Finite Group Databasebeta

← C2×#19144148 #25963537

Subgroups — C2×#19144148 #25963537

Order 11008.

2742 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063357C211yesmaximal, characteristic, complemented
2C22×#13063346C211yesmaximal, characteristic
3C2×#14583469C211yesmaximal, characteristic, complemented
4C2×#14583381C211yesmaximal, characteristic, complemented
5#19144148C2116yesmaximal, direct product factor
6C2×#14583119C211yesmaximal, characteristic, complemented
7C2×#14583109C211yesmaximal, characteristic, complemented
8C2×#14583107C211yesmaximal, characteristic, complemented
9C2×#14583113C211yesmaximal, characteristic, complemented
10C2×#14583111C211yesmaximal, characteristic, complemented
11C2×#14583105C211yesmaximal, characteristic, complemented
12C2×#14583103C211yesmaximal, characteristic, complemented
13C2×#14582924C211yesmaximal, characteristic, complemented
14C2×#14582897C211yesmaximal, characteristic, complemented
15C2×#103×D43C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×Q8×D43C2211yescharacteristic
20C2×#13063357—28no—
21C2×#13063357C2218yescomplemented
22C2×#13063346—28no—
23C2×#13063346C2218yes—
24C22×#10621885C2211yescharacteristic
25C22×#10621885C2211yescharacteristic
26C22×#10621873C2211yescharacteristic
27C22×#10621873C2211yescharacteristic
28C22×#10621884C2211yescharacteristic
29C22×#10621882C2211yescharacteristic
30C22×#10621872C2211yescharacteristic
31C22×C8×D43C2211yescharacteristic
32#14583469—24no—
33#14583469C2218yescomplemented
34C2×#13063325C2211yescharacteristic
35C2×#13063323C2211yescharacteristic
36C2×#13063312C2211yescharacteristic
37C2×#13063307—21no—
38C2×#13063307—21no—
39C2×#13063302—21no—
40C2×#13063302—21no—
41#14583381—24no—
42#14583381C2218yescomplemented
43C2×Q8×Dic43C2211yescharacteristic
44C2×C4×D172—21no—
45C2×C4×D172C2211yescharacteristic
46C2×#13063287—21no—
47C2×#13063287C2211yescharacteristic
48C2×#13063282—21no—
49C2×#13063282C2211yescharacteristic
50C2×C4⋊C4×D43—21no—
51C2×C4⋊C4×D43C2211yescharacteristic
52#14583119C2218yescomplemented
53#14583113C2218yescomplemented
54#14583111C2218yescomplemented
55#14583109C2218yescomplemented
56#14583107C2218yescomplemented
57#14583105C2218yescomplemented
58#14583103C2218yescomplemented
59#14582924C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63#14582897C2218yescomplemented
64C2×#13063250C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063249C2211yescharacteristic
67C2×#13063248C2211yescharacteristic
68C2×#13063248C2211yescharacteristic
69#103×D43C2218yescomplemented
70C2×#13063246C2211yescharacteristic
71C22×Q16×C43C2211yescharacteristic
72C22×SD16×C43C2211yescharacteristic
73C2×#124×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic
75C43×#464C2218yescomplemented
76C2×C4⋊C8×C43C2211yescharacteristic
77C2×#103×C43C2211yescharacteristic
78C2×#102×C43C2211yescharacteristic
79C2×#10621902—22no—
80C2×#10621902—24no—
81C2×#10621902D418yes—
82C2×#10621902C2314yes—
83C2×#10621900—24no—
84C2×#10621900—22no—
85C2×#10621900—24no—
86C2×#10621900C2314yes—
87C22×Dic86—21no—
88C22×Dic86C2311yescharacteristic
89C22×Dic86C2311yescharacteristic
90C2×Q8×D43—22no—
91C2×Q8×D43—24no—
92C2×Q8×D43—24no—
93C2×Q8×D43C2314yes—
94C22×D172—21no—
95C22×D172C2311yescharacteristic
96C22×C22⋊D43—21no—
97C23×Dic43—21no—
98C22×C4×D43—21no—
99C22×C4×D43—21no—
100C22×C4×D43—21no—
101C22×C4×D43—21no—
102C22×C4×D43—21no—
103C22×C4×D43C2311yescharacteristic
104#13063357—232no—
105#13063346—232no—
106C2×#10621885—24no—
107C2×#10621885—24no—
108C2×#10621885C2314yes—
109C2×#10621885C2314yes—
110C2×#10621873—24no—
111C2×#10621873—24no—
112C2×#10621873C2314yes—
113C2×#10621873C2314yes—
114C2×#10621884—24no—
115C2×#10621884C2314yes—
116C2×#10621882—24no—
117C2×#10621882C2314yes—
118C2×#10621872—24no—
119C2×#10621872C2314yes—
120C22×C43⋊C8C2311yescharacteristic
121C22×C43⋊C8C2311yescharacteristic
122C2×C8×D43—24no—
123C2×C8×D43C2314yes—
124#13063325—22no—
125#13063325C2314yes—
126#13063323—22no—
127#13063323C2314yes—
128#13063312—22no—
129#13063312C2314yes—
130#13063307—28no—
131#13063307—28no—
132#13063302—28no—
133#13063302—28no—
134Q8×Dic43—22no—
135Q8×Dic43C2314yes—
136C4×D172—22no—
137C4×D172—28no—
138C4×D172C2314yes—
139#13063287—28no—
140#13063287—22no—
141#13063287C2314yes—
142#13063282—28no—
143#13063282D414yes—
144#13063282C2314yes—
145C2×C4⋊Dic43—21no—
146C2×C4⋊Dic43—21no—
147C2×C4⋊Dic43—21no—
148C2×C4⋊Dic43C2311yescharacteristic
149C2×Dic43⋊C4—21no—
150C2×Dic43⋊C4—21no—
151C2×Dic43⋊C4—21no—
152C2×Dic43⋊C4D411yescharacteristic
153C2×Dic43⋊C4D411yescharacteristic
154C4⋊C4×D43—22no—
155C4⋊C4×D43—28no—
156C4⋊C4×D43C2314yes—
157C2×C22⋊Dic43—21no—
158C2×C22⋊Dic43—21no—
159C2×(C2×D43)⋊C4—21no—
160C2×(C2×D43)⋊C4—21no—
161C2×(C2×D43)⋊C4D411yescharacteristic
162C2×(C2×D43)⋊C4D411yescharacteristic
163C2×C4×Dic43—21no—
164C2×C4×Dic43C2311yescharacteristic
165C4⋊(C43⋊C8)C2314yes—
166Dic43⋊C8C2314yes—
167Dic43⋊C8C2314yes—
168#13063250C2314yes—
169#13063250C2314yes—
170#13063249C2314yes—
171#13063248C2314yes—
172#13063248C2314yes—
173#13063246C2314yes—
174C22×Q8×C43C2311yescharacteristic
175C22×Q8×C43C2311yescharacteristic
176C22×D4×C43C2311yescharacteristic
177C2×Q16×C43—24no—
178C2×Q16×C43C2314yes—
179C2×SD16×C43—24no—
180C2×SD16×C43C2314yes—
181C22×C8×C43C2311yescharacteristic
182C22×C8×C43C2311yescharacteristic
183#124×C43—22no—
184#124×C43C2314yes—
185C4×Q8×C43—22no—
186C4×Q8×C43C2314yes—
187C2×C4⋊C4×C43—21no—
188C2×C4⋊C4×C43C2311yescharacteristic
189C2×C22⋊C4×C43—21no—
190C2×C22⋊C4×C43—21no—
191C2×C42×C43—21no—
192C2×C42×C43C2311yescharacteristic
193C4⋊C8×C43C2314yes—
194#103×C43C2314yes—
195#102×C43C2314yes—
196C24×C43—21no—
197C23×D43—21no—
198C23×D43C2×D411yescharacteristic
199C2×Q8×C43—21no—
200C2×Q8×C43—21no—
201C2×Q8×C43—22no—
202C2×Q8×C43—22no—
203C2×Q8×C43—22no—
204C2×Q8×C43C2×D414yes—
205C2×Q8×C43C2412yes—
206C2×Q8×C43C2412yes—
207C2×D4×C43—21no—
208C2×D4×C43—22no—
209C2×D4×C43—22no—
210C2×D4×C43C2412yes—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—24no—
218C2×C22⋊D43—44no—
219C22×Dic43—24no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—44no—
224C22×Dic43C2×D411yescharacteristic
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227#10621902—216no—
228#10621902—28no—
229#10621902C2×D4116yes—
230Q8×D43—28no—
231Q8×D43—28no—
232Q8×D43—48no—
233#10621900—28no—
234#10621900—28no—
235#10621900—48no—
236C2×D172—21no—
237C2×D172—22no—
238C2×D172—28no—
239C2×D172—24no—
240C2×D172C2×D414yes—
241C2×D172C2412yes—
242C2×C4×D43—28no—
243C2×C4×D43—24no—
244C2×C4×D43—24no—
245C2×C4×D43—24no—
246C2×C4×D43—24no—
247C2×C4×D43—24no—
248C2×C4×D43—44no—
249C2×C4×D43—82no—
250C2×C4×D43—82no—
251C2×C4×D43—82no—
252C2×C4×D43C2×D414yes—
253C2×C4×D43C2×D412yes—
254C2×C4×D43#4114yes—
255C2×C4×D43C2412yes—
256C2×Dic86—22no—
257C2×Dic86—22no—
258C2×Dic86—22no—
259C2×Dic86—22no—
260C2×Dic86—21no—
261C2×Dic86—21no—
262C2×Dic86—24no—
263C2×Dic86—44no—
264C2×Dic86C2412yes—
265C2×Dic86C2412yes—
266Q16×C43—28no—
267SD16×C43—28no—
268C2×C8×C43—22no—
269C2×C8×C43—22no—
270C2×C8×C43C2412yes—
271C2×C8×C43C2412yes—
272C4⋊C4×C43—24no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43C2412yes—
275C22⋊C4×C43—24no—
276C22⋊C4×C43—24no—
277C42×C43—24no—
278C42×C43C2×D412yes—
279C42×C43C2412yes—
280C22⋊Dic43—24no—
281C22⋊Dic43—24no—
282#10621885—28no—
283#10621885—28no—
284#10621884—28no—
285#10621882—28no—
286(C2×D43)⋊C4—24no—
287(C2×D43)⋊C4—24no—
288(C2×D43)⋊C4C2×D414yes—
289(C2×D43)⋊C4C2×D414yes—
290C4⋊Dic43—21no—
291C4⋊Dic43—24no—
292C4⋊Dic43—24no—
293C4⋊Dic43—24no—
294C4⋊Dic43C2412yes—
295Dic43⋊C4—24no—
296Dic43⋊C4—24no—
297Dic43⋊C4—24no—
298Dic43⋊C4C2×D414yes—
299Dic43⋊C4C2×D414yes—
300C4×Dic43—24no—
301C4×Dic43C2×D412yes—
302C4×Dic43C2412yes—
303C2×C43⋊C8—22no—
304C2×C43⋊C8—22no—
305C2×C43⋊C8C2412yes—
306C2×C43⋊C8C2412yes—
307#10621873—28no—
308#10621873—28no—
309#10621872—28no—
310C8×D43—28no—
311C23×C43—22no—
312C23×C43—42no—
313C23×C43—42no—
314C23×C43—42no—
315C23×C43C22×D411yescharacteristic
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—24no—
319C22×D43—22no—
320C22×D43—42no—
321C22×D43—42no—
322C22×D43#12114yes—
323C22×D43C22×D412yes—
324Q8×C43—24no—
325Q8×C43—22no—
326Q8×C43—22no—
327Q8×C43—22no—
328Q8×C43—42no—
329Q8×C43C22×D414yes—
330D4×C43—22no—
331D4×C43—22no—
332D4×C43—42no—
333C2×C4×C43—24no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—42no—
340C2×C4×C43—42no—
341C2×C4×C43C22×D412yes—
342C2×C4×C43C22×D412yes—
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D412yes—
345C2×C4×C43C2×#4112yes—
346C2×C4×C43C2511yescharacteristic
347C22⋊D43—48no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—42no—
354C2×Dic43—42no—
355C2×Dic43—42no—
356C2×Dic43—48no—
357C2×Dic43#12114yes—
358C2×Dic43C22×D412yes—
359C2×Dic43C22×D412yes—
360C2×Dic43C22×D412yes—
361D172—216no—
362D172—24no—
363D172—22no—
364D172C22×D414yes—
365C4×D43—216no—
366C4×D43—48no—
367C4×D43—84no—
368C4×D43—84no—
369C4×D43—84no—
370C4×D43#12118yes—
371C4×D43C22×D414yes—
372C4×D43C2×#4114yes—
373Dic86—22no—
374Dic86—22no—
375Dic86—22no—
376Dic86—22no—
377Dic86—42no—
378Dic86—42no—
379Dic86—48no—
380C8×C43—22no—
381C8×C43—22no—
382C43⋊C8—22no—
383C43⋊C8—22no—
384C2×#3046—431nomaximal, Sylow
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—84no—
389C22×C43C2×#12112yes—
390C22×C43#57712yes—
391C22×C43#57812yes—
392C22×C43C23×D411yescharacteristic
393C2×D43—28no—
394C2×D43—22no—
395C2×D43—22no—
396C2×D43—24no—
397C2×D43—48no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43C2×#12114yes—
401C4×C43—24no—
402C4×C43—22no—
403C4×C43—22no—
404C4×C43—42no—
405C4×C43—42no—
406C4×C43C2×#12112yes—
407C4×C43C23×D411yescharacteristic
408C4×C43C22×#4111yescharacteristic
409Dic43—22no—
410Dic43—22no—
411Dic43—42no—
412Dic43—42no—
413Dic43—42no—
414Dic43C2×#12114yes—
415C22×#137—431no—
416C22×#135—431no—
417C2×#536—431no—
418C2×#520—431no—
419#3046—4316no—
420C2×#464—431no—
421C2×#464D4311yescharacteristic, complemented
422C2×#462—431no—
423C2×#462—431no—
424C2×#463—431no—
425C2×#463—431no—
426C2×#461—431no—
427C2×#461—431no—
428C2×#424—431no—
429C2×#417—431no—
430C22×#103—431no—
431C2×C43—82no—
432C2×C43#304614yescomplemented
433C2×C43C22×#12111yescharacteristic
434C2×C43C2×#57711yescharacteristic
435C2×C43C2×#57811yescharacteristic
436D43—24no—
437D43—44no—
438C22×#41—431no—
439C22×#41—431no—
440C23×Q8—431no—
441C2×#137—438no—
442C2×#137—868no—
443C2×#135—438no—
444C2×#135—868no—
445C22×Q16—431no—
446C22×Q16—431no—
447C22×Q16C2×D4311yescharacteristic
448C22×SD16—431no—
449C22×SD16—431no—
450C22×SD16—431no—
451C22×SD16C2×D4311yescharacteristic
452C22×D8—431no—
453C22×M16—431no—
454C23×C8—431no—
455#536—438no—
456#536—864no—
457C2×C4⋊Q8—431no—
458C2×C4⋊Q8—431no—
459C2×#124—431no—
460C2×#124C2×D4311yescharacteristic
461C2×#123—861no—
462C2×#123—861no—
463C2×C22⋊Q8—861no—
464C2×C22⋊Q8—861no—
465#520—438no—
466#520—864no—
467C2×C4×Q8—431no—
468C2×C4×Q8C2×D4311yescharacteristic
469C2×C4×D4—431no—
470C2×C4×D4—431no—
471C2×C4×D4—861no—
472C2×C4×D4—861no—
473C2×#117—431no—
474C2×#117—861no—
475C22×C4⋊C4—431no—
476C22×C4⋊C4—861no—
477#464—438no—
478#464C2×D4318yescomplemented
479#463—438no—
480#463—438no—
481#462—438no—
482#462—438no—
483#461—438no—
484#461—438no—
485#424—438no—
486C2×C4⋊C8—431no—
487C2×C4⋊C8—431no—
488C2×C4⋊C8—431no—
489C2×C4⋊C8C2×D4311yescharacteristic
490#417—438no—
491C2×#103—431no—
492C2×#103—431no—
493C2×#103—431no—
494C2×#103—431no—
495C2×#103—431no—
496C2×#103—438no—
497C2×#103C2×D4311yescharacteristic
498C2×#102—431no—
499C2×#102C2×D4311yescharacteristic
500C43C2×#304611yescharacteristic, complemented, Sylow
501C2×#41—438no—
502C2×#41—434no—
503C2×#41—434no—
504C2×#41—862no—
505C2×#41—862no—
506C2×#41—864no—
507C2×#41—864no—
508C2×#41—864no—
509C22×Q8—434no—
510C22×Q8—431no—
511C22×Q8—431no—
512C22×Q8—861no—
513C22×Q8—862no—
514C22×Q8—864no—
515C22×Q8—864no—
516C22×Q8C22×D4311yescharacteristic
517C22×Q8C22×D4311yescharacteristic
518C22×D4—431no—
519C22×D4—861no—
520C22×D4—861no—
521C22×D4C22×D4311yescharacteristic
522C23×C4—431no—
523C23×C4—861no—
524C23×C4—861no—
525C23×C4—861no—
526C23×C4—861no—
527C23×C4—861no—
528C23×C4—861no—
529#137—8632no—
530#135—8632no—
531C2×Q16—24no—
532C2×Q16—434no—
533C2×Q16—434no—
534C2×Q16—864no—
535C2×Q16—864no—
536C2×Q16C22×D4314yes—
537C2×SD16—24no—
538C2×SD16—434no—
539C2×SD16—434no—
540C2×SD16—434no—
541C2×SD16—864no—
542C2×SD16—864no—
543C2×SD16—864no—
544C2×SD16C22×D4314yes—
545C2×D8—434no—
546C2×D8—864no—
547C2×M16—434no—
548C2×M16—864no—
549C22×C8—431no—
550C22×C8—431no—
551C22×C8—434no—
552C22×C8—864no—
553C22×C8C22×D4311yescharacteristic
554C22×C8C22×D4311yescharacteristic
555C4⋊Q8—434no—
556C4⋊Q8—434no—
557C4⋊Q8—862no—
558C4⋊Q8—862no—
559#124—22no—
560#124—434no—
561#124—862no—
562#124C22×D4314yes—
563#123—868no—
564#123—868no—
565C22⋊Q8—868no—
566C22⋊Q8—868no—
567C4×Q8—22no—
568C4×Q8—434no—
569C4×Q8—862no—
570C4×Q8C22×D4314yes—
571C4×D4—434no—
572C4×D4—434no—
573C4×D4—868no—
574C4×D4—862no—
575C4×D4—868no—
576C4×D4—862no—
577#117—434no—
578#117—434no—
579#117—868no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—431no—
582C2×C4⋊C4—431no—
583C2×C4⋊C4—431no—
584C2×C4⋊C4—434no—
585C2×C4⋊C4—868no—
586C2×C4⋊C4—862no—
587C2×C4⋊C4—861no—
588C2×C4⋊C4—861no—
589C2×C4⋊C4—861no—
590C2×C4⋊C4—861no—
591C2×C4⋊C4—861no—
592C2×C4⋊C4—861no—
593C2×C4⋊C4C22×D4311yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—431no—
597C2×C22⋊C4—431no—
598C2×C22⋊C4—861no—
599C2×C22⋊C4—861no—
600C2×C22⋊C4—861no—
601C2×C22⋊C4—861no—
602C2×C42—21no—
603C2×C42—431no—
604C2×C42—861no—
605C2×C42C22×D4311yescharacteristic
606C4⋊C8—434no—
607C4⋊C8—434no—
608C4⋊C8—434no—
609C4⋊C8C22×D4314yes—
610#103—434no—
611#103—434no—
612#103—434no—
613#103—434no—
614#103—434no—
615#103C22×D4314yes—
616#102—434no—
617#102C22×D4314yes—
618C24—21no—
619C24—431no—
620C24—861no—
621#41—4316no—
622#41—8616no—
623#41—868no—
624#41—868no—
625#41—868no—
626#41—1728no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—432no—
633C2×Q8—432no—
634C2×Q8—864no—
635C2×Q8—868no—
636C2×Q8—868no—
637C2×Q8—861no—
638C2×Q8—861no—
639C2×Q8—862no—
640C2×Q8—862no—
641C2×Q8—862no—
642C2×Q8—862no—
643C2×Q8—1724no—
644C2×Q8—1728no—
645C2×Q8D4×D4314yes—
646C2×Q8C23×D4312yes—
647C2×Q8C23×D4312yes—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—22no—
651C2×D4—434no—
652C2×D4—432no—
653C2×D4—864no—
654C2×D4—868no—
655C2×D4—864no—
656C2×D4—861no—
657C2×D4—862no—
658C2×D4—1724no—
659C2×D4C23×D4312yes—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—431no—
664C22×C4—432no—
665C22×C4—434no—
666C22×C4—434no—
667C22×C4—432no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—864no—
671C22×C4—868no—
672C22×C4—864no—
673C22×C4—864no—
674C22×C4—864no—
675C22×C4—864no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—864no—
680C22×C4—3442no—
681C22×C4—3442no—
682C22×C4—3442no—
683C22×C4—1724no—
684C22×C4—1724no—
685C22×C4D4×D4311yescharacteristic
686C22×C4D4×D4311yescharacteristic
687C22×C4C23×D4311yescharacteristic
688Q16—28no—
689Q16—868no—
690Q16—868no—
691SD16—28no—
692SD16—868no—
693SD16—868no—
694SD16—868no—
695D8—868no—
696M16—868no—
697C2×C8—22no—
698C2×C8—22no—
699C2×C8—432no—
700C2×C8—432no—
701C2×C8—868no—
702C2×C8—862no—
703C2×C8—862no—
704C2×C8C23×D4312yes—
705C2×C8C23×D4312yes—
706C4⋊C4—24no—
707C4⋊C4—21no—
708C4⋊C4—434no—
709C4⋊C4—434no—
710C4⋊C4—432no—
711C4⋊C4—864no—
712C4⋊C4—864no—
713C4⋊C4—864no—
714C4⋊C4—864no—
715C4⋊C4—861no—
716C4⋊C4—864no—
717C4⋊C4—864no—
718C4⋊C4C23×D4312yes—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—434no—
722C22⋊C4—434no—
723C22⋊C4—864no—
724C22⋊C4—864no—
725C22⋊C4—864no—
726C22⋊C4—864no—
727C42—24no—
728C42—432no—
729C42—432no—
730C42—864no—
731C42D4×D4312yes—
732C42C23×D4312yes—
733C23—22no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—434no—
738C23—432no—
739C23—862no—
740C23—862no—
741C23—864no—
742C23—862no—
743C23—1722no—
744C23—1722no—
745C23C2×D4×D4311yescharacteristic
746Q8—24no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—42no—
751Q8—862no—
752Q8—862no—
753Q8—862no—
754Q8—862no—
755Q8—1728no—
756Q8—1722no—
757Q8—1722no—
758Q8C2×D4×D4314yes—
759D4—22no—
760D4—22no—
761D4—42no—
762D4—434no—
763D4—8616no—
764D4—864no—
765D4—862no—
766D4—1728no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—434no—
776C2×C4—432no—
777C2×C4—438no—
778C2×C4—434no—
779C2×C4—434no—
780C2×C4—432no—
781C2×C4—432no—
782C2×C4—8616no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—862no—
787C2×C4—862no—
788C2×C4—3444no—
789C2×C4—3444no—
790C2×C4—3444no—
791C2×C4—1728no—
792C2×C4—1728no—
793C2×C4—1722no—
794C2×C4—1722no—
795C2×C4—1722no—
796C2×C4C2×D4×D4312yes—
797C2×C4C2×D4×D4312yes—
798C2×C4C2×D4×D4311yescharacteristic
799C2×C4C2×D4×D4312yes—
800C2×C4#41×D4312yes—
801C2×C4C24×D4311yescharacteristic
802C8—22no—
803C8—22no—
804C8—862no—
805C8—862no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—84no—
810C22—434no—
811C22—862no—
812C22—862no—
813C22—868no—
814C22—864no—
815C22—1722no—
816C22—1722no—
817C22—1728no—
818C22#121×D4312yes—
819C22#1458370612yes—
820C22#1458371512yes—
821C22C22×D4×D4311yescharacteristic
822C4—24no—
823C4—22no—
824C4—22no—
825C4—42no—
826C4—42no—
827C4—434no—
828C4—862no—
829C4—862no—
830C4—1722no—
831C4—1722no—
832C4—1722no—
833C4#121×D4312yes—
834C4C22×D4×D4311yescharacteristic
835C4C2×#41×D4311yescharacteristic
836C2—82no—
837C2—864no—
838C2—1724no—
839C2#1914414814yesdirect product factor
840C2C2×#121×D4311yescharacteristic
841C2C2×#1458370611yescharacteristic
842C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC22×#13063346C2
hypercenterC2×#464D43
hypocenterC43C2×#3046
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#13063357C2semidirect
3. C2×#14583469C2semidirect
4. C2×#14583381C2semidirect
5. #19144148C2direct (N × H)
6. C2×#14583119C2semidirect
7. C2×#14583109C2semidirect
8. C2×#14583107C2semidirect
9. C2×#14583113C2semidirect
10. C2×#14583111C2semidirect
11. C2×#14583105C2semidirect
12. C2×#14583103C2semidirect
13. C2×#14582924C2semidirect
14. C2×#14582897C2semidirect
15. C2×#103×D43C2semidirect
16. C2×C43×#464C2semidirect
21. C2×#13063357C22semidirect
33. #14583469C22semidirect
42. #14583381C22semidirect
52. #14583119C22semidirect
53. #14583113C22semidirect
54. #14583111C22semidirect
55. #14583109C22semidirect
56. #14583107C22semidirect
57. #14583105C22semidirect
58. #14583103C22semidirect
59. #14582924C22semidirect
63. #14582897C22semidirect
69. #103×D43C22semidirect
75. C43×#464C22semidirect
421. C2×#464D43semidirect
432. C2×C43#3046semidirect
478. #464C2×D43semidirect
500. C43C2×#3046semidirect
839. C2#19144148direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633572
C22×#130633462
C2×#145834692
C2×#145833812
#191441482
C2×#145831192
C2×#145831092
C2×#145831072
C2×#145831132
C2×#145831112
C2×#145831052
C2×#145831032
C2×#145829242
C2×#145828972
C2×#103×D432
C2×C43×#4642
C2×#304643