Finite Group Databasebeta

← C83×#22389 #35250213

Subgroups — C83×#22389 #35250213

Order 21248.

788 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#124×C83C211yesmaximal, characteristic
2C83×#1985C211yesmaximal, characteristic, complemented
3C83×#1984C211yesmaximal, characteristic, complemented
4C83×#1924C211yesmaximal, characteristic, complemented
5C83×#1923C211yesmaximal, characteristic, complemented
6C83×#1923C211yesmaximal, characteristic, complemented
7C83×#1923C211yesmaximal, characteristic, complemented
8C83×#1870C211yesmaximal, characteristic
9C83×#1869C211yesmaximal, characteristic
10C83×#1851C211yesmaximal, characteristic, complemented
11C83×#1850C211yesmaximal, characteristic, complemented
12C83×#1839C211yesmaximal, characteristic, complemented
13C4×C4⋊C8×C83C211yesmaximal, characteristic, complemented
14C83×#1753C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C83C211yesmaximal, characteristic, complemented
16C22×M16×C83C2211yescharacteristic
17C23×C8×C83C2211yescharacteristic
18C2×#124×C83C411yescharacteristic
19C2×C4×Q8×C83C2211yescharacteristic
20C2×C4×D4×C83C2211yescharacteristic
21C2×C4⋊C8×C83C2211yescharacteristic
22C2×C4⋊C8×C83C2211yescharacteristic
23C2×C4⋊C8×C83C2211yescharacteristic
24C2×C4⋊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×C4×C8×C83C2211yescharacteristic
33C2×C4×C8×C83C2211yescharacteristic
34C2×C4×C8×C83C2211yescharacteristic
35#391×C83C411yescharacteristic
36#390×C83C411yescharacteristic
37#388×C83C411yescharacteristic
38#388×C83C411yescharacteristic
39#388×C83C411yescharacteristic
40#388×C83C411yescharacteristic
41#382×C83C411yescharacteristic
42C4×C22⋊C4×C83C2211yescharacteristic
43C4×C22⋊C4×C83C2211yescharacteristic
44C4×C22⋊C4×C83C2211yescharacteristic
45C4×C22⋊C4×C83C2211yescharacteristic
46C43×C83C2211yescharacteristic
47#336×C83C2211yescharacteristic
48#336×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×Q8×C83C2×C411yescharacteristic
60C22×D4×C83C2×C411yescharacteristic
61C23×C4×C83C2311yescharacteristic
62C23×C4×C83C2311yescharacteristic
63C2×M16×C83—22no—
64C2×M16×C83—41no—
65C2×M16×C83—41no—
66C22×C8×C83—22no—
67C22×C8×C83—41no—
68C22×C8×C83—41no—
69C22×C8×C83C2311yescharacteristic
70C22×C8×C83C2311yescharacteristic
71C22×C8×C83C2311yescharacteristic
72C22×C8×C83C2311yescharacteristic
73C22×C8×C83C2311yescharacteristic
74C22×C8×C83C2311yescharacteristic
75C22×C8×C83C2311yescharacteristic
76C22×C8×C83C2311yescharacteristic
77#124×C83—24no—
78C4×Q8×C83—41no—
79C4×Q8×C83—41no—
80C4×D4×C83—41no—
81C4×D4×C83—41no—
82C2×C4⋊C4×C83C2×C411yescharacteristic
83C2×C4⋊C4×C83C2×C411yescharacteristic
84C2×C4⋊C4×C83C2×C411yescharacteristic
85C2×C4⋊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×C22⋊C4×C83C2×C411yescharacteristic
95C2×C22⋊C4×C83C2×C411yescharacteristic
96C2×C42×C83C2×C411yescharacteristic
97C2×C42×C83C2×C411yescharacteristic
98C2×C42×C83C2×C411yescharacteristic
99C2×C42×C83C2×C411yescharacteristic
100C2×C42×C83C2311yescharacteristic
101C2×C42×C83C2311yescharacteristic
102C2×C42×C83C2311yescharacteristic
103C2×C42×C83C2311yescharacteristic
104C2×C42×C83C2311yescharacteristic
105C4⋊C8×C83—22no—
106C4⋊C8×C83—22no—
107C4⋊C8×C83—41no—
108C4⋊C8×C83—41no—
109C22⋊C8×C83—22no—
110C22⋊C8×C83—22no—
111C22⋊C8×C83—41no—
112C22⋊C8×C83—41no—
113C22⋊C8×C83—41no—
114C22⋊C8×C83—41no—
115#97×C83—41no—
116C4×C8×C83—41no—
117C4×C8×C83—41no—
118C4×C8×C83—41no—
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
126#95×C83C2×C411yescharacteristic
127C24×C83C22×C411yescharacteristic
128C24×C83C22×C411yescharacteristic
129C2×Q8×C83—22no—
130C2×Q8×C83—22no—
131C2×Q8×C83—41no—
132C2×D4×C83—22no—
133C2×D4×C83—22no—
134C2×D4×C83—41no—
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×C83—21no—
144C22×C4×C83—21no—
145C22×C4×C83—21no—
146C22×C4×C83—21no—
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×C83C22×C411yescharacteristic
156C22×C4×C83C22×C411yescharacteristic
157C22×C4×C83C22×C411yescharacteristic
158C22×C4×C83C22×C411yescharacteristic
159C22×C4×C83C2411yescharacteristic
160M16×C83—44no—
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—21no—
179C2×C8×C83—21no—
180C2×C8×C83—21no—
181C2×C8×C83—21no—
182C2×C8×C83—21no—
183C2×C8×C83—44no—
184C2×C8×C83#4112yes—
185C2×C8×C83#4112yes—
186C4⋊C4×C83—41no—
187C4⋊C4×C83—41no—
188C4⋊C4×C83—41no—
189C4⋊C4×C83—41no—
190C22⋊C4×C83—22no—
191C22⋊C4×C83—22no—
192C22⋊C4×C83—22no—
193C22⋊C4×C83—22no—
194C22⋊C4×C83—22no—
195C22⋊C4×C83—22no—
196C22⋊C4×C83—22no—
197C22⋊C4×C83—41no—
198C22⋊C4×C83—41no—
199C22⋊C4×C83M1614yescomplemented
200C42×C83—22no—
201C42×C83—22no—
202C42×C83—22no—
203C42×C83—22no—
204C42×C83—21no—
205C42×C83—21no—
206C42×C83—21no—
207C42×C83—21no—
208C42×C83—21no—
209C42×C83—21no—
210C42×C83—21no—
211C42×C83—21no—
212C42×C83—21no—
213C42×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—21no—
222C23×C83—21no—
223C23×C83—21no—
224C23×C83—21no—
225C23×C83—21no—
226C23×C83—21no—
227C23×C83C2×M1612yes—
228C23×C83C23×C411yescharacteristic
229Q8×C83—44no—
230D4×C83—44no—
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—21no—
260C2×C4×C83—21no—
261C2×C4×C83—21no—
262C2×C4×C83—41no—
263C2×C4×C83—41no—
264C2×C4×C83—41no—
265C2×C4×C83—41no—
266C2×C4×C83—41no—
267C2×C4×C83—41no—
268C2×C4×C83—41no—
269C2×C4×C83—41no—
270C2×C4×C83C2×M1612yes—
271C2×C4×C83C2×M1612yes—
272C2×C4×C83#13112yes—
273C2×C4×C83#13112yes—
274C2×C4×C83#13112yes—
275C2×C4×C83C2×#4111yescharacteristic
276C2×C4×C83C2×#4111yescharacteristic
277C2×C4×C83H(5,𝔽2)11yescharacteristic
278C2×C4×C83H(5,𝔽2)11yescharacteristic
279C2×C4×C83H(5,𝔽2)11yescharacteristic
280C2×C4×C832−1+411yescharacteristic
281C8×C83—22no—
282C8×C83—22no—
283C8×C83—41no—
284C8×C83—41no—
285C8×C83—41no—
286C8×C83—41no—
287C8×C83—41no—
288C8×C83—41no—
289C22×C83—22no—
290C22×C83—22no—
291C22×C83—22no—
292C22×C83—41no—
293C22×C83—41no—
294C22×C83—41no—
295C22×C83—41no—
296C22×C83—41no—
297C22×C83—41no—
298C22×C83—41no—
299C22×C83—41no—
300C22×C83—41no—
301C22×C83—41no—
302C22×C83—41no—
303C22×C83C4×#4111yescharacteristic
304C22×C83#51811yescharacteristic
305C22×C83#52011yescharacteristic
306C22×C83C22×M1611yescharacteristic
307C22×C83C2×#13111yescharacteristic
308C22×C83C2×#13111yescharacteristic
309C22×C83C2×#13111yescharacteristic
310C4×C83—22no—
311C4×C83—22no—
312C4×C83—22no—
313C4×C83—22no—
314C4×C83—22no—
315C4×C83—41no—
316C4×C83—41no—
317C4×C83—41no—
318C4×C83—41no—
319C4×C83—41no—
320C4×C83—41no—
321C4×C83—41no—
322C4×C83#53811yescharacteristic
323C4×C83#53811yescharacteristic
324C4×C83#54211yescharacteristic
325C4×C83#54211yescharacteristic
326#22389C8311yesmaximal, characteristic, direct product factor, Sylow
327C2×C83—42no—
328C2×C83—81no—
329C2×C83#233711yescharacteristic
330C2×C83#296511yescharacteristic
331C2×C83#296611yescharacteristic
332C2×C83#297411yescharacteristic
333C2×C83#297911yescharacteristic
334C2×C83#299011yescharacteristic
335C2×C83#299411yescharacteristic
336C4×#124C2×C8311yescharacteristic
337#1985C2×C8311yescharacteristic, complemented
338#1984C2×C8311yescharacteristic, complemented
339#1924C2×C8311yescharacteristic, complemented
340#1923C2×C8311yescharacteristic, complemented
341#1923C2×C8311yescharacteristic, complemented
342#1923C2×C8311yescharacteristic, complemented
343#1870C2×C8311yescharacteristic
344#1869C2×C8311yescharacteristic
345#1851C2×C8311yescharacteristic, complemented
346#1850C2×C8311yescharacteristic, complemented
347#1839C2×C8311yescharacteristic, complemented
348C4×C4⋊C8C2×C8311yescharacteristic, complemented
349#1753C2×C8311yescharacteristic, complemented
350C8×C22⋊C4C2×C8311yescharacteristic, complemented
351C83#2238911yescharacteristic, direct product factor, Sylow
352C22×M16C22×C8311yescharacteristic
353C23×C8C22×C8311yescharacteristic
354C2×#124C4×C8311yescharacteristic
355C2×C4×Q8C22×C8311yescharacteristic
356C2×C4×D4C22×C8311yescharacteristic
357C2×C4⋊C8C22×C8311yescharacteristic
358C2×C4⋊C8C22×C8311yescharacteristic
359C2×C4⋊C8C22×C8311yescharacteristic
360C2×C4⋊C8C22×C8311yescharacteristic
361C2×C22⋊C8C22×C8311yescharacteristic
362C2×C22⋊C8C22×C8311yescharacteristic
363C2×C22⋊C8C22×C8311yescharacteristic
364C2×C22⋊C8C22×C8311yescharacteristic
365C2×C22⋊C8C22×C8311yescharacteristic
366C2×C22⋊C8C22×C8311yescharacteristic
367C2×#97C22×C8311yescharacteristic
368C2×C4×C8C22×C8311yescharacteristic
369C2×C4×C8C22×C8311yescharacteristic
370C2×C4×C8C22×C8311yescharacteristic
371#391C4×C8311yescharacteristic
372#390C4×C8311yescharacteristic
373#388C4×C8311yescharacteristic
374#388C4×C8311yescharacteristic
375#388C4×C8311yescharacteristic
376#388C4×C8311yescharacteristic
377#382C4×C8311yescharacteristic
378C4×C22⋊C4C22×C8311yescharacteristic
379C4×C22⋊C4C22×C8311yescharacteristic
380C4×C22⋊C4C22×C8311yescharacteristic
381C4×C22⋊C4C22×C8311yescharacteristic
382C43C22×C8311yescharacteristic
383#336C22×C8311yescharacteristic
384#336C22×C8311yescharacteristic
385#336C22×C8311yescharacteristic
386#336C22×C8311yescharacteristic
387#336C22×C8311yescharacteristic
388#336C22×C8311yescharacteristic
389#336C22×C8311yescharacteristic
390#336C22×C8311yescharacteristic
391#336C22×C8311yescharacteristic
392#336C22×C8311yescharacteristic
393#336C22×C8311yescharacteristic
394#336C22×C8311yescharacteristic
395C22×Q8C2×C4×C8311yescharacteristic
396C22×D4C2×C4×C8311yescharacteristic
397C23×C4C23×C8311yescharacteristic
398C23×C4C23×C8311yescharacteristic
399C2×M16—22no—
400C2×M16—41no—
401C2×M16—41no—
402C22×C8—22no—
403C22×C8—41no—
404C22×C8—41no—
405C22×C8C23×C8311yescharacteristic
406C22×C8C23×C8311yescharacteristic
407C22×C8C23×C8311yescharacteristic
408C22×C8C23×C8311yescharacteristic
409C22×C8C23×C8311yescharacteristic
410C22×C8C23×C8311yescharacteristic
411C22×C8C23×C8311yescharacteristic
412C22×C8C23×C8311yescharacteristic
413#124—24no—
414C4×Q8—41no—
415C4×Q8—41no—
416C4×D4—41no—
417C4×D4—41no—
418C2×C4⋊C4C2×C4×C8311yescharacteristic
419C2×C4⋊C4C2×C4×C8311yescharacteristic
420C2×C4⋊C4C2×C4×C8311yescharacteristic
421C2×C4⋊C4C2×C4×C8311yescharacteristic
422C2×C22⋊C4C2×C4×C8311yescharacteristic
423C2×C22⋊C4C2×C4×C8311yescharacteristic
424C2×C22⋊C4C2×C4×C8311yescharacteristic
425C2×C22⋊C4C2×C4×C8311yescharacteristic
426C2×C22⋊C4C2×C4×C8311yescharacteristic
427C2×C22⋊C4C2×C4×C8311yescharacteristic
428C2×C22⋊C4C2×C4×C8311yescharacteristic
429C2×C22⋊C4C2×C4×C8311yescharacteristic
430C2×C22⋊C4C2×C4×C8311yescharacteristic
431C2×C22⋊C4C2×C4×C8311yescharacteristic
432C2×C42C2×C4×C8311yescharacteristic
433C2×C42C2×C4×C8311yescharacteristic
434C2×C42C2×C4×C8311yescharacteristic
435C2×C42C2×C4×C8311yescharacteristic
436C2×C42C23×C8311yescharacteristic
437C2×C42C23×C8311yescharacteristic
438C2×C42C23×C8311yescharacteristic
439C2×C42C23×C8311yescharacteristic
440C2×C42C23×C8311yescharacteristic
441C4⋊C8—22no—
442C4⋊C8—22no—
443C4⋊C8—41no—
444C4⋊C8—41no—
445C22⋊C8—22no—
446C22⋊C8—22no—
447C22⋊C8—41no—
448C22⋊C8—41no—
449C22⋊C8—41no—
450C22⋊C8—41no—
451#97—41no—
452C4×C8—41no—
453C4×C8—41no—
454C4×C8—41no—
455#95C2×C4×C8311yescharacteristic
456#95C2×C4×C8311yescharacteristic
457#95C2×C4×C8311yescharacteristic
458#95C2×C4×C8311yescharacteristic
459#95C2×C4×C8311yescharacteristic
460#95C2×C4×C8311yescharacteristic
461#95C2×C4×C8311yescharacteristic
462#95C2×C4×C8311yescharacteristic
463C24C22×C4×C8311yescharacteristic
464C24C22×C4×C8311yescharacteristic
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—41no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—41no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4C22×C4×C8311yescharacteristic
484C22×C4C22×C4×C8311yescharacteristic
485C22×C4C22×C4×C8311yescharacteristic
486C22×C4C22×C4×C8311yescharacteristic
487C22×C4C22×C4×C8311yescharacteristic
488C22×C4C22×C4×C8311yescharacteristic
489C22×C4C22×C4×C8311yescharacteristic
490C22×C4C22×C4×C8311yescharacteristic
491C22×C4C22×C4×C8311yescharacteristic
492C22×C4C22×C4×C8311yescharacteristic
493C22×C4C22×C4×C8311yescharacteristic
494C22×C4C22×C4×C8311yescharacteristic
495C22×C4C24×C8311yescharacteristic
496M16—44no—
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—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—44no—
520C2×C8#41×C8312yes—
521C2×C8#41×C8312yes—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4M16×C8314yescomplemented
536C42—22no—
537C42—22no—
538C42—22no—
539C42—22no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23C2×M16×C8312yes—
564C23C23×C4×C8311yescharacteristic
565Q8—44no—
566D4—44no—
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—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4C2×M16×C8312yes—
607C2×C4C2×M16×C8312yes—
608C2×C4#131×C8312yes—
609C2×C4#131×C8312yes—
610C2×C4#131×C8312yes—
611C2×C4C2×#41×C8311yescharacteristic
612C2×C4C2×#41×C8311yescharacteristic
613C2×C4H(5,𝔽2)×C8311yescharacteristic
614C2×C4H(5,𝔽2)×C8311yescharacteristic
615C2×C4H(5,𝔽2)×C8311yescharacteristic
616C2×C42−1+4×C8311yescharacteristic
617C8—22no—
618C8—22no—
619C8—41no—
620C8—41no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C4×#41×C8311yescharacteristic
640C22#518×C8311yescharacteristic
641C22#520×C8311yescharacteristic
642C22C22×M16×C8311yescharacteristic
643C22C2×#131×C8311yescharacteristic
644C22C2×#131×C8311yescharacteristic
645C22C2×#131×C8311yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—22no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4#538×C8311yescharacteristic
659C4#538×C8311yescharacteristic
660C4#542×C8311yescharacteristic
661C4#542×C8311yescharacteristic
662C2—42no—
663C2—81no—
664C2C83×#233711yescharacteristic
665C2C83×#296511yescharacteristic
666C2C83×#296611yescharacteristic
667C2C83×#297411yescharacteristic
668C2C83×#297911yescharacteristic
669C2C83×#299011yescharacteristic
670C2C83×#299411yescharacteristic
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
2. C83×#1985C2semidirect
3. C83×#1984C2semidirect
4. C83×#1924C2semidirect
5. C83×#1923C2semidirect
6. C83×#1923C2semidirect
7. C83×#1923C2semidirect
10. C83×#1851C2semidirect
11. C83×#1850C2semidirect
12. C83×#1839C2semidirect
13. C4×C4⋊C8×C83C2semidirect
14. C83×#1753C2semidirect
15. C8×C22⋊C4×C83C2semidirect
199. C22⋊C4×C83M16semidirect
326. #22389C83direct (N × H)
337. #1985C2×C83semidirect
338. #1984C2×C83semidirect
339. #1924C2×C83semidirect
340. #1923C2×C83semidirect
341. #1923C2×C83semidirect
342. #1923C2×C83semidirect
345. #1851C2×C83semidirect
346. #1850C2×C83semidirect
347. #1839C2×C83semidirect
348. C4×C4⋊C8C2×C83semidirect
349. #1753C2×C83semidirect
350. C8×C22⋊C4C2×C83semidirect
351. C83#22389direct (N × H)
535. C22⋊C4M16×C83semidirect

Maximal subgroups

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

subgroupindex
C4×#124×C832
C83×#19852
C83×#19842
C83×#19242
C83×#19232
C83×#18702
C83×#18692
C83×#18512
C83×#18502
C83×#18392
C4×C4⋊C8×C832
C83×#17532
C8×C22⋊C4×C832
#2238983