Finite Group Databasebeta

← #35325849

Subgroups — #35325849

Order 21248.

1662 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127566C211yesmaximal, characteristic
2C2×C4⋊C4×Dic83C211yesmaximal, characteristic
3C2×C4⋊C4×Dic83C211yesmaximal, characteristic
4C2×C4×Dic83⋊C4C211yesmaximal, characteristic
5C2×C4×C4⋊Dic83C211yesmaximal, characteristic
6#24905698C212yesmaximal
7#24905694C212yesmaximal
8#24905692C211yesmaximal, characteristic
9#24905687C212yesmaximal
10#95×Dic83C212yesmaximal
11C83×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic83C2211yescharacteristic
13C22×C4⋊Dic83C2211yescharacteristic
14C22×Dic83⋊C4C2211yescharacteristic
15C22×Dic83⋊C4C2211yescharacteristic
16C22×C4×Dic83C2212yes—
17C22×C4×Dic83C2212yes—
18C22×C4×Dic83C2211yescharacteristic
19C22×C4×Dic83C2212yes—
20C22×C4×Dic83C2211yescharacteristic
21#19127566C418yescomplemented
22C4⋊C4×Dic83—24no—
23C4⋊C4×Dic83C418yescomplemented
24C4×Dic83⋊C4C418yescomplemented
25C4×C4⋊Dic83—24no—
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2211yescharacteristic
33C2×C83⋊#95C2211yescharacteristic
34C2×C83⋊#95C2212yes—
35C22×C4⋊C4×C83C2211yescharacteristic
36C22×C4⋊C4×C83C2211yescharacteristic
37C22×C42×C83C2211yescharacteristic
38C2×#95×C83C2212yes—
39C2×#95×C83C2212yes—
40C23×Dic83C2311yescharacteristic
41C23×Dic83C2312yes—
42C23×Dic83C2311yescharacteristic
43C23×Dic83C2311yescharacteristic
44C23×Dic83C2312yes—
45C23×Dic83C2311yescharacteristic
46C2×C4⋊Dic83—22no—
47C2×C4⋊Dic83—22no—
48C2×C4⋊Dic83C2×C414yes—
49C2×C4⋊Dic83C2×C414yes—
50C2×C4⋊Dic83D414yes—
51C2×C4⋊Dic83Q814yes—
52C2×Dic83⋊C4—22no—
53C2×Dic83⋊C4—22no—
54C2×Dic83⋊C4—22no—
55C2×Dic83⋊C4—22no—
56C2×Dic83⋊C4C2×C414yes—
57C2×Dic83⋊C4C2×C414yes—
58C2×C4×Dic83—24no—
59C2×C4×Dic83—24no—
60C2×C4×Dic83—24no—
61C2×C4×Dic83—22no—
62C2×C4×Dic83—22no—
63C2×C4×Dic83—24no—
64C2×C4×Dic83—42no—
65C2×C4×Dic83—42no—
66C2×C4×Dic83—42no—
67C2×C4×Dic83—42no—
68C2×C4×Dic83C2×C414yes—
69C2×C4×Dic83C2×C418yes—
70C2×C4×Dic83C2×C414yes—
71C2×C4×Dic83C2×C414yes—
72C2×C4×Dic83C2×C414yes—
73C83⋊#95—24no—
74C83⋊#95—24no—
75C83⋊#95—24no—
76C83⋊#95—42no—
77C83⋊#95C2×C414yes—
78C83⋊#95C2×C414yes—
79C83⋊#95C2×C418yes—
80C83⋊#95C2×C418yes—
81C83⋊#95C2×C418yes—
82C23×C4×C83C2311yescharacteristic
83C23×C4×C83C2312yes—
84C23×C4×C83C2312yes—
85C23×C4×C83C2311yescharacteristic
86C23×C4×C83C2311yescharacteristic
87C2×C4⋊C4×C83—22no—
88C2×C4⋊C4×C83—22no—
89C2×C4⋊C4×C83—22no—
90C2×C4⋊C4×C83—22no—
91C2×C4⋊C4×C83C2×C414yes—
92C2×C4⋊C4×C83C2×C414yes—
93C2×C42×C83—22no—
94C2×C42×C83—22no—
95C2×C42×C83C2×C414yes—
96#95×C83—24no—
97#95×C83—42no—
98C22×Dic83—21no—
99C22×Dic83—22no—
100C22×Dic83—21no—
101C22×Dic83—22no—
102C22×Dic83—21no—
103C22×Dic83—21no—
104C22×Dic83—21no—
105C22×Dic83—21no—
106C22×Dic83—21no—
107C22×Dic83—22no—
108C22×Dic83—21no—
109C22×Dic83—21no—
110C22×Dic83—22no—
111C22×Dic83—21no—
112C22×Dic83—21no—
113C22×Dic83—21no—
114C22×Dic83—21no—
115C22×Dic83—22no—
116C22×Dic83—22no—
117C22×Dic83—21no—
118C22×Dic83—22no—
119C22×Dic83—21no—
120C22×Dic83—21no—
121C22×Dic83—22no—
122C22×Dic83—21no—
123C22×Dic83—22no—
124C22×Dic83—21no—
125C22×Dic83—22no—
126C22×Dic83C22×C414yes—
127C22×Dic83C22×C412yes—
128C22×Dic83C22×C412yes—
129C22×Dic83C22×C412yes—
130C22×Dic83C22×C412yes—
131C22×Dic83C22×C412yes—
132C22×Dic83C22×C412yes—
133C22×Dic83C22×C412yes—
134C22×Dic83C22×C414yes—
135C22×Dic83C22×C412yes—
136C22×Dic83C2×D414yes—
137C22×Dic83C2×Q814yes—
138C22×Dic83#4112yes—
139C22×Dic83#4112yes—
140C4⋊Dic83—28no—
141C4⋊Dic83C4⋊C4116yescomplemented
142Dic83⋊C4—28no—
143Dic83⋊C4—28no—
144C4×Dic83—28no—
145C4×Dic83—48no—
146C4×Dic83—48no—
147C4×Dic83—48no—
148C4×Dic83C42116yescomplemented
149C24×C83C2411yescharacteristic
150C22×C4×C83—21no—
151C22×C4×C83—21no—
152C22×C4×C83—21no—
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—22no—
156C22×C4×C83—22no—
157C22×C4×C83—22no—
158C22×C4×C83—21no—
159C22×C4×C83—22no—
160C22×C4×C83—22no—
161C22×C4×C83—22no—
162C22×C4×C83—22no—
163C22×C4×C83—22no—
164C22×C4×C83—21no—
165C22×C4×C83—21no—
166C22×C4×C83—21no—
167C22×C4×C83—22no—
168C22×C4×C83—22no—
169C22×C4×C83—22no—
170C22×C4×C83—22no—
171C22×C4×C83—21no—
172C22×C4×C83C22×C412yes—
173C22×C4×C83C22×C414yes—
174C22×C4×C83C22×C414yes—
175C22×C4×C83C22×C412yes—
176C22×C4×C83C22×C412yes—
177C22×C4×C83C22×C412yes—
178C22×C4×C83C22×C412yes—
179C22×C4×C83C2×D412yes—
180C22×C4×C83C2×Q812yes—
181C22×C4×C83#4112yes—
182C22×C4×C83#4112yes—
183C22×C4×C83#4112yes—
184C22×C4×C83#4112yes—
185C4⋊C4×C83—28no—
186C4⋊C4×C83—28no—
187C42×C83—28no—
188C23×C83C23×C411yescharacteristic
189C23×C83C23×C411yescharacteristic
190C23×C83C23×C411yescharacteristic
191C23×C83C22×D411yescharacteristic
192C23×C83C22×Q811yescharacteristic
193C23×C83C2×#4111yescharacteristic
194C23×C83C2×#4111yescharacteristic
195C23×C83C2×#4111yescharacteristic
196C23×C83C2×#4111yescharacteristic
197C23×C83C2×#4111yescharacteristic
198C23×C83C2×#4111yescharacteristic
199C23×C83H(5,𝔽2)11yescharacteristic
200C23×C83H(5,𝔽2)11yescharacteristic
201C23×C832−1+411yescharacteristic
202C23×C832−1+411yescharacteristic
203C2×C4×C83—22no—
204C2×C4×C83—22no—
205C2×C4×C83—22no—
206C2×C4×C83—22no—
207C2×C4×C83—22no—
208C2×C4×C83—22no—
209C2×C4×C83—24no—
210C2×C4×C83—22no—
211C2×C4×C83—22no—
212C2×C4×C83—24no—
213C2×C4×C83—24no—
214C2×C4×C83—24no—
215C2×C4×C83—24no—
216C2×C4×C83—24no—
217C2×C4×C83—22no—
218C2×C4×C83—41no—
219C2×C4×C83—42no—
220C2×C4×C83—42no—
221C2×C4×C83—41no—
222C2×C4×C83—41no—
223C2×C4×C83—41no—
224C2×C4×C83—42no—
225C2×C4×C83—42no—
226C2×C4×C83—42no—
227C2×C4×C83—42no—
228C2×C4×C83—42no—
229C2×C4×C83—42no—
230C2×C4×C83C2×C4214yes—
231C2×C4×C83C2×C4⋊C414yes—
232C2×C4×C83#11714yes—
233C2×C4×C83#11714yes—
234C2×C4×C83C4×D414yes—
235C2×C4×C83C4×D414yes—
236C2×C4×C83C4×Q814yes—
237C2×C4×C83C4×Q814yes—
238C2×Dic83—22no—
239C2×Dic83—22no—
240C2×Dic83—22no—
241C2×Dic83—22no—
242C2×Dic83—22no—
243C2×Dic83—24no—
244C2×Dic83—22no—
245C2×Dic83—22no—
246C2×Dic83—22no—
247C2×Dic83—24no—
248C2×Dic83—22no—
249C2×Dic83—22no—
250C2×Dic83—22no—
251C2×Dic83—22no—
252C2×Dic83—22no—
253C2×Dic83—22no—
254C2×Dic83—22no—
255C2×Dic83—24no—
256C2×Dic83—24no—
257C2×Dic83—22no—
258C2×Dic83—22no—
259C2×Dic83—22no—
260C2×Dic83—24no—
261C2×Dic83—24no—
262C2×Dic83—22no—
263C2×Dic83—22no—
264C2×Dic83—24no—
265C2×Dic83—24no—
266C2×Dic83—22no—
267C2×Dic83—24no—
268C2×Dic83—42no—
269C2×Dic83—41no—
270C2×Dic83—41no—
271C2×Dic83—42no—
272C2×Dic83—41no—
273C2×Dic83—41no—
274C2×Dic83—42no—
275C2×Dic83—42no—
276C2×Dic83C2×C4214yes—
277C2×Dic83C2×C4214yes—
278C2×Dic83C2×C4⋊C418yes—
279C2×Dic83#11714yes—
280C22×C83C22×C4211yescharacteristic
281C22×C83C22×C4⋊C411yescharacteristic
282C22×C83C2×#11711yescharacteristic
283C22×C83C2×#11711yescharacteristic
284C22×C83C2×#11711yescharacteristic
285C22×C83C2×C4×D411yescharacteristic
286C22×C83C2×C4×D411yescharacteristic
287C22×C83C2×C4×Q811yescharacteristic
288C22×C83C2×C4×Q811yescharacteristic
289C22×C83C4×#4111yescharacteristic
290C22×C83C4×#4111yescharacteristic
291C22×C83C4×#4111yescharacteristic
292C22×C83C4×#4111yescharacteristic
293C22×C83#51811yescharacteristic
294C22×C83#51911yescharacteristic
295C22×C83#52011yescharacteristic
296C22×C83#52011yescharacteristic
297C22×C83#52011yescharacteristic
298C22×C83#52011yescharacteristic
299C22×C83#54611yescharacteristic
300C22×C83#54611yescharacteristic
301C22×C83#54811yescharacteristic
302C22×C83#54811yescharacteristic
303C22×C83#55211yescharacteristic
304C22×C83#55211yescharacteristic
305C22×C83#55311yescharacteristic
306C22×C83#55311yescharacteristic
307C22×C83#55411yescharacteristic
308C22×C83#55411yescharacteristic
309C22×C83#55611yescharacteristic
310C22×C83#55611yescharacteristic
311C22×C83#55711yescharacteristic
312C22×C83#55711yescharacteristic
313C22×C83#55911yescharacteristic
314C22×C83#55911yescharacteristic
315C4×C83—24no—
316C4×C83—42no—
317C4×C83—44no—
318C4×C83—44no—
319C4×C83C4×C4⋊C418yes—
320Dic83—28no—
321Dic83—24no—
322Dic83—24no—
323Dic83—24no—
324Dic83—42no—
325Dic83—44no—
326#13804—831nomaximal, Sylow
327C2×C83C2×C4×C4⋊C411yescharacteristic
328C2×C83C4×#11711yescharacteristic
329C2×C83#227411yescharacteristic
330C2×C83#234911yescharacteristic
331C2×C83#235111yescharacteristic
332C2×C83#235211yescharacteristic
333C2×C83#235211yescharacteristic
334C2×C83#235511yescharacteristic
335C2×C83#235511yescharacteristic
336C2×C83#235611yescharacteristic
337C2×C83#235711yescharacteristic
338C2×C83#236711yescharacteristic
339C2×C83#236711yescharacteristic
340C2×C83#237011yescharacteristic
341C2×C83#237011yescharacteristic
342C2×#382—831no—
343C2×C4×C4⋊C4—831no—
344C2×C4×C4⋊C4—831no—
345C2×C4×C4⋊C4—831no—
346C2×C4×C4⋊C4—831no—
347#1436—832no—
348#1436—832no—
349C4⋊#95—831no—
350C4⋊#95D8311yescharacteristic
351#1434—832no—
352C4×#95—832no—
353C83#1380411yescharacteristic, complemented, Sylow
354C22×C4⋊C4—831no—
355C22×C4⋊C4—831no—
356C22×C4⋊C4—831no—
357C22×C4⋊C4—831no—
358C22×C4⋊C4C2×D8311yescharacteristic
359C22×C4⋊C4C2×D8311yescharacteristic
360C22×C42—832no—
361C22×C42—832no—
362C22×C42—832no—
363C22×C42—831no—
364C22×C42—831no—
365C22×C42C2×D8311yescharacteristic
366#382—838no—
367C4×C4⋊C4—838no—
368C4×C4⋊C4—838no—
369C4×C4⋊C4—1664no—
370C4×C4⋊C4—1664no—
371C2×#95—832no—
372C2×#95—831no—
373C2×#95—832no—
374C2×#95—831no—
375C2×#95—832no—
376C2×#95—832no—
377C2×#95—832no—
378C2×#95—832no—
379C2×#95—832no—
380C2×#95C2×D8312yes—
381C2×#95C2×D8312yes—
382C23×C4—831no—
383C23×C4—832no—
384C23×C4—831no—
385C23×C4—831no—
386C23×C4—832no—
387C23×C4—831no—
388C23×C4C22×D8311yescharacteristic
389C23×C4C22×D8312yes—
390C23×C4C22×D8312yes—
391C23×C4C22×D8311yescharacteristic
392C23×C4C22×D8311yescharacteristic
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—834no—
398C2×C4⋊C4—834no—
399C2×C4⋊C4—834no—
400C2×C4⋊C4—834no—
401C2×C4⋊C4—834no—
402C2×C4⋊C4—834no—
403C2×C4⋊C4—1662no—
404C2×C4⋊C4—1662no—
405C2×C4⋊C4—1662no—
406C2×C4⋊C4—1662no—
407C2×C4⋊C4—1662no—
408C2×C4⋊C4—1662no—
409C2×C4⋊C4C4×D8314yes—
410C2×C4⋊C4C4×D8314yes—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—3322no—
414C2×C42—3322no—
415C2×C42—3322no—
416C2×C42—3322no—
417C2×C42—838no—
418C2×C42—834no—
419C2×C42—834no—
420C2×C42—834no—
421C2×C42—834no—
422C2×C42—1664no—
423C2×C42—1664no—
424C2×C42—1664no—
425C2×C42—1664no—
426C2×C42—1662no—
427C2×C42—1662no—
428C2×C42C4×D8314yes—
429#95—24no—
430#95—42no—
431#95—3322no—
432#95—838no—
433#95—834no—
434#95—834no—
435#95—838no—
436#95—838no—
437#95—1664no—
438#95—1664no—
439#95—1664no—
440C24C23×D8311yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—832no—
464C22×C4—832no—
465C22×C4—832no—
466C22×C4—832no—
467C22×C4—834no—
468C22×C4—832no—
469C22×C4—832no—
470C22×C4—832no—
471C22×C4—834no—
472C22×C4—834no—
473C22×C4—832no—
474C22×C4—832no—
475C22×C4—834no—
476C22×C4—832no—
477C22×C4—1661no—
478C22×C4—1662no—
479C22×C4—1662no—
480C22×C4—1661no—
481C22×C4—1661no—
482C22×C4—1662no—
483C22×C4—1662no—
484C22×C4—1661no—
485C22×C4—1661no—
486C22×C4—1662no—
487C22×C4—1661no—
488C22×C4—1662no—
489C22×C4—1661no—
490C22×C4—1662no—
491C22×C4—1661no—
492C22×C4—1661no—
493C22×C4—1661no—
494C22×C4—1661no—
495C22×C4—1662no—
496C22×C4—1661no—
497C22×C4—1661no—
498C22×C4—1662no—
499C22×C4—1661no—
500C22×C4—1662no—
501C22×C4—1661no—
502C22×C4—1661no—
503C22×C4—1661no—
504C22×C4—1661no—
505C22×C4C2×C4×D8314yes—
506C22×C4C2×C4×D8314yes—
507C22×C4C2×C4×D8312yes—
508C22×C4C2×C4×D8312yes—
509C22×C4C2×C4×D8312yes—
510C22×C4C2×C4×D8312yes—
511C22×C4C2×C4×D8312yes—
512C22×C4D4×D8312yes—
513C22×C4Q8×D8312yes—
514C22×C4#1305058912yes—
515C22×C4#1305058912yes—
516C22×C4#1305058912yes—
517C22×C4#1305059112yes—
518C4⋊C4—28no—
519C4⋊C4—28no—
520C4⋊C4—8316no—
521C4⋊C4—1668no—
522C4⋊C4—1668no—
523C4⋊C4—1668no—
524C42—28no—
525C42—3328no—
526C42—3328no—
527C42—3328no—
528C42—8316no—
529C42—1668no—
530C23C22×C4×D8311yescharacteristic
531C23C22×C4×D8311yescharacteristic
532C23C22×C4×D8311yescharacteristic
533C23C2×D4×D8311yescharacteristic
534C23C2×Q8×D8311yescharacteristic
535C23#41×D8311yescharacteristic
536C23#41×D8311yescharacteristic
537C23C2×#1305058911yescharacteristic
538C23C2×#1305058911yescharacteristic
539C23C2×#1305058911yescharacteristic
540C23C2×#1305059111yescharacteristic
541C23#1458183711yescharacteristic
542C23#1458183811yescharacteristic
543C23#1458183911yescharacteristic
544C23#1458184011yescharacteristic
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—3322no—
573C2×C4—3321no—
574C2×C4—3321no—
575C2×C4—3322no—
576C2×C4—3321no—
577C2×C4—3321no—
578C2×C4—3322no—
579C2×C4—3322no—
580C2×C4—834no—
581C2×C4—834no—
582C2×C4—838no—
583C2×C4—834no—
584C2×C4—1662no—
585C2×C4—1662no—
586C2×C4—1664no—
587C2×C4—1664no—
588C2×C4—1662no—
589C2×C4—1664no—
590C2×C4—1664no—
591C2×C4—1662no—
592C2×C4—1664no—
593C2×C4—1662no—
594C2×C4—1662no—
595C2×C4—1662no—
596C2×C4—1664no—
597C2×C4—1662no—
598C2×C4—1662no—
599C2×C4—1664no—
600C2×C4—1662no—
601C2×C4—1662no—
602C2×C4—1662no—
603C2×C4—1664no—
604C2×C4—1662no—
605C2×C4—1662no—
606C2×C4—1662no—
607C2×C4—1664no—
608C2×C4—1662no—
609C2×C4—1662no—
610C2×C4—1662no—
611C2×C4—1662no—
612C2×C4—1662no—
613C2×C4—1662no—
614C2×C4C42×D8314yes—
615C2×C4C4⋊C4×D8314yes—
616C2×C4#1458174814yes—
617C2×C4#1458175014yes—
618C2×C4(C22⋊D83)⋊C414yes—
619C2×C4(C22⋊D83)⋊C414yes—
620C2×C4#1458175714yes—
621C2×C4#1458175714yes—
622C22C2×C42×D8311yescharacteristic
623C22C2×C4⋊C4×D8311yescharacteristic
624C22#117×D8311yescharacteristic
625C22C2×#1458174811yescharacteristic
626C22C2×#1458175011yescharacteristic
627C22C2×(C22⋊D83)⋊C411yescharacteristic
628C22C2×(C22⋊D83)⋊C411yescharacteristic
629C22C2×#1458175711yescharacteristic
630C22C2×#1458175711yescharacteristic
631C22C4×#1305058911yescharacteristic
632C22C4×#1305058911yescharacteristic
633C22C4×#1305059111yescharacteristic
634C22C4×#1305059111yescharacteristic
635C22#1912817311yescharacteristic
636C22#1912817711yescharacteristic
637C22#1912818011yescharacteristic
638C22#1912818111yescharacteristic
639C22#1912818211yescharacteristic
640C22#1912818311yescharacteristic
641C22#1912834211yescharacteristic
642C22#1912834811yescharacteristic
643C22#1912835711yescharacteristic
644C22#1912836111yescharacteristic
645C22#1912838511yescharacteristic
646C22#1912839311yescharacteristic
647C22#1912839811yescharacteristic
648C22#1912840311yescharacteristic
649C22#1912840711yescharacteristic
650C22#1912841211yescharacteristic
651C22#1912842011yescharacteristic
652C22#1912842511yescharacteristic
653C22#1912842611yescharacteristic
654C22#1912842811yescharacteristic
655C22#1912843311yescharacteristic
656C22#1912843711yescharacteristic
657C4—24no—
658C4—42no—
659C4—44no—
660C4—44no—
661C4—3322no—
662C4—3324no—
663C4—1668no—
664C4—1664no—
665C4—1664no—
666C4—1664no—
667C4#1912755218yes—
668C2C2×#1912755211yescharacteristic
669C2C4×#1458175011yescharacteristic
670C2#2490981711yescharacteristic
671C2#2491037211yescharacteristic
672C2#2491038211yescharacteristic
673C2#2491038511yescharacteristic
674C2#2491039411yescharacteristic
675C2#2491041511yescharacteristic
676C2#2491042211yescharacteristic
677C2#2491042711yescharacteristic
678C2#2491043511yescharacteristic
679C2#2491053311yescharacteristic
680C2#2491053911yescharacteristic
681C2#2491055811yescharacteristic
682C2#2491056411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC22×C83C22×C42
FittingC83×C4⋊#95C2
socle, prime radical, cosocleC24×C83C24
hypercenterC4⋊#95D83
hypocenterC83#13804
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
21. #19127566C4semidirect
23. C4⋊C4×Dic83C4semidirect
24. C4×Dic83⋊C4C4semidirect
141. C4⋊Dic83C4⋊C4semidirect
148. C4×Dic83C42semidirect
353. C83#13804semidirect

Maximal subgroups

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

subgroupindex
C2×#191275662
C2×C4⋊C4×Dic832
C2×C4×Dic83⋊C42
C2×C4×C4⋊Dic832
#249056982
#249056942
#249056922
#249056872
#95×Dic832
C83×C4⋊#952
#1380483