Finite Group Databasebeta

← C2×#19146234 #25971736

Subgroups — C2×#19146234 #25971736

Order 11008.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063357C211yesmaximal, characteristic, complemented
2C22×#13063356C211yesmaximal, characteristic, complemented
3C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
4C2×#14583551C211yesmaximal, characteristic
5#19146234C2116yesmaximal, direct product factor
6C2×#14583277C211yesmaximal, characteristic, complemented
7C2×#14583156C211yesmaximal, characteristic, complemented
8C2×#14583155C211yesmaximal, characteristic, complemented
9C2×#14583107C211yesmaximal, characteristic, complemented
10C2×#14583103C211yesmaximal, characteristic, complemented
11C2×#14583063C211yesmaximal, characteristic, complemented
12C2×#14583060C211yesmaximal, characteristic, complemented
13C2×#14583056C211yesmaximal, characteristic, complemented
14C2×#14582984C211yesmaximal, characteristic, complemented
15C2×#14582974C211yesmaximal, characteristic, complemented
16C2×C43×#451C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621898C2211yescharacteristic
19C22×Q8×D43C2211yescharacteristic
20C2×#13063357—28no—
21C2×#13063357C2218yescomplemented
22C2×#13063356—28no—
23C2×#13063356C2218yescomplemented
24C22×Dic172C2211yescharacteristic
25C22×#10621885C2211yescharacteristic
26C22×#10621885C2211yescharacteristic
27C22×#10621885C2211yescharacteristic
28C22×#10621873C2211yescharacteristic
29C22×#10621884C2211yescharacteristic
30C22×#10621884C2211yescharacteristic
31C22×#10621877C2211yescharacteristic
32C22×#10621872C2211yescharacteristic
33Q8×C22⋊D43—24no—
34Q8×C22⋊D43C2218yescomplemented
35#14583551—24no—
36#14583551C2218yes—
37C2×#13063323—21no—
38C2×#13063323C2211yescharacteristic
39C2×#13063323C2211yescharacteristic
40C2×#13063310—21no—
41C2×#13063307—21no—
42C2×#13063305C2211yescharacteristic
43C2×#13063304—21no—
44C2×#13063304C2211yescharacteristic
45C2×#13063301—21no—
46C2×#13063301C2211yescharacteristic
47C2×#13063298—21no—
48C2×Q8×Dic43C2211yescharacteristic
49C2×#13063287C2211yescharacteristic
50C2×C4×C22⋊D43—21no—
51C2×C4×C22⋊D43C2211yescharacteristic
52C2×C4⋊C4×D43—21no—
53#14583277C2218yescomplemented
54#14583156C2218yescomplemented
55#14583155C2218yescomplemented
56#14583107C2218yescomplemented
57#14583103C2218yescomplemented
58#14583063C2218yescomplemented
59#14583060C2218yescomplemented
60#14583056C2218yescomplemented
61#14582984C2218yescomplemented
62#14582974C2218yescomplemented
63C2×#13063256C2211yescharacteristic
64C2×Dic43⋊C8C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063249C2211yescharacteristic
67C2×#13063248C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic
70C2×C8×Dic43C2211yescharacteristic
71C23×Q8×C43C2211yescharacteristic
72C22×Q16×C43C2211yescharacteristic
73C22×Q16×C43C2211yescharacteristic
74C2×C22⋊Q8×C43C2211yescharacteristic
75C43×#451C2218yescomplemented
76C2×#103×C43C2211yescharacteristic
77C2×#103×C43C2211yescharacteristic
78C2×C22⋊C8×C43C2211yescharacteristic
79C2×#10621902—22no—
80C2×#10621902—24no—
81C2×#10621902—42no—
82C2×#10621902C2314yes—
83C2×#10621898—22no—
84C2×#10621898—24no—
85C2×#10621898—42no—
86C2×#10621898C2314yes—
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⋊D43D411yescharacteristic
98C22×C4×D43—21no—
99C22×C4×D43—21no—
100C22×C4×D43—21no—
101C22×C4×D43—21no—
102C22×C4×D43C2311yescharacteristic
103#13063357—232no—
104#13063356—232no—
105C2×Dic172—42no—
106C2×Dic172C2314yes—
107C2×#10621885—24no—
108C2×#10621885—24no—
109C2×#10621885—24no—
110C2×#10621885C2314yes—
111C2×#10621885C2314yes—
112C2×#10621885C2314yes—
113C2×#10621873—24no—
114C2×#10621873C2314yes—
115C2×#10621884—24no—
116C2×#10621884D418yescomplemented
117C2×#10621884C2314yes—
118C2×#10621884C2314yes—
119C2×#10621877—24no—
120C2×#10621877C2314yes—
121C2×#10621872—24no—
122C2×#10621872C2314yes—
123C22×C43⋊C8C2311yescharacteristic
124C22×C43⋊C8C2311yescharacteristic
125#13063323—28no—
126#13063323—22no—
127#13063323—22no—
128#13063323C2314yes—
129#13063323C2314yes—
130#13063310—28no—
131#13063307—28no—
132#13063305—22no—
133#13063305C2314yes—
134#13063304—22no—
135#13063304—28no—
136#13063304C2314yes—
137#13063301—22no—
138#13063301—28no—
139#13063301C2314yes—
140#13063298—28no—
141Q8×Dic43—22no—
142Q8×Dic43C2314yes—
143#13063287—22no—
144#13063287C2314yes—
145C4×C22⋊D43—28no—
146C4×C22⋊D43D414yes—
147C4×C22⋊D43C2314yes—
148C2×C4⋊Dic43—21no—
149C2×C4⋊Dic43—21no—
150C2×C4⋊Dic43C2311yescharacteristic
151C2×Dic43⋊C4—21no—
152C2×Dic43⋊C4—21no—
153C2×Dic43⋊C4—21no—
154C2×Dic43⋊C4—21no—
155C2×Dic43⋊C4—21no—
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4D411yescharacteristic
158C4⋊C4×D43—28no—
159C2×C22⋊Dic43—21no—
160C2×C22⋊Dic43D411yescharacteristic
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4D411yescharacteristic
165C2×C4×Dic43—21no—
166C2×C4×Dic43C2311yescharacteristic
167#13063256C2314yes—
168Dic43⋊C8C2314yes—
169#13063250C2314yes—
170#13063249C2314yes—
171#13063248C2314yes—
172#13063247C2314yes—
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×C43C2311yescharacteristic
181C22×Q8×C43C2314yes—
182C22×Q8×C43C2311yescharacteristic
183C23×C4×C43—21no—
184C23×C4×C43C2311yescharacteristic
185C2×Q16×C43—24no—
186C2×Q16×C43—42no—
187C2×Q16×C43C2314yes—
188C2×Q16×C43C2314yes—
189C22×C8×C43C2311yescharacteristic
190C22×C8×C43C2311yescharacteristic
191C22⋊Q8×C43—22no—
192C22⋊Q8×C43C2314yes—
193C2×C4⋊C4×C43—21no—
194C2×C4⋊C4×C43C2311yescharacteristic
195C2×C22⋊C4×C43—21no—
196#103×C43C2314yes—
197#103×C43C2314yes—
198C22⋊C8×C43C2314yes—
199C24×C43C2×D411yescharacteristic
200C23×D43—21no—
201C23×D43C2×D411yescharacteristic
202C2×Q8×C43—21no—
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—22no—
211C2×Q8×C43—22no—
212C2×Q8×C43—44no—
213C2×Q8×C43—44no—
214C2×Q8×C43—48no—
215C2×Q8×C43C2×D414yes—
216C2×Q8×C43C2412yes—
217C2×Q8×C43C2412yes—
218C2×Q8×C43C2412yes—
219C22×C4×C43—22no—
220C22×C4×C43—22no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—24no—
226C22×C4×C43—44no—
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2412yes—
230C22×C4×C43C2411yescharacteristic
231C2×C22⋊D43—24no—
232C2×C22⋊D43—24no—
233C2×C22⋊D43—44no—
234C2×C22⋊D43C2×D414yes—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43C2×D411yescharacteristic
239C22×Dic43C2×D411yescharacteristic
240C22×Dic43C2×D411yescharacteristic
241#10621902—28no—
242#10621902—44no—
243#10621902—48no—
244Q8×D43—28no—
245Q8×D43—44no—
246Q8×D43—48no—
247#10621898—28no—
248#10621898—44no—
249#10621898—48no—
250C2×D172—21no—
251C2×D172—22no—
252C2×D172—24no—
253C2×D172—44no—
254C2×D172C2×D414yes—
255C2×D172C2412yes—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—24no—
259C2×C4×D43—24no—
260C2×C4×D43—24no—
261C2×C4×D43—24no—
262C2×C4×D43—44no—
263C2×C4×D43—44no—
264C2×C4×D43—44no—
265C2×C4×D43—44no—
266C2×C4×D43C2×D412yes—
267C2×C4×D43C2412yes—
268C2×Dic86—22no—
269C2×Dic86—22no—
270C2×Dic86—22no—
271C2×Dic86—22no—
272C2×Dic86—21no—
273C2×Dic86—21no—
274C2×Dic86—24no—
275C2×Dic86—44no—
276C2×Dic86C2412yes—
277C2×Dic86C2412yes—
278Q16×C43—28no—
279Q16×C43—44no—
280C2×C8×C43—22no—
281C2×C8×C43—22no—
282C2×C8×C43C2412yes—
283C2×C8×C43C2412yes—
284C4⋊C4×C43—24no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43C2412yes—
287C22⋊C4×C43—24no—
288C22⋊Dic43—24no—
289C22⋊Dic43C2×D414yes—
290#10621885—28no—
291#10621885—28no—
292#10621885—28no—
293#10621884—28no—
294#10621884C2×D4116yescomplemented
295(C2×D43)⋊C4—24no—
296(C2×D43)⋊C4—24no—
297(C2×D43)⋊C4—24no—
298(C2×D43)⋊C4C2×D414yes—
299C4⋊Dic43—21no—
300C4⋊Dic43—24no—
301C4⋊Dic43—24no—
302C4⋊Dic43C2412yes—
303Dic43⋊C4—24no—
304Dic43⋊C4—24no—
305Dic43⋊C4—24no—
306Dic43⋊C4—24no—
307Dic43⋊C4—24no—
308Dic43⋊C4—24no—
309Dic43⋊C4C2×D414yes—
310C4×Dic43—24no—
311C4×Dic43C2×D412yes—
312C4×Dic43C2412yes—
313#10621877—28no—
314C2×C43⋊C8—22no—
315C2×C43⋊C8C2×D414yes—
316C2×C43⋊C8C2412yes—
317C2×C43⋊C8C2412yes—
318Dic172—44no—
319#10621873—28no—
320#10621872—28no—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—22no—
324C23×C43C22×D412yes—
325C23×C43C22×D411yescharacteristic
326C22×D43—22no—
327C22×D43—24no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—42no—
332C22×D43—42no—
333C22×D43C22×D412yes—
334Q8×C43—24no—
335Q8×C43—22no—
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—22no—
339Q8×C43—22no—
340Q8×C43—48no—
341Q8×C43—42no—
342Q8×C43—42no—
343Q8×C43C22×D414yes—
344C2×C4×C43—24no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—24no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—48no—
354C2×C4×C43—42no—
355C2×C4×C43—42no—
356C2×C4×C43—42no—
357C2×C4×C43C22×D412yes—
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D412yes—
360C2×C4×C43H(5,𝔽2)12yes—
361C2×C4×C43C2511yescharacteristic
362C22⋊D43—28no—
363C22⋊D43—48no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—42no—
370C2×Dic43—42no—
371C2×Dic43—42no—
372C2×Dic43#13714yescomplemented
373C2×Dic43C22×D412yes—
374C2×Dic43C22×D412yes—
375C2×Dic43C22×D412yes—
376D172—24no—
377D172—22no—
378D172—48no—
379D172C22×D414yes—
380C4×D43—24no—
381C4×D43—22no—
382C4×D43—22no—
383C4×D43—48no—
384C4×D43—48no—
385C4×D43—48no—
386C4×D43—48no—
387Dic86—22no—
388Dic86—22no—
389Dic86—22no—
390Dic86—22no—
391Dic86—48no—
392Dic86—42no—
393Dic86—42no—
394C8×C43—22no—
395C8×C43—22no—
396C43⋊C8—22no—
397C43⋊C8C22×D414yes—
398C2×#3276—431nomaximal, Sylow
399C22×C43—22no—
400C22×C43—22no—
401C22×C43—22no—
402C22×C43—44no—
403C22×C43D4212yes—
404C22×C43C2×#13712yes—
405C22×C43#57812yes—
406C22×C43C23×D411yescharacteristic
407C2×D43—24no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—44no—
412C2×D43—48no—
413C2×D43—42no—
414C2×D43—42no—
415C4×C43—24no—
416C4×C43—22no—
417C4×C43—42no—
418C4×C43—42no—
419C4×C43—42no—
420C4×C43D4212yes—
421C4×C43C23×D411yescharacteristic
422C4×C43C2×H(5,𝔽2)11yescharacteristic
423Dic43—22no—
424Dic43—22no—
425Dic43—42no—
426Dic43—42no—
427Dic43—42no—
428Dic43C2×#13714yescomplemented
429C22×#137—431no—
430C22×#137—431no—
431C2×D4×Q8—431no—
432C2×#547—431no—
433#3276—4316no—
434C2×#494—431no—
435C2×#470—431no—
436C2×#470—431no—
437C2×#462—431no—
438C2×#461—431no—
439C2×#452—431no—
440C2×#452—431no—
441C2×#451—431no—
442C2×#451D4311yescharacteristic, complemented
443C2×C4×SD16—431no—
444C2×#436—431no—
445C2×C43—42no—
446C2×C43#327614yescomplemented
447C2×C43C2×D4211yescharacteristic
448C2×C43C22×#13711yescharacteristic
449C2×C43C2×#57811yescharacteristic
450D43—42no—
451D43—44no—
452C22×#41—431no—
453C22×#41—431no—
454C23×Q8—431no—
455C23×Q8C2×D4311yescharacteristic
456C2×#137—438no—
457C2×#137—438no—
458C2×#137—868no—
459C2×#137—868no—
460C22×Q16—431no—
461C22×Q16—431no—
462C22×Q16—431no—
463C22×Q16—431no—
464C22×Q16C2×D4311yescharacteristic
465C22×Q16C2×D4311yescharacteristic
466C22×SD16—431no—
467C22×SD16—431no—
468C22×SD16—431no—
469C22×M16—431no—
470C22×M16—431no—
471D4×Q8—438no—
472D4×Q8—864no—
473#547—438no—
474#547—864no—
475C2×C4⋊Q8—431no—
476C2×C4⋊Q8—431no—
477C2×C4⋊Q8—861no—
478C2×#123—861no—
479C2×#123—861no—
480C2×C22⋊Q8—431no—
481C2×C22⋊Q8—431no—
482C2×C22⋊Q8—431no—
483C2×C22⋊Q8—861no—
484C2×C22⋊Q8—861no—
485C2×C22⋊Q8C2×D4311yescharacteristic
486C2×#121—861no—
487C2×C4×Q8—431no—
488C2×C4×D4—431no—
489C2×C4×D4—431no—
490C2×C4×D4—861no—
491C22×C4⋊C4—861no—
492#494—438no—
493#470—438no—
494#470—438no—
495#462—438no—
496#461—438no—
497#452—438no—
498#452—438no—
499#451—438no—
500#451C2×D4318yescomplemented
501C4×SD16—438no—
502#436—438no—
503C2×#106—431no—
504C2×C4⋊C8—431no—
505C2×#103—431no—
506C2×#103—431no—
507C2×#103—431no—
508C2×#103C2×D4311yescharacteristic
509C2×#103C2×D4311yescharacteristic
510C2×#102—431no—
511C2×C22⋊C8—431no—
512C2×C22⋊C8C2×D4311yescharacteristic
513C2×C4×C8—431no—
514C43C2×#327611yescharacteristic, complemented, Sylow
515C2×#41—434no—
516C2×#41—434no—
517C2×#41—864no—
518C2×#41—862no—
519C2×#41—862no—
520C2×#41—864no—
521C2×#41—1722no—
522C2×#41—1722no—
523C22×Q8—21no—
524C22×Q8—22no—
525C22×Q8—24no—
526C22×Q8—42no—
527C22×Q8—434no—
528C22×Q8—431no—
529C22×Q8—431no—
530C22×Q8—861no—
531C22×Q8—862no—
532C22×Q8—864no—
533C22×Q8—1722no—
534C22×Q8C22×D4311yescharacteristic
535C22×Q8C22×D4311yescharacteristic
536C22×Q8C22×D4314yes—
537C22×Q8C22×D4311yescharacteristic
538C22×D4—431no—
539C22×D4—431no—
540C22×D4—861no—
541C22×D4—861no—
542C23×C4—21no—
543C23×C4—431no—
544C23×C4—861no—
545C23×C4—861no—
546C23×C4—861no—
547C23×C4—861no—
548C23×C4C22×D4311yescharacteristic
549#137—8632no—
550#137—8632no—
551C2×Q16—24no—
552C2×Q16—42no—
553C2×Q16—434no—
554C2×Q16—434no—
555C2×Q16—434no—
556C2×Q16—434no—
557C2×Q16—864no—
558C2×Q16—864no—
559C2×Q16—864no—
560C2×Q16—1722no—
561C2×Q16C22×D4314yes—
562C2×Q16C22×D4314yes—
563C2×SD16—438no—
564C2×SD16—434no—
565C2×SD16—434no—
566C2×SD16—434no—
567C2×SD16—864no—
568C2×SD16—864no—
569C2×M16—434no—
570C2×M16—434no—
571C2×M16—864no—
572C2×M16—864no—
573C22×C8—431no—
574C22×C8—431no—
575C22×C8C22×D4311yescharacteristic
576C22×C8C22×D4311yescharacteristic
577C4⋊Q8—434no—
578C4⋊Q8—434no—
579C4⋊Q8—862no—
580C4⋊Q8—862no—
581C4⋊Q8—868no—
582#123—868no—
583#123—868no—
584C22⋊Q8—22no—
585C22⋊Q8—434no—
586C22⋊Q8—434no—
587C22⋊Q8—434no—
588C22⋊Q8—868no—
589C22⋊Q8—868no—
590C22⋊Q8—862no—
591C22⋊Q8—862no—
592C22⋊Q8—862no—
593C22⋊Q8C22×D4314yes—
594#121—868no—
595C4×Q8—434no—
596C4×Q8—862no—
597C4×D4—434no—
598C4×D4—434no—
599C4×D4—434no—
600C4×D4—862no—
601C4×D4—868no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4—431no—
605C2×C4⋊C4—868no—
606C2×C4⋊C4—861no—
607C2×C4⋊C4—861no—
608C2×C4⋊C4—861no—
609C2×C4⋊C4—861no—
610C2×C4⋊C4—861no—
611C2×C4⋊C4—861no—
612C2×C4⋊C4—861no—
613C2×C4⋊C4—861no—
614C2×C4⋊C4C22×D4311yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—431no—
617C2×C22⋊C4—431no—
618C2×C22⋊C4—861no—
619C2×C22⋊C4—861no—
620C2×C22⋊C4—861no—
621C2×C22⋊C4—861no—
622C2×C42—431no—
623C2×C42—861no—
624#106—434no—
625C4⋊C8—434no—
626#103—434no—
627#103—434no—
628#103—434no—
629#103C22×D4314yes—
630#103C22×D4314yes—
631#102—434no—
632C22⋊C8—434no—
633C22⋊C8C22×D4314yes—
634C4×C8—434no—
635C24—431no—
636C24—861no—
637C24D4×D4311yescharacteristic
638#41—868no—
639#41—868no—
640#41—1724no—
641#41—1728no—
642#41—1724no—
643#41—1728no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—24no—
647C2×Q8—21no—
648C2×Q8—22no—
649C2×Q8—28no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—22no—
654C2×Q8—44no—
655C2×Q8—44no—
656C2×Q8—48no—
657C2×Q8—432no—
658C2×Q8—432no—
659C2×Q8—864no—
660C2×Q8—861no—
661C2×Q8—861no—
662C2×Q8—868no—
663C2×Q8—862no—
664C2×Q8—862no—
665C2×Q8—862no—
666C2×Q8—862no—
667C2×Q8—1724no—
668C2×Q8—1724no—
669C2×Q8—1728no—
670C2×Q8D4×D4314yes—
671C2×Q8C23×D4312yes—
672C2×Q8C23×D4312yes—
673C2×Q8C23×D4312yes—
674C2×D4—434no—
675C2×D4—434no—
676C2×D4—432no—
677C2×D4—864no—
678C2×D4—864no—
679C2×D4—864no—
680C2×D4—861no—
681C2×D4—862no—
682C2×D4—1724no—
683C2×D4—1724no—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—44no—
692C22×C4—431no—
693C22×C4—431no—
694C22×C4—431no—
695C22×C4—432no—
696C22×C4—432no—
697C22×C4—864no—
698C22×C4—864no—
699C22×C4—864no—
700C22×C4—862no—
701C22×C4—862no—
702C22×C4—861no—
703C22×C4—861no—
704C22×C4—861no—
705C22×C4—864no—
706C22×C4—1724no—
707C22×C4—1724no—
708C22×C4—1724no—
709C22×C4—1724no—
710C22×C4D4×D4312yes—
711C22×C4D4×D4311yescharacteristic
712C22×C4C23×D4312yes—
713C22×C4C23×D4311yescharacteristic
714Q16—28no—
715Q16—44no—
716Q16—868no—
717Q16—868no—
718Q16—868no—
719Q16—1724no—
720SD16—4316no—
721SD16—868no—
722SD16—868no—
723M16—868no—
724M16—868no—
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—434no—
728C2×C8—432no—
729C2×C8—432no—
730C2×C8—862no—
731C2×C8C23×D4312yes—
732C2×C8C23×D4312yes—
733C4⋊C4—24no—
734C4⋊C4—21no—
735C4⋊C4—434no—
736C4⋊C4—432no—
737C4⋊C4—864no—
738C4⋊C4—864no—
739C4⋊C4—864no—
740C4⋊C4—864no—
741C4⋊C4—864no—
742C4⋊C4—864no—
743C4⋊C4—864no—
744C4⋊C4—861no—
745C4⋊C4—864no—
746C4⋊C4C23×D4312yes—
747C22⋊C4—24no—
748C22⋊C4—434no—
749C22⋊C4—434no—
750C22⋊C4—864no—
751C22⋊C4—864no—
752C22⋊C4—864no—
753C22⋊C4—864no—
754C42—432no—
755C42—432no—
756C42—864no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—432no—
761C23—862no—
762C23—862no—
763C23—862no—
764C23—862no—
765C23—864no—
766C23—1722no—
767C23—1722no—
768C23C2×D4×D4312yes—
769C23C2×D4×D4311yescharacteristic
770Q8—22no—
771Q8—24no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—22no—
776Q8—48no—
777Q8—42no—
778Q8—42no—
779Q8—862no—
780Q8—862no—
781Q8—862no—
782Q8—862no—
783Q8—1728no—
784Q8—1722no—
785Q8—1722no—
786Q8C2×D4×D4314yes—
787D4—434no—
788D4—868no—
789D4—862no—
790D4—864no—
791D4—1728no—
792D4—1728no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—48no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—434no—
807C2×C4—432no—
808C2×C4—432no—
809C2×C4—432no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—862no—
813C2×C4—862no—
814C2×C4—864no—
815C2×C4—862no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—1728no—
819C2×C4—1728no—
820C2×C4—1728no—
821C2×C4—1728no—
822C2×C4—1722no—
823C2×C4—1722no—
824C2×C4—1722no—
825C2×C4C2×D4×D4312yes—
826C2×C4C2×D4×D4312yes—
827C2×C4C2×D4×D4311yescharacteristic
828C2×C4#1306337012yes—
829C2×C4C24×D4311yescharacteristic
830C8—22no—
831C8—22no—
832C8—434no—
833C8—862no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—44no—
838C22—862no—
839C22—862no—
840C22—862no—
841C22—864no—
842C22—1722no—
843C22—1722no—
844C22—1724no—
845C22—1728no—
846C22#1458353112yes—
847C22#137×D4312yes—
848C22#1458371212yes—
849C22C22×D4×D4311yescharacteristic
850C4—22no—
851C4—24no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—434no—
856C4—862no—
857C4—862no—
858C4—1722no—
859C4—1722no—
860C4—1722no—
861C4#1458353112yes—
862C4C22×D4×D4311yescharacteristic
863C4C2×#1306337011yescharacteristic
864C2—42no—
865C2—1722no—
866C2—1724no—
867C2#1914623414yesdirect product factor
868C2C2×#1458353111yescharacteristic
869C2C2×#137×D4311yescharacteristic
870C2C2×#1458371211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#451C2
socleC23×C43C22×D4
prime radicalC2×#14583551C2
hypercenterC2×#451D43
hypocenterC43C2×#3276
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C22×#13063357C2semidirect
2. C22×#13063356C2semidirect
3. C2×Q8×C22⋊D43C2semidirect
5. #19146234C2direct (N × H)
6. C2×#14583277C2semidirect
7. C2×#14583156C2semidirect
8. C2×#14583155C2semidirect
9. C2×#14583107C2semidirect
10. C2×#14583103C2semidirect
11. C2×#14583063C2semidirect
12. C2×#14583060C2semidirect
13. C2×#14583056C2semidirect
14. C2×#14582984C2semidirect
15. C2×#14582974C2semidirect
16. C2×C43×#451C2semidirect
21. C2×#13063357C22semidirect
23. C2×#13063356C22semidirect
34. Q8×C22⋊D43C22semidirect
53. #14583277C22semidirect
54. #14583156C22semidirect
55. #14583155C22semidirect
56. #14583107C22semidirect
57. #14583103C22semidirect
58. #14583063C22semidirect
59. #14583060C22semidirect
60. #14583056C22semidirect
61. #14582984C22semidirect
62. #14582974C22semidirect
75. C43×#451C22semidirect
116. C2×#10621884D4semidirect
294. #10621884C2×D4semidirect
372. C2×Dic43#137semidirect
428. Dic43C2×#137semidirect
442. C2×#451D43semidirect
446. C2×C43#3276semidirect
500. #451C2×D43semidirect
514. C43C2×#3276semidirect
867. C2#19146234direct (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×#130633562
C2×Q8×C22⋊D432
C2×#145835512
#191462342
C2×#145832772
C2×#145831562
C2×#145831552
C2×#145831072
C2×#145831032
C2×#145830632
C2×#145830602
C2×#145830562
C2×#145829842
C2×#145829742
C2×C43×#4512
C2×#327643