Finite Group Databasebeta

← C2×#19143887 #25963028

Subgroups — C2×#19143887 #25963028

Order 11008.

4718 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063372C211yesmaximal, characteristic
2C22×#13063354C211yesmaximal, characteristic, complemented
3C22×Q16×D43C211yesmaximal, characteristic, complemented
4C2×#14583472C211yesmaximal, characteristic, complemented
5#19143887C2116yesmaximal, direct product factor
6C2×#14583062C211yesmaximal, characteristic, complemented
7C2×#14583061C211yesmaximal, characteristic, complemented
8C2×#14583058C211yesmaximal, characteristic, complemented
9C2×#14583057C211yesmaximal, characteristic, complemented
10C2×#14583056C211yesmaximal, characteristic, complemented
11C2×#14583054C211yesmaximal, characteristic, complemented
12C2×#14583053C211yesmaximal, characteristic, complemented
13C2×#14582906C211yesmaximal, characteristic, complemented
14C2×#14582892C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#452C211yesmaximal, characteristic, complemented
17C2×#13063372—24no—
18C2×#13063372—28no—
19C2×#13063372—28no—
20C2×#13063372C2218yes—
21C22×#10621898—21no—
22C22×#10621898C2211yescharacteristic
23C22×#10621900—21no—
24C22×#10621900—21no—
25C22×#10621900C2211yescharacteristic
26C22×#10621900C2211yescharacteristic
27C23×Dic86—21no—
28C23×Dic86C2211yescharacteristic
29C22×Q8×D43C2211yescharacteristic
30C22×Q8×D43C2211yescharacteristic
31C22×Q8×D43C2211yescharacteristic
32C2×#13063354—28no—
33C2×#13063354C2218yescomplemented
34C22×Dic172C2211yescharacteristic
35C22×Dic172C2211yescharacteristic
36C22×#10621885C2211yescharacteristic
37C22×#10621885C2211yescharacteristic
38C22×#10621885C2211yescharacteristic
39C2×Q16×D43—28no—
40C2×Q16×D43C2218yescomplemented
41C22×#10621883C2211yescharacteristic
42C22×#10621872C2211yescharacteristic
43C22×C8×D43C2211yescharacteristic
44#14583472—24no—
45#14583472C2218yescomplemented
46C2×#13063324—21no—
47C2×#13063311—21no—
48C2×#13063310—21no—
49C2×#13063307—21no—
50C2×#13063305C2211yescharacteristic
51C2×#13063304C2211yescharacteristic
52C2×#13063301C2211yescharacteristic
53C2×#13063283C2211yescharacteristic
54#14583062C2218yescomplemented
55#14583061C2218yescomplemented
56#14583058C2218yescomplemented
57#14583057C2218yescomplemented
58#14583056C2218yescomplemented
59#14583054C2218yescomplemented
60#14583053C2218yescomplemented
61#14582906C2218yescomplemented
62#14582892C2218yescomplemented
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063249C2211yescharacteristic
66C2×#13063248C2211yescharacteristic
67C2×#13063248C2211yescharacteristic
68C2×#13063246C2211yescharacteristic
69#14582864C2218yescomplemented
70C2×C22⋊(C43⋊C8)C2211yescharacteristic
71C2×(C2×D43)⋊C8C2211yescharacteristic
72C2×(C2×D43)⋊C8C2211yescharacteristic
73C22×#41×C43C2211yescharacteristic
74C22×Q16×C43C2211yescharacteristic
75C22×SD16×C43C2211yescharacteristic
76C2×C22⋊Q8×C43C2211yescharacteristic
77C43×#452C2218yescomplemented
78C2×#103×C43C2211yescharacteristic
79C2×#102×C43C2211yescharacteristic
80C2×C22⋊C8×C43C2211yescharacteristic
81#13063372—264no—
82#13063372—232no—
83#13063372—232no—
84C2×#10621898—216no—
85C2×#10621898—28no—
86C2×#10621898—24no—
87C2×#10621898—24no—
88C2×#10621898D414yes—
89C2×#10621898C2314yes—
90C2×#10621900—216no—
91C2×#10621900—216no—
92C2×#10621900—24no—
93C2×#10621900—28no—
94C2×#10621900—28no—
95C2×#10621900—24no—
96C2×#10621900—22no—
97C2×#10621900—22no—
98C2×#10621900—24no—
99C2×#10621900D418yes—
100C2×#10621900C2314yes—
101C2×#10621900C2314yes—
102C22×Dic86—216no—
103C22×Dic86—21no—
104C22×Dic86—22no—
105C22×Dic86—21no—
106C22×Dic86—21no—
107C22×Dic86—28no—
108C22×Dic86—24no—
109C22×Dic86—24no—
110C22×Dic86—21no—
111C22×Dic86D411yescharacteristic
112C22×Dic86C2314yes—
113C22×Dic86C2311yescharacteristic
114C22×Dic86C2311yescharacteristic
115C22×Dic86C2311yescharacteristic
116C2×Q8×D43—24no—
117C2×Q8×D43—24no—
118C2×Q8×D43—22no—
119C2×Q8×D43—22no—
120C2×Q8×D43—22no—
121C2×Q8×D43—24no—
122C2×Q8×D43—24no—
123C2×Q8×D43—24no—
124C2×Q8×D43D418yes—
125C2×Q8×D43C2314yes—
126C2×Q8×D43C2314yes—
127C2×Q8×D43C2314yes—
128C22×D172D411yescharacteristic
129C22×C22⋊D43—21no—
130C22×C22⋊D43—21no—
131C22×C22⋊D43D411yescharacteristic
132C22×C22⋊D43D411yescharacteristic
133C23×Dic43—21no—
134C23×Dic43—21no—
135C23×Dic43—21no—
136C22×C4×D43—21no—
137C22×C4×D43—21no—
138C22×C4×D43—21no—
139C22×C4×D43C2311yescharacteristic
140C22×C4×D43C2311yescharacteristic
141#13063354—232no—
142C2×Dic172—24no—
143C2×Dic172—24no—
144C2×Dic172C2314yes—
145C2×Dic172C2314yes—
146C2×#10621885—24no—
147C2×#10621885—24no—
148C2×#10621885—24no—
149C2×#10621885C2314yes—
150C2×#10621885C2314yes—
151C2×#10621885C2314yes—
152Q16×D43—232no—
153C2×#10621883—24no—
154C2×#10621883C2314yes—
155C2×#10621872—24no—
156C2×#10621872C2314yes—
157C22×C43⋊C8C2311yescharacteristic
158C22×C43⋊C8C2311yescharacteristic
159C2×C8×D43—24no—
160C2×C8×D43C2314yes—
161#13063324—28no—
162#13063311—28no—
163#13063310—28no—
164#13063307—28no—
165#13063305—22no—
166#13063305C2314yes—
167#13063304—22no—
168#13063304C2314yes—
169#13063301—22no—
170#13063301C2314yes—
171#13063283—22no—
172#13063283C2314yes—
173C2×C4⋊Dic43—21no—
174C2×C4⋊Dic43C2311yescharacteristic
175C2×Dic43⋊C4—21no—
176C2×Dic43⋊C4—21no—
177C2×C22⋊Dic43—21no—
178C2×(C2×D43)⋊C4—21no—
179C2×(C2×D43)⋊C4—21no—
180C2×(C2×D43)⋊C4—21no—
181C2×C4×Dic43—21no—
182#13063250C2314yes—
183#13063250C2314yes—
184#13063249C2314yes—
185#13063248C2314yes—
186#13063248C2314yes—
187#13063246C2314yes—
188C22⋊(C43⋊C8)C2314yes—
189(C2×D43)⋊C8C2314yes—
190(C2×D43)⋊C8C2314yes—
191C2×#41×C43—24no—
192C2×#41×C43—24no—
193C2×#41×C43—22no—
194C2×#41×C43C2314yes—
195C22×Q8×C43C2311yescharacteristic
196C22×Q8×C43C2311yescharacteristic
197C22×D4×C43—21no—
198C22×D4×C43C2311yescharacteristic
199C23×C4×C43—21no—
200C23×C4×C43C2311yescharacteristic
201C2×Q16×C43—24no—
202C2×Q16×C43C2314yes—
203C2×SD16×C43—24no—
204C2×SD16×C43C2314yes—
205C22×C8×C43C2311yescharacteristic
206C22×C8×C43C2311yescharacteristic
207C22⋊Q8×C43—22no—
208C22⋊Q8×C43C2314yes—
209C2×C4⋊C4×C43—21no—
210C2×C4⋊C4×C43C2311yescharacteristic
211C2×C22⋊C4×C43—21no—
212#103×C43C2314yes—
213#102×C43C2314yes—
214C22⋊C8×C43C2314yes—
215C24×C43—21no—
216C24×C43C2×D411yescharacteristic
217C23×D43C2×D411yescharacteristic
218C23×D43C2×D411yescharacteristic
219#41×C43—216no—
220#41×C43—28no—
221#41×C43—28no—
222C2×Q8×C43—22no—
223C2×Q8×C43—21no—
224C2×Q8×C43—21no—
225C2×Q8×C43—22no—
226C2×Q8×C43—22no—
227C2×Q8×C43C2×D414yes—
228C2×Q8×C43C2412yes—
229C2×Q8×C43C2412yes—
230C2×D4×C43—28no—
231C2×D4×C43—22no—
232C2×D4×C43—21no—
233C2×D4×C43—24no—
234C2×D4×C43C2×D414yes—
235C2×D4×C43C2412yes—
236C22×C4×C43—28no—
237C22×C4×C43—24no—
238C22×C4×C43—22no—
239C22×C4×C43—22no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43C2×D411yescharacteristic
244C22×C4×C43C2×D412yes—
245C22×C4×C43C2412yes—
246C22×C4×C43C2411yescharacteristic
247C2×C22⋊D43—28no—
248C2×C22⋊D43—24no—
249C2×C22⋊D43—28no—
250C2×C22⋊D43—24no—
251C2×C22⋊D43—24no—
252C2×C22⋊D43—24no—
253C2×C22⋊D43C2×D414yes—
254C2×C22⋊D43C2×D414yes—
255C22×Dic43—28no—
256C22×Dic43—28no—
257C22×Dic43—28no—
258C22×Dic43—24no—
259C22×Dic43—24no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—24no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43C2×D411yescharacteristic
266C22×Dic43C2×D411yescharacteristic
267Q8×D43—216no—
268Q8×D43—28no—
269Q8×D43—216no—
270Q8×D43—28no—
271Q8×D43—28no—
272Q8×D43—28no—
273Q8×D43—28no—
274Q8×D43—48no—
275Q8×D43C2×D4116yes—
276#10621900—264no—
277#10621900—216no—
278#10621900—264no—
279#10621900—28no—
280#10621900—216no—
281#10621900—28no—
282#10621900—28no—
283#10621900C2×D4116yes—
284#10621898—264no—
285#10621898—216no—
286#10621898—28no—
287#10621898—28no—
288C2×D172—24no—
289C2×D172C2×D414yes—
290C2×C4×D43—28no—
291C2×C4×D43—22no—
292C2×C4×D43—22no—
293C2×C4×D43—28no—
294C2×C4×D43—24no—
295C2×C4×D43—24no—
296C2×C4×D43—24no—
297C2×C4×D43—44no—
298C2×C4×D43C2×D414yes—
299C2×C4×D43C2×D414yes—
300C2×C4×D43C2×D412yes—
301C2×C4×D43C2×D412yes—
302C2×C4×D43C2412yes—
303C2×C4×D43C2412yes—
304C2×Dic86—28no—
305C2×Dic86—28no—
306C2×Dic86—216no—
307C2×Dic86—264no—
308C2×Dic86—21no—
309C2×Dic86—21no—
310C2×Dic86—22no—
311C2×Dic86—22no—
312C2×Dic86—24no—
313C2×Dic86—28no—
314C2×Dic86—24no—
315C2×Dic86—24no—
316C2×Dic86—24no—
317C2×Dic86—28no—
318C2×Dic86—28no—
319C2×Dic86—22no—
320C2×Dic86—22no—
321C2×Dic86—21no—
322C2×Dic86—24no—
323C2×Dic86—44no—
324C2×Dic86C2×D414yes—
325C2×Dic86C2×D414yes—
326C2×Dic86C2×D414yes—
327C2×Dic86C2412yes—
328C2×Dic86C2412yes—
329C2×Dic86C2412yes—
330Q16×C43—28no—
331SD16×C43—28no—
332C2×C8×C43—22no—
333C2×C8×C43—22no—
334C2×C8×C43C2412yes—
335C2×C8×C43C2412yes—
336C4⋊C4×C43—24no—
337C4⋊C4×C43—21no—
338C4⋊C4×C43C2412yes—
339C22⋊C4×C43—24no—
340C22⋊Dic43—24no—
341#10621885—28no—
342#10621885—28no—
343#10621885—28no—
344#10621883—28no—
345(C2×D43)⋊C4—24no—
346(C2×D43)⋊C4—24no—
347(C2×D43)⋊C4—24no—
348C4⋊Dic43—21no—
349C4⋊Dic43—24no—
350C4⋊Dic43C2412yes—
351Dic43⋊C4—24no—
352Dic43⋊C4—24no—
353C4×Dic43—24no—
354C2×C43⋊C8—22no—
355C2×C43⋊C8—22no—
356C2×C43⋊C8C2412yes—
357C2×C43⋊C8C2412yes—
358Dic172—28no—
359Dic172—28no—
360#10621872—28no—
361C8×D43—28no—
362C23×C43—22no—
363C23×C43—24no—
364C23×C43—22no—
365C23×C43—22no—
366C23×C43—22no—
367C23×C43—42no—
368C23×C43—42no—
369C23×C43C22×D412yes—
370C23×C43C22×D411yescharacteristic
371C22×D43—22no—
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—22no—
376C22×D43#12014yes—
377C22×D43C22×D412yes—
378C22×D43C22×D412yes—
379Q8×C43—24no—
380Q8×C43—22no—
381Q8×C43—22no—
382Q8×C43—22no—
383Q8×C43—42no—
384Q8×C43C22×D414yes—
385D4×C43—216no—
386D4×C43—24no—
387D4×C43—22no—
388D4×C43C22×D414yes—
389C2×C4×C43—216no—
390C2×C4×C43—22no—
391C2×C4×C43—24no—
392C2×C4×C43—22no—
393C2×C4×C43—24no—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—42no—
399C2×C4×C43—42no—
400C2×C4×C43C22×D412yes—
401C2×C4×C43C22×D411yescharacteristic
402C2×C4×C43C22×D412yes—
403C2×C4×C43C22×D412yes—
404C2×C4×C43C2511yescharacteristic
405C22⋊D43—216no—
406C22⋊D43—28no—
407C22⋊D43—216no—
408C22⋊D43—28no—
409C2×Dic43—216no—
410C2×Dic43—216no—
411C2×Dic43—22no—
412C2×Dic43—24no—
413C2×Dic43—24no—
414C2×Dic43—22no—
415C2×Dic43—22no—
416C2×Dic43—216no—
417C2×Dic43—22no—
418C2×Dic43—22no—
419C2×Dic43—42no—
420C2×Dic43—42no—
421C2×Dic43#12014yes—
422C2×Dic43C22×D412yes—
423C2×Dic43C22×D412yes—
424D172—28no—
425C4×D43—216no—
426C4×D43—216no—
427C4×D43—24no—
428C4×D43—22no—
429C4×D43—22no—
430C4×D43—48no—
431C4×D43#12018yes—
432C4×D43C22×D414yes—
433C4×D43C22×D414yes—
434Dic86—216no—
435Dic86—216no—
436Dic86—24no—
437Dic86—24no—
438Dic86—22no—
439Dic86—22no—
440Dic86—28no—
441Dic86—216no—
442Dic86—22no—
443Dic86—22no—
444Dic86—42no—
445Dic86—48no—
446Dic86C22×D414yes—
447Dic86C22×D414yes—
448C8×C43—22no—
449C8×C43—22no—
450C43⋊C8—22no—
451C43⋊C8—22no—
452C2×#3011—431nomaximal, Sylow
453C22×C43—24no—
454C22×C43—22no—
455C22×C43—22no—
456C22×C43—22no—
457C22×C43—44no—
458C22×C43—48no—
459C22×C43—42no—
460C22×C43—42no—
461C22×C43C2×#12012yes—
462C22×C43#57812yes—
463C22×C43#57812yes—
464C22×C43C23×D411yescharacteristic
465C2×D43—28no—
466C2×D43—22no—
467C2×D43—22no—
468C2×D43—22no—
469C2×D43—22no—
470C2×D43—22no—
471C2×D43—44no—
472C2×D43C2×#12014yes—
473C4×C43—22no—
474C4×C43—24no—
475C4×C43—42no—
476C4×C43—42no—
477C4×C43C2×#12012yes—
478C4×C43C23×D411yescharacteristic
479C4×C43C23×D411yescharacteristic
480Dic43—22no—
481Dic43—24no—
482Dic43—24no—
483Dic43—42no—
484Dic43—42no—
485Dic43C2×#12014yes—
486C22×2−1+4—431no—
487C22×#137—431no—
488C23×Q16—431no—
489C2×#536—431no—
490#3011—4316no—
491C2×#452—431no—
492C2×#452—431no—
493C2×#452—431no—
494C2×#452D4311yescharacteristic, complemented
495C2×#451—431no—
496C2×#451—431no—
497C2×#451—431no—
498C2×#451—431no—
499C2×#419—431no—
500C2×#416—431no—
501C2×#408—431no—
502C2×C43—42no—
503C2×C43—44no—
504C2×C43#301114yescomplemented
505C2×C43C22×#12011yescharacteristic
506C2×C43C2×#57811yescharacteristic
507C2×C43C2×#57811yescharacteristic
508D43—24no—
509D43—42no—
510C2×2−1+4—438no—
511C2×2−1+4—868no—
512C2×2−1+4—868no—
513C2×2−1+4—864no—
514C22×#41—431no—
515C22×#41—431no—
516C22×#41—431no—
517C22×#41—861no—
518C22×#41—861no—
519C22×#41—861no—
520C22×#41C2×D4311yescharacteristic
521C23×Q8—431no—
522C23×Q8—431no—
523C23×Q8—431no—
524C23×Q8—431no—
525C23×Q8—861no—
526C2×#137—438no—
527C2×#137—868no—
528C22×Q16—431no—
529C22×Q16—431no—
530C22×Q16—431no—
531C22×Q16—438no—
532C22×Q16—431no—
533C22×Q16—431no—
534C22×Q16—868no—
535C22×Q16C2×D4311yescharacteristic
536C22×SD16—431no—
537C22×SD16C2×D4311yescharacteristic
538C22×M16—431no—
539C23×C8—431no—
540#536—438no—
541#536—864no—
542C2×C4⋊Q8—861no—
543C2×#124—861no—
544C2×#123—861no—
545C2×#123—861no—
546C2×C22⋊Q8—431no—
547C2×C22⋊Q8—431no—
548C2×C22⋊Q8—431no—
549C2×C22⋊Q8C2×D4311yescharacteristic
550C2×#117—431no—
551#452—438no—
552#452—438no—
553#452—438no—
554#452C2×D4318yescomplemented
555#451—438no—
556#451—438no—
557#451—438no—
558#451—438no—
559#419—438no—
560#416—438no—
561C2×#103—431no—
562C2×#103—431no—
563C2×#103—431no—
564C2×#103—431no—
565C2×#103—431no—
566C2×#103C2×D4311yescharacteristic
567C2×#102—431no—
568C2×#102C2×D4311yescharacteristic
569#408—438no—
570C2×C22⋊C8—431no—
571C2×C22⋊C8—431no—
572C2×C22⋊C8—431no—
573C2×C22⋊C8C2×D4311yescharacteristic
574C43C2×#301111yescharacteristic, complemented, Sylow
5752−1+4—8632no—
5762−1+4—8632no—
5772−1+4—8664no—
578C2×#41—24no—
579C2×#41—24no—
580C2×#41—22no—
581C2×#41—434no—
582C2×#41—434no—
583C2×#41—438no—
584C2×#41—434no—
585C2×#41—434no—
586C2×#41—864no—
587C2×#41—864no—
588C2×#41—868no—
589C2×#41—8616no—
590C2×#41—862no—
591C2×#41—864no—
592C2×#41—862no—
593C2×#41—868no—
594C2×#41—868no—
595C2×#41—864no—
596C2×#41—8616no—
597C2×#41—8616no—
598C2×#41—864no—
599C2×#41C22×D4314yes—
600C22×Q8—431no—
601C22×Q8—438no—
602C22×Q8—434no—
603C22×Q8—434no—
604C22×Q8—434no—
605C22×Q8—431no—
606C22×Q8—431no—
607C22×Q8—431no—
608C22×Q8—434no—
609C22×Q8—861no—
610C22×Q8—861no—
611C22×Q8—861no—
612C22×Q8—864no—
613C22×Q8—864no—
614C22×Q8—868no—
615C22×Q8—8616no—
616C22×Q8—862no—
617C22×Q8—864no—
618C22×Q8—862no—
619C22×Q8—862no—
620C22×Q8—864no—
621C22×Q8—864no—
622C22×Q8—864no—
623C22×Q8—864no—
624C22×Q8—861no—
625C22×Q8—862no—
626C22×Q8C22×D4311yescharacteristic
627C22×Q8C22×D4311yescharacteristic
628C22×D4—21no—
629C22×D4—431no—
630C22×D4—431no—
631C22×D4—431no—
632C22×D4—861no—
633C22×D4—861no—
634C22×D4C22×D4311yescharacteristic
635C23×C4—21no—
636C23×C4—431no—
637C23×C4—431no—
638C23×C4—861no—
639C23×C4—861no—
640C23×C4—861no—
641C23×C4—861no—
642C23×C4—861no—
643C23×C4—861no—
644C23×C4C22×D4311yescharacteristic
645#137—8632no—
646C2×Q16—24no—
647C2×Q16—434no—
648C2×Q16—434no—
649C2×Q16—434no—
650C2×Q16—434no—
651C2×Q16—434no—
652C2×Q16—864no—
653C2×Q16—864no—
654C2×Q16—8632no—
655C2×Q16—864no—
656C2×Q16—864no—
657C2×Q16—864no—
658C2×Q16C22×D4314yes—
659C2×SD16—24no—
660C2×SD16—434no—
661C2×SD16—864no—
662C2×SD16C22×D4314yes—
663C2×M16—434no—
664C2×M16—864no—
665C22×C8—431no—
666C22×C8—431no—
667C22×C8—434no—
668C22×C8—864no—
669C22×C8C22×D4311yescharacteristic
670C22×C8C22×D4311yescharacteristic
671C4⋊Q8—868no—
672#124—868no—
673#123—868no—
674#123—868no—
675C22⋊Q8—22no—
676C22⋊Q8—434no—
677C22⋊Q8—434no—
678C22⋊Q8—434no—
679C22⋊Q8—862no—
680C22⋊Q8—862no—
681C22⋊Q8—862no—
682C22⋊Q8C22×D4314yes—
683#117—434no—
684#117—862no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—431no—
687C2×C4⋊C4—861no—
688C2×C4⋊C4—861no—
689C2×C4⋊C4—861no—
690C2×C4⋊C4C22×D4311yescharacteristic
691C2×C22⋊C4—21no—
692C2×C22⋊C4—861no—
693C2×C22⋊C4—861no—
694C2×C22⋊C4—861no—
695C2×C22⋊C4—861no—
696C2×C42—861no—
697#103—434no—
698#103—434no—
699#103—434no—
700#103—434no—
701#103—434no—
702#103C22×D4314yes—
703#102—434no—
704#102C22×D4314yes—
705C22⋊C8—434no—
706C22⋊C8—434no—
707C22⋊C8—434no—
708C22⋊C8C22×D4314yes—
709C24—21no—
710C24—431no—
711C24—431no—
712C24D4×D4311yescharacteristic
713#41—216no—
714#41—28no—
715#41—28no—
716#41—4316no—
717#41—8616no—
718#41—868no—
719#41—868no—
720#41—8664no—
721#41—8616no—
722#41—868no—
723#41—868no—
724#41—8664no—
725#41—8664no—
726#41—8616no—
727#41—868no—
728C2×Q8—22no—
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—434no—
734C2×Q8—4316no—
735C2×Q8—434no—
736C2×Q8—434no—
737C2×Q8—432no—
738C2×Q8—432no—
739C2×Q8—432no—
740C2×Q8—864no—
741C2×Q8—868no—
742C2×Q8—864no—
743C2×Q8—864no—
744C2×Q8—864no—
745C2×Q8—868no—
746C2×Q8—868no—
747C2×Q8—868no—
748C2×Q8—868no—
749C2×Q8—8664no—
750C2×Q8—8616no—
751C2×Q8—8616no—
752C2×Q8—868no—
753C2×Q8—868no—
754C2×Q8—868no—
755C2×Q8—868no—
756C2×Q8—8616no—
757C2×Q8—868no—
758C2×Q8—862no—
759C2×Q8—862no—
760C2×Q8—864no—
761C2×Q8—861no—
762C2×Q8—861no—
763C2×Q8—861no—
764C2×Q8—862no—
765C2×Q8—862no—
766C2×Q8—1724no—
767C2×Q8—1728no—
768C2×Q8D4×D4314yes—
769C2×Q8C23×D4312yes—
770C2×Q8C23×D4312yes—
771C2×D4—28no—
772C2×D4—24no—
773C2×D4—21no—
774C2×D4—22no—
775C2×D4—434no—
776C2×D4—434no—
777C2×D4—434no—
778C2×D4—864no—
779C2×D4—864no—
780C2×D4—864no—
781C2×D4—868no—
782C2×D4—864no—
783C2×D4—864no—
784C2×D4—868no—
785C2×D4D4×D4314yes—
786C2×D4C23×D4312yes—
787C22×C4—28no—
788C22×C4—21no—
789C22×C4—24no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—431no—
795C22×C4—432no—
796C22×C4—434no—
797C22×C4—434no—
798C22×C4—432no—
799C22×C4—431no—
800C22×C4—432no—
801C22×C4—432no—
802C22×C4—868no—
803C22×C4—864no—
804C22×C4—864no—
805C22×C4—868no—
806C22×C4—864no—
807C22×C4—868no—
808C22×C4—864no—
809C22×C4—864no—
810C22×C4—868no—
811C22×C4—868no—
812C22×C4—864no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—862no—
816C22×C4—862no—
817C22×C4—861no—
818C22×C4—861no—
819C22×C4—1724no—
820C22×C4D4×D4312yes—
821C22×C4D4×D4311yescharacteristic
822C22×C4C23×D4312yes—
823C22×C4C23×D4311yescharacteristic
824Q16—28no—
825Q16—868no—
826Q16—868no—
827Q16—868no—
828Q16—868no—
829Q16—868no—
830SD16—28no—
831SD16—868no—
832M16—868no—
833C2×C8—22no—
834C2×C8—22no—
835C2×C8—432no—
836C2×C8—432no—
837C2×C8—868no—
838C2×C8—862no—
839C2×C8—862no—
840C2×C8C23×D4312yes—
841C2×C8C23×D4312yes—
842C4⋊C4—24no—
843C4⋊C4—21no—
844C4⋊C4—432no—
845C4⋊C4—864no—
846C4⋊C4—864no—
847C4⋊C4—861no—
848C4⋊C4—864no—
849C4⋊C4C23×D4312yes—
850C22⋊C4—24no—
851C22⋊C4—864no—
852C22⋊C4—864no—
853C22⋊C4—864no—
854C22⋊C4—864no—
855C42—864no—
856C23—22no—
857C23—24no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—42no—
862C23—42no—
863C23—434no—
864C23—432no—
865C23—432no—
866C23—862no—
867C23—862no—
868C23—862no—
869C23—862no—
870C23—862no—
871C23C2×D4×D4312yes—
872C23C2×D4×D4311yescharacteristic
873Q8—24no—
874Q8—22no—
875Q8—22no—
876Q8—22no—
877Q8—42no—
878Q8—434no—
879Q8—434no—
880Q8—868no—
881Q8—8616no—
882Q8—8616no—
883Q8—8616no—
884Q8—864no—
885Q8—864no—
886Q8—862no—
887Q8—862no—
888Q8—862no—
889Q8—862no—
890Q8—1728no—
891Q8—1722no—
892Q8C2×D4×D4314yes—
893D4—216no—
894D4—24no—
895D4—22no—
896D4—868no—
897D4—868no—
898D4—868no—
899D4—8616no—
900D4—8616no—
901D4C2×D4×D4314yes—
902C2×C4—216no—
903C2×C4—22no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—24no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—434no—
914C2×C4—432no—
915C2×C4—438no—
916C2×C4—434no—
917C2×C4—434no—
918C2×C4—432no—
919C2×C4—8616no—
920C2×C4—8616no—
921C2×C4—8616no—
922C2×C4—8616no—
923C2×C4—8616no—
924C2×C4—862no—
925C2×C4—864no—
926C2×C4—864no—
927C2×C4—862no—
928C2×C4—862no—
929C2×C4—864no—
930C2×C4—862no—
931C2×C4—862no—
932C2×C4—862no—
933C2×C4—862no—
934C2×C4—1728no—
935C2×C4—1722no—
936C2×C4—1722no—
937C2×C4C2×D4×D4312yes—
938C2×C4C2×D4×D4311yescharacteristic
939C2×C4C2×D4×D4312yes—
940C2×C4C2×D4×D4312yes—
941C2×C4C24×D4311yescharacteristic
942C8—22no—
943C8—22no—
944C8—862no—
945C8—862no—
946C22—22no—
947C22—24no—
948C22—22no—
949C22—22no—
950C22—42no—
951C22—42no—
952C22—44no—
953C22—48no—
954C22—434no—
955C22—862no—
956C22—862no—
957C22—868no—
958C22—862no—
959C22—862no—
960C22—862no—
961C22—1724no—
962C22#120×D4312yes—
963C22#1458371312yes—
964C22#1458371512yes—
965C22C22×D4×D4311yescharacteristic
966C4—22no—
967C4—24no—
968C4—42no—
969C4—42no—
970C4—434no—
971C4—862no—
972C4—864no—
973C4—864no—
974C4—1722no—
975C4—1722no—
976C4#120×D4312yes—
977C4C22×D4×D4311yescharacteristic
978C4C22×D4×D4311yescharacteristic
979C2—42no—
980C2—44no—
981C2—864no—
982C2—1722no—
983C2#1914388714yesdirect product factor
984C2C2×#120×D4311yescharacteristic
985C2C2×#1458371311yescharacteristic
986C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
prime radicalC22×#13063372C2
hypercenterC2×#452D43
hypocenterC43C2×#3011
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C22×#13063354C2semidirect
3. C22×Q16×D43C2semidirect
4. C2×#14583472C2semidirect
5. #19143887C2direct (N × H)
6. C2×#14583062C2semidirect
7. C2×#14583061C2semidirect
8. C2×#14583058C2semidirect
9. C2×#14583057C2semidirect
10. C2×#14583056C2semidirect
11. C2×#14583054C2semidirect
12. C2×#14583053C2semidirect
13. C2×#14582906C2semidirect
14. C2×#14582892C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#452C2semidirect
33. C2×#13063354C22semidirect
40. C2×Q16×D43C22semidirect
45. #14583472C22semidirect
54. #14583062C22semidirect
55. #14583061C22semidirect
56. #14583058C22semidirect
57. #14583057C22semidirect
58. #14583056C22semidirect
59. #14583054C22semidirect
60. #14583053C22semidirect
61. #14582906C22semidirect
62. #14582892C22semidirect
69. #14582864C22semidirect
77. C43×#452C22semidirect
494. C2×#452D43semidirect
504. C2×C43#3011semidirect
554. #452C2×D43semidirect
574. C43C2×#3011semidirect
983. C2#19143887direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633722
C22×#130633542
C22×Q16×D432
C2×#145834722
#191438872
C2×#145830622
C2×#145830612
C2×#145830582
C2×#145830572
C2×#145830562
C2×#145830542
C2×#145830532
C2×#145829062
C2×#145828922
C2×#145828642
C2×C43×#4522
C2×#301143