Finite Group Databasebeta

← C4×#19127673 #35402053

Subgroups — C4×#19127673 #35402053

Order 21248.

1666 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#13050589C211yesmaximal, characteristic
2C2×#19127673C212yesmaximal
3C4×#14581748C212yesmaximal, complemented
4#99×Dic83C212yesmaximal, complemented
5C4×#14581706C212yesmaximal, complemented
6C4×#14581707C211yesmaximal, characteristic, complemented
7#24907250C212yesmaximal, complemented
8#24907194C212yesmaximal, complemented
9C4×#99×C83C211yesmaximal, characteristic, complemented
10C22×#13050589C2211yescharacteristic
11C4×#13050589—22no—
12C4×#13050589—22no—
13C4×#13050589—22no—
14C4×#13050589—22no—
15C2×C4×Dic166C411yescharacteristic, complemented
16C2×#14581757C411yescharacteristic, complemented
17C2×D4×Dic83C2211yescharacteristic
18C2×C4×C22⋊D83C411yescharacteristic, complemented
19C2×C4×C22⋊D83C2211yescharacteristic
20C2×(C22⋊D83)⋊C4C411yescharacteristic, complemented
21C2×(C22⋊D83)⋊C4C2211yescharacteristic
22C2×#14581750C411yescharacteristic, complemented
23C2×#14581748C411yescharacteristic, complemented
24C2×#14581748C2214yes—
25C2×#14581748C2211yescharacteristic
26C22×C4×Dic83C411yescharacteristic, complemented
27C22×C4×Dic83C2211yescharacteristic
28C2×C42×D83C411yescharacteristic, complemented
29#19127673C4116yesdirect product factor
30C2×#14581707C2212yes—
31C2×#14581706C2214yes—
32C4×Dic83⋊C4—22no—
33#19127552—22no—
34C22⋊C4×Dic83C2214yes—
35C4×C22⋊Dic83C2212yes—
36#19127546—22no—
37C42×Dic83—22no—
38#19127468C2212yes—
39#19127467C2214yes—
40C2×C4×D4×C83C2211yescharacteristic
41C2×#99×C83C2212yes—
42C4×C22⋊C4×C83C2212yes—
43#342×C83C2212yes—
44C2×#13050589—22no—
45C2×#13050589—22no—
46C2×#13050589—24no—
47C2×#13050589C2×C418yes—
48C22×Dic166C2×C411yescharacteristic
49C22×C22⋊D83C2×C411yescharacteristic
50C22×C22⋊D83C2311yescharacteristic
51C23×Dic83C2×C411yescharacteristic
52C23×Dic83C2×C411yescharacteristic
53C23×Dic83C2311yescharacteristic
54C23×Dic83C2311yescharacteristic
55C22×C4×D83C2×C411yescharacteristic
56C22×C4×D83C2×C411yescharacteristic
57C22×C4×D83C2×C411yescharacteristic
58C4×Dic166—22no—
59C4×Dic166—22no—
60#14581757—22no—
61#14581757—22no—
62D4×Dic83—22no—
63D4×Dic83—22no—
64C4×C22⋊D83—22no—
65C4×C22⋊D83—22no—
66C4×C22⋊D83—22no—
67C4×C22⋊D83—22no—
68(C22⋊D83)⋊C4—22no—
69(C22⋊D83)⋊C4—22no—
70(C22⋊D83)⋊C4—22no—
71(C22⋊D83)⋊C4—22no—
72#14581750—22no—
73#14581750—22no—
74#14581748—22no—
75#14581748—22no—
76#14581748—28no—
77#14581748—22no—
78#14581748—22no—
79#14581748C2×C4116yescomplemented
80C2×C4⋊Dic83C2×C411yescharacteristic
81C2×Dic83⋊C4—24no—
82C2×Dic83⋊C4C2×C411yescharacteristic
83C2×Dic83⋊C4C2×C411yescharacteristic
84C2×Dic83⋊C4C2×C411yescharacteristic
85C2×Dic83⋊C4C2×C411yescharacteristic
86C2×C22⋊Dic83C2×C411yescharacteristic
87C2×C22⋊Dic83C2311yescharacteristic
88C2×C22⋊Dic83C2314yes—
89C2×(C2×D83)⋊C4C2×C411yescharacteristic
90C2×(C2×D83)⋊C4C2×C411yescharacteristic
91C2×C4×Dic83—24no—
92C2×C4×Dic83—21no—
93C2×C4×Dic83—21no—
94C2×C4×Dic83—21no—
95C2×C4×Dic83—21no—
96C2×C4×Dic83—24no—
97C2×C4×Dic83—22no—
98C2×C4×Dic83C2×C411yescharacteristic
99C2×C4×Dic83C2×C411yescharacteristic
100C2×C4×Dic83C2×C411yescharacteristic
101C2×C4×Dic83C2×C411yescharacteristic
102C2×C4×Dic83C2×C411yescharacteristic
103C2×C4×Dic83C2×C411yescharacteristic
104C2×C4×Dic83C2×C411yescharacteristic
105C2×C4×Dic83C2×C411yescharacteristic
106C2×C4×Dic83C2×C411yescharacteristic
107C2×C4×Dic83D412yes—
108C2×C4×Dic83D412yes—
109C2×C4×Dic83D412yes—
110C2×C4×Dic83D412yes—
111C42×D83—21no—
112C42×D83—21no—
113C42×D83—21no—
114C42×D83—21no—
115#14581707C2×C418yescomplemented
116#14581706C2×C4116yescomplemented
117C83⋊#95—24no—
118C83⋊#95—22no—
119C22×D4×C83C2311yescharacteristic
120C23×C4×C83C2×C411yescharacteristic
121C23×C4×C83C2311yescharacteristic
122C4×D4×C83—22no—
123C4×D4×C83—22no—
124C2×C4⋊C4×C83C2×C411yescharacteristic
125C2×C22⋊C4×C83C2×C411yescharacteristic
126C2×C22⋊C4×C83C2311yescharacteristic
127C2×C22⋊C4×C83C2314yes—
128C2×C42×C83—22no—
129C2×C42×C83C2×C411yescharacteristic
130#99×C83C2×C418yescomplemented
131#95×C83—22no—
132C23×D83C22×C411yescharacteristic
133#13050589—216no—
134#13050589—216no—
135C2×Dic166—22no—
136C2×Dic166—22no—
137C2×Dic166C4214yescomplemented
138C2×C22⋊D83—22no—
139C2×C22⋊D83—22no—
140C2×C22⋊D83—22no—
141C2×C22⋊D83—22no—
142C2×C22⋊D83C4214yescomplemented
143C2×C22⋊D83C22×C414yes—
144C22×Dic83—21no—
145C22×Dic83—21no—
146C22×Dic83—22no—
147C22×Dic83—24no—
148C22×Dic83—21no—
149C22×Dic83—21no—
150C22×Dic83—42no—
151C22×Dic83—42no—
152C22×Dic83C4214yescomplemented
153C22×Dic83C22×C411yescharacteristic
154C22×Dic83C22×C411yescharacteristic
155C22×Dic83C22×C411yescharacteristic
156C22×Dic83C22×C411yescharacteristic
157C22×Dic83C22×C411yescharacteristic
158C22×Dic83C22×C411yescharacteristic
159C22×Dic83C22×C411yescharacteristic
160C22×Dic83C22×C414yes—
161C22×Dic83C2×D412yes—
162C22×Dic83C2×D412yes—
163C22×Dic83C2×D412yes—
164C22×Dic83C2×D412yes—
165C22×Dic83#4114yes—
166C2×C4×D83—21no—
167C2×C4×D83—21no—
168C2×C4×D83—22no—
169C2×C4×D83—21no—
170C2×C4×D83—21no—
171C2×C4×D83—21no—
172C2×C4×D83—21no—
173C2×C4×D83—42no—
174C2×C4×D83—42no—
175C2×C4×D83C4214yescomplemented
176C4⋊Dic83—22no—
177Dic83⋊C4—22no—
178Dic83⋊C4—22no—
179Dic83⋊C4—22no—
180Dic83⋊C4—22no—
181Dic83⋊C4—216no—
182C22⋊Dic83—22no—
183C22⋊Dic83—24no—
184C22⋊Dic83—22no—
185C22⋊Dic83C22×C418yes—
186(C2×D83)⋊C4—22no—
187(C2×D83)⋊C4—22no—
188C4×Dic83—21no—
189C4×Dic83—21no—
190C4×Dic83—21no—
191C4×Dic83—21no—
192C4×Dic83—21no—
193C4×Dic83—21no—
194C4×Dic83—21no—
195C4×Dic83—21no—
196C4×Dic83—21no—
197C4×Dic83—21no—
198C4×Dic83—216no—
199C4×Dic83—48no—
200C4×Dic83—44no—
201C4×Dic83C22⋊C411yescharacteristic
202C4×Dic83C22⋊C411yescharacteristic
203C4×Dic83C22⋊C411yescharacteristic
204C4×Dic83C22⋊C411yescharacteristic
205C4×Dic83C22⋊C412yes—
206C4×Dic83C22⋊C412yes—
207C4×Dic83C22⋊C412yes—
208C4×Dic83C22⋊C412yes—
209C4×Dic83C22⋊C412yes—
210C4×Dic83C22⋊C412yes—
211C24×C83C22×C411yescharacteristic
212C24×C83C2411yescharacteristic
213C2×D4×C83—22no—
214C2×D4×C83—22no—
215C2×D4×C83C22×C414yes—
216C22×C4×C83—24no—
217C22×C4×C83—21no—
218C22×C4×C83—21no—
219C22×C4×C83—42no—
220C22×C4×C83—42no—
221C22×C4×C83C22×C411yescharacteristic
222C22×C4×C83C22×C411yescharacteristic
223C22×C4×C83C22×C411yescharacteristic
224C22×C4×C83C22×C411yescharacteristic
225C22×C4×C83C22×C411yescharacteristic
226C22×C4×C83C2×D412yes—
227C22×C4×C83C2×D412yes—
228C4⋊C4×C83—22no—
229C22⋊C4×C83—22no—
230C22⋊C4×C83—24no—
231C22⋊C4×C83—22no—
232C22⋊C4×C83C22×C418yes—
233C42×C83—21no—
234C42×C83—21no—
235C42×C83—44no—
236C23×C83—21no—
237C23×C83—21no—
238C23×C83—41no—
239C23×C83—41no—
240C23×C83—41no—
241C23×C83—41no—
242C23×C83C2×C4212yes—
243C23×C83C23×C411yescharacteristic
244C23×C83C23×C412yes—
245C23×C83C22×D412yes—
246C23×C83C2×#4112yes—
247C22×D83—21no—
248C22×D83—21no—
249C22×D83—41no—
250C22×D83—41no—
251C22×D83C2×C4212yes—
252D4×C83—28no—
253C2×C4×C83—21no—
254C2×C4×C83—21no—
255C2×C4×C83—24no—
256C2×C4×C83—22no—
257C2×C4×C83—21no—
258C2×C4×C83—21no—
259C2×C4×C83—28no—
260C2×C4×C83—41no—
261C2×C4×C83—42no—
262C2×C4×C83—42no—
263C2×C4×C83—44no—
264C2×C4×C83—44no—
265C2×C4×C83—42no—
266C2×C4×C83—41no—
267C2×C4×C83—41no—
268C2×C4×C83C2×C4212yes—
269C2×C4×C83C2×C22⋊C411yescharacteristic
270C2×C4×C83C2×C22⋊C412yes—
271C2×C4×C83C2×C22⋊C411yescharacteristic
272C22⋊D83—28no—
273C22⋊D83—28no—
274C2×Dic83—21no—
275C2×Dic83—21no—
276C2×Dic83—24no—
277C2×Dic83—24no—
278C2×Dic83—24no—
279C2×Dic83—22no—
280C2×Dic83—21no—
281C2×Dic83—21no—
282C2×Dic83—28no—
283C2×Dic83—41no—
284C2×Dic83—42no—
285C2×Dic83—42no—
286C2×Dic83—44no—
287C2×Dic83—44no—
288C2×Dic83—42no—
289C2×Dic83—41no—
290C2×Dic83—41no—
291C2×Dic83C2×C4212yes—
292C2×Dic83C2×C4212yes—
293C2×Dic83C2×C4212yes—
294C2×Dic83C2×C22⋊C411yescharacteristic
295C2×Dic83C2×C22⋊C412yes—
296C2×Dic83C2×C22⋊C411yescharacteristic
297C2×Dic83C2×C22⋊C411yescharacteristic
298C2×Dic83C2×C22⋊C412yes—
299C2×Dic83C2×C22⋊C411yescharacteristic
300C2×Dic83#11712yes—
301C2×Dic83#11712yes—
302C2×Dic83C4×D418yes—
303C2×Dic83C4×D418yes—
304C4×D83—24no—
305C4×D83—24no—
306C4×D83—42no—
307C4×D83—42no—
308C4×D83—42no—
309C4×D83—42no—
310Dic166—28no—
311C22×C83—22no—
312C22×C83—21no—
313C22×C83—22no—
314C22×C83—21no—
315C22×C83—22no—
316C22×C83—42no—
317C22×C83—42no—
318C22×C83—42no—
319C22×C83—42no—
320C22×C83—41no—
321C22×C83—41no—
322C22×C83C22×C4211yescharacteristic
323C22×C83C22×C22⋊C411yescharacteristic
324C22×C83C2×#11711yescharacteristic
325C22×C83C2×C4×D414yes—
326C2×D83—22no—
327C2×D83—42no—
328C2×D83—41no—
329C2×D83—41no—
330C2×D83—42no—
331C4×C83—21no—
332C4×C83—22no—
333C4×C83—22no—
334C4×C83—48no—
335C4×C83—41no—
336C4×C83—41no—
337C4×C83#41012yescomplemented
338Dic83—21no—
339Dic83—22no—
340Dic83—22no—
341Dic83—48no—
342Dic83—41no—
343Dic83—41no—
344Dic83C4×C22⋊C414yes—
345Dic83C4×C22⋊C412yes—
346Dic83C4×C22⋊C412yes—
347Dic83#41012yescomplemented
348C4×#410—831nomaximal, Sylow
349C2×C83—24no—
350C2×C83—21no—
351C2×C83—21no—
352C2×C83—42no—
353C2×C83C2×C4×C22⋊C411yescharacteristic
354C2×C83C2×#41011yescharacteristic
355C2×C83C2×#41011yescharacteristic
356D83—42no—
357C2×C4×#41—831no—
358C2×#410—832no—
359C4×#117—832no—
360C4×#99—832no—
361C4×#99—832no—
362C4×#99—832no—
363C4×#99—831no—
364C4×#99D8311yescharacteristic, complemented
365#1740—832no—
366C83C4×#41011yescharacteristic, complemented, Sylow
367C22×#41—831no—
368C4×#41—1662no—
369C4×#41—1662no—
370C4×#41—1662no—
371C4×#41—1662no—
372C2×C4×Q8—831no—
373C2×C4×Q8—831no—
374C2×C4×D4—831no—
375C2×C4×D4—831no—
376C2×C4×D4—831no—
377C2×C4×D4—831no—
378C2×C4×D4—831no—
379C2×C4×D4C2×D8311yescharacteristic
380C2×#117—831no—
381C2×#117—831no—
382C2×#117—831no—
383C2×#117—834no—
384C22×C42—831no—
385C22×C42—831no—
386C22×C42—831no—
387#410—8316no—
388C2×#99—832no—
389C2×#99—834no—
390C2×#99C2×D8312yes—
391C4×C4⋊C4—1662no—
392C4×C4⋊C4—1662no—
393C4×C22⋊C4—832no—
394C4×C22⋊C4—834no—
395C4×C22⋊C4C2×D8312yes—
396#376—1662no—
397C43—1662no—
398#342—834no—
399#342—832no—
400#342C2×D8312yes—
401C2×#41—838no—
402C2×#41—1662no—
403C2×#41—1662no—
404C2×#41—1664no—
405C22×Q8—831no—
406C22×D4—831no—
407C22×D4—831no—
408C22×D4C22×D8311yescharacteristic
409C23×C4—831no—
410C23×C4—831no—
411C23×C4—831no—
412C23×C4—831no—
413C23×C4—831no—
414C23×C4—831no—
415C23×C4—831no—
416C23×C4C4×D8311yescharacteristic
417C23×C4C22×D8311yescharacteristic
418C4×Q8—1662no—
419C4×Q8—1662no—
420C4×Q8—1662no—
421C4×Q8—1662no—
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—1662no—
425C4×D4—1662no—
426C4×D4—1662no—
427C4×D4—1662no—
428C4×D4—1662no—
429C4×D4—1662no—
430C4×D4—1662no—
431C4×D4—1662no—
432C4×D4—1662no—
433C4×D4—1662no—
434#117—8316no—
435#117—1662no—
436#117—1662no—
437#117—1662no—
438#117—1662no—
439#117—1662no—
440#117—1662no—
441#117—1668no—
442C2×C4⋊C4—831no—
443C2×C4⋊C4—831no—
444C2×C4⋊C4—831no—
445C2×C4⋊C4—831no—
446C2×C4⋊C4—831no—
447C2×C4⋊C4—1664no—
448C2×C4⋊C4C4×D8311yescharacteristic
449C2×C22⋊C4—834no—
450C2×C22⋊C4—831no—
451C2×C22⋊C4—831no—
452C2×C22⋊C4—831no—
453C2×C22⋊C4—831no—
454C2×C22⋊C4C4×D8311yescharacteristic
455C2×C22⋊C4C22×D8311yescharacteristic
456C2×C22⋊C4C22×D8314yes—
457C2×C42—22no—
458C2×C42—831no—
459C2×C42—831no—
460C2×C42—831no—
461C2×C42—831no—
462C2×C42—832no—
463C2×C42—832no—
464C2×C42—832no—
465C2×C42—832no—
466C2×C42—831no—
467C2×C42—831no—
468C2×C42—831no—
469C2×C42—831no—
470C2×C42—831no—
471C2×C42—1661no—
472C2×C42—1661no—
473C2×C42—1661no—
474C2×C42—1661no—
475C2×C42—1664no—
476C2×C42—1662no—
477C2×C42—1661no—
478C2×C42—1661no—
479C2×C42—1661no—
480C2×C42—1661no—
481C2×C42—1664no—
482C2×C42C4×D8311yescharacteristic
483#99—838no—
484#99—8316no—
485#99C4×D8318yescomplemented
486#95—22no—
487#95—1664no—
488#95—1662no—
489C24—831no—
490C24C2×C4×D8311yescharacteristic
491C24C23×D8311yescharacteristic
492#41—16616no—
493#41—16616no—
494C2×Q8—834no—
495C2×Q8—1662no—
496C2×Q8—1662no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—834no—
500C2×D4—834no—
501C2×D4—1662no—
502C2×D4—1662no—
503C2×D4—1662no—
504C2×D4—1662no—
505C2×D4C2×C4×D8314yes—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—3322no—
512C22×C4—3322no—
513C22×C4—3322no—
514C22×C4—3322no—
515C22×C4—831no—
516C22×C4—832no—
517C22×C4—831no—
518C22×C4—831no—
519C22×C4—831no—
520C22×C4—831no—
521C22×C4—834no—
522C22×C4—832no—
523C22×C4—832no—
524C22×C4—834no—
525C22×C4—831no—
526C22×C4—831no—
527C22×C4—832no—
528C22×C4—834no—
529C22×C4—834no—
530C22×C4—1661no—
531C22×C4—1661no—
532C22×C4—1661no—
533C22×C4—1661no—
534C22×C4—1662no—
535C22×C4—1661no—
536C22×C4—1661no—
537C22×C4—1664no—
538C22×C4—1661no—
539C22×C4—1661no—
540C22×C4—1661no—
541C22×C4—1661no—
542C22×C4—1662no—
543C22×C4C2×C4×D8311yescharacteristic
544C22×C4C2×C4×D8311yescharacteristic
545C22×C4C2×C4×D8311yescharacteristic
546C22×C4C2×C4×D8311yescharacteristic
547C22×C4C2×C4×D8311yescharacteristic
548C22×C4D4×D8312yes—
549C22×C4D4×D8312yes—
550C4⋊C4—22no—
551C4⋊C4—1662no—
552C4⋊C4—1662no—
553C4⋊C4—1662no—
554C4⋊C4—1662no—
555C4⋊C4—16616no—
556C4⋊C4—1662no—
557C22⋊C4—22no—
558C22⋊C4—24no—
559C22⋊C4—22no—
560C22⋊C4—838no—
561C22⋊C4—1662no—
562C22⋊C4—1662no—
563C22⋊C4—1662no—
564C22⋊C4—1664no—
565C22⋊C4—1662no—
566C22⋊C4C2×C4×D8318yes—
567C42—21no—
568C42—21no—
569C42—44no—
570C42—3324no—
571C42—3328no—
572C42—831no—
573C42—831no—
574C42—832no—
575C42—832no—
576C42—832no—
577C42—832no—
578C42—832no—
579C42—831no—
580C42—831no—
581C42—832no—
582C42—1661no—
583C42—1661no—
584C42—1661no—
585C42—1661no—
586C42—1661no—
587C42—1661no—
588C42—1661no—
589C42—1661no—
590C42—16616no—
591C42—1661no—
592C42—1661no—
593C23—21no—
594C23—21no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—3321no—
600C23—3321no—
601C23—832no—
602C23—1661no—
603C23—1661no—
604C23C42×D8312yes—
605C23C22×C4×D8311yescharacteristic
606C23C22×C4×D8312yes—
607C23C2×D4×D8312yes—
608C23#41×D8312yes—
609Q8—1668no—
610D4—28no—
611D4—1668no—
612D4—1668no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—28no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—3322no—
629C2×C4—3322no—
630C2×C4—3322no—
631C2×C4—3324no—
632C2×C4—3324no—
633C2×C4—3322no—
634C2×C4—3322no—
635C2×C4—3322no—
636C2×C4—3321no—
637C2×C4—3321no—
638C2×C4—3322no—
639C2×C4—3321no—
640C2×C4—832no—
641C2×C4—832no—
642C2×C4—831no—
643C2×C4—831no—
644C2×C4—831no—
645C2×C4—832no—
646C2×C4—832no—
647C2×C4—832no—
648C2×C4—838no—
649C2×C4—838no—
650C2×C4—832no—
651C2×C4—831no—
652C2×C4—832no—
653C2×C4—1664no—
654C2×C4—1664no—
655C2×C4—1661no—
656C2×C4—1661no—
657C2×C4—1668no—
658C2×C4—1664no—
659C2×C4—1662no—
660C2×C4—1664no—
661C2×C4—1664no—
662C2×C4—1661no—
663C2×C4—1661no—
664C2×C4C42×D8312yes—
665C2×C4C22⋊C4×D8311yescharacteristic
666C2×C4C22⋊C4×D8312yes—
667C2×C4C22⋊C4×D8311yescharacteristic
668C22—22no—
669C22—21no—
670C22—22no—
671C22—21no—
672C22—22no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—41no—
678C22—41no—
679C22—3322no—
680C22—3322no—
681C22—3321no—
682C22—3321no—
683C22—1662no—
684C22C2×C42×D8311yescharacteristic
685C22C2×C22⋊C4×D8311yescharacteristic
686C22#117×D8311yescharacteristic
687C22C4×D4×D8314yes—
688C4—21no—
689C4—22no—
690C4—22no—
691C4—48no—
692C4—41no—
693C4—41no—
694C4—3328no—
695C4—3321no—
696C4—3321no—
697C4—832no—
698C4—832no—
699C4—832no—
700C4—834no—
701C4—1661no—
702C4—1662no—
703C4—1662no—
704C4#1912767312yesdirect product factor
705C2—24no—
706C2—21no—
707C2—21no—
708C2—42no—
709C2—3322no—
710C2C4×C22⋊C4×D8311yescharacteristic
711C2#410×D8311yescharacteristic
712C2C2×#1912767311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D83
commutatorC22×C83C22×C42
FrattiniC24C23×D83
FittingC4×#99×C83C2
socleC22×C83C22×C22⋊C4
prime radicalC22×#13050589C22
cosocleC24×C83C24
hypercenterC4×#99D83
hypocenterC83C4×#410
LCSG ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. C4×#14581748C2semidirect
4. #99×Dic83C2semidirect
5. C4×#14581706C2semidirect
6. C4×#14581707C2semidirect
7. #24907250C2semidirect
8. #24907194C2semidirect
9. C4×#99×C83C2semidirect
15. C2×C4×Dic166C4semidirect
16. C2×#14581757C4semidirect
18. C2×C4×C22⋊D83C4semidirect
20. C2×(C22⋊D83)⋊C4C4semidirect
22. C2×#14581750C4semidirect
23. C2×#14581748C4semidirect
26. C22×C4×Dic83C4semidirect
28. C2×C42×D83C4semidirect
29. #19127673C4direct (N × H)
79. #14581748C2×C4semidirect
115. #14581707C2×C4semidirect
116. #14581706C2×C4semidirect
130. #99×C83C2×C4semidirect
137. C2×Dic166C42semidirect
142. C2×C22⋊D83C42semidirect
152. C22×Dic83C42semidirect
175. C2×C4×D83C42semidirect
337. C4×C83#410semidirect
347. Dic83#410semidirect
364. C4×#99D83semidirect
366. C83C4×#410semidirect
485. #99C4×D83semidirect
704. C4#19127673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#130505892
C2×#191276732
C4×#145817482
#99×Dic832
C4×#145817062
C4×#145817072
#249072502
#249071942
C4×#99×C832
C4×#41083