Finite Group Databasebeta

← #7630615

Subgroups — #7630615

Order 512.

11102 conjugacy classes of subgroups.

The subgroup lattice has 1027 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3449C211yesmaximal, characteristic, complemented
2C2×#3449C211yesmaximal, characteristic, complemented
3C22×#537C211yesmaximal, characteristic, complemented
4C2×#3428C211yesmaximal, characteristic, complemented
5#35661C214yesmaximal, complemented
6#35564C218yesmaximal, complemented
7#35518C218yesmaximal, complemented
8#35514C214yesmaximal, complemented
9#35358C218yesmaximal, complemented
10#35328C214yesmaximal, complemented
11#35308C214yesmaximal, complemented
12#35306C214yesmaximal, complemented
13#35273C214yesmaximal, complemented
14#35256C214yesmaximal, complemented
15#35252C214yesmaximal, complemented
16C2×#2317C211yesmaximal, characteristic, complemented
17#34044C211yesmaximal, characteristic, complemented
18C2×#2311C211yesmaximal, characteristic, complemented
19C23×#41C2211yescharacteristic
20C23×#41C2211yescharacteristic
21C23×#41C2211yescharacteristic
22#3449—216no—
23#3449—216no—
24C2×#537—216no—
25C2×#537C2214yes—
26C2×#537C2214yes—
27C2×#537C2212yescomplemented
28C2×#537C2214yescomplemented
29C2×#537C2212yescomplemented
30C2×#537C2214yescomplemented
31C2×#537C2214yescomplemented
32C2×#536C2212yes—
33C2×#536C2212yes—
34C2×#536C2212yescomplemented
35C2×#536C2212yescomplemented
36C2×#535C2212yes—
37C2×#535C2212yes—
38C2×#535C2212yescomplemented
39C2×#535C2212yescomplemented
40C2×#534C2214yes—
41C2×#534C2214yes—
42C2×#532C2214yescomplemented
43C2×#532C2214yescomplemented
44C2×#525C2214yes—
45C2×#525C2214yes—
46C2×#525C2214yescomplemented
47C2×#525C2214yescomplemented
48C22×C22⋊Q8C2212yescomplemented
49C22×C22⋊Q8C2212yescomplemented
50C22×#121C2214yes—
51C22×#121C2212yescomplemented
52C22×#121C2212yescomplemented
53#3428—216no—
54C2×#520C2214yescomplemented
55C2×#520C2214yescomplemented
56C2×#519C2212yescomplemented
57C2×#518C2214yes—
58C2×#518C2212yescomplemented
59C2×C4×#41C2214yescomplemented
60C2×C4×#41C2214yescomplemented
61C22×#117C2211yescharacteristic
62C22×#117C2211yescharacteristic
63C22×#117C2211yescharacteristic
64C22×#117C2214yescomplemented
65C23×C4⋊C4C2211yescharacteristic
66#2857C2218yescomplemented
67#2856C2218yescomplemented
68#2850C2218yescomplemented
69#2850C2218yescomplemented
70#2621C2218yescomplemented
71#2620C2218yescomplemented
72#2620C2218yescomplemented
73#2619C2218yescomplemented
74#2543C22132yescomplemented
75#2538C22116yescomplemented
76#2537C22116yescomplemented
77#2536C22116yescomplemented
78#2535C22116yescomplemented
79#2429C22116yescomplemented
80#2428C22116yescomplemented
81#2427C22116yescomplemented
82#2426C22116yescomplemented
83#2425C22132yescomplemented
84#2424C22132yescomplemented
85#2417C22116yescomplemented
86#2416C22132yescomplemented
87#2416C22116yescomplemented
88#2415C22116yescomplemented
89#2414C22116yescomplemented
90#2413C22116yescomplemented
91#2412C22116yescomplemented
92#2411C22116yescomplemented
93#2410C22116yescomplemented
94#2317C2214yescomplemented
95#2317C2214yescomplemented
96#2317C2214yescomplemented
97#2317C2214yescomplemented
98#2311C2214yes—
99#2311C2214yes—
100#2311C2212yescomplemented
101#2311C2214yescomplemented
102#2311C2214yescomplemented
103#2311C2212yescomplemented
104#2311C2214yescomplemented
105#2310C2212yescomplemented
106#2309C2212yescomplemented
107#2308C2214yes—
108#2297C2214yescomplemented
109#2297C2214yescomplemented
110C2×#391C2212yescomplemented
111C2×#390C2212yescomplemented
112C2×#389C2214yescomplemented
113C2×#386C2214yes—
114C2×#385C2214yes—
115C2×#384C2212yescomplemented
116C2×#382C2212yescomplemented
117#2280C2214yescomplemented
118C2×#380C2214yescomplemented
119C22×#41—28no—
120C22×#41—28no—
121C22×#41—28no—
122C22×#41—28no—
123C22×#41—28no—
124C22×#41—28no—
125C22×#41—28no—
126C22×#41—28no—
127C22×#41D4116yescomplemented
128C22×#41C2312yes—
129C22×#41C2312yes—
130C22×#41C2312yes—
131C22×#41C2312yes—
132C22×#41C2312yes—
133C22×#41C2312yes—
134C22×#41C2312yes—
135C22×#41C2312yes—
136C22×#41C2312yes—
137C22×#41C2312yes—
138C22×#41C2312yes—
139C22×#41C2312yes—
140C23×Q8C2311yescharacteristic
141C23×Q8C2311yescharacteristic
142C23×Q8C2311yescharacteristic
143C23×D4C2312yes—
144C23×D4C2311yescharacteristic
145C23×D4C2312yes—
146C23×D4C2311yescharacteristic
147C23×D4C2312yes—
148C23×D4C2311yescharacteristic
149C23×D4C2314yes—
150C24×C4C2312yes—
151C24×C4C2312yes—
152C24×C4C2312yes—
153C24×C4C2312yes—
154C24×C4C2311yescharacteristic
155#537—232no—
156#537—232no—
157#537—232no—
158#537—232no—
159#537—216no—
160#537—216no—
161#537—232no—
162#536—216no—
163#536—216no—
164#536—216no—
165#536—216no—
166#535—216no—
167#535—216no—
168#535—216no—
169#535—216no—
170#534—232no—
171#534—232no—
172#532—232no—
173#532—232no—
174C2×C4⋊Q8C2314yes—
175C2×C4⋊Q8C2314yes—
176C2×#127C2314yes—
177C2×#127C2314yes—
178C2×#124C2314yes—
179C2×#124C2314yes—
180C2×#124C2314yes—
181C2×#124C2314yes—
182#525—232no—
183#525—232no—
184#525—232no—
185#525—232no—
186C2×#123C2318yes—
187C2×#123C2318yes—
188C2×#123C2318yes—
189C2×#123C2318yes—
190C2×C22⋊Q8—216no—
191C2×C22⋊Q8—216no—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2318yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2318yes—
197C2×C22⋊Q8C2318yes—
198C2×C22⋊Q8C2318yes—
199C2×C22⋊Q8C2318yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2314yes—
202C2×#121—232no—
203C2×#121—216no—
204C2×#121—216no—
205C2×#121C2314yes—
206C2×#121C2318yes—
207C2×#121C2314yes—
208C2×#121C23116yes—
209C2×#121C23116yes—
210C2×#121C2318yes—
211C2×#121C2318yes—
212C2×#121C2318yes—
213C2×#121C2318yes—
214C2×#121C2318yes—
215C2×#121C2314yes—
216C2×#121C2314yes—
217C2×#121C2318yes—
218C2×#121C23116yes—
219C2×#121C2318yes—
220C2×#121C23132yes—
221C2×#120C2318yes—
222C2×#120C2318yes—
223C2×#120C2318yes—
224C2×#120C2318yes—
225#520—232no—
226#520—232no—
227#519—216no—
228#518—216no—
229#518—232no—
230C4×#41—232no—
231C4×#41—232no—
232C2×C4×Q8C2318yes—
233C2×C4×Q8C2318yes—
234C2×C4×D4C23116yes—
235C2×C4×D4C23116yes—
236C2×C4×D4C2318yes—
237C2×C4×D4C2318yes—
238C2×C4×D4C2318yes—
239C2×C4×D4C2318yes—
240C2×C4×D4C23116yes—
241C2×#117—28no—
242C2×#117—28no—
243C2×#117—232no—
244C2×#117D4116yescomplemented
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2318yes—
254C2×#117C2318yes—
255C2×#117C2318yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C22×C4⋊C4—28no—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2318yes—
271C22×C4⋊C4C2314yes—
272C22×C4⋊C4C2318yes—
273C22×C4⋊C4C2312yes—
274C22×C22⋊C4C2312yes—
275C22×C22⋊C4C2312yes—
276C22×C22⋊C4C2318yes—
277C22×C22⋊C4C2314yes—
278C22×C22⋊C4C2314yes—
279C22×C22⋊C4C2318yes—
280C22×C22⋊C4C2312yes—
281C22×C42C2318yes—
282C22×C42C2312yes—
283C22×C42C2312yes—
284C22×C42C2312yes—
285#398C23132yes—
286#397C23132yes—
287#396C23132yes—
288#396C23132yes—
289#394C23132yes—
290#394C23132yes—
291#394C23132yes—
292#392C23132yes—
293#391C2314yes—
294#391C2314yes—
295#391C2318yes—
296#391C2318yes—
297#391C2318yes—
298#390C2314yes—
299#390C2314yes—
300#390C2318yes—
301#390C2318yes—
302#390C2318yes—
303#390C23132yes—
304#389C23116yes—
305#389C23116yes—
306#389C23132yes—
307#388C23132yes—
308#388C23132yes—
309#386C2318yes—
310#386C23116yes—
311#386C2318yes—
312#386C23116yes—
313#386C23116yes—
314#386C23132yes—
315#386C23132yes—
316#385C23116yes—
317#385C23116yes—
318#384C2318yes—
319#384C2318yes—
320#382C2318yes—
321#382C2318yes—
322#381C2318yes—
323#380C23116yes—
324#380C23116yes—
325#380C2318yes—
326#380C2318yes—
327#380C23132yes—
328#379C2318yes—
329C4×C22⋊C4C23116yes—
330C2×#95C2318yes—
331C2×#95C2318yes—
332C25C2412yes—
333C25C2412yes—
334C25C2412yes—
335C25C2411yescharacteristic
336C2×#41—2128no—
337C2×#41—28no—
338C2×#41—28no—
339C2×#41—28no—
340C2×#41—28no—
341C2×#41—28no—
342C2×#41—28no—
343C2×#41—28no—
344C2×#41—28no—
345C2×#41—28no—
346C2×#41—28no—
347C2×#41—28no—
348C2×#41—28no—
349C2×#41—28no—
350C2×#41—28no—
351C2×#41—28no—
352C2×#41—28no—
353C2×#41—28no—
354C2×#41—28no—
355C2×#41—28no—
356C2×#41—28no—
357C2×#41—28no—
358C2×#41—28no—
359C2×#41—28no—
360C2×#41—28no—
361C2×#41—28no—
362C2×#41—28no—
363C2×#41—28no—
364C2×#41—28no—
365C2×#41—28no—
366C2×#41—28no—
367C2×#41—28no—
368C2×#41—28no—
369C2×#41—464no—
370C2×#41—464no—
371C2×#41C2×D4116yes—
372C2×#41C2×D4116yes—
373C2×#41C2×D4116yes—
374C2×#41C2×D4116yes—
375C22×Q8—24no—
376C22×Q8—24no—
377C22×Q8—24no—
378C22×Q8—24no—
379C22×Q8—24no—
380C22×Q8—24no—
381C22×Q8—24no—
382C22×Q8—24no—
383C22×Q8C2×D418yes—
384C22×Q8C2412yes—
385C22×Q8C2412yes—
386C22×Q8C2412yes—
387C22×Q8C2412yes—
388C22×Q8C2412yes—
389C22×Q8C2412yes—
390C22×D4—28no—
391C22×D4—28no—
392C22×D4—28no—
393C22×D4—28no—
394C22×D4—28no—
395C22×D4—28no—
396C22×D4—28no—
397C22×D4—28no—
398C22×D4—216no—
399C22×D4—24no—
400C22×D4—24no—
401C22×D4—24no—
402C22×D4—24no—
403C22×D4—24no—
404C22×D4—24no—
405C22×D4—24no—
406C22×D4—24no—
407C22×D4—88no—
408C22×D4C2×D4116yes—
409C22×D4C2×D418yes—
410C22×D4C2414yes—
411C22×D4C2414yes—
412C22×D4C2414yes—
413C22×D4C2414yes—
414C22×D4C2412yes—
415C22×D4C2412yes—
416C22×D4C2412yes—
417C22×D4C2412yes—
418C22×D4C2414yes—
419C22×D4C2414yes—
420C22×D4C2412yes—
421C22×D4C2412yes—
422C22×D4C2418yes—
423C22×D4C24116yes—
424C22×D4C2418yes—
425C22×D4C24116yes—
426C23×C4—28no—
427C23×C4—28no—
428C23×C4—28no—
429C23×C4—28no—
430C23×C4—28no—
431C23×C4—28no—
432C23×C4—28no—
433C23×C4—28no—
434C23×C4—28no—
435C23×C4—84no—
436C23×C4C2×D4116yes—
437C23×C4C2×D418yes—
438C23×C4C2×D418yes—
439C23×C4#4118yes—
440C23×C4C2412yes—
441C23×C4C2414yes—
442C23×C4C2414yes—
443C23×C4C2414yes—
444C23×C4C2414yes—
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2414yes—
448C23×C4C2414yes—
449C23×C4C2414yes—
450C23×C4C2414yes—
451C23×C4C2414yes—
452C23×C4C2412yes—
453C23×C4C24116yes—
454C23×C4C2412yes—
455C23×C4C2414yes—
456C23×C4C2414yes—
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C4⋊Q8—216no—
464C4⋊Q8—216no—
465#127—216no—
466#127—216no—
467#124—216no—
468#124—216no—
469#124—216no—
470#124—216no—
471#123—232no—
472#123—232no—
473#123—232no—
474#123—232no—
475C22⋊Q8—232no—
476C22⋊Q8—232no—
477C22⋊Q8—216no—
478C22⋊Q8—216no—
479C22⋊Q8—232no—
480C22⋊Q8—232no—
481C22⋊Q8—216no—
482C22⋊Q8—216no—
483C22⋊Q8—232no—
484C22⋊Q8—232no—
485#121—232no—
486#121—232no—
487#121—264no—
488#121—264no—
489#121—216no—
490#121—216no—
491#121—232no—
492#121—232no—
493#121—232no—
494#121—232no—
495#121—216no—
496#121—216no—
497#121—264no—
498#121—232no—
499#121—232no—
500#121—832no—
501#120—232no—
502#120—232no—
503#120—232no—
504#120—232no—
505C4×Q8—232no—
506C4×Q8—232no—
507C4×D4—264no—
508C4×D4—232no—
509C4×D4—232no—
510C4×D4—232no—
511C4×D4—264no—
512C4×D4—232no—
513C4×D4—264no—
514#117—28no—
515#117—28no—
516#117—28no—
517#117—28no—
518#117—28no—
519#117—28no—
520#117—28no—
521#117—28no—
522#117—232no—
523#117—232no—
524#117—232no—
525#117C2×D4116yes—
526#117C2×D4116yes—
527#117C2×D4116yescomplemented
528#117C2×D4116yescomplemented
529C2×C4⋊C4—28no—
530C2×C4⋊C4—28no—
531C2×C4⋊C4—28no—
532C2×C4⋊C4—28no—
533C2×C4⋊C4—28no—
534C2×C4⋊C4—28no—
535C2×C4⋊C4—28no—
536C2×C4⋊C4—24no—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—216no—
539C2×C4⋊C4—232no—
540C2×C4⋊C4—88no—
541C2×C4⋊C4C2×D4116yescomplemented
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C24116yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C24116yes—
554C2×C4⋊C4C24116yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C24132yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C22⋊C4—28no—
561C2×C22⋊C4—28no—
562C2×C22⋊C4—216no—
563C2×C22⋊C4—216no—
564C2×C22⋊C4—232no—
565C2×C22⋊C4—88no—
566C2×C22⋊C4C2×D4116yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C24116yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C24116yes—
573C2×C22⋊C4C24116yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C24116yes—
577C2×C22⋊C4C24116yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C24132yes—
581C2×C22⋊C4C24116yes—
582C2×C22⋊C4C24116yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C42—28no—
586C2×C42—28no—
587C2×C42—232no—
588C2×C42C2×D4116yescomplemented
589C2×C42C2414yes—
590C2×C42C2414yes—
591C2×C42C2414yes—
592C2×C42C24116yes—
593C2×C42C2414yes—
594C2×C42C2414yes—
595C2×C42C2414yes—
596#95C24132yes—
597#95C24132yes—
598#95C24116yes—
599#95C24116yes—
600C24—24no—
601C24—24no—
602C24—24no—
603C24—24no—
604C24—24no—
605C24—24no—
606C24—24no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—44no—
611C24—44no—
612C24—44no—
613C24—44no—
614C24—44no—
615C24—44no—
616C24C22×D418yes—
617C24C22×D414yes—
618C24C22×D414yes—
619C24C2×#4114yes—
620C24C2514yes—
621C24C2514yes—
622C24C2514yes—
623C24C2511yescharacteristic
624C24C2511yescharacteristic
625C24C2511yescharacteristic
626#41—264no—
627#41—264no—
628#41—264no—
629#41—264no—
630#41—432no—
631#41—432no—
632#41—432no—
633#41—432no—
634#41—432no—
635#41—432no—
636#41—432no—
637#41—432no—
638C2×Q8—232no—
639C2×Q8—24no—
640C2×Q8—24no—
641C2×Q8—24no—
642C2×Q8—24no—
643C2×Q8—24no—
644C2×Q8—24no—
645C2×Q8—24no—
646C2×Q8—24no—
647C2×Q8—24no—
648C2×Q8—24no—
649C2×Q8—24no—
650C2×Q8—24no—
651C2×Q8—24no—
652C2×Q8—24no—
653C2×Q8—24no—
654C2×Q8—24no—
655C2×Q8—416no—
656C2×Q8—416no—
657C2×Q8C22×D418yes—
658C2×Q8C22×D418yes—
659C2×D4—264no—
660C2×D4—28no—
661C2×D4—28no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—28no—
675C2×D4—28no—
676C2×D4—216no—
677C2×D4—216no—
678C2×D4—232no—
679C2×D4—232no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—24no—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—232no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—416no—
698C2×D4—416no—
699C2×D4—432no—
700C2×D4—416no—
701C2×D4—416no—
702C2×D4—432no—
703C2×D4—432no—
704C2×D4—416no—
705C2×D4—416no—
706C2×D4—832no—
707C2×D4C22×D4116yes—
708C2×D4C22×D4116yes—
709C2×D4C22×D418yes—
710C2×D4C22×D418yes—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—264no—
714C22×C4—28no—
715C22×C4—28no—
716C22×C4—28no—
717C22×C4—28no—
718C22×C4—28no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—28no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—232no—
743C22×C4—44no—
744C22×C4—48no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—48no—
748C22×C4—44no—
749C22×C4—48no—
750C22×C4—416no—
751C22×C4—416no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—432no—
755C22×C4—432no—
756C22×C4—816no—
757C22×C4#121164yescomplemented
758C22×C4C22×D418yes—
759C22×C4C22×D4116yes—
760C22×C4C22×D4116yes—
761C22×C4C22×D4116yes—
762C22×C4C22×D414yes—
763C22×C4C22×D414yes—
764C22×C4C22×D414yes—
765C22×C4C22×D414yes—
766C22×C4C22×D414yes—
767C22×C4C22×D414yes—
768C22×C4C22×D414yes—
769C22×C4C22×D414yes—
770C22×C4C22×D414yes—
771C22×C4C22×D414yes—
772C22×C4C22×D414yes—
773C22×C4C22×D414yes—
774C22×C4C2×#4114yes—
775C22×C4C2×#4114yes—
776C22×C4C2×#4114yes—
777C22×C4C2×#4114yes—
778C22×C4C2×#4114yes—
779C22×C4C2×#4114yes—
780C22×C4C2514yes—
781C22×C4C2518yes—
782C22×C4C2518yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2518yes—
787C22×C4C2514yes—
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2511yescharacteristic
791C22×C4C2511yescharacteristic
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—232no—
798C4⋊C4—28no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—232no—
804C4⋊C4—216no—
805C4⋊C4—216no—
806C4⋊C4—232no—
807C4⋊C4—432no—
808C4⋊C4C22×D4116yes—
809C4⋊C4C22×D4116yes—
810C22⋊C4—28no—
811C22⋊C4—28no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—232no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—232no—
818C22⋊C4—232no—
819C22⋊C4—216no—
820C22⋊C4—216no—
821C22⋊C4—232no—
822C22⋊C4—232no—
823C22⋊C4—432no—
824C22⋊C4—416no—
825C22⋊C4—416no—
826C22⋊C4C22×D4116yes—
827C22⋊C4C22×D4116yes—
828C42—28no—
829C42—28no—
830C42—232no—
831C42—28no—
832C42—28no—
833C42C22×D4116yes—
834C42C22×D4116yes—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—24no—
842C23—24no—
843C23—28no—
844C23—28no—
845C23—216no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—28no—
853C23—28no—
854C23—28no—
855C23—28no—
856C23—44no—
857C23—48no—
858C23—44no—
859C23—48no—
860C23—48no—
861C23—48no—
862C23—48no—
863C23—416no—
864C23—48no—
865C23—48no—
866C23—48no—
867C23—84no—
868C23—88no—
869C23—88no—
870C23—88no—
871C23—88no—
872C23—88no—
873C23—84no—
874C23C2×#121116yes—
875C23C23×D418yes—
876C23C23×D412yes—
877C23C23×D412yes—
878C23C23×D412yes—
879C23C23×D412yes—
880C23C23×D412yes—
881C23C23×D412yes—
882C23C22×#4112yes—
883C23C22×#4112yes—
884C23C22×#4112yes—
885C23C2611yescharacteristic
886Q8—216no—
887Q8—216no—
888Q8—48no—
889Q8—48no—
890Q8—48no—
891Q8—48no—
892D4—232no—
893D4—232no—
894D4—216no—
895D4—216no—
896D4—416no—
897D4—416no—
898D4—416no—
899D4—416no—
900D4—48no—
901D4—48no—
902D4—48no—
903D4—48no—
904D4—832no—
905D4—816no—
906D4—816no—
907D4—832no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—28no—
911C2×C4—28no—
912C2×C4—216no—
913C2×C4—232no—
914C2×C4—232no—
915C2×C4—28no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—216no—
928C2×C4—28no—
929C2×C4—28no—
930C2×C4—416no—
931C2×C4—416no—
932C2×C4—48no—
933C2×C4—48no—
934C2×C4—416no—
935C2×C4—416no—
936C2×C4—416no—
937C2×C4—416no—
938C2×C4—832no—
939C2×C4—84no—
940C2×C4—88no—
941C2×C4—84no—
942C2×C4—88no—
943C2×C4—88no—
944C2×C4C2×#121116yes—
945C2×C4C2×#121116yes—
946C2×C4C2×#121116yes—
947C2×C4C2×#121116yes—
948C2×C4C2×#121116yes—
949C2×C4C2×#121116yes—
950C2×C4C23×D4116yes—
951C2×C4C23×D418yes—
952C2×C4C23×D412yes—
953C2×C4C23×D412yes—
954C2×C4C23×D412yes—
955C2×C4C23×D412yes—
956C2×C4C23×D412yes—
957C2×C4C23×D412yes—
958C2×C4C23×D412yes—
959C2×C4C23×D412yes—
960C2×C4C22×#4112yes—
961C2×C4C22×#4112yes—
962C2×C4C22×#4112yes—
963C2×C4C22×#4112yes—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—24no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—28no—
977C22—28no—
978C22—28no—
979C22—416no—
980C22—48no—
981C22—48no—
982C22—44no—
983C22—44no—
984C22—48no—
985C22—48no—
986C22—48no—
987C22—48no—
988C22—44no—
989C22—44no—
990C22—44no—
991C22—44no—
992C22—816no—
993C22—816no—
994C22—816no—
995C22C22×#12114yes—
996C22C22×#12114yes—
997C22C22×#12114yes—
998C22C24×D411yescharacteristic
999C22C24×D411yescharacteristic
1000C22C23×#4111yescharacteristic
1001C22H(7,𝔽2)12yes—
1002C222−1+612yes—
1003C4—216no—
1004C4—28no—
1005C4—48no—
1006C4—44no—
1007C4—48no—
1008C4—44no—
1009C4—44no—
1010C4—44no—
1011C4C22×#12114yes—
1012C4C22×#12114yes—
1013C4C22×#12114yes—
1014C4C22×#12114yes—
1015C2—24no—
1016C2—24no—
1017C2—24no—
1018C2—48no—
1019C2—84no—
1020C2—84no—
1021C2C23×#12111yescharacteristic
1022C2#6285211yescharacteristic
1023C2#6285312yes—
1024C2#6285612yes—
1025C2#6285911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3449C2semidirect
2. C2×#3449C2semidirect
3. C22×#537C2semidirect
4. C2×#3428C2semidirect
5. #35661C2semidirect
6. #35564C2semidirect
7. #35518C2semidirect
8. #35514C2semidirect
9. #35358C2semidirect
10. #35328C2semidirect
11. #35308C2semidirect
12. #35306C2semidirect
13. #35273C2semidirect
14. #35256C2semidirect
15. #35252C2semidirect
16. C2×#2317C2semidirect
17. #34044C2semidirect
18. C2×#2311C2semidirect
27. C2×#537C22semidirect
28. C2×#537C22semidirect
29. C2×#537C22semidirect
30. C2×#537C22semidirect
31. C2×#537C22semidirect
34. C2×#536C22semidirect
35. C2×#536C22semidirect
38. C2×#535C22semidirect
39. C2×#535C22semidirect
42. C2×#532C22semidirect
43. C2×#532C22semidirect
46. C2×#525C22semidirect
47. C2×#525C22semidirect
48. C22×C22⋊Q8C22semidirect
49. C22×C22⋊Q8C22semidirect
51. C22×#121C22semidirect
52. C22×#121C22semidirect
54. C2×#520C22semidirect
55. C2×#520C22semidirect
56. C2×#519C22semidirect
58. C2×#518C22semidirect
59. C2×C4×#41C22semidirect
60. C2×C4×#41C22semidirect
64. C22×#117C22semidirect
66. #2857C22semidirect
67. #2856C22semidirect
68. #2850C22semidirect
69. #2850C22semidirect
70. #2621C22semidirect
71. #2620C22semidirect
72. #2620C22semidirect
73. #2619C22semidirect
74. #2543C22semidirect
75. #2538C22semidirect
76. #2537C22semidirect
77. #2536C22semidirect
78. #2535C22semidirect
79. #2429C22semidirect
80. #2428C22semidirect
81. #2427C22semidirect
82. #2426C22semidirect
83. #2425C22semidirect
84. #2424C22semidirect
85. #2417C22semidirect
86. #2416C22semidirect
87. #2416C22semidirect
88. #2415C22semidirect
89. #2414C22semidirect
90. #2413C22semidirect
91. #2412C22semidirect
92. #2411C22semidirect
93. #2410C22semidirect
94. #2317C22semidirect
95. #2317C22semidirect
96. #2317C22semidirect
97. #2317C22semidirect
100. #2311C22semidirect
101. #2311C22semidirect
102. #2311C22semidirect
103. #2311C22semidirect
104. #2311C22semidirect
105. #2310C22semidirect
106. #2309C22semidirect
108. #2297C22semidirect
109. #2297C22semidirect
110. C2×#391C22semidirect
111. C2×#390C22semidirect
112. C2×#389C22semidirect
115. C2×#384C22semidirect
116. C2×#382C22semidirect
117. #2280C22semidirect
118. C2×#380C22semidirect
127. C22×#41D4semidirect
244. C2×#117D4semidirect
527. #117C2×D4semidirect
528. #117C2×D4semidirect
541. C2×C4⋊C4C2×D4semidirect
588. C2×C42C2×D4semidirect
757. C22×C4#121semidirect

Maximal subgroups

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

subgroupindex
C2×#34492
C22×#5372
C2×#34282
#356612
#355642
#355182
#355142
#353582
#353282
#353082
#353062
#352732
#352562
#352522
C2×#23172
#340442
C2×#23112