Finite Group Databasebeta

← C2×C4×#14581706 #35402051

Subgroups — C2×C4×#14581706 #35402051

Order 21248.

2242 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D83C211yesmaximal, characteristic
2C22×#14581706C212yesmaximal
3C2×C4×C22⋊Dic83C211yesmaximal, characteristic, complemented
4C4×#14581706C218yesmaximal, direct product factor
5C2×#19127467C212yesmaximal, complemented
6C2×C4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
7C23×C22⋊D83C2211yescharacteristic
8C23×C4×D83C411yescharacteristic, complemented
9C2×C4×C22⋊D83—21no—
10C2×C4×C22⋊D83—21no—
11C2×C4×C22⋊D83—22no—
12C2×C4×C22⋊D83—21no—
13C2×C4×C22⋊D83—21no—
14C2×C4×C22⋊D83—22no—
15C2×C4×C22⋊D83C414yescomplemented
16C2×C4×C22⋊D83C2214yes—
17C22×Dic83⋊C4C411yescharacteristic, complemented
18C22×C22⋊Dic83C2212yes—
19C22×C22⋊Dic83C2211yescharacteristic
20C22×(C2×D83)⋊C4C411yescharacteristic, complemented
21C22×C4×Dic83—21no—
22C22×C4×Dic83C411yescharacteristic, complemented
23C2×#14581706C4116yesdirect product factor
24C2×#14581706C2218yes—
25C4×C22⋊Dic83—22no—
26C4×C22⋊Dic83C2214yescomplemented
27C2×C83⋊#95—21no—
28#19127467C2218yescomplemented
29C24×C4×C83C2211yescharacteristic
30C22×C22⋊C4×C83C2212yes—
31C22×C42×C83—21no—
32C4×C22⋊C4×C83—22no—
33C4×C22⋊C4×C83C2214yescomplemented
34C2×#95×C83—21no—
35C24×D83C2×C411yescharacteristic
36C22×C22⋊D83—21no—
37C22×C22⋊D83—21no—
38C22×C22⋊D83—21no—
39C22×C22⋊D83—21no—
40C22×C22⋊D83—24no—
41C22×C22⋊D83C2×C418yes—
42C22×C22⋊D83C2×C412yes—
43C22×C22⋊D83C2312yes—
44C23×Dic83—22no—
45C23×Dic83C2×C411yescharacteristic
46C23×Dic83C2×C411yescharacteristic
47C23×Dic83C2×C411yescharacteristic
48C22×C4×D83—21no—
49C22×C4×D83—22no—
50C22×C4×D83—21no—
51C22×C4×D83—44no—
52C22×C4×D83C2×C414yescomplemented
53C4×C22⋊D83—24no—
54C4×C22⋊D83—24no—
55C4×C22⋊D83—24no—
56C4×C22⋊D83—24no—
57C4×C22⋊D83—24no—
58C4×C22⋊D83—24no—
59C4×C22⋊D83—24no—
60C4×C22⋊D83—24no—
61C2×Dic83⋊C4—21no—
62C2×Dic83⋊C4—21no—
63C2×Dic83⋊C4—22no—
64C2×Dic83⋊C4C2×C414yescomplemented
65C2×C22⋊Dic83—21no—
66C2×C22⋊Dic83—21no—
67C2×C22⋊Dic83—21no—
68C2×C22⋊Dic83—21no—
69C2×C22⋊Dic83—22no—
70C2×C22⋊Dic83—24no—
71C2×C22⋊Dic83C2×C412yes—
72C2×C22⋊Dic83C2×C418yescomplemented
73C2×C22⋊Dic83C2312yes—
74C2×C22⋊Dic83C2314yes—
75C2×(C2×D83)⋊C4—21no—
76C2×(C2×D83)⋊C4—21no—
77C2×(C2×D83)⋊C4—22no—
78C2×(C2×D83)⋊C4C2×C414yescomplemented
79C2×C4×Dic83—21no—
80C2×C4×Dic83—22no—
81C2×C4×Dic83—21no—
82C2×C4×Dic83—24no—
83C2×C4×Dic83—44no—
84C2×C4×Dic83C2×C414yescomplemented
85#14581706C2×C4132yesdirect product factor
86C83⋊#95—24no—
87C25×C83C2311yescharacteristic
88C23×C4×C83—22no—
89C23×C4×C83—44no—
90C23×C4×C83C2×C411yescharacteristic
91C23×C4×C83C2×C411yescharacteristic
92C23×C4×C83C2×C412yes—
93C23×C4×C83D411yescharacteristic
94C23×C4×C83D411yescharacteristic
95C23×C4×C83D412yes—
96C23×C4×C83D411yescharacteristic
97C23×C4×C83D411yescharacteristic
98C23×C4×C83D412yes—
99C23×C4×C83C2312yes—
100C2×C22⋊C4×C83—22no—
101C2×C22⋊C4×C83—24no—
102C2×C22⋊C4×C83C2×C418yescomplemented
103C2×C22⋊C4×C83C2314yes—
104C2×C42×C83—24no—
105C2×C42×C83—44no—
106#95×C83—24no—
107C23×D83—21no—
108C23×D83—21no—
109C23×D83—22no—
110C23×D83—42no—
111C23×D83—42no—
112C23×D83C4214yescomplemented
113C23×D83C22×C412yes—
114C2×C22⋊D83—22no—
115C2×C22⋊D83—22no—
116C2×C22⋊D83—24no—
117C2×C22⋊D83—28no—
118C2×C22⋊D83—28no—
119C2×C22⋊D83—28no—
120C2×C22⋊D83—28no—
121C2×C22⋊D83—22no—
122C2×C22⋊D83—22no—
123C2×C22⋊D83—24no—
124C2×C22⋊D83C4218yescomplemented
125C2×C22⋊D83C22×C418yes—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83—22no—
129C22×Dic83—21no—
130C22×Dic83—21no—
131C22×Dic83—21no—
132C22×Dic83—21no—
133C22×Dic83—28no—
134C22×Dic83—24no—
135C22×Dic83—44no—
136C22×Dic83—44no—
137C22×Dic83—42no—
138C22×Dic83—42no—
139C22×Dic83C4214yescomplemented
140C22×Dic83C22×C412yes—
141C22×Dic83C22×C412yes—
142C22×Dic83C22×C412yes—
143C2×C4×D83—24no—
144C2×C4×D83—24no—
145C2×C4×D83—44no—
146C2×C4×D83—48no—
147C2×C4×D83—44no—
148C2×C4×D83—48no—
149Dic83⋊C4—24no—
150Dic83⋊C4—24no—
151C22⋊Dic83—22no—
152C22⋊Dic83—22no—
153C22⋊Dic83—28no—
154C22⋊Dic83—22no—
155C22⋊Dic83—22no—
156C22⋊Dic83—24no—
157C22⋊Dic83C22×C418yescomplemented
158(C2×D83)⋊C4—24no—
159(C2×D83)⋊C4—24no—
160C4×Dic83—24no—
161C4×Dic83—24no—
162C4×Dic83—48no—
163C24×C83—42no—
164C24×C83—42no—
165C24×C83C22×C411yescharacteristic
166C24×C83C22×C411yescharacteristic
167C24×C83C22×C414yes—
168C24×C83C2×D411yescharacteristic
169C24×C83C2×D411yescharacteristic
170C24×C83C2×D411yescharacteristic
171C24×C83C2×D411yescharacteristic
172C24×C83#4114yes—
173C24×C83C2411yescharacteristic
174C22×C4×C83—24no—
175C22×C4×C83—24no—
176C22×C4×C83—24no—
177C22×C4×C83—28no—
178C22×C4×C83—24no—
179C22×C4×C83—44no—
180C22×C4×C83—44no—
181C22×C4×C83—44no—
182C22×C4×C83—44no—
183C22×C4×C83—42no—
184C22×C4×C83—42no—
185C22×C4×C83—42no—
186C22×C4×C83—44no—
187C22×C4×C83—44no—
188C22×C4×C83C22⋊C411yescharacteristic
189C22×C4×C83C22⋊C412yes—
190C22×C4×C83C22⋊C411yescharacteristic
191C22×C4×C83C22⋊C411yescharacteristic
192C22×C4×C83C22⋊C412yes—
193C22×C4×C83C22⋊C412yes—
194C22×C4×C83C22⋊C412yes—
195C22×C4×C83C22⋊C412yes—
196C22×C4×C83C22⋊C412yes—
197C22×C4×C83C22⋊C411yescharacteristic
198C22×C4×C83C22×C412yes—
199C22×C4×C83C22×C412yes—
200C22×C4×C83C2×D412yes—
201C22×C4×C83C2×D412yes—
202C22×C4×C83C2×D412yes—
203C22×C4×C83C2×D412yes—
204C22⋊C4×C83—28no—
205C22⋊C4×C83—24no—
206C22⋊C4×C83C22×C418yescomplemented
207C42×C83—48no—
208C23×C83—22no—
209C23×C83—22no—
210C23×C83—22no—
211C23×C83—22no—
212C23×C83—22no—
213C23×C83—22no—
214C23×C83—41no—
215C23×C83—41no—
216C23×C83—41no—
217C23×C83—41no—
218C23×C83—41no—
219C23×C83—48no—
220C23×C83—41no—
221C23×C83—41no—
222C23×C83—48no—
223C23×C83—41no—
224C23×C83C2×C4212yes—
225C23×C83C2×C4212yes—
226C23×C83C2×C22⋊C411yescharacteristic
227C23×C83C2×C22⋊C411yescharacteristic
228C23×C83C2×C22⋊C411yescharacteristic
229C23×C83C2×C22⋊C411yescharacteristic
230C23×C83#11712yes—
231C23×C83#11712yes—
232C23×C83C4×D414yes—
233C23×C83C4×D414yes—
234C23×C83C4×D414yes—
235C23×C83C4×D414yes—
236C23×C83C23×C411yescharacteristic
237C23×C83C23×C412yes—
238C23×C83C22×D411yescharacteristic
239C23×C83C22×D411yescharacteristic
240C23×C83C2×#4112yes—
241C22×D83—22no—
242C22×D83—22no—
243C22×D83—24no—
244C22×D83—24no—
245C22×D83—42no—
246C22×D83—42no—
247C22×D83—48no—
248C22×D83—42no—
249C22×D83—42no—
250C22×D83—42no—
251C22×D83—48no—
252C22×D83—42no—
253C22×D83C2×C4214yescomplemented
254C2×C4×C83—22no—
255C2×C4×C83—22no—
256C2×C4×C83—22no—
257C2×C4×C83—24no—
258C2×C4×C83—24no—
259C2×C4×C83—24no—
260C2×C4×C83—24no—
261C2×C4×C83—24no—
262C2×C4×C83—24no—
263C2×C4×C83—28no—
264C2×C4×C83—42no—
265C2×C4×C83—42no—
266C2×C4×C83—42no—
267C2×C4×C83—42no—
268C2×C4×C83—42no—
269C2×C4×C83—42no—
270C2×C4×C83—44no—
271C2×C4×C83—44no—
272C2×C4×C83—416no—
273C2×C4×C83#9914yescomplemented
274C2×C4×C83C2×C22⋊C412yes—
275C2×C4×C83C2×C22⋊C412yes—
276C2×C4×C83C2×C22⋊C412yes—
277C2×C4×C83C2×C22⋊C412yes—
278C22⋊D83—28no—
279C22⋊D83—28no—
280C22⋊D83—28no—
281C22⋊D83—28no—
282C2×Dic83—22no—
283C2×Dic83—22no—
284C2×Dic83—24no—
285C2×Dic83—24no—
286C2×Dic83—22no—
287C2×Dic83—22no—
288C2×Dic83—28no—
289C2×Dic83—44no—
290C2×Dic83—42no—
291C2×Dic83—44no—
292C2×Dic83—416no—
293C2×Dic83—42no—
294C2×Dic83—42no—
295C2×Dic83—42no—
296C2×Dic83—42no—
297C2×Dic83—42no—
298C2×Dic83C2×C4214yescomplemented
299C4×D83—48no—
300C4×D83—48no—
301C22×C83—21no—
302C22×C83—21no—
303C22×C83—21no—
304C22×C83—21no—
305C22×C83—21no—
306C22×C83—21no—
307C22×C83—21no—
308C22×C83—21no—
309C22×C83—21no—
310C22×C83—21no—
311C22×C83—21no—
312C22×C83—21no—
313C22×C83—28no—
314C22×C83—28no—
315C22×C83—24no—
316C22×C83—24no—
317C22×C83—42no—
318C22×C83—42no—
319C22×C83—44no—
320C22×C83—44no—
321C22×C83—42no—
322C22×C83—42no—
323C22×C83C4×C22⋊C412yes—
324C22×C83C4×C22⋊C412yes—
325C22×C83C4×C22⋊C412yes—
326C22×C83C4×C22⋊C412yes—
327C22×C83C2×#9912yes—
328C22×C83#41012yes—
329C22×C83C22×C4211yescharacteristic
330C22×C83C22×C22⋊C411yescharacteristic
331C22×C83C2×#11711yescharacteristic
332C22×C83C2×C4×D412yes—
333C22×C83C2×C4×D412yes—
334C2×D83—24no—
335C2×D83—44no—
336C2×D83—48no—
337C2×D83—42no—
338C2×D83—42no—
339C2×D83—48no—
340C2×D83—44no—
341C4×C83—22no—
342C4×C83—22no—
343C4×C83—22no—
344C4×C83—48no—
345C4×C83C2×#9914yescomplemented
346Dic83—24no—
347Dic83—48no—
348Dic83—42no—
349Dic83—42no—
350C2×C4×#99—831nomaximal, Sylow
351C2×C83—22no—
352C2×C83—22no—
353C2×C83—21no—
354C2×C83—22no—
355C2×C83—21no—
356C2×C83—22no—
357C2×C83—22no—
358C2×C83C4×#9914yescomplemented
359C2×C83C2×C4×C22⋊C411yescharacteristic
360C2×C83C22×#9911yescharacteristic
361C2×C83C2×#41011yescharacteristic
362D83—44no—
363C22×C4×D4—831no—
364C22×#99—832no—
365C2×C4×C22⋊C4—831no—
366C2×C4×C22⋊C4D8311yescharacteristic, complemented
367C4×#99—838no—
368C2×#342—832no—
369C83C2×C4×#9911yescharacteristic, complemented, Sylow
370C23×D4—831no—
371C24×C4—831no—
372C24×C4C2×D8311yescharacteristic
373C2×C4×D4—834no—
374C2×C4×D4—834no—
375C2×C4×D4—1661no—
376C2×C4×D4—1662no—
377C2×C4×D4—1661no—
378C2×C4×D4—1661no—
379C2×C4×D4—1662no—
380C2×C4×D4—1661no—
381C22×C4⋊C4—831no—
382C22×C22⋊C4—832no—
383C22×C22⋊C4—831no—
384C22×C22⋊C4—831no—
385C22×C22⋊C4C2×D8312yes—
386C22×C42—21no—
387C22×C42—831no—
388C22×C42—1661no—
389C2×#99—8316no—
390C2×#99—838no—
391C4×C22⋊C4—22no—
392C4×C22⋊C4—834no—
393C4×C22⋊C4—1662no—
394C4×C22⋊C4C2×D8314yescomplemented
395C2×#95—21no—
396C2×#95—1661no—
397#342—838no—
398C25—831no—
399C25C22×D8311yescharacteristic
400C22×D4—832no—
401C22×D4—838no—
402C22×D4—832no—
403C22×D4—1661no—
404C22×D4—1661no—
405C22×D4—1661no—
406C22×D4—1661no—
407C22×D4—1664no—
408C23×C4—22no—
409C23×C4—44no—
410C23×C4—3324no—
411C23×C4—831no—
412C23×C4—831no—
413C23×C4—834no—
414C23×C4—831no—
415C23×C4—1662no—
416C23×C4—1661no—
417C23×C4—1662no—
418C23×C4—1661no—
419C23×C4C4×D8311yescharacteristic
420C23×C4C4×D8311yescharacteristic
421C23×C4C4×D8312yes—
422C23×C4D33211yescharacteristic
423C23×C4D33211yescharacteristic
424C23×C4D33212yes—
425C23×C4C22⋊D8311yescharacteristic
426C23×C4C22⋊D8311yescharacteristic
427C23×C4C22⋊D8312yes—
428C23×C4C22×D8312yes—
429C4×D4—1664no—
430C4×D4—1664no—
431C4×D4—1664no—
432C4×D4—1664no—
433C4×D4—1664no—
434C4×D4—1664no—
435C4×D4—1664no—
436C4×D4—1664no—
437C2×C4⋊C4—834no—
438C2×C4⋊C4—1661no—
439C2×C4⋊C4—1661no—
440C2×C4⋊C4—1662no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—838no—
444C2×C22⋊C4—834no—
445C2×C22⋊C4—832no—
446C2×C22⋊C4—832no—
447C2×C22⋊C4—834no—
448C2×C22⋊C4—1661no—
449C2×C22⋊C4—1661no—
450C2×C22⋊C4—1661no—
451C2×C22⋊C4—1661no—
452C2×C22⋊C4—1662no—
453C2×C22⋊C4—1664no—
454C2×C22⋊C4—1661no—
455C2×C22⋊C4—1661no—
456C2×C22⋊C4—1662no—
457C2×C22⋊C4C4×D8318yescomplemented
458C2×C22⋊C4C22×D8314yes—
459C2×C42—24no—
460C2×C42—44no—
461C2×C42—3324no—
462C2×C42—834no—
463C2×C42—1664no—
464C2×C42—1661no—
465C2×C42—1662no—
466C2×C42—1661no—
467#99—8332no—
468#95—24no—
469#95—1664no—
470C24—42no—
471C24—42no—
472C24—3322no—
473C24—3322no—
474C24—832no—
475C24—834no—
476C24—1661no—
477C24—1661no—
478C24—1662no—
479C24C2×C4×D8311yescharacteristic
480C24C2×C4×D8311yescharacteristic
481C24C2×C4×D8314yes—
482C24C2×C22⋊D8311yescharacteristic
483C24C2×C22⋊D8311yescharacteristic
484C24C2×D33211yescharacteristic
485C24C2×D33211yescharacteristic
486C24#1305059014yes—
487C24C23×D8311yescharacteristic
488C2×D4—838no—
489C2×D4—838no—
490C2×D4—1662no—
491C2×D4—1662no—
492C2×D4—1664no—
493C2×D4—1662no—
494C2×D4—1662no—
495C2×D4—1664no—
496C2×D4—1668no—
497C2×D4—1668no—
498C2×D4—1668no—
499C2×D4—1668no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—28no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—3324no—
515C22×C4—3328no—
516C22×C4—3328no—
517C22×C4—3324no—
518C22×C4—3324no—
519C22×C4—3324no—
520C22×C4—3322no—
521C22×C4—3322no—
522C22×C4—832no—
523C22×C4—832no—
524C22×C4—832no—
525C22×C4—834no—
526C22×C4—1664no—
527C22×C4—1661no—
528C22×C4—1661no—
529C22×C4—1661no—
530C22×C4—1661no—
531C22×C4—1668no—
532C22×C4—1664no—
533C22×C4—1664no—
534C22×C4—1661no—
535C22×C4—1661no—
536C22×C4—1662no—
537C22×C4(C2×D83)⋊C411yescharacteristic
538C22×C4(C2×D83)⋊C412yes—
539C22×C4(C2×D83)⋊C411yescharacteristic
540C22×C4(C2×D83)⋊C411yescharacteristic
541C22×C4(C2×D83)⋊C412yes—
542C22×C4(C2×D83)⋊C412yes—
543C22×C4(C2×D83)⋊C412yes—
544C22×C4(C2×D83)⋊C412yes—
545C22×C4(C2×D83)⋊C412yes—
546C22×C4(C2×D83)⋊C411yescharacteristic
547C22×C4C2×C4×D8312yes—
548C22×C4C2×C4×D8312yes—
549C22×C4C2×C22⋊D8312yes—
550C22×C4C2×C22⋊D8312yes—
551C22×C4C2×D33212yes—
552C22×C4C2×D33212yes—
553C4⋊C4—1664no—
554C4⋊C4—1664no—
555C22⋊C4—24no—
556C22⋊C4—28no—
557C22⋊C4—838no—
558C22⋊C4—1662no—
559C22⋊C4—1662no—
560C22⋊C4—1664no—
561C22⋊C4—1662no—
562C22⋊C4—1662no—
563C22⋊C4—1668no—
564C22⋊C4—1664no—
565C22⋊C4—1664no—
566C22⋊C4C2×C4×D8318yescomplemented
567C42—48no—
568C42—3328no—
569C42—1664no—
570C42—1664no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—48no—
583C23—41no—
584C23—41no—
585C23—48no—
586C23—41no—
587C23—3322no—
588C23—3322no—
589C23—3328no—
590C23—3322no—
591C23—3322no—
592C23—3328no—
593C23—3322no—
594C23—3322no—
595C23—834no—
596C23—1662no—
597C23—1662no—
598C23—1664no—
599C23—1664no—
600C23C42×D8312yes—
601C23C42×D8312yes—
602C23C2×(C2×D83)⋊C411yescharacteristic
603C23C2×(C2×D83)⋊C411yescharacteristic
604C23C2×(C2×D83)⋊C411yescharacteristic
605C23C2×(C2×D83)⋊C411yescharacteristic
606C23#1458174912yes—
607C23#1458174912yes—
608C23C4×C22⋊D8314yes—
609C23C4×C22⋊D8314yes—
610C23C4×D33214yes—
611C23C4×D33214yes—
612C23C22×C4×D8311yescharacteristic
613C23C22×C4×D8312yes—
614C23C22×C22⋊D8311yescharacteristic
615C23C22×D33211yescharacteristic
616C23C2×#1305059012yes—
617D4—1668no—
618D4—1668no—
619D4—1668no—
620D4—1668no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—28no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—416no—
640C2×C4—3328no—
641C2×C4—3324no—
642C2×C4—3322no—
643C2×C4—3324no—
644C2×C4—33216no—
645C2×C4—3322no—
646C2×C4—3322no—
647C2×C4—3322no—
648C2×C4—3328no—
649C2×C4—3322no—
650C2×C4—3322no—
651C2×C4—834no—
652C2×C4—1662no—
653C2×C4—1662no—
654C2×C4—1668no—
655C2×C4—1662no—
656C2×C4—1662no—
657C2×C4—1664no—
658C2×C4—1664no—
659C2×C4#1458170614yesdirect product factor
660C2×C4C2×(C2×D83)⋊C412yes—
661C2×C4C2×(C2×D83)⋊C412yes—
662C2×C4C2×(C2×D83)⋊C412yes—
663C2×C4C2×(C2×D83)⋊C412yes—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—28no—
677C22—28no—
678C22—24no—
679C22—24no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—44no—
685C22—44no—
686C22—3324no—
687C22—3324no—
688C22—3328no—
689C22—3322no—
690C22—3322no—
691C22—3328no—
692C22—1664no—
693C22C4×(C2×D83)⋊C412yes—
694C22C4×(C2×D83)⋊C412yes—
695C22C4×(C2×D83)⋊C412yes—
696C22C4×(C2×D83)⋊C412yes—
697C22C2×#1458170612yes—
698C22#1912767412yes—
699C22C2×C42×D8311yescharacteristic
700C22C22×(C2×D83)⋊C411yescharacteristic
701C22C2×#1458174911yescharacteristic
702C22C2×C4×C22⋊D8312yes—
703C22C2×C4×D33212yes—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—48no—
708C4—3328no—
709C4—3322no—
710C4—3322no—
711C4—1664no—
712C4C2×#1458170614yesdirect product factor
713C2—22no—
714C2—22no—
715C2—21no—
716C2—21no—
717C2—22no—
718C2—22no—
719C2—22no—
720C2—3324no—
721C2C4×#1458170614yesdirect product factor
722C2C2×C4×(C2×D83)⋊C411yescharacteristic
723C2C22×#1458170611yescharacteristic
724C2C2×#1912767411yescharacteristic
subgroupG/H
centerC22×C4(C2×D83)⋊C4
commutatorC22×C83C22×C42
FrattiniC24C23×D83
FittingC2×C4×C22⋊C4×C83C2
socleC23×C83C2×C22⋊C4
prime radicalC23×C22⋊D83C22
cosocleC24×C83C24
hypercenterC2×C4×C22⋊C4D83
hypocenterC83C2×C4×#99
LCSG ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊Dic83C2semidirect
4. C4×#14581706C2direct (N × H)
5. C2×#19127467C2semidirect
6. C2×C4×C22⋊C4×C83C2semidirect
8. C23×C4×D83C4semidirect
15. C2×C4×C22⋊D83C4semidirect
17. C22×Dic83⋊C4C4semidirect
20. C22×(C2×D83)⋊C4C4semidirect
22. C22×C4×Dic83C4semidirect
23. C2×#14581706C4direct (N × H)
26. C4×C22⋊Dic83C22semidirect
28. #19127467C22semidirect
33. C4×C22⋊C4×C83C22semidirect
52. C22×C4×D83C2×C4semidirect
64. C2×Dic83⋊C4C2×C4semidirect
72. C2×C22⋊Dic83C2×C4semidirect
78. C2×(C2×D83)⋊C4C2×C4semidirect
84. C2×C4×Dic83C2×C4semidirect
85. #14581706C2×C4direct (N × H)
102. C2×C22⋊C4×C83C2×C4semidirect
112. C23×D83C42semidirect
124. C2×C22⋊D83C42semidirect
139. C22×Dic83C42semidirect
157. C22⋊Dic83C22×C4semidirect
206. C22⋊C4×C83C22×C4semidirect
253. C22×D83C2×C42semidirect
273. C2×C4×C83#99semidirect
298. C2×Dic83C2×C42semidirect
345. C4×C83C2×#99semidirect
358. C2×C83C4×#99semidirect
366. C2×C4×C22⋊C4D83semidirect
369. C83C2×C4×#99semidirect
394. C4×C22⋊C4C2×D83semidirect
457. C2×C22⋊C4C4×D83semidirect
566. C22⋊C4C2×C4×D83semidirect
659. C2×C4#14581706direct (N × H)
712. C4C2×#14581706direct (N × H)
721. C2C4×#14581706direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D832
C22×#145817062
C2×C4×C22⋊Dic832
C4×#145817062
C2×#191274672
C2×C4×C22⋊C4×C832
C2×C4×#9983