Finite Group Databasebeta

← #35310059

Subgroups — #35310059

Order 21248.

914 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic83C211yesmaximal, characteristic
2C2×#19127464C211yesmaximal, characteristic
3C2×#19127463C211yesmaximal, characteristic
4C2×#19127463C211yesmaximal, characteristic
5C2×#19127455C211yesmaximal, characteristic
6#24905692C211yesmaximal, characteristic
7C2×#340×C83C211yesmaximal, characteristic
8C23×C83⋊C8C2211yescharacteristic
9C22×C4⋊Dic83C2211yescharacteristic
10C22×C4⋊Dic83C2211yescharacteristic
11C22×C4×Dic83—21no—
12C22×C4×Dic83C2211yescharacteristic
13C4⋊C4×Dic83—22no—
14C4⋊C4×Dic83C414yescomplemented
15C2×C83⋊#95—21no—
16C2×C83⋊#95—21no—
17C2×C83⋊#95—21no—
18#19127464C414yescomplemented
19#19127463—22no—
20#19127463C414yescomplemented
21#19127455—22no—
22C23×C8×C83C2211yescharacteristic
23C22×C4⋊C4×C83C2211yescharacteristic
24C22×C4⋊C4×C83C2211yescharacteristic
25#340×C83—22no—
26C23×Dic83—21no—
27C23×Dic83—21no—
28C23×Dic83D411yescharacteristic
29C23×Dic83D411yescharacteristic
30C22×C83⋊C8—21no—
31C22×C83⋊C8—21no—
32C22×C83⋊C8—21no—
33C22×C83⋊C8—21no—
34C22×C83⋊C8—21no—
35C22×C83⋊C8—21no—
36C22×C83⋊C8C2×C412yes—
37C2×C4⋊Dic83—21no—
38C2×C4⋊Dic83—21no—
39C2×C4⋊Dic83—21no—
40C2×C4⋊Dic83—21no—
41C2×C4⋊Dic83—21no—
42C2×C4⋊Dic83—21no—
43C2×C4⋊Dic83—21no—
44C2×C4⋊Dic83—21no—
45C2×C4⋊Dic83C2×C412yes—
46C2×C4⋊Dic83C2×C412yes—
47C2×C4⋊Dic83C2×C412yes—
48C2×C4⋊Dic83C2×C412yes—
49C2×C4×Dic83—24no—
50C2×C4×Dic83—21no—
51C2×C4×Dic83—21no—
52C2×C4×Dic83—21no—
53C2×C4×Dic83—21no—
54C2×C4×Dic83—42no—
55C2×C4×Dic83—42no—
56C2×C4×Dic83C2×C412yes—
57C2×C4×Dic83D412yes—
58C83⋊#95—24no—
59C83⋊#95—42no—
60C83⋊#95—42no—
61C23×C4×C83—21no—
62C23×C4×C83—21no—
63C23×C4×C83C2311yescharacteristic
64C22×C8×C83—21no—
65C22×C8×C83—21no—
66C22×C8×C83—21no—
67C22×C8×C83—21no—
68C22×C8×C83—21no—
69C22×C8×C83—21no—
70C22×C8×C83C2×C412yes—
71C2×C4⋊C4×C83—21no—
72C2×C4⋊C4×C83—21no—
73C2×C4⋊C4×C83—21no—
74C2×C4⋊C4×C83—21no—
75C2×C4⋊C4×C83—21no—
76C2×C4⋊C4×C83—21no—
77C2×C4⋊C4×C83—21no—
78C2×C4⋊C4×C83—21no—
79C2×C4⋊C4×C83C2×C412yes—
80C2×C4⋊C4×C83C2×C412yes—
81C2×C4⋊C4×C83D412yes—
82C2×C4⋊C4×C83Q812yes—
83C22×Dic83—21no—
84C22×Dic83—21no—
85C22×Dic83—21no—
86C22×Dic83—21no—
87C22×Dic83—22no—
88C22×Dic83—22no—
89C22×Dic83—22no—
90C22×Dic83—21no—
91C22×Dic83—21no—
92C22×Dic83—21no—
93C22×Dic83—21no—
94C22×Dic83—21no—
95C22×Dic83—21no—
96C22×Dic83—22no—
97C22×Dic83—41no—
98C22×Dic83—41no—
99C22×Dic83—41no—
100C22×Dic83—41no—
101C22×Dic83—41no—
102C22×Dic83—41no—
103C22×Dic83—41no—
104C22×Dic83—41no—
105C22×Dic83—41no—
106C22×Dic83—41no—
107C22×Dic83C22⋊C412yes—
108C22×Dic83C22⋊C412yes—
109C22×Dic83D812yes—
110C22×Dic83SD1612yes—
111C2×C83⋊C8—22no—
112C2×C83⋊C8—22no—
113C2×C83⋊C8—22no—
114C2×C83⋊C8—41no—
115C2×C83⋊C8—41no—
116C2×C83⋊C8—41no—
117C2×C83⋊C8—41no—
118C4⋊Dic83—22no—
119C4⋊Dic83—22no—
120C4⋊Dic83—22no—
121C4⋊Dic83—22no—
122C4⋊Dic83—22no—
123C4⋊Dic83—41no—
124C4⋊Dic83—41no—
125C4⋊Dic83C4214yes—
126C4×Dic83—22no—
127C4×Dic83—22no—
128C4×Dic83—22no—
129C4×Dic83—22no—
130C4×Dic83—48no—
131C24×C83C2×D411yescharacteristic
132C22×C4×C83—22no—
133C22×C4×C83—22no—
134C22×C4×C83—22no—
135C22×C4×C83—22no—
136C22×C4×C83—41no—
137C22×C4×C83—41no—
138C22×C4×C83—41no—
139C22×C4×C83—41no—
140C22×C4×C83—41no—
141C22×C4×C83—41no—
142C22×C4×C83—41no—
143C22×C4×C83—41no—
144C22×C4×C83—41no—
145C22×C4×C83—41no—
146C22×C4×C83C22×C411yescharacteristic
147C22×C4×C83C22×C411yescharacteristic
148C22×C4×C83C22×C411yescharacteristic
149C22×C4×C83C2×D411yescharacteristic
150C22×C4×C83C2×D411yescharacteristic
151C22×C4×C83C2×Q811yescharacteristic
152C22×C4×C83#4111yescharacteristic
153C22×C4×C83#4111yescharacteristic
154C22×C4×C83#4111yescharacteristic
155C22×C4×C83#4111yescharacteristic
156C22×C4×C83#4111yescharacteristic
157C22×C4×C83#4111yescharacteristic
158C22×C4×C83#4111yescharacteristic
159C22×C4×C83#4111yescharacteristic
160C2×C8×C83—22no—
161C2×C8×C83—22no—
162C2×C8×C83—22no—
163C2×C8×C83—41no—
164C2×C8×C83—41no—
165C2×C8×C83—41no—
166C2×C8×C83—41no—
167C4⋊C4×C83—22no—
168C4⋊C4×C83—22no—
169C4⋊C4×C83—22no—
170C4⋊C4×C83—22no—
171C4⋊C4×C83—22no—
172C4⋊C4×C83—41no—
173C4⋊C4×C83—41no—
174C4⋊C4×C83C4⋊C414yes—
175C23×C83C2×C22⋊C411yescharacteristic
176C23×C83C4×D411yescharacteristic
177C23×C83C4×D411yescharacteristic
178C23×C83#12111yescharacteristic
179C23×C83C22⋊Q811yescharacteristic
180C23×C83#12311yescharacteristic
181C23×C83#12311yescharacteristic
182C23×C83C2×D811yescharacteristic
183C23×C83C2×SD1611yescharacteristic
184C23×C83#13511yescharacteristic
185C23×C83#13511yescharacteristic
186C23×C83AGL(1,ℤ/8)11yescharacteristic
187C23×C83#13711yescharacteristic
188C23×C83#13711yescharacteristic
189C23×C83#13711yescharacteristic
190C2×C4×C83—24no—
191C2×C4×C83—42no—
192C2×C4×C83—42no—
193C2×C4×C83—42no—
194C2×C4×C83—42no—
195C2×C4×C83—42no—
196C2×C4×C83—42no—
197C2×C4×C83—42no—
198C2×C4×C83—42no—
199C2×C4×C83—42no—
200C2×C4×C83—81no—
201C2×C4×C83—81no—
202C2×C4×C83—81no—
203C2×C4×C83—81no—
204C2×C4×C83C2×C4211yescharacteristic
205C2×C4×C83C2×C4⋊C411yescharacteristic
206C2×C4×C83#11711yescharacteristic
207C2×C4×C83#11711yescharacteristic
208C2×C4×C83#11711yescharacteristic
209C2×C4×C83#11711yescharacteristic
210C2×C4×C83#11711yescharacteristic
211C2×C4×C83#11711yescharacteristic
212C2×C4×C83#11711yescharacteristic
213C2×C4×C83#11711yescharacteristic
214C2×C4×C83C4×D411yescharacteristic
215C2×C4×C83C4×D411yescharacteristic
216C2×C4×C83C4×D411yescharacteristic
217C2×C4×C83C4×D411yescharacteristic
218C2×C4×C83C4×Q811yescharacteristic
219C2×C4×C83C4×Q811yescharacteristic
220C2×C4×C83#12111yescharacteristic
221C2×C4×C83C22⋊Q811yescharacteristic
222C2×C4×C83#12311yescharacteristic
223C2×C4×C83#12311yescharacteristic
224C2×C4×C83#12411yescharacteristic
225C2×C4×C83#12411yescharacteristic
226C2×C4×C83#12511yescharacteristic
227C2×C4×C83#12511yescharacteristic
228C2×C4×C83#12611yescharacteristic
229C2×C4×C83#12611yescharacteristic
230C2×C4×C83#12611yescharacteristic
231C2×C4×C83#12611yescharacteristic
232C2×Dic83—22no—
233C2×Dic83—22no—
234C2×Dic83—22no—
235C2×Dic83—22no—
236C2×Dic83—22no—
237C2×Dic83—22no—
238C2×Dic83—24no—
239C2×Dic83—22no—
240C2×Dic83—22no—
241C2×Dic83—22no—
242C2×Dic83—42no—
243C2×Dic83—42no—
244C2×Dic83—42no—
245C2×Dic83—42no—
246C2×Dic83—42no—
247C2×Dic83—42no—
248C2×Dic83—41no—
249C2×Dic83—41no—
250C2×Dic83—41no—
251C2×Dic83—41no—
252C2×Dic83—42no—
253C2×Dic83—42no—
254C2×Dic83—42no—
255C2×Dic83—81no—
256C2×Dic83—81no—
257C2×Dic83—81no—
258C2×Dic83—81no—
259C2×Dic83#10214yes—
260C8×C83—42no—
261C83⋊C8—42no—
262C22×C83C4×C22⋊C411yescharacteristic
263C22×C83#38011yescharacteristic
264C22×C83#38111yescharacteristic
265C22×C83#38711yescharacteristic
266C22×C83#38711yescharacteristic
267C22×C83#38811yescharacteristic
268C22×C83#38811yescharacteristic
269C22×C83C2×#10211yescharacteristic
270C22×C83#41611yescharacteristic
271C22×C83#41711yescharacteristic
272C22×C83#41911yescharacteristic
273C22×C83C4×D811yescharacteristic
274C22×C83C4×D811yescharacteristic
275C22×C83C4×SD1611yescharacteristic
276C22×C83C4×SD1611yescharacteristic
277C22×C83#44011yescharacteristic
278C22×C83#44011yescharacteristic
279C22×C83#44111yescharacteristic
280C22×C83#44111yescharacteristic
281C22×C83#45911yescharacteristic
282C22×C83#46111yescharacteristic
283C22×C83#46411yescharacteristic
284C22×C83#46411yescharacteristic
285C22×C83#47411yescharacteristic
286C22×C83#47611yescharacteristic
287C22×C83#47911yescharacteristic
288C22×C83#47911yescharacteristic
289C22×C83#48011yescharacteristic
290C22×C83#48011yescharacteristic
291C22×C83#48211yescharacteristic
292C22×C83#48211yescharacteristic
293C22×C83#48311yescharacteristic
294C22×C83#48311yescharacteristic
295C22×C83#48511yescharacteristic
296C22×C83#48511yescharacteristic
297C4×C83—44no—
298C4×C83—82no—
299C4×C83#37611yescharacteristic
300C4×C83C4×C4⋊C411yescharacteristic
301C4×C83#38211yescharacteristic
302C4×C83#38311yescharacteristic
303C4×C83#38711yescharacteristic
304C4×C83#38711yescharacteristic
305C4×C83#38811yescharacteristic
306C4×C83#38811yescharacteristic
307Dic83—24no—
308Dic83—42no—
309Dic83—44no—
310Dic83—82no—
311#10806—831nomaximal, Sylow
312C2×C83#143411yescharacteristic
313C2×C83C4×#10211yescharacteristic
314C2×C83#176311yescharacteristic
315C2×C83#180211yescharacteristic
316C2×C83#180511yescharacteristic
317C2×C83#182311yescharacteristic
318C2×C83#182511yescharacteristic
319C2×C83#191811yescharacteristic
320C2×C83#191811yescharacteristic
321C2×C83#192011yescharacteristic
322C2×C83#192011yescharacteristic
323C2×C83#192511yescharacteristic
324C2×C83#192511yescharacteristic
325C2×C83#192711yescharacteristic
326C2×C83#192711yescharacteristic
327C2×C4×C4⋊C4—831no—
328C2×#340—831no—
329C2×#340—831no—
330C2×#340—831no—
331C2×#340D8311yescharacteristic
332C2×#336—831no—
333C4⋊#95—831no—
334C83#1080611yescharacteristic, complemented, Sylow
335C23×C8—831no—
336C23×C8C2×D8311yescharacteristic
337C22×C4⋊C4—831no—
338C22×C4⋊C4—831no—
339C22×C4⋊C4C2×D8311yescharacteristic
340C22×C4⋊C4C2×D8311yescharacteristic
341C22×C42—831no—
342C22×C42—1661no—
343C4×C4⋊C4—834no—
344C4×C4⋊C4—1662no—
345C2×#95—1661no—
346C2×#95—1661no—
347C2×#95—1661no—
348#340—22no—
349#340—834no—
350#340—834no—
351#340—1662no—
352#336—1662no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—831no—
356C23×C4—831no—
357C23×C4—1661no—
358C23×C4—1661no—
359C23×C4C22×D8311yescharacteristic
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—832no—
367C22×C8—1661no—
368C22×C8—1661no—
369C22×C8—1661no—
370C22×C8—1661no—
371C22×C8—1661no—
372C22×C8—1661no—
373C22×C8C4×D8312yes—
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—832no—
383C2×C4⋊C4—832no—
384C2×C4⋊C4—832no—
385C2×C4⋊C4—832no—
386C2×C4⋊C4—1661no—
387C2×C4⋊C4—1661no—
388C2×C4⋊C4—1661no—
389C2×C4⋊C4—1661no—
390C2×C4⋊C4—1661no—
391C2×C4⋊C4—1661no—
392C2×C4⋊C4—1661no—
393C2×C4⋊C4—1661no—
394C2×C4⋊C4Dic16612yes—
395C2×C4⋊C4C4×D8312yes—
396C2×C4⋊C4C4×D8312yes—
397C2×C4⋊C4C22⋊D8312yes—
398C2×C42—3322no—
399C2×C42—3322no—
400C2×C42—832no—
401C2×C42—832no—
402C2×C42—1664no—
403C2×C42—1661no—
404C2×C42—1661no—
405C2×C42—1661no—
406C2×C42—1661no—
407#95—3322no—
408#95—3322no—
409#95—1664no—
410C24D4×D8311yescharacteristic
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—3321no—
426C22×C4—3321no—
427C22×C4—3321no—
428C22×C4—3321no—
429C22×C4—3321no—
430C22×C4—3321no—
431C22×C4—3321no—
432C22×C4—3321no—
433C22×C4—3321no—
434C22×C4—3321no—
435C22×C4—832no—
436C22×C4—832no—
437C22×C4—832no—
438C22×C4—832no—
439C22×C4—1662no—
440C22×C4—1661no—
441C22×C4—1661no—
442C22×C4—1661no—
443C22×C4—1661no—
444C22×C4—1661no—
445C22×C4—1661no—
446C22×C4—1662no—
447C22×C4—1662no—
448C22×C4—1662no—
449C22×C4—1661no—
450C22×C4—1661no—
451C22×C4—1661no—
452C22×C4—1661no—
453C22×C4C2×C4×D8311yescharacteristic
454C22×C4C2×C4×D8311yescharacteristic
455C22×C4C2×C4×D8311yescharacteristic
456C22×C4D4×D8311yescharacteristic
457C22×C4C2×C22⋊D8311yescharacteristic
458C22×C4C2×Dic16611yescharacteristic
459C22×C4#1305058911yescharacteristic
460C22×C4#1305058911yescharacteristic
461C22×C4#1305058911yescharacteristic
462C22×C4#1305058911yescharacteristic
463C22×C4#1305059011yescharacteristic
464C22×C4#1305059011yescharacteristic
465C22×C4#1305059111yescharacteristic
466C22×C4#1305059111yescharacteristic
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—3321no—
475C2×C8—3321no—
476C2×C8—3321no—
477C2×C8—3321no—
478C2×C8—1662no—
479C2×C8—1662no—
480C2×C8—1662no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—3321no—
489C4⋊C4—3321no—
490C4⋊C4—834no—
491C4⋊C4—1662no—
492C4⋊C4—1662no—
493C4⋊C4—1662no—
494C4⋊C4—1662no—
495C4⋊C4—1662no—
496C4⋊C4Dic83⋊C414yes—
497C42—3328no—
498C42—1662no—
499C42—1662no—
500C42—1662no—
501C42—1662no—
502C23C22⋊C4×D8311yescharacteristic
503C23(C22⋊D83)⋊C411yescharacteristic
504C23#1458175411yescharacteristic
505C23#1458176411yescharacteristic
506C23#1458176911yescharacteristic
507C23#1458177411yescharacteristic
508C23#1458177711yescharacteristic
509C23D8×D8311yescharacteristic
510C23SD16×D8311yescharacteristic
511C23#1458181311yescharacteristic
512C23#1458181511yescharacteristic
513C23#1458181611yescharacteristic
514C23#1458182111yescharacteristic
515C23#1458182111yescharacteristic
516C23#1458182411yescharacteristic
517C2×C4—24no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—81no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—3322no—
532C2×C4—3322no—
533C2×C4—3321no—
534C2×C4—3321no—
535C2×C4—3322no—
536C2×C4—3322no—
537C2×C4—3321no—
538C2×C4—3322no—
539C2×C4—3322no—
540C2×C4—3321no—
541C2×C4—3322no—
542C2×C4—3322no—
543C2×C4—3322no—
544C2×C4—834no—
545C2×C4—6641no—
546C2×C4—6641no—
547C2×C4—6641no—
548C2×C4—6641no—
549C2×C4—1662no—
550C2×C4—1662no—
551C2×C4—1662no—
552C2×C4—1664no—
553C2×C4—1662no—
554C2×C4—1662no—
555C2×C4—1662no—
556C2×C4—1662no—
557C2×C4—1662no—
558C2×C4—1662no—
559C2×C4C42×D8311yescharacteristic
560C2×C4C2×Dic83⋊C411yescharacteristic
561C2×C4#1458174811yescharacteristic
562C2×C4#1458174811yescharacteristic
563C2×C4#1458174811yescharacteristic
564C2×C4#1458174911yescharacteristic
565C2×C4#1458175011yescharacteristic
566C2×C4#1458175011yescharacteristic
567C2×C4#1458175011yescharacteristic
568C2×C4#1458175011yescharacteristic
569C2×C4(C22⋊D83)⋊C411yescharacteristic
570C2×C4C4×C22⋊D8311yescharacteristic
571C2×C4C4×C22⋊D8311yescharacteristic
572C2×C4#1458175411yescharacteristic
573C2×C4C4×Dic16611yescharacteristic
574C2×C4C4×Dic16611yescharacteristic
575C2×C4#1458176411yescharacteristic
576C2×C4#1458176911yescharacteristic
577C2×C4#1458177411yescharacteristic
578C2×C4#1458177711yescharacteristic
579C2×C4#1458177911yescharacteristic
580C2×C4#1458178111yescharacteristic
581C2×C4#1458178311yescharacteristic
582C2×C4#1458178311yescharacteristic
583C2×C4#1458178511yescharacteristic
584C2×C4#1458178511yescharacteristic
585C2×C4#1458178711yescharacteristic
586C2×C4#1458178711yescharacteristic
587C8—42no—
588C8—3322no—
589C22#1912754811yescharacteristic
590C22#1912755911yescharacteristic
591C22#1912756311yescharacteristic
592C22#1912758411yescharacteristic
593C22#1912758811yescharacteristic
594C22#1912759111yescharacteristic
595C22#1912759511yescharacteristic
596C22#102×D8311yescharacteristic
597C22#1912769611yescharacteristic
598C22#1912769911yescharacteristic
599C22#1912770811yescharacteristic
600C22#1912778111yescharacteristic
601C22#1912778311yescharacteristic
602C22#1912778611yescharacteristic
603C22#1912778811yescharacteristic
604C22#1912779811yescharacteristic
605C22#1912780011yescharacteristic
606C22#1912780511yescharacteristic
607C22#1912780711yescharacteristic
608C22#1912789411yescharacteristic
609C22#1912790411yescharacteristic
610C22#1912792111yescharacteristic
611C22#1912792511yescharacteristic
612C22#1912797911yescharacteristic
613C22#1912798911yescharacteristic
614C22#1912800611yescharacteristic
615C22#1912801011yescharacteristic
616C22#1912801311yescharacteristic
617C22#1912801611yescharacteristic
618C22#1912802411yescharacteristic
619C22#1912802811yescharacteristic
620C22#1912803011yescharacteristic
621C22#1912803311yescharacteristic
622C22#1912804111yescharacteristic
623C22#1912804511yescharacteristic
624C4—44no—
625C4—82no—
626C4—3324no—
627C4—3322no—
628C4—6642no—
629C4—1664no—
630C4#1912754611yescharacteristic
631C4C4×Dic83⋊C411yescharacteristic
632C4#1912756611yescharacteristic
633C4#1912756811yescharacteristic
634C4#1912758411yescharacteristic
635C4#1912758811yescharacteristic
636C4#1912759111yescharacteristic
637C4#1912759511yescharacteristic
638C2#2490568911yescharacteristic
639C2#2490727711yescharacteristic
640C2#2490729211yescharacteristic
641C2#2490746111yescharacteristic
642C2#2490747611yescharacteristic
643C2#2490754811yescharacteristic
644C2#2490755711yescharacteristic
645C2#2490803311yescharacteristic
646C2#2490803711yescharacteristic
647C2#2490804711yescharacteristic
648C2#2490805111yescharacteristic
649C2#2490808211yescharacteristic
650C2#2490808611yescharacteristic
651C2#2490809611yescharacteristic
652C2#2490810011yescharacteristic
subgroupG/H
centerC24D4×D83
commutatorC2×C4×C83C2×C42
FrattiniC23×C4C22×D83
FittingC2×#340×C83C2
socle, prime radicalC24×C83C2×D4
cosocleC23×C4×C83C23
hypercenterC2×#340D83
hypocenterC83#10806
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
14. C4⋊C4×Dic83C4semidirect
18. #19127464C4semidirect
20. #19127463C4semidirect
334. C83#10806semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic832
C2×#191274642
C2×#191274632
C2×#191274552
#249056922
C2×#340×C832
#1080683