Finite Group Databasebeta

← C2×#19147097 #25975194

Subgroups — C2×#19147097 #25975194

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×#14583614C211yesmaximal, characteristic, complemented
2C2×#14583595C211yesmaximal, characteristic, complemented
3#19147097C2116yesmaximal, direct product factor
4C2×#14583308C211yesmaximal, characteristic, complemented
5C2×#14583224C211yesmaximal, characteristic, complemented
6C2×#14583224C211yesmaximal, characteristic, complemented
7C2×#14583224C211yesmaximal, characteristic, complemented
8C2×#14583213C211yesmaximal, characteristic, complemented
9C2×#14583200C211yesmaximal, characteristic, complemented
10C2×#14583180C211yesmaximal, characteristic, complemented
11C2×#14583152C211yesmaximal, characteristic, complemented
12C2×#14583135C211yesmaximal, characteristic, complemented
13C2×#14583012C211yesmaximal, characteristic, complemented
14C2×#14582941C211yesmaximal, characteristic, complemented
15C2×#14582937C211yesmaximal, characteristic, complemented
16C2×C43×#435C211yesmaximal, characteristic, complemented
17C22×D344C2211yescharacteristic
18#14583614—24no—
19#14583614C2218yescomplemented
20#14583595—24no—
21#14583595C2218yescomplemented
22C2×#13063325C2211yescharacteristic
23C2×#13063320—21no—
24C2×#13063317C2211yescharacteristic
25C2×#13063311—21no—
26C2×#13063311—21no—
27C2×#13063307—21no—
28C2×#13063299C2211yescharacteristic
29C2×#13063299C2211yescharacteristic
30C2×#13063299C2211yescharacteristic
31C2×#13063299C2211yescharacteristic
32C2×#13063297—21no—
33C2×#13063296—21no—
34C2×C4×D172C2211yescharacteristic
35C2×C4×D172C2211yescharacteristic
36C2×(C22⋊D43)⋊C4—21no—
37C2×#13063284C2211yescharacteristic
38C2×#13063284C2211yescharacteristic
39C2×#13063284C2211yescharacteristic
40C2×#13063283—21no—
41C22×C4⋊Dic43C2211yescharacteristic
42#14583308C2218yescomplemented
43#14583224C2218yescomplemented
44#14583224C2218yescomplemented
45#14583224C2218yescomplemented
46#14583213C2218yescomplemented
47#14583200C2218yescomplemented
48#14583180C2218yescomplemented
49#14583152C2218yescomplemented
50#14583135C2218yescomplemented
51#14583012C2218yescomplemented
52#14582941C2218yescomplemented
53#14582937C2218yescomplemented
54C2×#13063259C2211yescharacteristic
55C2×#13063259C2211yescharacteristic
56C2×#13063259C2211yescharacteristic
57C2×#13063259C2211yescharacteristic
58C2×#13063259C2211yescharacteristic
59C2×#13063257C2211yescharacteristic
60C2×#13063257C2211yescharacteristic
61C2×#13063257C2211yescharacteristic
62C2×#13063257C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#435C2218yescomplemented
73C2×C4⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×C22⋊C8×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×D172C2311yescharacteristic
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C23×Dic43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C2×D344—24no—
88C2×D344C2314yes—
89#13063325—22no—
90#13063325C2314yes—
91#13063320—28no—
92#13063317—22no—
93#13063317C2314yes—
94#13063311—28no—
95#13063311—28no—
96#13063307—28no—
97#13063299—22no—
98#13063299—22no—
99#13063299—22no—
100#13063299—22no—
101#13063299C2314yes—
102#13063299C2314yes—
103#13063299C2314yes—
104#13063299C2314yes—
105#13063297—28no—
106#13063296—28no—
107C4×D172—22no—
108C4×D172—22no—
109C4×D172C2314yes—
110C4×D172C2314yes—
111(C22⋊D43)⋊C4—28no—
112#13063284—22no—
113#13063284—22no—
114#13063284—22no—
115#13063284C2314yes—
116#13063284C2314yes—
117#13063284C2314yes—
118#13063283—28no—
119C2×C4⋊Dic43—22no—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43C2314yes—
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×C22⋊Dic43—21no—
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43—21no—
143#13063259C2314yes—
144#13063259C2314yes—
145#13063259C2314yes—
146#13063259C2314yes—
147#13063259C2314yes—
148#13063257C2314yes—
149#13063257C2314yes—
150#13063257C2314yes—
151#13063257C2314yes—
152#13063247C2314yes—
153#13063247C2314yes—
154#13063247C2314yes—
155#13063247C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158C22×D4×C43D411yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C23×C4×C43C2311yescharacteristic
161C2×M16×C43—24no—
162C2×M16×C43C2314yes—
163C22×C8×C43—24no—
164C22×C8×C43C2314yes—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C4×D4×C43D414yes—
170C4×D4×C43C2314yes—
171C2×C4⋊C4×C43D411yescharacteristic
172C2×C22⋊C4×C43D411yescharacteristic
173C2×C22⋊C4×C43D411yescharacteristic
174C2×C42×C43C2311yescharacteristic
175C4⋊C8×C43C2314yes—
176C22⋊C8×C43C2314yes—
177C22⋊C8×C43C2314yes—
178#97×C43C2314yes—
179C24×C43C2×D411yescharacteristic
180C24×C43C2×D411yescharacteristic
181C23×D43—21no—
182C23×D43—21no—
183C2×D4×C43—42no—
184C2×D4×C43C2×D414yes—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2×D412yes—
195C22×C4×C43C2412yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2411yescharacteristic
198C2×C22⋊D43—24no—
199C2×C22⋊D43—24no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—44no—
203C2×C22⋊D43—82no—
204C2×C22⋊D43—82no—
205C2×C22⋊D43—82no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—24no—
213C22×Dic43—82no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—22no—
217C2×D172—22no—
218C2×D172—22no—
219C2×D172—22no—
220C2×D172C2412yes—
221C2×D172C2412yes—
222C2×C4×D43—24no—
223C2×C4×D43—24no—
224C2×C4×D43—44no—
225C2×C4×D43—82no—
226C2×Dic86—24no—
227C2×Dic86—82no—
228M16×C43—28no—
229C2×C8×C43—22no—
230C2×C8×C43—22no—
231C2×C8×C43—22no—
232C2×C8×C43—28no—
233C2×C8×C43#4114yes—
234C2×C8×C43C2412yes—
235C2×C8×C43C2412yes—
236C2×C8×C43C2412yes—
237C2×C8×C43C2412yes—
238C4⋊C4×C43C2×D414yes—
239C22⋊C4×C43C2×D414yes—
240C22⋊C4×C43C2×D414yes—
241C42×C43C2×D412yes—
242C42×C43C2412yes—
243C22⋊Dic43—24no—
244C22⋊Dic43—24no—
245C22⋊Dic43—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
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—24no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43C2412yes—
261C4⋊Dic43C2412yes—
262C4⋊Dic43C2412yes—
263C4⋊Dic43C2412yes—
264C4⋊Dic43C2412yes—
265C4⋊Dic43C2412yes—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268C4×Dic43—24no—
269C4×Dic43—24no—
270C4×Dic43—24no—
271D344—28no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43C22×D412yes—
279C23×C43C22×D412yes—
280C23×C43C22×D411yescharacteristic
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43—42no—
288C22×D43—42no—
289D4×C43—44no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—24no—
295C2×C4×C43—24no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43C22×D412yes—
301C2×C4×C43C22×D412yes—
302C2×C4×C43C22×D412yes—
303C2×C4×C43C22×D412yes—
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4112yes—
306C2×C4×C432−1+412yes—
307C2×C4×C43C2511yescharacteristic
308C22⋊D43—48no—
309C22⋊D43—84no—
310C22⋊D43—84no—
311C22⋊D43—84no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—84no—
325D172—22no—
326D172—22no—
327D172—22no—
328D172—22no—
329D172—42no—
330D172—42no—
331C4×D43—48no—
332C4×D43—84no—
333Dic86—84no—
334C8×C43—22no—
335C8×C43—22no—
336C8×C43—22no—
337C8×C43C2×#4114yes—
338C2×#3347—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#54712yes—
348C22×C43#57512yes—
349C22×C43#57612yes—
350C22×C43C23×D411yescharacteristic
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—84no—
358C2×D43—84no—
359C4×C43—22no—
360C4×C43—22no—
361C4×C43—22no—
362C4×C43—22no—
363C4×C43#54712yes—
364C4×C43C22×#4111yescharacteristic
365C4×C43C2×2−1+411yescharacteristic
366Dic43—42no—
367Dic43—42no—
368Dic43—42no—
369Dic43—42no—
370Dic43—42no—
371Dic43—42no—
372C2×#555—431no—
373C2×#553—431no—
374#3347—4316no—
375C2×#501—431no—
376C2×#482—431no—
377C2×#482—431no—
378C2×#482—431no—
379C2×#480—431no—
380C2×#478—431no—
381C2×#474—431no—
382C2×#469—431no—
383C2×#466—431no—
384C2×#442—431no—
385C2×#435D4311yescharacteristic, complemented
386C2×#428—431no—
387C2×#427—431no—
388C2×C43—42no—
389C2×C43—42no—
390C2×C43#334714yescomplemented
391C2×C43C2×#54711yescharacteristic
392C2×C43C2×#57511yescharacteristic
393C2×C43C2×#57611yescharacteristic
394D43—82no—
395D43—82no—
396C22×D8—431no—
397C22×M16C2×D4311yescharacteristic
398C23×C8C2×D4311yescharacteristic
399#555—438no—
400#555—864no—
401#553—438no—
402#553—864no—
403C2×C4⋊Q8—431no—
404C2×#126—861no—
405C2×#125—431no—
406C2×#124—861no—
407C2×#124—861no—
408C2×#123—861no—
409C2×#121—431no—
410C2×#121—431no—
411C2×#121—431no—
412C2×#121—431no—
413C2×#121—861no—
414C2×#121—861no—
415C2×C4×D4—431no—
416C2×C4×D4—431no—
417C2×C4×D4—861no—
418C2×C4×D4C2×D4311yescharacteristic
419C2×#117—431no—
420C2×#117—431no—
421C2×#117—431no—
422C2×#117—861no—
423C22×C4⋊C4—431no—
424#501—438no—
425#482—438no—
426#482—438no—
427#482—438no—
428#480—438no—
429#478—438no—
430#474—438no—
431#469—438no—
432#466—438no—
433#442—438no—
434#435C2×D4318yescomplemented
435#428—438no—
436#427—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⋊C8C2×D4311yescharacteristic
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×C22⋊C8C2×D4311yescharacteristic
454C2×C22⋊C8C2×D4311yescharacteristic
455C2×#97C2×D4311yescharacteristic
456C43C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—861no—
458C22×D4—431no—
459C22×D4—431no—
460C22×D4—861no—
461C22×D4—861no—
462C22×D4—861no—
463C22×D4—861no—
464C22×D4D17211yescharacteristic
465C23×C4—861no—
466C23×C4—861no—
467C23×C4—861no—
468C23×C4C22×D4311yescharacteristic
469C23×C4C22×D4311yescharacteristic
470C2×D8—434no—
471C2×D8—864no—
472C2×M16—24no—
473C2×M16C22×D4314yes—
474C22×C8—24no—
475C22×C8C22×D4311yescharacteristic
476C22×C8C22×D4314yes—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479C22×C8C22×D4311yescharacteristic
480C4⋊Q8—434no—
481C4⋊Q8—862no—
482#126—868no—
483#125—434no—
484#125—862no—
485#124—868no—
486#124—868no—
487#123—868no—
488#121—434no—
489#121—434no—
490#121—434no—
491#121—434no—
492#121—868no—
493#121—868no—
494#121—862no—
495#121—862no—
496#121—862no—
497#121—862no—
498C4×D4—434no—
499C4×D4—434no—
500C4×D4—868no—
501C4×D4—862no—
502C4×D4—862no—
503C4×D4D17214yes—
504C4×D4C22×D4314yes—
505#117—434no—
506#117—434no—
507#117—434no—
508#117—862no—
509#117—862no—
510#117—862no—
511#117—868no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—434no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—862no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4D17211yescharacteristic
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4D17211yescharacteristic
535C2×C22⋊C4D17211yescharacteristic
536C2×C42—861no—
537C2×C42—861no—
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⋊C8C22×D4314yes—
550#102—434no—
551#102—434no—
552#102—434no—
553#102—434no—
554#102—434no—
555#102—434no—
556C22⋊C8C22×D4314yes—
557C22⋊C8C22×D4314yes—
558#97C22×D4314yes—
559C24—861no—
560C24—861no—
561C24C2×D17211yescharacteristic
562C24C2×D17211yescharacteristic
563C2×Q8—864no—
564C2×Q8—3442no—
565C2×D4—42no—
566C2×D4—432no—
567C2×D4—432no—
568C2×D4—864no—
569C2×D4—864no—
570C2×D4—864no—
571C2×D4—864no—
572C2×D4—861no—
573C2×D4—861no—
574C2×D4—862no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—862no—
578C2×D4—3442no—
579C2×D4—3442no—
580C2×D4—3442no—
581C2×D4—1724no—
582C2×D4C2×D17214yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—864no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—864no—
595C22×C4—864no—
596C22×C4—3442no—
597C22×C4—3442no—
598C22×C4—1724no—
599C22×C4C2×D17212yes—
600C22×C4C2×D17212yes—
601C22×C4C2×D17211yescharacteristic
602C22×C4C2×D17211yescharacteristic
603C22×C4C2×D17211yescharacteristic
604C22×C4C2×D17211yescharacteristic
605C22×C4C23×D4312yes—
606C22×C4C23×D4312yes—
607C22×C4C23×D4311yescharacteristic
608D8—868no—
609M16—28no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—28no—
614C2×C8#1062190014yes—
615C2×C8C23×D4312yes—
616C2×C8C23×D4312yes—
617C2×C8C23×D4312yes—
618C2×C8C23×D4312yes—
619C4⋊C4—432no—
620C4⋊C4—432no—
621C4⋊C4—432no—
622C4⋊C4—432no—
623C4⋊C4—432no—
624C4⋊C4—432no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—864no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—864no—
633C4⋊C4—864no—
634C4⋊C4—864no—
635C4⋊C4C2×D17214yes—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—864no—
639C22⋊C4—864no—
640C22⋊C4—864no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4C2×D17214yes—
646C22⋊C4C2×D17214yes—
647C42—864no—
648C42—864no—
649C42—864no—
650C42C2×D17212yes—
651C42C23×D4312yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—862no—
659C23—862no—
660C23—1722no—
661C23—1722no—
662C23—1722no—
663C23—1722no—
664C23—1722no—
665C23—1722no—
666C23C22×D17212yes—
667C23C22×D17212yes—
668C23C22×D17211yescharacteristic
669Q8—3444no—
670D4—44no—
671D4—862no—
672D4—862no—
673D4—862no—
674D4—862no—
675D4—3444no—
676D4—3444no—
677D4—3444no—
678D4—1728no—
679D4—1722no—
680D4—1722no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—3444no—
698C2×C4—3444no—
699C2×C4—1728no—
700C2×C4—1722no—
701C2×C4—1722no—
702C2×C4—1722no—
703C2×C4—1722no—
704C2×C4—1722no—
705C2×C4—1722no—
706C2×C4C22×D17212yes—
707C2×C4C22×D17212yes—
708C2×C4C22×D17212yes—
709C2×C4C22×D17212yes—
710C2×C4C22×D17211yescharacteristic
711C2×C4C2×#1062190012yes—
712C2×C4#1306337212yes—
713C2×C4C24×D4311yescharacteristic
714C8—22no—
715C8—22no—
716C8—22no—
717C8C2×#1062190014yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—3444no—
727C22—3444no—
728C22—1722no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22—1722no—
733C22—1722no—
734C22#1458355312yes—
735C22#1458369912yes—
736C22#1458370412yes—
737C22C23×D17211yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—1722no—
743C4—1722no—
744C4—1722no—
745C4—1722no—
746C4—1722no—
747C4—1722no—
748C4#1458355312yes—
749C4C22×#1062190011yescharacteristic
750C4C2×#1306337211yescharacteristic
751C2—42no—
752C2—42no—
753C2—3442no—
754C2—3442no—
755C2#1914709714yesdirect product factor
756C2C2×#1458355311yescharacteristic
757C2C2×#1458369911yescharacteristic
758C2C2×#1458370411yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
hypercenterC2×#435D43
hypocenterC43C2×#3347
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#14583614C2semidirect
2. C2×#14583595C2semidirect
3. #19147097C2direct (N × H)
4. C2×#14583308C2semidirect
5. C2×#14583224C2semidirect
6. C2×#14583224C2semidirect
7. C2×#14583224C2semidirect
8. C2×#14583213C2semidirect
9. C2×#14583200C2semidirect
10. C2×#14583180C2semidirect
11. C2×#14583152C2semidirect
12. C2×#14583135C2semidirect
13. C2×#14583012C2semidirect
14. C2×#14582941C2semidirect
15. C2×#14582937C2semidirect
16. C2×C43×#435C2semidirect
19. #14583614C22semidirect
21. #14583595C22semidirect
42. #14583308C22semidirect
43. #14583224C22semidirect
44. #14583224C22semidirect
45. #14583224C22semidirect
46. #14583213C22semidirect
47. #14583200C22semidirect
48. #14583180C22semidirect
49. #14583152C22semidirect
50. #14583135C22semidirect
51. #14583012C22semidirect
52. #14582941C22semidirect
53. #14582937C22semidirect
72. C43×#435C22semidirect
385. C2×#435D43semidirect
390. C2×C43#3347semidirect
434. #435C2×D43semidirect
456. C43C2×#3347semidirect
755. C2#19147097direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836142
C2×#145835952
#191470972
C2×#145833082
C2×#145832242
C2×#145832132
C2×#145832002
C2×#145831802
C2×#145831522
C2×#145831352
C2×#145830122
C2×#145829412
C2×#145829372
C2×C43×#4352
C2×#334743