Finite Group Databasebeta

← #72316902

Subgroups — #72316902

Order 1024.

2261 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#6375057C211yesmaximal, characteristic
2#353804C211yesmaximal, characteristic
3#353776C211yesmaximal, characteristic
4#181789C211yesmaximal, characteristic
5#181124C211yesmaximal, characteristic
6#180880C211yesmaximal, characteristic
7#180871C211yesmaximal, characteristic
8C2×#2920C2211yescharacteristic
9C2×#2920C2211yescharacteristic
10C2×#2920C2211yescharacteristic
11C22×C4×M16C2211yescharacteristic
12#34012C2211yescharacteristic
13#34012C2211yescharacteristic
14#34012C2211yescharacteristic
15#21985—22no—
16#21985—22no—
17#21964—22no—
18#21943—22no—
19#21364—22no—
20#21364—22no—
21#20825C414yescomplemented
22#10848—22no—
23#10837—22no—
24#10729—22no—
25#10717—22no—
26C4×#344—22no—
27C4×H(3,ℤ/4)—22no—
28#8074—22no—
29#8071—22no—
30#8070—22no—
31#7946—22no—
32#7944—22no—
33#7941—22no—
34#7862—22no—
35#7861C414yescomplemented
36#7860—22no—
37#7858—22no—
38#7858—22no—
39#7856C414yescomplemented
40C23×M16D412yes—
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#2920C2×C412yes—
59#2920C2×C412yes—
60#2920C2×C412yes—
61#2920C2×C412yes—
62#2920D412yes—
63#2920D412yes—
64#2920Q812yes—
65#2920Q812yes—
66C2×#432—21no—
67C2×#432—21no—
68C2×#432—21no—
69C2×#432—21no—
70C2×#432—21no—
71C2×#432—21no—
72C2×#431—21no—
73C2×#431—21no—
74C2×#431—21no—
75C2×#431D412yes—
76C2×#431D412yes—
77C2×#431Q812yes—
78C2×#423—21no—
79C2×#423—21no—
80C2×#423—21no—
81C2×#407—21no—
82C2×#407—21no—
83C2×#407—21no—
84C2×C4×M16—21no—
85C2×C4×M16—21no—
86C2×C4×M16—21no—
87C2×C4×M16—21no—
88C2×C4×M16—21no—
89C2×C4×M16—21no—
90C2×C4×M16—21no—
91C2×C4×M16—21no—
92C2×C4×M16—21no—
93C2×C4×M16—21no—
94C2×C4×M16—21no—
95C2×C4×M16—21no—
96C2×C4×M16—21no—
97C2×C4×M16C2×C412yes—
98C2×C4×M16D412yes—
99C22×#97C2×C412yes—
100C22×C4×C8Q812yes—
101#2285—21no—
102#2285—21no—
103#2285—21no—
104#2285—21no—
105#2285—21no—
106#2285—21no—
107#2285—21no—
108#2285D412yes—
109#2285D412yes—
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#2283—21no—
124#2283—21no—
125#2283—21no—
126#2283C2×C412yes—
127#2283C2×C412yes—
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×#117—21no—
141C4×#117—21no—
142C4×#117C2×C412yes—
143C4×#117D412yes—
144C4×#117D412yes—
145C4×#117Q812yes—
146#1948—24no—
147#1948—24no—
148#1947—24no—
149#1947—24no—
150#1854—28no—
151#1854—28no—
152#1846—24no—
153#1835—24no—
154#1809—28no—
155#1776—28no—
156C2×#344—28no—
157C2×H(3,ℤ/4)—28no—
158#1300—28no—
159#1284—28no—
160#1275—28no—
161#1274—28no—
162C24×C4C2×D411yescharacteristic
163C24×C4C2×D411yescharacteristic
164C24×C4#4111yescharacteristic
165C22×M16—22no—
166C22×M16—22no—
167C22×M16—22no—
168C22×M16—22no—
169C22×M16—22no—
170C22×M16—22no—
171C22×M16—22no—
172C22×M16—22no—
173C22×M16—48no—
174C22×M16—41no—
175C23×C8C4⋊C414yes—
176C2×#117—22no—
177C2×#117—22no—
178C2×#117—22no—
179C2×#117—22no—
180C2×#117—22no—
181C2×#117—22no—
182C2×#117—22no—
183C2×#117—41no—
184C2×#117—41no—
185C22×C42C22×C411yescharacteristic
186C22×C42C22×C411yescharacteristic
187C22×C42C22×C411yescharacteristic
188C22×C42C2×D411yescharacteristic
189C22×C42C2×D411yescharacteristic
190C22×C42C2×D411yescharacteristic
191C22×C42C2×D411yescharacteristic
192C22×C42C2×D411yescharacteristic
193C22×C42C2×D411yescharacteristic
194C22×C42C2×D411yescharacteristic
195C22×C42C2×D411yescharacteristic
196C22×C42C2×D411yescharacteristic
197C22×C42C2×Q811yescharacteristic
198C22×C42C2×Q811yescharacteristic
199C22×C42C2×Q811yescharacteristic
200C22×C42C2×Q811yescharacteristic
201C22×C42C2×Q811yescharacteristic
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
211C22×C42#4111yescharacteristic
212C22×C42#4111yescharacteristic
213#432—22no—
214#432—22no—
215#432—22no—
216#432—22no—
217#432—22no—
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—22no—
227#432—22no—
228#432—22no—
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#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—41no—
251#431—41no—
252#431—41no—
253#431—41no—
254#431—41no—
255#431—41no—
256#431C22⋊C414yes—
257#431C22⋊C414yes—
258#431C4⋊C414yes—
259#431C4⋊C414yes—
260#431C4⋊C414yes—
261C2×#107—28no—
262C2×#106—28no—
263#423—22no—
264#423—22no—
265#423—22no—
266#423—22no—
267#423—22no—
268#423—22no—
269#423—22no—
270#423—22no—
271#423—41no—
272#423—41no—
273#423—41no—
274#423—41no—
275C2×C4⋊C8—22no—
276C2×C4⋊C8—22no—
277C2×C4⋊C8—22no—
278C2×C4⋊C8—41no—
279C2×C4⋊C8—41no—
280C2×C4⋊C8—41no—
281#407—22no—
282#407—22no—
283#407—22no—
284#407—22no—
285#407—22no—
286#407—22no—
287#407—22no—
288#407—22no—
289#407—41no—
290#407—41no—
291#407—41no—
292#407—41no—
293C2×C22⋊C8—22no—
294C2×C22⋊C8—22no—
295C2×C22⋊C8—22no—
296C2×C22⋊C8—41no—
297C2×C22⋊C8—41no—
298C2×C22⋊C8—41no—
299C4×M16—22no—
300C4×M16—22no—
301C4×M16—22no—
302C4×M16—22no—
303C4×M16—22no—
304C4×M16—22no—
305C4×M16—22no—
306C4×M16—41no—
307C4×M16—41no—
308C4×M16—41no—
309C4×M16—41no—
310C4×M16—41no—
311C4×M16—41no—
312C4×M16—41no—
313C4×M16—41no—
314C4×M16—41no—
315C4×M16—41no—
316C4×M16—41no—
317C4×M16—41no—
318C4×M16—41no—
319C4×M16—41no—
320C4×M16—41no—
321C4×M16—41no—
322C4×M16—41no—
323C4×M16—41no—
324C4×M16C4214yes—
325C4×M16C4⋊C414yes—
326C4×M16C4⋊C414yes—
327C2×#97—22no—
328C2×#97—22no—
329C2×#97—22no—
330C2×#97—22no—
331C2×#97—22no—
332C2×#97—22no—
333C2×#97—22no—
334C2×#97—22no—
335C2×#97—41no—
336C2×C4×C8—22no—
337C2×C4×C8—22no—
338C2×C4×C8—22no—
339C2×C4×C8—22no—
340C2×C4×C8—22no—
341C2×C4×C8—22no—
342C2×C4×C8—22no—
343C2×C4×C8—22no—
344C2×C4×C8C22⋊C414yes—
345#384—22no—
346#384—22no—
347#384—41no—
348#383—22no—
349#383—22no—
350#383—41no—
351#383—41no—
352#383—41no—
353#383—41no—
354#382—22no—
355#382—22no—
356#382—22no—
357#382—22no—
358#382—41no—
359#382—41no—
360#382—41no—
361#382—41no—
362#382—41no—
363#381—22no—
364#381—22no—
365#381—22no—
366#381—41no—
367#381—41no—
368#381—41no—
369#381—41no—
370#381—41no—
371#381—41no—
372#380—22no—
373#380—22no—
374#380—22no—
375#380—22no—
376#380—22no—
377#380—41no—
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#380—41no—
388#380—41no—
389#380C22⋊C414yes—
390#379—22no—
391#379—41no—
392#379—41no—
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—22no—
404C4×C4⋊C4—41no—
405C4×C4⋊C4—41no—
406C4×C4⋊C4—41no—
407C4×C4⋊C4—41no—
408C4×C4⋊C4—41no—
409C4×C4⋊C4—41no—
410C4×C4⋊C4C22⋊C414yes—
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—22no—
422C4×C22⋊C4—22no—
423C4×C22⋊C4—41no—
424C4×C22⋊C4—41no—
425C4×C22⋊C4—41no—
426C4×C22⋊C4—41no—
427C4×C22⋊C4—41no—
428C4×C22⋊C4—41no—
429#376—22no—
430#376—22no—
431#376—22no—
432#376—22no—
433#376—22no—
434#376—22no—
435#376—41no—
436#376—41no—
437#376—41no—
438C43—22no—
439C43—41no—
440C43C4⋊C414yes—
441#344—416no—
442#340—28no—
443#340—28no—
444H(3,ℤ/4)—416no—
445C25#12111yescharacteristic
446C23×C4—44no—
447C23×C4—81no—
448C23×C4—81no—
449C23×C4—82no—
450C23×C4C2×C22⋊C411yescharacteristic
451C23×C4C2×C4⋊C411yescharacteristic
452C23×C4#11711yescharacteristic
453C23×C4C4×D411yescharacteristic
454C23×C4C4×D411yescharacteristic
455C23×C4C4×D411yescharacteristic
456C23×C4C4×D411yescharacteristic
457C23×C4C4×D411yescharacteristic
458C23×C4C4×Q811yescharacteristic
459C23×C4#12011yescharacteristic
460C23×C4#12011yescharacteristic
461C23×C4#12011yescharacteristic
462C23×C4#12011yescharacteristic
463C23×C4#12011yescharacteristic
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×C4#12311yescharacteristic
478C23×C4#12311yescharacteristic
479C23×C4#12311yescharacteristic
480C23×C4#12311yescharacteristic
481C23×C4#12311yescharacteristic
482C23×C4#12411yescharacteristic
483C23×C4#12411yescharacteristic
484C23×C4#12511yescharacteristic
485C23×C4#12511yescharacteristic
486C23×C4#12511yescharacteristic
487C23×C4#12611yescharacteristic
488C23×C4#12611yescharacteristic
489C23×C4#12711yescharacteristic
490C23×C4C4⋊Q811yescharacteristic
491C23×C4C4⋊Q811yescharacteristic
492C2×M16—28no—
493C2×M16—28no—
494C2×M16—28no—
495C2×M16—24no—
496C2×M16—24no—
497C2×M16—24no—
498C2×M16—48no—
499C2×M16—48no—
500C2×M16—48no—
501C2×M16—44no—
502C2×M16—44no—
503C2×M16—44no—
504C2×M16—42no—
505C2×M16—42no—
506C2×M16—42no—
507C2×M16—42no—
508C2×M16—42no—
509C2×M16—42no—
510C2×M16—42no—
511C2×M16—48no—
512C2×M16—82no—
513C2×M16—82no—
514C2×M16—82no—
515C2×M16—82no—
516C22×C8—24no—
517C22×C8—24no—
518C22×C8—24no—
519C22×C8—24no—
520C22×C8—48no—
521C22×C8—42no—
522C22×C8—42no—
523#117—48no—
524#117—48no—
525#117—48no—
526#117—84no—
527#117—82no—
528#117—82no—
529#117—82no—
530#117—82no—
531#117—84no—
532#117—84no—
533#117—82no—
534#117—82no—
535C2×C4⋊C4—24no—
536C2×C4⋊C4—24no—
537C2×C4⋊C4—42no—
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×C22⋊C4—24no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C42—24no—
554C2×C42—24no—
555C2×C42—24no—
556C2×C42—24no—
557C2×C42—42no—
558C2×C42—42no—
559C2×C42—42no—
560C2×C42—42no—
561C2×C42—42no—
562C2×C42C2×C4211yescharacteristic
563C2×C42C2×C22⋊C411yescharacteristic
564C2×C42C2×C22⋊C411yescharacteristic
565C2×C42C2×C22⋊C411yescharacteristic
566C2×C42C2×C22⋊C411yescharacteristic
567C2×C42C2×C4⋊C411yescharacteristic
568C2×C42C2×C4⋊C411yescharacteristic
569C2×C42C2×C4⋊C411yescharacteristic
570C2×C42C2×C4⋊C411yescharacteristic
571C2×C42C2×C4⋊C411yescharacteristic
572C2×C42C2×C4⋊C411yescharacteristic
573C2×C42#11711yescharacteristic
574C2×C42#11711yescharacteristic
575C2×C42#11711yescharacteristic
576C2×C42#11711yescharacteristic
577C2×C42#11711yescharacteristic
578C2×C42C4×D411yescharacteristic
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×Q811yescharacteristic
590C2×C42C4×Q811yescharacteristic
591C2×C42C4×Q811yescharacteristic
592C2×C42C4×Q811yescharacteristic
593C2×C42C4×Q811yescharacteristic
594C2×C42C4×Q811yescharacteristic
595C2×C42C4×Q811yescharacteristic
596C2×C42#12011yescharacteristic
597C2×C42#12011yescharacteristic
598C2×C42#12011yescharacteristic
599C2×C42#12111yescharacteristic
600C2×C42#12111yescharacteristic
601C2×C42#12111yescharacteristic
602C2×C42#12111yescharacteristic
603C2×C42#12111yescharacteristic
604C2×C42#12111yescharacteristic
605C2×C42#12111yescharacteristic
606C2×C42#12111yescharacteristic
607C2×C42#12111yescharacteristic
608C2×C42#12111yescharacteristic
609C2×C42#12111yescharacteristic
610C2×C42#12111yescharacteristic
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×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×C42C22⋊Q811yescharacteristic
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#12311yescharacteristic
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#12611yescharacteristic
660C2×C42#12611yescharacteristic
661C2×C42#12611yescharacteristic
662C2×C42#12611yescharacteristic
663C2×C42#12611yescharacteristic
664C2×C42#12611yescharacteristic
665C2×C42#12711yescharacteristic
666C2×C42C4⋊Q811yescharacteristic
667C2×C42C4⋊Q811yescharacteristic
668C2×C42C4⋊Q811yescharacteristic
669C2×C42C4⋊Q811yescharacteristic
670C2×C42C4⋊Q811yescharacteristic
671C2×C42C4⋊Q811yescharacteristic
672C2×C42C4⋊Q811yescharacteristic
673C2×C42C4⋊Q811yescharacteristic
674#107—88no—
675#106—88no—
676C4⋊C8—24no—
677C4⋊C8—24no—
678C4⋊C8—24no—
679C4⋊C8—24no—
680C4⋊C8—24no—
681C4⋊C8—42no—
682C4⋊C8—42no—
683C4⋊C8—42no—
684C4⋊C8—42no—
685C4⋊C8—42no—
686C4⋊C8—42no—
687C4⋊C8—42no—
688C22⋊C8—24no—
689C22⋊C8—24no—
690C22⋊C8—24no—
691C22⋊C8—24no—
692C22⋊C8—24no—
693C22⋊C8—42no—
694C22⋊C8—42no—
695C22⋊C8—42no—
696C22⋊C8—42no—
697C22⋊C8—42no—
698C22⋊C8—42no—
699C22⋊C8—42no—
700#97—24no—
701#97—24no—
702#97—24no—
703#97—42no—
704#97—42no—
705#97—42no—
706#97—42no—
707#97—42no—
708#97—42no—
709#97—42no—
710C4×C8—24no—
711C4×C8—24no—
712C4×C8—24no—
713C4×C8—42no—
714C4×C8—42no—
715C4×C8—42no—
716C4×C8—42no—
717C4×C8—42no—
718C4×C8—42no—
719C4×C8#9518yes—
720#95—24no—
721#95—24no—
722#95—42no—
723#95—42no—
724#95—42no—
725#95—42no—
726#95—42no—
727#95—42no—
728#95—42no—
729#95—42no—
730#95—42no—
731#95—42no—
732#95—42no—
733#95—42no—
734#95—42no—
735#95—42no—
736#95—42no—
737#95—42no—
738C24—42no—
739C24—81no—
740C24—81no—
741C24#38611yescharacteristic
742C24#38811yescharacteristic
743C24#38911yescharacteristic
744C24#39211yescharacteristic
745C24#39411yescharacteristic
746C24#39611yescharacteristic
747C24#39811yescharacteristic
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—42no—
752C22×C4—41no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—41no—
774C22×C4—41no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—41no—
779C22×C4—41no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—81no—
787C22×C4—81no—
788C22×C4—81no—
789C22×C4—81no—
790C22×C4—81no—
791C22×C4—81no—
792C22×C4—81no—
793C22×C4—81no—
794C22×C4—81no—
795C22×C4—81no—
796C22×C4—81no—
797C22×C4—81no—
798C22×C4—81no—
799C22×C4—81no—
800C22×C4C4×C22⋊C411yescharacteristic
801C22×C4C4×C4⋊C411yescharacteristic
802C22×C4C4×C4⋊C411yescharacteristic
803C22×C4#37911yescharacteristic
804C22×C4#38011yescharacteristic
805C22×C4#38011yescharacteristic
806C22×C4#38011yescharacteristic
807C22×C4#38211yescharacteristic
808C22×C4#38411yescharacteristic
809C22×C4#38511yescharacteristic
810C22×C4#38511yescharacteristic
811C22×C4#38511yescharacteristic
812C22×C4#38511yescharacteristic
813C22×C4#38511yescharacteristic
814C22×C4#38511yescharacteristic
815C22×C4#38511yescharacteristic
816C22×C4#38511yescharacteristic
817C22×C4#38611yescharacteristic
818C22×C4#38611yescharacteristic
819C22×C4#38611yescharacteristic
820C22×C4#38611yescharacteristic
821C22×C4#38611yescharacteristic
822C22×C4#38711yescharacteristic
823C22×C4#38711yescharacteristic
824C22×C4#38711yescharacteristic
825C22×C4#38711yescharacteristic
826C22×C4#38711yescharacteristic
827C22×C4#38711yescharacteristic
828C22×C4#38711yescharacteristic
829C22×C4#38711yescharacteristic
830C22×C4#38711yescharacteristic
831C22×C4#38711yescharacteristic
832C22×C4#38811yescharacteristic
833C22×C4#38811yescharacteristic
834C22×C4#38811yescharacteristic
835C22×C4#38911yescharacteristic
836C22×C4#38911yescharacteristic
837C22×C4#38911yescharacteristic
838C22×C4#38911yescharacteristic
839C22×C4#38911yescharacteristic
840C22×C4#38911yescharacteristic
841C22×C4#38911yescharacteristic
842C22×C4#39011yescharacteristic
843C22×C4#39011yescharacteristic
844C22×C4#39011yescharacteristic
845C22×C4#39111yescharacteristic
846C22×C4#39111yescharacteristic
847C22×C4#39111yescharacteristic
848C22×C4#39211yescharacteristic
849C22×C4#39211yescharacteristic
850C22×C4#39211yescharacteristic
851C22×C4#39311yescharacteristic
852C22×C4#39311yescharacteristic
853C22×C4#39411yescharacteristic
854C22×C4#39411yescharacteristic
855C22×C4#39411yescharacteristic
856C22×C4#39411yescharacteristic
857C22×C4#39411yescharacteristic
858C22×C4#39411yescharacteristic
859C22×C4#39511yescharacteristic
860C22×C4#39511yescharacteristic
861C22×C4#39511yescharacteristic
862C22×C4#39511yescharacteristic
863C22×C4#39511yescharacteristic
864C22×C4#39611yescharacteristic
865C22×C4#39611yescharacteristic
866C22×C4#39611yescharacteristic
867C22×C4#39711yescharacteristic
868C22×C4#39711yescharacteristic
869C22×C4#39811yescharacteristic
870C22×C4#39811yescharacteristic
871C22×C4#39811yescharacteristic
872C22×C4#39811yescharacteristic
873C22×C4#39811yescharacteristic
874C22×C4#39811yescharacteristic
875C22×C4#39811yescharacteristic
876C22×C4#39811yescharacteristic
877C22×C4#39911yescharacteristic
878C22×C4#39911yescharacteristic
879C22×C4#40011yescharacteristic
880C22×C4#40011yescharacteristic
881C22×C4#40011yescharacteristic
882C22×C4#40011yescharacteristic
883C22×C4#40011yescharacteristic
884M16—48no—
885M16—48no—
886M16—48no—
887M16—48no—
888M16—48no—
889M16—84no—
890M16—84no—
891M16—84no—
892M16—84no—
893M16—84no—
894C2×C8—28no—
895C2×C8—28no—
896C2×C8—28no—
897C2×C8—28no—
898C2×C8—44no—
899C2×C8—44no—
900C2×C8—44no—
901C2×C8—44no—
902C2×C8—44no—
903C2×C8—44no—
904C2×C8—44no—
905C2×C8—44no—
906C2×C8—84no—
907C2×C8—82no—
908C2×C8—82no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—84no—
914C4⋊C4—84no—
915C4⋊C4—82no—
916C4⋊C4—82no—
917C4⋊C4—84no—
918C4⋊C4—84no—
919C4⋊C4—84no—
920C4⋊C4—84no—
921C22⋊C4—48no—
922C22⋊C4—84no—
923C22⋊C4—84no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C42—48no—
931C42—48no—
932C42—48no—
933C42—84no—
934C42—84no—
935C42—84no—
936C42—84no—
937C42—84no—
938C42—84no—
939C42C2×#9511yescharacteristic
940C42C4×C22⋊C411yescharacteristic
941C42C4×C4⋊C411yescharacteristic
942C42C4×C4⋊C411yescharacteristic
943C42#38011yescharacteristic
944C42#38011yescharacteristic
945C42#38011yescharacteristic
946C42#38111yescharacteristic
947C42#38211yescharacteristic
948C42#38411yescharacteristic
949C42#38511yescharacteristic
950C42#38511yescharacteristic
951C42#38511yescharacteristic
952C42#38511yescharacteristic
953C42#38611yescharacteristic
954C42#38611yescharacteristic
955C42#38711yescharacteristic
956C42#38711yescharacteristic
957C42#38711yescharacteristic
958C42#38711yescharacteristic
959C42#38711yescharacteristic
960C42#38711yescharacteristic
961C42#38811yescharacteristic
962C42#38811yescharacteristic
963C42#38811yescharacteristic
964C42#38811yescharacteristic
965C42#38911yescharacteristic
966C42#38911yescharacteristic
967C42#38911yescharacteristic
968C42#38911yescharacteristic
969C42#38911yescharacteristic
970C42#38911yescharacteristic
971C42#38911yescharacteristic
972C42#38911yescharacteristic
973C42#39011yescharacteristic
974C42#39111yescharacteristic
975C42#39111yescharacteristic
976C42#39111yescharacteristic
977C42#39111yescharacteristic
978C42#39111yescharacteristic
979C42#39311yescharacteristic
980C42#39311yescharacteristic
981C42#39411yescharacteristic
982C42#39511yescharacteristic
983C42#39511yescharacteristic
984C42#39511yescharacteristic
985C42#39611yescharacteristic
986C42#39611yescharacteristic
987C42#39611yescharacteristic
988C42#39611yescharacteristic
989C42#39711yescharacteristic
990C42#39711yescharacteristic
991C42#39811yescharacteristic
992C42#39811yescharacteristic
993C42#39811yescharacteristic
994C42#39811yescharacteristic
995C42#39811yescharacteristic
996C42#39811yescharacteristic
997C42#39811yescharacteristic
998C42#39911yescharacteristic
999C42#39911yescharacteristic
1000C42#40011yescharacteristic
1001C42#40011yescharacteristic
1002C42#40011yescharacteristic
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—88no—
1025C23#143611yescharacteristic
1026C23#143811yescharacteristic
1027C23#143911yescharacteristic
1028C23#144111yescharacteristic
1029C23#144111yescharacteristic
1030C23#144211yescharacteristic
1031C23#144411yescharacteristic
1032C2×C4—22no—
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—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
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—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—84no—
1123C2×C4—84no—
1124C2×C4—84no—
1125C2×C4—84no—
1126C2×C4—84no—
1127C2×C4—84no—
1128C2×C4—84no—
1129C2×C4—84no—
1130C2×C4—84no—
1131C2×C4C22⋊#9511yescharacteristic
1132C2×C4C4⋊#9511yescharacteristic
1133C2×C4C4⋊#9511yescharacteristic
1134C2×C4#143611yescharacteristic
1135C2×C4#143611yescharacteristic
1136C2×C4#143611yescharacteristic
1137C2×C4#143911yescharacteristic
1138C2×C4#143911yescharacteristic
1139C2×C4#143911yescharacteristic
1140C2×C4#144111yescharacteristic
1141C2×C4#144111yescharacteristic
1142C2×C4#144111yescharacteristic
1143C2×C4#144111yescharacteristic
1144C2×C4#144111yescharacteristic
1145C2×C4#144111yescharacteristic
1146C2×C4#144211yescharacteristic
1147C2×C4#144211yescharacteristic
1148C2×C4#144211yescharacteristic
1149C2×C4#144411yescharacteristic
1150C2×C4#144411yescharacteristic
1151C2×C4#144411yescharacteristic
1152C2×C4#144511yescharacteristic
1153C2×C4#144511yescharacteristic
1154C2×C4#144611yescharacteristic
1155C2×C4#201014yes—
1156C8—48no—
1157C8—48no—
1158C8—84no—
1159C8—84no—
1160C22—21no—
1161C22—21no—
1162C22—21no—
1163C22—21no—
1164C22—21no—
1165C22—21no—
1166C22—21no—
1167C22—21no—
1168C22—21no—
1169C22—21no—
1170C22—21no—
1171C22—21no—
1172C22—21no—
1173C22—21no—
1174C22—21no—
1175C22—21no—
1176C22—21no—
1177C22—21no—
1178C22—21no—
1179C22—21no—
1180C22—44no—
1181C22—82no—
1182C22—82no—
1183C22—82no—
1184C22—82no—
1185C22—82no—
1186C22—82no—
1187C22#755711yescharacteristic
1188C22#1104112yes—
1189C4—21no—
1190C4—21no—
1191C4—21no—
1192C4—21no—
1193C4—21no—
1194C4—21no—
1195C4—21no—
1196C4—21no—
1197C4—21no—
1198C4—21no—
1199C4—21no—
1200C4—21no—
1201C4—21no—
1202C4—21no—
1203C4—21no—
1204C4—21no—
1205C4—21no—
1206C4—21no—
1207C4—21no—
1208C4—21no—
1209C4—164no—
1210C4—164no—
1211C4—164no—
1212C4#1110012yes—
1213C4#1124512yes—
1214C4#1133512yes—
1215C4#1138911yescharacteristic
1216C4#1138911yescharacteristic
1217C2—22no—
1218C2—41no—
1219C2—41no—
1220C2—41no—
1221C2—41no—
1222C2—41no—
1223C2—41no—
1224C2#12390111yescharacteristic
1225C2#12390511yescharacteristic
1226C2#12391111yescharacteristic
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
21. #20825C4semidirect
35. #7861C4semidirect
39. #7856C4semidirect

Maximal subgroups

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

subgroupindex
#63750572
#3538042
#3537762
#1817892
#1811242
#1808802
#1808712