no—
238C2×#67—22no—
239C2×#67—21no—
240C2×#67—21no—
241C2×#67—22no—
242C2×#67—42no—
243C2×#67—44no—
244C2×#67—42no—
245C2×#67—44no—
246C2×#67—42no—
247C2×#67—44no—
248C2×#67—42no—
249C2×#67—81no—
250C2×#67C22⋊C412yes—
251C2×#67C22⋊C412yes—
252C2×#67C22⋊C411yescharacteristic
253C2×#67C22⋊C411yescharacteristic
254C2×#67C22⋊C411yescharacteristic
255C2×#67C22⋊C412yes—
256C2×#67C22⋊C412yes—
257C2×#67C22⋊C412yes—
258C2×#67C22⋊C412yes—
259C2×#67C22⋊C411yescharacteristic
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—42no—
263C22×Dic3C22×C411yescharacteristic
264C22×Dic3C22×C411yescharacteristic
265C22×Dic3C22×C411yescharacteristic
266C22×Dic3C22×C411yescharacteristic
267C22×Dic3C22×C411yescharacteristic
268C22×Dic3C2×D412yes—
269C22×Dic3C2×D412yes—
270#235—44no—
271#235—44no—
272#235—44no—
273#235—44no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—22no—
277C2×D12—42no—
278C2×D12—81no—
279C2×C4×D3—21no—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—42no—
286C2×C4×D3—42no—
287C2×C4×D3—44no—
288C2×C4×D3—44no—
289C2×C4×D3—82no—
290C2×C4×D3—81no—
291C2×Dic6—21no—
292C2×Dic6—21no—
293C2×Dic6—42no—
294C3×C22⋊C4—22no—
295C3×C22⋊C4—22no—
296C3×C22⋊C4—22no—
297C3×C22⋊C4—22no—
298C3×C22⋊C4—22no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—44no—
302C3×C22⋊C4#4114yescomplemented
303#217—22no—
304#217—21no—
305#217—21no—
306#217—22no—
307#217—22no—
308#217—22no—
309#217—22no—
310#217—22no—
311#217—44no—
312#217—82no—
313(C2×D3)⋊C4—22no—
314(C2×D3)⋊C4—22no—
315(C2×D3)⋊C4—21no—
316(C2×D3)⋊C4—21no—
317(C2×D3)⋊C4—22no—
318(C2×D3)⋊C4—22no—
319(C2×D3)⋊C4—44no—
320(C2×D3)⋊C4—44no—
321(C2×D3)⋊C4—82no—
322C4⋊Dic3—22no—
323Dic3⋊C4—21no—
324Dic3⋊C4—21no—
325Dic3⋊C4—22no—
326Dic3⋊C4—22no—
327Dic3⋊C4—44no—
328C4×Dic3—21no—
329C4×Dic3—21no—
330C4×Dic3—44no—
331C25—31no—
332C25C22×D311yescharacteristic
333C2×#41—61no—
334C2×#41—61no—
335C2×#41—61no—
336C2×#41—61no—
337C2×#41—124no—
338C22×Q8—31no—
339C22×D4—31no—
340C22×D4—32no—
341C22×D4—31no—
342C22×D4—31no—
343C22×D4—31no—
344C22×D4—32no—
345C22×D4—32no—
346C22×D4—32no—
347C22×D4—31no—
348C22×D4—31no—
349C22×D4—31no—
350C22×D4—31no—
351C22×D4—31no—
352C22×D4—124no—
353C23×C4—22no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—62no—
359C23×C4C4×D311yescharacteristic, complemented
360C23×C4C4×D311yescharacteristic, complemented
361#124—62no—
362#124—62no—
363#123—62no—
364#123—62no—
365#123—62no—
366#123—62no—
367C22⋊Q8—62no—
368C22⋊Q8—62no—
369#121—62no—
370#121—62no—
371#121—62no—
372#121—62no—
373#121—62no—
374#121—62no—
375#120—62no—
376#120—62no—
377#120—62no—
378#120—62no—
379C4×D4—62no—
380C4×D4—62no—
381C4×D4—61no—
382C4×D4—61no—
383C4×D4—61no—
384C4×D4—61no—
385C4×D4—128no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—62no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—31no—
396C2×C22⋊C4—31no—
397C2×C22⋊C4—31no—
398C2×C22⋊C4—31no—
399C2×C22⋊C4—31no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—31no—
402C2×C22⋊C4—31no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—64no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—122no—
415C2×C22⋊C4C4×D311yescharacteristic, complemented
416C2×C22⋊C4C4×D311yescharacteristic, complemented
417C2×C22⋊C4C22×D312yes—
418C2×C22⋊C4C22×D311yescharacteristic
419C2×C22⋊C4C22×D311yescharacteristic
420C2×C22⋊C4C22×D312yes—
421C2×C42—31no—
422C2×C42—62no—
423#99—64no—
424#99—122no—
425#95—62no—
426#95—62no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—24no—
432C23×C3—22no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—42no—
440C23×C3—41no—
441C23×C3—42no—
442C23×C3—41no—
443C23×C3—42no—
444C23×C3—41no—
445C23×C3—84no—
446C23×C3—82no—
447C23×C3—82no—
448C23×C3C2×C22⋊C412yes—
449C23×C3C2×C22⋊C411yescharacteristic
450C23×C3C2×C22⋊C411yescharacteristic
451C23×C3C23×C411yescharacteristic
452C23×C3C22×D412yes—
453C23×C3C2×#4112yes—
454C23×C3H(5,𝔽2)11yescharacteristic
455C23×C32−1+411yescharacteristic
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—24no—
465C22×D3—22no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—41no—
470C22×D3—42no—
471C22×D3—42no—
472C22×D3—41no—
473C22×D3—41no—
474C22×D3—42no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—82no—
478C22×D3—84no—
479C22×D3—82no—
480C22×D3C2×C22⋊C412yes—
481C22×D3C2×C22⋊C411yescharacteristic
482C22×D3C2×C22⋊C411yescharacteristic
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—24no—
488C2×C3×C4—42no—
489C2×C3×C4—42no—
490C2×C3×C4—42no—
491C2×C3×C4—42no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—42no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—81no—
500C2×C3×C4—81no—
501C2×C3×C4—88no—
502#67—22no—
503#67—24no—
504#67—22no—
505#67—24no—
506#67—22no—
507#67—24no—
508#67—42no—
509#67—42no—
510#67—42no—
511#67—42no—
512#67—42no—
513#67—42no—
514#67—42no—
515#67—82no—
516#67#9914yescomplemented
517C2×Dic3—24no—
518C2×Dic3—22no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—41no—
525C2×Dic3—42no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—42no—
529C2×Dic3—42no—
530C2×Dic3—42no—
531C2×Dic3—42no—
532C2×Dic3—42no—
533C2×Dic3—42no—
534C2×Dic3C2×C22⋊C411yescharacteristic
535C2×Dic3C2×C22⋊C412yes—
536C2×Dic3C2×C22⋊C411yescharacteristic
537D12—42no—
538D12—42no—
539D12—82no—
540C4×D3—42no—
541C4×D3—42no—
542C4×D3—42no—
543C4×D3—42no—
544C4×D3—81no—
545C4×D3—81no—
546C4×D3—88no—
547Dic6—42no—
548Dic6—42no—
549C24—22no—
550C24—21no—
551C24—21no—
552C24—31no—
553C24—32no—
554C24—31no—
555C24—32no—
556C24—31no—
557C24—42no—
558C24—62no—
559C24—61no—
560C24—61no—
561C24—81no—
562C24—122no—
563C24—241no—
564C24C2×C4×D311yescharacteristic
565C24C2×C4×D311yescharacteristic
566C24D3×D412yes—
567C24D3×D412yes—
568C24C23×D311yescharacteristic
569#41—124no—
570#41—124no—
571#41—124no—
572#41—124no—
573C2×Q8—61no—
574C2×Q8—61no—
575C2×Q8—122no—
576C2×D4—31no—
577C2×D4—31no—
578C2×D4—31no—
579C2×D4—31no—
580C2×D4—32no—
581C2×D4—32no—
582C2×D4—32no—
583C2×D4—32no—
584C2×D4—32no—
585C2×D4—32no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—62no—
589C2×D4—68no—
590C2×D4—64no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—62no—
594C2×D4—62no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—62no—
598C2×D4—122no—
599C2×D4—124no—
600C2×D4—122no—
601C2×D4—124no—
602C2×D4—122no—
603C2×D4—124no—
604C2×D4—122no—
605C2×D4—122no—
606C2×D4—241no—
607C2×D4—241no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—31no—
615C22×C4—32no—
616C22×C4—31no—
617C22×C4—32no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—44no—
622C22×C4—42no—
623C22×C4—44no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4—82no—
633C22×C4—81no—
634C22×C4—124no—
635C22×C4—122no—
636C22×C4—122no—
637C22×C4—124no—
638C22×C4—122no—
639C22×C4—242no—
640C22×C4—241no—
641C22×C4C2×C4×D311yescharacteristic
642C22×C4C2×C4×D311yescharacteristic
643C22×C4C2×C4×D311yescharacteristic
644C22×C4C2×C4×D311yescharacteristic
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—62no—
648C4⋊C4—62no—
649C4⋊C4—62no—
650C4⋊C4—124no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—44no—
659C22⋊C4—62no—
660C22⋊C4—62no—
661C22⋊C4—62no—
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4—62no—
665C22⋊C4—61no—
666C22⋊C4—61no—
667C22⋊C4—62no—
668C22⋊C4—62no—
669C22⋊C4—62no—
670C22⋊C4—62no—
671C22⋊C4—62no—
672C22⋊C4—62no—
673C22⋊C4—124no—
674C22⋊C4—124no—
675C22⋊C4—124no—
676C22⋊C4—242no—
677C22⋊C4—242no—
678C22⋊C4#23514yescomplemented
679C42—61no—
680C42—61no—
681C42—124no—
682C22×C3—21no—
683C22×C3—22no—
684C22×C3—21no—
685C22×C3—22no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—22no—
690C22×C3—21no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—21no—
694C22×C3—42no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—44no—
698C22×C3—44no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—82no—
702C22×C3—82no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3C2×#9912yes—
706C22×C3C22×C22⋊C411yescharacteristic
707C22×C3C4×#4111yescharacteristic
708C22×C3#52011yescharacteristic
709C22×C3#54612yes—
710C22×C3#54712yes—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—22no—
715C2×D3—21no—
716C2×D3—22no—
717C2×D3—21no—
718C2×D3—22no—
719C2×D3—44no—
720C2×D3—44no—
721C2×D3—42no—
722C2×D3—42no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—82no—
727C2×D3—82no—
728C2×D3—81no—
729C2×D3—81no—
730C2×D3—81no—
731C2×D3—81no—
732C2×D3C2×#9912yes—
733C3×C4—44no—
734C3×C4—41no—
735C3×C4—41no—
736C3×C4—41no—
737C3×C4—41no—
738C3×C4—82no—
739Dic3—21no—
740Dic3—22no—
741Dic3—41no—
742Dic3—41no—
743Dic3—41no—
744Dic3—82no—
745Dic3—82no—
746Dic3C2×#9912yes—
747C23—21no—
748C23—22no—
749C23—21no—
750C23—22no—
751C23—24no—
752C23—22no—
753C23—21no—
754C23—22no—
755C23—21no—
756C23—22no—
757C23—31no—
758C23—32no—
759C23—31no—
760C23—41no—
761C23—42no—
762C23—41no—
763C23—41no—
764C23—42no—
765C23—41no—
766C23—42no—
767C23—41no—
768C23—64no—
769C23—62no—
770C23—61no—
771C23—62no—
772C23—61no—
773C23—62no—
774C23—61no—
775C23—62no—
776C23—61no—
777C23—62no—
778C23—61no—
779C23—61no—
780C23—61no—
781C23—84no—
782C23—82no—
783C23—82no—
784C23—122no—
785C23—121no—
786C23—122no—
787C23—122no—
788C23—121no—
789C23—121no—
790C23—121no—
791C23—121no—
792C23—244no—
793C23—242no—
794C23—242no—
795C23D3×C22⋊C412yes—
796C23D3×C22⋊C411yescharacteristic
797C23D3×C22⋊C411yescharacteristic
798C23C22×C4×D311yescharacteristic
799C23C2×#23512yes—
800C23C2×D3×D412yes—
801C23#100411yescharacteristic
802C23#100711yescharacteristic
803Q8—122no—
804Q8—122no—
805D4—34no—
806D4—62no—
807D4—64no—
808D4—62no—
809D4—64no—
810D4—62no—
811D4—64no—
812D4—122no—
813D4—122no—
814D4—122no—
815D4—122no—
816D4—122no—
817D4—122no—
818D4—122no—
819D4—122no—
820D4—122no—
821D4—242no—
822D4—242no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—24no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—32no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—64no—
843C2×C4—62no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—88no—
852C2×C4—122no—
853C2×C4—122no—
854C2×C4—122no—
855C2×C4—122no—
856C2×C4—122no—
857C2×C4—121no—
858C2×C4—121no—
859C2×C4—121no—
860C2×C4—122no—
861C2×C4—122no—
862C2×C4—122no—
863C2×C4—122no—
864C2×C4—122no—
865C2×C4—122no—
866C2×C4—241no—
867C2×C4—241no—
868C2×C4—248no—
869C2×C3—22no—
870C2×C3—22no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—22no—
874C2×C3—41no—
875C2×C3—42no—
876C2×C3#233911yescharacteristic
877C2×C3C22×#9911yescharacteristic
878C2×C3#288311yescharacteristic
879D3—22no—
880D3—41no—
881D3—42no—
882D3—81no—
883C22—22no—
884C22—21no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—21no—
889C22—21no—
890C22—22no—
891C22—21no—
892C22—22no—
893C22—21no—
894C22—22no—
895C22—32no—
896C22—42no—
897C22—41no—
898C22—41no—
899C22—44no—
900C22—44no—
901C22—42no—
902C22—42no—
903C22—61no—
904C22—61no—
905C22—61no—
906C22—62no—
907C22—61no—
908C22—62no—
909C22—62no—
910C22—61no—
911C22—82no—
912C22—82no—
913C22—81no—
914C22—81no—
915C22—124no—
916C22—124no—
917C22—122no—
918C22—122no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—242no—
923C22—242no—
924C22—241no—
925C22—241no—
926C22—241no—
927C22—241no—
928C22D3×#9912yes—
929C22C4×#23511yescharacteristic
930C22C2×D3×C22⋊C411yescharacteristic
931C22#549012yes—
932C22#550411yescharacteristic
933C22#550712yes—
934C4—32no—
935C4—44no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—61no—
941C4—62no—
942C4—82no—
943C4—121no—
944C4—121no—
945C4—121no—
946C4—242no—
947C4—242no—
948C3#2247611yescharacteristic, complemented, Sylow
949C2—22no—
950C2—22no—
951C2—22no—
952C2—21no—
953C2—21no—
954C2—41no—
955C2—42no—
956C2—62no—
957C2—121no—
958C2—122no—
959C2—241no—
960C2#7336811yescharacteristic
961C2C2×D3×#9911yescharacteristic
962C2#7868811yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC2×C3×#342C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5490C2
cosocleC24×C3C24
hypercenterC2×#342D3
hypocenterC3#22476
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×#67C2semidirect
3. C2×C3×#342C2semidirect
4. #71543C2semidirect
5. #71542C2semidirect
6. #68970C2semidirect
7. #68969C2semidirect
8. D3×#342C2semidirect
9. #68959C2semidirect
10. #68955C2semidirect
11. #68952C2semidirect
14. C22×#235C4semidirect
18. C2×#930C4semidirect
19. C2×#929C4semidirect
21. C2×C4×#67C4semidirect
22. C2×#885C4semidirect
27. C2×#884C4semidirect
28. C2×#884C4semidirect
29. C2×#883C4semidirect
62. C2×#342D3semidirect
66. C23×C3×C4C2×C4semidirect
67. C23×C3×C4C2×C4semidirect
73. C22×#67C2×C4semidirect
74. C22×#67C2×C4semidirect
86. C22×D12C2×C4semidirect
87. C22×D12C2×C4semidirect
89. C22×C4×D3C2×C4semidirect
90. C22×C4×D3C2×C4semidirect
91. C22×C4×D3C2×C4semidirect
92. C22×Dic6C2×C4semidirect
98. C2×C3×C22⋊C4C2×C4semidirect
99. C2×C3×C22⋊C4C2×C4semidirect
108. C2×#217C2×C4semidirect
109. C2×#217C2×C4semidirect
125. C2×(C2×D3)⋊C4C2×C4semidirect
126. C2×(C2×D3)⋊C4C2×C4semidirect
127. C2×(C2×D3)⋊C4C2×C4semidirect
128. C2×(C2×D3)⋊C4C2×C4semidirect
129. C2×(C2×D3)⋊C4C2×C4semidirect
130. C2×C4⋊Dic3C2×C4semidirect
132. C2×Dic3⋊C4C2×C4semidirect
133. C2×Dic3⋊C4C2×C4semidirect
134. C2×Dic3⋊C4C2×C4semidirect
136. C2×C4×Dic3C2×C4semidirect
302. C3×C22⋊C4#41semidirect
359. C23×C4C4×D3semidirect
360. C23×C4C4×D3semidirect
415. C2×C22⋊C4C4×D3semidirect
416. C2×C22⋊C4C4×D3semidirect
516. #67#99semidirect
678. C22⋊C4#235semidirect
948. C3#22476semidirect

Maximal subgroups

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

subgroupindex
C2×#54902
C22⋊C4×#672
C2×C3×#3422
#715432
#715422
#689702
#689692
D3×#3422
#689592
#689552
#689522
#224763