Finite Group Databasebeta

← #72211375

Subgroups — #72211375

Order 2048.

3824 conjugacy classes of subgroups.

The subgroup lattice has 1420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126586C211yesmaximal, characteristic
2#72211357C211yesmaximal, characteristic
3C22×#7014C211yesmaximal, characteristic
4#72210220C214yesmaximal, complemented
5C2×#33418—21no—
6#6371170C411yescharacteristic
7C22×#1744—21no—
8C22×#1744C2211yescharacteristic
9C2×#17793C411yescharacteristic
10#353780—21no—
11#180965—21no—
12#126586—22no—
13#126586C414yescomplemented
14C2×#7143—21no—
15C2×#7143C2212yes—
16#109001C412yes—
17#109001C2212yes—
18#109000—21no—
19#109000—21no—
20C2×#7014—21no—
21C2×#7014—22no—
22C2×#7014C414yescomplemented
23C2×#7014C2212yes—
24C2×#2920—21no—
25C23×C4×C8—22no—
26C23×C4×C8C2×C411yescharacteristic
27C23×C4×C8D411yescharacteristic
28#34012—21no—
29C22×C43D411yescharacteristic
30#33418—24no—
31#33418—24no—
32#33418—42no—
33#33418—42no—
34C2×#2163—22no—
35C2×#2163—22no—
36C2×#2162—41no—
37C2×#2162—41no—
38C2×#2150—41no—
39C2×#2112—41no—
40C2×C4×M32—22no—
41#20818—41no—
42#20818—41no—
43#20817C812yescomplemented
44#20817C2×C412yes—
45#20816—21no—
46#20816—21no—
47#20797C812yescomplemented
48#20760—21no—
49#20658—41no—
50C4×#427—41no—
51C2×#1744—24no—
52C2×#1744—22no—
53C2×#1744—24no—
54C2×#1744—22no—
55C2×#1744—41no—
56C2×#1744—42no—
57C2×#1744—41no—
58C2×#1744—42no—
59C2×#1744—41no—
60C2×#1744—42no—
61C2×#1744C2×C412yes—
62C2×#1744C2×C412yes—
63C2×#1744C2×C411yescharacteristic
64C2×#1744D411yescharacteristic
65C2×#1744D412yes—
66C2×#1744D411yescharacteristic
67C2×#1744Q812yes—
68C2×#1744C2311yescharacteristic
69C22×#336—41no—
70C22×#336—41no—
71C22×#336—41no—
72#17793—22no—
73#17793—42no—
74#17793C814yescomplemented
75C2×#1568—41no—
76C2×#1567—21no—
77C2×#1566C2×C412yes—
78C2×#1564—41no—
79#10839—22no—
80#10839—22no—
81#10719—41no—
82#10719—41no—
83C4×#339—41no—
84C4×#339—41no—
85#7898—41no—
86#7898—41no—
87#7897—22no—
88#7897—22no—
89#7890—41no—
90#7890—41no—
91#7143—24no—
92#7143—22no—
93#7143C2×C414yes—
94#7014—24no—
95#7014—22no—
96#7014C2×C414yes—
97C24×C8—21no—
98C24×C8—21no—
99C24×C8—42no—
100C23×C42—21no—
101C23×C42—21no—
102C23×C42C22⋊C411yescharacteristic
103C23×C42D811yescharacteristic
104C23×C42SD1611yescharacteristic
105C22×M32—42no—
106#2920—24no—
107#2920—42no—
108#2920—42no—
109#2920—42no—
110C2×#432—41no—
111C2×#432—41no—
112C2×#431—41no—
113C2×#431—41no—
114C2×#427—42no—
115C2×#423—22no—
116C2×#407—41no—
117C2×C4×M16—41no—
118C22×C4×C8—21no—
119C22×C4×C8—22no—
120C22×C4×C8—21no—
121C22×C4×C8—22no—
122C22×C4×C8—21no—
123C22×C4×C8—21no—
124C22×C4×C8—22no—
125C22×C4×C8—21no—
126C22×C4×C8—21no—
127C22×C4×C8—22no—
128C22×C4×C8—28no—
129C22×C4×C8—24no—
130C22×C4×C8—216no—
131C22×C4×C8—42no—
132C22×C4×C8—44no—
133C22×C4×C8—48no—
134C22×C4×C8C4212yes—
135C22×C4×C8C22⋊C411yescharacteristic
136C22×C4×C8C22⋊C411yescharacteristic
137C22×C4×C8C22⋊C412yes—
138C22×C4×C8C4⋊C412yes—
139C22×C4×C8C4⋊C412yes—
140C22×C4×C8C2×C811yescharacteristic
141C22×C4×C8C2×C811yescharacteristic
142C22×C4×C8C2×C812yes—
143C22×C4×C8M1611yescharacteristic
144C22×C4×C8M1611yescharacteristic
145C22×C4×C8M1612yes—
146C22×C4×C8D811yescharacteristic
147C22×C4×C8D811yescharacteristic
148C22×C4×C8SD1612yes—
149C22×C4×C8SD1611yescharacteristic
150C22×C4×C8SD1611yescharacteristic
151C22×C4×C8Q1612yes—
152C22×C4×C8C22×C411yescharacteristic
153C22×C4×C8C2×D411yescharacteristic
154#2285—22no—
155#2285—22no—
156#2285—22no—
157#2283—41no—
158#2283—41no—
159#2283—41no—
160#2283—41no—
161#2283—41no—
162#2283—41no—
163#2280—41no—
164#2280—41no—
165#2280—41no—
166C4×#117—41no—
167C4×#117—41no—
168C4×#117—41no—
169C2×C43—22no—
170C2×C43—21no—
171C2×C43—22no—
172C2×C43—21no—
173C2×C43C22⋊C411yescharacteristic
174C2×C43C22⋊C412yes—
175C2×C43C4⋊C412yes—
176C2×C43D811yescharacteristic
177C2×C43SD1612yes—
178C2×C43SD1611yescharacteristic
179C2×C43Q1612yes—
180C2×C43C2×D411yescharacteristic
181#2163—28no—
182#2163—24no—
183#2163—24no—
184#2163—44no—
185#2163—42no—
186#2163—42no—
187#2162—44no—
188#2162—44no—
189#2162—44no—
190#2162—44no—
191#2150—44no—
192#2150—44no—
193C2×C4⋊C16—42no—
194C2×C4⋊C16—42no—
195#2112—44no—
196#2112—44no—
197C2×C22⋊C16—42no—
198C2×C22⋊C16—42no—
199C4×M32—28no—
200C4×M32—44no—
201C2×#346—24no—
202C2×C4×C16—42no—
203#1846—42no—
204#1845C2×C814yescomplemented
205#1844—22no—
206#1835—42no—
207#1834—22no—
208#1834—22no—
209#1808—42no—
210#1808—42no—
211#1807—42no—
212#1807—42no—
213C4×#107—42no—
214C4×#107—42no—
215C4×#106—42no—
216C4×#106—42no—
217#1744—28no—
218#1744—24no—
219#1744—24no—
220#1744—41no—
221#1744—42no—
222#1744—42no—
223#1744—41no—
224#1744—41no—
225#1744—42no—
226#1744—42no—
227#1744—41no—
228#1744—44no—
229#1744—44no—
230#1744—44no—
231#1744—44no—
232#1744—42no—
233#1744—44no—
234#1744—42no—
235#1744C4212yes—
236#1744C22⋊C412yes—
237#1744C22⋊C412yes—
238#1744C4⋊C412yes—
239#1744C4⋊C412yes—
240#1744C4⋊C412yes—
241#1744C22×C411yescharacteristic
242#1744C22×C411yescharacteristic
243#1744C2×D411yescharacteristic
244#1744C2×Q811yescharacteristic
245#1735—42no—
246C2×#339—42no—
247C2×#339—42no—
248C2×#339—42no—
249C2×#339—42no—
250C2×#336—42no—
251C2×#336—42no—
252C2×#336—41no—
253C2×#336—42no—
254C2×#336—41no—
255C2×#336—41no—
256C2×#336—42no—
257C2×#336—41no—
258C2×#336—42no—
259C2×#336—44no—
260C2×#336—42no—
261C2×#336—44no—
262C2×#336—44no—
263C2×#336—42no—
264C2×#336—44no—
265C2×#336—42no—
266#1568—44no—
267#1568—44no—
268#1567—24no—
269#1567—42no—
270#1566—22no—
271#1566—42no—
272#1566C2×C814yescomplemented
273#1564—44no—
274#1564—44no—
275C2×#335—42no—
276C2×#334—42no—
277#1279—42no—
278#1279—42no—
279#1279—42no—
280#1279—42no—
281C24×C4—21no—
282C24×C4—21no—
283C24×C4#9911yescharacteristic
284C24×C4#10211yescharacteristic
285C24×C4#10411yescharacteristic
286C22×M16—42no—
287C23×C8—21no—
288C23×C8—21no—
289C23×C8—21no—
290C23×C8—21no—
291C23×C8—21no—
292C23×C8—21no—
293C23×C8—22no—
294C23×C8—22no—
295C23×C8—21no—
296C23×C8—21no—
297C23×C8—22no—
298C23×C8—22no—
299C23×C8—22no—
300C23×C8—22no—
301C23×C8—22no—
302C23×C8—22no—
303C23×C8—21no—
304C23×C8—21no—
305C23×C8—21no—
306C23×C8—21no—
307C23×C8—48no—
308C23×C8—44no—
309C23×C8—416no—
310C23×C8—84no—
311C23×C8—84no—
312C23×C8—88no—
313C23×C8—88no—
314C2×#117—42no—
315C2×#117—42no—
316C2×#117—42no—
317C22×C42—28no—
318C22×C42—28no—
319C22×C42—21no—
320C22×C42—21no—
321C22×C42—22no—
322C22×C42—22no—
323C22×C42—22no—
324C22×C42—22no—
325C22×C42—21no—
326C22×C42—21no—
327C22×C42—21no—
328C22×C42—21no—
329C22×C42—21no—
330C22×C42—22no—
331C22×C42—21no—
332C22×C42—22no—
333C22×C42—22no—
334C22×C42—22no—
335C22×C42—22no—
336C22×C42—22no—
337C22×C42—21no—
338C22×C42—21no—
339C22×C42—82no—
340C22×C42—82no—
341C22×C42—84no—
342C22×C42#9512yes—
343C22×C42C22⋊C812yes—
344C22×C42C22⋊C811yescharacteristic
345C22×C42C22⋊C811yescharacteristic
346C22×C42#9912yes—
347C22×C42#9911yescharacteristic
348C22×C42#10011yescharacteristic
349C22×C42#10011yescharacteristic
350C22×C42#10112yes—
351C22×C42#10211yescharacteristic
352C22×C42#10211yescharacteristic
353C22×C42#10212yes—
354C22×C42#10211yescharacteristic
355C22×C42#10211yescharacteristic
356C22×C42#10211yescharacteristic
357C22×C42#10312yes—
358C22×C42#10312yes—
359C22×C42#10312yes—
360C22×C42#10412yes—
361C22×C42#10411yescharacteristic
362C22×C42#10412yes—
363C22×C42#10411yescharacteristic
364C22×C42#10411yescharacteristic
365C22×C42#10612yes—
366C22×C42#10712yes—
367C22×C42C2×C22⋊C411yescharacteristic
368C22×C42C2×D811yescharacteristic
369C22×C42C2×SD1611yescharacteristic
370C2×M32—48no—
371C2×M32—88no—
372C22×C16—44no—
373#432—44no—
374#432—44no—
375#432—82no—
376#432—82no—
377#431—44no—
378#431—44no—
379#431—82no—
380#431—82no—
381#427—88no—
382C2×#107—44no—
383C2×#106—44no—
384#423—24no—
385#423—42no—
386#423—42no—
387#423—42no—
388C2×C4⋊C8—42no—
389C2×C4⋊C8—42no—
390#407—44no—
391#407—82no—
392C2×C22⋊C8—81no—
393C2×C22⋊C8—81no—
394C4×M16—44no—
395C4×M16—82no—
396C2×#97—81no—
397C2×C4×C8—22no—
398C2×C4×C8—22no—
399C2×C4×C8—22no—
400C2×C4×C8—22no—
401C2×C4×C8—21no—
402C2×C4×C8—21no—
403C2×C4×C8—21no—
404C2×C4×C8—21no—
405C2×C4×C8—22no—
406C2×C4×C8—22no—
407C2×C4×C8—22no—
408C2×C4×C8—22no—
409C2×C4×C8—22no—
410C2×C4×C8—22no—
411C2×C4×C8—21no—
412C2×C4×C8—21no—
413C2×C4×C8—22no—
414C2×C4×C8—22no—
415C2×C4×C8—21no—
416C2×C4×C8—21no—
417C2×C4×C8—22no—
418C2×C4×C8—22no—
419C2×C4×C8—22no—
420C2×C4×C8—22no—
421C2×C4×C8—22no—
422C2×C4×C8—22no—
423C2×C4×C8—22no—
424C2×C4×C8—22no—
425C2×C4×C8—22no—
426C2×C4×C8—22no—
427C2×C4×C8—22no—
428C2×C4×C8—22no—
429C2×C4×C8—22no—
430C2×C4×C8—22no—
431C2×C4×C8—22no—
432C2×C4×C8—22no—
433C2×C4×C8—22no—
434C2×C4×C8—22no—
435C2×C4×C8—22no—
436C2×C4×C8—22no—
437C2×C4×C8—21no—
438C2×C4×C8—21no—
439C2×C4×C8—21no—
440C2×C4×C8—21no—
441C2×C4×C8—21no—
442C2×C4×C8—21no—
443C2×C4×C8—21no—
444C2×C4×C8—21no—
445C2×C4×C8—21no—
446C2×C4×C8—21no—
447C2×C4×C8—21no—
448C2×C4×C8—21no—
449C2×C4×C8—232no—
450C2×C4×C8—216no—
451C2×C4×C8—28no—
452C2×C4×C8—416no—
453C2×C4×C8—48no—
454C2×C4×C8—416no—
455C2×C4×C8—432no—
456C2×C4×C8—48no—
457C2×C4×C8—44no—
458C2×C4×C8—81no—
459C2×C4×C8#9512yes—
460C2×C4×C8#9512yes—
461C2×C4×C8C4×C812yes—
462C2×C4×C8C4×C812yes—
463C2×C4×C8#9712yes—
464C2×C4×C8#9712yes—
465C2×C4×C8C22⋊C812yes—
466C2×C4×C8C22⋊C811yescharacteristic
467C2×C4×C8C22⋊C811yescharacteristic
468C2×C4×C8#10211yescharacteristic
469C2×C4×C8#10211yescharacteristic
470C2×C4×C8#10212yes—
471C2×C4×C8#10212yes—
472C2×C4×C8#10312yes—
473C2×C4×C8#10312yes—
474C2×C4×C8#10312yes—
475C2×C4×C8C4⋊C812yes—
476C2×C4×C8C4⋊C812yes—
477C2×C4×C8C4⋊C812yes—
478C2×C4×C8C4⋊C812yes—
479C2×C4×C8#10612yes—
480C2×C4×C8#10612yes—
481C2×C4×C8#10712yes—
482C2×C4×C8#10712yes—
483C2×C4×C8C2×C4211yescharacteristic
484C2×C4×C8C2×C22⋊C411yescharacteristic
485C2×C4×C8C2×C4⋊C411yescharacteristic
486C2×C4×C8C2×C4⋊C411yescharacteristic
487C2×C4×C8C22×C811yescharacteristic
488C2×C4×C8C22×C811yescharacteristic
489C2×C4×C8C2×M1611yescharacteristic
490C2×C4×C8C2×M1611yescharacteristic
491C2×C4×C8C2×D811yescharacteristic
492C2×C4×C8C2×SD1611yescharacteristic
493C2×C4×C8C2×SD1611yescharacteristic
494C2×C4×C8C2×Q1611yescharacteristic
495#384—24no—
496#383—81no—
497#383—81no—
498#382—42no—
499#382—42no—
500#382—42no—
501#381—81no—
502#381—81no—
503#381—81no—
504#380—42no—
505#380—42no—
506#380—42no—
507#380—42no—
508#380—42no—
509#380—42no—
510#379—81no—
511C4×C4⋊C4—42no—
512C4×C4⋊C4—42no—
513C4×C4⋊C4—42no—
514C4×C4⋊C4—42no—
515C4×C4⋊C4—42no—
516C4×C4⋊C4—42no—
517C4×C22⋊C4—81no—
518C4×C22⋊C4—81no—
519C4×C22⋊C4—81no—
520C4×C22⋊C4—81no—
521C4×C22⋊C4—81no—
522C4×C22⋊C4—81no—
523#376—81no—
524#376—81no—
525#376—81no—
526C43—22no—
527C43—22no—
528C43—22no—
529C43—22no—
530C43—22no—
531C43—22no—
532C43—22no—
533C43—22no—
534C43—22no—
535C43—22no—
536C43—21no—
537C43—21no—
538C43—21no—
539C43—21no—
540C43—81no—
541C43#9512yes—
542C43#10212yes—
543C43#10312yes—
544C43#10312yes—
545C43#10612yes—
546C43#10712yes—
547C43C2×C22⋊C411yescharacteristic
548C43C2×C4⋊C411yescharacteristic
549C43C2×SD1611yescharacteristic
550C43C2×Q1611yescharacteristic
551C4⋊C16—48no—
552C4⋊C16—44no—
553C4⋊C16—44no—
554C22⋊C16—48no—
555C22⋊C16—44no—
556C22⋊C16—44no—
557#346—28no—
558#346—44no—
559C4×C16—48no—
560#340—44no—
561#340—44no—
562#339—84no—
563#339—84no—
564#339—84no—
565#339—84no—
566#336—42no—
567#336—42no—
568#336—42no—
569#336—42no—
570#336—42no—
571#336—42no—
572#336—41no—
573#336—41no—
574#336—41no—
575#336—41no—
576#336—48no—
577#336—48no—
578#336—44no—
579#336—44no—
580#336—44no—
581#336—44no—
582#335—48no—
583#334—44no—
584#334—44no—
585C25#32711yescharacteristic
586C23×C4—24no—
587C23×C4—24no—
588C23×C4—28no—
589C23×C4—28no—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—22no—
594C23×C4—21no—
595C23×C4—21no—
596C23×C4—21no—
597C23×C4—21no—
598C23×C4—44no—
599C23×C4—42no—
600C23×C4—42no—
601C23×C4—44no—
602C23×C4—44no—
603C23×C4—44no—
604C23×C4—44no—
605C23×C4#32311yescharacteristic
606C23×C4#32311yescharacteristic
607C23×C4#32412yes—
608C23×C4D4⋊C811yescharacteristic
609C23×C4D4⋊C812yes—
610C23×C4D4⋊C811yescharacteristic
611C23×C4D4⋊C811yescharacteristic
612C23×C4D4⋊C811yescharacteristic
613C23×C4Q8⋊C812yes—
614C23×C4#32711yescharacteristic
615C23×C4#32711yescharacteristic
616C23×C4#32711yescharacteristic
617C23×C4#32711yescharacteristic
618C23×C4#32711yescharacteristic
619C23×C4#32712yes—
620C23×C4#32812yes—
621C23×C4#32812yes—
622C23×C4#32812yes—
623C23×C4#32911yescharacteristic
624C23×C4#32911yescharacteristic
625C23×C4#33012yes—
626C23×C4#33111yescharacteristic
627C23×C4#33111yescharacteristic
628C23×C4#33212yes—
629C23×C4#33912yes—
630C23×C4#34012yes—
631C23×C4#34212yes—
632C23×C4C2×#9911yescharacteristic
633C23×C4C2×#10211yescharacteristic
634C23×C4C2×#10411yescharacteristic
635C2×M16—44no—
636C2×M16—82no—
637C2×M16—82no—
638C2×M16—82no—
639C2×M16—82no—
640C2×M16—82no—
641C22×C8—22no—
642C22×C8—22no—
643C22×C8—22no—
644C22×C8—22no—
645C22×C8—22no—
646C22×C8—22no—
647C22×C8—22no—
648C22×C8—22no—
649C22×C8—21no—
650C22×C8—21no—
651C22×C8—21no—
652C22×C8—21no—
653C22×C8—21no—
654C22×C8—21no—
655C22×C8—21no—
656C22×C8—21no—
657C22×C8—22no—
658C22×C8—22no—
659C22×C8—22no—
660C22×C8—22no—
661C22×C8—22no—
662C22×C8—22no—
663C22×C8—22no—
664C22×C8—22no—
665C22×C8—22no—
666C22×C8—21no—
667C22×C8—21no—
668C22×C8—21no—
669C22×C8—22no—
670C22×C8—22no—
671C22×C8—21no—
672C22×C8—21no—
673C22×C8—21no—
674C22×C8—21no—
675C22×C8—22no—
676C22×C8—21no—
677C22×C8—44no—
678C22×C8—44no—
679C22×C8—44no—
680C22×C8—44no—
681C22×C8—48no—
682C22×C8—416no—
683C22×C8—432no—
684C22×C8—82no—
685C22×C8—82no—
686C22×C8—82no—
687C22×C8—82no—
688C22×C8—82no—
689C22×C8—82no—
690C22×C8—84no—
691C22×C8—84no—
692C22×C8—84no—
693C22×C8—84no—
694C22×C8—84no—
695C22×C8—82no—
696C22×C8—84no—
697C22×C8—84no—
698C22×C8—82no—
699C22×C8—84no—
700C22×C8—88no—
701C22×C8—816no—
702C22×C8—816no—
703C22×C8—864no—
704C22×C8—88no—
705C22×C8—82no—
706#117—82no—
707#117—82no—
708#117—82no—
709#117—82no—
710#117—88no—
711#117—84no—
712#117—84no—
713C2×C4⋊C4—44no—
714C2×C4⋊C4—44no—
715C2×C4⋊C4—44no—
716C2×C22⋊C4—82no—
717C2×C22⋊C4—82no—
718C2×C22⋊C4—82no—
719C2×C42—28no—
720C2×C42—24no—
721C2×C42—28no—
722C2×C42—24no—
723C2×C42—28no—
724C2×C42—216no—
725C2×C42—28no—
726C2×C42—28no—
727C2×C42—24no—
728C2×C42—24no—
729C2×C42—28no—
730C2×C42—216no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—22no—
735C2×C42—22no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—22no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—22no—
742C2×C42—22no—
743C2×C42—22no—
744C2×C42—22no—
745C2×C42—22no—
746C2×C42—22no—
747C2×C42—22no—
748C2×C42—22no—
749C2×C42—21no—
750C2×C42—22no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42—21no—
757C2×C42—22no—
758C2×C42—21no—
759C2×C42—42no—
760C2×C42—42no—
761C2×C42—42no—
762C2×C42—42no—
763C2×C42—82no—
764C2×C42—82no—
765C2×C42—82no—
766C2×C42—82no—
767C2×C42—82no—
768C2×C42—82no—
769C2×C42—84no—
770C2×C42—84no—
771C2×C42—84no—
772C2×C42—84no—
773C2×C42—82no—
774C2×C42—82no—
775C2×C42—82no—
776C2×C42—82no—
777C2×C42—84no—
778C2×C42—84no—
779C2×C42—82no—
780C2×C42—82no—
781C2×C42—82no—
782C2×C42#32311yescharacteristic
783C2×C42#32311yescharacteristic
784C2×C42#32312yes—
785C2×C42#32312yes—
786C2×C42#32412yes—
787C2×C42#32412yes—
788C2×C42#32412yes—
789C2×C42D4⋊C812yes—
790C2×C42D4⋊C812yes—
791C2×C42D4⋊C812yes—
792C2×C42D4⋊C811yescharacteristic
793C2×C42D4⋊C811yescharacteristic
794C2×C42D4⋊C811yescharacteristic
795C2×C42D4⋊C811yescharacteristic
796C2×C42Q8⋊C812yes—
797C2×C42Q8⋊C812yes—
798C2×C42Q8⋊C812yes—
799C2×C42Q8⋊C812yes—
800C2×C42Q8⋊C812yes—
801C2×C42Q8⋊C812yes—
802C2×C42Q8⋊C812yes—
803C2×C42#32711yescharacteristic
804C2×C42#32711yescharacteristic
805C2×C42#32712yes—
806C2×C42#32712yes—
807C2×C42#32712yes—
808C2×C42#32812yes—
809C2×C42#32812yes—
810C2×C42#32812yes—
811C2×C42#32812yes—
812C2×C42#32812yes—
813C2×C42#32911yescharacteristic
814C2×C42#32911yescharacteristic
815C2×C42#32912yes—
816C2×C42#32912yes—
817C2×C42#33012yes—
818C2×C42#33012yes—
819C2×C42#33012yes—
820C2×C42#33111yescharacteristic
821C2×C42#33111yescharacteristic
822C2×C42#33212yes—
823C2×C42#33212yes—
824C2×C42#33212yes—
825C2×C42#33312yes—
826C2×C42#33312yes—
827C2×C42#33612yes—
828C2×C42#33612yes—
829C2×C42#33912yes—
830C2×C42#33912yes—
831C2×C42#33912yes—
832C2×C42#34012yes—
833C2×C42#34012yes—
834C2×C42#34012yes—
835C2×C42#34012yes—
836C2×C42#34012yes—
837C2×C42#34212yes—
838C2×C42#34312yes—
839C2×C42#34312yes—
840C2×C42C2×#9511yescharacteristic
841C2×C42C2×C22⋊C811yescharacteristic
842C2×C42C2×C22⋊C811yescharacteristic
843C2×C42C2×#9911yescharacteristic
844C2×C42C2×#10011yescharacteristic
845C2×C42C2×#10111yescharacteristic
846C2×C42C2×#10211yescharacteristic
847C2×C42C2×#10211yescharacteristic
848C2×C42C2×#10311yescharacteristic
849C2×C42C2×#10311yescharacteristic
850C2×C42C2×#10311yescharacteristic
851C2×C42C2×#10411yescharacteristic
852C2×C42C2×#10411yescharacteristic
853C2×C42C2×#10411yescharacteristic
854C2×C42C2×#10611yescharacteristic
855C2×C42C2×#10711yescharacteristic
856M32—816no—
857C2×C16—48no—
858C2×C16—88no—
859#107—88no—
860#106—88no—
861C4⋊C8—44no—
862C4⋊C8—44no—
863C4⋊C8—82no—
864C4⋊C8—82no—
865C22⋊C8—84no—
866C22⋊C8—84no—
867#97—84no—
868C4×C8—216no—
869C4×C8—22no—
870C4×C8—22no—
871C4×C8—22no—
872C4×C8—22no—
873C4×C8—22no—
874C4×C8—22no—
875C4×C8—22no—
876C4×C8—22no—
877C4×C8—22no—
878C4×C8—22no—
879C4×C8—22no—
880C4×C8—22no—
881C4×C8—22no—
882C4×C8—22no—
883C4×C8—22no—
884C4×C8—22no—
885C4×C8—21no—
886C4×C8—21no—
887C4×C8—22no—
888C4×C8—21no—
889C4×C8—21no—
890C4×C8—21no—
891C4×C8—21no—
892C4×C8—21no—
893C4×C8—22no—
894C4×C8—21no—
895C4×C8—22no—
896C4×C8—21no—
897C4×C8—21no—
898C4×C8—21no—
899C4×C8—21no—
900C4×C8—21no—
901C4×C8—21no—
902C4×C8—21no—
903C4×C8—22no—
904C4×C8—21no—
905C4×C8—416no—
906C4×C8—432no—
907C4×C8—48no—
908C4×C8—84no—
909C4×C8#33612yes—
910C4×C8#33612yes—
911C4×C8#34012yes—
912C4×C8#34012yes—
913C4×C8C2×C4×C811yescharacteristic
914C4×C8C2×#9711yescharacteristic
915C4×C8C2×#10211yescharacteristic
916C4×C8C2×#10311yescharacteristic
917C4×C8C2×C4⋊C811yescharacteristic
918C4×C8C2×C4⋊C811yescharacteristic
919C4×C8C2×#10611yescharacteristic
920C4×C8C2×#10711yescharacteristic
921#95—82no—
922#95—82no—
923#95—82no—
924#95—82no—
925#95—82no—
926#95—82no—
927C24—22no—
928C24—22no—
929C24—24no—
930C24—24no—
931C24#127011yescharacteristic
932C24#127011yescharacteristic
933C24#127112yes—
934C24#129412yes—
935C24C2×#32711yescharacteristic
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—28no—
954C22×C4—28no—
955C22×C4—24no—
956C22×C4—28no—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—28no—
961C22×C4—28no—
962C22×C4—28no—
963C22×C4—22no—
964C22×C4—22no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—44no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—44no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—44no—
979C22×C4—42no—
980C22×C4—44no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—44no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—44no—
987C22×C4—42no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—432no—
1000C22×C4—432no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—84no—
1006C22×C4#127011yescharacteristic
1007C22×C4#127011yescharacteristic
1008C22×C4#127011yescharacteristic
1009C22×C4#127011yescharacteristic
1010C22×C4#127011yescharacteristic
1011C22×C4#127012yes—
1012C22×C4#127012yes—
1013C22×C4#127011yescharacteristic
1014C22×C4#127112yes—
1015C22×C4#127112yes—
1016C22×C4#127112yes—
1017C22×C4#127112yes—
1018C22×C4#127112yes—
1019C22×C4#127112yes—
1020C22×C4#127112yes—
1021C22×C4#127112yes—
1022C22×C4#127112yes—
1023C22×C4#127212yes—
1024C22×C4#127212yes—
1025C22×C4#127212yes—
1026C22×C4#127212yes—
1027C22×C4#127912yes—
1028C22×C4#127912yes—
1029C22×C4#127912yes—
1030C22×C4#127912yes—
1031C22×C4#128012yes—
1032C22×C4#128012yes—
1033C22×C4#129412yes—
1034C22×C4#129412yes—
1035C22×C4#129412yes—
1036C22×C4#129412yes—
1037C22×C4#129412yes—
1038C22×C4#129512yes—
1039C22×C4#129512yes—
1040C22×C4#129612yes—
1041C22×C4#129612yes—
1042C22×C4#133514yes—
1043C22×C4#133614yes—
1044C22×C4C2×#32311yescharacteristic
1045C22×C4C2×#32411yescharacteristic
1046C22×C4C2×D4⋊C811yescharacteristic
1047C22×C4C2×D4⋊C811yescharacteristic
1048C22×C4C2×D4⋊C811yescharacteristic
1049C22×C4C2×Q8⋊C811yescharacteristic
1050C22×C4C2×#32711yescharacteristic
1051C22×C4C2×#32711yescharacteristic
1052C22×C4C2×#32811yescharacteristic
1053C22×C4C2×#32811yescharacteristic
1054C22×C4C2×#32811yescharacteristic
1055C22×C4C2×#32911yescharacteristic
1056C22×C4C2×#33011yescharacteristic
1057C22×C4C2×#33111yescharacteristic
1058C22×C4C2×#33211yescharacteristic
1059C22×C4C2×#33911yescharacteristic
1060C22×C4C2×#34011yescharacteristic
1061C22×C4C2×#34211yescharacteristic
1062M16—84no—
1063M16—84no—
1064M16—162no—
1065M16—162no—
1066C2×C8—22no—
1067C2×C8—22no—
1068C2×C8—21no—
1069C2×C8—21no—
1070C2×C8—21no—
1071C2×C8—21no—
1072C2×C8—22no—
1073C2×C8—22no—
1074C2×C8—21no—
1075C2×C8—21no—
1076C2×C8—21no—
1077C2×C8—21no—
1078C2×C8—42no—
1079C2×C8—42no—
1080C2×C8—42no—
1081C2×C8—44no—
1082C2×C8—42no—
1083C2×C8—42no—
1084C2×C8—42no—
1085C2×C8—42no—
1086C2×C8—42no—
1087C2×C8—44no—
1088C2×C8—44no—
1089C2×C8—44no—
1090C2×C8—44no—
1091C2×C8—44no—
1092C2×C8—44no—
1093C2×C8—44no—
1094C2×C8—416no—
1095C2×C8—81no—
1096C2×C8—82no—
1097C2×C8—81no—
1098C2×C8—82no—
1099C2×C8—82no—
1100C2×C8—81no—
1101C2×C8—81no—
1102C2×C8—81no—
1103C2×C8—82no—
1104C2×C8—82no—
1105C2×C8—82no—
1106C2×C8—82no—
1107C2×C8—82no—
1108C2×C8—82no—
1109C2×C8—82no—
1110C2×C8—82no—
1111C2×C8—81no—
1112C2×C8—81no—
1113C2×C8—82no—
1114C2×C8—81no—
1115C2×C8—88no—
1116C2×C8—864no—
1117C2×C8—832no—
1118C2×C8—88no—
1119C2×C8—84no—
1120C2×C8—162no—
1121C2×C8—162no—
1122C4⋊C4—88no—
1123C4⋊C4—84no—
1124C4⋊C4—84no—
1125C4⋊C4—84no—
1126C4⋊C4—84no—
1127C22⋊C4—162no—
1128C22⋊C4—162no—
1129C22⋊C4—164no—
1130C22⋊C4—164no—
1131C42—22no—
1132C42—22no—
1133C42—24no—
1134C42—28no—
1135C42—24no—
1136C42—22no—
1137C42—24no—
1138C42—22no—
1139C42—24no—
1140C42—28no—
1141C42—28no—
1142C42—28no—
1143C42—28no—
1144C42—42no—
1145C42—42no—
1146C42—41no—
1147C42—41no—
1148C42—41no—
1149C42—41no—
1150C42—81no—
1151C42—81no—
1152C42—81no—
1153C42—81no—
1154C42—82no—
1155C42—82no—
1156C42—82no—
1157C42—82no—
1158C42—81no—
1159C42—82no—
1160C42—81no—
1161C42—82no—
1162C42—82no—
1163C42—82no—
1164C42—82no—
1165C42—81no—
1166C42—82no—
1167C42—81no—
1168C42—164no—
1169C42—162no—
1170C42—162no—
1171C42—164no—
1172C42#127012yes—
1173C42#127012yes—
1174C42#127112yes—
1175C42#127112yes—
1176C42#127112yes—
1177C42#127112yes—
1178C42#127112yes—
1179C42#127112yes—
1180C42#127212yes—
1181C42#127212yes—
1182C42#127212yes—
1183C42#127212yes—
1184C42#127912yes—
1185C42#127912yes—
1186C42#127912yes—
1187C42#127912yes—
1188C42#128012yes—
1189C42#128012yes—
1190C42#129412yes—
1191C42#129412yes—
1192C42#129512yes—
1193C42#129512yes—
1194C42#129612yes—
1195C42#129612yes—
1196C42C2×#32311yescharacteristic
1197C42C2×#32411yescharacteristic
1198C42C2×D4⋊C811yescharacteristic
1199C42C2×Q8⋊C811yescharacteristic
1200C42C2×Q8⋊C811yescharacteristic
1201C42C2×Q8⋊C811yescharacteristic
1202C42C2×#32711yescharacteristic
1203C42C2×#32811yescharacteristic
1204C42C2×#32911yescharacteristic
1205C42C2×#33011yescharacteristic
1206C42C2×#33211yescharacteristic
1207C42C2×#33311yescharacteristic
1208C42C2×#33611yescharacteristic
1209C42C2×#33911yescharacteristic
1210C42C2×#34011yescharacteristic
1211C42C2×#34311yescharacteristic
1212C16—88no—
1213C23—216no—
1214C23—216no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—24no—
1224C23—24no—
1225C23—24no—
1226C23—24no—
1227C23—24no—
1228C23#702512yes—
1229C23#702512yes—
1230C23#711414yes—
1231C23#711514yes—
1232C23C2×#127011yescharacteristic
1233C23C2×#127111yescharacteristic
1234C23C2×#129411yescharacteristic
1235C23#1168512yes—
1236C23#1168812yes—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—41no—
1282C2×C4—42no—
1283C2×C4—41no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—42no—
1289C2×C4—42no—
1290C2×C4—42no—
1291C2×C4—42no—
1292C2×C4—42no—
1293C2×C4—42no—
1294C2×C4—42no—
1295C2×C4—42no—
1296C2×C4—42no—
1297C2×C4—42no—
1298C2×C4—42no—
1299C2×C4—41no—
1300C2×C4—42no—
1301C2×C4—42no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—416no—
1306C2×C4—48no—
1307C2×C4—416no—
1308C2×C4—416no—
1309C2×C4—416no—
1310C2×C4—48no—
1311C2×C4—48no—
1312C2×C4—48no—
1313C2×C4—41no—
1314C2×C4—42no—
1315C2×C4—41no—
1316C2×C4—42no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—164no—
1320C2×C4—164no—
1321C2×C4—164no—
1322C2×C4#702512yes—
1323C2×C4#702512yes—
1324C2×C4#702512yes—
1325C2×C4#702512yes—
1326C2×C4#702512yes—
1327C2×C4#702512yes—
1328C2×C4#711414yes—
1329C2×C4#711918yes—
1330C2×C4#717914yes—
1331C2×C4#718214yes—
1332C2×C4C2×#127011yescharacteristic
1333C2×C4C2×#127111yescharacteristic
1334C2×C4C2×#127111yescharacteristic
1335C2×C4C2×#127111yescharacteristic
1336C2×C4C2×#127211yescharacteristic
1337C2×C4C2×#127211yescharacteristic
1338C2×C4C2×#127911yescharacteristic
1339C2×C4C2×#127911yescharacteristic
1340C2×C4C2×#128011yescharacteristic
1341C2×C4C2×#129411yescharacteristic
1342C2×C4C2×#129511yescharacteristic
1343C2×C4C2×#129611yescharacteristic
1344C2×C4C2×#133512yes—
1345C2×C4C2×#133612yes—
1346C8—41no—
1347C8—42no—
1348C8—42no—
1349C8—41no—
1350C8—41no—
1351C8—41no—
1352C8—42no—
1353C8—42no—
1354C8—41no—
1355C8—41no—
1356C8—41no—
1357C8—41no—
1358C8—816no—
1359C8—164no—
1360C22—28no—
1361C22—28no—
1362C22—216no—
1363C22—21no—
1364C22—22no—
1365C22—21no—
1366C22—21no—
1367C22—22no—
1368C22—21no—
1369C22—22no—
1370C22—22no—
1371C22—24no—
1372C22—24no—
1373C22—28no—
1374C22—28no—
1375C22#9337614yes—
1376C22#9338614yes—
1377C22C2×#702511yescharacteristic
1378C22C2×#711512yes—
1379C22#12406612yes—
1380C22C2×#711412yes—
1381C22#12409812yes—
1382C22#12750411yescharacteristic
1383C22#12750611yescharacteristic
1384C4—21no—
1385C4—22no—
1386C4—21no—
1387C4—21no—
1388C4—21no—
1389C4—22no—
1390C4—22no—
1391C4—21no—
1392C4—21no—
1393C4—21no—
1394C4—21no—
1395C4—22no—
1396C4—22no—
1397C4—21no—
1398C4—21no—
1399C4—42no—
1400C4—44no—
1401C4—42no—
1402C4—42no—
1403C4—44no—
1404C4—42no—
1405C4—324no—
1406C4#9338614yes—
1407C4C2×#711912yes—
1408C4C2×#717911yescharacteristic
1409C4C2×#718211yescharacteristic
1410C2—21no—
1411C2—21no—
1412C2—24no—
1413C2—22no—
1414C2—24no—
1415C2C2×#9338611yescharacteristic
1416C2C2×#9337611yescharacteristic
1417C2#7221137111yescharacteristic
1418C2#7221137314yes—
subgroupG/H
centerC22×C4#1270
commutatorC4×C8C2×C4×C8
Frattini, cosocleC2×#1744C23
socleC23C2×#1270
prime radicalC25#327
LCSG ▷ C4×C8 ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ C22×#1744 ◁ G
LECSG ▷ C2×#1744 ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #72210220C2semidirect
13. #126586C4semidirect
22. C2×#7014C4semidirect
43. #20817C8semidirect
47. #20797C8semidirect
74. #17793C8semidirect
204. #1845C2×C8semidirect
272. #1566C2×C8semidirect

Maximal subgroups

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

subgroupindex
C2×#1265862
#722113572
C22×#70142
#722102202