Finite Group Databasebeta

← C2×#19144884 #25964941

Subgroups — C2×#19144884 #25964941

Order 11008.

2122 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583503C211yesmaximal, characteristic
2C2×#14583375C211yesmaximal, characteristic, complemented
3#19144884C2116yesmaximal, direct product factor
4C2×#14583222C211yesmaximal, characteristic, complemented
5C2×#14583221C211yesmaximal, characteristic, complemented
6C2×#14583207C211yesmaximal, characteristic, complemented
7C2×#14583206C211yesmaximal, characteristic, complemented
8C2×#14583096C211yesmaximal, characteristic, complemented
9C2×#14583036C211yesmaximal, characteristic, complemented
10C2×#14583036C211yesmaximal, characteristic, complemented
11C2×#14583000C211yesmaximal, characteristic, complemented
12C2×#14582996C211yesmaximal, characteristic, complemented
13C2×#14582990C211yesmaximal, characteristic, complemented
14C2×SD16×Dic43C211yesmaximal, characteristic, complemented
15C2×#14582959C211yesmaximal, characteristic, complemented
16C2×C43×#460C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20#14583503—24no—
21#14583503C2218yes—
22C2×#13063317C2211yescharacteristic
23C2×#13063306—21no—
24C2×#13063306—21no—
25C2×#13063297—21no—
26C2×#13063297—21no—
27C2×#13063296C2211yescharacteristic
28C2×#13063296C2211yescharacteristic
29#14583375—24no—
30#14583375C2218yescomplemented
31C2×Q8×Dic43C2211yescharacteristic
32C2×C4×Dic86—21no—
33C2×C4×Dic86C2211yescharacteristic
34C2×#13063290—21no—
35C2×#13063290C2211yescharacteristic
36C2×D4×Dic43C2211yescharacteristic
37C2×D4×Dic43C2211yescharacteristic
38C2×#13063283—21no—
39C2×#13063283C2211yescharacteristic
40C2×#13063282—21no—
41C2×#13063282C2211yescharacteristic
42#14583222C2218yescomplemented
43#14583221C2218yescomplemented
44#14583207C2218yescomplemented
45#14583206C2218yescomplemented
46#14583096C2218yescomplemented
47#14583036C2218yescomplemented
48#14583036C2218yescomplemented
49#14583000C2218yescomplemented
50#14582996C2218yescomplemented
51#14582990C2218yescomplemented
52SD16×Dic43C2218yescomplemented
53#14582959C2218yescomplemented
54C2×#13063259C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×#127×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C43×#460C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C2×Q8×D43—24no—
80C2×Q8×D43—22no—
81C2×Q8×D43—24no—
82C2×Q8×D43C2314yes—
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C23×Dic43—21no—
86C23×Dic43—21no—
87C22×C4×D43—21no—
88C22×C4×D43C2311yescharacteristic
89C2×#10621883—24no—
90C2×#10621883—24no—
91C2×#10621883C2314yes—
92C2×#10621883C2314yes—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95#13063317—22no—
96#13063317C2314yes—
97#13063306—28no—
98#13063306—28no—
99#13063297—28no—
100#13063297—28no—
101#13063296—22no—
102#13063296—22no—
103#13063296C2314yes—
104#13063296C2314yes—
105Q8×Dic43—22no—
106Q8×Dic43C2314yes—
107C4×Dic86—22no—
108C4×Dic86—28no—
109C4×Dic86C2314yes—
110#13063290—28no—
111#13063290—22no—
112#13063290C2314yes—
113D4×Dic43—22no—
114D4×Dic43—22no—
115D4×Dic43C2314yes—
116D4×Dic43C2314yes—
117#13063283—22no—
118#13063283—28no—
119#13063283C2314yes—
120#13063282—28no—
121#13063282D414yes—
122#13063282C2314yes—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4D411yescharacteristic
132C2×Dic43⋊C4D411yescharacteristic
133C2×C22⋊Dic43—21no—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43—21no—
136C2×C22⋊Dic43—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4D411yescharacteristic
139C2×(C2×D43)⋊C4D411yescharacteristic
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43C2311yescharacteristic
145#13063259C2314yes—
146#13063258C2314yes—
147#13063257C2314yes—
148#13063256C2314yes—
149C4⋊(C43⋊C8)C2314yes—
150#13063250C2314yes—
151#13063250C2314yes—
152#13063249C2314yes—
153#13063249C2314yes—
154#13063246C2314yes—
155#13063246C2314yes—
156(C2×D43)⋊C8C2314yes—
157(C2×D43)⋊C8C2314yes—
158#13063235C2314yes—
159C8×Dic43C2314yes—
160C22×Q8×C43C2311yescharacteristic
161C22×D4×C43—21no—
162C22×D4×C43—21no—
163C22×D4×C43C2311yescharacteristic
164C22×D4×C43C2311yescharacteristic
165C2×SD16×C43—24no—
166C2×SD16×C43—24no—
167C2×SD16×C43C2314yes—
168C2×SD16×C43C2314yes—
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171#127×C43—22no—
172#127×C43C2314yes—
173C4×Q8×C43—22no—
174C4×Q8×C43C2314yes—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C42×C43—21no—
178C2×C42×C43C2311yescharacteristic
179C4⋊C8×C43C2314yes—
180#102×C43C2314yes—
181#102×C43C2314yes—
182C24×C43—21no—
183C24×C43—21no—
184C23×D43C2×D411yescharacteristic
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43#4114yes—
188C2×Q8×C43C2412yes—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—24no—
192C2×D4×C43—24no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—82no—
198C2×D4×C43—82no—
199C2×D4×C43C2412yes—
200C2×D4×C43C2412yes—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—24no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—82no—
209C2×C22⋊D43—82no—
210C22×Dic43—24no—
211C22×Dic43—24no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—82no—
217C22×Dic43—82no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221Q8×D43—216no—
222Q8×D43—28no—
223Q8×D43—28no—
224C2×C4×D43—28no—
225C2×C4×D43—22no—
226C2×C4×D43—22no—
227C2×C4×D43—24no—
228C2×C4×D43C2×D412yes—
229C2×C4×D43C2412yes—
230C2×Dic86—28no—
231C2×Dic86—21no—
232C2×Dic86—22no—
233C2×Dic86—24no—
234C2×Dic86#4114yes—
235C2×Dic86C2412yes—
236SD16×C43—28no—
237SD16×C43—28no—
238C2×C8×C43—22no—
239C2×C8×C43—22no—
240C2×C8×C43C2412yes—
241C2×C8×C43C2412yes—
242C4⋊C4×C43—24no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43C2412yes—
245C42×C43—24no—
246C42×C43C2×D412yes—
247C42×C43C2412yes—
248C22⋊Dic43—24no—
249C22⋊Dic43—24no—
250C22⋊Dic43—24no—
251C22⋊Dic43—24no—
252#10621883—28no—
253#10621883—28no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4C2×D414yes—
256(C2×D43)⋊C4C2×D414yes—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—24no—
261C4⋊Dic43C2412yes—
262C4⋊Dic43C2412yes—
263C4⋊Dic43C2412yes—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268Dic43⋊C4C2×D414yes—
269Dic43⋊C4C2×D414yes—
270C4×Dic43—24no—
271C4×Dic43—24no—
272C4×Dic43—24no—
273C4×Dic43—24no—
274C4×Dic43C2×D412yes—
275C4×Dic43C2412yes—
276C2×C43⋊C8—22no—
277C2×C43⋊C8—22no—
278C2×C43⋊C8C2412yes—
279C2×C43⋊C8C2412yes—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—42no—
283C23×C43—42no—
284C23×C43—42no—
285C23×C43—42no—
286C23×C43—42no—
287C23×C43—42no—
288C23×C43C22×D411yescharacteristic
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43C22×D412yes—
293Q8×C43—24no—
294Q8×C43—22no—
295Q8×C43C2×#4114yes—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43—22no—
300D4×C43—42no—
301D4×C43—42no—
302D4×C43—84no—
303D4×C43—84no—
304C2×C4×C43—24no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—42no—
310C2×C4×C43C22×D412yes—
311C2×C4×C43C22×D412yes—
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C2×#4112yes—
314C2×C4×C43C2×#4112yes—
315C2×C4×C43C2511yescharacteristic
316C22⋊D43—84no—
317C22⋊D43—84no—
318C2×Dic43—22no—
319C2×Dic43—24no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—84no—
330C2×Dic43—84no—
331C2×Dic43C22×D412yes—
332C2×Dic43C22×D412yes—
333C2×Dic43C22×D412yes—
334C4×D43—216no—
335C4×D43—24no—
336C4×D43—22no—
337C4×D43—22no—
338Dic86—216no—
339Dic86—24no—
340Dic86—22no—
341Dic86C2×#4114yes—
342C8×C43—22no—
343C8×C43—22no—
344C43⋊C8—22no—
345C43⋊C8—22no—
346C2×#3126—431nomaximal, Sylow
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—84no—
354C22×C43—84no—
355C22×C43#52512yes—
356C22×C43#57712yes—
357C22×C43#57712yes—
358C22×C43C23×D411yescharacteristic
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—44no—
363C4×C43—24no—
364C4×C43—22no—
365C4×C43—22no—
366C4×C43—42no—
367C4×C43#52512yes—
368C4×C43C22×#4111yescharacteristic
369C4×C43C22×#4111yescharacteristic
370Dic43—22no—
371Dic43—24no—
372Dic43—22no—
373Dic43—22no—
374Dic43—42no—
375Dic43—42no—
376Dic43—42no—
377C2×#540—431no—
378C2×#519—431no—
379#3126—4316no—
380C2×#482—431no—
381C2×#482—431no—
382C2×#479—431no—
383C2×#479—431no—
384C2×#460—431no—
385C2×#460D4311yescharacteristic, complemented
386C2×#448—431no—
387C2×#448—431no—
388C2×#440—431no—
389C2×#440—431no—
390C2×C4×SD16—431no—
391C2×C4×SD16—431no—
392C2×#433—431no—
393C2×C43—82no—
394C2×C43—82no—
395C2×C43#312614yescomplemented
396C2×C43C2×#52511yescharacteristic
397C2×C43C2×#57711yescharacteristic
398C2×C43C2×#57711yescharacteristic
399D43—42no—
400C23×Q8—431no—
401C22×SD16—431no—
402C22×SD16—431no—
403C22×SD16C2×D4311yescharacteristic
404C22×SD16C2×D4311yescharacteristic
405#540—438no—
406#540—864no—
407C2×#127C2×D4311yescharacteristic
408C2×#125—431no—
409C2×#123—861no—
410C2×#123—861no—
411C2×#121—431no—
412C2×#121—431no—
413C2×#121—861no—
414C2×#121—861no—
415#519—438no—
416#519—864no—
417C2×C4×Q8—431no—
418C2×C4×Q8—431no—
419C2×C4×Q8—431no—
420C2×C4×Q8—861no—
421C2×C4×Q8—861no—
422C2×C4×Q8C2×D4311yescharacteristic
423C2×C4×D4—431no—
424C2×C4×D4—431no—
425C2×#117—431no—
426C2×#117—431no—
427C2×#117—861no—
428C2×#117—861no—
429#482—438no—
430#482—438no—
431#479—438no—
432#479—438no—
433#460—438no—
434#460C2×D4318yescomplemented
435#448—438no—
436#448—438no—
437#440—438no—
438#440—438no—
439C4×SD16—438no—
440C4×SD16—438no—
441#433—438no—
442C2×#107—431no—
443C2×#107—431no—
444C2×#106—431no—
445C2×#106—431no—
446C2×C4⋊C8—431no—
447C2×C4⋊C8C2×D4311yescharacteristic
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102C2×D4311yescharacteristic
455C2×#102C2×D4311yescharacteristic
456C2×C22⋊C8—431no—
457C2×C22⋊C8—431no—
458C2×#97—431no—
459C2×C4×C8—431no—
460C43C2×#312611yescharacteristic, complemented, Sylow
461C22×Q8—434no—
462C22×Q8—431no—
463C22×Q8—861no—
464C22×Q8—862no—
465C22×Q8—864no—
466C22×Q8—864no—
467C22×Q8C22×D4311yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—861no—
471C22×D4—861no—
472C22×D4C22×D4311yescharacteristic
473C22×D4C22×D4311yescharacteristic
474C23×C4—431no—
475C23×C4—861no—
476C23×C4—861no—
477C23×C4—861no—
478C2×SD16—24no—
479C2×SD16—24no—
480C2×SD16—434no—
481C2×SD16—434no—
482C2×SD16—864no—
483C2×SD16—864no—
484C2×SD16C22×D4314yes—
485C2×SD16C22×D4314yes—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490#127—22no—
491#127C22×D4314yes—
492#125—434no—
493#125—862no—
494#123—868no—
495#123—868no—
496#121—434no—
497#121—434no—
498#121—868no—
499#121—868no—
500#121—862no—
501#121—862no—
502C4×Q8—22no—
503C4×Q8—434no—
504C4×Q8—434no—
505C4×Q8—434no—
506C4×Q8—868no—
507C4×Q8—862no—
508C4×Q8—862no—
509C4×Q8—868no—
510C4×Q8—862no—
511C4×Q8C22×D4314yes—
512C4×D4—434no—
513C4×D4—434no—
514C4×D4—862no—
515C4×D4—862no—
516#117—434no—
517#117—434no—
518#117—434no—
519#117—868no—
520#117—868no—
521#117—862no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4—431no—
526C2×C4⋊C4—431no—
527C2×C4⋊C4—431no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4C22×D4311yescharacteristic
534C2×C22⋊C4—431no—
535C2×C22⋊C4—431no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C42—21no—
542C2×C42—431no—
543C2×C42—861no—
544C2×C42—861no—
545C2×C42—861no—
546C2×C42—861no—
547C2×C42C22×D4311yescharacteristic
548#107—434no—
549#107—434no—
550#106—434no—
551#106—434no—
552C4⋊C8—434no—
553C4⋊C8C22×D4314yes—
554#103—434no—
555#103—434no—
556#103—434no—
557#103—434no—
558#102—434no—
559#102—434no—
560#102C22×D4314yes—
561#102C22×D4314yes—
562C22⋊C8—434no—
563C22⋊C8—434no—
564#97—434no—
565C4×C8—434no—
566C24—21no—
567C24—21no—
568C24—431no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—434no—
572C2×Q8—432no—
573C2×Q8—864no—
574C2×Q8—868no—
575C2×Q8—868no—
576C2×Q8—8616no—
577C2×Q8—868no—
578C2×Q8—861no—
579C2×Q8—862no—
580C2×Q8#1062190014yes—
581C2×Q8C23×D4312yes—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—24no—
585C2×D4—24no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—82no—
591C2×D4—82no—
592C2×D4—864no—
593C2×D4—864no—
594C2×D4—3442no—
595C2×D4—3442no—
596C2×D4C23×D4312yes—
597C2×D4C23×D4312yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—432no—
604C22×C4—432no—
605C22×C4—864no—
606C22×C4—868no—
607C22×C4—864no—
608C22×C4—864no—
609C22×C4—861no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—3442no—
616C22×C4—3442no—
617C22×C4D4×D4311yescharacteristic
618C22×C4D4×D4311yescharacteristic
619C22×C4C23×D4311yescharacteristic
620SD16—28no—
621SD16—28no—
622SD16—868no—
623SD16—868no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—432no—
627C2×C8—432no—
628C2×C8—862no—
629C2×C8—862no—
630C2×C8C23×D4312yes—
631C2×C8C23×D4312yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—434no—
635C4⋊C4—434no—
636C4⋊C4—432no—
637C4⋊C4—432no—
638C4⋊C4—432no—
639C4⋊C4—864no—
640C4⋊C4—864no—
641C4⋊C4—861no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—864no—
645C4⋊C4—864no—
646C4⋊C4—864no—
647C4⋊C4C23×D4312yes—
648C22⋊C4—434no—
649C22⋊C4—434no—
650C22⋊C4—864no—
651C22⋊C4—864no—
652C22⋊C4—864no—
653C22⋊C4—864no—
654C22⋊C4—864no—
655C42—24no—
656C42—432no—
657C42—432no—
658C42—864no—
659C42—864no—
660C42—864no—
661C42—864no—
662C42D4×D4312yes—
663C42C23×D4312yes—
664C23—22no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—432no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23C2×D4×D4311yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—434no—
680Q8—8616no—
681Q8—864no—
682Q8—862no—
683Q8C2×#1062190014yes—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—42no—
689D4—42no—
690D4—84no—
691D4—84no—
692D4—3444no—
693D4—3444no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—42no—
700C2×C4—432no—
701C2×C4—432no—
702C2×C4—432no—
703C2×C4—8616no—
704C2×C4—862no—
705C2×C4—864no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—864no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—3444no—
716C2×C4—3444no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4C2×D4×D4312yes—
721C2×C4C2×D4×D4312yes—
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4#41×D4312yes—
724C2×C4C2×#1062190012yes—
725C2×C4C24×D4311yescharacteristic
726C8—22no—
727C8—22no—
728C8—862no—
729C8—862no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—84no—
737C22—84no—
738C22—862no—
739C22—862no—
740C22—862no—
741C22—1724no—
742C22#1458340912yes—
743C22#1458370512yes—
744C22#1458370912yes—
745C22C22×D4×D4311yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—862no—
751C4—862no—
752C4—862no—
753C4—864no—
754C4—1722no—
755C4—1722no—
756C4—1722no—
757C4#1458340912yes—
758C4C2×#41×D4311yescharacteristic
759C4C22×#1062190011yescharacteristic
760C2—82no—
761C2—82no—
762C2—1722no—
763C2#1914488414yesdirect product factor
764C2C2×#1458340911yescharacteristic
765C2C2×#1458370511yescharacteristic
766C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#460C2
socleC23×C43C22×D4
prime radicalC2×#14583503C2
hypercenterC2×#460D43
hypocenterC43C2×#3126
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. C2×#14583375C2semidirect
3. #19144884C2direct (N × H)
4. C2×#14583222C2semidirect
5. C2×#14583221C2semidirect
6. C2×#14583207C2semidirect
7. C2×#14583206C2semidirect
8. C2×#14583096C2semidirect
9. C2×#14583036C2semidirect
10. C2×#14583036C2semidirect
11. C2×#14583000C2semidirect
12. C2×#14582996C2semidirect
13. C2×#14582990C2semidirect
14. C2×SD16×Dic43C2semidirect
15. C2×#14582959C2semidirect
16. C2×C43×#460C2semidirect
30. #14583375C22semidirect
42. #14583222C22semidirect
43. #14583221C22semidirect
44. #14583207C22semidirect
45. #14583206C22semidirect
46. #14583096C22semidirect
47. #14583036C22semidirect
48. #14583036C22semidirect
49. #14583000C22semidirect
50. #14582996C22semidirect
51. #14582990C22semidirect
52. SD16×Dic43C22semidirect
53. #14582959C22semidirect
73. C43×#460C22semidirect
385. C2×#460D43semidirect
395. C2×C43#3126semidirect
434. #460C2×D43semidirect
460. C43C2×#3126semidirect
763. C2#19144884direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835032
C2×#145833752
#191448842
C2×#145832222
C2×#145832212
C2×#145832072
C2×#145832062
C2×#145830962
C2×#145830362
C2×#145830002
C2×#145829962
C2×#145829902
C2×SD16×Dic432
C2×#145829592
C2×C43×#4602
C2×#312643