Finite Group Databasebeta

← C83×#21772 #35249596

Subgroups — C83×#21772 #35249596

Order 21248.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C83C211yesmaximal, characteristic
2C2×#408×C83C211yesmaximal, characteristic, complemented
3C83×#2311C211yesmaximal, characteristic, complemented
4C83×#1895C211yesmaximal, characteristic, complemented
5C83×#1894C211yesmaximal, characteristic, complemented
6C83×#1893C211yesmaximal, characteristic, complemented
7C83×#1892C211yesmaximal, characteristic, complemented
8C83×#1875C211yesmaximal, characteristic, complemented
9C83×#1874C211yesmaximal, characteristic, complemented
10C83×#1873C211yesmaximal, characteristic, complemented
11C83×#1872C211yesmaximal, characteristic, complemented
12C83×#1824C211yesmaximal, characteristic, complemented
13C83×#1823C211yesmaximal, characteristic, complemented
14C83×#1788C211yesmaximal, characteristic, complemented
15C83×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C22×#41×C83C2211yescharacteristic
18C22×M16×C83C2211yescharacteristic
19C23×C8×C83C2211yescharacteristic
20#537×C83—24no—
21#537×C83C418yescomplemented
22C2×C22⋊Q8×C83—21no—
23C2×C22⋊Q8×C83C2211yescharacteristic
24C2×C22⋊Q8×C83C2211yescharacteristic
25C2×#121×C83—21no—
26C2×#121×C83—21no—
27C2×#121×C83—21no—
28C2×#121×C83C2211yescharacteristic
29C2×#121×C83C2211yescharacteristic
30C2×#117×C83C2211yescharacteristic
31C22×C4⋊C4×C83C2211yescharacteristic
32C22×C4⋊C4×C83C2211yescharacteristic
33C2×#103×C83C2211yescharacteristic
34C2×#103×C83C2211yescharacteristic
35C2×#103×C83C2211yescharacteristic
36C2×#103×C83C2211yescharacteristic
37C2×#102×C83C2211yescharacteristic
38C2×#102×C83C2211yescharacteristic
39C2×#102×C83C2211yescharacteristic
40C2×#102×C83C2211yescharacteristic
41#408×C83—24no—
42C2×C22⋊C8×C83C2211yescharacteristic
43C2×C22⋊C8×C83C2211yescharacteristic
44C2×C22⋊C8×C83C2211yescharacteristic
45C2×C22⋊C8×C83C2211yescharacteristic
46#391×C83—21no—
47#390×C83—21no—
48#386×C83—21no—
49#386×C83—21no—
50#380×C83C2211yescharacteristic
51#380×C83C2211yescharacteristic
52#380×C83C2211yescharacteristic
53#380×C83C2211yescharacteristic
54#340×C83C2211yescharacteristic
55#340×C83C2211yescharacteristic
56#340×C83C2211yescharacteristic
57#340×C83C2211yescharacteristic
58#340×C83C2211yescharacteristic
59#340×C83C2211yescharacteristic
60#340×C83C2211yescharacteristic
61#340×C83C2211yescharacteristic
62C2×#41×C83—22no—
63C2×#41×C83—41no—
64C2×#41×C83—41no—
65C2×#41×C83—41no—
66C2×#41×C83—41no—
67C2×#41×C83—41no—
68C2×#41×C83—41no—
69C2×#41×C83—41no—
70C2×#41×C83—41no—
71C2×#41×C83C2×C414yes—
72C2×#41×C83C2×C414yescomplemented
73C2×#41×C83D414yes—
74C22×Q8×C83D411yescharacteristic
75C22×Q8×C83C2311yescharacteristic
76C22×D4×C83—21no—
77C22×D4×C83—21no—
78C22×D4×C83—21no—
79C22×D4×C83D411yescharacteristic
80C22×D4×C83D411yescharacteristic
81C22×D4×C83D411yescharacteristic
82C22×D4×C83C2311yescharacteristic
83C23×C4×C83—21no—
84C23×C4×C83—21no—
85C23×C4×C83—21no—
86C23×C4×C83C2311yescharacteristic
87C23×C4×C83C2311yescharacteristic
88C23×C4×C83C2311yescharacteristic
89C2×M16×C83—22no—
90C2×M16×C83—41no—
91C2×M16×C83—41no—
92C22×C8×C83—22no—
93C22×C8×C83—41no—
94C22×C8×C83—41no—
95C22×C8×C83C2311yescharacteristic
96C22×C8×C83C2311yescharacteristic
97C22×C8×C83C2311yescharacteristic
98C22×C8×C83C2311yescharacteristic
99C22⋊Q8×C83—28no—
100C22⋊Q8×C83—22no—
101C22⋊Q8×C83—22no—
102C22⋊Q8×C83C2×C414yes—
103C22⋊Q8×C83C2×C414yescomplemented
104#121×C83—28no—
105#121×C83—28no—
106#121×C83—28no—
107#121×C83—22no—
108#121×C83—22no—
109#121×C83C2×C414yes—
110#121×C83C2×C414yescomplemented
111#117×C83—41no—
112#117×C83—41no—
113C2×C4⋊C4×C83—21no—
114C2×C4⋊C4×C83—22no—
115C2×C4⋊C4×C83—21no—
116C2×C4⋊C4×C83—21no—
117C2×C4⋊C4×C83—21no—
118C2×C4⋊C4×C83—41no—
119C2×C4⋊C4×C83—41no—
120C2×C4⋊C4×C83C2×C414yescomplemented
121C2×C4⋊C4×C83C2311yescharacteristic
122C2×C4⋊C4×C83C2311yescharacteristic
123C2×C4⋊C4×C83C2311yescharacteristic
124C2×C4⋊C4×C83C2311yescharacteristic
125C2×C4⋊C4×C83C2311yescharacteristic
126C2×C4⋊C4×C83C2311yescharacteristic
127C2×C22⋊C4×C83—21no—
128C2×C22⋊C4×C83—21no—
129C2×C22⋊C4×C83—21no—
130C2×C22⋊C4×C83—21no—
131C2×C22⋊C4×C83—21no—
132C2×C22⋊C4×C83—21no—
133C2×C22⋊C4×C83—21no—
134C2×C22⋊C4×C83—21no—
135C2×C22⋊C4×C83—21no—
136C2×C42×C83—21no—
137#103×C83—41no—
138#103×C83—41no—
139#103×C83—41no—
140#103×C83—41no—
141#102×C83—41no—
142#102×C83—41no—
143#102×C83—41no—
144#102×C83—41no—
145C22⋊C8×C83—22no—
146C22⋊C8×C83—22no—
147C22⋊C8×C83—22no—
148C22⋊C8×C83—22no—
149#95×C83—21no—
150#95×C83—21no—
151#95×C83—21no—
152#95×C83—21no—
153C24×C83—21no—
154C24×C83C2×D411yescharacteristic
155C24×C83C2×D411yescharacteristic
156C24×C83C2×D411yescharacteristic
157#41×C83—44no—
158#41×C83—44no—
159#41×C83—44no—
160#41×C83—44no—
161#41×C83—44no—
162#41×C83—44no—
163#41×C83—44no—
164#41×C83—44no—
165C2×Q8×C83—21no—
166C2×Q8×C83—21no—
167C2×Q8×C83—21no—
168C2×Q8×C83—21no—
169C2×Q8×C83—21no—
170C2×Q8×C83—41no—
171C2×Q8×C83—41no—
172C2×Q8×C83C22⋊C414yes—
173C2×Q8×C83C22×C412yes—
174C2×D4×C83—24no—
175C2×D4×C83—24no—
176C2×D4×C83—24no—
177C2×D4×C83—21no—
178C2×D4×C83—21no—
179C2×D4×C83—21no—
180C2×D4×C83—21no—
181C2×D4×C83—21no—
182C2×D4×C83—41no—
183C2×D4×C83—41no—
184C2×D4×C83—41no—
185C2×D4×C83—41no—
186C2×D4×C83—41no—
187C2×D4×C83—41no—
188C2×D4×C83—42no—
189C2×D4×C83—42no—
190C2×D4×C83—81no—
191C2×D4×C83—81no—
192C2×D4×C83—81no—
193C2×D4×C83—81no—
194C2×D4×C83C22⋊C414yes—
195C2×D4×C83C22⋊C414yes—
196C2×D4×C83C22⋊C414yes—
197C2×D4×C83C22×C412yes—
198C22×C4×C83—21no—
199C22×C4×C83—21no—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—21no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
207C22×C4×C83—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—24no—
214C22×C4×C83—24no—
215C22×C4×C83—21no—
216C22×C4×C83—21no—
217C22×C4×C83—21no—
218C22×C4×C83—21no—
219C22×C4×C83—42no—
220C22×C4×C83—42no—
221C22×C4×C83—42no—
222C22×C4×C83—81no—
223C22×C4×C83—81no—
224C22×C4×C83—81no—
225C22×C4×C83—81no—
226C22×C4×C83C22×C412yes—
227C22×C4×C83C22×C412yes—
228C22×C4×C83C22×C412yes—
229C22×C4×C83C2×D411yescharacteristic
230C22×C4×C83C2×D411yescharacteristic
231C22×C4×C83C2×D411yescharacteristic
232C22×C4×C83C2×D412yes—
233C22×C4×C83C2×D412yes—
234C22×C4×C83C2×D412yes—
235C22×C4×C83C2411yescharacteristic
236M16×C83—44no—
237C2×C8×C83—21no—
238C2×C8×C83—21no—
239C2×C8×C83—21no—
240C2×C8×C83—21no—
241C2×C8×C83—21no—
242C2×C8×C83—21no—
243C2×C8×C83—21no—
244C2×C8×C83—21no—
245C2×C8×C83—21no—
246C2×C8×C83—21no—
247C2×C8×C83—21no—
248C2×C8×C83—21no—
249C2×C8×C83—44no—
250C4⋊C4×C83—24no—
251C4⋊C4×C83—24no—
252C4⋊C4×C83—24no—
253C4⋊C4×C83—21no—
254C4⋊C4×C83—21no—
255C4⋊C4×C83—21no—
256C4⋊C4×C83—21no—
257C4⋊C4×C83—21no—
258C4⋊C4×C83—21no—
259C4⋊C4×C83—21no—
260C4⋊C4×C83—21no—
261C4⋊C4×C83—21no—
262C4⋊C4×C83—21no—
263C4⋊C4×C83—42no—
264C4⋊C4×C83C22×C412yes—
265C4⋊C4×C83C22×C412yes—
266C22⋊C4×C83—24no—
267C22⋊C4×C83—24no—
268C22⋊C4×C83—24no—
269C22⋊C4×C83—24no—
270C22⋊C4×C83—42no—
271C22⋊C4×C83—81no—
272C22⋊C4×C83—81no—
273C22⋊C4×C83—81no—
274C22⋊C4×C83—81no—
275C42×C83—42no—
276C23×C83—21no—
277C23×C83—21no—
278C23×C83—21no—
279C23×C83—21no—
280C23×C83—21no—
281C23×C83—21no—
282C23×C83—21no—
283C23×C83—21no—
284C23×C83—21no—
285C23×C83—21no—
286C23×C83—21no—
287C23×C83—21no—
288C23×C83—21no—
289C23×C83—21no—
290C23×C83—21no—
291C23×C83—21no—
292C23×C83—21no—
293C23×C83—21no—
294C23×C83—22no—
295C23×C83—41no—
296C23×C83—41no—
297C23×C83—41no—
298C23×C83—41no—
299C23×C83—41no—
300C23×C83—41no—
301C23×C83C2×C22⋊C412yes—
302C23×C83C2×C22⋊C412yes—
303C23×C83C2×C22⋊C412yes—
304C23×C83C22×D411yescharacteristic
305Q8×C83—22no—
306Q8×C83—22no—
307Q8×C83—44no—
308Q8×C83—41no—
309Q8×C83—41no—
310D4×C83—22no—
311D4×C83—22no—
312D4×C83—44no—
313D4×C83—44no—
314D4×C83—44no—
315D4×C83—48no—
316D4×C83—41no—
317D4×C83—41no—
318D4×C83—84no—
319D4×C83—84no—
320C2×C4×C83—21no—
321C2×C4×C83—21no—
322C2×C4×C83—21no—
323C2×C4×C83—21no—
324C2×C4×C83—21no—
325C2×C4×C83—21no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
331C2×C4×C83—22no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
334C2×C4×C83—22no—
335C2×C4×C83—22no—
336C2×C4×C83—22no—
337C2×C4×C83—22no—
338C2×C4×C83—22no—
339C2×C4×C83—22no—
340C2×C4×C83—22no—
341C2×C4×C83—48no—
342C2×C4×C83—41no—
343C2×C4×C83—41no—
344C2×C4×C83—41no—
345C2×C4×C83—41no—
346C2×C4×C83—41no—
347C2×C4×C83—41no—
348C2×C4×C83—41no—
349C2×C4×C83—41no—
350C2×C4×C83—41no—
351C2×C4×C83—41no—
352C2×C4×C83—41no—
353C2×C4×C83—41no—
354C2×C4×C83—41no—
355C2×C4×C83—41no—
356C2×C4×C83—41no—
357C2×C4×C83—41no—
358C2×C4×C83—41no—
359C2×C4×C83—41no—
360C2×C4×C83—84no—
361C2×C4×C83—84no—
362C2×C4×C83C2×C22⋊C412yes—
363C2×C4×C83C2×C22⋊C412yes—
364C2×C4×C83C2×C22⋊C412yes—
365C2×C4×C83C23×C411yescharacteristic
366C2×C4×C83C22×D411yescharacteristic
367C2×C4×C83H(5,𝔽2)11yescharacteristic
368C2×C4×C83H(5,𝔽2)11yescharacteristic
369C2×C4×C83H(5,𝔽2)11yescharacteristic
370C2×C4×C83H(5,𝔽2)11yescharacteristic
371C8×C83—41no—
372C8×C83—41no—
373C8×C83—41no—
374C8×C83—41no—
375C22×C83—22no—
376C22×C83—22no—
377C22×C83—22no—
378C22×C83—22no—
379C22×C83—22no—
380C22×C83—22no—
381C22×C83—22no—
382C22×C83—22no—
383C22×C83—22no—
384C22×C83—41no—
385C22×C83—41no—
386C22×C83—41no—
387C22×C83—41no—
388C22×C83—41no—
389C22×C83—41no—
390C22×C83—41no—
391C22×C83—41no—
392C22×C83—41no—
393C22×C83—41no—
394C22×C83—41no—
395C22×C83—41no—
396C22×C83—42no—
397C22×C83—42no—
398C22×C83—42no—
399C22×C83—81no—
400C22×C83—81no—
401C22×C83—81no—
402C22×C83—81no—
403C22×C83C22×C22⋊C411yescharacteristic
404C22×C83#53411yescharacteristic
405C22×C83#53411yescharacteristic
406C22×C83#57611yescharacteristic
407C22×C83#57711yescharacteristic
408C22×C83#57711yescharacteristic
409C22×C83#57811yescharacteristic
410C4×C83—22no—
411C4×C83—22no—
412C4×C83—22no—
413C4×C83—42no—
414C4×C83—42no—
415C4×C83—42no—
416C4×C83—81no—
417C4×C83—81no—
418C4×C83—81no—
419C4×C83—81no—
420C4×C83#51811yescharacteristic
421C4×C83#51811yescharacteristic
422C4×C83#53411yescharacteristic
423C4×C83#53411yescharacteristic
424#21772C8311yesmaximal, characteristic, direct product factor, Sylow
425C2×C83—42no—
426C2×C83—42no—
427C2×C83—42no—
428C2×C83—82no—
429C2×C83#230811yescharacteristic
430C2×C83#289711yescharacteristic
431C2×C83#289811yescharacteristic
432C2×C83#319811yescharacteristic
433C2×C83#320111yescharacteristic
434C2×C83#320311yescharacteristic
435C2×C83#320411yescharacteristic
436C2×#537C2×C8311yescharacteristic
437C2×#408C2×C8311yescharacteristic, complemented
438#2311C2×C8311yescharacteristic, complemented
439#1895C2×C8311yescharacteristic, complemented
440#1894C2×C8311yescharacteristic, complemented
441#1893C2×C8311yescharacteristic, complemented
442#1892C2×C8311yescharacteristic, complemented
443#1875C2×C8311yescharacteristic, complemented
444#1874C2×C8311yescharacteristic, complemented
445#1873C2×C8311yescharacteristic, complemented
446#1872C2×C8311yescharacteristic, complemented
447#1824C2×C8311yescharacteristic, complemented
448#1823C2×C8311yescharacteristic, complemented
449#1788C2×C8311yescharacteristic, complemented
450#1788C2×C8311yescharacteristic, complemented
451C83#2177211yescharacteristic, direct product factor, Sylow
452C22×#41C22×C8311yescharacteristic
453C22×#41C22×C8311yescharacteristic
454C22×M16C22×C8311yescharacteristic
455C23×C8C22×C8311yescharacteristic
456#537—24no—
457#537C4×C8318yescomplemented
458C2×C22⋊Q8—21no—
459C2×C22⋊Q8C22×C8311yescharacteristic
460C2×C22⋊Q8C22×C8311yescharacteristic
461C2×#121—21no—
462C2×#121—21no—
463C2×#121—21no—
464C2×#121C22×C8311yescharacteristic
465C2×#121C22×C8311yescharacteristic
466C2×#117C22×C8311yescharacteristic
467C22×C4⋊C4C22×C8311yescharacteristic
468C22×C4⋊C4C22×C8311yescharacteristic
469C2×#103C22×C8311yescharacteristic
470C2×#103C22×C8311yescharacteristic
471C2×#103C22×C8311yescharacteristic
472C2×#103C22×C8311yescharacteristic
473C2×#102C22×C8311yescharacteristic
474C2×#102C22×C8311yescharacteristic
475C2×#102C22×C8311yescharacteristic
476C2×#102C22×C8311yescharacteristic
477#408—24no—
478C2×C22⋊C8C22×C8311yescharacteristic
479C2×C22⋊C8C22×C8311yescharacteristic
480C2×C22⋊C8C22×C8311yescharacteristic
481C2×C22⋊C8C22×C8311yescharacteristic
482#391—21no—
483#390—21no—
484#386—21no—
485#386—21no—
486#380C22×C8311yescharacteristic
487#380C22×C8311yescharacteristic
488#380C22×C8311yescharacteristic
489#380C22×C8311yescharacteristic
490#340C22×C8311yescharacteristic
491#340C22×C8311yescharacteristic
492#340C22×C8311yescharacteristic
493#340C22×C8311yescharacteristic
494#340C22×C8311yescharacteristic
495#340C22×C8311yescharacteristic
496#340C22×C8311yescharacteristic
497#340C22×C8311yescharacteristic
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×C4×C8314yes—
508C2×#41C2×C4×C8314yescomplemented
509C2×#41D4×C8314yes—
510C22×Q8D4×C8311yescharacteristic
511C22×Q8C23×C8311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C8311yescharacteristic
516C22×D4D4×C8311yescharacteristic
517C22×D4D4×C8311yescharacteristic
518C22×D4C23×C8311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C8311yescharacteristic
523C23×C4C23×C8311yescharacteristic
524C23×C4C23×C8311yescharacteristic
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C23×C8311yescharacteristic
532C22×C8C23×C8311yescharacteristic
533C22×C8C23×C8311yescharacteristic
534C22×C8C23×C8311yescharacteristic
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×C4×C8314yes—
539C22⋊Q8C2×C4×C8314yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×C4×C8314yes—
546#121C2×C4×C8314yescomplemented
547#117—41no—
548#117—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4C2×C4×C8314yescomplemented
557C2×C4⋊C4C23×C8311yescharacteristic
558C2×C4⋊C4C23×C8311yescharacteristic
559C2×C4⋊C4C23×C8311yescharacteristic
560C2×C4⋊C4C23×C8311yescharacteristic
561C2×C4⋊C4C23×C8311yescharacteristic
562C2×C4⋊C4C23×C8311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C42—21no—
573#103—41no—
574#103—41no—
575#103—41no—
576#103—41no—
577#102—41no—
578#102—41no—
579#102—41no—
580#102—41no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—22no—
584C22⋊C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C8311yescharacteristic
591C24C2×D4×C8311yescharacteristic
592C24C2×D4×C8311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊C4×C8314yes—
609C2×Q8C22×C4×C8312yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊C4×C8314yes—
631C2×D4C22⋊C4×C8314yes—
632C2×D4C22⋊C4×C8314yes—
633C2×D4C22×C4×C8312yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C22×C4×C8312yes—
663C22×C4C22×C4×C8312yes—
664C22×C4C22×C4×C8312yes—
665C22×C4C2×D4×C8311yescharacteristic
666C22×C4C2×D4×C8311yescharacteristic
667C22×C4C2×D4×C8311yescharacteristic
668C22×C4C2×D4×C8312yes—
669C22×C4C2×D4×C8312yes—
670C22×C4C2×D4×C8312yes—
671C22×C4C24×C8311yescharacteristic
672M16—44no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—44no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4C22×C4×C8312yes—
701C4⋊C4C22×C4×C8312yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C42—42no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊C4×C8312yes—
738C23C2×C22⋊C4×C8312yes—
739C23C2×C22⋊C4×C8312yes—
740C23C22×D4×C8311yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4—84no—
798C2×C4C2×C22⋊C4×C8312yes—
799C2×C4C2×C22⋊C4×C8312yes—
800C2×C4C2×C22⋊C4×C8312yes—
801C2×C4C23×C4×C8311yescharacteristic
802C2×C4C22×D4×C8311yescharacteristic
803C2×C4H(5,𝔽2)×C8311yescharacteristic
804C2×C4H(5,𝔽2)×C8311yescharacteristic
805C2×C4H(5,𝔽2)×C8311yescharacteristic
806C2×C4H(5,𝔽2)×C8311yescharacteristic
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊C4×C8311yescharacteristic
840C22#534×C8311yescharacteristic
841C22#534×C8311yescharacteristic
842C22#576×C8311yescharacteristic
843C22#577×C8311yescharacteristic
844C22#577×C8311yescharacteristic
845C22#578×C8311yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4#518×C8311yescharacteristic
857C4#518×C8311yescharacteristic
858C4#534×C8311yescharacteristic
859C4#534×C8311yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2C83×#230811yescharacteristic
865C2C83×#289711yescharacteristic
866C2C83×#289811yescharacteristic
867C2C83×#319811yescharacteristic
868C2C83×#320111yescharacteristic
869C2C83×#320311yescharacteristic
870C2C83×#320411yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutatorC2×C4C23×C4×C83
Frattini, cosocleC22×C4C24×C83
prime radicalC2×#537×C83C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C22×#41×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#408×C83C2semidirect
3. C83×#2311C2semidirect
4. C83×#1895C2semidirect
5. C83×#1894C2semidirect
6. C83×#1893C2semidirect
7. C83×#1892C2semidirect
8. C83×#1875C2semidirect
9. C83×#1874C2semidirect
10. C83×#1873C2semidirect
11. C83×#1872C2semidirect
12. C83×#1824C2semidirect
13. C83×#1823C2semidirect
14. C83×#1788C2semidirect
15. C83×#1788C2semidirect
21. #537×C83C4semidirect
72. C2×#41×C83C2×C4semidirect
103. C22⋊Q8×C83C2×C4semidirect
110. #121×C83C2×C4semidirect
120. C2×C4⋊C4×C83C2×C4semidirect
424. #21772C83direct (N × H)
437. C2×#408C2×C83semidirect
438. #2311C2×C83semidirect
439. #1895C2×C83semidirect
440. #1894C2×C83semidirect
441. #1893C2×C83semidirect
442. #1892C2×C83semidirect
443. #1875C2×C83semidirect
444. #1874C2×C83semidirect
445. #1873C2×C83semidirect
446. #1872C2×C83semidirect
447. #1824C2×C83semidirect
448. #1823C2×C83semidirect
449. #1788C2×C83semidirect
450. #1788C2×C83semidirect
451. C83#21772direct (N × H)
457. #537C4×C83semidirect
508. C2×#41C2×C4×C83semidirect
539. C22⋊Q8C2×C4×C83semidirect
546. #121C2×C4×C83semidirect
556. C2×C4⋊C4C2×C4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C832
C2×#408×C832
C83×#23112
C83×#18952
C83×#18942
C83×#18932
C83×#18922
C83×#18752
C83×#18742
C83×#18732
C83×#18722
C83×#18242
C83×#18232
C83×#17882
#2177283