Finite Group Databasebeta

← C2×#19144773 #25964822

Subgroups — C2×#19144773 #25964822

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×#14583373C211yesmaximal, characteristic, complemented
2#19144773C2116yesmaximal, direct product factor
3C2×#14583237C211yesmaximal, characteristic, complemented
4C2×#14583220C211yesmaximal, characteristic, complemented
5C2×#14583186C211yesmaximal, characteristic, complemented
6C2×#14583176C211yesmaximal, characteristic, complemented
7C2×#14583111C211yesmaximal, characteristic, complemented
8C2×#14583111C211yesmaximal, characteristic, complemented
9C2×#14583049C211yesmaximal, characteristic, complemented
10C2×#14583032C211yesmaximal, characteristic
11C2×#14583009C211yesmaximal, characteristic, complemented
12C2×#14582997C211yesmaximal, characteristic, complemented
13C2×C4×#10621884C211yesmaximal, characteristic, complemented
14C2×C4×#10621882C211yesmaximal, characteristic, complemented
15C2×#14582960C211yesmaximal, characteristic, complemented
16C2×C43×#542C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22#14583373—24no—
23#14583373C2218yescomplemented
24C2×C4×D172C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×#13063287—21no—
29C2×#13063287—21no—
30C2×#13063284C2211yescharacteristic
31C2×C22⋊C4×D43—21no—
32C2×C22⋊C4×D43—21no—
33#14583237C2218yescomplemented
34#14583220C2218yescomplemented
35#14583186C2218yescomplemented
36#14583176C2218yescomplemented
37#14583111C2218yescomplemented
38#14583111C2218yescomplemented
39#14583049C2218yescomplemented
40#14583032C2218yes—
41#14583009C2218yescomplemented
42#14582997C2218yescomplemented
43C4×#10621884C2218yescomplemented
44C4×#10621882C2218yescomplemented
45#14582960C2218yescomplemented
46C2×#13063258C2211yescharacteristic, complemented
47C2×#13063258C2211yescharacteristic, complemented
48C2×#13063256C2211yescharacteristic, complemented
49C2×#13063256C2211yescharacteristic, complemented
50C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
51C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
52C2×#13063249C2211yescharacteristic, complemented
53C2×#13063249C2211yescharacteristic, complemented
54C2×#13063246C2211yescharacteristic, complemented
55C2×#13063246C2211yescharacteristic, complemented
56C2×#13063245C2211yescharacteristic
57C2×#13063245C2211yescharacteristic
58C2×#13063245C2211yescharacteristic
59C2×#13063245C2211yescharacteristic
60C2×C22⋊(C43⋊C8)C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×#13063236C2211yescharacteristic, complemented
63C2×C4×C43⋊C8C2211yescharacteristic, complemented
64C43×#542—24no—
65C43×#542C2218yescomplemented
66C2×C4⋊Q8×C43C2211yescharacteristic, complemented
67C2×#126×C43—21no—
68C2×#124×C43—21no—
69C2×#124×C43C2211yescharacteristic, complemented
70C2×#123×C43—21no—
71C2×C22⋊Q8×C43—21no—
72C2×C22⋊Q8×C43C2211yescharacteristic
73C2×#121×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic, complemented
75C2×C4×D4×C43C2211yescharacteristic, complemented
76C2×#117×C43C2211yescharacteristic
77C24×D43—21no—
78C22×D172—21no—
79C22×D172—22no—
80C22×D172—24no—
81C22×D172—24no—
82C22×D172C2314yes—
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C2×#10621884—24no—
90C2×#10621884—24no—
91C2×#10621884C2314yes—
92C2×#10621884C2314yes—
93C2×#10621882—24no—
94C2×#10621882—24no—
95C2×#10621882C2314yes—
96C2×#10621882C2314yes—
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101C4×D172—22no—
102C4×D172—22no—
103C4×D172—22no—
104C4×D172—22no—
105C4×D172C2314yes—
106C4×D172C2314yes—
107C4×D172C2314yes—
108C4×D172C2314yes—
109#13063287—28no—
110#13063287—28no—
111#13063284—22no—
112#13063284C2314yes—
113C2×C4⋊Dic43C2311yescharacteristic
114C2×C4⋊Dic43C2311yescharacteristic
115C2×C22⋊Dic43—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C22⋊C4×D43—28no—
121C22⋊C4×D43—28no—
122C2×C4×Dic43—21no—
123#13063258C2314yescomplemented
124#13063258C2314yescomplemented
125#13063256C2314yescomplemented
126#13063256C2314yescomplemented
127C4⋊(C43⋊C8)C2314yescomplemented
128C4⋊(C43⋊C8)C2314yescomplemented
129#13063249C2314yescomplemented
130#13063249C2314yescomplemented
131#13063246C2314yescomplemented
132#13063246C2314yescomplemented
133#13063245C2314yes—
134#13063245C2314yes—
135#13063245C2314yes—
136#13063245C2314yes—
137C22⋊(C43⋊C8)C2314yes—
138C22⋊(C43⋊C8)C2314yes—
139#13063236C2314yescomplemented
140C4×C43⋊C8C2314yescomplemented
141C22×Q8×C43—21no—
142C22×Q8×C43C2311yescharacteristic
143C22×D4×C43—21no—
144C22×D4×C43C2311yescharacteristic
145C23×C4×C43—21no—
146C23×C4×C43C2311yescharacteristic
147C4⋊Q8×C43—22no—
148C4⋊Q8×C43C2314yescomplemented
149#126×C43—28no—
150#124×C43—28no—
151#124×C43—22no—
152#124×C43C2314yescomplemented
153#123×C43—28no—
154C22⋊Q8×C43—22no—
155C22⋊Q8×C43—28no—
156C22⋊Q8×C43C2314yes—
157#121×C43—22no—
158#121×C43C2314yes—
159C4×Q8×C43—22no—
160C4×Q8×C43C2314yescomplemented
161C4×D4×C43—22no—
162C4×D4×C43C2314yescomplemented
163#117×C43D414yes—
164#117×C43C2314yes—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43D411yescharacteristic
169C2×C4⋊C4×C43D411yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C22⋊C4×C43D411yescharacteristic
178C2×C22⋊C4×C43D411yescharacteristic
179C2×C42×C43—21no—
180C2×C42×C43C2311yescharacteristic
181C2×C42×C43C2311yescharacteristic
182C24×C43—21no—
183C24×C43C2×D411yescharacteristic
184C23×D43—21no—
185C23×D43—21no—
186C23×D43—28no—
187C23×D43—24no—
188C23×D43—82no—
189C23×D43—82no—
190C2×Q8×C43—21no—
191C2×Q8×C43—24no—
192C2×Q8×C43—22no—
193C2×Q8×C43—22no—
194C2×Q8×C43—82no—
195C2×Q8×C43C2412yes—
196C2×D4×C43—21no—
197C2×D4×C43—24no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43—82no—
201C2×D4×C43C2412yes—
202C22×C4×C43—22no—
203C22×C4×C43—22no—
204C22×C4×C43—24no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—82no—
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2411yescharacteristic
217C22×Dic43—21no—
218C22×Dic43—21no—
219C2×D172—28no—
220C2×D172—216no—
221C2×D172—24no—
222C2×D172—21no—
223C2×D172—21no—
224C2×D172—22no—
225C2×D172—22no—
226C2×D172—28no—
227C2×D172—28no—
228C2×D172#4114yes—
229C2×D172#4114yes—
230C2×D172C2412yes—
231C2×D172C2412yes—
232C2×C4×D43—24no—
233C2×C4×D43—24no—
234C2×C4×D43—24no—
235C2×C4×D43—24no—
236C2×C4×D43—82no—
237C2×C4×D43—82no—
238C2×C4×D43—82no—
239C2×C4×D43—82no—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—24no—
242C4⋊C4×C43—24no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43C2×D414yes—
246C4⋊C4×C43C2×D414yes—
247C4⋊C4×C43C2412yes—
248C4⋊C4×C43C2412yes—
249C22⋊C4×C43—24no—
250C22⋊C4×C43—24no—
251C22⋊C4×C43—24no—
252C22⋊C4×C43—24no—
253C22⋊C4×C43—24no—
254C22⋊C4×C43C2×D414yes—
255C22⋊C4×C43C2×D414yes—
256C42×C43—24no—
257C42×C43C2×D412yes—
258C42×C43C2×D412yes—
259C42×C43C2412yes—
260C42×C43C2412yes—
261C22⋊Dic43—24no—
262#10621884—28no—
263#10621884—28no—
264#10621882—28no—
265#10621882—28no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43C2412yes—
273C4⋊Dic43C2412yes—
274C4×Dic43—24no—
275C2×C43⋊C8—22no—
276C2×C43⋊C8—22no—
277C2×C43⋊C8—22no—
278C2×C43⋊C8—22no—
279C2×C43⋊C8C2412yes—
280C2×C43⋊C8C2412yes—
281C2×C43⋊C8C2412yes—
282C2×C43⋊C8C2412yes—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—22no—
287C23×C43—42no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43C22×D412yes—
291C23×C43C22×D411yescharacteristic
292C22×D43—24no—
293C22×D43—24no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—216no—
297C22×D43—42no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43—84no—
302C22×D43—84no—
303C22×D43—816no—
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—42no—
307Q8×C43—84no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—42no—
311D4×C43—84no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—24no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43—84no—
327C2×C4×C43C22×D412yes—
328C2×C4×C43C22×D412yes—
329C2×C4×C43C22×D412yes—
330C2×C4×C43C22×D412yes—
331C2×C4×C43C22×D412yes—
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C2×#4112yes—
334C2×C4×C43C2×#4112yes—
335C2×C4×C43C2511yescharacteristic
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340D172—216no—
341D172—24no—
342D172—24no—
343D172—22no—
344D172—22no—
345D172C2×#4114yes—
346D172C2×#4114yes—
347C4×D43—84no—
348C4×D43—84no—
349C4×D43—84no—
350C4×D43—84no—
351C43⋊C8—22no—
352C43⋊C8—22no—
353C43⋊C8—22no—
354C43⋊C8—22no—
355C2×#3118—431nomaximal, Sylow
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—44no—
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—24no—
369C2×D43—24no—
370C2×D43—48no—
371C2×D43—48no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—816no—
377C4×C43—22no—
378C4×C43—22no—
379C4×C43—22no—
380C4×C43—22no—
381C4×C43—22no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43—42no—
385C4×C43#52512yes—
386C4×C43C22×#4111yescharacteristic
387C4×C43C22×#4111yescharacteristic
388Dic43—42no—
389Dic43—42no—
390C2×#542D4311yescharacteristic, complemented
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×D8—431no—
405C2×#433—431no—
406C2×C43—42no—
407C2×C43—82no—
408C2×C43#311814yescomplemented
409C2×C43C2×#52511yescharacteristic
410C2×C43C2×#57611yescharacteristic
411C2×C43C2×#57711yescharacteristic
412D43—44no—
413D43—44no—
414C23×D4—431no—
415C22×SD16—431no—
416C22×SD16—431no—
417C22×D8—431no—
418C22×D8—431no—
419#542—24no—
420#542C2×D4318yescomplemented
421C2×C4⋊Q8C2×D4311yescharacteristic, complemented
422C2×#126—21no—
423C2×#124—21no—
424C2×#124C2×D4311yescharacteristic, complemented
425C2×#123—21no—
426C2×C22⋊Q8—21no—
427C2×C22⋊Q8C2×D4311yescharacteristic
428C2×#121C2×D4311yescharacteristic
429#518—438no—
430#518—864no—
431C2×C4×Q8C2×D4311yescharacteristic, complemented
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—861no—
437C2×C4×D4—861no—
438C2×C4×D4C2×D4311yescharacteristic, complemented
439C2×#117—431no—
440C2×#117C2×D4311yescharacteristic
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×D8—438no—
455#433—438no—
456C2×#107—431no—
457C2×#107—431no—
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×#102—431no—
469C2×#102—431no—
470C2×C22⋊C8—431no—
471C2×C22⋊C8—431no—
472C2×#97—431no—
473C2×C4×C8—431no—
474C43C2×#311811yescharacteristic, complemented, Sylow
475C25—861no—
476C22×Q8—21no—
477C22×Q8C22×D4311yescharacteristic
478C22×D4—21no—
479C22×D4—431no—
480C22×D4—431no—
481C22×D4—434no—
482C22×D4—864no—
483C22×D4—864no—
484C22×D4—861no—
485C22×D4—862no—
486C22×D4C22×D4311yescharacteristic
487C23×C4—21no—
488C23×C4—861no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4—861no—
492C23×C4C22×D4311yescharacteristic
493C2×SD16—434no—
494C2×SD16—434no—
495C2×SD16—864no—
496C2×SD16—864no—
497C2×D8—434no—
498C2×D8—434no—
499C2×D8—864no—
500C2×D8—864no—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8—431no—
504C22×C8—431no—
505C4⋊Q8—22no—
506C4⋊Q8C22×D4314yescomplemented
507#126—28no—
508#124—28no—
509#124—22no—
510#124C22×D4314yescomplemented
511#123—28no—
512C22⋊Q8—22no—
513C22⋊Q8—28no—
514C22⋊Q8C22×D4314yes—
515#121—22no—
516#121C22×D4314yes—
517C4×Q8—22no—
518C4×Q8C22×D4314yescomplemented
519C4×D4—22no—
520C4×D4—434no—
521C4×D4—434no—
522C4×D4—434no—
523C4×D4—434no—
524C4×D4—868no—
525C4×D4—868no—
526C4×D4—862no—
527C4×D4—862no—
528C4×D4—862no—
529C4×D4—862no—
530C4×D4C22×D4314yescomplemented
531#117—434no—
532#117—862no—
533#117C22⋊D4314yes—
534#117C22×D4314yes—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4C22⋊D4311yescharacteristic
541C2×C4⋊C4C22⋊D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—868no—
555C2×C22⋊C4—868no—
556C2×C22⋊C4C22⋊D4311yescharacteristic
557C2×C22⋊C4C22⋊D4311yescharacteristic
558C2×C42—21no—
559C2×C42—861no—
560C2×C42C22×D4311yescharacteristic
561C2×C42C22×D4311yescharacteristic
562#107—434no—
563#107—434no—
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#102—434no—
575#102—434no—
576C22⋊C8—434no—
577C22⋊C8—434no—
578#97—434no—
579C4×C8—434no—
580C24—21no—
581C24—868no—
582C24—864no—
583C24—861no—
584C24—861no—
585C24—3442no—
586C24—3442no—
587C24C2×C22⋊D4311yescharacteristic
588C2×Q8—21no—
589C2×Q8—24no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—82no—
593C2×Q8C23×D4312yes—
594C2×D4—24no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—82no—
599C2×D4—434no—
600C2×D4—434no—
601C2×D4—432no—
602C2×D4—432no—
603C2×D4—868no—
604C2×D4—868no—
605C2×D4—868no—
606C2×D4—8616no—
607C2×D4—864no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—862no—
611C2×D4—862no—
612C2×D4C23×D4312yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—82no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—864no—
623C22×C4—864no—
624C22×C4—864no—
625C22×C4—864no—
626C22×C4—3442no—
627C22×C4—3442no—
628C22×C4—3442no—
629C22×C4—3442no—
630C22×C4C2×C22⋊D4312yes—
631C22×C4C2×C22⋊D4311yescharacteristic
632C22×C4C2×C22⋊D4311yescharacteristic
633C22×C4C2×C22⋊D4311yescharacteristic
634C22×C4C2×C22⋊D4311yescharacteristic
635C22×C4C2×C22⋊D4311yescharacteristic
636C22×C4C23×D4312yes—
637C22×C4C23×D4311yescharacteristic
638SD16—868no—
639SD16—868no—
640D8—868no—
641D8—868no—
642C2×C8—432no—
643C2×C8—432no—
644C2×C8—432no—
645C2×C8—432no—
646C2×C8—862no—
647C2×C8—862no—
648C2×C8—862no—
649C2×C8—862no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—432no—
656C4⋊C4—432no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4C2×C22⋊D4314yes—
660C4⋊C4C2×C22⋊D4314yes—
661C4⋊C4C23×D4312yes—
662C4⋊C4C23×D4312yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C22⋊C4—864no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C22⋊C4C2×C22⋊D4314yes—
674C22⋊C4C2×C22⋊D4314yes—
675C42—24no—
676C42—864no—
677C42C2×C22⋊D4312yes—
678C42C2×C22⋊D4312yes—
679C42C23×D4312yes—
680C42C23×D4312yes—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—8616no—
689C23—864no—
690C23—864no—
691C23—862no—
692C23—862no—
693C23—3444no—
694C23—3444no—
695C23—34416no—
696C23—1722no—
697C23—1722no—
698C23—1722no—
699C23—1722no—
700C23C22×C22⋊D4312yes—
701C23C22×C22⋊D4311yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—84no—
706D4—22no—
707D4—22no—
708D4—42no—
709D4—84no—
710D4—434no—
711D4—434no—
712D4—8616no—
713D4—864no—
714D4—864no—
715D4—862no—
716D4—862no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—84no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—3444no—
735C2×C4—3444no—
736C2×C4—3444no—
737C2×C4—3444no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4C22×C22⋊D4312yes—
741C2×C4C22×C22⋊D4312yes—
742C2×C4C22×C22⋊D4312yes—
743C2×C4C22×C22⋊D4312yes—
744C2×C4C22×C22⋊D4312yes—
745C2×C4C22×C22⋊D4311yescharacteristic
746C2×C4#41×D4312yes—
747C2×C4#41×D4312yes—
748C2×C4C24×D4311yescharacteristic
749C8—862no—
750C8—862no—
751C8—862no—
752C8—862no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—864no—
762C22—864no—
763C22—34416no—
764C22—1722no—
765C22—1722no—
766C22—1722no—
767C22—1722no—
768C22—1728no—
769C22—1728no—
770C22#1458340612yes—
771C22#1458370212yes—
772C22#1458370712yes—
773C22C23×C22⋊D4311yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—1722no—
783C4—1722no—
784C4#1458340612yes—
785C4C2×#41×D4311yescharacteristic
786C4C2×#41×D4311yescharacteristic
787C2—42no—
788C2—82no—
789C2—1724no—
790C2—1724no—
791C2#1914477314yesdirect product factor
792C2C2×#1458340611yescharacteristic
793C2C2×#1458370211yescharacteristic
794C2C2×#1458370711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#542C2
socleC23×C43C22×D4
prime radicalC2×#14583032C2
hypercenterC2×#542D43
hypocenterC43C2×#3118
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#14583373C2semidirect
2. #19144773C2direct (N × H)
3. C2×#14583237C2semidirect
4. C2×#14583220C2semidirect
5. C2×#14583186C2semidirect
6. C2×#14583176C2semidirect
7. C2×#14583111C2semidirect
8. C2×#14583111C2semidirect
9. C2×#14583049C2semidirect
11. C2×#14583009C2semidirect
12. C2×#14582997C2semidirect
13. C2×C4×#10621884C2semidirect
14. C2×C4×#10621882C2semidirect
15. C2×#14582960C2semidirect
16. C2×C43×#542C2semidirect
23. #14583373C22semidirect
33. #14583237C22semidirect
34. #14583220C22semidirect
35. #14583186C22semidirect
36. #14583176C22semidirect
37. #14583111C22semidirect
38. #14583111C22semidirect
39. #14583049C22semidirect
41. #14583009C22semidirect
42. #14582997C22semidirect
43. C4×#10621884C22semidirect
44. C4×#10621882C22semidirect
45. #14582960C22semidirect
46. C2×#13063258C22semidirect
47. C2×#13063258C22semidirect
48. C2×#13063256C22semidirect
49. C2×#13063256C22semidirect
50. C2×C4⋊(C43⋊C8)C22semidirect
51. C2×C4⋊(C43⋊C8)C22semidirect
52. C2×#13063249C22semidirect
53. C2×#13063249C22semidirect
54. C2×#13063246C22semidirect
55. C2×#13063246C22semidirect
62. C2×#13063236C22semidirect
63. C2×C4×C43⋊C8C22semidirect
65. C43×#542C22semidirect
66. C2×C4⋊Q8×C43C22semidirect
69. C2×#124×C43C22semidirect
74. C2×C4×Q8×C43C22semidirect
75. C2×C4×D4×C43C22semidirect
123. #13063258C23semidirect
124. #13063258C23semidirect
125. #13063256C23semidirect
126. #13063256C23semidirect
127. C4⋊(C43⋊C8)C23semidirect
128. C4⋊(C43⋊C8)C23semidirect
129. #13063249C23semidirect
130. #13063249C23semidirect
131. #13063246C23semidirect
132. #13063246C23semidirect
139. #13063236C23semidirect
140. C4×C43⋊C8C23semidirect
148. C4⋊Q8×C43C23semidirect
152. #124×C43C23semidirect
160. C4×Q8×C43C23semidirect
162. C4×D4×C43C23semidirect
390. C2×#542D43semidirect
408. C2×C43#3118semidirect
420. #542C2×D43semidirect
421. C2×C4⋊Q8C2×D43semidirect
424. C2×#124C2×D43semidirect
431. C2×C4×Q8C2×D43semidirect
438. C2×C4×D4C2×D43semidirect
474. C43C2×#3118semidirect
506. C4⋊Q8C22×D43semidirect
510. #124C22×D43semidirect
518. C4×Q8C22×D43semidirect
530. C4×D4C22×D43semidirect
791. C2#19144773direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145833732
#191447732
C2×#145832372
C2×#145832202
C2×#145831862
C2×#145831762
C2×#145831112
C2×#145830492
C2×#145830322
C2×#145830092
C2×#145829972
C2×C4×#106218842
C2×C4×#106218822
C2×#145829602
C2×C43×#5422
C2×#311843