Finite Group Databasebeta

← C2×#19138266 #25265240

Subgroups — C2×#19138266 #25265240

Order 11008.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063303C211yesmaximal, characteristic
2C22×#13063283C211yesmaximal, characteristic
3#19138266C2116yesmaximal, direct product factor
4C2×#14582841C211yesmaximal, characteristic, complemented
5C2×#14582833C211yesmaximal, characteristic, complemented
6C2×#14582819C211yesmaximal, characteristic, complemented
7C2×#14582804C211yesmaximal, characteristic, complemented
8C2×#14582794C211yesmaximal, characteristic, complemented
9C2×#14582781C211yesmaximal, characteristic, complemented
10C2×#14582780C211yesmaximal, characteristic, complemented
11C2×#14582770C211yesmaximal, characteristic
12C2×#14582770C211yesmaximal, characteristic
13C2×#14582761C211yesmaximal, characteristic
14C2×#14582758C211yesmaximal, characteristic
15C2×#95×D43C211yesmaximal, characteristic
16C2×C43×#398C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063303—28no—
22C2×#13063303C2218yes—
23C2×#13063283—28no—
24C2×#13063283C2218yes—
25C22×C4⋊Dic43C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38#14582841C2218yescomplemented
39#14582833C2218yescomplemented
40#14582819C2218yescomplemented
41#14582804C2218yescomplemented
42#14582794C2218yescomplemented
43#14582781C2218yescomplemented
44#14582780C2218yescomplemented
45#14582770C2218yes—
46#14582770C2218yes—
47#14582761C2218yes—
48#14582758C2218yes—
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60#95×D43C2218yes—
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C43×#398C2218yescomplemented
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C24×D43C2311yescharacteristic
70C22×Dic86—24no—
71C22×Dic86—24no—
72C22×Dic86—42no—
73C22×Dic86C2314yes—
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C22×C4×D43—24no—
82C22×C4×D43—24no—
83C22×C4×D43—24no—
84C22×C4×D43—24no—
85C22×C4×D43—24no—
86C22×C4×D43—24no—
87C22×C4×D43—42no—
88C22×C4×D43—42no—
89C22×C4×D43Q818yescomplemented
90C22×C4×D43C2314yes—
91C22×C4×D43C2314yes—
92C22×C4×D43C2314yes—
93#13063303—232no—
94#13063283—232no—
95C2×C4⋊Dic43—24no—
96C2×C4⋊Dic43C2314yes—
97C2×Dic43⋊C4—24no—
98C2×Dic43⋊C4—24no—
99C2×Dic43⋊C4—24no—
100C2×Dic43⋊C4—24no—
101C2×Dic43⋊C4—24no—
102C2×Dic43⋊C4—42no—
103C2×Dic43⋊C4C2314yes—
104C2×Dic43⋊C4C2314yes—
105C2×Dic43⋊C4C2314yes—
106C2×Dic43⋊C4C2314yes—
107C2×Dic43⋊C4C2314yes—
108C2×Dic43⋊C4C2314yes—
109C2×(C2×D43)⋊C4—24no—
110C2×(C2×D43)⋊C4—24no—
111C2×(C2×D43)⋊C4—24no—
112C2×(C2×D43)⋊C4D418yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×(C2×D43)⋊C4C2314yes—
116C2×(C2×D43)⋊C4C2314yes—
117C2×C4×Dic43—24no—
118C2×C4×Dic43—24no—
119C2×C4×Dic43C2314yes—
120C2×C4×Dic43C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43—24no—
140C2×C4⋊C4×C43—24no—
141C2×C4⋊C4×C43—42no—
142C2×C4⋊C4×C43—42no—
143C2×C4⋊C4×C43C2314yes—
144C2×C4⋊C4×C43C2314yes—
145C2×C4⋊C4×C43C2314yes—
146C2×C4⋊C4×C43C2314yes—
147#95×C43C2314yes—
148#95×C43C2314yes—
149#95×C43C2314yes—
150C24×C43C2411yescharacteristic
151C23×D43—22no—
152C23×D43—22no—
153C23×D43—22no—
154C23×D43—22no—
155C23×D43C2×D414yes—
156C23×D43C2×Q814yes—
157C23×D43#4114yes—
158C23×D43C2412yes—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43C2×D414yes—
179C22×C4×C43C2×Q814yes—
180C22×C4×C43C2412yes—
181C22×C4×C43C2412yes—
182C22×C4×C43C2412yes—
183C22×C4×C43C2412yes—
184C22×C4×C43C2412yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2412yes—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43C2×D414yes—
205C22×Dic43C2×Q814yes—
206C22×Dic43#4114yes—
207C22×Dic43#4114yes—
208C22×Dic43C2412yes—
209C22×Dic43C2412yes—
210C22×Dic43C2412yes—
211C22×Dic43C2412yes—
212C22×Dic43C2412yes—
213C22×Dic43C2412yes—
214C22×Dic43C2412yes—
215C2×C4×D43—28no—
216C2×C4×D43—28no—
217C2×C4×D43—232no—
218C2×C4×D43—28no—
219C2×C4×D43—28no—
220C2×C4×D43—28no—
221C2×C4×D43—28no—
222C2×C4×D43—44no—
223C2×C4×D43—44no—
224C2×C4×D43—416no—
225C2×C4×D43—416no—
226C2×C4×D43C2×Q8116yescomplemented
227C2×Dic86—28no—
228C2×Dic86—28no—
229C2×Dic86—44no—
230C2×Dic86—416no—
231C4⋊C4×C43—28no—
232C4⋊C4×C43—28no—
233C4⋊C4×C43—44no—
234C4⋊C4×C43—44no—
235(C2×D43)⋊C4—28no—
236(C2×D43)⋊C4—28no—
237(C2×D43)⋊C4—28no—
238(C2×D43)⋊C4C2×D4116yes—
239C4⋊Dic43—28no—
240Dic43⋊C4—28no—
241Dic43⋊C4—28no—
242Dic43⋊C4—28no—
243Dic43⋊C4—28no—
244Dic43⋊C4—28no—
245Dic43⋊C4—44no—
246C4×Dic43—28no—
247C4×Dic43—28no—
248C23×C43C22×D412yes—
249C23×C43C22×Q812yes—
250C23×C43C2×#4112yes—
251C23×C43C2×#4112yes—
252C23×C43C2×#4112yes—
253C23×C43H(5,𝔽2)12yes—
254C23×C432−1+412yes—
255C23×C43C2511yescharacteristic
256C22×D43—28no—
257C22×D43—28no—
258C22×D43—28no—
259C22×D43—28no—
260C22×D43—28no—
261C22×D43—28no—
262C22×D43—22no—
263C22×D43—22no—
264C22×D43—22no—
265C22×D43—22no—
266C22×D43C22⋊Q8116yes—
267C22×D43C22×D414yes—
268C22×D43C22×Q814yes—
269C22×D43C2×#4114yes—
270C2×C4×C43—28no—
271C2×C4×C43—28no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—44no—
292C2×C4×C43—44no—
293C2×C4×C43—44no—
294C2×C4×C43—44no—
295C2×C4×C43—44no—
296C2×C4×C43C22×D414yes—
297C2×C4×C43C22×Q814yes—
298C2×Dic43—28no—
299C2×Dic43—28no—
300C2×Dic43—28no—
301C2×Dic43—28no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—44no—
320C2×Dic43—44no—
321C2×Dic43—44no—
322C2×Dic43C22×D414yes—
323C2×Dic43C22×Q814yes—
324C2×Dic43C2×#4114yes—
325C2×Dic43C2×#4114yes—
326C4×D43—232no—
327C4×D43—416no—
328C4×D43—416no—
329Dic86—416no—
330C2×#2438—431nomaximal, Sylow
331C22×C43C2×C22⋊Q814yes—
332C22×C43#53314yes—
333C22×C43#54414yes—
334C22×C43#54614yes—
335C22×C43#54714yes—
336C22×C43#55114yes—
337C22×C43#55214yes—
338C22×C43C23×D411yescharacteristic
339C22×C43C23×Q811yescharacteristic
340C22×C43C22×#4111yescharacteristic
341C22×C43C22×#4111yescharacteristic
342C22×C43C22×#4111yescharacteristic
343C22×C43C2×H(5,𝔽2)11yescharacteristic
344C22×C43C2×2−1+411yescharacteristic
345C2×D43—24no—
346C2×D43—24no—
347C2×D43—232no—
348C2×D43—24no—
349C2×D43—24no—
350C2×D43—24no—
351C2×D43—24no—
352C2×D43C2×C22⋊Q818yes—
353C4×C43—24no—
354C4×C43—24no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43—42no—
358C4×C43—42no—
359C4×C43—42no—
360Dic43—24no—
361Dic43—24no—
362Dic43—24no—
363Dic43—24no—
364Dic43—42no—
365Dic43—42no—
366Dic43—42no—
367C22×C22⋊Q8—431no—
368C22×#117—431no—
369#2438—4316no—
370C2×#400—431no—
371C2×#398—431no—
372C2×#398D4311yescharacteristic, complemented
373C2×#395—431no—
374C2×#391—431no—
375C2×#389—431no—
376C2×#387—431no—
377C2×#387—431no—
378C2×#385—431no—
379C2×#385—431no—
380C2×#381—431no—
381C2×#380—431no—
382C22×#95—431no—
383C2×C43#243818yescomplemented
384C2×C43C22×C22⋊Q811yescharacteristic
385C2×C43C2×#53311yescharacteristic
386C2×C43C2×#54411yescharacteristic
387C2×C43C2×#54611yescharacteristic
388C2×C43C2×#54711yescharacteristic
389C2×C43C2×#55111yescharacteristic
390C2×C43C2×#55211yescharacteristic
391D43—28no—
392C23×Q8—431no—
393C24×C4—431no—
394C24×C4—431no—
395C24×C4—431no—
396C2×C22⋊Q8—438no—
397C2×C22⋊Q8—868no—
398C2×#117—438no—
399C2×#117—868no—
400C22×C4⋊C4—431no—
401C22×C4⋊C4—431no—
402C22×C4⋊C4—431no—
403C22×C4⋊C4—431no—
404C22×C4⋊C4—431no—
405C22×C4⋊C4—431no—
406C22×C4⋊C4—431no—
407C22×C4⋊C4C2×D4311yescharacteristic
408C22×C4⋊C4C2×D4311yescharacteristic
409C22×C4⋊C4C2×D4311yescharacteristic
410C22×C4⋊C4C2×D4311yescharacteristic
411C22×C22⋊C4—431no—
412C22×C22⋊C4—431no—
413C22×C22⋊C4—431no—
414C22×C22⋊C4—431no—
415C22×C42—431no—
416C22×C42—431no—
417#400—438no—
418#398—438no—
419#398C2×D4318yescomplemented
420#395—438no—
421#391—438no—
422#389—438no—
423#387—438no—
424#387—438no—
425#385—438no—
426#385—438no—
427#381—438no—
428#380—438no—
429C2×#95—431no—
430C2×#95—431no—
431C2×#95—431no—
432C2×#95—431no—
433C2×#95—431no—
434C2×#95—431no—
435C2×#95—431no—
436C2×#95—431no—
437C2×#95—431no—
438C2×#95—431no—
439C2×#95—431no—
440C2×#95—438no—
441C2×#95C2×D4311yescharacteristic
442C2×#95C2×D4311yescharacteristic
443C2×#95C2×D4311yescharacteristic
444C43C2×#243811yescharacteristic, complemented, Sylow
445C25—431no—
446C22×Q8—434no—
447C22×Q8—864no—
448C22×Q8—864no—
449C22×Q8—1722no—
450C23×C4—431no—
451C23×C4—431no—
452C23×C4—431no—
453C23×C4—431no—
454C23×C4—438no—
455C23×C4—434no—
456C23×C4—431no—
457C23×C4—431no—
458C23×C4—431no—
459C23×C4—434no—
460C23×C4—434no—
461C23×C4—864no—
462C23×C4—864no—
463C23×C4—864no—
464C23×C4—864no—
465C23×C4—864no—
466C23×C4—864no—
467C23×C4—1722no—
468C23×C4—1722no—
469C23×C4C22×D4311yescharacteristic
470C23×C4C22×D4311yescharacteristic
471C23×C4C22×D4311yescharacteristic
472C23×C4C22×D4311yescharacteristic
473C23×C4C22×D4311yescharacteristic
474C23×C4C22×D4311yescharacteristic
475C23×C4C22×D4311yescharacteristic
476C22⋊Q8—8632no—
477#117—8632no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—434no—
483C2×C4⋊C4—434no—
484C2×C4⋊C4—434no—
485C2×C4⋊C4—434no—
486C2×C4⋊C4—434no—
487C2×C4⋊C4—434no—
488C2×C4⋊C4—434no—
489C2×C4⋊C4—864no—
490C2×C4⋊C4—864no—
491C2×C4⋊C4—864no—
492C2×C4⋊C4—864no—
493C2×C4⋊C4—864no—
494C2×C4⋊C4—864no—
495C2×C4⋊C4—1722no—
496C2×C4⋊C4C22×D4314yes—
497C2×C4⋊C4C22×D4314yes—
498C2×C4⋊C4C22×D4314yes—
499C2×C4⋊C4C22×D4314yes—
500C2×C22⋊C4—438no—
501C2×C22⋊C4—434no—
502C2×C22⋊C4—434no—
503C2×C22⋊C4—434no—
504C2×C22⋊C4—434no—
505C2×C22⋊C4—864no—
506C2×C22⋊C4—864no—
507C2×C22⋊C4—864no—
508C2×C42—434no—
509C2×C42—434no—
510C2×C42—864no—
511C2×C42—864no—
512#95—434no—
513#95—434no—
514#95—434no—
515#95—434no—
516#95—434no—
517#95—434no—
518#95—434no—
519#95—434no—
520#95—434no—
521#95—434no—
522#95—434no—
523#95C22×D4314yes—
524#95C22×D4314yes—
525#95C22×D4314yes—
526C24—434no—
527C24—434no—
528C24—434no—
529C24—432no—
530C24—862no—
531C24—862no—
532C24—862no—
533C24—862no—
534C24C23×D4311yescharacteristic
535C2×Q8—868no—
536C2×Q8—868no—
537C2×Q8—1724no—
538C2×Q8—17216no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—434no—
559C22×C4—434no—
560C22×C4—434no—
561C22×C4—434no—
562C22×C4—432no—
563C22×C4—432no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—4316no—
567C22×C4—432no—
568C22×C4—432no—
569C22×C4—432no—
570C22×C4—868no—
571C22×C4—868no—
572C22×C4—868no—
573C22×C4—8632no—
574C22×C4—868no—
575C22×C4—868no—
576C22×C4—868no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—1724no—
595C22×C4—1724no—
596C22×C4—17216no—
597C22×C4—17216no—
598C22×C4D4×D4314yes—
599C22×C4Q8×D4314yes—
600C22×C4C23×D4312yes—
601C22×C4C23×D4312yes—
602C22×C4C23×D4312yes—
603C22×C4C23×D4312yes—
604C22×C4C23×D4312yes—
605C22×C4C23×D4312yes—
606C22×C4C23×D4312yes—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—868no—
612C4⋊C4—868no—
613C4⋊C4—868no—
614C4⋊C4—868no—
615C4⋊C4—868no—
616C4⋊C4—868no—
617C4⋊C4—1724no—
618C22⋊C4—4316no—
619C22⋊C4—868no—
620C22⋊C4—868no—
621C22⋊C4—868no—
622C42—868no—
623C42—868no—
624C23—4316no—
625C23—434no—
626C23—434no—
627C23—434no—
628C23—868no—
629C23—868no—
630C23—868no—
631C23—862no—
632C23—862no—
633C23—862no—
634C23—862no—
635C23—868no—
636C23—868no—
637C23—868no—
638C23C2×D4×D4312yes—
639C23C2×Q8×D4312yes—
640C23#41×D4312yes—
641C23#41×D4312yes—
642C23#41×D4312yes—
643C23#1306337012yes—
644C23#1306337312yes—
645C23C24×D4311yescharacteristic
646Q8—17216no—
647C2×C4—28no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—28no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—434no—
674C2×C4—434no—
675C2×C4—434no—
676C2×C4—434no—
677C2×C4—8632no—
678C2×C4—868no—
679C2×C4—868no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—868no—
689C2×C4—868no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—17216no—
700C2×C4—17216no—
701C2×C4—1724no—
702C2×C4—1724no—
703C2×C4—1724no—
704C2×C4C2×D4×D4314yes—
705C2×C4C2×Q8×D4314yes—
706C22—438no—
707C22—864no—
708C22—864no—
709C22—864no—
710C22—864no—
711C22—864no—
712C22—864no—
713C22—8632no—
714C22C22⋊Q8×D4314yes—
715C22#1458345514yes—
716C22#1458352614yes—
717C22#1458353814yes—
718C22#1458355114yes—
719C22#1458357714yes—
720C22#1458358114yes—
721C22C22×D4×D4311yescharacteristic
722C22C22×Q8×D4311yescharacteristic
723C22C2×#41×D4311yescharacteristic
724C22C2×#41×D4311yescharacteristic
725C22C2×#41×D4311yescharacteristic
726C22C2×#1306337011yescharacteristic
727C22C2×#1306337311yescharacteristic
728C4—24no—
729C4—24no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—864no—
736C4—864no—
737C4—864no—
738C4—864no—
739C4—1722no—
740C4—1722no—
741C4—1722no—
742C2—868no—
743C2#1913826618yesdirect product factor
744C2C2×C22⋊Q8×D4311yescharacteristic
745C2C2×#1458345511yescharacteristic
746C2C2×#1458352611yescharacteristic
747C2C2×#1458353811yescharacteristic
748C2C2×#1458355111yescharacteristic
749C2C2×#1458357711yescharacteristic
750C2C2×#1458358111yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#398C2
socleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#398D43
hypocenterC43C2×#2438
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #19138266C2direct (N × H)
4. C2×#14582841C2semidirect
5. C2×#14582833C2semidirect
6. C2×#14582819C2semidirect
7. C2×#14582804C2semidirect
8. C2×#14582794C2semidirect
9. C2×#14582781C2semidirect
10. C2×#14582780C2semidirect
16. C2×C43×#398C2semidirect
38. #14582841C22semidirect
39. #14582833C22semidirect
40. #14582819C22semidirect
41. #14582804C22semidirect
42. #14582794C22semidirect
43. #14582781C22semidirect
44. #14582780C22semidirect
65. C43×#398C22semidirect
89. C22×C4×D43Q8semidirect
226. C2×C4×D43C2×Q8semidirect
372. C2×#398D43semidirect
383. C2×C43#2438semidirect
419. #398C2×D43semidirect
444. C43C2×#2438semidirect
743. C2#19138266direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633032
C22×#130632832
#191382662
C2×#145828412
C2×#145828332
C2×#145828192
C2×#145828042
C2×#145827942
C2×#145827812
C2×#145827802
C2×#145827702
C2×#145827612
C2×#145827582
C2×#95×D432
C2×C43×#3982
C2×#243843