Finite Group Databasebeta

← C83×#22372 #35250196

Subgroups — C83×#22372 #35250196

Order 21248.

716 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#2395C211yesmaximal, characteristic
2C83×#1955C211yesmaximal, characteristic
3C83×#1940C211yesmaximal, characteristic, complemented
4C83×#1924C211yesmaximal, characteristic, complemented
5C83×#1923C211yesmaximal, characteristic, complemented
6C83×#1923C211yesmaximal, characteristic, complemented
7C83×#1923C211yesmaximal, characteristic, complemented
8C83×#1917C211yesmaximal, characteristic, complemented
9C83×#1916C211yesmaximal, characteristic, complemented
10C83×#1869C211yesmaximal, characteristic
11C83×#1850C211yesmaximal, characteristic, complemented
12C83×#1798C211yesmaximal, characteristic, complemented
13C83×#1770C211yesmaximal, characteristic, complemented
14C83×#1752C211yesmaximal, characteristic, complemented
15C83×#1750C211yesmaximal, characteristic, complemented
16C23×C8×C83C2211yescharacteristic
17C2×C4×D4×C83C2211yescharacteristic
18C2×#117×C83C2211yescharacteristic
19C2×C4⋊C8×C83C2211yescharacteristic
20C2×C4⋊C8×C83C2211yescharacteristic
21C2×C4⋊C8×C83C2211yescharacteristic
22C2×C4⋊C8×C83C2211yescharacteristic
23C2×C4⋊C8×C83C2211yescharacteristic
24C2×C22⋊C8×C83C2211yescharacteristic
25C2×C22⋊C8×C83C2211yescharacteristic
26C2×C22⋊C8×C83C2211yescharacteristic
27C2×C22⋊C8×C83C2211yescharacteristic
28C2×C22⋊C8×C83C2211yescharacteristic
29C2×C22⋊C8×C83C2211yescharacteristic
30C2×C22⋊C8×C83C2211yescharacteristic
31C2×#97×C83C2211yescharacteristic
32C2×#97×C83C2211yescharacteristic
33C2×#97×C83C2211yescharacteristic
34C2×C4×C8×C83C2211yescharacteristic
35C2×C4×C8×C83C2211yescharacteristic
36#400×C83C411yescharacteristic
37#399×C83C411yescharacteristic
38#398×C83C411yescharacteristic
39#397×C83C411yescharacteristic
40#397×C83C411yescharacteristic
41#397×C83C411yescharacteristic
42#394×C83C411yescharacteristic
43#394×C83C411yescharacteristic
44C4×C4⋊C4×C83C2211yescharacteristic
45C4×C4⋊C4×C83C2211yescharacteristic
46C4×C22⋊C4×C83C2211yescharacteristic
47C4×C22⋊C4×C83C2211yescharacteristic
48C4×C22⋊C4×C83C2211yescharacteristic
49#336×C83C2211yescharacteristic
50#336×C83C2211yescharacteristic
51#336×C83C2211yescharacteristic
52#336×C83C2211yescharacteristic
53#336×C83C2211yescharacteristic
54#336×C83C2211yescharacteristic
55#336×C83C2211yescharacteristic
56#336×C83C2211yescharacteristic
57#336×C83C2211yescharacteristic
58#336×C83C2211yescharacteristic
59C22×D4×C83C2×C411yescharacteristic
60C23×C4×C83C2311yescharacteristic
61C23×C4×C83C2311yescharacteristic
62C22×C8×C83—22no—
63C22×C8×C83—41no—
64C22×C8×C83—41no—
65C22×C8×C83C2311yescharacteristic
66C22×C8×C83C2311yescharacteristic
67C22×C8×C83C2311yescharacteristic
68C22×C8×C83C2311yescharacteristic
69C22×C8×C83C2311yescharacteristic
70C22×C8×C83C2311yescharacteristic
71C22×C8×C83C2311yescharacteristic
72C22×C8×C83C2311yescharacteristic
73C4×D4×C83—41no—
74C4×D4×C83—41no—
75#117×C83—41no—
76#117×C83—41no—
77C2×C4⋊C4×C83C2×C411yescharacteristic
78C2×C4⋊C4×C83C2×C411yescharacteristic
79C2×C4⋊C4×C83C2×C411yescharacteristic
80C2×C4⋊C4×C83C2×C411yescharacteristic
81C2×C4⋊C4×C83C2×C411yescharacteristic
82C2×C4⋊C4×C83C2×C411yescharacteristic
83C2×C4⋊C4×C83C2×C411yescharacteristic
84C2×C22⋊C4×C83C2×C411yescharacteristic
85C2×C22⋊C4×C83C2×C411yescharacteristic
86C2×C22⋊C4×C83C2×C411yescharacteristic
87C2×C22⋊C4×C83C2×C411yescharacteristic
88C2×C22⋊C4×C83C2×C411yescharacteristic
89C2×C22⋊C4×C83C2×C411yescharacteristic
90C2×C22⋊C4×C83C2×C411yescharacteristic
91C2×C22⋊C4×C83C2×C411yescharacteristic
92C2×C22⋊C4×C83C2×C411yescharacteristic
93C2×C22⋊C4×C83C2×C411yescharacteristic
94C2×C42×C83C2311yescharacteristic
95C2×C42×C83C2311yescharacteristic
96C2×C42×C83C2311yescharacteristic
97C2×C42×C83C2311yescharacteristic
98C2×C42×C83C2311yescharacteristic
99C4⋊C8×C83—22no—
100C4⋊C8×C83—41no—
101C4⋊C8×C83—41no—
102C4⋊C8×C83—41no—
103C4⋊C8×C83—41no—
104C22⋊C8×C83—22no—
105C22⋊C8×C83—22no—
106C22⋊C8×C83—22no—
107C22⋊C8×C83—41no—
108C22⋊C8×C83—41no—
109C22⋊C8×C83—41no—
110C22⋊C8×C83—41no—
111#97×C83—41no—
112#97×C83—41no—
113#97×C83—41no—
114C4×C8×C83—22no—
115C4×C8×C83—41no—
116#95×C83C2×C411yescharacteristic
117#95×C83C2×C411yescharacteristic
118#95×C83C2×C411yescharacteristic
119#95×C83C2×C411yescharacteristic
120#95×C83C2×C411yescharacteristic
121#95×C83C2×C411yescharacteristic
122#95×C83C2×C411yescharacteristic
123#95×C83C2×C411yescharacteristic
124#95×C83C2×C411yescharacteristic
125#95×C83C2×C411yescharacteristic
126C24×C83C22×C411yescharacteristic
127C24×C83C22×C411yescharacteristic
128C2×D4×C83—22no—
129C2×D4×C83—41no—
130C2×D4×C83—41no—
131C22×C4×C83—21no—
132C22×C4×C83—21no—
133C22×C4×C83—21no—
134C22×C4×C83—21no—
135C22×C4×C83—21no—
136C22×C4×C83—21no—
137C22×C4×C83—21no—
138C22×C4×C83—21no—
139C22×C4×C83—21no—
140C22×C4×C83—21no—
141C22×C4×C83—21no—
142C22×C4×C83—21no—
143C22×C4×C83C22×C411yescharacteristic
144C22×C4×C83C22×C411yescharacteristic
145C22×C4×C83C22×C411yescharacteristic
146C22×C4×C83C22×C411yescharacteristic
147C22×C4×C83C22×C411yescharacteristic
148C22×C4×C83C22×C411yescharacteristic
149C22×C4×C83C22×C411yescharacteristic
150C22×C4×C83C22×C411yescharacteristic
151C22×C4×C83C22×C411yescharacteristic
152C22×C4×C83C22×C411yescharacteristic
153C22×C4×C83C22×C411yescharacteristic
154C22×C4×C83C22×C411yescharacteristic
155C22×C4×C83C2411yescharacteristic
156C2×C8×C83—21no—
157C2×C8×C83—21no—
158C2×C8×C83—21no—
159C2×C8×C83—21no—
160C2×C8×C83—21no—
161C2×C8×C83—21no—
162C2×C8×C83—21no—
163C2×C8×C83—21no—
164C2×C8×C83—21no—
165C2×C8×C83—21no—
166C2×C8×C83—21no—
167C2×C8×C83—21no—
168C2×C8×C83—21no—
169C2×C8×C83—21no—
170C2×C8×C83—21no—
171C2×C8×C83—21no—
172C2×C8×C83—21no—
173C2×C8×C83—21no—
174C2×C8×C83—21no—
175C2×C8×C83—21no—
176C2×C8×C83—21no—
177C2×C8×C83—21no—
178C2×C8×C83—44no—
179C2×C8×C83#4112yes—
180C2×C8×C83#4112yes—
181C4⋊C4×C83—22no—
182C4⋊C4×C83—41no—
183C4⋊C4×C83—41no—
184C4⋊C4×C83—41no—
185C4⋊C4×C83—41no—
186C4⋊C4×C83—41no—
187C4⋊C4×C83—41no—
188C22⋊C4×C83—22no—
189C22⋊C4×C83—22no—
190C22⋊C4×C83—22no—
191C22⋊C4×C83—22no—
192C22⋊C4×C83—41no—
193C22⋊C4×C83—41no—
194C22⋊C4×C83—41no—
195C22⋊C4×C83—41no—
196C22⋊C4×C83—41no—
197C22⋊C4×C83—41no—
198C42×C83—21no—
199C42×C83—21no—
200C42×C83—21no—
201C42×C83—21no—
202C42×C83—21no—
203C42×C83—21no—
204C42×C83—21no—
205C42×C83—21no—
206C42×C83—21no—
207C42×C83—21no—
208C23×C83—21no—
209C23×C83—21no—
210C23×C83—21no—
211C23×C83—21no—
212C23×C83—21no—
213C23×C83—21no—
214C23×C83—21no—
215C23×C83—21no—
216C23×C83—21no—
217C23×C83—21no—
218C23×C83—21no—
219C23×C83—21no—
220C23×C83—21no—
221C23×C83#13112yes—
222C23×C83C23×C411yescharacteristic
223D4×C83—44no—
224C2×C4×C83—21no—
225C2×C4×C83—21no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—21no—
232C2×C4×C83—21no—
233C2×C4×C83—21no—
234C2×C4×C83—21no—
235C2×C4×C83—21no—
236C2×C4×C83—21no—
237C2×C4×C83—21no—
238C2×C4×C83—21no—
239C2×C4×C83—21no—
240C2×C4×C83—21no—
241C2×C4×C83—21no—
242C2×C4×C83—21no—
243C2×C4×C83—21no—
244C2×C4×C83—21no—
245C2×C4×C83—21no—
246C2×C4×C83—21no—
247C2×C4×C83—21no—
248C2×C4×C83—21no—
249C2×C4×C83—21no—
250C2×C4×C83—21no—
251C2×C4×C83—21no—
252C2×C4×C83—21no—
253C2×C4×C83—21no—
254C2×C4×C83—21no—
255C2×C4×C83—21no—
256C2×C4×C83—21no—
257C2×C4×C83—21no—
258C2×C4×C83—21no—
259C2×C4×C83—41no—
260C2×C4×C83—41no—
261C2×C4×C83—41no—
262C2×C4×C83—41no—
263C2×C4×C83—41no—
264C2×C4×C83—41no—
265C2×C4×C83—41no—
266C2×C4×C83—41no—
267C2×C4×C83#13112yes—
268C2×C4×C83C2×#4111yescharacteristic
269C2×C4×C83C2×#4111yescharacteristic
270C2×C4×C83H(5,𝔽2)11yescharacteristic
271C2×C4×C83H(5,𝔽2)11yescharacteristic
272C2×C4×C83H(5,𝔽2)11yescharacteristic
273C2×C4×C832−1+411yescharacteristic
274C8×C83—22no—
275C8×C83—22no—
276C8×C83—41no—
277C8×C83—41no—
278C8×C83—41no—
279C8×C83—41no—
280C8×C83—41no—
281C8×C83—41no—
282C22×C83—22no—
283C22×C83—22no—
284C22×C83—22no—
285C22×C83—41no—
286C22×C83—41no—
287C22×C83—41no—
288C22×C83—41no—
289C22×C83—41no—
290C22×C83—41no—
291C22×C83—41no—
292C22×C83—41no—
293C22×C83—41no—
294C22×C83—41no—
295C22×C83—41no—
296C22×C83C4×#4111yescharacteristic
297C22×C83#51811yescharacteristic
298C22×C83#52011yescharacteristic
299C22×C83C2×#13111yescharacteristic
300C22×C83C2×#13111yescharacteristic
301C22×C83#56811yescharacteristic
302C22×C83#56811yescharacteristic
303C4×C83—22no—
304C4×C83—41no—
305C4×C83—41no—
306C4×C83—41no—
307C4×C83—41no—
308C4×C83—41no—
309C4×C83—41no—
310C4×C83—41no—
311C4×C83—41no—
312C4×C83—41no—
313C4×C83—41no—
314C4×C83—41no—
315C4×C83#53811yescharacteristic
316C4×C83#53911yescharacteristic
317C4×C83#54011yescharacteristic
318C4×C83#54211yescharacteristic
319#22372C8311yesmaximal, characteristic, direct product factor, Sylow
320C2×C83—42no—
321C2×C83—81no—
322C2×C83#233511yescharacteristic
323C2×C83#296811yescharacteristic
324C2×C83#296811yescharacteristic
325C2×C83#297611yescharacteristic
326C2×C83#298111yescharacteristic
327C2×C83#299411yescharacteristic
328C2×C83#299511yescharacteristic
329#2395C2×C8311yescharacteristic
330#1955C2×C8311yescharacteristic
331#1940C2×C8311yescharacteristic, complemented
332#1924C2×C8311yescharacteristic, complemented
333#1923C2×C8311yescharacteristic, complemented
334#1923C2×C8311yescharacteristic, complemented
335#1923C2×C8311yescharacteristic, complemented
336#1917C2×C8311yescharacteristic, complemented
337#1916C2×C8311yescharacteristic, complemented
338#1869C2×C8311yescharacteristic
339#1850C2×C8311yescharacteristic, complemented
340#1798C2×C8311yescharacteristic, complemented
341#1770C2×C8311yescharacteristic, complemented
342#1752C2×C8311yescharacteristic, complemented
343#1750C2×C8311yescharacteristic, complemented
344C83#2237211yescharacteristic, direct product factor, Sylow
345C23×C8C22×C8311yescharacteristic
346C2×C4×D4C22×C8311yescharacteristic
347C2×#117C22×C8311yescharacteristic
348C2×C4⋊C8C22×C8311yescharacteristic
349C2×C4⋊C8C22×C8311yescharacteristic
350C2×C4⋊C8C22×C8311yescharacteristic
351C2×C4⋊C8C22×C8311yescharacteristic
352C2×C4⋊C8C22×C8311yescharacteristic
353C2×C22⋊C8C22×C8311yescharacteristic
354C2×C22⋊C8C22×C8311yescharacteristic
355C2×C22⋊C8C22×C8311yescharacteristic
356C2×C22⋊C8C22×C8311yescharacteristic
357C2×C22⋊C8C22×C8311yescharacteristic
358C2×C22⋊C8C22×C8311yescharacteristic
359C2×C22⋊C8C22×C8311yescharacteristic
360C2×#97C22×C8311yescharacteristic
361C2×#97C22×C8311yescharacteristic
362C2×#97C22×C8311yescharacteristic
363C2×C4×C8C22×C8311yescharacteristic
364C2×C4×C8C22×C8311yescharacteristic
365#400C4×C8311yescharacteristic
366#399C4×C8311yescharacteristic
367#398C4×C8311yescharacteristic
368#397C4×C8311yescharacteristic
369#397C4×C8311yescharacteristic
370#397C4×C8311yescharacteristic
371#394C4×C8311yescharacteristic
372#394C4×C8311yescharacteristic
373C4×C4⋊C4C22×C8311yescharacteristic
374C4×C4⋊C4C22×C8311yescharacteristic
375C4×C22⋊C4C22×C8311yescharacteristic
376C4×C22⋊C4C22×C8311yescharacteristic
377C4×C22⋊C4C22×C8311yescharacteristic
378#336C22×C8311yescharacteristic
379#336C22×C8311yescharacteristic
380#336C22×C8311yescharacteristic
381#336C22×C8311yescharacteristic
382#336C22×C8311yescharacteristic
383#336C22×C8311yescharacteristic
384#336C22×C8311yescharacteristic
385#336C22×C8311yescharacteristic
386#336C22×C8311yescharacteristic
387#336C22×C8311yescharacteristic
388C22×D4C2×C4×C8311yescharacteristic
389C23×C4C23×C8311yescharacteristic
390C23×C4C23×C8311yescharacteristic
391C22×C8—22no—
392C22×C8—41no—
393C22×C8—41no—
394C22×C8C23×C8311yescharacteristic
395C22×C8C23×C8311yescharacteristic
396C22×C8C23×C8311yescharacteristic
397C22×C8C23×C8311yescharacteristic
398C22×C8C23×C8311yescharacteristic
399C22×C8C23×C8311yescharacteristic
400C22×C8C23×C8311yescharacteristic
401C22×C8C23×C8311yescharacteristic
402C4×D4—41no—
403C4×D4—41no—
404#117—41no—
405#117—41no—
406C2×C4⋊C4C2×C4×C8311yescharacteristic
407C2×C4⋊C4C2×C4×C8311yescharacteristic
408C2×C4⋊C4C2×C4×C8311yescharacteristic
409C2×C4⋊C4C2×C4×C8311yescharacteristic
410C2×C4⋊C4C2×C4×C8311yescharacteristic
411C2×C4⋊C4C2×C4×C8311yescharacteristic
412C2×C4⋊C4C2×C4×C8311yescharacteristic
413C2×C22⋊C4C2×C4×C8311yescharacteristic
414C2×C22⋊C4C2×C4×C8311yescharacteristic
415C2×C22⋊C4C2×C4×C8311yescharacteristic
416C2×C22⋊C4C2×C4×C8311yescharacteristic
417C2×C22⋊C4C2×C4×C8311yescharacteristic
418C2×C22⋊C4C2×C4×C8311yescharacteristic
419C2×C22⋊C4C2×C4×C8311yescharacteristic
420C2×C22⋊C4C2×C4×C8311yescharacteristic
421C2×C22⋊C4C2×C4×C8311yescharacteristic
422C2×C22⋊C4C2×C4×C8311yescharacteristic
423C2×C42C23×C8311yescharacteristic
424C2×C42C23×C8311yescharacteristic
425C2×C42C23×C8311yescharacteristic
426C2×C42C23×C8311yescharacteristic
427C2×C42C23×C8311yescharacteristic
428C4⋊C8—22no—
429C4⋊C8—41no—
430C4⋊C8—41no—
431C4⋊C8—41no—
432C4⋊C8—41no—
433C22⋊C8—22no—
434C22⋊C8—22no—
435C22⋊C8—22no—
436C22⋊C8—41no—
437C22⋊C8—41no—
438C22⋊C8—41no—
439C22⋊C8—41no—
440#97—41no—
441#97—41no—
442#97—41no—
443C4×C8—22no—
444C4×C8—41no—
445#95C2×C4×C8311yescharacteristic
446#95C2×C4×C8311yescharacteristic
447#95C2×C4×C8311yescharacteristic
448#95C2×C4×C8311yescharacteristic
449#95C2×C4×C8311yescharacteristic
450#95C2×C4×C8311yescharacteristic
451#95C2×C4×C8311yescharacteristic
452#95C2×C4×C8311yescharacteristic
453#95C2×C4×C8311yescharacteristic
454#95C2×C4×C8311yescharacteristic
455C24C22×C4×C8311yescharacteristic
456C24C22×C4×C8311yescharacteristic
457C2×D4—22no—
458C2×D4—41no—
459C2×D4—41no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4C22×C4×C8311yescharacteristic
473C22×C4C22×C4×C8311yescharacteristic
474C22×C4C22×C4×C8311yescharacteristic
475C22×C4C22×C4×C8311yescharacteristic
476C22×C4C22×C4×C8311yescharacteristic
477C22×C4C22×C4×C8311yescharacteristic
478C22×C4C22×C4×C8311yescharacteristic
479C22×C4C22×C4×C8311yescharacteristic
480C22×C4C22×C4×C8311yescharacteristic
481C22×C4C22×C4×C8311yescharacteristic
482C22×C4C22×C4×C8311yescharacteristic
483C22×C4C22×C4×C8311yescharacteristic
484C22×C4C24×C8311yescharacteristic
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—44no—
508C2×C8#41×C8312yes—
509C2×C8#41×C8312yes—
510C4⋊C4—22no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23#131×C8312yes—
551C23C23×C4×C8311yescharacteristic
552D4—44no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4#131×C8312yes—
597C2×C4C2×#41×C8311yescharacteristic
598C2×C4C2×#41×C8311yescharacteristic
599C2×C4H(5,𝔽2)×C8311yescharacteristic
600C2×C4H(5,𝔽2)×C8311yescharacteristic
601C2×C4H(5,𝔽2)×C8311yescharacteristic
602C2×C42−1+4×C8311yescharacteristic
603C8—22no—
604C8—22no—
605C8—41no—
606C8—41no—
607C8—41no—
608C8—41no—
609C8—41no—
610C8—41no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22C4×#41×C8311yescharacteristic
626C22#518×C8311yescharacteristic
627C22#520×C8311yescharacteristic
628C22C2×#131×C8311yescharacteristic
629C22C2×#131×C8311yescharacteristic
630C22#568×C8311yescharacteristic
631C22#568×C8311yescharacteristic
632C4—22no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4#538×C8311yescharacteristic
645C4#539×C8311yescharacteristic
646C4#540×C8311yescharacteristic
647C4#542×C8311yescharacteristic
648C2—42no—
649C2—81no—
650C2C83×#233511yescharacteristic
651C2C83×#296811yescharacteristic
652C2C83×#296811yescharacteristic
653C2C83×#297611yescharacteristic
654C2C83×#298111yescharacteristic
655C2C83×#299411yescharacteristic
656C2C83×#299511yescharacteristic
subgroupG/H
centerC22×C4×C83C24
commutatorC23C23×C4×C83
Frattini, cosocleC22×C4C24×C83
socleC23×C83C23×C4
prime radicalC22×D4×C83C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
3. C83×#1940C2semidirect
4. C83×#1924C2semidirect
5. C83×#1923C2semidirect
6. C83×#1923C2semidirect
7. C83×#1923C2semidirect
8. C83×#1917C2semidirect
9. C83×#1916C2semidirect
11. C83×#1850C2semidirect
12. C83×#1798C2semidirect
13. C83×#1770C2semidirect
14. C83×#1752C2semidirect
15. C83×#1750C2semidirect
319. #22372C83direct (N × H)
331. #1940C2×C83semidirect
332. #1924C2×C83semidirect
333. #1923C2×C83semidirect
334. #1923C2×C83semidirect
335. #1923C2×C83semidirect
336. #1917C2×C83semidirect
337. #1916C2×C83semidirect
339. #1850C2×C83semidirect
340. #1798C2×C83semidirect
341. #1770C2×C83semidirect
342. #1752C2×C83semidirect
343. #1750C2×C83semidirect
344. C83#22372direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#23952
C83×#19552
C83×#19402
C83×#19242
C83×#19232
C83×#19172
C83×#19162
C83×#18692
C83×#18502
C83×#17982
C83×#17702
C83×#17522
C83×#17502
#2237283