Finite Group Databasebeta

← C2×#19147195 #25975319

Subgroups — C2×#19147195 #25975319

Order 11008.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583595C211yesmaximal, characteristic, complemented
2#19147195C2116yesmaximal, direct product factor
3C2×#14583298C211yesmaximal, characteristic, complemented
4C2×#14583223C211yesmaximal, characteristic, complemented
5C2×#14583220C211yesmaximal, characteristic, complemented
6C2×#14583212C211yesmaximal, characteristic, complemented
7C2×#14583210C211yesmaximal, characteristic, complemented
8C2×#14583199C211yesmaximal, characteristic, complemented
9C2×#14583196C211yesmaximal, characteristic, complemented
10C2×#14583150C211yesmaximal, characteristic, complemented
11C2×#14583150C211yesmaximal, characteristic, complemented
12C2×C4×#10621882C211yesmaximal, characteristic, complemented
13C2×#14582977C211yesmaximal, characteristic, complemented
14C2×#14582942C211yesmaximal, characteristic, complemented
15C2×#14582939C211yesmaximal, characteristic, complemented
16C2×C43×#553C211yesmaximal, characteristic, complemented
17C22×#10621882C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20#14583595—24no—
21#14583595C2218yescomplemented
22C2×#13063320—21no—
23C2×#13063317C2211yescharacteristic
24C2×#13063307—21no—
25C2×#13063299C2211yescharacteristic
26C2×#13063299C2211yescharacteristic
27C2×#13063297—21no—
28C2×C4×D172C2211yescharacteristic
29C2×(C22⋊D43)⋊C4—21no—
30C2×#13063284C2211yescharacteristic
31C22×C4⋊Dic43C2211yescharacteristic
32#14583298C2218yescomplemented
33#14583223C2218yescomplemented
34#14583220C2218yescomplemented
35#14583212C2218yescomplemented
36#14583210C2218yescomplemented
37#14583199C2218yescomplemented
38#14583196C2218yescomplemented
39#14583150C2218yescomplemented
40#14583150C2218yescomplemented
41C4×#10621882C2218yescomplemented
42#14582977C2218yescomplemented
43#14582942C2218yescomplemented
44#14582939C2218yescomplemented
45C2×#13063258C2211yescharacteristic
46C2×#13063258C2211yescharacteristic
47C2×#13063258C2211yescharacteristic
48C2×#13063258C2211yescharacteristic
49C2×#13063258C2211yescharacteristic
50C2×#13063256C2211yescharacteristic
51C2×#13063256C2211yescharacteristic
52C2×#13063256C2211yescharacteristic
53C2×#13063256C2211yescharacteristic
54C2×C4⋊(C43⋊C8)C2211yescharacteristic
55C2×#13063246C2211yescharacteristic
56C2×#13063246C2211yescharacteristic
57C2×#13063246C2211yescharacteristic
58C2×#13063245C2211yescharacteristic
59C2×#13063245C2211yescharacteristic
60C2×#13063245C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×C22⋊(C43⋊C8)C2211yescharacteristic
63C2×C4×C43⋊C8C2211yescharacteristic
64C43×#553—24no—
65C43×#553C2218yescomplemented
66C2×#126×C43—21no—
67C2×#125×C43C2211yescharacteristic
68C2×#123×C43—21no—
69C2×#121×C43—21no—
70C2×#121×C43C2211yescharacteristic
71C2×#121×C43C2211yescharacteristic
72C2×C4×D4×C43—21no—
73C2×C4×D4×C43C2211yescharacteristic
74C2×C4×D4×C43C2211yescharacteristic
75C2×#117×C43C2211yescharacteristic
76C22×C4⋊C4×C43C2211yescharacteristic
77C22×D172C2311yescharacteristic
78C22×C22⋊D43—21no—
79C22×C22⋊D43—21no—
80C23×Dic43—21no—
81C22×C4×D43—21no—
82C2×#10621882—24no—
83C2×#10621882C2314yes—
84C2×#10621877—24no—
85C2×#10621877—24no—
86C2×#10621877C2314yes—
87C2×#10621877C2314yes—
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92#13063320—28no—
93#13063317—22no—
94#13063317C2314yes—
95#13063307—28no—
96#13063299—22no—
97#13063299—22no—
98#13063299C2314yes—
99#13063299C2314yes—
100#13063297—28no—
101C4×D172—22no—
102C4×D172C2314yes—
103(C22⋊D43)⋊C4—28no—
104#13063284—22no—
105#13063284C2314yes—
106C2×C4⋊Dic43—22no—
107C2×C4⋊Dic43—21no—
108C2×C4⋊Dic43C2314yes—
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×C4⋊Dic43C2311yescharacteristic
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C2×C22⋊Dic43—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×C4×Dic43—21no—
119#13063258C2314yes—
120#13063258C2314yes—
121#13063258C2314yes—
122#13063258C2314yes—
123#13063258C2314yes—
124#13063256C2314yes—
125#13063256C2314yes—
126#13063256C2314yes—
127#13063256C2314yes—
128C4⋊(C43⋊C8)C2314yes—
129#13063246C2314yes—
130#13063246C2314yes—
131#13063246C2314yes—
132#13063245C2314yes—
133#13063245C2314yes—
134#13063245C2314yes—
135C22⋊(C43⋊C8)C2314yes—
136C22⋊(C43⋊C8)C2314yes—
137C4×C43⋊C8C2314yes—
138C22×D4×C43—21no—
139C22×D4×C43—21no—
140C22×D4×C43D411yescharacteristic
141C22×D4×C43C2311yescharacteristic
142C23×C4×C43—21no—
143C23×C4×C43—21no—
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146#126×C43—28no—
147#125×C43—22no—
148#125×C43C2314yes—
149#123×C43—28no—
150#121×C43—28no—
151#121×C43—22no—
152#121×C43—22no—
153#121×C43C2314yes—
154#121×C43C2314yes—
155C4×D4×C43—28no—
156C4×D4×C43—22no—
157C4×D4×C43D414yes—
158C4×D4×C43C2314yes—
159C4×D4×C43C2314yes—
160#117×C43—22no—
161#117×C43C2314yes—
162C2×C4⋊C4×C43—21no—
163C2×C4⋊C4×C43—22no—
164C2×C4⋊C4×C43—21no—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43D411yescharacteristic
167C2×C4⋊C4×C43C2311yescharacteristic
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2314yes—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C22⋊C4×C43—21no—
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43D411yescharacteristic
176C2×C22⋊C4×C43D411yescharacteristic
177C2×C42×C43—21no—
178C2×C42×C43C2311yescharacteristic
179C24×C43—21no—
180C24×C43C2×D411yescharacteristic
181C24×C43C2×D411yescharacteristic
182C23×D43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—24no—
185C2×D4×C43—24no—
186C2×D4×C43—22no—
187C2×D4×C43—22no—
188C2×D4×C43—42no—
189C2×D4×C43—44no—
190C2×D4×C43—82no—
191C2×D4×C43C2×D414yes—
192C2×D4×C43C2412yes—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—22no—
196C22×C4×C43—22no—
197C22×C4×C43—24no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—24no—
202C22×C4×C43—82no—
203C22×C4×C43—82no—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D412yes—
209C22×C4×C43C2×D412yes—
210C22×C4×C43C2412yes—
211C22×C4×C43C2412yes—
212C22×C4×C43C2411yescharacteristic
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—44no—
216C2×C22⋊D43—82no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—24no—
221C22×Dic43—82no—
222C2×D172—21no—
223C2×D172—22no—
224C2×D172—22no—
225C2×D172C2412yes—
226C2×C4×D43—24no—
227C2×C4×D43—82no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—24no—
231C4⋊C4×C43—24no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43C2×D414yes—
235C4⋊C4×C43C2412yes—
236C4⋊C4×C43C2412yes—
237C4⋊C4×C43C2412yes—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—24no—
240C22⋊C4×C43—24no—
241C22⋊C4×C43—24no—
242C22⋊C4×C43C2×D414yes—
243C22⋊C4×C43C2×D414yes—
244C42×C43—24no—
245C42×C43C2×D412yes—
246C42×C43C2412yes—
247C22⋊Dic43—24no—
248#10621882—28no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—24no—
255C4⋊Dic43—21no—
256C4⋊Dic43C2412yes—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261C4×Dic43—24no—
262#10621877—28no—
263#10621877—28no—
264C2×C43⋊C8—22no—
265C2×C43⋊C8—22no—
266C2×C43⋊C8—22no—
267C2×C43⋊C8#4114yes—
268C2×C43⋊C8C2412yes—
269C2×C43⋊C8C2412yes—
270C2×C43⋊C8C2412yes—
271C2×C43⋊C8C2412yes—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—42no—
280C23×C43—42no—
281C23×C43—42no—
282C23×C43C22×D412yes—
283C23×C43C22×D412yes—
284C23×C43C22×D411yescharacteristic
285C22×D43—22no—
286C22×D43—42no—
287C22×D43—42no—
288C22×D43—42no—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—44no—
292D4×C43—48no—
293D4×C43—42no—
294D4×C43—84no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—24no—
300C2×C4×C43—24no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—84no—
312C2×C4×C43—84no—
313C2×C4×C43C22×D412yes—
314C2×C4×C43C22×D412yes—
315C2×C4×C43C22×D412yes—
316C2×C4×C43C22×D412yes—
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C2×#4112yes—
319C2×C4×C432−1+412yes—
320C2×C4×C43C2511yescharacteristic
321C22⋊D43—48no—
322C22⋊D43—84no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—84no—
330D172—22no—
331D172—22no—
332D172—42no—
333C4×D43—84no—
334C43⋊C8—22no—
335C43⋊C8—22no—
336C43⋊C8—22no—
337C43⋊C8C2×#4114yes—
338C2×#3355—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—44no—
346C22×C43—44no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—84no—
351C22×C43#54712yes—
352C22×C43#57512yes—
353C22×C43#57612yes—
354C22×C43C23×D411yescharacteristic
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—84no—
359C4×C43—22no—
360C4×C43—22no—
361C4×C43—22no—
362C4×C43—22no—
363C4×C43—42no—
364C4×C43—42no—
365C4×C43—42no—
366C4×C43#54712yes—
367C4×C43C22×#4111yescharacteristic
368C4×C43C2×2−1+411yescharacteristic
369Dic43—42no—
370Dic43—42no—
371Dic43—42no—
372C2×#553—431no—
373C2×#553D4311yescharacteristic, complemented
374#3355—4316no—
375C2×#499—431no—
376C2×#482—431no—
377C2×#482—431no—
378C2×#480—431no—
379C2×#480—431no—
380C2×#478—431no—
381C2×#478—431no—
382C2×#469—431no—
383C2×#469—431no—
384C2×C4×D8—431no—
385C2×#436—431no—
386C2×#428—431no—
387C2×#428—431no—
388C2×C43—42no—
389C2×C43—42no—
390C2×C43—82no—
391C2×C43#335514yescomplemented
392C2×C43C2×#54711yescharacteristic
393C2×C43C2×#57511yescharacteristic
394C2×C43C2×#57611yescharacteristic
395D43—82no—
396C22×D8—431no—
397C22×M16—431no—
398C22×M16—431no—
399#553—24no—
400#553—438no—
401#553—864no—
402#553C2×D4318yescomplemented
403C2×#126—21no—
404C2×#126—861no—
405C2×#125—431no—
406C2×#125C2×D4311yescharacteristic
407C2×#123—21no—
408C2×#123—861no—
409C2×#121—21no—
410C2×#121—431no—
411C2×#121—431no—
412C2×#121—861no—
413C2×#121C2×D4311yescharacteristic
414C2×#121C2×D4311yescharacteristic
415C2×C4×D4—21no—
416C2×C4×D4—431no—
417C2×C4×D4—861no—
418C2×C4×D4C2×D4311yescharacteristic
419C2×C4×D4C2×D4311yescharacteristic
420C2×#117—431no—
421C2×#117C2×D4311yescharacteristic
422C22×C4⋊C4—431no—
423C22×C4⋊C4C2×D4311yescharacteristic
424#499—438no—
425#482—438no—
426#482—438no—
427#480—438no—
428#480—438no—
429#478—438no—
430#478—438no—
431#469—438no—
432#469—438no—
433C4×D8—438no—
434#436—438no—
435#428—438no—
436#428—438no—
437C2×#107—431no—
438C2×#107—431no—
439C2×#107—431no—
440C2×#107—431no—
441C2×#107—431no—
442C2×#106—431no—
443C2×#106—431no—
444C2×#106—431no—
445C2×#106—431no—
446C2×C4⋊C8—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×C22⋊C8—431no—
454C2×C22⋊C8—431no—
455C2×C4×C8—431no—
456C43C2×#335511yescharacteristic, complemented, Sylow
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—431no—
460C22×D4—861no—
461C22×D4—861no—
462C22×D4C22⋊D4311yescharacteristic
463C22×D4C22×D4311yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—861no—
467C23×C4—861no—
468C23×C4C22×D4311yescharacteristic
469C23×C4C22×D4311yescharacteristic
470C2×D8—434no—
471C2×D8—864no—
472C2×M16—434no—
473C2×M16—434no—
474C2×M16—864no—
475C2×M16—864no—
476C22×C8—431no—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8—431no—
480#126—28no—
481#126—868no—
482#125—22no—
483#125—434no—
484#125—862no—
485#125C22×D4314yes—
486#123—28no—
487#123—868no—
488#121—28no—
489#121—22no—
490#121—22no—
491#121—434no—
492#121—434no—
493#121—868no—
494#121—862no—
495#121—862no—
496#121C22×D4314yes—
497#121C22×D4314yes—
498C4×D4—28no—
499C4×D4—22no—
500C4×D4—434no—
501C4×D4—868no—
502C4×D4—862no—
503C4×D4C22⋊D4314yes—
504C4×D4C22×D4314yes—
505C4×D4C22×D4314yes—
506#117—22no—
507#117—434no—
508#117—862no—
509#117C22×D4314yes—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—434no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—862no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4C22⋊D4311yescharacteristic
523C2×C4⋊C4C22×D4311yescharacteristic
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C4⋊C4C22×D4314yes—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4C22⋊D4311yescharacteristic
536C2×C22⋊C4C22⋊D4311yescharacteristic
537C2×C42—21no—
538C2×C42—861no—
539C2×C42C22×D4311yescharacteristic
540#107—434no—
541#107—434no—
542#107—434no—
543#107—434no—
544#107—434no—
545#106—434no—
546#106—434no—
547#106—434no—
548#106—434no—
549C4⋊C8—434no—
550#102—434no—
551#102—434no—
552#102—434no—
553#102—434no—
554#102—434no—
555#102—434no—
556C22⋊C8—434no—
557C22⋊C8—434no—
558C4×C8—434no—
559C24—21no—
560C24—861no—
561C24C2×C22⋊D4311yescharacteristic
562C24C2×C22⋊D4311yescharacteristic
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4—82no—
571C2×D4—432no—
572C2×D4—864no—
573C2×D4—864no—
574C2×D4—861no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—3442no—
578C2×D4—1724no—
579C2×D4C2×C22⋊D4314yes—
580C2×D4C23×D4312yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—864no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—864no—
597C22×C4—3442no—
598C22×C4—3442no—
599C22×C4C2×C22⋊D4312yes—
600C22×C4C2×C22⋊D4312yes—
601C22×C4C2×C22⋊D4311yescharacteristic
602C22×C4C2×C22⋊D4311yescharacteristic
603C22×C4C2×C22⋊D4311yescharacteristic
604C22×C4C2×C22⋊D4311yescharacteristic
605C22×C4C23×D4312yes—
606C22×C4C23×D4312yes—
607C22×C4C23×D4311yescharacteristic
608D8—868no—
609M16—868no—
610M16—868no—
611C2×C8—434no—
612C2×C8—432no—
613C2×C8—432no—
614C2×C8—432no—
615C2×C8—432no—
616C2×C8—862no—
617C2×C8—862no—
618C2×C8—862no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—432no—
626C4⋊C4—432no—
627C4⋊C4—432no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—864no—
631C4⋊C4—861no—
632C4⋊C4—864no—
633C4⋊C4—864no—
634C4⋊C4C2×C22⋊D4314yes—
635C4⋊C4C23×D4312yes—
636C4⋊C4C23×D4312yes—
637C4⋊C4C23×D4312yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4C2×C22⋊D4314yes—
647C22⋊C4C2×C22⋊D4314yes—
648C42—24no—
649C42—864no—
650C42C2×C22⋊D4312yes—
651C42C23×D4312yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—862no—
663C23—1722no—
664C23—1722no—
665C23—1722no—
666C23C22×C22⋊D4312yes—
667C23C22×C22⋊D4312yes—
668C23C22×C22⋊D4311yescharacteristic
669D4—22no—
670D4—22no—
671D4—44no—
672D4—48no—
673D4—42no—
674D4—84no—
675D4—862no—
676D4—862no—
677D4—3444no—
678D4—1728no—
679D4—1722no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—3444no—
702C2×C4—3444no—
703C2×C4—1722no—
704C2×C4—1722no—
705C2×C4—1722no—
706C2×C4C22×C22⋊D4312yes—
707C2×C4C22×C22⋊D4312yes—
708C2×C4C22×C22⋊D4312yes—
709C2×C4C22×C22⋊D4312yes—
710C2×C4C22×C22⋊D4311yescharacteristic
711C2×C4#41×D4312yes—
712C2×C4#1306337212yes—
713C2×C4C24×D4311yescharacteristic
714C8—434no—
715C8—862no—
716C8—862no—
717C8—862no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—3444no—
731C22—1722no—
732C22—1722no—
733C22—1722no—
734C22#1458354812yes—
735C22#1458369712yes—
736C22#1458370212yes—
737C22C23×C22⋊D4311yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—1722no—
746C4—1722no—
747C4—1722no—
748C4#1458354812yes—
749C4C2×#41×D4311yescharacteristic
750C4C2×#1306337211yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—3442no—
755C2#1914719514yesdirect product factor
756C2C2×#1458354811yescharacteristic
757C2C2×#1458369711yescharacteristic
758C2C2×#1458370211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#553C2
socleC23×C43C22×D4
hypercenterC2×#553D43
hypocenterC43C2×#3355
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#14583595C2semidirect
2. #19147195C2direct (N × H)
3. C2×#14583298C2semidirect
4. C2×#14583223C2semidirect
5. C2×#14583220C2semidirect
6. C2×#14583212C2semidirect
7. C2×#14583210C2semidirect
8. C2×#14583199C2semidirect
9. C2×#14583196C2semidirect
10. C2×#14583150C2semidirect
11. C2×#14583150C2semidirect
12. C2×C4×#10621882C2semidirect
13. C2×#14582977C2semidirect
14. C2×#14582942C2semidirect
15. C2×#14582939C2semidirect
16. C2×C43×#553C2semidirect
21. #14583595C22semidirect
32. #14583298C22semidirect
33. #14583223C22semidirect
34. #14583220C22semidirect
35. #14583212C22semidirect
36. #14583210C22semidirect
37. #14583199C22semidirect
38. #14583196C22semidirect
39. #14583150C22semidirect
40. #14583150C22semidirect
41. C4×#10621882C22semidirect
42. #14582977C22semidirect
43. #14582942C22semidirect
44. #14582939C22semidirect
65. C43×#553C22semidirect
373. C2×#553D43semidirect
391. C2×C43#3355semidirect
402. #553C2×D43semidirect
456. C43C2×#3355semidirect
755. C2#19147195direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835952
#191471952
C2×#145832982
C2×#145832232
C2×#145832202
C2×#145832122
C2×#145832102
C2×#145831992
C2×#145831962
C2×#145831502
C2×C4×#106218822
C2×#145829772
C2×#145829422
C2×#145829392
C2×C43×#5532
C2×#335543