Finite Group Databasebeta

← C2×#19143878 #25963018

Subgroups — C2×#19143878 #25963018

Order 11008.

4910 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063372C211yesmaximal, characteristic, complemented
2C22×#13063349C211yesmaximal, characteristic, complemented
3C22×SD16×D43C211yesmaximal, characteristic, complemented
4C2×#14583465C211yesmaximal, characteristic, complemented
5#19143878C2116yesmaximal, direct product factor
6C2×#14583045C211yesmaximal, characteristic, complemented
7C2×#14583044C211yesmaximal, characteristic, complemented
8C2×#14583041C211yesmaximal, characteristic, complemented
9C2×#14583040C211yesmaximal, characteristic, complemented
10C2×#14583039C211yesmaximal, characteristic, complemented
11C2×#14583037C211yesmaximal, characteristic, complemented
12C2×#14583036C211yesmaximal, characteristic, complemented
13C2×#14582906C211yesmaximal, characteristic, complemented
14C2×#14582892C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#449C211yesmaximal, characteristic, complemented
17C2×#13063372—24no—
18C2×#13063372—28no—
19C2×#13063372—28no—
20C2×#13063372C2218yescomplemented
21C22×#10621898—21no—
22C22×#10621898C2211yescharacteristic
23C22×#10621900—21no—
24C22×#10621900—21no—
25C22×#10621900C2211yescharacteristic
26C22×#10621900C2211yescharacteristic, complemented
27C23×Dic86—21no—
28C23×Dic86C2211yescharacteristic, complemented
29C22×Q8×D43C2211yescharacteristic
30C22×Q8×D43C2211yescharacteristic, complemented
31C22×D4×D43C2211yescharacteristic
32C2×#13063349—28no—
33C2×#13063349C2218yescomplemented
34C22×#10621873C2211yescharacteristic
35C22×#10621873C2211yescharacteristic
36C22×#10621883C2211yescharacteristic
37C22×#10621883C2211yescharacteristic
38C22×#10621884C2211yescharacteristic
39C2×SD16×D43—28no—
40C2×SD16×D43C2218yescomplemented
41C22×#10621882C2211yescharacteristic
42C22×#10621872C2211yescharacteristic
43C22×C8×D43C2211yescharacteristic
44#14583465—24no—
45#14583465C2218yescomplemented
46C2×#13063321—21no—
47C2×#13063311—21no—
48C2×#13063300C2211yescharacteristic
49C2×#13063299C2211yescharacteristic
50C2×#13063296C2211yescharacteristic
51C2×#13063295—21no—
52C2×#13063293—21no—
53C2×#13063283C2211yescharacteristic
54#14583045C2218yescomplemented
55#14583044C2218yescomplemented
56#14583041C2218yescomplemented
57#14583040C2218yescomplemented
58#14583039C2218yescomplemented
59#14583037C2218yescomplemented
60#14583036C2218yescomplemented
61#14582906C2218yescomplemented
62#14582892C2218yescomplemented
63C2×#13063250C2211yescharacteristic, complemented
64C2×#13063250C2211yescharacteristic, complemented
65C2×#13063249C2211yescharacteristic, complemented
66C2×#13063248C2211yescharacteristic, complemented
67C2×#13063248C2211yescharacteristic, complemented
68C2×#13063246C2211yescharacteristic, complemented
69#14582864C2218yescomplemented
70C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
71C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
72C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
73C22×#41×C43C2211yescharacteristic, complemented
74C22×SD16×C43C2211yescharacteristic
75C22×D8×C43C2211yescharacteristic
76C2×#121×C43C2211yescharacteristic
77C43×#449C2218yescomplemented
78C2×#103×C43C2211yescharacteristic, complemented
79C2×#102×C43C2211yescharacteristic, complemented
80C2×C22⋊C8×C43C2211yescharacteristic, complemented
81C24×D43—21no—
82#13063372—264no—
83#13063372—232no—
84#13063372—232no—
85C2×#10621898—216no—
86C2×#10621898—28no—
87C2×#10621898—24no—
88C2×#10621898—24no—
89C2×#10621898D414yes—
90C2×#10621898C2314yes—
91C2×#10621900—216no—
92C2×#10621900—216no—
93C2×#10621900—24no—
94C2×#10621900—28no—
95C2×#10621900—28no—
96C2×#10621900—24no—
97C2×#10621900—22no—
98C2×#10621900—22no—
99C2×#10621900—24no—
100C2×#10621900D418yescomplemented
101C2×#10621900C2314yes—
102C2×#10621900C2314yescomplemented
103C22×Dic86—216no—
104C22×Dic86—21no—
105C22×Dic86—22no—
106C22×Dic86—21no—
107C22×Dic86—21no—
108C22×Dic86—28no—
109C22×Dic86—24no—
110C22×Dic86—24no—
111C22×Dic86D411yescharacteristic
112C22×Dic86C2311yescharacteristic
113C22×Dic86C2311yescharacteristic
114C22×Dic86C2314yescomplemented
115C2×Q8×D43—24no—
116C2×Q8×D43—24no—
117C2×Q8×D43—22no—
118C2×Q8×D43—22no—
119C2×Q8×D43—24no—
120C2×Q8×D43D418yescomplemented
121C2×Q8×D43C2314yes—
122C2×Q8×D43C2314yescomplemented
123C22×D172—21no—
124C22×D172D411yescharacteristic
125C22×D172C2311yescharacteristic
126C22×C22⋊D43—21no—
127C22×C22⋊D43—21no—
128C22×C22⋊D43—21no—
129C22×C22⋊D43—21no—
130C22×C22⋊D43—21no—
131C22×C22⋊D43D411yescharacteristic
132C22×C22⋊D43D411yescharacteristic
133C2×D4×D43—24no—
134C2×D4×D43—24no—
135C2×D4×D43—22no—
136C2×D4×D43C2314yes—
137C23×Dic43—21no—
138C23×Dic43—21no—
139C23×Dic43—21no—
140C22×C4×D43—21no—
141C22×C4×D43—21no—
142C22×C4×D43C2311yescharacteristic
143C22×C4×D43C2311yescharacteristic
144#13063349—232no—
145C2×#10621873—24no—
146C2×#10621873—24no—
147C2×#10621873C2314yes—
148C2×#10621873C2314yes—
149C2×#10621883—24no—
150C2×#10621883—24no—
151C2×#10621883C2314yes—
152C2×#10621883C2314yes—
153C2×#10621884—24no—
154C2×#10621884C2314yes—
155SD16×D43—232no—
156C2×#10621882—24no—
157C2×#10621882C2314yes—
158C2×#10621872—24no—
159C2×#10621872C2314yes—
160C22×C43⋊C8C2311yescharacteristic
161C22×C43⋊C8C2311yescharacteristic
162C2×C8×D43—24no—
163C2×C8×D43C2314yes—
164#13063321—28no—
165#13063311—28no—
166#13063300—22no—
167#13063300C2314yes—
168#13063299—22no—
169#13063299C2314yes—
170#13063296—22no—
171#13063296C2314yes—
172#13063295—28no—
173#13063293—28no—
174#13063283—22no—
175#13063283C2314yes—
176C2×C4⋊Dic43C2311yescharacteristic
177C2×C22⋊Dic43—21no—
178C2×(C2×D43)⋊C4—21no—
179C2×(C2×D43)⋊C4—21no—
180C2×(C2×D43)⋊C4—21no—
181C2×C4×Dic43—21no—
182#13063250C2314yescomplemented
183#13063250C2314yescomplemented
184#13063249C2314yescomplemented
185#13063248C2314yescomplemented
186#13063248C2314yescomplemented
187#13063246C2314yescomplemented
188C22⋊(C43⋊C8)C2314yescomplemented
189(C2×D43)⋊C8C2314yescomplemented
190(C2×D43)⋊C8C2314yescomplemented
191C2×#41×C43—24no—
192C2×#41×C43—24no—
193C2×#41×C43—22no—
194C2×#41×C43C2314yescomplemented
195C22×Q8×C43C2311yescharacteristic
196C22×D4×C43—21no—
197C22×D4×C43—21no—
198C22×D4×C43C2311yescharacteristic
199C22×D4×C43C2311yescharacteristic
200C23×C4×C43—21no—
201C23×C4×C43C2311yescharacteristic
202C2×SD16×C43—24no—
203C2×SD16×C43C2314yes—
204C2×D8×C43—24no—
205C2×D8×C43C2314yes—
206C22×C8×C43C2311yescharacteristic
207C22×C8×C43C2311yescharacteristic
208#121×C43—22no—
209#121×C43C2314yes—
210C2×C4⋊C4×C43C2311yescharacteristic
211C2×C22⋊C4×C43—21no—
212#103×C43C2314yescomplemented
213#102×C43C2314yescomplemented
214C22⋊C8×C43C2314yescomplemented
215C24×C43—21no—
216C24×C43—21no—
217C24×C43C2×D411yescharacteristic
218C23×D43—21no—
219C23×D43—24no—
220C23×D43—44no—
221C23×D43—82no—
222C23×D43—82no—
223C23×D43C2×D411yescharacteristic
224C23×D43C2×D411yescharacteristic
225#41×C43—216no—
226#41×C43—28no—
227#41×C43—28no—
228C2×Q8×C43—22no—
229C2×Q8×C43—21no—
230C2×Q8×C43C2×D414yes—
231C2×Q8×C43C2412yes—
232C2×D4×C43—28no—
233C2×D4×C43—22no—
234C2×D4×C43—21no—
235C2×D4×C43—21no—
236C2×D4×C43—24no—
237C2×D4×C43—24no—
238C2×D4×C43—22no—
239C2×D4×C43—22no—
240C2×D4×C43—82no—
241C2×D4×C43C2×D414yes—
242C2×D4×C43C2412yes—
243C2×D4×C43C2412yes—
244C22×C4×C43—28no—
245C22×C4×C43—24no—
246C22×C4×C43—22no—
247C22×C4×C43—22no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43C2×D411yescharacteristic
251C22×C4×C43C2×D412yes—
252C22×C4×C43C2412yes—
253C22×C4×C43C2411yescharacteristic
254C2×C22⋊D43—28no—
255C2×C22⋊D43—24no—
256C2×C22⋊D43—24no—
257C2×C22⋊D43—24no—
258C2×C22⋊D43—28no—
259C2×C22⋊D43—24no—
260C2×C22⋊D43—24no—
261C2×C22⋊D43—24no—
262C2×C22⋊D43—24no—
263C2×C22⋊D43—44no—
264C2×C22⋊D43—82no—
265C2×C22⋊D43—82no—
266C2×C22⋊D43C2×D414yes—
267C2×C22⋊D43C2×D414yes—
268C22×Dic43—28no—
269C22×Dic43—28no—
270C22×Dic43—28no—
271C22×Dic43—24no—
272C22×Dic43—24no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—24no—
276C22×Dic43—21no—
277C22×Dic43C2×D411yescharacteristic
278C22×Dic43C2×D411yescharacteristic
279Q8×D43—216no—
280Q8×D43—28no—
281Q8×D43—216no—
282Q8×D43—28no—
283Q8×D43—28no—
284Q8×D43C2×D4116yescomplemented
285#10621900—264no—
286#10621900—216no—
287#10621900—264no—
288#10621900—28no—
289#10621900—216no—
290#10621900—28no—
291#10621900—28no—
292#10621900C2×D4116yescomplemented
293D4×D43—28no—
294D4×D43—28no—
295D4×D43—48no—
296#10621898—264no—
297#10621898—216no—
298#10621898—28no—
299#10621898—28no—
300C2×D172—21no—
301C2×D172—24no—
302C2×D172—24no—
303C2×D172—22no—
304C2×D172—22no—
305C2×D172—82no—
306C2×D172C2×D414yes—
307C2×D172C2412yes—
308C2×C4×D43—28no—
309C2×C4×D43—22no—
310C2×C4×D43—22no—
311C2×C4×D43—28no—
312C2×C4×D43—24no—
313C2×C4×D43—24no—
314C2×C4×D43C2×D414yes—
315C2×C4×D43C2×D414yes—
316C2×C4×D43C2×D412yes—
317C2×C4×D43C2×D412yes—
318C2×C4×D43C2412yes—
319C2×C4×D43C2412yes—
320C2×Dic86—28no—
321C2×Dic86—28no—
322C2×Dic86—216no—
323C2×Dic86—264no—
324C2×Dic86—21no—
325C2×Dic86—21no—
326C2×Dic86—22no—
327C2×Dic86—22no—
328C2×Dic86—24no—
329C2×Dic86—28no—
330C2×Dic86—24no—
331C2×Dic86—24no—
332C2×Dic86—24no—
333C2×Dic86—28no—
334C2×Dic86—28no—
335C2×Dic86C2×D414yes—
336C2×Dic86C2×D414yes—
337C2×Dic86C2×D414yes—
338C2×Dic86C2412yes—
339C2×Dic86C2412yes—
340SD16×C43—28no—
341D8×C43—28no—
342C2×C8×C43—22no—
343C2×C8×C43—22no—
344C2×C8×C43C2412yes—
345C2×C8×C43C2412yes—
346C4⋊C4×C43—21no—
347C4⋊C4×C43C2412yes—
348C22⋊C4×C43—24no—
349C22⋊Dic43—24no—
350#10621884—28no—
351#10621883—28no—
352#10621883—28no—
353#10621882—28no—
354(C2×D43)⋊C4—24no—
355(C2×D43)⋊C4—24no—
356(C2×D43)⋊C4—24no—
357C4⋊Dic43—21no—
358C4⋊Dic43C2412yes—
359C4×Dic43—24no—
360C2×C43⋊C8—22no—
361C2×C43⋊C8—22no—
362C2×C43⋊C8C2412yes—
363C2×C43⋊C8C2412yes—
364#10621873—28no—
365#10621873—28no—
366#10621872—28no—
367C8×D43—28no—
368C23×C43—22no—
369C23×C43—24no—
370C23×C43—22no—
371C23×C43—22no—
372C23×C43—22no—
373C23×C43—22no—
374C23×C43—42no—
375C23×C43—42no—
376C23×C43—42no—
377C23×C43—42no—
378C23×C43—42no—
379C23×C43C22×D412yes—
380C23×C43C22×D411yescharacteristic
381C22×D43—22no—
382C22×D43—22no—
383C22×D43—22no—
384C22×D43—22no—
385C22×D43—22no—
386C22×D43—22no—
387C22×D43—42no—
388C22×D43—42no—
389C22×D43—42no—
390C22×D43—48no—
391C22×D43—84no—
392C22×D43—84no—
393C22×D43—816no—
394C22×D43#12014yes—
395C22×D43C22×D412yes—
396C22×D43C22×D412yes—
397Q8×C43—24no—
398Q8×C43—22no—
399Q8×C43C22×D414yes—
400D4×C43—216no—
401D4×C43—24no—
402D4×C43—22no—
403D4×C43—22no—
404D4×C43—22no—
405D4×C43—42no—
406D4×C43—84no—
407D4×C43C22×D414yes—
408C2×C4×C43—216no—
409C2×C4×C43—22no—
410C2×C4×C43—24no—
411C2×C4×C43—22no—
412C2×C4×C43—24no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—42no—
417C2×C4×C43C22×D412yes—
418C2×C4×C43C22×D411yescharacteristic
419C2×C4×C43C22×D412yes—
420C2×C4×C43C22×D412yes—
421C2×C4×C43C2511yescharacteristic
422C22⋊D43—216no—
423C22⋊D43—28no—
424C22⋊D43—216no—
425C22⋊D43—28no—
426C22⋊D43—48no—
427C22⋊D43—84no—
428C22⋊D43—84no—
429C2×Dic43—216no—
430C2×Dic43—216no—
431C2×Dic43—22no—
432C2×Dic43—24no—
433C2×Dic43—24no—
434C2×Dic43—22no—
435C2×Dic43—22no—
436C2×Dic43—216no—
437C2×Dic43—22no—
438C2×Dic43—42no—
439C2×Dic43#12014yes—
440C2×Dic43C22×D412yes—
441C2×Dic43C22×D412yes—
442D172—28no—
443D172—22no—
444D172—22no—
445D172—42no—
446D172—84no—
447C4×D43—216no—
448C4×D43—216no—
449C4×D43—24no—
450C4×D43—22no—
451C4×D43—22no—
452C4×D43#12018yes—
453C4×D43C22×D414yes—
454C4×D43C22×D414yes—
455Dic86—216no—
456Dic86—216no—
457Dic86—24no—
458Dic86—24no—
459Dic86—22no—
460Dic86—22no—
461Dic86—28no—
462Dic86—216no—
463Dic86C22×D414yes—
464Dic86C22×D414yes—
465C8×C43—22no—
466C8×C43—22no—
467C43⋊C8—22no—
468C43⋊C8—22no—
469C2×#3010—431nomaximal, Sylow
470C22×C43—24no—
471C22×C43—22no—
472C22×C43—22no—
473C22×C43—22no—
474C22×C43—44no—
475C22×C43—48no—
476C22×C43—42no—
477C22×C43—42no—
478C22×C43—42no—
479C22×C43—42no—
480C22×C43—42no—
481C22×C43—84no—
482C22×C43C2×#12012yes—
483C22×C43#57712yes—
484C22×C43#57712yes—
485C22×C43C23×D411yescharacteristic
486C2×D43—28no—
487C2×D43—22no—
488C2×D43—22no—
489C2×D43—22no—
490C2×D43—22no—
491C2×D43—22no—
492C2×D43—44no—
493C2×D43—42no—
494C2×D43—42no—
495C2×D43—42no—
496C2×D43—816no—
497C2×D43—84no—
498C2×D43C2×#12014yes—
499C4×C43—22no—
500C4×C43—24no—
501C4×C43—42no—
502C4×C43C2×#12012yes—
503C4×C43C23×D411yescharacteristic
504C4×C43C23×D411yescharacteristic
505Dic43—22no—
506Dic43—24no—
507Dic43—24no—
508Dic43—42no—
509Dic43C2×#12014yes—
510C22×2−1+4—431no—
511C22×AGL(1,ℤ/8)—431no—
512C23×SD16—431no—
513C2×#535—431no—
514#3010—4316no—
515C2×#449—431no—
516C2×#449—431no—
517C2×#449—431no—
518C2×#449D4311yescharacteristic, complemented
519C2×#448—431no—
520C2×#448—431no—
521C2×#448—431no—
522C2×#448—431no—
523C2×#419—431no—
524C2×#416—431no—
525C2×#408—431no—
526C2×C43—42no—
527C2×C43—44no—
528C2×C43—82no—
529C2×C43#301014yescomplemented
530C2×C43C22×#12011yescharacteristic
531C2×C43C2×#57711yescharacteristic
532C2×C43C2×#57711yescharacteristic
533D43—24no—
534D43—42no—
535D43—82no—
536C2×2−1+4—438no—
537C2×2−1+4—868no—
538C2×2−1+4—868no—
539C2×2−1+4—864no—
540C22×#41—431no—
541C22×#41—431no—
542C22×#41—431no—
543C22×#41—861no—
544C22×#41—861no—
545C22×#41—861no—
546C22×#41C2×D4311yescharacteristic, complemented
547C23×Q8—431no—
548C23×Q8—431no—
549C23×Q8—431no—
550C23×Q8—861no—
551C23×D4—431no—
552C2×AGL(1,ℤ/8)—438no—
553C2×AGL(1,ℤ/8)—868no—
554C22×SD16—431no—
555C22×SD16—431no—
556C22×SD16—431no—
557C22×SD16—438no—
558C22×SD16—431no—
559C22×SD16—431no—
560C22×SD16—868no—
561C22×SD16C2×D4311yescharacteristic
562C22×D8—431no—
563C22×D8C2×D4311yescharacteristic
564C22×M16—431no—
565C23×C8—431no—
566#535—438no—
567#535—864no—
568C2×#127—861no—
569C2×#124—861no—
570C2×#121—431no—
571C2×#121—431no—
572C2×#121—431no—
573C2×#121C2×D4311yescharacteristic
574C2×#120—861no—
575C2×#120—861no—
576C2×#117—431no—
577#449—438no—
578#449—438no—
579#449—438no—
580#449C2×D4318yescomplemented
581#448—438no—
582#448—438no—
583#448—438no—
584#448—438no—
585#419—438no—
586#416—438no—
587C2×#103—431no—
588C2×#103—431no—
589C2×#103—431no—
590C2×#103—431no—
591C2×#103—431no—
592C2×#103C2×D4311yescharacteristic, complemented
593C2×#102—431no—
594C2×#102C2×D4311yescharacteristic, complemented
595#408—438no—
596C2×C22⋊C8—431no—
597C2×C22⋊C8—431no—
598C2×C22⋊C8—431no—
599C2×C22⋊C8C2×D4311yescharacteristic, complemented
600C43C2×#301011yescharacteristic, complemented, Sylow
601C25—861no—
6022−1+4—8632no—
6032−1+4—8632no—
6042−1+4—8664no—
605C2×#41—24no—
606C2×#41—24no—
607C2×#41—22no—
608C2×#41—434no—
609C2×#41—434no—
610C2×#41—438no—
611C2×#41—434no—
612C2×#41—434no—
613C2×#41—864no—
614C2×#41—864no—
615C2×#41—868no—
616C2×#41—8616no—
617C2×#41—862no—
618C2×#41—864no—
619C2×#41—862no—
620C2×#41—868no—
621C2×#41—868no—
622C2×#41—864no—
623C2×#41—8616no—
624C2×#41—8616no—
625C2×#41—864no—
626C2×#41C22×D4314yescomplemented
627C22×Q8—431no—
628C22×Q8—438no—
629C22×Q8—434no—
630C22×Q8—434no—
631C22×Q8—431no—
632C22×Q8—431no—
633C22×Q8—434no—
634C22×Q8—861no—
635C22×Q8—861no—
636C22×Q8—864no—
637C22×Q8—864no—
638C22×Q8—868no—
639C22×Q8—8616no—
640C22×Q8—862no—
641C22×Q8—864no—
642C22×Q8—862no—
643C22×Q8—864no—
644C22×Q8—864no—
645C22×Q8—861no—
646C22×Q8—862no—
647C22×Q8C22×D4311yescharacteristic
648C22×D4—21no—
649C22×D4—21no—
650C22×D4—431no—
651C22×D4—431no—
652C22×D4—434no—
653C22×D4—431no—
654C22×D4—431no—
655C22×D4—861no—
656C22×D4—864no—
657C22×D4—864no—
658C22×D4—862no—
659C22×D4—861no—
660C22×D4—861no—
661C22×D4—861no—
662C22×D4—861no—
663C22×D4—861no—
664C22×D4C22×D4311yescharacteristic
665C22×D4C22×D4311yescharacteristic
666C23×C4—21no—
667C23×C4—431no—
668C23×C4—431no—
669C23×C4—861no—
670C23×C4—861no—
671C23×C4—861no—
672C23×C4—861no—
673C23×C4—861no—
674C23×C4C22×D4311yescharacteristic
675AGL(1,ℤ/8)—8632no—
676C2×SD16—24no—
677C2×SD16—434no—
678C2×SD16—434no—
679C2×SD16—434no—
680C2×SD16—434no—
681C2×SD16—434no—
682C2×SD16—864no—
683C2×SD16—864no—
684C2×SD16—8632no—
685C2×SD16—864no—
686C2×SD16—864no—
687C2×SD16—864no—
688C2×SD16C22×D4314yes—
689C2×D8—24no—
690C2×D8—434no—
691C2×D8—864no—
692C2×D8C22×D4314yes—
693C2×M16—434no—
694C2×M16—864no—
695C22×C8—431no—
696C22×C8—431no—
697C22×C8—434no—
698C22×C8—864no—
699C22×C8C22×D4311yescharacteristic
700C22×C8C22×D4311yescharacteristic
701#127—868no—
702#124—868no—
703#121—22no—
704#121—434no—
705#121—434no—
706#121—434no—
707#121—862no—
708#121—862no—
709#121—862no—
710#121C22×D4314yes—
711#120—868no—
712#120—868no—
713#117—434no—
714#117—862no—
715C2×C4⋊C4—431no—
716C2×C4⋊C4C22×D4311yescharacteristic
717C2×C22⋊C4—21no—
718C2×C22⋊C4—861no—
719C2×C22⋊C4—861no—
720C2×C22⋊C4—861no—
721C2×C22⋊C4—861no—
722C2×C42—861no—
723#103—434no—
724#103—434no—
725#103—434no—
726#103—434no—
727#103—434no—
728#103C22×D4314yescomplemented
729#102—434no—
730#102C22×D4314yescomplemented
731C22⋊C8—434no—
732C22⋊C8—434no—
733C22⋊C8—434no—
734C22⋊C8C22×D4314yescomplemented
735C24—21no—
736C24—21no—
737C24—431no—
738C24—431no—
739C24—864no—
740C24—861no—
741C24—3442no—
742C24—3442no—
743C24—1724no—
744C24D4×D4311yescharacteristic
745#41—216no—
746#41—28no—
747#41—28no—
748#41—4316no—
749#41—8616no—
750#41—868no—
751#41—868no—
752#41—8664no—
753#41—8616no—
754#41—868no—
755#41—868no—
756#41—8664no—
757#41—8664no—
758#41—8616no—
759#41—868no—
760C2×Q8—22no—
761C2×Q8—21no—
762C2×Q8—434no—
763C2×Q8—4316no—
764C2×Q8—434no—
765C2×Q8—434no—
766C2×Q8—432no—
767C2×Q8—432no—
768C2×Q8—864no—
769C2×Q8—868no—
770C2×Q8—864no—
771C2×Q8—864no—
772C2×Q8—868no—
773C2×Q8—868no—
774C2×Q8—868no—
775C2×Q8—868no—
776C2×Q8—8664no—
777C2×Q8—8616no—
778C2×Q8—8616no—
779C2×Q8—868no—
780C2×Q8—868no—
781C2×Q8—8616no—
782C2×Q8—868no—
783C2×Q8—862no—
784C2×Q8—862no—
785C2×Q8—864no—
786C2×Q8—861no—
787C2×Q8—861no—
788C2×Q8D4×D4314yes—
789C2×Q8C23×D4312yes—
790C2×D4—28no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—21no—
798C2×D4—82no—
799C2×D4—434no—
800C2×D4—434no—
801C2×D4—434no—
802C2×D4—432no—
803C2×D4—864no—
804C2×D4—864no—
805C2×D4—868no—
806C2×D4—868no—
807C2×D4—864no—
808C2×D4—864no—
809C2×D4—864no—
810C2×D4—868no—
811C2×D4—864no—
812C2×D4—864no—
813C2×D4—868no—
814C2×D4—864no—
815C2×D4—864no—
816C2×D4—862no—
817C2×D4—862no—
818C2×D4—861no—
819C2×D4—3442no—
820C2×D4—3442no—
821C2×D4—3442no—
822C2×D4—1728no—
823C2×D4—1724no—
824C2×D4D4×D4314yes—
825C2×D4C23×D4312yes—
826C2×D4C23×D4312yes—
827C22×C4—28no—
828C22×C4—21no—
829C22×C4—24no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—431no—
834C22×C4—432no—
835C22×C4—434no—
836C22×C4—434no—
837C22×C4—432no—
838C22×C4—431no—
839C22×C4—432no—
840C22×C4—432no—
841C22×C4—868no—
842C22×C4—864no—
843C22×C4—864no—
844C22×C4—868no—
845C22×C4—868no—
846C22×C4—864no—
847C22×C4—864no—
848C22×C4—868no—
849C22×C4—868no—
850C22×C4—864no—
851C22×C4—861no—
852C22×C4—861no—
853C22×C4—862no—
854C22×C4—862no—
855C22×C4—861no—
856C22×C4D4×D4312yes—
857C22×C4D4×D4311yescharacteristic
858C22×C4C23×D4312yes—
859C22×C4C23×D4311yescharacteristic
860SD16—28no—
861SD16—868no—
862SD16—868no—
863SD16—868no—
864SD16—868no—
865SD16—868no—
866D8—28no—
867D8—868no—
868M16—868no—
869C2×C8—22no—
870C2×C8—22no—
871C2×C8—432no—
872C2×C8—432no—
873C2×C8—868no—
874C2×C8—862no—
875C2×C8—862no—
876C2×C8C23×D4312yes—
877C2×C8C23×D4312yes—
878C4⋊C4—21no—
879C4⋊C4—432no—
880C4⋊C4—861no—
881C4⋊C4C23×D4312yes—
882C22⋊C4—24no—
883C22⋊C4—864no—
884C22⋊C4—864no—
885C22⋊C4—864no—
886C22⋊C4—864no—
887C42—864no—
888C23—22no—
889C23—24no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—434no—
900C23—432no—
901C23—432no—
902C23—862no—
903C23—862no—
904C23—862no—
905C23—862no—
906C23—862no—
907C23—862no—
908C23—3444no—
909C23—3444no—
910C23—34416no—
911C23—1728no—
912C23—1722no—
913C23—1722no—
914C23—1722no—
915C23C2×D4×D4312yes—
916C23C2×D4×D4311yescharacteristic
917Q8—24no—
918Q8—22no—
919Q8—434no—
920Q8—434no—
921Q8—868no—
922Q8—8616no—
923Q8—8616no—
924Q8—8616no—
925Q8—864no—
926Q8—864no—
927Q8—862no—
928Q8—862no—
929Q8C2×D4×D4314yes—
930D4—216no—
931D4—24no—
932D4—22no—
933D4—22no—
934D4—22no—
935D4—42no—
936D4—84no—
937D4—868no—
938D4—868no—
939D4—868no—
940D4—8616no—
941D4—8616no—
942D4—862no—
943D4—862no—
944D4—3444no—
945D4—3444no—
946D4—3444no—
947D4—1728no—
948D4—1722no—
949D4C2×D4×D4314yes—
950C2×C4—216no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—42no—
959C2×C4—434no—
960C2×C4—432no—
961C2×C4—438no—
962C2×C4—434no—
963C2×C4—434no—
964C2×C4—432no—
965C2×C4—8616no—
966C2×C4—8616no—
967C2×C4—8616no—
968C2×C4—8616no—
969C2×C4—8616no—
970C2×C4—862no—
971C2×C4—864no—
972C2×C4—864no—
973C2×C4—862no—
974C2×C4—862no—
975C2×C4—864no—
976C2×C4—862no—
977C2×C4—862no—
978C2×C4—862no—
979C2×C4—1722no—
980C2×C4C2×D4×D4312yes—
981C2×C4C2×D4×D4311yescharacteristic
982C2×C4C2×D4×D4312yes—
983C2×C4C2×D4×D4312yes—
984C2×C4C24×D4311yescharacteristic
985C8—22no—
986C8—22no—
987C8—862no—
988C8—862no—
989C22—22no—
990C22—24no—
991C22—22no—
992C22—22no—
993C22—42no—
994C22—42no—
995C22—44no—
996C22—48no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22—84no—
1001C22—434no—
1002C22—862no—
1003C22—862no—
1004C22—868no—
1005C22—862no—
1006C22—862no—
1007C22—862no—
1008C22—34416no—
1009C22—3444no—
1010C22—1722no—
1011C22—1722no—
1012C22—1722no—
1013C22—1724no—
1014C22#120×D4312yes—
1015C22#1458370612yes—
1016C22#1458370912yes—
1017C22C22×D4×D4311yescharacteristic
1018C4—22no—
1019C4—24no—
1020C4—42no—
1021C4—434no—
1022C4—862no—
1023C4—864no—
1024C4—864no—
1025C4—1722no—
1026C4#120×D4312yes—
1027C4C22×D4×D4311yescharacteristic
1028C4C22×D4×D4311yescharacteristic
1029C2—42no—
1030C2—44no—
1031C2—82no—
1032C2—864no—
1033C2—3442no—
1034C2—1722no—
1035C2#1914387814yesdirect product factor
1036C2C2×#120×D4311yescharacteristic
1037C2C2×#1458370611yescharacteristic
1038C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#449C2
socleC23×C43C22×D4
hypercenterC2×#449D43
hypocenterC43C2×#3010
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C22×#13063372C2semidirect
2. C22×#13063349C2semidirect
3. C22×SD16×D43C2semidirect
4. C2×#14583465C2semidirect
5. #19143878C2direct (N × H)
6. C2×#14583045C2semidirect
7. C2×#14583044C2semidirect
8. C2×#14583041C2semidirect
9. C2×#14583040C2semidirect
10. C2×#14583039C2semidirect
11. C2×#14583037C2semidirect
12. C2×#14583036C2semidirect
13. C2×#14582906C2semidirect
14. C2×#14582892C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#449C2semidirect
20. C2×#13063372C22semidirect
26. C22×#10621900C22semidirect
28. C23×Dic86C22semidirect
30. C22×Q8×D43C22semidirect
33. C2×#13063349C22semidirect
40. C2×SD16×D43C22semidirect
45. #14583465C22semidirect
54. #14583045C22semidirect
55. #14583044C22semidirect
56. #14583041C22semidirect
57. #14583040C22semidirect
58. #14583039C22semidirect
59. #14583037C22semidirect
60. #14583036C22semidirect
61. #14582906C22semidirect
62. #14582892C22semidirect
63. C2×#13063250C22semidirect
64. C2×#13063250C22semidirect
65. C2×#13063249C22semidirect
66. C2×#13063248C22semidirect
67. C2×#13063248C22semidirect
68. C2×#13063246C22semidirect
69. #14582864C22semidirect
70. C2×C22⋊(C43⋊C8)C22semidirect
71. C2×(C2×D43)⋊C8C22semidirect
72. C2×(C2×D43)⋊C8C22semidirect
73. C22×#41×C43C22semidirect
77. C43×#449C22semidirect
78. C2×#103×C43C22semidirect
79. C2×#102×C43C22semidirect
80. C2×C22⋊C8×C43C22semidirect
100. C2×#10621900D4semidirect
102. C2×#10621900C23semidirect
114. C22×Dic86C23semidirect
120. C2×Q8×D43D4semidirect
122. C2×Q8×D43C23semidirect
182. #13063250C23semidirect
183. #13063250C23semidirect
184. #13063249C23semidirect
185. #13063248C23semidirect
186. #13063248C23semidirect
187. #13063246C23semidirect
188. C22⋊(C43⋊C8)C23semidirect
189. (C2×D43)⋊C8C23semidirect
190. (C2×D43)⋊C8C23semidirect
194. C2×#41×C43C23semidirect
212. #103×C43C23semidirect
213. #102×C43C23semidirect
214. C22⋊C8×C43C23semidirect
284. Q8×D43C2×D4semidirect
292. #10621900C2×D4semidirect
518. C2×#449D43semidirect
529. C2×C43#3010semidirect
546. C22×#41C2×D43semidirect
580. #449C2×D43semidirect
592. C2×#103C2×D43semidirect
594. C2×#102C2×D43semidirect
599. C2×C22⋊C8C2×D43semidirect
600. C43C2×#3010semidirect
626. C2×#41C22×D43semidirect
728. #103C22×D43semidirect
730. #102C22×D43semidirect
734. C22⋊C8C22×D43semidirect
1035. C2#19143878direct (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×#130633492
C22×SD16×D432
C2×#145834652
#191438782
C2×#145830452
C2×#145830442
C2×#145830412
C2×#145830402
C2×#145830392
C2×#145830372
C2×#145830362
C2×#145829062
C2×#145828922
C2×#145828642
C2×C43×#4492
C2×#301043