Finite Group Databasebeta

← C83×#11316 #35239140

Subgroups — C83×#11316 #35239140

Order 21248.

770 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#340×C83C211yesmaximal, characteristic
2C2×#340×C83C211yesmaximal, characteristic
3C2×#340×C83C211yesmaximal, characteristic
4C2×#340×C83C211yesmaximal, characteristic
5C2×#336×C83C211yesmaximal, characteristic
6C83×C4⋊#95C211yesmaximal, characteristic
7C83×C4⋊#95C211yesmaximal, characteristic
8C23×C8×C83C2211yescharacteristic
9C23×C8×C83C2211yescharacteristic
10C22×C4⋊C4×C83C2211yescharacteristic
11C22×C4⋊C4×C83C2211yescharacteristic
12C22×C4⋊C4×C83C2211yescharacteristic
13C22×C4⋊C4×C83C2211yescharacteristic
14C22×C42×C83C2211yescharacteristic
15C2×#95×C83—21no—
16C2×#95×C83—21no—
17C2×#95×C83—21no—
18C2×#95×C83—21no—
19#340×C83—22no—
20#340×C83—22no—
21#340×C83—22no—
22#340×C83C414yescomplemented
23#336×C83—22no—
24C23×C4×C83—21no—
25C23×C4×C83—21no—
26C23×C4×C83—21no—
27C23×C4×C83—21no—
28C23×C4×C83D411yescharacteristic
29C23×C4×C83D411yescharacteristic
30C23×C4×C83C2311yescharacteristic
31C22×C8×C83—21no—
32C22×C8×C83—21no—
33C22×C8×C83—21no—
34C22×C8×C83—21no—
35C22×C8×C83—21no—
36C22×C8×C83—21no—
37C22×C8×C83—21no—
38C22×C8×C83—21no—
39C22×C8×C83—21no—
40C22×C8×C83—21no—
41C22×C8×C83—21no—
42C22×C8×C83—21no—
43C22×C8×C83C2×C412yes—
44C22×C8×C83D412yes—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83—21no—
47C2×C4⋊C4×C83—21no—
48C2×C4⋊C4×C83—21no—
49C2×C4⋊C4×C83—21no—
50C2×C4⋊C4×C83—21no—
51C2×C4⋊C4×C83—21no—
52C2×C4⋊C4×C83—21no—
53C2×C4⋊C4×C83—21no—
54C2×C4⋊C4×C83—21no—
55C2×C4⋊C4×C83—21no—
56C2×C4⋊C4×C83—21no—
57C2×C4⋊C4×C83—21no—
58C2×C4⋊C4×C83—21no—
59C2×C4⋊C4×C83—21no—
60C2×C4⋊C4×C83—21no—
61C2×C4⋊C4×C83—21no—
62C2×C4⋊C4×C83—21no—
63C2×C4⋊C4×C83—21no—
64C2×C4⋊C4×C83—21no—
65C2×C4⋊C4×C83C2×C412yes—
66C2×C4⋊C4×C83C2×C412yes—
67C2×C4⋊C4×C83D412yes—
68C2×C4⋊C4×C83Q812yes—
69C2×C42×C83—21no—
70C2×C42×C83—21no—
71C2×C42×C83—21no—
72C2×C42×C83—21no—
73C2×C42×C83—21no—
74C2×C42×C83—21no—
75#95×C83—42no—
76#95×C83—42no—
77#95×C83—42no—
78#95×C83—42no—
79C24×C83C2×D411yescharacteristic
80C22×C4×C83—21no—
81C22×C4×C83—21no—
82C22×C4×C83—21no—
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83—21no—
86C22×C4×C83—21no—
87C22×C4×C83—21no—
88C22×C4×C83—21no—
89C22×C4×C83—21no—
90C22×C4×C83—21no—
91C22×C4×C83—21no—
92C22×C4×C83—22no—
93C22×C4×C83—22no—
94C22×C4×C83—22no—
95C22×C4×C83—22no—
96C22×C4×C83—41no—
97C22×C4×C83—41no—
98C22×C4×C83—41no—
99C22×C4×C83—41no—
100C22×C4×C83—41no—
101C22×C4×C83—41no—
102C22×C4×C83—41no—
103C22×C4×C83—41no—
104C22×C4×C83—41no—
105C22×C4×C83—41no—
106C22×C4×C83—41no—
107C22×C4×C83—41no—
108C22×C4×C83—41no—
109C22×C4×C83—41no—
110C22×C4×C83—41no—
111C22×C4×C83—41no—
112C22×C4×C83—41no—
113C22×C4×C83—41no—
114C22×C4×C83—41no—
115C22×C4×C83—41no—
116C22×C4×C83—41no—
117C22×C4×C83—41no—
118C22×C4×C83—41no—
119C22×C4×C83—41no—
120C22×C4×C83SD1612yes—
121C22×C4×C83Q1612yes—
122C22×C4×C83C22×C411yescharacteristic
123C22×C4×C83C2×D411yescharacteristic
124C22×C4×C83C2×D411yescharacteristic
125C22×C4×C83C2×Q811yescharacteristic
126C22×C4×C83#4111yescharacteristic
127C22×C4×C83#4111yescharacteristic
128C22×C4×C83#4111yescharacteristic
129C22×C4×C83#4111yescharacteristic
130C22×C4×C83#4111yescharacteristic
131C22×C4×C83#4111yescharacteristic
132C22×C4×C83#4111yescharacteristic
133C22×C4×C83#4111yescharacteristic
134C22×C4×C83#4111yescharacteristic
135C22×C4×C83#4111yescharacteristic
136C2×C8×C83—22no—
137C2×C8×C83—22no—
138C2×C8×C83—22no—
139C2×C8×C83—22no—
140C2×C8×C83—22no—
141C2×C8×C83—22no—
142C2×C8×C83—41no—
143C2×C8×C83—41no—
144C2×C8×C83—41no—
145C2×C8×C83—41no—
146C2×C8×C83—41no—
147C2×C8×C83—41no—
148C2×C8×C83—41no—
149C2×C8×C83—41no—
150C4⋊C4×C83—22no—
151C4⋊C4×C83—22no—
152C4⋊C4×C83—22no—
153C4⋊C4×C83—22no—
154C4⋊C4×C83—22no—
155C4⋊C4×C83—22no—
156C4⋊C4×C83—22no—
157C4⋊C4×C83—22no—
158C4⋊C4×C83—41no—
159C4⋊C4×C83—41no—
160C4⋊C4×C83—41no—
161C4⋊C4×C83—41no—
162C4⋊C4×C83—41no—
163C4⋊C4×C83—41no—
164C4⋊C4×C83—41no—
165C4⋊C4×C83—41no—
166C42×C83—41no—
167C42×C83—41no—
168C42×C83—41no—
169C42×C83—41no—
170C23×C83C4×D411yescharacteristic
171C23×C83#12111yescharacteristic
172C23×C83#12111yescharacteristic
173C23×C83C22⋊Q811yescharacteristic
174C23×C83#12311yescharacteristic
175C23×C83#12311yescharacteristic
176C23×C83#12411yescharacteristic
177C23×C83C2×SD1611yescharacteristic
178C23×C83C2×Q1611yescharacteristic
179C23×C83#13511yescharacteristic
180C23×C83#13511yescharacteristic
181C23×C83AGL(1,ℤ/8)11yescharacteristic
182C23×C83AGL(1,ℤ/8)11yescharacteristic
183C23×C83AGL(1,ℤ/8)11yescharacteristic
184C23×C83#13711yescharacteristic
185C2×C4×C83—22no—
186C2×C4×C83—22no—
187C2×C4×C83—22no—
188C2×C4×C83—22no—
189C2×C4×C83—22no—
190C2×C4×C83—22no—
191C2×C4×C83—41no—
192C2×C4×C83—41no—
193C2×C4×C83—41no—
194C2×C4×C83—41no—
195C2×C4×C83—41no—
196C2×C4×C83—41no—
197C2×C4×C83—41no—
198C2×C4×C83—41no—
199C2×C4×C83—42no—
200C2×C4×C83—42no—
201C2×C4×C83—42no—
202C2×C4×C83—42no—
203C2×C4×C83—42no—
204C2×C4×C83—42no—
205C2×C4×C83—42no—
206C2×C4×C83—42no—
207C2×C4×C83—42no—
208C2×C4×C83—42no—
209C2×C4×C83—42no—
210C2×C4×C83—42no—
211C2×C4×C83—81no—
212C2×C4×C83—81no—
213C2×C4×C83—81no—
214C2×C4×C83—81no—
215C2×C4×C83—81no—
216C2×C4×C83—81no—
217C2×C4×C83—81no—
218C2×C4×C83—81no—
219C2×C4×C83—81no—
220C2×C4×C83—81no—
221C2×C4×C83—81no—
222C2×C4×C83—81no—
223C2×C4×C83—81no—
224C2×C4×C83—81no—
225C2×C4×C83—81no—
226C2×C4×C83—81no—
227C2×C4×C83#11711yescharacteristic
228C2×C4×C83#11711yescharacteristic
229C2×C4×C83#11711yescharacteristic
230C2×C4×C83C4×D411yescharacteristic
231C2×C4×C83C4×D411yescharacteristic
232C2×C4×C83C4×Q811yescharacteristic
233C2×C4×C83#12111yescharacteristic
234C2×C4×C83C22⋊Q811yescharacteristic
235C2×C4×C83C22⋊Q811yescharacteristic
236C2×C4×C83#12311yescharacteristic
237C2×C4×C83#12311yescharacteristic
238C2×C4×C83#12311yescharacteristic
239C2×C4×C83#12311yescharacteristic
240C2×C4×C83#12411yescharacteristic
241C2×C4×C83#12411yescharacteristic
242C2×C4×C83#12511yescharacteristic
243C2×C4×C83#12511yescharacteristic
244C2×C4×C83#12511yescharacteristic
245C2×C4×C83#12611yescharacteristic
246C2×C4×C83#12611yescharacteristic
247C2×C4×C83#12611yescharacteristic
248C2×C4×C83#12611yescharacteristic
249C2×C4×C83#12611yescharacteristic
250C2×C4×C83#12611yescharacteristic
251C2×C4×C83#12611yescharacteristic
252C2×C4×C83#12611yescharacteristic
253C2×C4×C83#12611yescharacteristic
254C2×C4×C83#12611yescharacteristic
255C8×C83—42no—
256C8×C83—42no—
257C22×C83#38711yescharacteristic
258C22×C83#38811yescharacteristic
259C22×C83#38811yescharacteristic
260C22×C83#39611yescharacteristic
261C22×C83#39711yescharacteristic
262C22×C83#39711yescharacteristic
263C22×C83#40011yescharacteristic
264C22×C83C4×SD1611yescharacteristic
265C22×C83C4×Q1611yescharacteristic
266C22×C83#44011yescharacteristic
267C22×C83#44211yescharacteristic
268C22×C83#46011yescharacteristic
269C22×C83#46211yescharacteristic
270C22×C83#46311yescharacteristic
271C22×C83#46311yescharacteristic
272C22×C83#46511yescharacteristic
273C22×C83#46711yescharacteristic
274C22×C83#46811yescharacteristic
275C22×C83#46911yescharacteristic
276C22×C83#47611yescharacteristic
277C22×C83#47711yescharacteristic
278C22×C83#47811yescharacteristic
279C22×C83#47911yescharacteristic
280C22×C83#48111yescharacteristic
281C22×C83#48211yescharacteristic
282C22×C83#48211yescharacteristic
283C22×C83#48211yescharacteristic
284C22×C83#48311yescharacteristic
285C22×C83#48411yescharacteristic
286C22×C83#48411yescharacteristic
287C22×C83#48511yescharacteristic
288C22×C83#48711yescharacteristic
289C22×C83#48811yescharacteristic
290C22×C83#48911yescharacteristic
291C22×C83#49011yescharacteristic
292C4×C83—42no—
293C4×C83—42no—
294C4×C83—82no—
295C4×C83—82no—
296C4×C83—82no—
297C4×C83—82no—
298C4×C83#38311yescharacteristic
299C4×C83#38711yescharacteristic
300C4×C83#38711yescharacteristic
301C4×C83#38811yescharacteristic
302C4×C83#39711yescharacteristic
303C4×C83#40011yescharacteristic
304C4×C83#40011yescharacteristic
305C4×C83#40111yescharacteristic
306#11316C8311yesmaximal, characteristic, direct product factor, Sylow
307C2×C83#144311yescharacteristic
308C2×C83#192011yescharacteristic
309C2×C83#192111yescharacteristic
310C2×C83#192611yescharacteristic
311C2×C83#192811yescharacteristic
312C2×C83#193311yescharacteristic
313C2×C83#193611yescharacteristic
314C2×C83#206511yescharacteristic
315C2×C83#206811yescharacteristic
316C2×C83#207211yescharacteristic
317C2×C83#207311yescharacteristic
318C2×C83#207611yescharacteristic
319C2×C83#207711yescharacteristic
320C2×C83#210011yescharacteristic
321C2×C83#210111yescharacteristic
322C2×#340C2×C8311yescharacteristic
323C2×#340C2×C8311yescharacteristic
324C2×#340C2×C8311yescharacteristic
325C2×#340C2×C8311yescharacteristic
326C2×#336C2×C8311yescharacteristic
327C4⋊#95C2×C8311yescharacteristic
328C4⋊#95C2×C8311yescharacteristic
329C83#1131611yescharacteristic, direct product factor, Sylow
330C23×C8C22×C8311yescharacteristic
331C23×C8C22×C8311yescharacteristic
332C22×C4⋊C4C22×C8311yescharacteristic
333C22×C4⋊C4C22×C8311yescharacteristic
334C22×C4⋊C4C22×C8311yescharacteristic
335C22×C4⋊C4C22×C8311yescharacteristic
336C22×C42C22×C8311yescharacteristic
337C2×#95—21no—
338C2×#95—21no—
339C2×#95—21no—
340C2×#95—21no—
341#340—22no—
342#340—22no—
343#340—22no—
344#340C4×C8314yescomplemented
345#336—22no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4D4×C8311yescharacteristic
351C23×C4D4×C8311yescharacteristic
352C23×C4C23×C8311yescharacteristic
353C22×C8—21no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8C2×C4×C8312yes—
366C22×C8D4×C8312yes—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4C2×C4×C8312yes—
388C2×C4⋊C4C2×C4×C8312yes—
389C2×C4⋊C4D4×C8312yes—
390C2×C4⋊C4Q8×C8312yes—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401C24C2×D4×C8311yescharacteristic
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4SD16×C8312yes—
443C22×C4Q16×C8312yes—
444C22×C4C22×C4×C8311yescharacteristic
445C22×C4C2×D4×C8311yescharacteristic
446C22×C4C2×D4×C8311yescharacteristic
447C22×C4C2×Q8×C8311yescharacteristic
448C22×C4#41×C8311yescharacteristic
449C22×C4#41×C8311yescharacteristic
450C22×C4#41×C8311yescharacteristic
451C22×C4#41×C8311yescharacteristic
452C22×C4#41×C8311yescharacteristic
453C22×C4#41×C8311yescharacteristic
454C22×C4#41×C8311yescharacteristic
455C22×C4#41×C8311yescharacteristic
456C22×C4#41×C8311yescharacteristic
457C22×C4#41×C8311yescharacteristic
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—41no—
471C2×C8—41no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C42—41no—
489C42—41no—
490C42—41no—
491C42—41no—
492C23C4×D4×C8311yescharacteristic
493C23#121×C8311yescharacteristic
494C23#121×C8311yescharacteristic
495C23C22⋊Q8×C8311yescharacteristic
496C23#123×C8311yescharacteristic
497C23#123×C8311yescharacteristic
498C23#124×C8311yescharacteristic
499C23C2×SD16×C8311yescharacteristic
500C23C2×Q16×C8311yescharacteristic
501C23#135×C8311yescharacteristic
502C23#135×C8311yescharacteristic
503C23AGL(1,ℤ/8)×C8311yescharacteristic
504C23AGL(1,ℤ/8)×C8311yescharacteristic
505C23AGL(1,ℤ/8)×C8311yescharacteristic
506C23#137×C8311yescharacteristic
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—81no—
541C2×C4—81no—
542C2×C4—81no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4#117×C8311yescharacteristic
550C2×C4#117×C8311yescharacteristic
551C2×C4#117×C8311yescharacteristic
552C2×C4C4×D4×C8311yescharacteristic
553C2×C4C4×D4×C8311yescharacteristic
554C2×C4C4×Q8×C8311yescharacteristic
555C2×C4#121×C8311yescharacteristic
556C2×C4C22⋊Q8×C8311yescharacteristic
557C2×C4C22⋊Q8×C8311yescharacteristic
558C2×C4#123×C8311yescharacteristic
559C2×C4#123×C8311yescharacteristic
560C2×C4#123×C8311yescharacteristic
561C2×C4#123×C8311yescharacteristic
562C2×C4#124×C8311yescharacteristic
563C2×C4#124×C8311yescharacteristic
564C2×C4#125×C8311yescharacteristic
565C2×C4#125×C8311yescharacteristic
566C2×C4#125×C8311yescharacteristic
567C2×C4#126×C8311yescharacteristic
568C2×C4#126×C8311yescharacteristic
569C2×C4#126×C8311yescharacteristic
570C2×C4#126×C8311yescharacteristic
571C2×C4#126×C8311yescharacteristic
572C2×C4#126×C8311yescharacteristic
573C2×C4#126×C8311yescharacteristic
574C2×C4#126×C8311yescharacteristic
575C2×C4#126×C8311yescharacteristic
576C2×C4#126×C8311yescharacteristic
577C8—42no—
578C8—42no—
579C22#387×C8311yescharacteristic
580C22#388×C8311yescharacteristic
581C22#388×C8311yescharacteristic
582C22#396×C8311yescharacteristic
583C22#397×C8311yescharacteristic
584C22#397×C8311yescharacteristic
585C22#400×C8311yescharacteristic
586C22C4×SD16×C8311yescharacteristic
587C22C4×Q16×C8311yescharacteristic
588C22#440×C8311yescharacteristic
589C22#442×C8311yescharacteristic
590C22#460×C8311yescharacteristic
591C22#462×C8311yescharacteristic
592C22#463×C8311yescharacteristic
593C22#463×C8311yescharacteristic
594C22#465×C8311yescharacteristic
595C22#467×C8311yescharacteristic
596C22#468×C8311yescharacteristic
597C22#469×C8311yescharacteristic
598C22#476×C8311yescharacteristic
599C22#477×C8311yescharacteristic
600C22#478×C8311yescharacteristic
601C22#479×C8311yescharacteristic
602C22#481×C8311yescharacteristic
603C22#482×C8311yescharacteristic
604C22#482×C8311yescharacteristic
605C22#482×C8311yescharacteristic
606C22#483×C8311yescharacteristic
607C22#484×C8311yescharacteristic
608C22#484×C8311yescharacteristic
609C22#485×C8311yescharacteristic
610C22#487×C8311yescharacteristic
611C22#488×C8311yescharacteristic
612C22#489×C8311yescharacteristic
613C22#490×C8311yescharacteristic
614C4—42no—
615C4—42no—
616C4—82no—
617C4—82no—
618C4—82no—
619C4—82no—
620C4#383×C8311yescharacteristic
621C4#387×C8311yescharacteristic
622C4#387×C8311yescharacteristic
623C4#388×C8311yescharacteristic
624C4#397×C8311yescharacteristic
625C4#400×C8311yescharacteristic
626C4#400×C8311yescharacteristic
627C4#401×C8311yescharacteristic
628C2C83×#144311yescharacteristic
629C2C83×#192011yescharacteristic
630C2C83×#192111yescharacteristic
631C2C83×#192611yescharacteristic
632C2C83×#192811yescharacteristic
633C2C83×#193311yescharacteristic
634C2C83×#193611yescharacteristic
635C2C83×#206511yescharacteristic
636C2C83×#206811yescharacteristic
637C2C83×#207211yescharacteristic
638C2C83×#207311yescharacteristic
639C2C83×#207611yescharacteristic
640C2C83×#207711yescharacteristic
641C2C83×#210011yescharacteristic
642C2C83×#210111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C83C2×D4
commutatorC22×C4C22×C4×C83
Frattini, cosocleC23×C4C23×C83
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C83 ◁ C22×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
22. #340×C83C4semidirect
306. #11316C83direct (N × H)
329. C83#11316direct (N × H)
344. #340C4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#340×C832
C2×#336×C832
C83×C4⋊#952
#1131683