Finite Group Databasebeta

← #35312272

Subgroups — #35312272

Order 21248.

1186 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C2×D83)⋊C8C211yesmaximal, characteristic
2C2×#19127558C211yesmaximal, characteristic
3C2×#19127558C211yesmaximal, characteristic
4C2×#19127464C211yesmaximal, characteristic, complemented
5C2×#19127463C211yesmaximal, characteristic, complemented
6C2×#19127463C211yesmaximal, characteristic, complemented
7C2×#340×C83C211yesmaximal, characteristic, complemented
8C23×C4×D83C2211yescharacteristic
9C23×C83⋊C8C2211yescharacteristic
10C22×C4⋊Dic83C2211yescharacteristic
11C22×C4⋊Dic83C2211yescharacteristic
12C22×(C2×D83)⋊C4—21no—
13C22×(C2×D83)⋊C4—21no—
14C2×(C2×D83)⋊C8—22no—
15C2×(C2×D83)⋊C8—22no—
16C2×(C2×D83)⋊C8—22no—
17#19127558—22no—
18#19127558—22no—
19#19127558—22no—
20#19127558C414yescomplemented
21C2×C83⋊#95—21no—
22C2×C83⋊#95—21no—
23#19127464—22no—
24#19127463—22no—
25#19127463—22no—
26C23×C8×C83C2211yescharacteristic
27C22×C4⋊C4×C83C2211yescharacteristic
28C22×C4⋊C4×C83C2211yescharacteristic
29#340×C83—22no—
30C24×D83D411yescharacteristic
31C23×Dic83—21no—
32C23×Dic83—21no—
33C23×Dic83D411yescharacteristic
34C22×C4×D83—21no—
35C22×C4×D83—21no—
36C22×C4×D83—21no—
37C22×C4×D83—21no—
38C22×C4×D83—21no—
39C22×C4×D83—21no—
40C22×C4×D83—21no—
41C22×C4×D83—21no—
42C22×C4×D83—21no—
43C22×C4×D83—21no—
44C22×C4×D83—21no—
45C22×C4×D83—21no—
46C22×C4×D83C2×C412yes—
47C22×C4×D83D412yes—
48C22×C83⋊C8—21no—
49C22×C83⋊C8—21no—
50C22×C83⋊C8—21no—
51C22×C83⋊C8—21no—
52C22×C83⋊C8—21no—
53C22×C83⋊C8—21no—
54C22×C83⋊C8D412yes—
55C2×C4⋊Dic83—21no—
56C2×C4⋊Dic83—21no—
57C2×C4⋊Dic83—21no—
58C2×C4⋊Dic83—21no—
59C2×C4⋊Dic83—21no—
60C2×C4⋊Dic83—21no—
61C2×C4⋊Dic83—21no—
62C2×C4⋊Dic83—21no—
63C2×C4⋊Dic83—21no—
64C2×C4⋊Dic83—21no—
65C2×C4⋊Dic83C2×C412yes—
66C2×C4⋊Dic83D412yes—
67C2×(C2×D83)⋊C4—24no—
68C2×(C2×D83)⋊C4—24no—
69C2×(C2×D83)⋊C4—42no—
70C2×(C2×D83)⋊C4—42no—
71C2×(C2×D83)⋊C4—42no—
72C2×(C2×D83)⋊C4—42no—
73(C2×D83)⋊C8—28no—
74C83⋊#95—24no—
75C83⋊#95—24no—
76C23×C4×C83—21no—
77C23×C4×C83—21no—
78C23×C4×C83C2311yescharacteristic
79C22×C8×C83—21no—
80C22×C8×C83—21no—
81C22×C8×C83—21no—
82C22×C8×C83—21no—
83C22×C8×C83—21no—
84C22×C8×C83—21no—
85C22×C8×C83D412yes—
86C2×C4⋊C4×C83—21no—
87C2×C4⋊C4×C83—21no—
88C2×C4⋊C4×C83—21no—
89C2×C4⋊C4×C83—21no—
90C2×C4⋊C4×C83—21no—
91C2×C4⋊C4×C83—21no—
92C2×C4⋊C4×C83—21no—
93C2×C4⋊C4×C83—21no—
94C2×C4⋊C4×C83—21no—
95C2×C4⋊C4×C83—21no—
96C2×C4⋊C4×C83C2×C412yes—
97C2×C4⋊C4×C83D412yes—
98C23×D83—21no—
99C23×D83—21no—
100C23×D83—21no—
101C23×D83—21no—
102C23×D83—21no—
103C23×D83—21no—
104C23×D83—21no—
105C23×D83—21no—
106C23×D83—21no—
107C23×D83—21no—
108C23×D83—21no—
109C23×D83—21no—
110C23×D83C22⋊C412yes—
111C23×D83D812yes—
112C23×D83SD1612yes—
113C22×Dic83—21no—
114C22×Dic83—21no—
115C22×Dic83—21no—
116C22×Dic83—21no—
117C22×Dic83—21no—
118C22×Dic83—21no—
119C22×Dic83—22no—
120C22×Dic83—22no—
121C22×Dic83—41no—
122C22×Dic83—41no—
123C22×Dic83—41no—
124C22×Dic83—41no—
125C22×Dic83—41no—
126C22×Dic83—41no—
127C22×Dic83—41no—
128C22×Dic83—41no—
129C22×Dic83—41no—
130C22×Dic83—41no—
131C22×Dic83—41no—
132C22×Dic83—41no—
133C22×Dic83C22⋊C412yes—
134C2×C4×D83—22no—
135C2×C4×D83—22no—
136C2×C4×D83—22no—
137C2×C4×D83—22no—
138C2×C4×D83—22no—
139C2×C4×D83—22no—
140C2×C4×D83—22no—
141C2×C4×D83—22no—
142C2×C4×D83—22no—
143C2×C4×D83—22no—
144C2×C4×D83—22no—
145C2×C4×D83—22no—
146C2×C4×D83—41no—
147C2×C4×D83—41no—
148C2×C4×D83—41no—
149C2×C4×D83—41no—
150C2×C4×D83—41no—
151C2×C4×D83—41no—
152C2×C4×D83—41no—
153C2×C4×D83—41no—
154C2×C4×D83—41no—
155C2×C4×D83—41no—
156C2×C4×D83—41no—
157C2×C4×D83—41no—
158C2×C4×D83—41no—
159C2×C4×D83—41no—
160C2×C4×D83—41no—
161C2×C4×D83—41no—
162C2×C83⋊C8—22no—
163C2×C83⋊C8—22no—
164C2×C83⋊C8—22no—
165C2×C83⋊C8—41no—
166C2×C83⋊C8—41no—
167C2×C83⋊C8—41no—
168C2×C83⋊C8—41no—
169C4⋊Dic83—22no—
170C4⋊Dic83—22no—
171C4⋊Dic83—22no—
172C4⋊Dic83—22no—
173C4⋊Dic83—41no—
174C4⋊Dic83—41no—
175C4⋊Dic83—41no—
176C4⋊Dic83—41no—
177(C2×D83)⋊C4—48no—
178(C2×D83)⋊C4—48no—
179C24×C83C2×D411yescharacteristic
180C22×C4×C83—22no—
181C22×C4×C83—22no—
182C22×C4×C83—41no—
183C22×C4×C83—41no—
184C22×C4×C83—41no—
185C22×C4×C83—41no—
186C22×C4×C83—41no—
187C22×C4×C83—41no—
188C22×C4×C83—41no—
189C22×C4×C83—41no—
190C22×C4×C83—41no—
191C22×C4×C83—41no—
192C22×C4×C83—41no—
193C22×C4×C83—41no—
194C22×C4×C83C22×C411yescharacteristic
195C22×C4×C83C2×D411yescharacteristic
196C22×C4×C83C2×D411yescharacteristic
197C22×C4×C83C2×D411yescharacteristic
198C22×C4×C83C2×D411yescharacteristic
199C22×C4×C83C2×D411yescharacteristic
200C22×C4×C83#4111yescharacteristic
201C22×C4×C83#4111yescharacteristic
202C22×C4×C83#4111yescharacteristic
203C22×C4×C83#4111yescharacteristic
204C22×C4×C83#4111yescharacteristic
205C22×C4×C83#4111yescharacteristic
206C22×C4×C83#4111yescharacteristic
207C22×C4×C83#4111yescharacteristic
208C2×C8×C83—22no—
209C2×C8×C83—22no—
210C2×C8×C83—22no—
211C2×C8×C83—41no—
212C2×C8×C83—41no—
213C2×C8×C83—41no—
214C2×C8×C83—41no—
215C4⋊C4×C83—22no—
216C4⋊C4×C83—22no—
217C4⋊C4×C83—22no—
218C4⋊C4×C83—22no—
219C4⋊C4×C83—41no—
220C4⋊C4×C83—41no—
221C4⋊C4×C83—41no—
222C4⋊C4×C83—41no—
223C23×C83C2×C22⋊C411yescharacteristic
224C23×C83#12011yescharacteristic
225C23×C83#12111yescharacteristic
226C23×C83#12111yescharacteristic
227C23×C83#12311yescharacteristic
228C23×C83#12311yescharacteristic
229C23×C83#12311yescharacteristic
230C23×C83C2×D811yescharacteristic
231C23×C83C2×SD1611yescharacteristic
232C23×C83#13511yescharacteristic
233C23×C83#13511yescharacteristic
234C23×C83AGL(1,ℤ/8)11yescharacteristic
235C23×C83#13711yescharacteristic
236C23×C83#13711yescharacteristic
237C23×C83#13711yescharacteristic
238C22×D83—22no—
239C22×D83—22no—
240C22×D83—22no—
241C22×D83—22no—
242C22×D83—22no—
243C22×D83—22no—
244C22×D83—22no—
245C22×D83—22no—
246C22×D83—22no—
247C22×D83—22no—
248C22×D83—22no—
249C22×D83—22no—
250C22×D83—22no—
251C22×D83—22no—
252C22×D83—22no—
253C22×D83—22no—
254C22×D83—22no—
255C22×D83—22no—
256C22×D83—41no—
257C22×D83—41no—
258C22×D83—41no—
259C22×D83—41no—
260C22×D83—41no—
261C22×D83—41no—
262C22×D83—41no—
263C22×D83—41no—
264C22×D83—41no—
265C22×D83—41no—
266C22×D83—41no—
267C22×D83—41no—
268C22×D83—41no—
269C22×D83—41no—
270C22×D83—41no—
271C22×D83—41no—
272C22×D83#10214yes—
273C2×C4×C83—42no—
274C2×C4×C83—42no—
275C2×C4×C83—42no—
276C2×C4×C83—42no—
277C2×C4×C83—42no—
278C2×C4×C83—42no—
279C2×C4×C83—81no—
280C2×C4×C83—81no—
281C2×C4×C83—81no—
282C2×C4×C83—81no—
283C2×C4×C83—81no—
284C2×C4×C83—81no—
285C2×C4×C83—81no—
286C2×C4×C83—81no—
287C2×C4×C83#11711yescharacteristic
288C2×C4×C83#11711yescharacteristic
289C2×C4×C83C4×D411yescharacteristic
290C2×C4×C83C4×D411yescharacteristic
291C2×C4×C83C4×D411yescharacteristic
292C2×C4×C83C4×D411yescharacteristic
293C2×C4×C83#12011yescharacteristic
294C2×C4×C83#12111yescharacteristic
295C2×C4×C83#12111yescharacteristic
296C2×C4×C83#12111yescharacteristic
297C2×C4×C83#12111yescharacteristic
298C2×C4×C83#12111yescharacteristic
299C2×C4×C83#12111yescharacteristic
300C2×C4×C83#12311yescharacteristic
301C2×C4×C83#12311yescharacteristic
302C2×C4×C83#12311yescharacteristic
303C2×C4×C83#12311yescharacteristic
304C2×C4×C83#12311yescharacteristic
305C2×C4×C83#12311yescharacteristic
306C2×C4×C83#12311yescharacteristic
307C2×C4×C83#12411yescharacteristic
308C2×C4×C83#12411yescharacteristic
309C2×C4×C83#12411yescharacteristic
310C2×C4×C83#12411yescharacteristic
311C2×C4×C83#12611yescharacteristic
312C2×C4×C83#12611yescharacteristic
313C2×C4×C83#12611yescharacteristic
314C2×C4×C83#12611yescharacteristic
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—22no—
318C2×Dic83—41no—
319C2×Dic83—41no—
320C2×Dic83—41no—
321C2×Dic83—41no—
322C2×Dic83—42no—
323C2×Dic83—42no—
324C2×Dic83—42no—
325C2×Dic83—42no—
326C2×Dic83—42no—
327C2×Dic83—42no—
328C2×Dic83—81no—
329C2×Dic83—81no—
330C2×Dic83—81no—
331C2×Dic83—81no—
332C2×Dic83—81no—
333C2×Dic83—81no—
334C2×Dic83—81no—
335C2×Dic83—81no—
336C4×D83—42no—
337C4×D83—42no—
338C4×D83—42no—
339C4×D83—42no—
340C4×D83—42no—
341C4×D83—42no—
342C4×D83—42no—
343C4×D83—42no—
344C8×C83—42no—
345C83⋊C8—42no—
346C22×C83#38111yescharacteristic
347C22×C83#38611yescharacteristic
348C22×C83#38611yescharacteristic
349C22×C83#39411yescharacteristic
350C22×C83#39411yescharacteristic
351C22×C83#39711yescharacteristic
352C22×C83#39711yescharacteristic
353C22×C83C2×#10211yescharacteristic
354C22×C83#41611yescharacteristic
355C22×C83#41711yescharacteristic
356C22×C83#41911yescharacteristic
357C22×C83#44711yescharacteristic
358C22×C83#44811yescharacteristic
359C22×C83#45211yescharacteristic
360C22×C83#45211yescharacteristic
361C22×C83#46511yescharacteristic
362C22×C83#46511yescharacteristic
363C22×C83#46611yescharacteristic
364C22×C83#46611yescharacteristic
365C22×C83#46811yescharacteristic
366C22×C83#46811yescharacteristic
367C22×C83#47011yescharacteristic
368C22×C83#47011yescharacteristic
369C22×C83#48011yescharacteristic
370C22×C83#48011yescharacteristic
371C22×C83#48011yescharacteristic
372C22×C83#48111yescharacteristic
373C22×C83#48211yescharacteristic
374C22×C83#48211yescharacteristic
375C22×C83#48311yescharacteristic
376C22×C83#48311yescharacteristic
377C22×C83#48511yescharacteristic
378C22×C83#48511yescharacteristic
379C22×C83#48511yescharacteristic
380C22×C83#48511yescharacteristic
381C2×D83—24no—
382C2×D83—24no—
383C2×D83—24no—
384C2×D83—42no—
385C2×D83—42no—
386C2×D83—42no—
387C2×D83—42no—
388C2×D83—42no—
389C2×D83—42no—
390C2×D83—42no—
391C2×D83—42no—
392C2×D83—42no—
393C2×D83—42no—
394C2×D83—42no—
395C2×D83—42no—
396C4×C83—82no—
397C4×C83—82no—
398C4×C83#38811yescharacteristic
399C4×C83#38811yescharacteristic
400C4×C83#38811yescharacteristic
401C4×C83#38811yescharacteristic
402C4×C83#39411yescharacteristic
403C4×C83#39411yescharacteristic
404C4×C83#39711yescharacteristic
405C4×C83#39711yescharacteristic
406Dic83—42no—
407Dic83—82no—
408Dic83—82no—
409#11199—831nomaximal, Sylow
410C2×C83#144011yescharacteristic
411C2×C83#182311yescharacteristic
412C2×C83#182511yescharacteristic
413C2×C83#187311yescharacteristic
414C2×C83#187411yescharacteristic
415C2×C83#189311yescharacteristic
416C2×C83#189411yescharacteristic
417C2×C83#203311yescharacteristic
418C2×C83#203311yescharacteristic
419C2×C83#203511yescharacteristic
420C2×C83#203511yescharacteristic
421C2×C83#207511yescharacteristic
422C2×C83#207511yescharacteristic
423C2×C83#207711yescharacteristic
424C2×C83#207711yescharacteristic
425D83—44no—
426C22×C22⋊C8—831no—
427C2×#380—831no—
428C2×#380—831no—
429C2×#340—831no—
430C2×#340—831no—
431C2×#340—831no—
432C2×#340D8311yescharacteristic, complemented
433C83#1119911yescharacteristic, complemented, Sylow
434C24×C4—831no—
435C23×C8—831no—
436C23×C8C2×D8311yescharacteristic
437C22×C4⋊C4—831no—
438C22×C4⋊C4—831no—
439C22×C4⋊C4C2×D8311yescharacteristic
440C22×C4⋊C4C2×D8311yescharacteristic
441C22×C22⋊C4—1661no—
442C22×C22⋊C4—1661no—
443C2×C22⋊C8—1662no—
444C2×C22⋊C8—1662no—
445C2×C22⋊C8—1662no—
446#380—834no—
447#380—1662no—
448#380—1662no—
449#380—1662no—
450C2×#95—1661no—
451C2×#95—1661no—
452#340—22no—
453#340—1662no—
454#340—1662no—
455#340—1662no—
456C25—831no—
457C23×C4—21no—
458C23×C4—21no—
459C23×C4—831no—
460C23×C4—832no—
461C23×C4—832no—
462C23×C4—1661no—
463C23×C4—1661no—
464C23×C4—1661no—
465C23×C4—1661no—
466C23×C4—1661no—
467C23×C4—1661no—
468C23×C4—1661no—
469C23×C4—1661no—
470C23×C4—1661no—
471C23×C4—1661no—
472C23×C4—1661no—
473C23×C4—1661no—
474C23×C4—1661no—
475C23×C4—1661no—
476C23×C4C22×D8311yescharacteristic
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—832no—
484C22×C8—1661no—
485C22×C8—1661no—
486C22×C8—1661no—
487C22×C8—1661no—
488C22×C8—1661no—
489C22×C8—1661no—
490C22×C8D33212yes—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—832no—
502C2×C4⋊C4—832no—
503C2×C4⋊C4—1661no—
504C2×C4⋊C4—1661no—
505C2×C4⋊C4—1661no—
506C2×C4⋊C4—1661no—
507C2×C4⋊C4—1661no—
508C2×C4⋊C4—1661no—
509C2×C4⋊C4—1661no—
510C2×C4⋊C4—1661no—
511C2×C4⋊C4—1661no—
512C2×C4⋊C4—1661no—
513C2×C4⋊C4C4×D8312yes—
514C2×C4⋊C4C22⋊D8312yes—
515C2×C22⋊C4—3322no—
516C2×C22⋊C4—3322no—
517C2×C22⋊C4—3322no—
518C2×C22⋊C4—3322no—
519C2×C22⋊C4—1664no—
520C2×C22⋊C4—1664no—
521C22⋊C8—1668no—
522#95—1664no—
523#95—1664no—
524C24—832no—
525C24—832no—
526C24—832no—
527C24—1661no—
528C24—1661no—
529C24—1661no—
530C24—1661no—
531C24—1661no—
532C24—1661no—
533C24—1661no—
534C24—1661no—
535C24—1661no—
536C24—1661no—
537C24—1661no—
538C24—1661no—
539C24D4×D8311yescharacteristic
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—3321no—
555C22×C4—3321no—
556C22×C4—3321no—
557C22×C4—3321no—
558C22×C4—3321no—
559C22×C4—3321no—
560C22×C4—3321no—
561C22×C4—3321no—
562C22×C4—3321no—
563C22×C4—3321no—
564C22×C4—3321no—
565C22×C4—3321no—
566C22×C4—3321no—
567C22×C4—3321no—
568C22×C4—3321no—
569C22×C4—3321no—
570C22×C4—3321no—
571C22×C4—3321no—
572C22×C4—3321no—
573C22×C4—3321no—
574C22×C4—3321no—
575C22×C4—3321no—
576C22×C4—3321no—
577C22×C4—3321no—
578C22×C4—3321no—
579C22×C4—3321no—
580C22×C4—3321no—
581C22×C4—3321no—
582C22×C4—832no—
583C22×C4—1662no—
584C22×C4—1662no—
585C22×C4—1661no—
586C22×C4—1661no—
587C22×C4—1661no—
588C22×C4—1661no—
589C22×C4—1661no—
590C22×C4—1661no—
591C22×C4—1662no—
592C22×C4—1662no—
593C22×C4—1662no—
594C22×C4—1662no—
595C22×C4—1662no—
596C22×C4—1662no—
597C22×C4—1662no—
598C22×C4—1662no—
599C22×C4—1662no—
600C22×C4—1662no—
601C22×C4—1662no—
602C22×C4—1662no—
603C22×C4C2×C4×D8311yescharacteristic
604C22×C4D4×D8311yescharacteristic
605C22×C4D4×D8311yescharacteristic
606C22×C4D4×D8311yescharacteristic
607C22×C4C2×C22⋊D8311yescharacteristic
608C22×C4C2×D33211yescharacteristic
609C22×C4#1305058911yescharacteristic
610C22×C4#1305058911yescharacteristic
611C22×C4#1305059011yescharacteristic
612C22×C4#1305059011yescharacteristic
613C22×C4#1305059011yescharacteristic
614C22×C4#1305059011yescharacteristic
615C22×C4#1305059111yescharacteristic
616C22×C4#1305059111yescharacteristic
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—3321no—
625C2×C8—3321no—
626C2×C8—3321no—
627C2×C8—3321no—
628C2×C8—1662no—
629C2×C8—1662no—
630C2×C8—1662no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—3321no—
640C4⋊C4—3321no—
641C4⋊C4—3321no—
642C4⋊C4—3321no—
643C4⋊C4—1662no—
644C4⋊C4—1662no—
645C4⋊C4—1662no—
646C4⋊C4—1662no—
647C22⋊C4—3328no—
648C22⋊C4—3328no—
649C23—3321no—
650C23—3321no—
651C23—3321no—
652C23—3321no—
653C23—3321no—
654C23—3321no—
655C23—3321no—
656C23—3321no—
657C23—3321no—
658C23—3321no—
659C23—3321no—
660C23—3321no—
661C23—3321no—
662C23—3321no—
663C23—3321no—
664C23—3321no—
665C23—834no—
666C23—1662no—
667C23—1662no—
668C23—1662no—
669C23—1662no—
670C23—1662no—
671C23—1662no—
672C23—1662no—
673C23—1662no—
674C23—1662no—
675C23—1662no—
676C23—1662no—
677C23—1662no—
678C23—1662no—
679C23—1662no—
680C23—1662no—
681C23—1662no—
682C23—1662no—
683C23—1662no—
684C23C22⋊C4×D8311yescharacteristic
685C23#1458176011yescharacteristic
686C23#1458176511yescharacteristic
687C23#1458176711yescharacteristic
688C23#1458177411yescharacteristic
689C23#1458177411yescharacteristic
690C23#1458177711yescharacteristic
691C23D8×D8311yescharacteristic
692C23SD16×D8311yescharacteristic
693C23#1458181311yescharacteristic
694C23#1458181511yescharacteristic
695C23#1458181611yescharacteristic
696C23#1458182111yescharacteristic
697C23#1458182111yescharacteristic
698C23#1458182411yescharacteristic
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—3321no—
714C2×C4—3321no—
715C2×C4—3321no—
716C2×C4—3321no—
717C2×C4—3322no—
718C2×C4—3322no—
719C2×C4—3322no—
720C2×C4—3322no—
721C2×C4—3322no—
722C2×C4—3322no—
723C2×C4—3322no—
724C2×C4—3322no—
725C2×C4—3322no—
726C2×C4—3322no—
727C2×C4—3322no—
728C2×C4—3322no—
729C2×C4—3322no—
730C2×C4—3322no—
731C2×C4—6641no—
732C2×C4—6641no—
733C2×C4—6641no—
734C2×C4—6641no—
735C2×C4—6641no—
736C2×C4—6641no—
737C2×C4—6641no—
738C2×C4—6641no—
739C2×C4—1662no—
740C2×C4—1662no—
741C2×C4—1662no—
742C2×C4#1458174911yescharacteristic
743C2×C4#1458175011yescharacteristic
744C2×C4(C22⋊D83)⋊C411yescharacteristic
745C2×C4C4×C22⋊D8311yescharacteristic
746C2×C4#1458175411yescharacteristic
747C2×C4C4×D33211yescharacteristic
748C2×C4#1458176211yescharacteristic
749C2×C4#1458176311yescharacteristic
750C2×C4#1458176411yescharacteristic
751C2×C4#1458176511yescharacteristic
752C2×C4#1458176511yescharacteristic
753C2×C4#1458176611yescharacteristic
754C2×C4#1458176711yescharacteristic
755C2×C4#1458177411yescharacteristic
756C2×C4#1458177511yescharacteristic
757C2×C4#1458177611yescharacteristic
758C2×C4#1458177711yescharacteristic
759C2×C4#1458177711yescharacteristic
760C2×C4#1458177711yescharacteristic
761C2×C4#1458177711yescharacteristic
762C2×C4#1458177811yescharacteristic
763C2×C4#1458177811yescharacteristic
764C2×C4#1458178011yescharacteristic
765C2×C4#1458178111yescharacteristic
766C2×C4#1458178611yescharacteristic
767C2×C4#1458178711yescharacteristic
768C2×C4#1458178711yescharacteristic
769C2×C4#1458178711yescharacteristic
770C8—42no—
771C8—3322no—
772C22—3322no—
773C22—3322no—
774C22—3322no—
775C22—3322no—
776C22—3322no—
777C22—3322no—
778C22—3322no—
779C22—3322no—
780C22—3322no—
781C22—3322no—
782C22—3322no—
783C22—3322no—
784C22—1664no—
785C22—1664no—
786C22—1664no—
787C22#1912756311yescharacteristic
788C22#1912757711yescharacteristic
789C22#1912757911yescharacteristic
790C22#1912761611yescharacteristic
791C22#1912761811yescharacteristic
792C22#1912762811yescharacteristic
793C22#1912763011yescharacteristic
794C22#102×D8311yescharacteristic
795C22#1912769611yescharacteristic
796C22#1912769911yescharacteristic
797C22#1912770811yescharacteristic
798C22#1912783311yescharacteristic
799C22#1912783811yescharacteristic
800C22#1912786011yescharacteristic
801C22#1912786211yescharacteristic
802C22#1912793111yescharacteristic
803C22#1912793311yescharacteristic
804C22#1912793611yescharacteristic
805C22#1912793811yescharacteristic
806C22#1912794611yescharacteristic
807C22#1912794811yescharacteristic
808C22#1912795811yescharacteristic
809C22#1912796011yescharacteristic
810C22#1912801311yescharacteristic
811C22#1912801311yescharacteristic
812C22#1912801611yescharacteristic
813C22#1912801811yescharacteristic
814C22#1912802411yescharacteristic
815C22#1912802811yescharacteristic
816C22#1912803011yescharacteristic
817C22#1912803311yescharacteristic
818C22#1912804011yescharacteristic
819C22#1912804111yescharacteristic
820C22#1912804111yescharacteristic
821C22#1912804511yescharacteristic
822C4—82no—
823C4—82no—
824C4—3322no—
825C4—6642no—
826C4—6642no—
827C4#1912759011yescharacteristic
828C4#1912759111yescharacteristic
829C4#1912759211yescharacteristic
830C4#1912759311yescharacteristic
831C4#1912761711yescharacteristic
832C4#1912761911yescharacteristic
833C4#1912762711yescharacteristic
834C4#1912763011yescharacteristic
835C2—3324no—
836C2#2490571111yescharacteristic
837C2#2490754811yescharacteristic
838C2#2490755711yescharacteristic
839C2#2490777211yescharacteristic
840C2#2490777711yescharacteristic
841C2#2490789011yescharacteristic
842C2#2490789511yescharacteristic
843C2#2490864311yescharacteristic
844C2#2490864711yescharacteristic
845C2#2490865711yescharacteristic
846C2#2490866111yescharacteristic
847C2#2490888811yescharacteristic
848C2#2490889011yescharacteristic
849C2#2490889811yescharacteristic
850C2#2490890211yescharacteristic
subgroupG/H
centerC24D4×D83
commutatorC22×C4×C83C22×C4
FrattiniC23×C4C22×D83
FittingC2×#340×C83C2
socleC24×C83C2×D4
prime radicalC24×D83D4
cosocleC23×C4×C83C23
hypercenterC2×#340D83
hypocenterC83#11199
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#19127464C2semidirect
5. C2×#19127463C2semidirect
6. C2×#19127463C2semidirect
7. C2×#340×C83C2semidirect
20. #19127558C4semidirect
432. C2×#340D83semidirect
433. C83#11199semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D83)⋊C82
C2×#191275582
C2×#191274642
C2×#191274632
C2×#340×C832
#1119983