Finite Group Databasebeta

← #72257579

Subgroups — #72257579

Order 1024.

2161 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#6375020C211yesmaximal, characteristic
2#355942C211yesmaximal, characteristic
3#181791C211yesmaximal, characteristic
4#181175C211yesmaximal, characteristic
5#181122C211yesmaximal, characteristic
6#181122C211yesmaximal, characteristic
7#180871C211yesmaximal, characteristic
8C2×#2920C2211yescharacteristic
9C2×#2920C2211yescharacteristic
10C2×#2920C2211yescharacteristic
11C22×#423C2211yescharacteristic
12#34012C2211yescharacteristic
13#34012C2211yescharacteristic
14#34012C2211yescharacteristic
15#21975—22no—
16#21975—22no—
17#21952—22no—
18#21935—22no—
19#21356—22no—
20#21356C414yescomplemented
21#20811—22no—
22#10836—22no—
23#10836C414yescomplemented
24#10717—22no—
25#8081—22no—
26#8079—22no—
27#8077—22no—
28#7962—22no—
29#7960—22no—
30#7957—22no—
31#7946—22no—
32#7946—22no—
33#7945—22no—
34#7945C414yescomplemented
35#7940—22no—
36#7940—22no—
37#7858—22no—
38#7858—22no—
39#7856—22no—
40C23×M16—21no—
41C23×C42C2311yescharacteristic
42#2920—21no—
43#2920—21no—
44#2920—21no—
45#2920—21no—
46#2920—21no—
47#2920—21no—
48#2920—21no—
49#2920—21no—
50#2920—21no—
51#2920—21no—
52#2920—21no—
53#2920—21no—
54#2920—21no—
55#2920—21no—
56#2920—21no—
57#2920—21no—
58#2920—21no—
59#2920—21no—
60#2920—21no—
61#2920—21no—
62#2920—21no—
63#2920—21no—
64#2920C2×C412yes—
65#2920Q812yes—
66C2×#432—21no—
67C2×#432—21no—
68C2×#432—21no—
69C2×#432—21no—
70C2×#432—21no—
71C2×#432C2×C412yes—
72C2×#431—21no—
73C2×#431—21no—
74C2×#431D412yes—
75C2×#431D412yes—
76C2×#431D412yes—
77C2×#431D412yes—
78C2×#423—21no—
79C2×#423—21no—
80C2×#423—21no—
81C2×#423—21no—
82C2×#423—21no—
83C2×#423—21no—
84C2×#423—21no—
85C2×#423—21no—
86C2×#423—21no—
87C2×#423—21no—
88C2×#423—21no—
89C2×#423—21no—
90C2×#423—21no—
91C2×#423C2×C412yes—
92C2×#423D412yes—
93C22×C4⋊C8—21no—
94C22×C4⋊C8Q812yes—
95C2×#407—21no—
96C2×#407—21no—
97C2×#407D412yes—
98C2×C4×M16—21no—
99C2×C4×M16—21no—
100C2×C4×M16C2×C412yes—
101#2285—21no—
102#2285—21no—
103#2285—21no—
104#2285—21no—
105#2285—21no—
106#2285—21no—
107#2285—21no—
108#2285—21no—
109#2285C2×C412yes—
110#2283—21no—
111#2283—21no—
112#2283—21no—
113#2283—21no—
114#2283—21no—
115#2283—21no—
116#2283—21no—
117#2283—21no—
118#2283—21no—
119#2283—21no—
120#2283—21no—
121#2283—21no—
122#2283—21no—
123#2283C2×C412yes—
124#2283C2×C412yes—
125#2283D412yes—
126#2283Q812yes—
127#2283Q812yes—
128#2280—21no—
129#2280—21no—
130#2280—21no—
131#2280—21no—
132#2280—21no—
133#2280—21no—
134#2280—21no—
135#2280—21no—
136#2280D412yes—
137C4×#117—21no—
138C4×#117—21no—
139C4×#117—21no—
140C4×#117C2×C412yes—
141C4×#117C2×C412yes—
142C4×#117D412yes—
143C4×#117D412yes—
144C4×#117D412yes—
145C4×#117Q812yes—
146#1939—28no—
147#1939—28no—
148#1851—28no—
149#1851—28no—
150#1843—24no—
151#1832—24no—
152#1798—28no—
153#1767—28no—
154C2×H(3,ℤ/4)—28no—
155#1301—28no—
156#1286—28no—
157#1284—28no—
158#1284—28no—
159#1274—28no—
160C24×C4C2×D411yescharacteristic
161C24×C4C2×D411yescharacteristic
162C24×C4#4111yescharacteristic
163C22×M16—22no—
164C22×M16—22no—
165C22×M16—22no—
166C22×M16—22no—
167C22×M16—41no—
168C22×M16—41no—
169C22×M16—41no—
170C22×M16—41no—
171C22×M16—41no—
172C22×M16—84no—
173C23×C8—22no—
174C2×#117—22no—
175C2×#117—22no—
176C2×#117—22no—
177C2×#117—22no—
178C2×#117—22no—
179C2×#117—41no—
180C2×#117—41no—
181C2×#117—41no—
182C2×#117C22⋊C414yes—
183C22×C42C22×C411yescharacteristic
184C22×C42C22×C411yescharacteristic
185C22×C42C22×C411yescharacteristic
186C22×C42C2×D411yescharacteristic
187C22×C42C2×D411yescharacteristic
188C22×C42C2×D411yescharacteristic
189C22×C42C2×D411yescharacteristic
190C22×C42C2×D411yescharacteristic
191C22×C42C2×D411yescharacteristic
192C22×C42C2×D411yescharacteristic
193C22×C42C2×D411yescharacteristic
194C22×C42C2×D411yescharacteristic
195C22×C42C2×Q811yescharacteristic
196C22×C42C2×Q811yescharacteristic
197C22×C42C2×Q811yescharacteristic
198C22×C42C2×Q811yescharacteristic
199C22×C42C2×Q811yescharacteristic
200C22×C42#4111yescharacteristic
201C22×C42#4111yescharacteristic
202C22×C42#4111yescharacteristic
203C22×C42#4111yescharacteristic
204C22×C42#4111yescharacteristic
205C22×C42#4111yescharacteristic
206C22×C42#4111yescharacteristic
207C22×C42#4111yescharacteristic
208C22×C42#4111yescharacteristic
209C22×C42#4111yescharacteristic
210C22×C42#4111yescharacteristic
211#432—22no—
212#432—22no—
213#432—22no—
214#432—22no—
215#432—22no—
216#432—22no—
217#432—22no—
218#432—22no—
219#432—41no—
220#432—41no—
221#432—41no—
222#432—41no—
223#432—41no—
224#432—41no—
225#432—41no—
226#432—41no—
227#432—41no—
228#432—41no—
229#432—41no—
230#432—41no—
231#432—41no—
232#432—41no—
233#432—41no—
234#432—41no—
235#431—22no—
236#431—22no—
237#431—22no—
238#431—22no—
239#431—22no—
240#431—22no—
241#431—22no—
242#431—22no—
243#431—22no—
244#431—22no—
245#431—22no—
246#431—22no—
247#431—22no—
248#431—22no—
249#431—22no—
250#431—22no—
251#431—22no—
252#431—41no—
253#431—41no—
254#431—41no—
255#431—41no—
256#431—41no—
257#431—41no—
258#431C4⋊C414yes—
259#423—22no—
260#423—22no—
261#423—22no—
262#423—22no—
263#423—22no—
264#423—22no—
265#423—22no—
266#423—22no—
267#423—22no—
268#423—22no—
269#423—41no—
270#423—41no—
271#423—41no—
272#423—41no—
273#423—41no—
274#423—41no—
275#423—41no—
276#423—41no—
277#423—41no—
278#423—41no—
279#423—41no—
280#423—41no—
281#423—41no—
282#423—41no—
283#423—41no—
284#423—41no—
285#423—41no—
286#423—41no—
287C2×C4⋊C8—22no—
288C2×C4⋊C8—22no—
289C2×C4⋊C8—22no—
290C2×C4⋊C8—22no—
291C2×C4⋊C8—22no—
292C2×C4⋊C8—22no—
293C2×C4⋊C8—22no—
294C2×C4⋊C8—22no—
295C2×C4⋊C8—22no—
296C2×C4⋊C8—22no—
297C2×C4⋊C8—22no—
298C2×C4⋊C8—22no—
299C2×C4⋊C8—216no—
300C2×C4⋊C8—41no—
301C2×C4⋊C8—41no—
302C2×C4⋊C8—41no—
303C2×C4⋊C8—41no—
304C2×C4⋊C8—41no—
305C2×C4⋊C8C4⋊C414yes—
306#407—22no—
307#407—22no—
308#407—22no—
309#407—22no—
310#407—22no—
311#407—22no—
312#407—41no—
313#407—41no—
314#407—41no—
315#407—41no—
316#407—41no—
317#407—41no—
318C2×C22⋊C8—22no—
319C2×C22⋊C8—22no—
320C2×C22⋊C8—22no—
321C2×C22⋊C8—22no—
322C2×C22⋊C8—41no—
323C2×C22⋊C8C22⋊C414yes—
324C4×M16—22no—
325C4×M16—22no—
326C4×M16—22no—
327C4×M16—22no—
328C4×M16—22no—
329C4×M16—22no—
330C4×M16—41no—
331C4×M16—41no—
332C4×M16—41no—
333C4×M16—41no—
334C4×M16—41no—
335C4×M16—41no—
336C2×#97—22no—
337C2×#97—22no—
338C2×#97—41no—
339C2×C4×C8—22no—
340C2×C4×C8—22no—
341C2×C4×C8C22⋊C414yes—
342#384—22no—
343#384—41no—
344#384—41no—
345#383—22no—
346#383—22no—
347#383—41no—
348#383—41no—
349#383—41no—
350#383C4⋊C414yes—
351#382—22no—
352#382—22no—
353#382—22no—
354#382—22no—
355#382—22no—
356#382—22no—
357#382—41no—
358#382—41no—
359#382—41no—
360#381—22no—
361#381—22no—
362#381—22no—
363#381—22no—
364#381—22no—
365#381—22no—
366#381—41no—
367#381—41no—
368#381—41no—
369#380—22no—
370#380—22no—
371#380—22no—
372#380—22no—
373#380—22no—
374#380—22no—
375#380—22no—
376#380—22no—
377#380—22no—
378#380—41no—
379#380—41no—
380#380—41no—
381#380—41no—
382#380—41no—
383#380—41no—
384#380—41no—
385#380—41no—
386#380—41no—
387#379—22no—
388#379—41no—
389#379—41no—
390C4×C4⋊C4—22no—
391C4×C4⋊C4—22no—
392C4×C4⋊C4—22no—
393C4×C4⋊C4—22no—
394C4×C4⋊C4—22no—
395C4×C4⋊C4—22no—
396C4×C4⋊C4—22no—
397C4×C4⋊C4—22no—
398C4×C4⋊C4—22no—
399C4×C4⋊C4—22no—
400C4×C4⋊C4—22no—
401C4×C4⋊C4—22no—
402C4×C4⋊C4—22no—
403C4×C4⋊C4—41no—
404C4×C4⋊C4—41no—
405C4×C4⋊C4—41no—
406C4×C4⋊C4C4214yes—
407C4×C4⋊C4C4⋊C414yes—
408C4×C22⋊C4—22no—
409C4×C22⋊C4—22no—
410C4×C22⋊C4—22no—
411C4×C22⋊C4—22no—
412C4×C22⋊C4—22no—
413C4×C22⋊C4—22no—
414C4×C22⋊C4—22no—
415C4×C22⋊C4—22no—
416C4×C22⋊C4—22no—
417C4×C22⋊C4—22no—
418C4×C22⋊C4—22no—
419C4×C22⋊C4—22no—
420C4×C22⋊C4—22no—
421C4×C22⋊C4—41no—
422C4×C22⋊C4—41no—
423C4×C22⋊C4—41no—
424C4×C22⋊C4C22⋊C414yes—
425C4×C22⋊C4C4⋊C414yes—
426#376—22no—
427#376—22no—
428#376—22no—
429#376—22no—
430#376—22no—
431#376—22no—
432#376—22no—
433#376—22no—
434#376C4⋊C414yes—
435C43—41no—
436C43C22⋊C414yes—
437C43C4⋊C414yes—
438H(3,ℤ/4)—88no—
439#336—216no—
440C25#12111yescharacteristic
441C23×C4—42no—
442C23×C4—42no—
443C23×C4—82no—
444C23×C4—82no—
445C23×C4C2×C22⋊C411yescharacteristic
446C23×C4C2×C22⋊C411yescharacteristic
447C23×C4C2×C22⋊C411yescharacteristic
448C23×C4C2×C4⋊C411yescharacteristic
449C23×C4#11711yescharacteristic
450C23×C4C4×D411yescharacteristic
451C23×C4C4×D411yescharacteristic
452C23×C4C4×D411yescharacteristic
453C23×C4C4×D411yescharacteristic
454C23×C4#12011yescharacteristic
455C23×C4#12011yescharacteristic
456C23×C4#12011yescharacteristic
457C23×C4#12111yescharacteristic
458C23×C4#12111yescharacteristic
459C23×C4#12111yescharacteristic
460C23×C4#12111yescharacteristic
461C23×C4#12111yescharacteristic
462C23×C4#12111yescharacteristic
463C23×C4#12111yescharacteristic
464C23×C4#12111yescharacteristic
465C23×C4#12111yescharacteristic
466C23×C4C22⋊Q811yescharacteristic
467C23×C4C22⋊Q811yescharacteristic
468C23×C4C22⋊Q811yescharacteristic
469C23×C4C22⋊Q811yescharacteristic
470C23×C4C22⋊Q811yescharacteristic
471C23×C4C22⋊Q811yescharacteristic
472C23×C4C22⋊Q811yescharacteristic
473C23×C4C22⋊Q811yescharacteristic
474C23×C4C22⋊Q811yescharacteristic
475C23×C4C22⋊Q811yescharacteristic
476C23×C4#12311yescharacteristic
477C23×C4#12311yescharacteristic
478C23×C4#12311yescharacteristic
479C23×C4#12311yescharacteristic
480C23×C4#12311yescharacteristic
481C23×C4#12411yescharacteristic
482C23×C4#12511yescharacteristic
483C23×C4#12511yescharacteristic
484C23×C4#12611yescharacteristic
485C23×C4#12611yescharacteristic
486C23×C4C4⋊Q811yescharacteristic
487C2×M16—48no—
488C2×M16—42no—
489C2×M16—42no—
490C2×M16—42no—
491C2×M16—42no—
492C2×M16—42no—
493C2×M16—42no—
494C2×M16—42no—
495C2×M16—42no—
496C2×M16—42no—
497C2×M16—42no—
498C2×M16—84no—
499C2×M16—84no—
500C2×M16—84no—
501C2×M16—82no—
502C2×M16—82no—
503C2×M16—84no—
504C2×M16—84no—
505C2×M16—84no—
506C2×M16—84no—
507C22×C8—24no—
508C22×C8—24no—
509C22×C8—24no—
510C22×C8—42no—
511C22×C8—42no—
512C22×C8—42no—
513C22×C8—84no—
514#117—44no—
515#117—44no—
516#117—44no—
517#117—44no—
518#117—84no—
519#117—84no—
520#117—84no—
521#117—82no—
522#117—82no—
523#117—84no—
524#117—84no—
525#117—84no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—24no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—42no—
530C2×C4⋊C4—42no—
531C2×C4⋊C4—42no—
532C2×C4⋊C4—42no—
533C2×C4⋊C4—42no—
534C2×C4⋊C4—42no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C42—24no—
545C2×C42—24no—
546C2×C42—24no—
547C2×C42—24no—
548C2×C42—24no—
549C2×C42—42no—
550C2×C42—42no—
551C2×C42—42no—
552C2×C42#9518yes—
553C2×C42C2×C4211yescharacteristic
554C2×C42C2×C22⋊C411yescharacteristic
555C2×C42C2×C22⋊C411yescharacteristic
556C2×C42C2×C4⋊C411yescharacteristic
557C2×C42C2×C4⋊C411yescharacteristic
558C2×C42C2×C4⋊C411yescharacteristic
559C2×C42C2×C4⋊C411yescharacteristic
560C2×C42C2×C4⋊C411yescharacteristic
561C2×C42C2×C4⋊C411yescharacteristic
562C2×C42#11711yescharacteristic
563C2×C42#11711yescharacteristic
564C2×C42#11711yescharacteristic
565C2×C42#11711yescharacteristic
566C2×C42#11711yescharacteristic
567C2×C42C4×D411yescharacteristic
568C2×C42C4×D411yescharacteristic
569C2×C42C4×D411yescharacteristic
570C2×C42C4×D411yescharacteristic
571C2×C42C4×D411yescharacteristic
572C2×C42C4×D411yescharacteristic
573C2×C42C4×D411yescharacteristic
574C2×C42C4×D411yescharacteristic
575C2×C42C4×D411yescharacteristic
576C2×C42C4×D411yescharacteristic
577C2×C42C4×D411yescharacteristic
578C2×C42C4×D411yescharacteristic
579C2×C42C4×Q811yescharacteristic
580C2×C42C4×Q811yescharacteristic
581C2×C42C4×Q811yescharacteristic
582C2×C42C4×Q811yescharacteristic
583C2×C42C4×Q811yescharacteristic
584C2×C42C4×Q811yescharacteristic
585C2×C42C4×Q811yescharacteristic
586C2×C42C4×Q811yescharacteristic
587C2×C42#12011yescharacteristic
588C2×C42#12011yescharacteristic
589C2×C42#12011yescharacteristic
590C2×C42#12011yescharacteristic
591C2×C42#12011yescharacteristic
592C2×C42#12111yescharacteristic
593C2×C42#12111yescharacteristic
594C2×C42#12111yescharacteristic
595C2×C42#12111yescharacteristic
596C2×C42#12111yescharacteristic
597C2×C42#12111yescharacteristic
598C2×C42#12111yescharacteristic
599C2×C42#12111yescharacteristic
600C2×C42#12111yescharacteristic
601C2×C42#12111yescharacteristic
602C2×C42C22⋊Q811yescharacteristic
603C2×C42C22⋊Q811yescharacteristic
604C2×C42C22⋊Q811yescharacteristic
605C2×C42C22⋊Q811yescharacteristic
606C2×C42C22⋊Q811yescharacteristic
607C2×C42C22⋊Q811yescharacteristic
608C2×C42C22⋊Q811yescharacteristic
609C2×C42C22⋊Q811yescharacteristic
610C2×C42C22⋊Q811yescharacteristic
611C2×C42C22⋊Q811yescharacteristic
612C2×C42C22⋊Q811yescharacteristic
613C2×C42C22⋊Q811yescharacteristic
614C2×C42C22⋊Q811yescharacteristic
615C2×C42C22⋊Q811yescharacteristic
616C2×C42C22⋊Q811yescharacteristic
617C2×C42C22⋊Q811yescharacteristic
618C2×C42C22⋊Q811yescharacteristic
619C2×C42C22⋊Q811yescharacteristic
620C2×C42#12311yescharacteristic
621C2×C42#12311yescharacteristic
622C2×C42#12311yescharacteristic
623C2×C42#12311yescharacteristic
624C2×C42#12311yescharacteristic
625C2×C42#12311yescharacteristic
626C2×C42#12311yescharacteristic
627C2×C42#12311yescharacteristic
628C2×C42#12311yescharacteristic
629C2×C42#12311yescharacteristic
630C2×C42#12311yescharacteristic
631C2×C42#12411yescharacteristic
632C2×C42#12411yescharacteristic
633C2×C42#12411yescharacteristic
634C2×C42#12411yescharacteristic
635C2×C42#12411yescharacteristic
636C2×C42#12411yescharacteristic
637C2×C42#12411yescharacteristic
638C2×C42#12511yescharacteristic
639C2×C42#12511yescharacteristic
640C2×C42#12511yescharacteristic
641C2×C42#12511yescharacteristic
642C2×C42#12511yescharacteristic
643C2×C42#12511yescharacteristic
644C2×C42#12511yescharacteristic
645C2×C42#12511yescharacteristic
646C2×C42#12511yescharacteristic
647C2×C42#12511yescharacteristic
648C2×C42#12611yescharacteristic
649C2×C42#12611yescharacteristic
650C2×C42#12611yescharacteristic
651C2×C42#12611yescharacteristic
652C2×C42#12611yescharacteristic
653C2×C42#12611yescharacteristic
654C2×C42#12711yescharacteristic
655C2×C42#12711yescharacteristic
656C2×C42C4⋊Q811yescharacteristic
657C2×C42C4⋊Q811yescharacteristic
658C2×C42C4⋊Q811yescharacteristic
659C2×C42C4⋊Q811yescharacteristic
660C2×C42C4⋊Q811yescharacteristic
661C2×C42C4⋊Q811yescharacteristic
662C2×C42C4⋊Q811yescharacteristic
663C2×C42C4⋊Q811yescharacteristic
664C2×C42C4⋊Q811yescharacteristic
665C4⋊C8—24no—
666C4⋊C8—24no—
667C4⋊C8—24no—
668C4⋊C8—42no—
669C4⋊C8—42no—
670C4⋊C8—42no—
671C4⋊C8—42no—
672C4⋊C8—42no—
673C4⋊C8—42no—
674C4⋊C8—42no—
675C4⋊C8—42no—
676C4⋊C8—42no—
677C4⋊C8—42no—
678C4⋊C8—42no—
679C4⋊C8—42no—
680C4⋊C8—42no—
681C4⋊C8—42no—
682C4⋊C8—42no—
683C4⋊C8—42no—
684C4⋊C8—42no—
685C4⋊C8—816no—
686C22⋊C8—24no—
687C22⋊C8—24no—
688C22⋊C8—24no—
689C22⋊C8—42no—
690C22⋊C8—42no—
691C22⋊C8—42no—
692C22⋊C8—42no—
693C22⋊C8—42no—
694C22⋊C8—42no—
695C22⋊C8—42no—
696C22⋊C8—42no—
697C22⋊C8—42no—
698#97—42no—
699#97—42no—
700#97—42no—
701#97—42no—
702#97—42no—
703#97—42no—
704C4×C8—24no—
705C4×C8—24no—
706C4×C8—24no—
707C4×C8—42no—
708C4×C8—42no—
709C4×C8—42no—
710#95—24no—
711#95—24no—
712#95—24no—
713#95—24no—
714#95—24no—
715#95—24no—
716#95—24no—
717#95—24no—
718#95—24no—
719#95—42no—
720#95—42no—
721#95—42no—
722#95—42no—
723#95—42no—
724#95—42no—
725#95—42no—
726#95—42no—
727#95—42no—
728C24—42no—
729C24—81no—
730C24—81no—
731C24#38011yescharacteristic
732C24#38611yescharacteristic
733C24#38611yescharacteristic
734C24#39411yescharacteristic
735C24#39611yescharacteristic
736C24#39611yescharacteristic
737C24#39811yescharacteristic
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—28no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—41no—
752C22×C4—41no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—42no—
761C22×C4—41no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—81no—
777C22×C4—81no—
778C22×C4—81no—
779C22×C4—81no—
780C22×C4—81no—
781C22×C4—81no—
782C22×C4—81no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4—81no—
786C22×C4—81no—
787C22×C4—81no—
788C22×C4—81no—
789C22×C4—81no—
790C22×C4C2×#9511yescharacteristic
791C22×C4C4×C22⋊C411yescharacteristic
792C22×C4C4×C22⋊C411yescharacteristic
793C22×C4#37911yescharacteristic
794C22×C4#38011yescharacteristic
795C22×C4#38011yescharacteristic
796C22×C4#38011yescharacteristic
797C22×C4#38011yescharacteristic
798C22×C4#38011yescharacteristic
799C22×C4#38111yescharacteristic
800C22×C4#38511yescharacteristic
801C22×C4#38511yescharacteristic
802C22×C4#38511yescharacteristic
803C22×C4#38511yescharacteristic
804C22×C4#38511yescharacteristic
805C22×C4#38511yescharacteristic
806C22×C4#38511yescharacteristic
807C22×C4#38511yescharacteristic
808C22×C4#38611yescharacteristic
809C22×C4#38611yescharacteristic
810C22×C4#38611yescharacteristic
811C22×C4#38611yescharacteristic
812C22×C4#38711yescharacteristic
813C22×C4#38711yescharacteristic
814C22×C4#38711yescharacteristic
815C22×C4#38711yescharacteristic
816C22×C4#38711yescharacteristic
817C22×C4#38711yescharacteristic
818C22×C4#38711yescharacteristic
819C22×C4#38711yescharacteristic
820C22×C4#38811yescharacteristic
821C22×C4#38811yescharacteristic
822C22×C4#38811yescharacteristic
823C22×C4#38811yescharacteristic
824C22×C4#38911yescharacteristic
825C22×C4#38911yescharacteristic
826C22×C4#38911yescharacteristic
827C22×C4#38911yescharacteristic
828C22×C4#38911yescharacteristic
829C22×C4#38911yescharacteristic
830C22×C4#38911yescharacteristic
831C22×C4#38911yescharacteristic
832C22×C4#39011yescharacteristic
833C22×C4#39011yescharacteristic
834C22×C4#39111yescharacteristic
835C22×C4#39111yescharacteristic
836C22×C4#39111yescharacteristic
837C22×C4#39111yescharacteristic
838C22×C4#39211yescharacteristic
839C22×C4#39211yescharacteristic
840C22×C4#39311yescharacteristic
841C22×C4#39311yescharacteristic
842C22×C4#39411yescharacteristic
843C22×C4#39411yescharacteristic
844C22×C4#39411yescharacteristic
845C22×C4#39411yescharacteristic
846C22×C4#39411yescharacteristic
847C22×C4#39511yescharacteristic
848C22×C4#39511yescharacteristic
849C22×C4#39511yescharacteristic
850C22×C4#39511yescharacteristic
851C22×C4#39611yescharacteristic
852C22×C4#39611yescharacteristic
853C22×C4#39611yescharacteristic
854C22×C4#39611yescharacteristic
855C22×C4#39611yescharacteristic
856C22×C4#39611yescharacteristic
857C22×C4#39711yescharacteristic
858C22×C4#39711yescharacteristic
859C22×C4#39811yescharacteristic
860C22×C4#39811yescharacteristic
861C22×C4#39811yescharacteristic
862C22×C4#39811yescharacteristic
863C22×C4#39811yescharacteristic
864C22×C4#39811yescharacteristic
865C22×C4#39811yescharacteristic
866C22×C4#39811yescharacteristic
867C22×C4#39811yescharacteristic
868C22×C4#39911yescharacteristic
869C22×C4#39911yescharacteristic
870C22×C4#40011yescharacteristic
871C22×C4#40011yescharacteristic
872C22×C4#40011yescharacteristic
873C22×C4#40011yescharacteristic
874M16—84no—
875M16—84no—
876M16—84no—
877M16—84no—
878M16—84no—
879M16—84no—
880M16—84no—
881M16—84no—
882M16—84no—
883M16—84no—
884C2×C8—48no—
885C2×C8—48no—
886C2×C8—48no—
887C2×C8—44no—
888C2×C8—44no—
889C2×C8—44no—
890C2×C8—44no—
891C2×C8—84no—
892C2×C8—84no—
893C2×C8—82no—
894C2×C8—82no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—82no—
899C4⋊C4—82no—
900C4⋊C4—84no—
901C4⋊C4—82no—
902C4⋊C4—82no—
903C4⋊C4—84no—
904C4⋊C4—84no—
905C4⋊C4—84no—
906C4⋊C4—84no—
907C22⋊C4—84no—
908C22⋊C4—84no—
909C22⋊C4—84no—
910C22⋊C4—84no—
911C22⋊C4—84no—
912C22⋊C4—84no—
913C22⋊C4—84no—
914C22⋊C4—84no—
915C22⋊C4—84no—
916C42—48no—
917C42—48no—
918C42—48no—
919C42—48no—
920C42—84no—
921C42—84no—
922C42—84no—
923C42—84no—
924C42—84no—
925C42C4×C4⋊C411yescharacteristic
926C42C4×C4⋊C411yescharacteristic
927C42C4×C4⋊C411yescharacteristic
928C42C4×C4⋊C411yescharacteristic
929C42#38211yescharacteristic
930C42#38211yescharacteristic
931C42#38411yescharacteristic
932C42#38411yescharacteristic
933C42#38511yescharacteristic
934C42#38511yescharacteristic
935C42#38511yescharacteristic
936C42#38511yescharacteristic
937C42#38611yescharacteristic
938C42#38611yescharacteristic
939C42#38711yescharacteristic
940C42#38711yescharacteristic
941C42#38711yescharacteristic
942C42#38711yescharacteristic
943C42#38711yescharacteristic
944C42#38711yescharacteristic
945C42#38711yescharacteristic
946C42#38711yescharacteristic
947C42#38811yescharacteristic
948C42#38811yescharacteristic
949C42#38811yescharacteristic
950C42#38811yescharacteristic
951C42#38911yescharacteristic
952C42#38911yescharacteristic
953C42#38911yescharacteristic
954C42#38911yescharacteristic
955C42#38911yescharacteristic
956C42#38911yescharacteristic
957C42#38911yescharacteristic
958C42#38911yescharacteristic
959C42#39011yescharacteristic
960C42#39011yescharacteristic
961C42#39111yescharacteristic
962C42#39111yescharacteristic
963C42#39111yescharacteristic
964C42#39111yescharacteristic
965C42#39211yescharacteristic
966C42#39211yescharacteristic
967C42#39311yescharacteristic
968C42#39311yescharacteristic
969C42#39411yescharacteristic
970C42#39411yescharacteristic
971C42#39511yescharacteristic
972C42#39511yescharacteristic
973C42#39511yescharacteristic
974C42#39511yescharacteristic
975C42#39711yescharacteristic
976C42#39711yescharacteristic
977C42#39811yescharacteristic
978C42#39811yescharacteristic
979C42#39811yescharacteristic
980C42#39811yescharacteristic
981C42#39811yescharacteristic
982C42#39811yescharacteristic
983C42#39911yescharacteristic
984C42#39911yescharacteristic
985C42#40011yescharacteristic
986C42#40011yescharacteristic
987C42#40011yescharacteristic
988C42#40011yescharacteristic
989C23—22no—
990C23—22no—
991C23—22no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—88no—
1011C23C22⋊#9511yescharacteristic
1012C23#143911yescharacteristic
1013C23#143911yescharacteristic
1014C23#144111yescharacteristic
1015C23#144111yescharacteristic
1016C23#144111yescharacteristic
1017C23#144111yescharacteristic
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—48no—
1108C2×C4—48no—
1109C2×C4—48no—
1110C2×C4—84no—
1111C2×C4—84no—
1112C2×C4—84no—
1113C2×C4—84no—
1114C2×C4—84no—
1115C2×C4—84no—
1116C2×C4C4⋊#9511yescharacteristic
1117C2×C4C4⋊#9511yescharacteristic
1118C2×C4#143611yescharacteristic
1119C2×C4#143611yescharacteristic
1120C2×C4#143611yescharacteristic
1121C2×C4#143611yescharacteristic
1122C2×C4#143811yescharacteristic
1123C2×C4#143911yescharacteristic
1124C2×C4#143911yescharacteristic
1125C2×C4#144111yescharacteristic
1126C2×C4#144111yescharacteristic
1127C2×C4#144111yescharacteristic
1128C2×C4#144111yescharacteristic
1129C2×C4#144211yescharacteristic
1130C2×C4#144211yescharacteristic
1131C2×C4#144211yescharacteristic
1132C2×C4#144211yescharacteristic
1133C2×C4#144411yescharacteristic
1134C2×C4#144411yescharacteristic
1135C2×C4#144411yescharacteristic
1136C2×C4#144411yescharacteristic
1137C2×C4#144511yescharacteristic
1138C2×C4#144511yescharacteristic
1139C2×C4#144611yescharacteristic
1140C2×C4#190912yes—
1141C2×C4#191012yes—
1142C8—84no—
1143C8—84no—
1144C8—84no—
1145C8—84no—
1146C22—21no—
1147C22—21no—
1148C22—21no—
1149C22—21no—
1150C22—21no—
1151C22—21no—
1152C22—21no—
1153C22—21no—
1154C22—21no—
1155C22—21no—
1156C22—21no—
1157C22—21no—
1158C22—21no—
1159C22—21no—
1160C22—21no—
1161C22—21no—
1162C22—21no—
1163C22—21no—
1164C22—21no—
1165C22—21no—
1166C22—44no—
1167C22—82no—
1168C22—82no—
1169C22—82no—
1170C22—82no—
1171C22—82no—
1172C22—82no—
1173C22#755711yescharacteristic
1174C22#1074212yes—
1175C4—21no—
1176C4—21no—
1177C4—21no—
1178C4—21no—
1179C4—21no—
1180C4—21no—
1181C4—21no—
1182C4—21no—
1183C4—21no—
1184C4—21no—
1185C4—21no—
1186C4—21no—
1187C4—21no—
1188C4—21no—
1189C4—21no—
1190C4—21no—
1191C4—21no—
1192C4—21no—
1193C4—21no—
1194C4—21no—
1195C4—88no—
1196C4—164no—
1197C4—164no—
1198C4#1089012yes—
1199C4#1107311yescharacteristic
1200C4#1107411yescharacteristic
1201C4#1122512yes—
1202C4#1138912yes—
1203C2—22no—
1204C2—41no—
1205C2—41no—
1206C2—41no—
1207C2—41no—
1208C2—41no—
1209C2—41no—
1210C2#12391011yescharacteristic
1211C2#12391611yescharacteristic
1212C2#12402411yescharacteristic
subgroupG/H
center, socleC22#7557
commutatorC2×C42C2×C42
Frattini, cosocleC23×C42C23
prime radicalC25#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C42 ◁ G
LECSG ▷ C23×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
20. #21356C4semidirect
23. #10836C4semidirect
34. #7945C4semidirect

Maximal subgroups

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

subgroupindex
#63750202
#3559422
#1817912
#1811752
#1811222
#1808712