Finite Group Databasebeta

← C2×#19144775 #25964824

Subgroups — C2×#19144775 #25964824

Order 11008.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583514C211yesmaximal, characteristic, complemented
2C2×#14583371C211yesmaximal, characteristic, complemented
3#19144775C2116yesmaximal, direct product factor
4C2×#14583242C211yesmaximal, characteristic, complemented
5C2×#14583222C211yesmaximal, characteristic, complemented
6C2×#14583187C211yesmaximal, characteristic, complemented
7C2×#14583178C211yesmaximal, characteristic, complemented
8C2×#14583113C211yesmaximal, characteristic, complemented
9C2×#14583112C211yesmaximal, characteristic, complemented
10C2×#14583051C211yesmaximal, characteristic, complemented
11C2×#14583031C211yesmaximal, characteristic
12C2×#14583009C211yesmaximal, characteristic, complemented
13C2×#14582999C211yesmaximal, characteristic, complemented
14C2×C4×#10621873C211yesmaximal, characteristic, complemented
15C2×#14582958C211yesmaximal, characteristic, complemented
16C2×C4×D8×C43C211yesmaximal, characteristic, complemented
17C22×D4×D43C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21#14583514—24no—
22#14583514C2218yescomplemented
23C2×#13063324C2211yescharacteristic, complemented
24C2×#13063318—21no—
25C2×#13063312C2211yescharacteristic, complemented
26C2×#13063311—21no—
27C2×#13063308—21no—
28C2×#13063305C2211yescharacteristic
29C2×#13063304—21no—
30C2×#13063296C2211yescharacteristic
31#14583371—24no—
32#14583371C2218yescomplemented
33C2×C4×Dic86C2211yescharacteristic, complemented
34C2×C4×D172C2211yescharacteristic
35C2×D4×Dic43C2211yescharacteristic
36C2×#13063287C2211yescharacteristic
37C2×C4×C22⋊D43—21no—
38C2×(C22⋊D43)⋊C4—21no—
39C2×#13063283C2211yescharacteristic
40C2×#13063282C2211yescharacteristic
41C22×(C2×D43)⋊C4—21no—
42C2×C22⋊C4×D43—21no—
43#14583242C2218yescomplemented
44#14583222C2218yescomplemented
45#14583187C2218yescomplemented
46#14583178C2218yescomplemented
47#14583113C2218yescomplemented
48#14583112C2218yescomplemented
49#14583051C2218yescomplemented
50#14583031C2218yes—
51#14583009C2218yescomplemented
52#14582999C2218yescomplemented
53C4×#10621873C2218yescomplemented
54#14582958C2218yescomplemented
55C2×#13063258C2211yescharacteristic, complemented
56C2×#13063257C2211yescharacteristic, complemented
57C2×#13063256C2211yescharacteristic, complemented
58C2×Dic43⋊C8C2211yescharacteristic, complemented
59C2×Dic43⋊C8C2211yescharacteristic, complemented
60C2×#13063250C2211yescharacteristic, complemented
61C2×#13063248C2211yescharacteristic, complemented
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic, complemented
65C2×#13063245C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063236C2211yescharacteristic, complemented
69C22×D8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic, complemented
72C4×D8×C43C2218yescomplemented
73C2×#107×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic, complemented
76C2×C4×C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C22×Dic86—21no—
79C22×Dic86C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C2×D4×D43—24no—
84C2×D4×D43—24no—
85C2×D4×D43—22no—
86C2×D4×D43C2314yes—
87C23×Dic43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43C2311yescharacteristic
91C2×#10621873—24no—
92C2×#10621873C2314yes—
93C2×#10621883—24no—
94C2×#10621883C2314yes—
95C2×#10621882—24no—
96C2×#10621882C2314yes—
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99#13063324—22no—
100#13063324C2314yescomplemented
101#13063318—28no—
102#13063312—22no—
103#13063312C2314yescomplemented
104#13063311—28no—
105#13063308—28no—
106#13063305—22no—
107#13063305C2314yes—
108#13063304—28no—
109#13063296—22no—
110#13063296C2314yes—
111C4×Dic86—22no—
112C4×Dic86C2314yescomplemented
113C4×D172—22no—
114C4×D172C2314yes—
115D4×Dic43—22no—
116D4×Dic43C2314yes—
117#13063287—22no—
118#13063287C2314yes—
119C4×C22⋊D43—28no—
120(C22⋊D43)⋊C4—28no—
121#13063283—22no—
122#13063283C2314yes—
123#13063282D414yes—
124#13063282C2314yes—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4D411yescharacteristic
131C2×Dic43⋊C4D411yescharacteristic
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43—21no—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—28no—
141C2×(C2×D43)⋊C4D411yescharacteristic
142C2×(C2×D43)⋊C4D411yescharacteristic
143C22⋊C4×D43—28no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063258C2314yescomplemented
148#13063257C2314yescomplemented
149#13063256C2314yescomplemented
150Dic43⋊C8C2314yescomplemented
151Dic43⋊C8C2314yescomplemented
152#13063250C2314yescomplemented
153#13063248C2314yescomplemented
154#13063247C2314yes—
155#13063246C2314yes—
156#13063246C2314yescomplemented
157#13063245C2314yes—
158(C2×D43)⋊C8C2314yes—
159(C2×D43)⋊C8C2314yes—
160#13063236C2314yescomplemented
161C22×D4×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C23×C4×C43—21no—
165C2×D8×C43—24no—
166C2×D8×C43C2314yes—
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C4×D4×C43—22no—
170C4×D4×C43—22no—
171C4×D4×C43C2314yes—
172C4×D4×C43C2314yescomplemented
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C42×C43C2311yescharacteristic
178#107×C43C2314yescomplemented
179#102×C43C2314yes—
180#102×C43C2314yescomplemented
181C4×C8×C43C2314yescomplemented
182C24×C43—21no—
183C24×C43—21no—
184C23×D43—21no—
185C23×D43—28no—
186C23×D43—24no—
187C23×D43—82no—
188C23×D43—82no—
189C23×D43C2×D411yescharacteristic
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—22no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43#4114yes—
196C2×D4×C43C2412yes—
197C2×D4×C43C2412yes—
198C22×C4×C43—24no—
199C22×C4×C43—24no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—82no—
203C22×C4×C43—82no—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—28no—
208C2×C22⋊D43—24no—
209C2×C22⋊D43—24no—
210C2×C22⋊D43—82no—
211C22×Dic43—24no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—82no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219D4×D43—216no—
220D4×D43—28no—
221D4×D43—28no—
222C2×D172—21no—
223C2×D172—22no—
224C2×D172#4114yes—
225C2×D172C2412yes—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
228C2×C4×D43—24no—
229C2×C4×D43—24no—
230C2×C4×D43—82no—
231C2×C4×D43—82no—
232C2×C4×D43C2×D412yes—
233C2×C4×D43C2412yes—
234C2×Dic86—22no—
235C2×Dic86—22no—
236C2×Dic86—21no—
237C2×Dic86—24no—
238C2×Dic86—82no—
239C2×Dic86C2412yes—
240D8×C43—28no—
241C2×C8×C43—22no—
242C2×C8×C43—22no—
243C2×C8×C43C2412yes—
244C2×C8×C43C2412yes—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43C2412yes—
248C4⋊C4×C43C2412yes—
249C22⋊C4×C43—24no—
250C22⋊C4×C43—24no—
251C42×C43C2×D412yes—
252C42×C43C2412yes—
253C22⋊Dic43—24no—
254C22⋊Dic43—24no—
255C22⋊Dic43—24no—
256C22⋊Dic43—24no—
257#10621883—28no—
258#10621882—28no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4C2×D414yes—
264(C2×D43)⋊C4C2×D414yes—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—24no—
268C4⋊Dic43C2412yes—
269C4⋊Dic43C2412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4C2×D414yes—
273Dic43⋊C4C2×D414yes—
274C4×Dic43—24no—
275C4×Dic43—24no—
276C4×Dic43C2×D412yes—
277C4×Dic43C2412yes—
278C2×C43⋊C8—22no—
279C2×C43⋊C8—22no—
280C2×C43⋊C8C2412yes—
281C2×C43⋊C8C2412yes—
282#10621873—28no—
283C23×C43—24no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—42no—
287C23×C43—42no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43C22×D411yescharacteristic
292C22×D43—22no—
293C22×D43—24no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—216no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—84no—
301C22×D43—84no—
302C22×D43—816no—
303C22×D43C22×D412yes—
304D4×C43—24no—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—42no—
309D4×C43C2×#4114yes—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—84no—
317C2×C4×C43—84no—
318C2×C4×C43C22×D412yes—
319C2×C4×C43C22×D412yes—
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2×#4112yes—
322C2×C4×C43C2×#4112yes—
323C2×C4×C43C2511yescharacteristic
324C22⋊D43—216no—
325C22⋊D43—84no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—84no—
336C2×Dic43C22×D412yes—
337C2×Dic43C22×D412yes—
338C2×Dic43C22×D412yes—
339D172—24no—
340D172—22no—
341D172C2×#4114yes—
342C4×D43—24no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—84no—
346C4×D43—84no—
347Dic86—22no—
348Dic86—22no—
349Dic86—42no—
350Dic86—84no—
351C8×C43—22no—
352C8×C43—22no—
353C43⋊C8—22no—
354C43⋊C8—22no—
355C2×#3118—431nomaximal, Sylow
356C22×C43—24no—
357C22×C43—48no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—84no—
364C22×C43#52512yes—
365C22×C43#57612yes—
366C22×C43#57712yes—
367C22×C43C23×D411yescharacteristic
368C2×D43—22no—
369C2×D43—24no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—44no—
373C2×D43—48no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—816no—
377C4×C43—22no—
378C4×C43—22no—
379C4×C43—42no—
380C4×C43—42no—
381C4×C43#52512yes—
382C4×C43C22×#4111yescharacteristic
383C4×C43C22×#4111yescharacteristic
384Dic43—22no—
385Dic43—22no—
386Dic43—22no—
387Dic43—42no—
388Dic43—42no—
389Dic43—42no—
390C2×#542—431no—
391C2×#518—431no—
392#3118—4316no—
393C2×#485—431no—
394C2×#482—431no—
395C2×#476—431no—
396C2×#474—431no—
397C2×#463—431no—
398C2×#463—431no—
399C2×#450—431no—
400C2×#447—431no—
401C2×#442—431no—
402C2×#440—431no—
403C2×C4×SD16—431no—
404C2×C4×D8D4311yescharacteristic, complemented
405C2×#433—431no—
406C2×C43—44no—
407C2×C43—82no—
408C2×C43#311814yescomplemented
409C2×C43C2×#52511yescharacteristic
410C2×C43C2×#57611yescharacteristic
411C2×C43C2×#57711yescharacteristic
412D43—42no—
413D43—44no—
414C23×D4—431no—
415C22×SD16—431no—
416C22×SD16—431no—
417C22×D8—431no—
418C22×D8C2×D4311yescharacteristic
419#542—438no—
420#542—864no—
421C2×C4⋊Q8—431no—
422C2×#126—861no—
423C2×#124—431no—
424C2×#124—861no—
425C2×#123—861no—
426C2×C22⋊Q8—431no—
427C2×C22⋊Q8—861no—
428C2×#121—431no—
429#518—438no—
430#518—864no—
431C2×C4×Q8—431no—
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4—431no—
435C2×C4×D4—861no—
436C2×C4×D4—861no—
437C2×C4×D4C2×D4311yescharacteristic
438C2×C4×D4C2×D4311yescharacteristic, complemented
439C2×#117—431no—
440C2×#117—431no—
441C22×C22⋊C4—861no—
442C22×C22⋊C4—861no—
443#485—438no—
444#482—438no—
445#476—438no—
446#474—438no—
447#463—438no—
448#463—438no—
449#450—438no—
450#447—438no—
451#442—438no—
452#440—438no—
453C4×SD16—438no—
454C4×D8C2×D4318yescomplemented
455#433—438no—
456C2×#107—431no—
457C2×#107C2×D4311yescharacteristic, complemented
458C2×#106—431no—
459C2×#106—431no—
460C2×C4⋊C8—431no—
461C2×C4⋊C8—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102C2×D4311yescharacteristic
469C2×#102C2×D4311yescharacteristic, complemented
470C2×C22⋊C8—431no—
471C2×C22⋊C8—431no—
472C2×#97—431no—
473C2×C4×C8C2×D4311yescharacteristic, complemented
474C43C2×#311811yescharacteristic, complemented, Sylow
475C25—861no—
476C22×Q8—431no—
477C22×Q8—861no—
478C22×D4—434no—
479C22×D4—431no—
480C22×D4—862no—
481C22×D4—861no—
482C22×D4—864no—
483C22×D4—864no—
484C22×D4—861no—
485C22×D4C22×D4311yescharacteristic
486C22×D4C22×D4311yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—431no—
490C23×C4—861no—
491C23×C4—861no—
492C23×C4—861no—
493C2×SD16—434no—
494C2×SD16—434no—
495C2×SD16—864no—
496C2×SD16—864no—
497C2×D8—24no—
498C2×D8—434no—
499C2×D8—864no—
500C2×D8C22×D4314yes—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8C22×D4311yescharacteristic
504C22×C8C22×D4311yescharacteristic
505C4⋊Q8—434no—
506C4⋊Q8—862no—
507#126—868no—
508#124—434no—
509#124—862no—
510#124—868no—
511#123—868no—
512C22⋊Q8—434no—
513C22⋊Q8—862no—
514C22⋊Q8—868no—
515#121—434no—
516#121—862no—
517C4×Q8—434no—
518C4×Q8—862no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—434no—
522C4×D4—434no—
523C4×D4—434no—
524C4×D4—862no—
525C4×D4—862no—
526C4×D4—868no—
527C4×D4—868no—
528C4×D4—862no—
529C4×D4C22×D4314yes—
530C4×D4C22×D4314yescomplemented
531#117—434no—
532#117—434no—
533#117—434no—
534#117—862no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—431no—
547C2×C22⋊C4—431no—
548C2×C22⋊C4—868no—
549C2×C22⋊C4—868no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C42—431no—
559C2×C42—861no—
560C2×C42—861no—
561C2×C42C22×D4311yescharacteristic
562#107—434no—
563#107C22×D4314yescomplemented
564#106—434no—
565#106—434no—
566C4⋊C8—434no—
567C4⋊C8—434no—
568#103—434no—
569#103—434no—
570#102—434no—
571#102—434no—
572#102—434no—
573#102—434no—
574#102C22×D4314yes—
575#102C22×D4314yescomplemented
576C22⋊C8—434no—
577C22⋊C8—434no—
578#97—434no—
579C4×C8C22×D4314yescomplemented
580C24—21no—
581C24—21no—
582C24—431no—
583C24—864no—
584C24—868no—
585C24—861no—
586C24—3442no—
587C24—3442no—
588C2×Q8—432no—
589C2×Q8—864no—
590C2×Q8—861no—
591C2×Q8—862no—
592C2×Q8—862no—
593C2×Q8—3442no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—434no—
600C2×D4—432no—
601C2×D4—864no—
602C2×D4—868no—
603C2×D4—8616no—
604C2×D4—868no—
605C2×D4—868no—
606C2×D4—864no—
607C2×D4—861no—
608C2×D4—862no—
609C2×D4—3442no—
610C2×D4#1062189814yes—
611C2×D4C23×D4312yes—
612C2×D4C23×D4312yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—864no—
625C22×C4—864no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—864no—
632C22×C4—3442no—
633C22×C4—3442no—
634C22×C4—3442no—
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637C22×C4C23×D4311yescharacteristic
638SD16—868no—
639SD16—868no—
640D8—28no—
641D8—868no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—432no—
645C2×C8—432no—
646C2×C8—862no—
647C2×C8—862no—
648C2×C8C23×D4312yes—
649C2×C8C23×D4312yes—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—434no—
653C4⋊C4—434no—
654C4⋊C4—432no—
655C4⋊C4—432no—
656C4⋊C4—864no—
657C4⋊C4—864no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—864no—
661C4⋊C4C23×D4312yes—
662C4⋊C4C23×D4312yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—434no—
666C22⋊C4—434no—
667C22⋊C4—864no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C22⋊C4—864no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C22⋊C4—864no—
674C22⋊C4—864no—
675C42—432no—
676C42—432no—
677C42—864no—
678C42—864no—
679C42D4×D4312yes—
680C42C23×D4312yes—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—432no—
690C23—8616no—
691C23—862no—
692C23—864no—
693C23—862no—
694C23—862no—
695C23—862no—
696C23—3444no—
697C23—3444no—
698C23—34416no—
699C23—1722no—
700C23—1722no—
701C23C2×D4×D4311yescharacteristic
702Q8—862no—
703Q8—862no—
704Q8—3444no—
705Q8—1722no—
706D4—24no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—42no—
711D4—434no—
712D4—8616no—
713D4—864no—
714D4—862no—
715D4—3444no—
716D4C2×#1062189814yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—84no—
724C2×C4—84no—
725C2×C4—432no—
726C2×C4—432no—
727C2×C4—432no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—864no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—3444no—
738C2×C4—3444no—
739C2×C4—3444no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4—1722no—
743C2×C4C2×D4×D4312yes—
744C2×C4C2×D4×D4312yes—
745C2×C4C2×D4×D4311yescharacteristic
746C2×C4#41×D4312yes—
747C2×C4C2×#1062189812yes—
748C2×C4C24×D4311yescharacteristic
749C8—22no—
750C8—22no—
751C8—862no—
752C8—862no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—48no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—862no—
762C22—862no—
763C22—862no—
764C22—864no—
765C22—34416no—
766C22—1722no—
767C22—1722no—
768C22—1724no—
769C22—1728no—
770C22#1458340812yes—
771C22#1458370012yes—
772C22#1458370612yes—
773C22C22×D4×D4311yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—862no—
779C4—862no—
780C4—862no—
781C4—1722no—
782C4—1722no—
783C4—1722no—
784C4#1458340812yes—
785C4C2×#41×D4311yescharacteristic
786C4C22×#1062189811yescharacteristic
787C2—44no—
788C2—82no—
789C2—1722no—
790C2—1724no—
791C2#1914477514yesdirect product factor
792C2C2×#1458340811yescharacteristic
793C2C2×#1458370011yescharacteristic
794C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×D8×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583031C2
hypercenterC2×C4×D8D43
hypocenterC43C2×#3118
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14583514C2semidirect
2. C2×#14583371C2semidirect
3. #19144775C2direct (N × H)
4. C2×#14583242C2semidirect
5. C2×#14583222C2semidirect
6. C2×#14583187C2semidirect
7. C2×#14583178C2semidirect
8. C2×#14583113C2semidirect
9. C2×#14583112C2semidirect
10. C2×#14583051C2semidirect
12. C2×#14583009C2semidirect
13. C2×#14582999C2semidirect
14. C2×C4×#10621873C2semidirect
15. C2×#14582958C2semidirect
16. C2×C4×D8×C43C2semidirect
22. #14583514C22semidirect
23. C2×#13063324C22semidirect
25. C2×#13063312C22semidirect
32. #14583371C22semidirect
33. C2×C4×Dic86C22semidirect
43. #14583242C22semidirect
44. #14583222C22semidirect
45. #14583187C22semidirect
46. #14583178C22semidirect
47. #14583113C22semidirect
48. #14583112C22semidirect
49. #14583051C22semidirect
51. #14583009C22semidirect
52. #14582999C22semidirect
53. C4×#10621873C22semidirect
54. #14582958C22semidirect
55. C2×#13063258C22semidirect
56. C2×#13063257C22semidirect
57. C2×#13063256C22semidirect
58. C2×Dic43⋊C8C22semidirect
59. C2×Dic43⋊C8C22semidirect
60. C2×#13063250C22semidirect
61. C2×#13063248C22semidirect
64. C2×#13063246C22semidirect
68. C2×#13063236C22semidirect
71. C2×C4×D4×C43C22semidirect
72. C4×D8×C43C22semidirect
73. C2×#107×C43C22semidirect
75. C2×#102×C43C22semidirect
76. C2×C4×C8×C43C22semidirect
100. #13063324C23semidirect
103. #13063312C23semidirect
112. C4×Dic86C23semidirect
147. #13063258C23semidirect
148. #13063257C23semidirect
149. #13063256C23semidirect
150. Dic43⋊C8C23semidirect
151. Dic43⋊C8C23semidirect
152. #13063250C23semidirect
153. #13063248C23semidirect
156. #13063246C23semidirect
160. #13063236C23semidirect
172. C4×D4×C43C23semidirect
178. #107×C43C23semidirect
180. #102×C43C23semidirect
181. C4×C8×C43C23semidirect
404. C2×C4×D8D43semidirect
408. C2×C43#3118semidirect
438. C2×C4×D4C2×D43semidirect
454. C4×D8C2×D43semidirect
457. C2×#107C2×D43semidirect
469. C2×#102C2×D43semidirect
473. C2×C4×C8C2×D43semidirect
474. C43C2×#3118semidirect
530. C4×D4C22×D43semidirect
563. #107C22×D43semidirect
575. #102C22×D43semidirect
579. C4×C8C22×D43semidirect
791. C2#19144775direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835142
C2×#145833712
#191447752
C2×#145832422
C2×#145832222
C2×#145831872
C2×#145831782
C2×#145831132
C2×#145831122
C2×#145830512
C2×#145830312
C2×#145830092
C2×#145829992
C2×C4×#106218732
C2×#145829582
C2×C4×D8×C432
C2×#311843