Finite Group Databasebeta

← C2×#24919815 #36282822

Subgroups — C2×#24919815 #36282822

Order 21248.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128409C211yesmaximal, characteristic, complemented
2C2×#19128351C211yesmaximal, characteristic
3#24919815C2116yesmaximal, direct product factor
4C2×#19128098C211yesmaximal, characteristic, complemented
5C2×#19128018C211yesmaximal, characteristic, complemented
6C2×#19128017C211yesmaximal, characteristic, complemented
7C2×#19128030C211yesmaximal, characteristic, complemented
8C2×#19128029C211yesmaximal, characteristic, complemented
9C2×#19127984C211yesmaximal, characteristic, complemented
10C2×#19127989C211yesmaximal, characteristic, complemented
11C2×#19127927C211yesmaximal, characteristic, complemented
12C2×SD16×Dic83C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D83C211yesmaximal, characteristic, complemented
14C22×#14581724C211yesmaximal, characteristic, complemented
15C2×#106×D83C211yesmaximal, characteristic, complemented
16C2×#465×C83C211yesmaximal, characteristic, complemented
17C22×#13050589—21no—
18C22×C8×D83C2211yescharacteristic
19#19128409—24no—
20#19128409C2218yescomplemented
21#19128351—24no—
22#19128351C2218yes—
23C2×#14581791C2211yescharacteristic
24C2×#14581791C2211yescharacteristic
25C2×#14581782—21no—
26C2×#14581774—21no—
27C2×#14581773—21no—
28C2×#14581772—21no—
29C2×#14581769—21no—
30C2×#14581769—21no—
31C2×#14581768C2211yescharacteristic
32C2×#14581763C2211yescharacteristic
33C2×Q8×Dic83C2211yescharacteristic
34C2×D4×Dic83C2211yescharacteristic
35C2×C4×C22⋊D83C2211yescharacteristic
36C2×(C22⋊D83)⋊C4—21no—
37C22×C4⋊Dic83C2211yescharacteristic
38C22×C4⋊Dic83C2211yescharacteristic
39C2×C4⋊C4×D83C2211yescharacteristic
40C2×C4⋊C4×D83C2211yescharacteristic
41#19128098C2218yescomplemented
42#19128030C2218yescomplemented
43#19128029C2218yescomplemented
44#19128018C2218yescomplemented
45#19128017C2218yescomplemented
46#19127989C2218yescomplemented
47#19127984C2218yescomplemented
48#19127927C2218yescomplemented
49SD16×Dic83C2218yescomplemented
50C8×C22⋊D83C2218yescomplemented
51C2×#14581724C2211yescharacteristic
52C2×#14581724C2211yescharacteristic
53C2×#14581724C2211yescharacteristic
54C2×#14581724C2211yescharacteristic
55C2×#14581724C2218yescomplemented
56C2×#14581723C2211yescharacteristic
57C2×#14581723C2211yescharacteristic
58C2×#14581723C2211yescharacteristic
59C2×#14581723C2211yescharacteristic
60#106×D83C2218yescomplemented
61C2×Dic83⋊C8C2211yescharacteristic
62C2×#14581716C2211yescharacteristic
63C2×#14581716C2211yescharacteristic
64C2×#14581713C2211yescharacteristic
65C2×#14581713C2211yescharacteristic
66C2×C22⋊(C83⋊C8)C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C22×SD16×C83C2211yescharacteristic
70C23×C8×C83C2211yescharacteristic
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×#121×C83C2211yescharacteristic
73#465×C83C2218yescomplemented
74C2×#106×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×#102×C83C2211yescharacteristic
77C2×#13050589—28no—
78C2×#13050589—48no—
79C22×Dic166—21no—
80C22×Dic166—21no—
81C22×C22⋊D83—21no—
82C22×C22⋊D83D411yescharacteristic
83C23×Dic83—21no—
84C23×Dic83—21no—
85C23×Dic83—21no—
86C22×C4×D83—21no—
87C22×C4×D83—21no—
88C22×C4×D83C2311yescharacteristic
89C22×C83⋊C8C2311yescharacteristic
90C22×C83⋊C8C2311yescharacteristic
91C2×C8×D83—24no—
92C2×C8×D83C2314yes—
93#14581791—22no—
94#14581791—22no—
95#14581791C2314yes—
96#14581791C2314yes—
97#14581782—28no—
98#14581774—28no—
99#14581773—28no—
100#14581772—28no—
101#14581769—28no—
102#14581769—28no—
103#14581768—22no—
104#14581768C2314yes—
105#14581763—22no—
106#14581763C2314yes—
107Q8×Dic83—22no—
108Q8×Dic83C2314yes—
109D4×Dic83—22no—
110D4×Dic83C2314yes—
111C4×C22⋊D83D414yes—
112C4×C22⋊D83C2314yes—
113(C22⋊D83)⋊C4—28no—
114C2×C4⋊Dic83—21no—
115C2×C4⋊Dic83—22no—
116C2×C4⋊Dic83—22no—
117C2×C4⋊Dic83—21no—
118C2×C4⋊Dic83—21no—
119C2×C4⋊Dic83C2314yes—
120C2×C4⋊Dic83C2311yescharacteristic
121C2×C4⋊Dic83C2311yescharacteristic
122C2×C4⋊Dic83C2314yes—
123C2×C4⋊Dic83C2311yescharacteristic
124C2×C4⋊Dic83C2311yescharacteristic
125C2×Dic83⋊C4—21no—
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4D411yescharacteristic
131C4⋊C4×D83—22no—
132C4⋊C4×D83—22no—
133C4⋊C4×D83C2314yes—
134C4⋊C4×D83C2314yes—
135C2×C22⋊Dic83—21no—
136C2×C22⋊Dic83—21no—
137C2×C22⋊Dic83D411yescharacteristic
138C2×(C2×D83)⋊C4—21no—
139C2×(C2×D83)⋊C4D411yescharacteristic
140C2×C4×Dic83—21no—
141C2×C4×Dic83C2311yescharacteristic
142#14581724C2314yes—
143#14581724C2314yes—
144#14581724C2314yes—
145#14581724C2314yes—
146#14581723C2314yes—
147#14581723C2314yes—
148#14581723C2314yes—
149#14581723C2314yes—
150Dic83⋊C8C2314yes—
151#14581716C2314yes—
152#14581716C2314yes—
153#14581713C2314yes—
154#14581713C2314yes—
155C22⋊(C83⋊C8)C2314yes—
156(C2×D83)⋊C8C2314yes—
157C8×Dic83C2314yes—
158C22×Q8×C83C2311yescharacteristic
159C22×D4×C83—21no—
160C22×D4×C83C2311yescharacteristic
161C23×C4×C83C2311yescharacteristic
162C2×SD16×C83—24no—
163C2×SD16×C83C2314yes—
164C22×C8×C83—24no—
165C22×C8×C83C2314yes—
166C22×C8×C83C2311yescharacteristic
167C22×C8×C83C2311yescharacteristic
168C22⋊Q8×C83—22no—
169C22⋊Q8×C83C2314yes—
170#121×C83—22no—
171#121×C83C2314yes—
172C2×C4⋊C4×C83—21no—
173C2×C4⋊C4×C83C2311yescharacteristic
174C2×C4⋊C4×C83C2311yescharacteristic
175C2×C22⋊C4×C83—21no—
176C2×C22⋊C4×C83—21no—
177#106×C83C2314yes—
178#103×C83C2314yes—
179#102×C83C2314yes—
180C23×D83C2×D411yescharacteristic
181#13050589—432no—
182C2×Dic166—24no—
183C2×Dic166—24no—
184C2×Dic166—44no—
185C2×Dic166—82no—
186C2×C22⋊D83—24no—
187C2×C22⋊D83—44no—
188C2×C22⋊D83SD1618yescomplemented
189C2×C22⋊D83C2×D414yes—
190C22×Dic83—24no—
191C22×Dic83—21no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83—24no—
196C22×Dic83—24no—
197C22×Dic83—44no—
198C22×Dic83—44no—
199C22×Dic83—82no—
200C22×Dic83C2×D411yescharacteristic
201C22×Dic83C2×D411yescharacteristic
202C22×Dic83C2×D411yescharacteristic
203C2×C4×D83—22no—
204C2×C4×D83—22no—
205C2×C4×D83—24no—
206C2×C4×D83—24no—
207C2×C4×D83—44no—
208C2×C4×D83—82no—
209C2×C4×D83C2×D412yes—
210C2×C4×D83C2412yes—
211C2×C83⋊C8—22no—
212C2×C83⋊C8—22no—
213C2×C83⋊C8C2412yes—
214C2×C83⋊C8C2412yes—
215C8×D83—28no—
216C4⋊Dic83—21no—
217C4⋊Dic83—21no—
218C4⋊Dic83—24no—
219C4⋊Dic83—24no—
220C4⋊Dic83—21no—
221C4⋊Dic83—21no—
222C4⋊Dic83—24no—
223C4⋊Dic83C2412yes—
224C4⋊Dic83C2412yes—
225C4⋊Dic83C2412yes—
226C4⋊Dic83C2412yes—
227Dic83⋊C4—24no—
228Dic83⋊C4—24no—
229Dic83⋊C4—24no—
230Dic83⋊C4—24no—
231Dic83⋊C4—24no—
232Dic83⋊C4C2×D414yes—
233C22⋊Dic83—24no—
234C22⋊Dic83—24no—
235C22⋊Dic83C2×D414yes—
236(C2×D83)⋊C4—24no—
237(C2×D83)⋊C4C2×D414yes—
238C4×Dic83—24no—
239C4×Dic83C2×D412yes—
240C4×Dic83C2412yes—
241C24×C83—21no—
242C24×C83C2×D411yescharacteristic
243C2×Q8×C83—21no—
244C2×Q8×C83—22no—
245C2×Q8×C83—22no—
246C2×Q8×C83C2412yes—
247C2×D4×C83—24no—
248C2×D4×C83—21no—
249C2×D4×C83—22no—
250C2×D4×C83—22no—
251C2×D4×C83—44no—
252C2×D4×C83C2412yes—
253C22×C4×C83—22no—
254C22×C4×C83—22no—
255C22×C4×C83—21no—
256C22×C4×C83—21no—
257C22×C4×C83—21no—
258C22×C4×C83C2×D411yescharacteristic
259C22×C4×C83C2×D412yes—
260C22×C4×C83C2412yes—
261C22×C4×C83C2411yescharacteristic
262SD16×C83—28no—
263C2×C8×C83—22no—
264C2×C8×C83—28no—
265C2×C8×C83#4114yescomplemented
266C2×C8×C83C2412yes—
267C2×C8×C83C2412yes—
268C4⋊C4×C83—24no—
269C4⋊C4×C83—21no—
270C4⋊C4×C83—21no—
271C4⋊C4×C83C2412yes—
272C4⋊C4×C83C2412yes—
273C22⋊C4×C83—24no—
274C22⋊C4×C83—24no—
275C23×C83—22no—
276C23×C83—22no—
277C23×C83—22no—
278C23×C83—42no—
279C23×C83—42no—
280C23×C83—42no—
281C23×C83C2×SD1614yes—
282C23×C83C22×D412yes—
283C23×C83C22×D411yescharacteristic
284C22×D83—22no—
285C22×D83—22no—
286C22×D83C2×SD1614yes—
287C22×D83C22×D412yes—
288Q8×C83—22no—
289Q8×C83—22no—
290Q8×C83—42no—
291D4×C83—22no—
292D4×C83—22no—
293D4×C83—48no—
294D4×C83—42no—
295C2×C4×C83—22no—
296C2×C4×C83—24no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—42no—
303C2×C4×C83—42no—
304C2×C4×C83—42no—
305C2×C4×C83C22×D412yes—
306C2×C4×C83C22×D411yescharacteristic
307C2×C4×C83C2×#4112yes—
308C2×C4×C832−1+412yes—
309C2×C4×C83C2511yescharacteristic
310C22⋊D83—48no—
311C22⋊D83C2×SD16116yescomplemented
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—22no—
318C2×Dic83—42no—
319C2×Dic83—42no—
320C2×Dic83—48no—
321C2×Dic83—42no—
322C2×Dic83—42no—
323C2×Dic83—48no—
324C2×Dic83—84no—
325C2×Dic83C2×SD1614yes—
326C2×Dic83C22×D412yes—
327C2×Dic83C22×D412yes—
328C2×Dic83C22×D412yes—
329C4×D83—24no—
330C4×D83—22no—
331C4×D83—22no—
332C4×D83—48no—
333C4×D83—84no—
334Dic166—48no—
335Dic166—84no—
336C8×C83—22no—
337C8×C83C2×#4114yescomplemented
338C83⋊C8—22no—
339C83⋊C8—22no—
340C22×C83—28no—
341C22×C83—22no—
342C22×C83—22no—
343C22×C83—42no—
344C22×C83—42no—
345C22×C83—42no—
346C22×C83—84no—
347C22×C83#54712yes—
348C22×C83C22×SD1614yes—
349C22×C83C22×SD1612yes—
350C22×C83#57712yes—
351C22×C83C23×D411yescharacteristic
352C2×D83—28no—
353C2×D83—22no—
354C2×D83—22no—
355C2×D83C22×SD1614yes—
356C4×C83—22no—
357C4×C83—42no—
358C4×C83—42no—
359C4×C83—42no—
360C4×C83#54712yes—
361C4×C83C22×#4111yescharacteristic
362C4×C83C2×2−1+411yescharacteristic
363Dic83—22no—
364Dic83—22no—
365Dic83—42no—
366Dic83—42no—
367Dic83—42no—
368Dic83—42no—
369Dic83C22×SD1614yes—
370C2×#3335—831nomaximal, Sylow
371C2×C83—24no—
372C2×C83—82no—
373C2×C83#333514yescomplemented
374C2×C83C2×#54711yescharacteristic
375C2×C83C23×SD1611yescharacteristic
376C2×C83C2×#57711yescharacteristic
377D83—24no—
378C2×#554—831no—
379C2×#547—831no—
380#3335—8316no—
381C2×#498—831no—
382C2×#481—831no—
383C2×#481—831no—
384C2×#483—831no—
385C2×#483—831no—
386C2×#475—831no—
387C2×#476—831no—
388C2×#465—831no—
389C2×#465D8311yescharacteristic, complemented
390C2×C4×SD16—831no—
391C2×C8×D4—831no—
392C22×#106—831no—
393C22×#106—831no—
394C83C2×#333511yescharacteristic, complemented, Sylow
395C22×#41—1661no—
396C22×SD16C2×D8311yescharacteristic
397C23×C8—831no—
398C23×C8C2×D8311yescharacteristic
399#554—838no—
400#554—1664no—
401#547—838no—
402#547—1664no—
403C2×C4⋊Q8—831no—
404C2×C4⋊Q8—831no—
405C2×#125—1661no—
406C2×#123—1661no—
407C2×#123—1661no—
408C2×C22⋊Q8—831no—
409C2×C22⋊Q8—1661no—
410C2×C22⋊Q8—1661no—
411C2×C22⋊Q8—1661no—
412C2×C22⋊Q8C2×D8311yescharacteristic
413C2×#121—831no—
414C2×#121C2×D8311yescharacteristic
415C2×C4×Q8—831no—
416C2×C4×D4—831no—
417C2×C4×D4—831no—
418C2×C4×D4—1661no—
419C22×C4⋊C4—831no—
420C22×C4⋊C4—831no—
421C22×C4⋊C4—831no—
422C22×C4⋊C4—831no—
423#498—838no—
424#483—838no—
425#483—838no—
426#481—838no—
427#481—838no—
428#476—838no—
429#475—838no—
430#465—838no—
431#465C2×D8318yescomplemented
432C4×SD16—838no—
433C8×D4—838no—
434C2×#106—831no—
435C2×#106—838no—
436C2×#106—831no—
437C2×#106—831no—
438C2×#106—831no—
439C2×#106—831no—
440C2×#106—831no—
441C2×#106—831no—
442C2×#106—831no—
443C2×#106—838no—
444C2×#106C2×D8311yescharacteristic
445C2×C4⋊C8—831no—
446C2×#103—831no—
447C2×#103—831no—
448C2×#103C2×D8311yescharacteristic
449C2×#102—831no—
450C2×#102—831no—
451C2×#102C2×D8311yescharacteristic
452C2×C22⋊C8—831no—
453C2×C22⋊C8—831no—
454C2×C4×C8—831no—
455C2×#41—3328no—
456C2×#41—1668no—
457C22×Q8—1661no—
458C22×Q8—1661no—
459C22×Q8C22×D8311yescharacteristic
460C22×D4—21no—
461C22×D4—831no—
462C22×D4—1661no—
463C22×D4C22×D8311yescharacteristic
464C23×C4—831no—
465C23×C4—1661no—
466C23×C4—1661no—
467C23×C4—1661no—
468C23×C4—1661no—
469C23×C4—1661no—
470C23×C4C22×D8311yescharacteristic
471C2×SD16—24no—
472C2×SD16C22×D8314yes—
473C22×C8—24no—
474C22×C8—831no—
475C22×C8—831no—
476C22×C8—834no—
477C22×C8—1664no—
478C22×C8C22×D8311yescharacteristic
479C22×C8C22×D8314yes—
480C22×C8C22×D8311yescharacteristic
481C4⋊Q8—834no—
482C4⋊Q8—834no—
483C4⋊Q8—1662no—
484C4⋊Q8—1662no—
485#125—1668no—
486#123—1668no—
487#123—1668no—
488C22⋊Q8—22no—
489C22⋊Q8—834no—
490C22⋊Q8—1668no—
491C22⋊Q8—1668no—
492C22⋊Q8—1668no—
493C22⋊Q8—1662no—
494C22⋊Q8C22×D8314yes—
495#121—22no—
496#121—834no—
497#121—1662no—
498#121C22×D8314yes—
499C4×Q8—834no—
500C4×Q8—1662no—
501C4×D4—834no—
502C4×D4—834no—
503C4×D4—834no—
504C4×D4—1662no—
505C4×D4—1668no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—831no—
508C2×C4⋊C4—831no—
509C2×C4⋊C4—831no—
510C2×C4⋊C4—831no—
511C2×C4⋊C4—831no—
512C2×C4⋊C4—834no—
513C2×C4⋊C4—834no—
514C2×C4⋊C4—834no—
515C2×C4⋊C4—834no—
516C2×C4⋊C4—1662no—
517C2×C4⋊C4—1662no—
518C2×C4⋊C4—1661no—
519C2×C4⋊C4—1661no—
520C2×C4⋊C4—1661no—
521C2×C4⋊C4—1661no—
522C2×C4⋊C4—1661no—
523C2×C4⋊C4—1661no—
524C2×C4⋊C4—1661no—
525C2×C4⋊C4—1661no—
526C2×C4⋊C4—1662no—
527C2×C4⋊C4—1662no—
528C2×C4⋊C4C22×D8311yescharacteristic
529C2×C4⋊C4C22×D8311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—831no—
533C2×C22⋊C4—831no—
534C2×C22⋊C4—1661no—
535C2×C22⋊C4—1661no—
536C2×C22⋊C4—1661no—
537C2×C42—831no—
538C2×C42—1661no—
539#106—834no—
540#106—834no—
541#106—834no—
542#106—834no—
543#106—834no—
544#106—834no—
545#106—834no—
546#106—834no—
547#106C22×D8314yes—
548C4⋊C8—834no—
549#103—834no—
550#103—834no—
551#103C22×D8314yes—
552#102—834no—
553#102—834no—
554#102C22×D8314yes—
555C22⋊C8—834no—
556C22⋊C8—834no—
557C4×C8—834no—
558C24—21no—
559C24—831no—
560C24D4×D8311yescharacteristic
561#41—33232no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—3324no—
566C2×Q8—6642no—
567C2×Q8—1664no—
568C2×Q8—1664no—
569C2×Q8C23×D8312yes—
570C2×D4—24no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—44no—
575C2×D4—3324no—
576C2×D4—838no—
577C2×D4—834no—
578C2×D4—1664no—
579C2×D4C23×D8312yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—3324no—
586C22×C4—3324no—
587C22×C4—3324no—
588C22×C4—831no—
589C22×C4—831no—
590C22×C4—831no—
591C22×C4—832no—
592C22×C4—832no—
593C22×C4—6642no—
594C22×C4—6642no—
595C22×C4—1664no—
596C22×C4—1664no—
597C22×C4—1664no—
598C22×C4—1664no—
599C22×C4—1661no—
600C22×C4—1661no—
601C22×C4—1661no—
602C22×C4—1661no—
603C22×C4—1664no—
604C22×C4—1662no—
605C22×C4—1662no—
606C22×C4D4×D8312yes—
607C22×C4D4×D8311yescharacteristic
608C22×C4C23×D8312yes—
609C22×C4C23×D8311yescharacteristic
610SD16—28no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8—832no—
614C2×C8—832no—
615C2×C8—1662no—
616C2×C8—1662no—
617C2×C8—1668no—
618C2×C8#1305058914yescomplemented
619C2×C8C23×D8312yes—
620C2×C8C23×D8312yes—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—834no—
625C4⋊C4—832no—
626C4⋊C4—832no—
627C4⋊C4—832no—
628C4⋊C4—832no—
629C4⋊C4—1664no—
630C4⋊C4—1664no—
631C4⋊C4—1664no—
632C4⋊C4—1664no—
633C4⋊C4—1664no—
634C4⋊C4—1664no—
635C4⋊C4—1661no—
636C4⋊C4—1661no—
637C4⋊C4—1661no—
638C4⋊C4—1664no—
639C4⋊C4—1664no—
640C4⋊C4—1661no—
641C4⋊C4C23×D8312yes—
642C4⋊C4C23×D8312yes—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—834no—
646C22⋊C4—834no—
647C22⋊C4—1664no—
648C22⋊C4—1664no—
649C22⋊C4—1664no—
650C42—832no—
651C42—832no—
652C42—1664no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—834no—
660C23—832no—
661C23—1662no—
662C23—1662no—
663C23SD16×D8314yes—
664C23C2×D4×D8312yes—
665C23C2×D4×D8311yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—3328no—
670Q8—6644no—
671D4—22no—
672D4—22no—
673D4—48no—
674D4—42no—
675D4—3328no—
676D4—8316no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—3328no—
688C2×C4—3322no—
689C2×C4—3322no—
690C2×C4—3328no—
691C2×C4—3322no—
692C2×C4—3322no—
693C2×C4—3328no—
694C2×C4—834no—
695C2×C4—832no—
696C2×C4—832no—
697C2×C4—832no—
698C2×C4—6644no—
699C2×C4—6644no—
700C2×C4—1662no—
701C2×C4—1662no—
702C2×C4—1662no—
703C2×C4—1662no—
704C2×C4—1662no—
705C2×C4—1662no—
706C2×C4—1664no—
707C2×C4—1662no—
708C2×C4—1662no—
709C2×C4C2×D4×D8312yes—
710C2×C4C2×D4×D8311yescharacteristic
711C2×C4C2×#1305058912yes—
712C2×C4#1458183912yes—
713C2×C4C24×D8311yescharacteristic
714C8—22no—
715C8—1662no—
716C8—1662no—
717C8C2×#1305058914yescomplemented
718C22—28no—
719C22—22no—
720C22—22no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—834no—
726C22—1668no—
727C22—1662no—
728C22—1662no—
729C22#1912835112yes—
730C22C2×SD16×D8314yes—
731C22C2×SD16×D8312yes—
732C22#1912850812yes—
733C22C22×D4×D8311yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—3322no—
739C4—3322no—
740C4—3322no—
741C4—3322no—
742C4—834no—
743C4—1662no—
744C4—1662no—
745C4#1912835112yes—
746C4C22×#1305058911yescharacteristic
747C4C2×#1458183911yescharacteristic
748C2—24no—
749C2—82no—
750C2—1664no—
751C2#2491981514yesdirect product factor
752C2C2×#1912835111yescharacteristic
753C2C22×SD16×D8311yescharacteristic
754C2C2×#1912850811yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#465×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128351C2
hypercenterC2×#465D83
hypocenterC83C2×#3335
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#19128409C2semidirect
3. #24919815C2direct (N × H)
4. C2×#19128098C2semidirect
5. C2×#19128018C2semidirect
6. C2×#19128017C2semidirect
7. C2×#19128030C2semidirect
8. C2×#19128029C2semidirect
9. C2×#19127984C2semidirect
10. C2×#19127989C2semidirect
11. C2×#19127927C2semidirect
12. C2×SD16×Dic83C2semidirect
13. C2×C8×C22⋊D83C2semidirect
14. C22×#14581724C2semidirect
15. C2×#106×D83C2semidirect
16. C2×#465×C83C2semidirect
20. #19128409C22semidirect
41. #19128098C22semidirect
42. #19128030C22semidirect
43. #19128029C22semidirect
44. #19128018C22semidirect
45. #19128017C22semidirect
46. #19127989C22semidirect
47. #19127984C22semidirect
48. #19127927C22semidirect
49. SD16×Dic83C22semidirect
50. C8×C22⋊D83C22semidirect
55. C2×#14581724C22semidirect
60. #106×D83C22semidirect
73. #465×C83C22semidirect
188. C2×C22⋊D83SD16semidirect
265. C2×C8×C83#41semidirect
311. C22⋊D83C2×SD16semidirect
337. C8×C83C2×#41semidirect
373. C2×C83#3335semidirect
389. C2×#465D83semidirect
394. C83C2×#3335semidirect
431. #465C2×D83semidirect
618. C2×C8#13050589semidirect
717. C8C2×#13050589semidirect
751. C2#24919815direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284092
C2×#191283512
#249198152
C2×#191280982
C2×#191280182
C2×#191280172
C2×#191280302
C2×#191280292
C2×#191279842
C2×#191279892
C2×#191279272
C2×SD16×Dic832
C2×C8×C22⋊D832
C22×#145817242
C2×#106×D832
C2×#465×C832
C2×#333583