Finite Group Databasebeta

← C4⋊C4×Dic83⋊C4 #35325841

Subgroups — C4⋊C4×Dic83⋊C4 #35325841

Order 21248.

1838 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127570C211yesmaximal, characteristic
2C2×C4⋊C4×Dic83C211yesmaximal, characteristic
3C2×C4⋊C4×Dic83C211yesmaximal, characteristic
4C2×C4×Dic83⋊C4C212yesmaximal
5C2×C4×Dic83⋊C4C211yesmaximal, characteristic
6#24905696C212yesmaximal
7#24905694C212yesmaximal
8#24905693C211yesmaximal, characteristic
9#24905692C211yesmaximal, characteristic
10Dic83⋊#95C212yesmaximal
11C2×C4×C4⋊C4×C83C211yesmaximal, characteristic
12C22×C4⋊Dic83C2211yescharacteristic
13C22×C4⋊Dic83C2211yescharacteristic
14C22×Dic83⋊C4C2212yes—
15C22×Dic83⋊C4C2211yescharacteristic
16C22×Dic83⋊C4C2212yes—
17C22×Dic83⋊C4C2211yescharacteristic
18C22×C4×Dic83C2212yes—
19C22×C4×Dic83C2212yes—
20C22×C4×Dic83C2211yescharacteristic
21C22×C4×Dic83C2211yescharacteristic
22#19127570C418yescomplemented
23C4⋊C4×Dic83—24no—
24C4⋊C4×Dic83C418yescomplemented
25C4×Dic83⋊C4—28no—
26C4×Dic83⋊C4C418yescomplemented
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2211yescharacteristic
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2211yescharacteristic
35C22×C4⋊C4×C83C2211yescharacteristic
36C22×C4⋊C4×C83C2211yescharacteristic
37C22×C42×C83C2212yes—
38C22×C42×C83C2211yescharacteristic
39C4×C4⋊C4×C83—24no—
40C2×#95×C83C2212yes—
41C23×Dic83C2312yes—
42C23×Dic83C2311yescharacteristic
43C23×Dic83C2312yes—
44C23×Dic83C2311yescharacteristic
45C23×Dic83C2311yescharacteristic
46C23×Dic83C2311yescharacteristic
47C2×C4⋊Dic83—22no—
48C2×C4⋊Dic83—22no—
49C2×C4⋊Dic83—22no—
50C2×C4⋊Dic83—22no—
51C2×C4⋊Dic83C2×C414yes—
52C2×C4⋊Dic83C2×C414yes—
53C2×Dic83⋊C4—24no—
54C2×Dic83⋊C4—22no—
55C2×Dic83⋊C4—22no—
56C2×Dic83⋊C4—24no—
57C2×Dic83⋊C4—42no—
58C2×Dic83⋊C4—42no—
59C2×Dic83⋊C4C2×C414yes—
60C2×Dic83⋊C4C2×C418yes—
61C2×Dic83⋊C4C2×C418yes—
62C2×Dic83⋊C4C2×C414yes—
63C2×Dic83⋊C4D414yes—
64C2×Dic83⋊C4Q814yes—
65C2×C4×Dic83—24no—
66C2×C4×Dic83—24no—
67C2×C4×Dic83—24no—
68C2×C4×Dic83—22no—
69C2×C4×Dic83—24no—
70C2×C4×Dic83—22no—
71C2×C4×Dic83—42no—
72C2×C4×Dic83C2×C414yes—
73C2×C4×Dic83C2×C418yes—
74C2×C4×Dic83C2×C414yes—
75C2×C4×Dic83C2×C414yes—
76C2×C4×Dic83C2×C414yes—
77C83⋊#95—24no—
78C83⋊#95—24no—
79C83⋊#95—24no—
80C83⋊#95—42no—
81C83⋊#95—42no—
82C83⋊#95C2×C414yes—
83C83⋊#95C2×C414yes—
84C83⋊#95C2×C418yes—
85C23×C4×C83C2312yes—
86C23×C4×C83C2311yescharacteristic
87C23×C4×C83C2311yescharacteristic
88C23×C4×C83C2312yes—
89C23×C4×C83C2311yescharacteristic
90C2×C4⋊C4×C83—22no—
91C2×C4⋊C4×C83—22no—
92C2×C4⋊C4×C83C2×C414yes—
93C2×C4⋊C4×C83C2×C414yes—
94C2×C4⋊C4×C83D414yes—
95C2×C4⋊C4×C83Q814yes—
96C2×C42×C83—22no—
97C2×C42×C83—22no—
98C2×C42×C83—24no—
99C2×C42×C83—24no—
100C2×C42×C83—42no—
101C2×C42×C83C2×C414yes—
102#95×C83—24no—
103C22×Dic83—21no—
104C22×Dic83—21no—
105C22×Dic83—21no—
106C22×Dic83—21no—
107C22×Dic83—21no—
108C22×Dic83—21no—
109C22×Dic83—21no—
110C22×Dic83—21no—
111C22×Dic83—22no—
112C22×Dic83—21no—
113C22×Dic83—22no—
114C22×Dic83—22no—
115C22×Dic83—22no—
116C22×Dic83—21no—
117C22×Dic83—21no—
118C22×Dic83—21no—
119C22×Dic83—22no—
120C22×Dic83—22no—
121C22×Dic83—22no—
122C22×Dic83—22no—
123C22×Dic83—21no—
124C22×Dic83—22no—
125C22×Dic83—22no—
126C22×Dic83—22no—
127C22×Dic83—21no—
128C22×Dic83—22no—
129C22×Dic83C22×C412yes—
130C22×Dic83C22×C414yes—
131C22×Dic83C22×C414yes—
132C22×Dic83C22×C412yes—
133C22×Dic83C22×C412yes—
134C22×Dic83C22×C412yes—
135C22×Dic83C22×C412yes—
136C22×Dic83C22×C412yes—
137C22×Dic83C22×C412yes—
138C22×Dic83C22×C412yes—
139C22×Dic83C2×D412yes—
140C22×Dic83C2×D412yes—
141C22×Dic83C2×Q812yes—
142C22×Dic83C2×Q812yes—
143C22×Dic83#4112yes—
144C22×Dic83#4112yes—
145C4⋊Dic83—28no—
146C4⋊Dic83—28no—
147Dic83⋊C4—28no—
148Dic83⋊C4—216no—
149Dic83⋊C4—48no—
150Dic83⋊C4C4⋊C4116yesdirect product factor
151C4×Dic83—28no—
152C4×Dic83—216no—
153C4×Dic83—48no—
154C4×Dic83C42116yescomplemented
155C24×C83C2411yescharacteristic
156C22×C4×C83—21no—
157C22×C4×C83—22no—
158C22×C4×C83—21no—
159C22×C4×C83—22no—
160C22×C4×C83—21no—
161C22×C4×C83—22no—
162C22×C4×C83—22no—
163C22×C4×C83—21no—
164C22×C4×C83—21no—
165C22×C4×C83—22no—
166C22×C4×C83—22no—
167C22×C4×C83—21no—
168C22×C4×C83—22no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—22no—
172C22×C4×C83—22no—
173C22×C4×C83—21no—
174C22×C4×C83—22no—
175C22×C4×C83—21no—
176C22×C4×C83C22×C412yes—
177C22×C4×C83C22×C414yes—
178C22×C4×C83C22×C412yes—
179C22×C4×C83C22×C414yes—
180C22×C4×C83C22×C412yes—
181C22×C4×C83C22×C412yes—
182C22×C4×C83C22×C412yes—
183C22×C4×C83C2×D412yes—
184C22×C4×C83C2×D414yes—
185C22×C4×C83C2×D412yes—
186C22×C4×C83C2×Q812yes—
187C22×C4×C83C2×Q814yes—
188C22×C4×C83C2×Q812yes—
189C22×C4×C83#4112yes—
190C22×C4×C83#4112yes—
191C4⋊C4×C83—28no—
192C4⋊C4×C83C4⋊C4116yescomplemented
193C42×C83—28no—
194C42×C83—48no—
195C23×C83C23×C411yescharacteristic
196C23×C83C23×C411yescharacteristic
197C23×C83C23×C411yescharacteristic
198C23×C83C22×D411yescharacteristic
199C23×C83C22×D411yescharacteristic
200C23×C83C22×Q811yescharacteristic
201C23×C83C22×Q811yescharacteristic
202C23×C83C2×#4111yescharacteristic
203C23×C83C2×#4111yescharacteristic
204C23×C83C2×#4111yescharacteristic
205C23×C83C2×#4111yescharacteristic
206C23×C83H(5,𝔽2)11yescharacteristic
207C23×C83H(5,𝔽2)11yescharacteristic
208C23×C832−1+411yescharacteristic
209C23×C832−1+411yescharacteristic
210C2×C4×C83—22no—
211C2×C4×C83—24no—
212C2×C4×C83—24no—
213C2×C4×C83—22no—
214C2×C4×C83—22no—
215C2×C4×C83—24no—
216C2×C4×C83—24no—
217C2×C4×C83—22no—
218C2×C4×C83—22no—
219C2×C4×C83—24no—
220C2×C4×C83—22no—
221C2×C4×C83—24no—
222C2×C4×C83—22no—
223C2×C4×C83—22no—
224C2×C4×C83—24no—
225C2×C4×C83—24no—
226C2×C4×C83—24no—
227C2×C4×C83—22no—
228C2×C4×C83—42no—
229C2×C4×C83—41no—
230C2×C4×C83—41no—
231C2×C4×C83—42no—
232C2×C4×C83—42no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—42no—
236C2×C4×C83C2×C4214yes—
237C2×C4×C83C2×C4⋊C414yes—
238C2×C4×C83C2×C4⋊C418yes—
239C2×C4×C83C2×C4⋊C414yes—
240C2×C4×C83#11714yes—
241C2×C4×C83C4×D414yes—
242C2×C4×C83C4×D414yes—
243C2×C4×C83C4×Q814yes—
244C2×C4×C83C4×Q814yes—
245C2×Dic83—22no—
246C2×Dic83—22no—
247C2×Dic83—22no—
248C2×Dic83—22no—
249C2×Dic83—22no—
250C2×Dic83—22no—
251C2×Dic83—22no—
252C2×Dic83—22no—
253C2×Dic83—22no—
254C2×Dic83—22no—
255C2×Dic83—22no—
256C2×Dic83—22no—
257C2×Dic83—22no—
258C2×Dic83—24no—
259C2×Dic83—24no—
260C2×Dic83—22no—
261C2×Dic83—24no—
262C2×Dic83—24no—
263C2×Dic83—24no—
264C2×Dic83—22no—
265C2×Dic83—24no—
266C2×Dic83—42no—
267C2×Dic83—41no—
268C2×Dic83—42no—
269C2×Dic83—41no—
270C2×Dic83—42no—
271C2×Dic83—42no—
272C2×Dic83—42no—
273C2×Dic83—41no—
274C2×Dic83—42no—
275C2×Dic83—41no—
276C2×Dic83—42no—
277C2×Dic83—42no—
278C2×Dic83C2×C4214yes—
279C2×Dic83C2×C4214yes—
280C2×Dic83C2×C4⋊C414yes—
281C2×Dic83C2×C4⋊C414yes—
282C2×Dic83#11714yes—
283C2×Dic83C4×D414yes—
284C2×Dic83C4×D414yes—
285C2×Dic83C4×Q814yes—
286C2×Dic83C4×Q814yes—
287C22×C83C22×C4211yescharacteristic
288C22×C83C22×C4⋊C411yescharacteristic
289C22×C83C22×C4⋊C411yescharacteristic
290C22×C83C2×#11711yescharacteristic
291C22×C83C2×#11711yescharacteristic
292C22×C83C2×C4×D411yescharacteristic
293C22×C83C2×C4×D411yescharacteristic
294C22×C83C2×C4×D411yescharacteristic
295C22×C83C2×C4×D411yescharacteristic
296C22×C83C2×C4×Q811yescharacteristic
297C22×C83C2×C4×Q811yescharacteristic
298C22×C83C2×C4×Q811yescharacteristic
299C22×C83C2×C4×Q811yescharacteristic
300C22×C83#51811yescharacteristic
301C22×C83#51911yescharacteristic
302C22×C83#52011yescharacteristic
303C22×C83#52011yescharacteristic
304C22×C83#52011yescharacteristic
305C22×C83#52011yescharacteristic
306C22×C83D4211yescharacteristic
307C22×C83#54711yescharacteristic
308C22×C83#54711yescharacteristic
309C22×C83D4×Q811yescharacteristic
310C22×C83D4×Q811yescharacteristic
311C22×C83#55011yescharacteristic
312C22×C83#55011yescharacteristic
313C22×C83#55411yescharacteristic
314C22×C83#55411yescharacteristic
315C22×C83#55511yescharacteristic
316C22×C83#55611yescharacteristic
317C22×C83#55611yescharacteristic
318C22×C83#55711yescharacteristic
319C22×C83#55711yescharacteristic
320C22×C83Q8211yescharacteristic
321C22×C83#55911yescharacteristic
322C4×C83—28no—
323C4×C83—24no—
324C4×C83—42no—
325C4×C83—44no—
326C4×C83C4×C4⋊C418yescomplemented
327Dic83—24no—
328Dic83—24no—
329Dic83—44no—
330Dic83—42no—
331Dic83—44no—
332Dic83C4×C4⋊C418yescomplemented
333C4⋊C42—831nomaximal, Sylow
334C2×C83C2×C4×C4⋊C411yescharacteristic
335C2×C83C2×C4×C4⋊C411yescharacteristic
336C2×C83#227411yescharacteristic
337C2×C83D4×C4⋊C411yescharacteristic
338C2×C83D4×C4⋊C411yescharacteristic
339C2×C83Q8×C4⋊C411yescharacteristic
340C2×C83Q8×C4⋊C411yescharacteristic
341C2×C83#235411yescharacteristic
342C2×C83#235411yescharacteristic
343C2×C83#235511yescharacteristic
344C2×C83#235511yescharacteristic
345C2×C83#236511yescharacteristic
346C2×C83#236511yescharacteristic
347C2×C83#236611yescharacteristic
348C2×C83#236911yescharacteristic
349C2×#384—831no—
350C2×C4×C4⋊C4—831no—
351C2×C4×C4⋊C4—832no—
352C2×C4×C4⋊C4—831no—
353C2×C4×C4⋊C4—831no—
354C2×C4×C4⋊C4D8311yescharacteristic
355#1436—832no—
356#1436—832no—
357C4⋊#95—831no—
358C4⋊#95—832no—
359C4⋊#95—831no—
360C83C4⋊C4211yescharacteristic, complemented, Sylow
361C22×C4⋊C4—832no—
362C22×C4⋊C4—831no—
363C22×C4⋊C4—831no—
364C22×C4⋊C4—832no—
365C22×C4⋊C4—831no—
366C22×C4⋊C4—831no—
367C22×C4⋊C4C2×D8311yescharacteristic
368C22×C4⋊C4C2×D8311yescharacteristic
369C22×C42—832no—
370C22×C42—831no—
371C22×C42—832no—
372C22×C42—831no—
373C22×C42C2×D8312yes—
374C22×C42C2×D8311yescharacteristic
375#384—838no—
376C4×C4⋊C4—24no—
377C4×C4⋊C4—838no—
378C4×C4⋊C4—838no—
379C4×C4⋊C4—1668no—
380C4×C4⋊C4—1664no—
381C2×#95—832no—
382C2×#95—832no—
383C2×#95—831no—
384C2×#95—831no—
385C2×#95—832no—
386C2×#95—832no—
387C2×#95—832no—
388C2×#95—832no—
389C2×#95C2×D8312yes—
390C23×C4—831no—
391C23×C4—831no—
392C23×C4—831no—
393C23×C4—832no—
394C23×C4—832no—
395C23×C4—831no—
396C23×C4C22×D8312yes—
397C23×C4C22×D8311yescharacteristic
398C23×C4C22×D8311yescharacteristic
399C23×C4C22×D8312yes—
400C23×C4C22×D8311yescharacteristic
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—3322no—
404C2×C4⋊C4—3322no—
405C2×C4⋊C4—838no—
406C2×C4⋊C4—834no—
407C2×C4⋊C4—834no—
408C2×C4⋊C4—834no—
409C2×C4⋊C4—834no—
410C2×C4⋊C4—834no—
411C2×C4⋊C4—838no—
412C2×C4⋊C4—834no—
413C2×C4⋊C4—1664no—
414C2×C4⋊C4—1662no—
415C2×C4⋊C4—1662no—
416C2×C4⋊C4—1664no—
417C2×C4⋊C4—1662no—
418C2×C4⋊C4—1662no—
419C2×C4⋊C4—1662no—
420C2×C4⋊C4—1662no—
421C2×C4⋊C4Dic16614yes—
422C2×C4⋊C4C4×D8314yes—
423C2×C4⋊C4C4×D8314yes—
424C2×C4⋊C4C22⋊D8314yes—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—42no—
430C2×C42—3322no—
431C2×C42—834no—
432C2×C42—834no—
433C2×C42—834no—
434C2×C42—838no—
435C2×C42—834no—
436C2×C42—1664no—
437C2×C42—1664no—
438C2×C42—1664no—
439C2×C42—1664no—
440C2×C42—1662no—
441C2×C42—1662no—
442C2×C42C4×D8314yes—
443#95—24no—
444#95—3322no—
445#95—3322no—
446#95—834no—
447#95—834no—
448#95—838no—
449#95—1664no—
450#95—1664no—
451#95—1664no—
452C24C23×D8311yescharacteristic
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—832no—
474C22×C4—832no—
475C22×C4—832no—
476C22×C4—832no—
477C22×C4—832no—
478C22×C4—832no—
479C22×C4—832no—
480C22×C4—832no—
481C22×C4—832no—
482C22×C4—832no—
483C22×C4—832no—
484C22×C4—832no—
485C22×C4—832no—
486C22×C4—832no—
487C22×C4—834no—
488C22×C4—834no—
489C22×C4—1662no—
490C22×C4—1662no—
491C22×C4—1661no—
492C22×C4—1662no—
493C22×C4—1662no—
494C22×C4—1661no—
495C22×C4—1661no—
496C22×C4—1662no—
497C22×C4—1661no—
498C22×C4—1662no—
499C22×C4—1662no—
500C22×C4—1662no—
501C22×C4—1662no—
502C22×C4—1661no—
503C22×C4—1662no—
504C22×C4—1662no—
505C22×C4—1661no—
506C22×C4—1662no—
507C22×C4—1661no—
508C22×C4—1661no—
509C22×C4—1661no—
510C22×C4—1661no—
511C22×C4—1661no—
512C22×C4—1661no—
513C22×C4—1661no—
514C22×C4—1661no—
515C22×C4C2×C4×D8312yes—
516C22×C4C2×C4×D8314yes—
517C22×C4C2×C4×D8312yes—
518C22×C4C2×C4×D8314yes—
519C22×C4C2×C4×D8312yes—
520C22×C4C2×C4×D8312yes—
521C22×C4C2×C4×D8312yes—
522C22×C4D4×D8312yes—
523C22×C4C2×C22⋊D8314yes—
524C22×C4C2×C22⋊D8312yes—
525C22×C4Q8×D8312yes—
526C22×C4C2×Dic16614yes—
527C22×C4C2×Dic16612yes—
528C22×C4#1305059012yes—
529C22×C4#1305059012yes—
530C4⋊C4—28no—
531C4⋊C4—3328no—
532C4⋊C4—8316no—
533C4⋊C4—1668no—
534C4⋊C4—16616no—
535C4⋊C4—1668no—
536C4⋊C4—1668no—
537C4⋊C4Dic83⋊C4116yesdirect product factor
538C42—28no—
539C42—48no—
540C42—3328no—
541C42—8316no—
542C42—16616no—
543C42—1668no—
544C23C22×C4×D8311yescharacteristic
545C23C22×C4×D8311yescharacteristic
546C23C22×C4×D8311yescharacteristic
547C23C2×D4×D8311yescharacteristic
548C23C22×C22⋊D8311yescharacteristic
549C23C2×Q8×D8311yescharacteristic
550C23C22×Dic16611yescharacteristic
551C23#41×D8311yescharacteristic
552C23#41×D8311yescharacteristic
553C23C2×#1305059011yescharacteristic
554C23C2×#1305059011yescharacteristic
555C23#1458183711yescharacteristic
556C23#1458183811yescharacteristic
557C23#1458183911yescharacteristic
558C23#1458184011yescharacteristic
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—3322no—
586C2×C4—3321no—
587C2×C4—3322no—
588C2×C4—3321no—
589C2×C4—3322no—
590C2×C4—3322no—
591C2×C4—3322no—
592C2×C4—3322no—
593C2×C4—3321no—
594C2×C4—3321no—
595C2×C4—3322no—
596C2×C4—3322no—
597C2×C4—834no—
598C2×C4—834no—
599C2×C4—834no—
600C2×C4—834no—
601C2×C4—834no—
602C2×C4—834no—
603C2×C4—834no—
604C2×C4—834no—
605C2×C4—834no—
606C2×C4—1662no—
607C2×C4—1664no—
608C2×C4—1664no—
609C2×C4—1664no—
610C2×C4—1662no—
611C2×C4—1664no—
612C2×C4—1664no—
613C2×C4—1662no—
614C2×C4—1664no—
615C2×C4—1662no—
616C2×C4—1662no—
617C2×C4—1662no—
618C2×C4—1662no—
619C2×C4—1662no—
620C2×C4—1662no—
621C2×C4—1662no—
622C2×C4—1662no—
623C2×C4—1662no—
624C2×C4—1662no—
625C2×C4—1662no—
626C2×C4—1662no—
627C2×C4C42×D8314yes—
628C2×C4C4⋊C4×D8314yes—
629C2×C4C2×Dic83⋊C418yes—
630C2×C4C2×Dic83⋊C414yes—
631C2×C4#1458174914yes—
632C2×C4C4×C22⋊D8314yes—
633C2×C4C4×C22⋊D8314yes—
634C2×C4C4×Dic16614yes—
635C2×C4C4×Dic16614yes—
636C22C2×C42×D8311yescharacteristic
637C22C2×C4⋊C4×D8311yescharacteristic
638C22C22×Dic83⋊C411yescharacteristic
639C22#117×D8311yescharacteristic
640C22C2×#1458174911yescharacteristic
641C22C4×D4×D8311yescharacteristic
642C22C4×D4×D8311yescharacteristic
643C22C2×C4×C22⋊D8311yescharacteristic
644C22C2×C4×C22⋊D8311yescharacteristic
645C22C4×Q8×D8311yescharacteristic
646C22C4×Q8×D8311yescharacteristic
647C22C2×C4×Dic16611yescharacteristic
648C22C2×C4×Dic16611yescharacteristic
649C22#1912817311yescharacteristic
650C22#1912817711yescharacteristic
651C22#1912818011yescharacteristic
652C22#1912818111yescharacteristic
653C22#1912818211yescharacteristic
654C22#1912818311yescharacteristic
655C22D4×C22⋊D8311yescharacteristic
656C22#1912835011yescharacteristic
657C22#1912835211yescharacteristic
658C22Q8×C22⋊D8311yescharacteristic
659C22D4×Dic16611yescharacteristic
660C22#1912837011yescharacteristic
661C22#1912837211yescharacteristic
662C22#1912840611yescharacteristic
663C22#1912841011yescharacteristic
664C22#1912841411yescharacteristic
665C22#1912841911yescharacteristic
666C22#1912842311yescharacteristic
667C22#1912842711yescharacteristic
668C22#1912842911yescharacteristic
669C22Q8×Dic16611yescharacteristic
670C22#1912843411yescharacteristic
671C4—28no—
672C4—24no—
673C4—42no—
674C4—44no—
675C4—3324no—
676C4—3322no—
677C4—3324no—
678C4—838no—
679C4—1664no—
680C4—1664no—
681C4C4×Dic83⋊C418yescomplemented
682C2C4×C4⋊C4×D8311yescharacteristic
683C2C2×C4×Dic83⋊C411yescharacteristic
684C2#2490981711yescharacteristic
685C2D4×Dic83⋊C411yescharacteristic
686C2C4⋊C4×C22⋊D8311yescharacteristic
687C2Q8×Dic83⋊C411yescharacteristic
688C2C4⋊C4×Dic16611yescharacteristic
689C2#2491040811yescharacteristic
690C2#2491041311yescharacteristic
691C2#2491041611yescharacteristic
692C2#2491042111yescharacteristic
693C2#2491051711yescharacteristic
694C2#2491052211yescharacteristic
695C2#2491052511yescharacteristic
696C2#2491055011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC22×C83C22×C42
FittingC2×C4×C4⋊C4×C83C2
socle, prime radical, cosocleC24×C83C24
hypercenterC2×C4×C4⋊C4D83
hypocenterC83C4⋊C42
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. #19127570C4semidirect
24. C4⋊C4×Dic83C4semidirect
26. C4×Dic83⋊C4C4semidirect
150. Dic83⋊C4C4⋊C4direct (N × H)
154. C4×Dic83C42semidirect
192. C4⋊C4×C83C4⋊C4semidirect
326. C4×C83C4×C4⋊C4semidirect
332. Dic83C4×C4⋊C4semidirect
360. C83C4⋊C42semidirect
537. C4⋊C4Dic83⋊C4direct (N × H)
681. C4C4×Dic83⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#191275702
C2×C4⋊C4×Dic832
C2×C4×Dic83⋊C42
#249056962
#249056942
#249056932
#249056922
Dic83⋊#952
C2×C4×C4⋊C4×C832
C4⋊C4283