Finite Group Databasebeta

← C4×#548×C83 #35261982

Subgroups — C4×#548×C83 #35261982

Order 21248.

3232 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C83C211yesmaximal, characteristic
2C2×C4×#41×C83C211yesmaximal, characteristic, complemented
3C22×C4×Q8×C83C211yesmaximal, characteristic, complemented
4C83×#2367C213yesmaximal, complemented
5C83×#2362C213yesmaximal, complemented
6C83×#2361C213yesmaximal, complemented
7C83×#2352C213yesmaximal, complemented
8C83×#2351C211yesmaximal, characteristic, complemented
9C83×#2341C211yesmaximal, characteristic, complemented
10Q8×C22⋊C4×C83C211yesmaximal, characteristic, complemented
11C4×#124×C83C213yesmaximal, complemented
12C4×C22⋊Q8×C83C213yesmaximal, complemented
13C4×#121×C83C213yesmaximal, complemented
14C42×Q8×C83C211yesmaximal, characteristic, complemented
15C42×D4×C83C213yesmaximal, complemented
16C22×#41×C83C2211yescharacteristic
17C23×Q8×C83C2211yescharacteristic
18#548×C83C4116yesdirect product factor
19C2×#124×C83C2213yes—
20C2×C22⋊Q8×C83C2213yes—
21C2×#121×C83C2213yes—
22C4×#41×C83—28no—
23C2×C4×Q8×C83—28no—
24C2×C4×Q8×C83C2211yescharacteristic
25C2×C4×Q8×C83C2213yes—
26C2×C4×Q8×C83C2211yescharacteristic
27C2×C4×Q8×C83C2211yescharacteristic
28C2×C4×Q8×C83C2213yes—
29C2×C4×Q8×C83C2211yescharacteristic
30C2×C4×Q8×C83C2211yescharacteristic
31C2×C4×D4×C83C2213yes—
32C2×C4×D4×C83C2213yes—
33C2×C4×D4×C83C2213yes—
34C2×C4×D4×C83C2213yes—
35C2×C4×D4×C83C2213yes—
36C2×#117×C83C2213yes—
37C22×C4⋊C4×C83C2213yes—
38C22×C42×C83C2213yes—
39C22×C42×C83C2213yes—
40#391×C83C2213yes—
41#391×C83C2213yes—
42#390×C83C2213yes—
43#390×C83C2213yes—
44#389×C83C2213yes—
45#389×C83C2213yes—
46#388×C83C2216yes—
47#388×C83C2216yes—
48#388×C83C2216yes—
49#387×C83C2216yes—
50#386×C83C2216yes—
51#385×C83C2216yes—
52#382×C83C2213yes—
53#380×C83C2213yes—
54#380×C83C2213yes—
55C4×C4⋊C4×C83C2213yes—
56C4×C4⋊C4×C83C2213yes—
57C4×C4⋊C4×C83C2213yes—
58C4×C4⋊C4×C83C2213yes—
59C4×C4⋊C4×C83C2213yes—
60C4×C4⋊C4×C83C2213yes—
61C4×C22⋊C4×C83C2211yescharacteristic
62C4×C22⋊C4×C83C2213yes—
63C4×C22⋊C4×C83C2213yes—
64C4×C22⋊C4×C83C2213yes—
65C4×C22⋊C4×C83C2213yes—
66C4×C22⋊C4×C83C2213yes—
67C4×C22⋊C4×C83C2216yes—
68C43×C83C2213yes—
69C2×#41×C83—24no—
70C2×#41×C83—24no—
71C2×#41×C83C2×C418yescomplemented
72C22×Q8×C83—24no—
73C22×Q8×C83—24no—
74C22×Q8×C83C2×C418yescomplemented
75C22×Q8×C83C2313yes—
76C22×Q8×C83C2311yescharacteristic
77C22×D4×C83C2313yes—
78C22×D4×C83C2313yes—
79C23×C4×C83C2313yes—
80C23×C4×C83C2313yes—
81C23×C4×C83C2313yes—
82C23×C4×C83C2313yes—
83C23×C4×C83C2313yes—
84C23×C4×C83C2311yescharacteristic
85#124×C83C2×C4124yescomplemented
86C22⋊Q8×C83C2×C4124yescomplemented
87#121×C83C2×C4124yescomplemented
88C4×Q8×C83—24no—
89C4×Q8×C83—24no—
90C4×Q8×C83—24no—
91C4×Q8×C83—212no—
92C4×Q8×C83—212no—
93C4×Q8×C83C2×C418yescomplemented
94C4×Q8×C83D418yescomplemented
95C4×D4×C83—212no—
96C4×D4×C83—212no—
97C4×D4×C83—212no—
98C4×D4×C83—212no—
99C4×D4×C83C2×C4124yescomplemented
100#117×C83—212no—
101C2×C4⋊C4×C83—212no—
102C2×C4⋊C4×C83C2313yes—
103C2×C4⋊C4×C83C2316yes—
104C2×C4⋊C4×C83C2313yes—
105C2×C4⋊C4×C83C2313yes—
106C2×C4⋊C4×C83C2313yes—
107C2×C4⋊C4×C83C2313yes—
108C2×C4⋊C4×C83C2313yes—
109C2×C4⋊C4×C83C2313yes—
110C2×C4⋊C4×C83C2313yes—
111C2×C22⋊C4×C83C2316yes—
112C2×C22⋊C4×C83C2313yes—
113C2×C22⋊C4×C83C2313yes—
114C2×C22⋊C4×C83C2313yes—
115C2×C22⋊C4×C83C2316yes—
116C2×C22⋊C4×C83C2311yescharacteristic
117C2×C22⋊C4×C83C2313yes—
118C2×C22⋊C4×C83C2316yes—
119C2×C22⋊C4×C83C2311yescharacteristic
120C2×C42×C83—212no—
121C2×C42×C83—212no—
122C2×C42×C83C2313yes—
123C2×C42×C83C2313yes—
124C2×C42×C83C2313yes—
125C2×C42×C83C2313yes—
126C2×C42×C83C2313yes—
127C2×C42×C83C2313yes—
128C2×C42×C83C2311yescharacteristic
129C2×C42×C83C2313yes—
130C2×C42×C83C2313yes—
131C2×C42×C83C2311yescharacteristic
132C2×C42×C83C2313yes—
133C2×C42×C83C2313yes—
134C2×C42×C83C2313yes—
135#95×C83C2311yescharacteristic
136#95×C83C2311yescharacteristic
137#95×C83C2313yes—
138#95×C83C2313yes—
139#95×C83C2313yes—
140#95×C83C2313yes—
141#95×C83C2316yes—
142#95×C83C2316yes—
143#95×C83C2316yes—
144C24×C83C2413yes—
145C24×C83C2411yescharacteristic
146#41×C83—232no—
147C2×Q8×C83—232no—
148C2×Q8×C83—26no—
149C2×Q8×C83—26no—
150C2×Q8×C83C22×C4112yes—
151C2×Q8×C83C22×C414yes—
152C2×Q8×C83C2×D414yes—
153C2×Q8×C83#4114yes—
154C2×D4×C83—26no—
155C2×D4×C83—26no—
156C2×D4×C83—26no—
157C2×D4×C83—26no—
158C2×D4×C83C22×C4112yes—
159C2×D4×C83C22×C4112yes—
160C22×C4×C83—22no—
161C22×C4×C83—26no—
162C22×C4×C83—26no—
163C22×C4×C83—26no—
164C22×C4×C83—26no—
165C22×C4×C83—22no—
166C22×C4×C83—26no—
167C22×C4×C83—26no—
168C22×C4×C83—26no—
169C22×C4×C83—26no—
170C22×C4×C83—26no—
171C22×C4×C83—26no—
172C22×C4×C83—26no—
173C22×C4×C83—43no—
174C22×C4×C83—43no—
175C22×C4×C83C22×C4112yes—
176C22×C4×C83C22×C4112yes—
177C22×C4×C83#4114yescomplemented
178C22×C4×C83C2413yes—
179C22×C4×C83C2413yes—
180C22×C4×C83C2413yes—
181C22×C4×C83C2411yescharacteristic
182C22×C4×C83C2411yescharacteristic
183C22×C4×C83C2413yes—
184C22×C4×C83C2413yes—
185C22×C4×C83C2413yes—
186C22×C4×C83C2411yescharacteristic
187C22×C4×C83C2411yescharacteristic
188C22×C4×C83C2411yescharacteristic
189C22×C4×C83C2413yes—
190C22×C4×C83C2411yescharacteristic
191C4⋊C4×C83—212no—
192C4⋊C4×C83—26no—
193C4⋊C4×C83—26no—
194C4⋊C4×C83—26no—
195C4⋊C4×C83—26no—
196C4⋊C4×C83—26no—
197C4⋊C4×C83C22×C4112yes—
198C4⋊C4×C83C22×C4112yes—
199C4⋊C4×C83C2×D4112yes—
200C22⋊C4×C83—26no—
201C22⋊C4×C83—212no—
202C22⋊C4×C83—26no—
203C22⋊C4×C83—26no—
204C22⋊C4×C83—46no—
205C22⋊C4×C83C22×C414yes—
206C22⋊C4×C83C22×C4112yes—
207C22⋊C4×C83C22×C4124yes—
208C22⋊C4×C83#4114yescomplemented
209C42×C83—22no—
210C42×C83—26no—
211C42×C83—26no—
212C42×C83—26no—
213C42×C83—26no—
214C42×C83—26no—
215C42×C83—26no—
216C42×C83—26no—
217C42×C83—26no—
218C42×C83—22no—
219C42×C83—43no—
220C42×C83C22×C4112yes—
221C42×C83C2×D4112yes—
222C23×C83—21no—
223C23×C83—21no—
224C23×C83—21no—
225C23×C83—21no—
226C23×C83—23no—
227C23×C83—23no—
228C23×C83—23no—
229C23×C83—23no—
230C23×C83—23no—
231C23×C83—23no—
232C23×C83C23×C416yes—
233C23×C83C23×C412yes—
234C23×C83C2×#4112yes—
235C23×C83C2×#4112yes—
236C23×C83C2511yescharacteristic
237Q8×C83—224no—
238Q8×C83C4×D4116yescomplemented
239D4×C83—224no—
240D4×C83—224no—
241C2×C4×C83—21no—
242C2×C4×C83—21no—
243C2×C4×C83—21no—
244C2×C4×C83—23no—
245C2×C4×C83—21no—
246C2×C4×C83—23no—
247C2×C4×C83—23no—
248C2×C4×C83—23no—
249C2×C4×C83—21no—
250C2×C4×C83—23no—
251C2×C4×C83—21no—
252C2×C4×C83—21no—
253C2×C4×C83—21no—
254C2×C4×C83—21no—
255C2×C4×C83—23no—
256C2×C4×C83—21no—
257C2×C4×C83—224no—
258C2×C4×C83—224no—
259C2×C4×C83—28no—
260C2×C4×C83—23no—
261C2×C4×C83—23no—
262C2×C4×C83—23no—
263C2×C4×C83—23no—
264C2×C4×C83—23no—
265C2×C4×C83—23no—
266C2×C4×C83—23no—
267C2×C4×C83—23no—
268C2×C4×C83—23no—
269C2×C4×C83—412no—
270C2×C4×C83—412no—
271C2×C4×C83—412no—
272C2×C4×C83C23×C412yes—
273C2×C4×C83C23×C416yes—
274C2×C4×C83C23×C416yes—
275C2×C4×C83C23×C412yes—
276C2×C4×C83C23×C416yes—
277C2×C4×C83C22×D416yes—
278C2×C4×C83C22×D416yes—
279C2×C4×C83C22×D412yes—
280C2×C4×C83C2×#4112yes—
281C2×C4×C83C2×#4112yes—
282C2×C4×C83C2×#4112yes—
283C2×C4×C83C2×#4116yes—
284C2×C4×C83C2×#4112yes—
285C2×C4×C832−1+412yes—
286C22×C83—22no—
287C22×C83—22no—
288C22×C83—22no—
289C22×C83—22no—
290C22×C83—22no—
291C22×C83—22no—
292C22×C83—26no—
293C22×C83—26no—
294C22×C83—26no—
295C22×C83—43no—
296C22×C83—43no—
297C22×C83—43no—
298C22×C83—43no—
299C22×C83C4×#4114yescomplemented
300C22×C83C24×C411yescharacteristic
301C22×C83C23×D411yescharacteristic
302C22×C83C22×#4111yescharacteristic
303C22×C83C22×#4111yescharacteristic
304C22×C83C22×#4111yescharacteristic
305C22×C83C2×2−1+411yescharacteristic
306C22×C83#58511yescharacteristic
307C4×C83—22no—
308C4×C83—26no—
309C4×C83—26no—
310C4×C83—22no—
311C4×C83—22no—
312C4×C83—22no—
313C4×C83—26no—
314C4×C83—22no—
315C4×C83—43no—
316C4×C83—43no—
317C4×C83—43no—
318C4×C83C2×C4×D4112yes—
319C4×C83#54814yesdirect product factor
320C4×#548C8311yesmaximal, characteristic, direct product factor, Sylow
321C2×C83—24no—
322C2×C83—46no—
323C2×C83C22×C4×D411yescharacteristic
324C2×C83C2×C4×#4111yescharacteristic
325C2×C83C4×2−1+411yescharacteristic
326C2×C83C2×#54811yescharacteristic
327C2×C83D4×#4111yescharacteristic
328C2×C83#348011yescharacteristic
329C2×C83#348211yescharacteristic
330C2×#548C2×C8311yescharacteristic
331C2×C4×#41C2×C8311yescharacteristic, complemented
332C22×C4×Q8C2×C8311yescharacteristic, complemented
333#2367C2×C8313yescomplemented
334#2362C2×C8313yescomplemented
335#2361C2×C8313yescomplemented
336#2352C2×C8313yescomplemented
337#2351C2×C8311yescharacteristic, complemented
338#2341C2×C8311yescharacteristic, complemented
339Q8×C22⋊C4C2×C8311yescharacteristic, complemented
340C4×#124C2×C8313yescomplemented
341C4×C22⋊Q8C2×C8313yescomplemented
342C4×#121C2×C8313yescomplemented
343C42×Q8C2×C8311yescharacteristic, complemented
344C42×D4C2×C8313yescomplemented
345C83C4×#54811yescharacteristic, direct product factor, Sylow
346C22×#41C22×C8311yescharacteristic
347C23×Q8C22×C8311yescharacteristic
348#548C4×C83116yesdirect product factor
349C2×#124C22×C8313yes—
350C2×C22⋊Q8C22×C8313yes—
351C2×#121C22×C8313yes—
352C4×#41—28no—
353C2×C4×Q8—28no—
354C2×C4×Q8C22×C8311yescharacteristic
355C2×C4×Q8C22×C8311yescharacteristic
356C2×C4×Q8C22×C8311yescharacteristic
357C2×C4×Q8C22×C8313yes—
358C2×C4×Q8C22×C8313yes—
359C2×C4×Q8C22×C8311yescharacteristic
360C2×C4×Q8C22×C8311yescharacteristic
361C2×C4×D4C22×C8313yes—
362C2×C4×D4C22×C8313yes—
363C2×C4×D4C22×C8313yes—
364C2×C4×D4C22×C8313yes—
365C2×C4×D4C22×C8313yes—
366C2×#117C22×C8313yes—
367C22×C4⋊C4C22×C8313yes—
368C22×C42C22×C8313yes—
369C22×C42C22×C8313yes—
370#391C22×C8313yes—
371#391C22×C8313yes—
372#390C22×C8313yes—
373#390C22×C8313yes—
374#389C22×C8313yes—
375#389C22×C8313yes—
376#388C22×C8316yes—
377#388C22×C8316yes—
378#388C22×C8316yes—
379#387C22×C8316yes—
380#386C22×C8316yes—
381#385C22×C8316yes—
382#382C22×C8313yes—
383#380C22×C8313yes—
384#380C22×C8313yes—
385C4×C4⋊C4C22×C8313yes—
386C4×C4⋊C4C22×C8313yes—
387C4×C4⋊C4C22×C8313yes—
388C4×C4⋊C4C22×C8313yes—
389C4×C4⋊C4C22×C8313yes—
390C4×C4⋊C4C22×C8313yes—
391C4×C22⋊C4C22×C8313yes—
392C4×C22⋊C4C22×C8313yes—
393C4×C22⋊C4C22×C8313yes—
394C4×C22⋊C4C22×C8313yes—
395C4×C22⋊C4C22×C8311yescharacteristic
396C4×C22⋊C4C22×C8313yes—
397C4×C22⋊C4C22×C8316yes—
398C43C22×C8313yes—
399C2×#41—24no—
400C2×#41—24no—
401C2×#41C2×C4×C8318yescomplemented
402C22×Q8—24no—
403C22×Q8—24no—
404C22×Q8C2×C4×C8318yescomplemented
405C22×Q8C23×C8313yes—
406C22×Q8C23×C8311yescharacteristic
407C22×D4C23×C8313yes—
408C22×D4C23×C8313yes—
409C23×C4C23×C8313yes—
410C23×C4C23×C8313yes—
411C23×C4C23×C8313yes—
412C23×C4C23×C8313yes—
413C23×C4C23×C8313yes—
414C23×C4C23×C8311yescharacteristic
415#124C2×C4×C83124yescomplemented
416C22⋊Q8C2×C4×C83124yescomplemented
417#121C2×C4×C83124yescomplemented
418C4×Q8—24no—
419C4×Q8—24no—
420C4×Q8—24no—
421C4×Q8—212no—
422C4×Q8—212no—
423C4×Q8C2×C4×C8318yescomplemented
424C4×Q8D4×C8318yescomplemented
425C4×D4—212no—
426C4×D4—212no—
427C4×D4—212no—
428C4×D4—212no—
429C4×D4C2×C4×C83124yescomplemented
430#117—212no—
431C2×C4⋊C4—212no—
432C2×C4⋊C4C23×C8313yes—
433C2×C4⋊C4C23×C8316yes—
434C2×C4⋊C4C23×C8313yes—
435C2×C4⋊C4C23×C8313yes—
436C2×C4⋊C4C23×C8313yes—
437C2×C4⋊C4C23×C8313yes—
438C2×C4⋊C4C23×C8313yes—
439C2×C4⋊C4C23×C8313yes—
440C2×C4⋊C4C23×C8313yes—
441C2×C22⋊C4C23×C8316yes—
442C2×C22⋊C4C23×C8313yes—
443C2×C22⋊C4C23×C8313yes—
444C2×C22⋊C4C23×C8313yes—
445C2×C22⋊C4C23×C8316yes—
446C2×C22⋊C4C23×C8311yescharacteristic
447C2×C22⋊C4C23×C8313yes—
448C2×C22⋊C4C23×C8316yes—
449C2×C22⋊C4C23×C8311yescharacteristic
450C2×C42—212no—
451C2×C42—212no—
452C2×C42C23×C8313yes—
453C2×C42C23×C8313yes—
454C2×C42C23×C8313yes—
455C2×C42C23×C8313yes—
456C2×C42C23×C8313yes—
457C2×C42C23×C8313yes—
458C2×C42C23×C8313yes—
459C2×C42C23×C8313yes—
460C2×C42C23×C8311yescharacteristic
461C2×C42C23×C8311yescharacteristic
462C2×C42C23×C8313yes—
463C2×C42C23×C8313yes—
464C2×C42C23×C8313yes—
465#95C23×C8311yescharacteristic
466#95C23×C8311yescharacteristic
467#95C23×C8313yes—
468#95C23×C8313yes—
469#95C23×C8313yes—
470#95C23×C8313yes—
471#95C23×C8316yes—
472#95C23×C8316yes—
473#95C23×C8316yes—
474C24C24×C8313yes—
475C24C24×C8311yescharacteristic
476#41—232no—
477C2×Q8—232no—
478C2×Q8—26no—
479C2×Q8—26no—
480C2×Q8C22×C4×C83112yes—
481C2×Q8C22×C4×C8314yes—
482C2×Q8C2×D4×C8314yes—
483C2×Q8#41×C8314yes—
484C2×D4—26no—
485C2×D4—26no—
486C2×D4—26no—
487C2×D4—26no—
488C2×D4C22×C4×C83112yes—
489C2×D4C22×C4×C83112yes—
490C22×C4—22no—
491C22×C4—26no—
492C22×C4—26no—
493C22×C4—26no—
494C22×C4—26no—
495C22×C4—22no—
496C22×C4—26no—
497C22×C4—26no—
498C22×C4—26no—
499C22×C4—26no—
500C22×C4—26no—
501C22×C4—26no—
502C22×C4—26no—
503C22×C4—43no—
504C22×C4—43no—
505C22×C4C22×C4×C83112yes—
506C22×C4C22×C4×C83112yes—
507C22×C4#41×C8314yescomplemented
508C22×C4C24×C8313yes—
509C22×C4C24×C8313yes—
510C22×C4C24×C8313yes—
511C22×C4C24×C8311yescharacteristic
512C22×C4C24×C8311yescharacteristic
513C22×C4C24×C8313yes—
514C22×C4C24×C8313yes—
515C22×C4C24×C8313yes—
516C22×C4C24×C8311yescharacteristic
517C22×C4C24×C8311yescharacteristic
518C22×C4C24×C8311yescharacteristic
519C22×C4C24×C8313yes—
520C22×C4C24×C8311yescharacteristic
521C4⋊C4—212no—
522C4⋊C4—26no—
523C4⋊C4—26no—
524C4⋊C4—26no—
525C4⋊C4—26no—
526C4⋊C4—26no—
527C4⋊C4C22×C4×C83112yes—
528C4⋊C4C22×C4×C83112yes—
529C4⋊C4C2×D4×C83112yes—
530C22⋊C4—26no—
531C22⋊C4—212no—
532C22⋊C4—26no—
533C22⋊C4—26no—
534C22⋊C4—46no—
535C22⋊C4C22×C4×C8314yes—
536C22⋊C4C22×C4×C83112yes—
537C22⋊C4C22×C4×C83124yes—
538C22⋊C4#41×C8314yescomplemented
539C42—22no—
540C42—26no—
541C42—26no—
542C42—26no—
543C42—26no—
544C42—26no—
545C42—26no—
546C42—26no—
547C42—26no—
548C42—22no—
549C42—43no—
550C42C22×C4×C83112yes—
551C42C2×D4×C83112yes—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—23no—
557C23—23no—
558C23—23no—
559C23—23no—
560C23—23no—
561C23—23no—
562C23C23×C4×C8316yes—
563C23C23×C4×C8312yes—
564C23C2×#41×C8312yes—
565C23C2×#41×C8312yes—
566C23C25×C8311yescharacteristic
567Q8—224no—
568Q8C4×D4×C83116yescomplemented
569D4—224no—
570D4—224no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—23no—
575C2×C4—21no—
576C2×C4—23no—
577C2×C4—23no—
578C2×C4—23no—
579C2×C4—21no—
580C2×C4—23no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—23no—
586C2×C4—21no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—28no—
590C2×C4—23no—
591C2×C4—23no—
592C2×C4—23no—
593C2×C4—23no—
594C2×C4—23no—
595C2×C4—23no—
596C2×C4—23no—
597C2×C4—23no—
598C2×C4—23no—
599C2×C4—412no—
600C2×C4—412no—
601C2×C4—412no—
602C2×C4C23×C4×C8312yes—
603C2×C4C23×C4×C8316yes—
604C2×C4C23×C4×C8316yes—
605C2×C4C23×C4×C8312yes—
606C2×C4C23×C4×C8316yes—
607C2×C4C22×D4×C8316yes—
608C2×C4C22×D4×C8316yes—
609C2×C4C22×D4×C8312yes—
610C2×C4C2×#41×C8312yes—
611C2×C4C2×#41×C8312yes—
612C2×C4C2×#41×C8312yes—
613C2×C4C2×#41×C8316yes—
614C2×C4C2×#41×C8312yes—
615C2×C42−1+4×C8312yes—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—26no—
623C22—26no—
624C22—26no—
625C22—43no—
626C22—43no—
627C22—43no—
628C22—43no—
629C22C4×#41×C8314yescomplemented
630C22C24×C4×C8311yescharacteristic
631C22C23×D4×C8311yescharacteristic
632C22C22×#41×C8311yescharacteristic
633C22C22×#41×C8311yescharacteristic
634C22C22×#41×C8311yescharacteristic
635C22C2×2−1+4×C8311yescharacteristic
636C22#585×C8311yescharacteristic
637C4—22no—
638C4—26no—
639C4—26no—
640C4—22no—
641C4—22no—
642C4—22no—
643C4—26no—
644C4—22no—
645C4—43no—
646C4—43no—
647C4—43no—
648C4C2×C4×D4×C83112yes—
649C4#548×C8314yesdirect product factor
650C2—24no—
651C2—46no—
652C2C22×C4×D4×C8311yescharacteristic
653C2C2×C4×#41×C8311yescharacteristic
654C2C4×2−1+4×C8311yescharacteristic
655C2C2×#548×C8311yescharacteristic
656C2D4×#41×C8311yescharacteristic
657C2C83×#348011yescharacteristic
658C2C83×#348211yescharacteristic
subgroupG/H
centerC22×C4×C83C24
commutatorC22C24×C4×C83
Frattini, cosocleC23C25×C83
socleC23×C83C25
prime radicalC2×#548×C83C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×#41×C83C2semidirect
3. C22×C4×Q8×C83C2semidirect
4. C83×#2367C2semidirect
5. C83×#2362C2semidirect
6. C83×#2361C2semidirect
7. C83×#2352C2semidirect
8. C83×#2351C2semidirect
9. C83×#2341C2semidirect
10. Q8×C22⋊C4×C83C2semidirect
11. C4×#124×C83C2semidirect
12. C4×C22⋊Q8×C83C2semidirect
13. C4×#121×C83C2semidirect
14. C42×Q8×C83C2semidirect
15. C42×D4×C83C2semidirect
18. #548×C83C4direct (N × H)
71. C2×#41×C83C2×C4semidirect
74. C22×Q8×C83C2×C4semidirect
85. #124×C83C2×C4semidirect
86. C22⋊Q8×C83C2×C4semidirect
87. #121×C83C2×C4semidirect
93. C4×Q8×C83C2×C4semidirect
94. C4×Q8×C83D4semidirect
99. C4×D4×C83C2×C4semidirect
177. C22×C4×C83#41semidirect
208. C22⋊C4×C83#41semidirect
238. Q8×C83C4×D4semidirect
299. C22×C83C4×#41semidirect
319. C4×C83#548direct (N × H)
320. C4×#548C83direct (N × H)
331. C2×C4×#41C2×C83semidirect
332. C22×C4×Q8C2×C83semidirect
333. #2367C2×C83semidirect
334. #2362C2×C83semidirect
335. #2361C2×C83semidirect
336. #2352C2×C83semidirect
337. #2351C2×C83semidirect
338. #2341C2×C83semidirect
339. Q8×C22⋊C4C2×C83semidirect
340. C4×#124C2×C83semidirect
341. C4×C22⋊Q8C2×C83semidirect
342. C4×#121C2×C83semidirect
343. C42×Q8C2×C83semidirect
344. C42×D4C2×C83semidirect
345. C83C4×#548direct (N × H)
348. #548C4×C83direct (N × H)
401. C2×#41C2×C4×C83semidirect
404. C22×Q8C2×C4×C83semidirect
415. #124C2×C4×C83semidirect
416. C22⋊Q8C2×C4×C83semidirect
417. #121C2×C4×C83semidirect
423. C4×Q8C2×C4×C83semidirect
424. C4×Q8D4×C83semidirect
429. C4×D4C2×C4×C83semidirect
507. C22×C4#41×C83semidirect
538. C22⋊C4#41×C83semidirect
568. Q8C4×D4×C83semidirect
629. C22C4×#41×C83semidirect
649. C4#548×C83direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#548×C832
C2×C4×#41×C832
C22×C4×Q8×C832
C83×#23672
C83×#23622
C83×#23612
C83×#23522
C83×#23512
C83×#23412
Q8×C22⋊C4×C832
C4×#124×C832
C4×C22⋊Q8×C832
C4×#121×C832
C42×Q8×C832
C42×D4×C832
C4×#54883