Finite Group Databasebeta

← #385508

Subgroups — #385508

Order 512.

1490 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1869C211yesmaximal, characteristic
2C2×#1854C211yesmaximal, characteristic, complemented
3C2×#1808C211yesmaximal, characteristic, complemented
4#13906C211yesmaximal, characteristic
5#13871C211yesmaximal, characteristic
6#11324C211yesmaximal, characteristic, complemented
7#11267C211yesmaximal, characteristic, complemented
8#11096C211yesmaximal, characteristic, complemented
9#11096C211yesmaximal, characteristic, complemented
10#11096C211yesmaximal, characteristic, complemented
11#11095C211yesmaximal, characteristic, complemented
12#10908C211yesmaximal, characteristic, complemented
13#10907C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic, complemented
15#10721C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C2×#390—21no—
27C2×#384C2211yescharacteristic
28C2×#380C2211yescharacteristic
29C2×#380C2211yescharacteristic
30C2×#380C2211yescharacteristic
31C2×#380C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×#380C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36#1869C418yescomplemented
37#1854—24no—
38#1808—24no—
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53#1440—21no—
54#1439—21no—
55#1439—21no—
56#1438—21no—
57#1437—21no—
58#1436—21no—
59C4⋊#95—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C23×D4D411yescharacteristic
63C24×C4C2311yescharacteristic
64C24×C4C2311yescharacteristic
65C23×C8—22no—
66C23×C8—22no—
67C23×C8—41no—
68C23×C8—41no—
69C23×C8—41no—
70C23×C8—41no—
71C23×C8C2×C414yes—
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C2×C4×D4—41no—
77C2×C4×D4—41no—
78C2×C4×D4—41no—
79C2×C4×D4—41no—
80C2×C4×D4C2×C414yes—
81C2×C4×D4Q814yes—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—41no—
85C2×#117—41no—
86C2×#117—41no—
87C2×#117—41no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4D411yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C22⋊C4D411yescharacteristic
108C22×C22⋊C4D411yescharacteristic
109C22×C42—21no—
110C22×C42—21no—
111C22×C42C2311yescharacteristic
112C2×#107—22no—
113C2×#107—41no—
114C2×#107—41no—
115C2×#107—41no—
116C2×#107—41no—
117C2×#107—41no—
118C2×#107—41no—
119C2×#107—41no—
120C2×#107D414yescomplemented
121C2×#106—22no—
122C2×#106—22no—
123C2×#106—41no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—41no—
127C2×C22⋊C8—41no—
128C2×C22⋊C8—41no—
129C2×C22⋊C8—41no—
130C2×C22⋊C8C2×C414yes—
131C2×C22⋊C8C2×C414yes—
132C2×C22⋊C8C2×C414yes—
133#390—44no—
134#384—41no—
135#384—41no—
136#380—22no—
137#380—22no—
138#380—22no—
139#380—22no—
140#380—22no—
141#380—22no—
142#380—41no—
143#380—41no—
144#380—41no—
145#380—41no—
146#380—41no—
147#380—41no—
148#380—41no—
149#380—41no—
150C4×C4⋊C4—41no—
151C4×C4⋊C4—41no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—41no—
171#340—41no—
172#340—41no—
173#340—41no—
174#340—41no—
175#340—41no—
176#336C2×C414yes—
177#336C2×C414yes—
178C25C2×D411yescharacteristic
179C25C2×D411yescharacteristic
180C22×D4—22no—
181C22×D4—22no—
182C22×D4—22no—
183C22×D4—22no—
184C22×D4—41no—
185C22×D4—41no—
186C22×D4C4⋊C414yes—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4C22×C412yes—
220C23×C4C22×C412yes—
221C23×C4C2×D411yescharacteristic
222C23×C4C2×D411yescharacteristic
223C23×C4C2×D411yescharacteristic
224C23×C4C2×D411yescharacteristic
225C23×C4C2×Q812yes—
226C23×C4C2×Q812yes—
227C23×C4C2411yescharacteristic
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—28no—
251C22×C8—44no—
252C22×C8—44no—
253C22×C8—44no—
254C22×C8—44no—
255C22×C8—44no—
256C22×C8—44no—
257C22×C8C22×C412yes—
258C22×C8C22×C412yes—
259C22×C8C22×C412yes—
260C22×C8C22×C412yes—
261C22×C8C2×D412yes—
262C22×C8#4112yes—
263C4×D4—44no—
264C4×D4—44no—
265C4×D4—44no—
266C4×D4—44no—
267#117—44no—
268#117—44no—
269#117—44no—
270#117—44no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—81no—
322C2×C4⋊C4—81no—
323C2×C4⋊C4C4⋊C414yes—
324C2×C4⋊C4C2×D412yes—
325C2×C4⋊C4C2×D412yes—
326C2×C4⋊C4#4112yes—
327C2×C4⋊C4#4112yes—
328C2×C22⋊C4—41no—
329C2×C22⋊C4—41no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—81no—
349C2×C22⋊C4—81no—
350C2×C22⋊C4—81no—
351C2×C22⋊C4—81no—
352C2×C22⋊C4—81no—
353C2×C22⋊C4—81no—
354C2×C22⋊C4—81no—
355C2×C22⋊C4—81no—
356C2×C22⋊C4C4⋊C414yes—
357C2×C22⋊C4C4⋊C414yes—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—42no—
363C2×C42—42no—
364C2×C42—42no—
365C2×C42—42no—
366C2×C42—42no—
367C2×C42—42no—
368C2×C42C22×C412yes—
369C2×C42C2×Q812yes—
370#107—44no—
371#107—44no—
372#107—44no—
373#106—44no—
374C22⋊C8—28no—
375C22⋊C8—44no—
376C22⋊C8—44no—
377#95—42no—
378#95—42no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95—42no—
383#95—42no—
384#95—42no—
385#95—42no—
386#95—42no—
387#95—81no—
388#95—81no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24C2×C4⋊C412yes—
416C24C2×C4⋊C412yes—
417C24AGL(1,ℤ/8)12yes—
418C24#13712yes—
419C24C22×D411yescharacteristic
420C2×D4—28no—
421C2×D4—28no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4C2×C4⋊C412yes—
562C22×C4C2×C4⋊C412yes—
563C22×C4C2×C4⋊C412yes—
564C22×C4C2×C4⋊C412yes—
565C22×C4#13512yes—
566C22×C4#13512yes—
567C22×C4C23×C411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×Q811yescharacteristic
570C22×C4C2×#4111yescharacteristic
571C22×C4C2×#4111yescharacteristic
572C22×C4C2×#4111yescharacteristic
573C22×C4H(5,𝔽2)11yescharacteristic
574C22×C4H(5,𝔽2)11yescharacteristic
575C22×C4H(5,𝔽2)11yescharacteristic
576C22×C4H(5,𝔽2)11yescharacteristic
577C22×C4H(5,𝔽2)11yescharacteristic
578C22×C4H(5,𝔽2)11yescharacteristic
579C22×C4H(5,𝔽2)11yescharacteristic
580C22×C42−1+411yescharacteristic
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—416no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8C4×D414yes—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—44no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—41no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—84no—
644C4⋊C4—84no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—48no—
648C22⋊C4—84no—
649C22⋊C4—84no—
650C22⋊C4—84no—
651C22⋊C4—84no—
652C22⋊C4—84no—
653C22⋊C4—84no—
654C22⋊C4—84no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—48no—
660C42—84no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23#42814yes—
731C23C22×C4⋊C411yescharacteristic
732C23#53411yescharacteristic
733C23#53411yescharacteristic
734C23D4211yescharacteristic
735C23#54611yescharacteristic
736C23#54611yescharacteristic
737C23#54711yescharacteristic
738C23C2×#13511yescharacteristic
739C23C2×#13511yescharacteristic
740C23C2×AGL(1,ℤ/8)11yescharacteristic
741C23C2×#13711yescharacteristic
742C23#57611yescharacteristic
743C23#57611yescharacteristic
744C23#57811yescharacteristic
745C23#57811yescharacteristic
746D4—416no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4#42714yes—
847C2×C4C2×C4×D411yescharacteristic
848C2×C4C4×#4111yescharacteristic
849C2×C4#51811yescharacteristic
850C2×C4#51811yescharacteristic
851C2×C4#51811yescharacteristic
852C2×C4#52011yescharacteristic
853C2×C4#53411yescharacteristic
854C2×C4#53511yescharacteristic
855C2×C4#53811yescharacteristic
856C2×C4#53811yescharacteristic
857C2×C4#53811yescharacteristic
858C2×C4#53911yescharacteristic
859C2×C4#54011yescharacteristic
860C2×C4#54211yescharacteristic
861C2×C4#54311yescharacteristic
862C2×C4#54311yescharacteristic
863C2×C4#54611yescharacteristic
864C2×C4D4×Q811yescharacteristic
865C2×C4#55011yescharacteristic
866C2×C4#55311yescharacteristic
867C2×C4#55411yescharacteristic
868C2×C4#55411yescharacteristic
869C2×C4#55411yescharacteristic
870C2×C4#55511yescharacteristic
871C2×C4#56011yescharacteristic
872C2×C4#56011yescharacteristic
873C2×C4#56211yescharacteristic
874C2×C4#56211yescharacteristic
875C8—24no—
876C8—42no—
877C8—42no—
878C8—42no—
879C22—24no—
880C22—24no—
881C22—24no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22#231511yescharacteristic
910C22D4×C4⋊C411yescharacteristic
911C22#234911yescharacteristic
912C22#266811yescharacteristic
913C22#267311yescharacteristic
914C22#268611yescharacteristic
915C22#270811yescharacteristic
916C22C2×#42711yescharacteristic
917C22C2×#42811yescharacteristic
918C22#291311yescharacteristic
919C22#291311yescharacteristic
920C22#318811yescharacteristic
921C22#318811yescharacteristic
922C22#319011yescharacteristic
923C22#319011yescharacteristic
924C22#319911yescharacteristic
925C22#320211yescharacteristic
926C22#320311yescharacteristic
927C22#320311yescharacteristic
928C22#326411yescharacteristic
929C22#327011yescharacteristic
930C22#328311yescharacteristic
931C22#328711yescharacteristic
932C22#330211yescharacteristic
933C22#330211yescharacteristic
934C22#330511yescharacteristic
935C22#330511yescharacteristic
936C22#330811yescharacteristic
937C22#331211yescharacteristic
938C22#331411yescharacteristic
939C22#331811yescharacteristic
940C22#334111yescharacteristic
941C22#334211yescharacteristic
942C22#334311yescharacteristic
943C22#334611yescharacteristic
944C4—24no—
945C4—42no—
946C4—42no—
947C4—42no—
948C4—82no—
949C4—82no—
950C4—82no—
951C4—82no—
952C4—161no—
953C4—161no—
954C4—161no—
955C4—161no—
956C4#232111yescharacteristic
957C4#233511yescharacteristic
958C4#236311yescharacteristic
959C4#237711yescharacteristic
960C4#269211yescharacteristic
961C4#273211yescharacteristic
962C4#278011yescharacteristic
963C4#278411yescharacteristic
964C2—44no—
965C2—82no—
966C2#1440711yescharacteristic
967C2#2194111yescharacteristic
968C2#2194711yescharacteristic
969C2#2265811yescharacteristic
970C2#2266111yescharacteristic
971C2#2270711yescharacteristic
972C2#2270911yescharacteristic
973C2#3040211yescharacteristic
974C2#3040911yescharacteristic
975C2#3071211yescharacteristic
976C2#3071411yescharacteristic
977C2#3132711yescharacteristic
978C2#3133311yescharacteristic
979C2#3200311yescharacteristic
980C2#3200911yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1854C2semidirect
3. C2×#1808C2semidirect
6. #11324C2semidirect
7. #11267C2semidirect
8. #11096C2semidirect
9. #11096C2semidirect
10. #11096C2semidirect
11. #11095C2semidirect
12. #10908C2semidirect
13. #10907C2semidirect
14. #10731C2semidirect
15. #10721C2semidirect
36. #1869C4semidirect
120. C2×#107D4semidirect

Maximal subgroups

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

subgroupindex
C2×#18692
C2×#18542
C2×#18082
#139062
#138712
#113242
#112672
#110962
#110952
#109082
#109072
#107312
#107212