Finite Group Databasebeta

← C2×#19146259 #25971763

Subgroups — C2×#19146259 #25971763

Order 11008.

2794 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063356C211yesmaximal, characteristic, complemented
2C22×#13063354C211yesmaximal, characteristic, complemented
3C2×#14583567C211yesmaximal, characteristic
4C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
5#19146259C2116yesmaximal, direct product factor
6C2×#14583270C211yesmaximal, characteristic, complemented
7C2×#14583148C211yesmaximal, characteristic, complemented
8C2×#14583143C211yesmaximal, characteristic, complemented
9C2×#14583108C211yesmaximal, characteristic, complemented
10C2×#14583097C211yesmaximal, characteristic, complemented
11C2×#14583063C211yesmaximal, characteristic, complemented
12C2×#14583058C211yesmaximal, characteristic, complemented
13C2×#14583039C211yesmaximal, characteristic, complemented
14C2×#14582991C211yesmaximal, characteristic, complemented
15C2×#14582974C211yesmaximal, characteristic, complemented
16C2×C43×#448C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×Q8×D43C2211yescharacteristic
20C2×#13063356—28no—
21C2×#13063356C2218yescomplemented
22C2×#13063354—28no—
23C2×#13063354C2218yescomplemented
24C22×Dic172C2211yescharacteristic
25C22×#10621885C2211yescharacteristic
26C22×#10621885C2211yescharacteristic
27C22×#10621873C2211yescharacteristic
28C22×#10621883C2211yescharacteristic
29C22×#10621884C2211yescharacteristic
30C22×#10621884C2211yescharacteristic
31C22×#10621877C2211yescharacteristic
32C22×#10621872C2211yescharacteristic
33#14583567—24no—
34#14583567C2218yes—
35Q8×C22⋊D43—24no—
36Q8×C22⋊D43C2218yescomplemented
37C2×#13063323—21no—
38C2×#13063323C2211yescharacteristic
39C2×#13063321—21no—
40C2×#13063321C2211yescharacteristic
41C2×#13063304—21no—
42C2×#13063304C2211yescharacteristic
43C2×#13063301—21no—
44C2×#13063301C2211yescharacteristic
45C2×#13063300C2211yescharacteristic
46C2×#13063298—21no—
47C2×#13063297—21no—
48C2×Q8×Dic43C2211yescharacteristic
49C2×#13063290C2211yescharacteristic
50C2×C4×C22⋊D43—21no—
51C2×C4×C22⋊D43C2211yescharacteristic
52C2×(C22⋊D43)⋊C4—21no—
53#14583270C2218yescomplemented
54#14583148C2218yescomplemented
55#14583143C2218yescomplemented
56#14583108C2218yescomplemented
57#14583097C2218yescomplemented
58#14583063C2218yescomplemented
59#14583058C2218yescomplemented
60#14583039C2218yescomplemented
61#14582991C2218yescomplemented
62#14582974C2218yescomplemented
63C2×#13063258C2211yescharacteristic
64C2×Dic43⋊C8C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063248C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063246C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic
70C2×C8×Dic43C2211yescharacteristic
71C23×Q8×C43C2211yescharacteristic
72C22×SD16×C43C2211yescharacteristic
73C22×SD16×C43C2211yescharacteristic
74C2×#121×C43C2211yescharacteristic
75C43×#448C2218yescomplemented
76C2×#103×C43C2211yescharacteristic
77C2×#103×C43C2211yescharacteristic
78C2×C22⋊C8×C43C2211yescharacteristic
79C2×#10621898—22no—
80C2×#10621898—24no—
81C2×#10621898—42no—
82C2×#10621898C2314yes—
83C2×#10621900—22no—
84C2×#10621900—24no—
85C2×#10621900—42no—
86C2×#10621900C2314yes—
87C22×Dic86—21no—
88C22×Dic86C2311yescharacteristic
89C22×Dic86C2311yescharacteristic
90C2×Q8×D43—22no—
91C2×Q8×D43—24no—
92C2×Q8×D43—42no—
93C2×Q8×D43C2314yes—
94C22×D172—21no—
95C22×D172C2311yescharacteristic
96C22×C22⋊D43—21no—
97C22×C22⋊D43—21no—
98C22×C22⋊D43—21no—
99C22×C22⋊D43—21no—
100C22×C22⋊D43D411yescharacteristic
101C23×Dic43—21no—
102C22×C4×D43—21no—
103C22×C4×D43—21no—
104C22×C4×D43C2311yescharacteristic
105#13063356—232no—
106#13063354—232no—
107C2×Dic172—24no—
108C2×Dic172C2314yes—
109C2×#10621885—24no—
110C2×#10621885D418yescomplemented
111C2×#10621885C2314yes—
112C2×#10621885C2314yes—
113C2×#10621873—42no—
114C2×#10621873C2314yes—
115C2×#10621883—24no—
116C2×#10621883C2314yes—
117C2×#10621884—24no—
118C2×#10621884—24no—
119C2×#10621884C2314yes—
120C2×#10621884C2314yes—
121C2×#10621877—24no—
122C2×#10621877C2314yes—
123C2×#10621872—24no—
124C2×#10621872C2314yes—
125C22×C43⋊C8C2311yescharacteristic
126C22×C43⋊C8C2311yescharacteristic
127#13063323—28no—
128#13063323—22no—
129#13063323C2314yes—
130#13063321—28no—
131#13063321—22no—
132#13063321C2314yes—
133#13063304—22no—
134#13063304—28no—
135#13063304C2314yes—
136#13063301—22no—
137#13063301—28no—
138#13063301C2314yes—
139#13063300—22no—
140#13063300C2314yes—
141#13063298—28no—
142#13063297—28no—
143Q8×Dic43—22no—
144Q8×Dic43C2314yes—
145#13063290—22no—
146#13063290C2314yes—
147C4×C22⋊D43—28no—
148C4×C22⋊D43D414yes—
149C4×C22⋊D43C2314yes—
150(C22⋊D43)⋊C4—28no—
151C2×C4⋊Dic43—21no—
152C2×C4⋊Dic43C2311yescharacteristic
153C2×Dic43⋊C4—21no—
154C2×Dic43⋊C4—21no—
155C2×Dic43⋊C4—21no—
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4D411yescharacteristic
159C2×C22⋊Dic43—21no—
160C2×C22⋊Dic43D411yescharacteristic
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4D411yescharacteristic
164C2×C4×Dic43—21no—
165C2×C4×Dic43—21no—
166C2×C4×Dic43C2311yescharacteristic
167#13063258C2314yes—
168Dic43⋊C8C2314yes—
169#13063250C2314yes—
170#13063248C2314yes—
171#13063247C2314yes—
172#13063246C2314yes—
173(C2×D43)⋊C8C2314yes—
174C8×Dic43C2314yes—
175C22×Q8×C43—22no—
176C22×Q8×C43—21no—
177C22×Q8×C43—24no—
178C22×Q8×C43—42no—
179C22×Q8×C43C2311yescharacteristic
180C22×Q8×C43C2314yes—
181C22×Q8×C43C2311yescharacteristic
182C22×D4×C43—21no—
183C22×D4×C43C2311yescharacteristic
184C23×C4×C43—21no—
185C23×C4×C43C2311yescharacteristic
186C2×SD16×C43—24no—
187C2×SD16×C43—42no—
188C2×SD16×C43C2314yes—
189C2×SD16×C43C2314yes—
190C22×C8×C43C2311yescharacteristic
191C22×C8×C43C2311yescharacteristic
192#121×C43—22no—
193#121×C43C2314yes—
194C2×C4⋊C4×C43C2311yescharacteristic
195C2×C22⋊C4×C43—21no—
196#103×C43C2314yes—
197#103×C43C2314yes—
198C22⋊C8×C43C2314yes—
199C24×C43—21no—
200C24×C43C2×D411yescharacteristic
201C23×D43—21no—
202C23×D43C2×D411yescharacteristic
203C2×Q8×C43—21no—
204C2×Q8×C43—24no—
205C2×Q8×C43—21no—
206C2×Q8×C43—22no—
207C2×Q8×C43—28no—
208C2×Q8×C43—22no—
209C2×Q8×C43—22no—
210C2×Q8×C43—44no—
211C2×Q8×C43—44no—
212C2×Q8×C43—48no—
213C2×Q8×C43C2×D414yes—
214C2×Q8×C43C2412yes—
215C2×Q8×C43C2412yes—
216C2×D4×C43—21no—
217C2×D4×C43—24no—
218C2×D4×C43—22no—
219C2×D4×C43—22no—
220C2×D4×C43—82no—
221C2×D4×C43C2412yes—
222C22×C4×C43—22no—
223C22×C4×C43—22no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—24no—
228C22×C4×C43—44no—
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D412yes—
231C22×C4×C43C2412yes—
232C22×C4×C43C2411yescharacteristic
233C2×C22⋊D43—24no—
234C2×C22⋊D43—24no—
235C2×C22⋊D43—24no—
236C2×C22⋊D43—24no—
237C2×C22⋊D43—24no—
238C2×C22⋊D43—44no—
239C2×C22⋊D43—44no—
240C2×C22⋊D43—44no—
241C2×C22⋊D43—82no—
242C2×C22⋊D43C2×D414yes—
243C22×Dic43—24no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—44no—
248C22×Dic43C2×D411yescharacteristic
249C22×Dic43C2×D411yescharacteristic
250C22×Dic43C2×D411yescharacteristic
251Q8×D43—28no—
252Q8×D43—44no—
253Q8×D43—48no—
254#10621900—28no—
255#10621900—44no—
256#10621900—48no—
257#10621898—28no—
258#10621898—44no—
259#10621898—48no—
260C2×D172—21no—
261C2×D172—24no—
262C2×D172—22no—
263C2×D172—22no—
264C2×D172—82no—
265C2×D172C2412yes—
266C2×C4×D43—22no—
267C2×C4×D43—22no—
268C2×C4×D43—24no—
269C2×C4×D43—24no—
270C2×C4×D43—44no—
271C2×C4×D43—44no—
272C2×C4×D43C2×D412yes—
273C2×C4×D43C2412yes—
274C2×Dic86—21no—
275C2×Dic86—22no—
276C2×Dic86—22no—
277C2×Dic86—22no—
278C2×Dic86—21no—
279C2×Dic86—24no—
280C2×Dic86—44no—
281C2×Dic86C2×D414yes—
282C2×Dic86C2412yes—
283C2×Dic86C2412yes—
284SD16×C43—28no—
285SD16×C43—44no—
286C2×C8×C43—22no—
287C2×C8×C43—22no—
288C2×C8×C43C2412yes—
289C2×C8×C43C2412yes—
290C4⋊C4×C43—21no—
291C4⋊C4×C43C2412yes—
292C22⋊C4×C43—24no—
293C22⋊Dic43—24no—
294C22⋊Dic43C2×D414yes—
295#10621885—28no—
296#10621885C2×D4116yescomplemented
297#10621884—28no—
298#10621884—28no—
299#10621883—28no—
300(C2×D43)⋊C4—24no—
301(C2×D43)⋊C4—24no—
302(C2×D43)⋊C4C2×D414yes—
303C4⋊Dic43—21no—
304C4⋊Dic43—24no—
305C4⋊Dic43C2412yes—
306Dic43⋊C4—24no—
307Dic43⋊C4—24no—
308Dic43⋊C4—24no—
309Dic43⋊C4—24no—
310Dic43⋊C4—24no—
311Dic43⋊C4C2×D414yes—
312C4×Dic43—24no—
313C4×Dic43—24no—
314C4×Dic43C2×D412yes—
315C4×Dic43C2412yes—
316#10621877—28no—
317C2×C43⋊C8—22no—
318C2×C43⋊C8C2×D414yes—
319C2×C43⋊C8C2412yes—
320C2×C43⋊C8C2412yes—
321Dic172—28no—
322#10621873—44no—
323#10621872—28no—
324C23×C43—22no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—42no—
329C23×C43—42no—
330C23×C43—42no—
331C23×C43C22×D412yes—
332C23×C43C22×D411yescharacteristic
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—42no—
338C22×D43—42no—
339C22×D43—42no—
340C22×D43C22×D412yes—
341Q8×C43—24no—
342Q8×C43—22no—
343Q8×C43—22no—
344Q8×C43—22no—
345Q8×C43—48no—
346Q8×C43—42no—
347Q8×C43C22×D414yes—
348D4×C43—22no—
349D4×C43—22no—
350D4×C43—42no—
351D4×C43—84no—
352C2×C4×C43—24no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—24no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—48no—
361C2×C4×C43—42no—
362C2×C4×C43—42no—
363C2×C4×C43C22×D412yes—
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C22×D412yes—
366C2×C4×C43H(5,𝔽2)12yes—
367C2×C4×C43C2511yescharacteristic
368C22⋊D43—28no—
369C22⋊D43—48no—
370C22⋊D43—48no—
371C22⋊D43—48no—
372C22⋊D43—84no—
373C2×Dic43—24no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—48no—
380C2×Dic43—42no—
381C2×Dic43—42no—
382C2×Dic43#13714yescomplemented
383C2×Dic43C22×D412yes—
384C2×Dic43C22×D412yes—
385C2×Dic43C22×D412yes—
386D172—22no—
387D172—22no—
388D172—42no—
389D172—84no—
390C4×D43—24no—
391C4×D43—22no—
392C4×D43—22no—
393C4×D43—48no—
394C4×D43—48no—
395Dic86—24no—
396Dic86—22no—
397Dic86—22no—
398Dic86—22no—
399Dic86—48no—
400Dic86—42no—
401Dic86C22×D414yes—
402C8×C43—22no—
403C8×C43—22no—
404C43⋊C8—22no—
405C43⋊C8C22×D414yes—
406C2×#3278—431nomaximal, Sylow
407C22×C43—22no—
408C22×C43—22no—
409C22×C43—22no—
410C22×C43—44no—
411C22×C43—42no—
412C22×C43—42no—
413C22×C43—42no—
414C22×C43—84no—
415C22×C43D4212yes—
416C22×C43C2×#13712yes—
417C22×C43#57712yes—
418C22×C43C23×D411yescharacteristic
419C2×D43—22no—
420C2×D43—22no—
421C2×D43—22no—
422C2×D43—44no—
423C2×D43—42no—
424C2×D43—42no—
425C2×D43—42no—
426C2×D43—84no—
427C4×C43—24no—
428C4×C43—22no—
429C4×C43—42no—
430C4×C43—42no—
431C4×C43D4212yes—
432C4×C43C23×D411yescharacteristic
433C4×C43C2×H(5,𝔽2)11yescharacteristic
434Dic43—24no—
435Dic43—22no—
436Dic43—22no—
437Dic43—42no—
438Dic43—42no—
439Dic43C2×#13714yescomplemented
440C22×#137—431no—
441C22×#137—431no—
442C2×#550—431no—
443C2×D4×Q8—431no—
444#3278—4316no—
445C2×#492—431no—
446C2×#468—431no—
447C2×#468—431no—
448C2×#462—431no—
449C2×#460—431no—
450C2×#452—431no—
451C2×#452—431no—
452C2×#448—431no—
453C2×#448D4311yescharacteristic, complemented
454C2×C4×Q16—431no—
455C2×#436—431no—
456C2×C43—42no—
457C2×C43—82no—
458C2×C43#327814yescomplemented
459C2×C43C2×D4211yescharacteristic
460C2×C43C22×#13711yescharacteristic
461C2×C43C2×#57711yescharacteristic
462D43—42no—
463D43—82no—
464C22×#41—431no—
465C22×#41—431no—
466C23×Q8—431no—
467C23×Q8C2×D4311yescharacteristic
468C2×#137—438no—
469C2×#137—438no—
470C2×#137—868no—
471C2×#137—868no—
472C22×Q16—431no—
473C22×Q16—431no—
474C22×Q16—431no—
475C22×SD16—431no—
476C22×SD16—431no—
477C22×SD16—431no—
478C22×SD16—431no—
479C22×SD16C2×D4311yescharacteristic
480C22×SD16C2×D4311yescharacteristic
481C22×M16—431no—
482C22×M16—431no—
483#550—438no—
484#550—864no—
485D4×Q8—438no—
486D4×Q8—864no—
487C2×C4⋊Q8—431no—
488C2×C4⋊Q8—861no—
489C2×#127—431no—
490C2×#127—861no—
491C2×C22⋊Q8—431no—
492C2×C22⋊Q8—431no—
493C2×C22⋊Q8—861no—
494C2×C22⋊Q8—861no—
495C2×#121—431no—
496C2×#121—861no—
497C2×#121—861no—
498C2×#121C2×D4311yescharacteristic
499C2×C4×Q8—431no—
500C2×C4×Q8—431no—
501C2×C4×D4—431no—
502C2×C4×D4—861no—
503C2×C4×D4—861no—
504#492—438no—
505#468—438no—
506#468—438no—
507#462—438no—
508#460—438no—
509#452—438no—
510#452—438no—
511#448—438no—
512#448C2×D4318yescomplemented
513C4×Q16—438no—
514#436—438no—
515C2×#107—431no—
516C2×C4⋊C8—431no—
517C2×#103—431no—
518C2×#103—431no—
519C2×#103C2×D4311yescharacteristic
520C2×#103C2×D4311yescharacteristic
521C2×#102—431no—
522C2×#102—431no—
523C2×C22⋊C8—431no—
524C2×C22⋊C8C2×D4311yescharacteristic
525C2×C4×C8—431no—
526C43C2×#327811yescharacteristic, complemented, Sylow
527C2×#41—434no—
528C2×#41—434no—
529C2×#41—864no—
530C2×#41—862no—
531C2×#41—862no—
532C2×#41—864no—
533C2×#41—1722no—
534C2×#41—1722no—
535C22×Q8—21no—
536C22×Q8—22no—
537C22×Q8—24no—
538C22×Q8—42no—
539C22×Q8—434no—
540C22×Q8—431no—
541C22×Q8—431no—
542C22×Q8—861no—
543C22×Q8—862no—
544C22×Q8—864no—
545C22×Q8—1722no—
546C22×Q8C22×D4311yescharacteristic
547C22×Q8C22×D4314yes—
548C22×Q8C22×D4311yescharacteristic
549C22×D4—21no—
550C22×D4—431no—
551C22×D4—431no—
552C22×D4—861no—
553C22×D4—861no—
554C22×D4—861no—
555C22×D4—861no—
556C22×D4—861no—
557C22×D4C22×D4311yescharacteristic
558C23×C4—21no—
559C23×C4—431no—
560C23×C4—861no—
561C23×C4—861no—
562C23×C4—861no—
563C23×C4C22×D4311yescharacteristic
564#137—8632no—
565#137—8632no—
566C2×Q16—438no—
567C2×Q16—434no—
568C2×Q16—434no—
569C2×Q16—434no—
570C2×Q16—864no—
571C2×Q16—864no—
572C2×SD16—24no—
573C2×SD16—42no—
574C2×SD16—434no—
575C2×SD16—434no—
576C2×SD16—434no—
577C2×SD16—434no—
578C2×SD16—864no—
579C2×SD16—864no—
580C2×SD16—864no—
581C2×SD16—1722no—
582C2×SD16C22×D4314yes—
583C2×SD16C22×D4314yes—
584C2×M16—434no—
585C2×M16—434no—
586C2×M16—864no—
587C2×M16—864no—
588C22×C8—431no—
589C22×C8—431no—
590C22×C8C22×D4311yescharacteristic
591C22×C8C22×D4311yescharacteristic
592C4⋊Q8—434no—
593C4⋊Q8—862no—
594C4⋊Q8—868no—
595#127—434no—
596#127—862no—
597#127—868no—
598C22⋊Q8—434no—
599C22⋊Q8—434no—
600C22⋊Q8—868no—
601C22⋊Q8—868no—
602C22⋊Q8—862no—
603C22⋊Q8—862no—
604#121—22no—
605#121—434no—
606#121—868no—
607#121—868no—
608#121—862no—
609#121C22×D4314yes—
610C4×Q8—434no—
611C4×Q8—434no—
612C4×Q8—862no—
613C4×Q8—862no—
614C4×D4—434no—
615C4×D4—434no—
616C4×D4—868no—
617C4×D4—868no—
618C2×C4⋊C4—431no—
619C2×C4⋊C4—431no—
620C2×C4⋊C4—861no—
621C2×C4⋊C4—861no—
622C2×C4⋊C4—861no—
623C2×C4⋊C4—861no—
624C2×C4⋊C4—861no—
625C2×C4⋊C4—861no—
626C2×C4⋊C4C22×D4311yescharacteristic
627C2×C22⋊C4—21no—
628C2×C22⋊C4—431no—
629C2×C22⋊C4—431no—
630C2×C22⋊C4—861no—
631C2×C22⋊C4—861no—
632C2×C22⋊C4—861no—
633C2×C42—431no—
634C2×C42—861no—
635C2×C42—861no—
636#107—434no—
637C4⋊C8—434no—
638#103—434no—
639#103—434no—
640#103C22×D4314yes—
641#103C22×D4314yes—
642#102—434no—
643#102—434no—
644C22⋊C8—434no—
645C22⋊C8C22×D4314yes—
646C4×C8—434no—
647C24—21no—
648C24—431no—
649C24—861no—
650C24D4×D4311yescharacteristic
651#41—868no—
652#41—868no—
653#41—1724no—
654#41—1728no—
655#41—1724no—
656#41—1728no—
657C2×Q8—21no—
658C2×Q8—24no—
659C2×Q8—21no—
660C2×Q8—22no—
661C2×Q8—28no—
662C2×Q8—22no—
663C2×Q8—22no—
664C2×Q8—44no—
665C2×Q8—44no—
666C2×Q8—48no—
667C2×Q8—434no—
668C2×Q8—432no—
669C2×Q8—432no—
670C2×Q8—864no—
671C2×Q8—861no—
672C2×Q8—861no—
673C2×Q8—862no—
674C2×Q8—868no—
675C2×Q8—862no—
676C2×Q8—862no—
677C2×Q8—1724no—
678C2×Q8—1724no—
679C2×Q8—1728no—
680C2×Q8D4×D4314yes—
681C2×Q8C23×D4312yes—
682C2×Q8C23×D4312yes—
683C2×D4—24no—
684C2×D4—22no—
685C2×D4—21no—
686C2×D4—22no—
687C2×D4—82no—
688C2×D4—434no—
689C2×D4—432no—
690C2×D4—864no—
691C2×D4—864no—
692C2×D4—864no—
693C2×D4—864no—
694C2×D4—864no—
695C2×D4—864no—
696C2×D4—862no—
697C2×D4—861no—
698C2×D4—862no—
699C2×D4—3442no—
700C2×D4—3442no—
701C2×D4—1724no—
702C2×D4—1724no—
703C2×D4—1724no—
704C2×D4C23×D4312yes—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—44no—
712C22×C4—431no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—432no—
716C22×C4—432no—
717C22×C4—864no—
718C22×C4—864no—
719C22×C4—861no—
720C22×C4—862no—
721C22×C4—862no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—864no—
725C22×C4—1724no—
726C22×C4—1724no—
727C22×C4—1724no—
728C22×C4D4×D4312yes—
729C22×C4D4×D4311yescharacteristic
730C22×C4C23×D4312yes—
731C22×C4C23×D4311yescharacteristic
732Q16—4316no—
733Q16—868no—
734Q16—868no—
735SD16—28no—
736SD16—44no—
737SD16—868no—
738SD16—868no—
739SD16—868no—
740SD16—1724no—
741M16—868no—
742M16—868no—
743C2×C8—22no—
744C2×C8—22no—
745C2×C8—434no—
746C2×C8—432no—
747C2×C8—432no—
748C2×C8—862no—
749C2×C8C23×D4312yes—
750C2×C8C23×D4312yes—
751C4⋊C4—21no—
752C4⋊C4—434no—
753C4⋊C4—432no—
754C4⋊C4—864no—
755C4⋊C4—864no—
756C4⋊C4—864no—
757C4⋊C4—864no—
758C4⋊C4—864no—
759C4⋊C4—861no—
760C4⋊C4—864no—
761C4⋊C4C23×D4312yes—
762C22⋊C4—24no—
763C22⋊C4—434no—
764C22⋊C4—434no—
765C22⋊C4—864no—
766C22⋊C4—864no—
767C22⋊C4—864no—
768C42—432no—
769C42—432no—
770C42—864no—
771C42—864no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—432no—
780C23—862no—
781C23—862no—
782C23—862no—
783C23—862no—
784C23—1722no—
785C23—1722no—
786C23—1722no—
787C23C2×D4×D4312yes—
788C23C2×D4×D4311yescharacteristic
789Q8—22no—
790Q8—24no—
791Q8—22no—
792Q8—22no—
793Q8—48no—
794Q8—42no—
795Q8—434no—
796Q8—862no—
797Q8—864no—
798Q8—862no—
799Q8—862no—
800Q8—1728no—
801Q8—1722no—
802Q8C2×D4×D4314yes—
803D4—22no—
804D4—22no—
805D4—42no—
806D4—84no—
807D4—868no—
808D4—862no—
809D4—862no—
810D4—3444no—
811D4—3444no—
812D4—1728no—
813D4—1728no—
814D4—1728no—
815D4—1722no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—48no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—434no—
828C2×C4—432no—
829C2×C4—432no—
830C2×C4—432no—
831C2×C4—862no—
832C2×C4—862no—
833C2×C4—862no—
834C2×C4—864no—
835C2×C4—862no—
836C2×C4—862no—
837C2×C4—864no—
838C2×C4—862no—
839C2×C4—862no—
840C2×C4—1728no—
841C2×C4—1728no—
842C2×C4—1728no—
843C2×C4—1722no—
844C2×C4—1722no—
845C2×C4C2×D4×D4312yes—
846C2×C4C2×D4×D4312yes—
847C2×C4C2×D4×D4311yescharacteristic
848C2×C4#1306337012yes—
849C2×C4C24×D4311yescharacteristic
850C8—22no—
851C8—22no—
852C8—434no—
853C8—862no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—44no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—84no—
862C22—862no—
863C22—862no—
864C22—862no—
865C22—3444no—
866C22—1722no—
867C22—1722no—
868C22—1722no—
869C22—1724no—
870C22#1458353112yes—
871C22#137×D4312yes—
872C22#1458370512yes—
873C22C22×D4×D4311yescharacteristic
874C4—22no—
875C4—24no—
876C4—42no—
877C4—42no—
878C4—434no—
879C4—862no—
880C4—862no—
881C4—864no—
882C4—1722no—
883C4—1722no—
884C4#1458353112yes—
885C4C22×D4×D4311yescharacteristic
886C4C2×#1306337011yescharacteristic
887C2—42no—
888C2—82no—
889C2—3442no—
890C2—1722no—
891C2#1914625914yesdirect product factor
892C2C2×#1458353111yescharacteristic
893C2C2×#137×D4311yescharacteristic
894C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#448C2
socleC23×C43C22×D4
prime radicalC2×#14583567C2
hypercenterC2×#448D43
hypocenterC43C2×#3278
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C22×#13063356C2semidirect
2. C22×#13063354C2semidirect
4. C2×Q8×C22⋊D43C2semidirect
5. #19146259C2direct (N × H)
6. C2×#14583270C2semidirect
7. C2×#14583148C2semidirect
8. C2×#14583143C2semidirect
9. C2×#14583108C2semidirect
10. C2×#14583097C2semidirect
11. C2×#14583063C2semidirect
12. C2×#14583058C2semidirect
13. C2×#14583039C2semidirect
14. C2×#14582991C2semidirect
15. C2×#14582974C2semidirect
16. C2×C43×#448C2semidirect
21. C2×#13063356C22semidirect
23. C2×#13063354C22semidirect
36. Q8×C22⋊D43C22semidirect
53. #14583270C22semidirect
54. #14583148C22semidirect
55. #14583143C22semidirect
56. #14583108C22semidirect
57. #14583097C22semidirect
58. #14583063C22semidirect
59. #14583058C22semidirect
60. #14583039C22semidirect
61. #14582991C22semidirect
62. #14582974C22semidirect
75. C43×#448C22semidirect
110. C2×#10621885D4semidirect
296. #10621885C2×D4semidirect
382. C2×Dic43#137semidirect
439. Dic43C2×#137semidirect
453. C2×#448D43semidirect
458. C2×C43#3278semidirect
512. #448C2×D43semidirect
526. C43C2×#3278semidirect
891. C2#19146259direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633562
C22×#130633542
C2×#145835672
C2×Q8×C22⋊D432
#191462592
C2×#145832702
C2×#145831482
C2×#145831432
C2×#145831082
C2×#145830972
C2×#145830632
C2×#145830582
C2×#145830392
C2×#145829912
C2×#145829742
C2×C43×#4482
C2×#327843