Finite Group Databasebeta

← #72249751

Subgroups — #72249751

Order 1024.

2441 conjugacy classes of subgroups.

The subgroup lattice has 1241 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#6372285C211yesmaximal, characteristic
2#355975C211yesmaximal, characteristic
3#353788C211yesmaximal, characteristic
4#181801C211yesmaximal, characteristic
5#181176C211yesmaximal, characteristic
6#181119C211yesmaximal, characteristic
7C2×#7861C211yesmaximal, characteristic
8C2×#2920C2211yescharacteristic
9C2×#2920C2211yescharacteristic
10C2×#2920C2211yescharacteristic
11C23×#97C2211yescharacteristic
12#34012C2211yescharacteristic
13C2×#2285C2211yescharacteristic
14C2×#2283C2211yescharacteristic
15#21355—22no—
16#21355C414yescomplemented
17#21353—22no—
18#21353—22no—
19#21144—22no—
20#20834—22no—
21#20427—22no—
22#10843—22no—
23#10837C414yescomplemented
24#10836—22no—
25#10721—22no—
26#10716—22no—
27#10703—22no—
28#8098—22no—
29#8095—22no—
30#8094—22no—
31#7962—22no—
32#7959—22no—
33#7958—22no—
34#7944C414yescomplemented
35#7943—22no—
36#7940—22no—
37#7861—22no—
38#7861—22no—
39C2×#1275—22no—
40C24×C8D412yes—
41C22×#117—21no—
42C23×C42C2311yescharacteristic
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#2920—21no—
65#2920C2×C412yes—
66#2920D412yes—
67C2×#432—21no—
68C2×#432—21no—
69C2×#432—21no—
70C2×#432—21no—
71C2×#432—21no—
72C2×#432C2×C412yes—
73C2×#431—21no—
74C2×#431—21no—
75C2×#431D412yes—
76C2×#431D412yes—
77C2×#431Q812yes—
78C2×#431Q812yes—
79C2×#424—24no—
80C2×#423—21no—
81C2×#423—21no—
82C2×#423D412yes—
83C2×#407—21no—
84C2×#407—21no—
85C2×#407—21no—
86C2×C4×M16—21no—
87C2×C4×M16—21no—
88C2×C4×M16C2×C412yes—
89C22×#97—21no—
90C22×#97—21no—
91C22×#97—21no—
92C22×#97—21no—
93C22×#97—21no—
94C22×#97—21no—
95C22×#97—21no—
96C22×#97—21no—
97C22×#97—21no—
98C22×#97—21no—
99C22×#97—21no—
100C22×#97—21no—
101C22×#97C2×C412yes—
102C22×#97D412yes—
103#2285—21no—
104#2285—21no—
105#2285—21no—
106#2285—21no—
107#2285—21no—
108#2285—21no—
109#2285—21no—
110#2285—21no—
111#2285C2×C412yes—
112#2285C2×C412yes—
113#2285Q812yes—
114C2×#384—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#2283—21no—
124#2283—21no—
125#2283C2×C412yes—
126#2283C2×C412yes—
127#2283Q812yes—
128#2283Q812yes—
129C2×#383—21no—
130C2×#382—21no—
131C2×#382D412yes—
132#2280—21no—
133#2280—21no—
134#2280D412yes—
135C2×#381—21no—
136C2×#380—21no—
137C2×#380—21no—
138C2×#380—21no—
139C4×#117C2×C412yes—
140C4×#117D412yes—
141C4×#117D412yes—
142C2×C4×C4⋊C4—21no—
143C2×C4×C4⋊C4—21no—
144C2×C4×C4⋊C4D412yes—
145C2×C4×C22⋊C4—21no—
146C2×#376—21no—
147#1940—28no—
148#1940—28no—
149#1850—28no—
150#1850—28no—
151#1768—28no—
152#1767—28no—
153C2×#340—28no—
154C2×H(3,ℤ/4)—28no—
155#1729—24no—
156#1303—28no—
157#1286—28no—
158#1284—28no—
159#1275—28no—
160C24×C4C2×D411yescharacteristic
161C24×C4C2×D411yescharacteristic
162C24×C4#4111yescharacteristic
163C22×M16—22no—
164C22×M16—22no—
165C22×M16—41no—
166C23×C8—22no—
167C23×C8—22no—
168C23×C8—22no—
169C23×C8—22no—
170C23×C8—22no—
171C23×C8—22no—
172C23×C8—48no—
173C23×C8C22⋊C414yes—
174C2×#117—22no—
175C2×#117—22no—
176C2×#117—22no—
177C2×#117—22no—
178C2×#117—41no—
179C2×#117—41no—
180C2×#117—84no—
181C2×#117C22⋊C414yes—
182C22×C4⋊C4—22no—
183C22×C4⋊C4—22no—
184C22×C4⋊C4—41no—
185C22×C4⋊C4—41no—
186C22×C22⋊C4—41no—
187C22×C22⋊C4—41no—
188C22×C42—22no—
189C22×C42—41no—
190C22×C42C22×C411yescharacteristic
191C22×C42C22×C411yescharacteristic
192C22×C42C22×C411yescharacteristic
193C22×C42C2×D411yescharacteristic
194C22×C42C2×D411yescharacteristic
195C22×C42C2×D411yescharacteristic
196C22×C42C2×D411yescharacteristic
197C22×C42C2×D411yescharacteristic
198C22×C42C2×D411yescharacteristic
199C22×C42C2×D411yescharacteristic
200C22×C42C2×D411yescharacteristic
201C22×C42C2×D411yescharacteristic
202C22×C42C2×Q811yescharacteristic
203C22×C42C2×Q811yescharacteristic
204C22×C42C2×Q811yescharacteristic
205C22×C42C2×Q811yescharacteristic
206C22×C42C2×Q811yescharacteristic
207C22×C42#4111yescharacteristic
208C22×C42#4111yescharacteristic
209C22×C42#4111yescharacteristic
210C22×C42#4111yescharacteristic
211C22×C42#4111yescharacteristic
212C22×C42#4111yescharacteristic
213C22×C42#4111yescharacteristic
214C22×C42#4111yescharacteristic
215C22×C42#4111yescharacteristic
216C22×C42#4111yescharacteristic
217C22×C42#4111yescharacteristic
218#432—22no—
219#432—22no—
220#432—22no—
221#432—22no—
222#432—22no—
223#432—22no—
224#432—22no—
225#432—22no—
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#432—41no—
236#432—41no—
237#432—41no—
238#432—41no—
239#432—41no—
240#432—41no—
241#432—41no—
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—22no—
253#431—22no—
254#431—22no—
255#431—22no—
256#431—22no—
257#431—22no—
258#431—22no—
259#431—41no—
260#431—41no—
261#431—41no—
262#431—41no—
263#431—41no—
264#431—41no—
265#431C4⋊C414yes—
266#424—416no—
267#423—22no—
268#423—22no—
269#423—22no—
270#423—22no—
271#423—22no—
272#423—22no—
273#423—41no—
274#423—41no—
275#423—41no—
276#423—41no—
277#423—41no—
278#423—41no—
279C2×C4⋊C8—22no—
280C2×C4⋊C8—216no—
281C2×C4⋊C8—22no—
282C2×C4⋊C8—22no—
283C2×C4⋊C8—22no—
284C2×C4⋊C8—41no—
285C2×C4⋊C8C22⋊C414yes—
286#407—22no—
287#407—22no—
288#407—41no—
289#407—41no—
290#407—41no—
291#407—41no—
292#407—41no—
293#407—41no—
294#407—41no—
295#407—41no—
296#407—41no—
297#407—41no—
298C2×C22⋊C8—22no—
299C2×C22⋊C8—22no—
300C2×C22⋊C8—22no—
301C2×C22⋊C8—22no—
302C2×C22⋊C8—22no—
303C2×C22⋊C8—41no—
304C4×M16—22no—
305C4×M16—22no—
306C4×M16—22no—
307C4×M16—22no—
308C4×M16—22no—
309C4×M16—22no—
310C4×M16—41no—
311C4×M16—41no—
312C4×M16—41no—
313C4×M16—41no—
314C4×M16—41no—
315C4×M16—41no—
316C2×#97—22no—
317C2×#97—22no—
318C2×#97—22no—
319C2×#97—22no—
320C2×#97—22no—
321C2×#97—22no—
322C2×#97—22no—
323C2×#97—22no—
324C2×#97—22no—
325C2×#97—22no—
326C2×#97—22no—
327C2×#97—22no—
328C2×#97—22no—
329C2×#97—22no—
330C2×#97—41no—
331C2×#97—41no—
332C2×#97—41no—
333C2×#97—41no—
334C2×#97—41no—
335C2×#97—41no—
336C2×#97—41no—
337C2×#97—41no—
338C2×#97—41no—
339C2×#97—41no—
340C2×#97—41no—
341C2×#97—41no—
342C2×#97—41no—
343C2×#97—41no—
344C2×#97—41no—
345C2×#97—41no—
346C2×#97—41no—
347C2×C4×C8—22no—
348C2×C4×C8—22no—
349C2×C4×C8C4⋊C414yes—
350#384—22no—
351#384—22no—
352#384—22no—
353#384—41no—
354#384—41no—
355#383—22no—
356#383—22no—
357#383—22no—
358#383—22no—
359#383—41no—
360#383—41no—
361#382—22no—
362#382—22no—
363#382—22no—
364#382—22no—
365#382—22no—
366#382—22no—
367#382—22no—
368#382—22no—
369#382—41no—
370#382—41no—
371#382C4⋊C414yes—
372#381—22no—
373#381—22no—
374#381—22no—
375#381—22no—
376#381—22no—
377#381—41no—
378#381—41no—
379#380—22no—
380#380—22no—
381#380—22no—
382#380—22no—
383#380—22no—
384#380—22no—
385#380—22no—
386#380—22no—
387#380—22no—
388#380—22no—
389#380—22no—
390#380—22no—
391#380—41no—
392#380—41no—
393#380—41no—
394#380—41no—
395#380—41no—
396#380—41no—
397#379—22no—
398C4×C4⋊C4—22no—
399C4×C4⋊C4—22no—
400C4×C4⋊C4—22no—
401C4×C4⋊C4—22no—
402C4×C4⋊C4—22no—
403C4×C4⋊C4—22no—
404C4×C4⋊C4—22no—
405C4×C4⋊C4—22no—
406C4×C4⋊C4—22no—
407C4×C4⋊C4—22no—
408C4×C4⋊C4—22no—
409C4×C4⋊C4—41no—
410C4×C4⋊C4—41no—
411C4×C4⋊C4—41no—
412C4×C4⋊C4—41no—
413C4×C4⋊C4C4214yes—
414C4×C4⋊C4C4⋊C414yes—
415C4×C4⋊C4C4⋊C414yes—
416C4×C22⋊C4—22no—
417C4×C22⋊C4—22no—
418C4×C22⋊C4—22no—
419C4×C22⋊C4—22no—
420C4×C22⋊C4—22no—
421C4×C22⋊C4—22no—
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—41no—
431#376—41no—
432#376C4⋊C414yes—
433C2×#95—22no—
434C2×#95—22no—
435C2×#95—22no—
436C2×#95—41no—
437C2×#95—41no—
438C2×#95—41no—
439C43C22⋊C414yes—
440#340—416no—
441H(3,ℤ/4)—88no—
442#336—216no—
443C25#12111yescharacteristic
444C23×C4—44no—
445C23×C4—42no—
446C23×C4—42no—
447C23×C4—42no—
448C23×C4—42no—
449C23×C4—82no—
450C23×C4C2×C22⋊C411yescharacteristic
451C23×C4C2×C22⋊C411yescharacteristic
452C23×C4C2×C22⋊C411yescharacteristic
453C23×C4C2×C4⋊C411yescharacteristic
454C23×C4#11711yescharacteristic
455C23×C4C4×D411yescharacteristic
456C23×C4C4×D411yescharacteristic
457C23×C4C4×D411yescharacteristic
458C23×C4C4×D411yescharacteristic
459C23×C4#12011yescharacteristic
460C23×C4#12011yescharacteristic
461C23×C4#12011yescharacteristic
462C23×C4#12111yescharacteristic
463C23×C4#12111yescharacteristic
464C23×C4#12111yescharacteristic
465C23×C4#12111yescharacteristic
466C23×C4#12111yescharacteristic
467C23×C4#12111yescharacteristic
468C23×C4#12111yescharacteristic
469C23×C4#12111yescharacteristic
470C23×C4#12111yescharacteristic
471C23×C4C22⋊Q811yescharacteristic
472C23×C4C22⋊Q811yescharacteristic
473C23×C4C22⋊Q811yescharacteristic
474C23×C4C22⋊Q811yescharacteristic
475C23×C4C22⋊Q811yescharacteristic
476C23×C4C22⋊Q811yescharacteristic
477C23×C4C22⋊Q811yescharacteristic
478C23×C4C22⋊Q811yescharacteristic
479C23×C4C22⋊Q811yescharacteristic
480C23×C4C22⋊Q811yescharacteristic
481C23×C4#12311yescharacteristic
482C23×C4#12311yescharacteristic
483C23×C4#12311yescharacteristic
484C23×C4#12311yescharacteristic
485C23×C4#12311yescharacteristic
486C23×C4#12411yescharacteristic
487C23×C4#12511yescharacteristic
488C23×C4#12511yescharacteristic
489C23×C4#12611yescharacteristic
490C23×C4#12611yescharacteristic
491C23×C4C4⋊Q811yescharacteristic
492C2×M16—44no—
493C2×M16—44no—
494C2×M16—48no—
495C2×M16—42no—
496C2×M16—42no—
497C2×M16—42no—
498C2×M16—42no—
499C2×M16—42no—
500C2×M16—42no—
501C2×M16—82no—
502C2×M16—82no—
503C22×C8—28no—
504C22×C8—28no—
505C22×C8—28no—
506C22×C8—24no—
507C22×C8—24no—
508C22×C8—24no—
509C22×C8—24no—
510C22×C8—24no—
511C22×C8—48no—
512C22×C8—48no—
513C22×C8—48no—
514C22×C8—48no—
515C22×C8—44no—
516C22×C8—44no—
517C22×C8—44no—
518C22×C8—42no—
519C22×C8—42no—
520C22×C8—42no—
521C22×C8—42no—
522C22×C8—42no—
523#117—48no—
524#117—44no—
525#117—44no—
526#117—48no—
527#117—84no—
528#117—84no—
529#117—84no—
530#117—84no—
531C2×C4⋊C4—24no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4—24no—
536C2×C4⋊C4—48no—
537C2×C4⋊C4—48no—
538C2×C4⋊C4—42no—
539C2×C4⋊C4—42no—
540C2×C4⋊C4—42no—
541C2×C4⋊C4—42no—
542C2×C4⋊C4—42no—
543C2×C4⋊C4—42no—
544C2×C4⋊C4—84no—
545C2×C4⋊C4—84no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—82no—
554C2×C22⋊C4—82no—
555C2×C22⋊C4—84no—
556C2×C42—24no—
557C2×C42—24no—
558C2×C42—24no—
559C2×C42—42no—
560C2×C42—42no—
561C2×C42—42no—
562C2×C42—84no—
563C2×C42—84no—
564C2×C42#9518yes—
565C2×C42C2×C4211yescharacteristic
566C2×C42C2×C22⋊C411yescharacteristic
567C2×C42C2×C22⋊C411yescharacteristic
568C2×C42C2×C4⋊C411yescharacteristic
569C2×C42C2×C4⋊C411yescharacteristic
570C2×C42C2×C4⋊C411yescharacteristic
571C2×C42C2×C4⋊C411yescharacteristic
572C2×C42C2×C4⋊C411yescharacteristic
573C2×C42C2×C4⋊C411yescharacteristic
574C2×C42#11711yescharacteristic
575C2×C42#11711yescharacteristic
576C2×C42#11711yescharacteristic
577C2×C42#11711yescharacteristic
578C2×C42#11711yescharacteristic
579C2×C42C4×D411yescharacteristic
580C2×C42C4×D411yescharacteristic
581C2×C42C4×D411yescharacteristic
582C2×C42C4×D411yescharacteristic
583C2×C42C4×D411yescharacteristic
584C2×C42C4×D411yescharacteristic
585C2×C42C4×D411yescharacteristic
586C2×C42C4×D411yescharacteristic
587C2×C42C4×D411yescharacteristic
588C2×C42C4×D411yescharacteristic
589C2×C42C4×D411yescharacteristic
590C2×C42C4×D411yescharacteristic
591C2×C42C4×Q811yescharacteristic
592C2×C42C4×Q811yescharacteristic
593C2×C42C4×Q811yescharacteristic
594C2×C42C4×Q811yescharacteristic
595C2×C42C4×Q811yescharacteristic
596C2×C42C4×Q811yescharacteristic
597C2×C42C4×Q811yescharacteristic
598C2×C42C4×Q811yescharacteristic
599C2×C42#12011yescharacteristic
600C2×C42#12011yescharacteristic
601C2×C42#12011yescharacteristic
602C2×C42#12011yescharacteristic
603C2×C42#12011yescharacteristic
604C2×C42#12111yescharacteristic
605C2×C42#12111yescharacteristic
606C2×C42#12111yescharacteristic
607C2×C42#12111yescharacteristic
608C2×C42#12111yescharacteristic
609C2×C42#12111yescharacteristic
610C2×C42#12111yescharacteristic
611C2×C42#12111yescharacteristic
612C2×C42#12111yescharacteristic
613C2×C42#12111yescharacteristic
614C2×C42C22⋊Q811yescharacteristic
615C2×C42C22⋊Q811yescharacteristic
616C2×C42C22⋊Q811yescharacteristic
617C2×C42C22⋊Q811yescharacteristic
618C2×C42C22⋊Q811yescharacteristic
619C2×C42C22⋊Q811yescharacteristic
620C2×C42C22⋊Q811yescharacteristic
621C2×C42C22⋊Q811yescharacteristic
622C2×C42C22⋊Q811yescharacteristic
623C2×C42C22⋊Q811yescharacteristic
624C2×C42C22⋊Q811yescharacteristic
625C2×C42C22⋊Q811yescharacteristic
626C2×C42C22⋊Q811yescharacteristic
627C2×C42C22⋊Q811yescharacteristic
628C2×C42C22⋊Q811yescharacteristic
629C2×C42C22⋊Q811yescharacteristic
630C2×C42C22⋊Q811yescharacteristic
631C2×C42C22⋊Q811yescharacteristic
632C2×C42#12311yescharacteristic
633C2×C42#12311yescharacteristic
634C2×C42#12311yescharacteristic
635C2×C42#12311yescharacteristic
636C2×C42#12311yescharacteristic
637C2×C42#12311yescharacteristic
638C2×C42#12311yescharacteristic
639C2×C42#12311yescharacteristic
640C2×C42#12311yescharacteristic
641C2×C42#12311yescharacteristic
642C2×C42#12311yescharacteristic
643C2×C42#12411yescharacteristic
644C2×C42#12411yescharacteristic
645C2×C42#12411yescharacteristic
646C2×C42#12411yescharacteristic
647C2×C42#12411yescharacteristic
648C2×C42#12411yescharacteristic
649C2×C42#12411yescharacteristic
650C2×C42#12511yescharacteristic
651C2×C42#12511yescharacteristic
652C2×C42#12511yescharacteristic
653C2×C42#12511yescharacteristic
654C2×C42#12511yescharacteristic
655C2×C42#12511yescharacteristic
656C2×C42#12511yescharacteristic
657C2×C42#12511yescharacteristic
658C2×C42#12511yescharacteristic
659C2×C42#12511yescharacteristic
660C2×C42#12611yescharacteristic
661C2×C42#12611yescharacteristic
662C2×C42#12611yescharacteristic
663C2×C42#12611yescharacteristic
664C2×C42#12611yescharacteristic
665C2×C42#12611yescharacteristic
666C2×C42#12711yescharacteristic
667C2×C42#12711yescharacteristic
668C2×C42C4⋊Q811yescharacteristic
669C2×C42C4⋊Q811yescharacteristic
670C2×C42C4⋊Q811yescharacteristic
671C2×C42C4⋊Q811yescharacteristic
672C2×C42C4⋊Q811yescharacteristic
673C2×C42C4⋊Q811yescharacteristic
674C2×C42C4⋊Q811yescharacteristic
675C2×C42C4⋊Q811yescharacteristic
676C2×C42C4⋊Q811yescharacteristic
677C4⋊C8—24no—
678C4⋊C8—24no—
679C4⋊C8—24no—
680C4⋊C8—432no—
681C4⋊C8—42no—
682C4⋊C8—42no—
683C4⋊C8—42no—
684C4⋊C8—42no—
685C4⋊C8—42no—
686C4⋊C8—42no—
687C4⋊C8—42no—
688C4⋊C8—42no—
689C4⋊C8—42no—
690C22⋊C8—24no—
691C22⋊C8—42no—
692C22⋊C8—42no—
693C22⋊C8—42no—
694C22⋊C8—42no—
695C22⋊C8—42no—
696C22⋊C8—42no—
697C22⋊C8—42no—
698C22⋊C8—42no—
699C22⋊C8—42no—
700C22⋊C8—42no—
701C22⋊C8—42no—
702#97—42no—
703#97—42no—
704#97—42no—
705#97—42no—
706#97—42no—
707#97—42no—
708#97—42no—
709#97—42no—
710#97—42no—
711#97—42no—
712#97—42no—
713#97—42no—
714#97—42no—
715#97—42no—
716C4×C8—24no—
717C4×C8—24no—
718C4×C8—24no—
719C4×C8—42no—
720C4×C8—42no—
721C4×C8—42no—
722#95—24no—
723#95—24no—
724#95—24no—
725#95—24no—
726#95—24no—
727#95—24no—
728#95—24no—
729#95—24no—
730#95—24no—
731#95—42no—
732#95—42no—
733#95—42no—
734#95—42no—
735#95—42no—
736#95—42no—
737#95—42no—
738#95—42no—
739#95—42no—
740C24—22no—
741C24—22no—
742C24—42no—
743C24—42no—
744C24#38011yescharacteristic
745C24#38611yescharacteristic
746C24#38611yescharacteristic
747C24#39411yescharacteristic
748C24#39611yescharacteristic
749C24#39611yescharacteristic
750C24#39811yescharacteristic
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—28no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—41no—
768C22×C4—42no—
769C22×C4—41no—
770C22×C4—42no—
771C22×C4—41no—
772C22×C4—41no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—41no—
778C22×C4—41no—
779C22×C4—41no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—41no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—81no—
795C22×C4—81no—
796C22×C4—81no—
797C22×C4—81no—
798C22×C4—81no—
799C22×C4—81no—
800C22×C4—81no—
801C22×C4—81no—
802C22×C4—84no—
803C22×C4—84no—
804C22×C4—82no—
805C22×C4—82no—
806C22×C4—84no—
807C22×C4—84no—
808C22×C4—84no—
809C22×C4C2×#9511yescharacteristic
810C22×C4C4×C22⋊C411yescharacteristic
811C22×C4C4×C22⋊C411yescharacteristic
812C22×C4#37911yescharacteristic
813C22×C4#38011yescharacteristic
814C22×C4#38011yescharacteristic
815C22×C4#38011yescharacteristic
816C22×C4#38011yescharacteristic
817C22×C4#38011yescharacteristic
818C22×C4#38111yescharacteristic
819C22×C4#38511yescharacteristic
820C22×C4#38511yescharacteristic
821C22×C4#38511yescharacteristic
822C22×C4#38511yescharacteristic
823C22×C4#38511yescharacteristic
824C22×C4#38511yescharacteristic
825C22×C4#38511yescharacteristic
826C22×C4#38511yescharacteristic
827C22×C4#38611yescharacteristic
828C22×C4#38611yescharacteristic
829C22×C4#38611yescharacteristic
830C22×C4#38611yescharacteristic
831C22×C4#38711yescharacteristic
832C22×C4#38711yescharacteristic
833C22×C4#38711yescharacteristic
834C22×C4#38711yescharacteristic
835C22×C4#38711yescharacteristic
836C22×C4#38711yescharacteristic
837C22×C4#38711yescharacteristic
838C22×C4#38711yescharacteristic
839C22×C4#38811yescharacteristic
840C22×C4#38811yescharacteristic
841C22×C4#38811yescharacteristic
842C22×C4#38811yescharacteristic
843C22×C4#38911yescharacteristic
844C22×C4#38911yescharacteristic
845C22×C4#38911yescharacteristic
846C22×C4#38911yescharacteristic
847C22×C4#38911yescharacteristic
848C22×C4#38911yescharacteristic
849C22×C4#38911yescharacteristic
850C22×C4#38911yescharacteristic
851C22×C4#39011yescharacteristic
852C22×C4#39011yescharacteristic
853C22×C4#39111yescharacteristic
854C22×C4#39111yescharacteristic
855C22×C4#39111yescharacteristic
856C22×C4#39111yescharacteristic
857C22×C4#39211yescharacteristic
858C22×C4#39211yescharacteristic
859C22×C4#39311yescharacteristic
860C22×C4#39311yescharacteristic
861C22×C4#39411yescharacteristic
862C22×C4#39411yescharacteristic
863C22×C4#39411yescharacteristic
864C22×C4#39411yescharacteristic
865C22×C4#39411yescharacteristic
866C22×C4#39511yescharacteristic
867C22×C4#39511yescharacteristic
868C22×C4#39511yescharacteristic
869C22×C4#39511yescharacteristic
870C22×C4#39611yescharacteristic
871C22×C4#39611yescharacteristic
872C22×C4#39611yescharacteristic
873C22×C4#39611yescharacteristic
874C22×C4#39611yescharacteristic
875C22×C4#39611yescharacteristic
876C22×C4#39711yescharacteristic
877C22×C4#39711yescharacteristic
878C22×C4#39811yescharacteristic
879C22×C4#39811yescharacteristic
880C22×C4#39811yescharacteristic
881C22×C4#39811yescharacteristic
882C22×C4#39811yescharacteristic
883C22×C4#39811yescharacteristic
884C22×C4#39811yescharacteristic
885C22×C4#39811yescharacteristic
886C22×C4#39811yescharacteristic
887C22×C4#39911yescharacteristic
888C22×C4#39911yescharacteristic
889C22×C4#40011yescharacteristic
890C22×C4#40011yescharacteristic
891C22×C4#40011yescharacteristic
892C22×C4#40011yescharacteristic
893M16—82no—
894M16—82no—
895M16—84no—
896M16—84no—
897M16—82no—
898M16—82no—
899M16—84no—
900M16—84no—
901C2×C8—28no—
902C2×C8—28no—
903C2×C8—28no—
904C2×C8—44no—
905C2×C8—48no—
906C2×C8—44no—
907C2×C8—44no—
908C2×C8—48no—
909C2×C8—48no—
910C2×C8—44no—
911C2×C8—48no—
912C2×C8—48no—
913C2×C8—48no—
914C2×C8—44no—
915C2×C8—44no—
916C2×C8—44no—
917C2×C8—84no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—84no—
922C4⋊C4—84no—
923C4⋊C4—84no—
924C4⋊C4—84no—
925C4⋊C4—84no—
926C4⋊C4—84no—
927C4⋊C4—84no—
928C4⋊C4—84no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C42—48no—
938C42—48no—
939C42—48no—
940C42—84no—
941C42—84no—
942C42—84no—
943C42—84no—
944C42C4×C4⋊C411yescharacteristic
945C42C4×C4⋊C411yescharacteristic
946C42C4×C4⋊C411yescharacteristic
947C42C4×C4⋊C411yescharacteristic
948C42#38211yescharacteristic
949C42#38211yescharacteristic
950C42#38411yescharacteristic
951C42#38411yescharacteristic
952C42#38511yescharacteristic
953C42#38511yescharacteristic
954C42#38511yescharacteristic
955C42#38511yescharacteristic
956C42#38611yescharacteristic
957C42#38611yescharacteristic
958C42#38711yescharacteristic
959C42#38711yescharacteristic
960C42#38711yescharacteristic
961C42#38711yescharacteristic
962C42#38711yescharacteristic
963C42#38711yescharacteristic
964C42#38711yescharacteristic
965C42#38711yescharacteristic
966C42#38811yescharacteristic
967C42#38811yescharacteristic
968C42#38811yescharacteristic
969C42#38811yescharacteristic
970C42#38911yescharacteristic
971C42#38911yescharacteristic
972C42#38911yescharacteristic
973C42#38911yescharacteristic
974C42#38911yescharacteristic
975C42#38911yescharacteristic
976C42#38911yescharacteristic
977C42#38911yescharacteristic
978C42#39011yescharacteristic
979C42#39011yescharacteristic
980C42#39111yescharacteristic
981C42#39111yescharacteristic
982C42#39111yescharacteristic
983C42#39111yescharacteristic
984C42#39211yescharacteristic
985C42#39211yescharacteristic
986C42#39311yescharacteristic
987C42#39311yescharacteristic
988C42#39411yescharacteristic
989C42#39411yescharacteristic
990C42#39511yescharacteristic
991C42#39511yescharacteristic
992C42#39511yescharacteristic
993C42#39511yescharacteristic
994C42#39711yescharacteristic
995C42#39711yescharacteristic
996C42#39811yescharacteristic
997C42#39811yescharacteristic
998C42#39811yescharacteristic
999C42#39811yescharacteristic
1000C42#39811yescharacteristic
1001C42#39811yescharacteristic
1002C42#39911yescharacteristic
1003C42#39911yescharacteristic
1004C42#40011yescharacteristic
1005C42#40011yescharacteristic
1006C42#40011yescharacteristic
1007C42#40011yescharacteristic
1008C23—21no—
1009C23—21no—
1010C23—22no—
1011C23—22no—
1012C23—21no—
1013C23—21no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—48no—
1031C23—48no—
1032C23C22⋊#9511yescharacteristic
1033C23#143911yescharacteristic
1034C23#143911yescharacteristic
1035C23#144111yescharacteristic
1036C23#144111yescharacteristic
1037C23#144111yescharacteristic
1038C23#144111yescharacteristic
1039C23#190912yes—
1040C23#191012yes—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
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—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—48no—
1129C2×C4—48no—
1130C2×C4—48no—
1131C2×C4—84no—
1132C2×C4—84no—
1133C2×C4—84no—
1134C2×C4—84no—
1135C2×C4—84no—
1136C2×C4—84no—
1137C2×C4—168no—
1138C2×C4—164no—
1139C2×C4—164no—
1140C2×C4C4⋊#9511yescharacteristic
1141C2×C4C4⋊#9511yescharacteristic
1142C2×C4#143611yescharacteristic
1143C2×C4#143611yescharacteristic
1144C2×C4#143611yescharacteristic
1145C2×C4#143611yescharacteristic
1146C2×C4#143811yescharacteristic
1147C2×C4#143911yescharacteristic
1148C2×C4#143911yescharacteristic
1149C2×C4#144111yescharacteristic
1150C2×C4#144111yescharacteristic
1151C2×C4#144111yescharacteristic
1152C2×C4#144111yescharacteristic
1153C2×C4#144211yescharacteristic
1154C2×C4#144211yescharacteristic
1155C2×C4#144211yescharacteristic
1156C2×C4#144211yescharacteristic
1157C2×C4#144411yescharacteristic
1158C2×C4#144411yescharacteristic
1159C2×C4#144411yescharacteristic
1160C2×C4#144411yescharacteristic
1161C2×C4#144511yescharacteristic
1162C2×C4#144511yescharacteristic
1163C2×C4#144611yescharacteristic
1164C2×C4#201014yes—
1165C8—48no—
1166C8—84no—
1167C8—84no—
1168C8—84no—
1169C22—24no—
1170C22—24no—
1171C22—21no—
1172C22—21no—
1173C22—21no—
1174C22—21no—
1175C22—21no—
1176C22—21no—
1177C22—21no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—42no—
1188C22—42no—
1189C22—44no—
1190C22—44no—
1191C22—44no—
1192C22—44no—
1193C22—42no—
1194C22—42no—
1195C22#755711yescharacteristic
1196C22#1074212yes—
1197C22#1107311yescharacteristic
1198C22#1107411yescharacteristic
1199C22#1108312yes—
1200C22#1122512yes—
1201C22#1124512yes—
1202C4—21no—
1203C4—21no—
1204C4—21no—
1205C4—21no—
1206C4—21no—
1207C4—21no—
1208C4—21no—
1209C4—21no—
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—21no—
1215C4—21no—
1216C4—21no—
1217C4—21no—
1218C4—21no—
1219C4—21no—
1220C4—21no—
1221C4—21no—
1222C4—21no—
1223C4—21no—
1224C4—88no—
1225C4—164no—
1226C4—164no—
1227C4#1099412yes—
1228C4#1133512yes—
1229C2—22no—
1230C2—21no—
1231C2—22no—
1232C2—21no—
1233C2—22no—
1234C2—22no—
1235C2—41no—
1236C2—41no—
1237C2#12391311yescharacteristic
1238C2#12391411yescharacteristic
1239C2#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
16. #21355C4semidirect
23. #10837C4semidirect
34. #7944C4semidirect

Maximal subgroups

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

subgroupindex
#63722852
#3559752
#3537882
#1818012
#1811762
#1811192
C2×#78612