Finite Group Databasebeta

← C2×#19143914 #25963057

Subgroups — C2×#19143914 #25963057

Order 11008.

4782 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063372C211yesmaximal, characteristic, complemented
2C22×#13063357C211yesmaximal, characteristic, complemented
3C22×#13063346C211yesmaximal, characteristic, complemented
4C2×#14583479C211yesmaximal, characteristic, complemented
5#19143914C2116yesmaximal, direct product factor
6C2×#14583058C211yesmaximal, characteristic, complemented
7C2×#14583045C211yesmaximal, characteristic, complemented
8C2×#14583044C211yesmaximal, characteristic, complemented
9C2×#14583054C211yesmaximal, characteristic, complemented
10C2×#14583053C211yesmaximal, characteristic, complemented
11C2×#14583040C211yesmaximal, characteristic, complemented
12C2×#14583039C211yesmaximal, characteristic, complemented
13C2×#14582897C211yesmaximal, characteristic, complemented
14C2×#103×D43C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#452C211yesmaximal, characteristic, complemented
17C2×#13063372—24no—
18C2×#13063372—28no—
19C2×#13063372—28no—
20C2×#13063372C2218yescomplemented
21C22×#10621902C2211yescharacteristic
22C22×#10621898—21no—
23C22×#10621898C2211yescharacteristic
24C22×#10621900—21no—
25C22×#10621900—21no—
26C22×#10621900C2211yescharacteristic
27C22×#10621900C2211yescharacteristic
28C23×Dic86—21no—
29C23×Dic86C2211yescharacteristic
30C22×Q8×D43C2211yescharacteristic
31C22×Q8×D43C2211yescharacteristic
32C2×#13063357—28no—
33C2×#13063357C2218yescomplemented
34C2×#13063346—28no—
35C2×#13063346C2218yescomplemented
36C22×#10621885C2211yescharacteristic
37C22×#10621885C2211yescharacteristic
38C22×#10621873C2211yescharacteristic
39C22×#10621873C2211yescharacteristic
40C22×#10621884C2211yescharacteristic
41C22×#10621882C2211yescharacteristic
42C22×#10621872C2211yescharacteristic
43C22×C8×D43C2211yescharacteristic
44#14583479—24no—
45#14583479C2218yescomplemented
46C2×#13063303—21no—
47C2×#13063301C2211yescharacteristic
48C2×#13063300—21no—
49C2×#13063300C2211yescharacteristic
50C2×#13063299C2211yescharacteristic
51C2×#13063298—21no—
52C2×#13063298—21no—
53C2×C4⋊C4×D43C2211yescharacteristic
54#14583058C2218yescomplemented
55#14583054C2218yescomplemented
56#14583053C2218yescomplemented
57#14583045C2218yescomplemented
58#14583044C2218yescomplemented
59#14583040C2218yescomplemented
60#14583039C2218yescomplemented
61#14582897C2218yescomplemented
62C2×#13063250C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063249C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×#13063248C2211yescharacteristic
67#103×D43C2218yescomplemented
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×#10621902—22no—
85C2×#10621902—24no—
86C2×#10621902—24no—
87C2×#10621902C2314yes—
88C2×#10621898—216no—
89C2×#10621898—28no—
90C2×#10621898—24no—
91C2×#10621898—24no—
92C2×#10621898D414yes—
93C2×#10621898C2314yes—
94C2×#10621900—216no—
95C2×#10621900—216no—
96C2×#10621900—24no—
97C2×#10621900—28no—
98C2×#10621900—28no—
99C2×#10621900—24no—
100C2×#10621900—22no—
101C2×#10621900—22no—
102C2×#10621900—24no—
103C2×#10621900D418yescomplemented
104C2×#10621900C2314yes—
105C2×#10621900C2314yes—
106C22×Dic86—216no—
107C22×Dic86—21no—
108C22×Dic86—22no—
109C22×Dic86—21no—
110C22×Dic86—21no—
111C22×Dic86—28no—
112C22×Dic86—24no—
113C22×Dic86—24no—
114C22×Dic86D411yescharacteristic
115C22×Dic86C2314yes—
116C22×Dic86C2311yescharacteristic
117C22×Dic86C2311yescharacteristic
118C2×Q8×D43—24no—
119C2×Q8×D43—24no—
120C2×Q8×D43—22no—
121C2×Q8×D43—22no—
122C2×Q8×D43—24no—
123C2×Q8×D43D418yescomplemented
124C2×Q8×D43C2314yes—
125C2×Q8×D43C2314yes—
126C22×D172—21no—
127C22×D172—21no—
128C22×D172D411yescharacteristic
129C22×D172C2311yescharacteristic
130C22×C22⋊D43—21no—
131C22×C22⋊D43—21no—
132C22×C22⋊D43—21no—
133C22×C22⋊D43D411yescharacteristic
134C22×C22⋊D43D411yescharacteristic
135C23×Dic43—21no—
136C23×Dic43—21no—
137C23×Dic43—21no—
138C22×C4×D43—21no—
139C22×C4×D43—21no—
140C22×C4×D43—21no—
141C22×C4×D43—21no—
142C22×C4×D43C2311yescharacteristic
143C22×C4×D43C2311yescharacteristic
144#13063357—232no—
145#13063346—232no—
146C2×#10621885—24no—
147C2×#10621885—24no—
148C2×#10621885C2314yes—
149C2×#10621885C2314yes—
150C2×#10621873—24no—
151C2×#10621873—24no—
152C2×#10621873C2314yes—
153C2×#10621873C2314yes—
154C2×#10621884—24no—
155C2×#10621884C2314yes—
156C2×#10621882—24no—
157C2×#10621882C2314yes—
158C2×#10621872—24no—
159C2×#10621872C2314yes—
160C22×C43⋊C8C2311yescharacteristic
161C22×C43⋊C8C2311yescharacteristic
162C2×C8×D43—24no—
163C2×C8×D43C2314yes—
164#13063303—28no—
165#13063301—22no—
166#13063301C2314yes—
167#13063300—28no—
168#13063300—22no—
169#13063300C2314yes—
170#13063299—22no—
171#13063299C2314yes—
172#13063298—28no—
173#13063298—28no—
174C2×C4⋊Dic43C2311yescharacteristic
175C2×Dic43⋊C4—21no—
176C2×Dic43⋊C4—21no—
177C4⋊C4×D43—22no—
178C4⋊C4×D43C2314yes—
179C2×(C2×D43)⋊C4—21no—
180C2×(C2×D43)⋊C4—21no—
181C2×(C2×D43)⋊C4—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×D43—21no—
218C23×D43C2×D411yescharacteristic
219C23×D43C2×D411yescharacteristic
220#41×C43—216no—
221#41×C43—28no—
222#41×C43—28no—
223C2×Q8×C43—22no—
224C2×Q8×C43—21no—
225C2×Q8×C43—21no—
226C2×Q8×C43—22no—
227C2×Q8×C43—22no—
228C2×Q8×C43C2×D414yes—
229C2×Q8×C43C2412yes—
230C2×Q8×C43C2412yes—
231C2×D4×C43—28no—
232C2×D4×C43—22no—
233C2×D4×C43—21no—
234C2×D4×C43—24no—
235C2×D4×C43C2×D414yes—
236C2×D4×C43C2412yes—
237C22×C4×C43—28no—
238C22×C4×C43—24no—
239C22×C4×C43—22no—
240C22×C4×C43—22no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43C2×D411yescharacteristic
245C22×C4×C43C2×D412yes—
246C22×C4×C43C2412yes—
247C22×C4×C43C2411yescharacteristic
248C2×C22⋊D43—28no—
249C2×C22⋊D43—24no—
250C2×C22⋊D43—24no—
251C2×C22⋊D43—28no—
252C2×C22⋊D43—24no—
253C2×C22⋊D43—24no—
254C2×C22⋊D43—24no—
255C2×C22⋊D43—82no—
256C2×C22⋊D43C2×D414yes—
257C2×C22⋊D43C2×D414yes—
258C22×Dic43—28no—
259C22×Dic43—28no—
260C22×Dic43—28no—
261C22×Dic43—24no—
262C22×Dic43—24no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—24no—
266C22×Dic43—21no—
267C22×Dic43C2×D411yescharacteristic
268C22×Dic43C2×D411yescharacteristic
269#10621902—28no—
270#10621902—28no—
271#10621902—48no—
272Q8×D43—216no—
273Q8×D43—28no—
274Q8×D43—216no—
275Q8×D43—28no—
276Q8×D43—28no—
277Q8×D43C2×D4116yescomplemented
278#10621900—264no—
279#10621900—216no—
280#10621900—264no—
281#10621900—28no—
282#10621900—216no—
283#10621900—28no—
284#10621900—28no—
285#10621900C2×D4116yescomplemented
286#10621898—264no—
287#10621898—216no—
288#10621898—28no—
289#10621898—28no—
290C2×D172—21no—
291C2×D172—24no—
292C2×D172—24no—
293C2×D172—24no—
294C2×D172—22no—
295C2×D172—22no—
296C2×D172—44no—
297C2×D172—82no—
298C2×D172C2×D414yes—
299C2×D172C2412yes—
300C2×C4×D43—28no—
301C2×C4×D43—22no—
302C2×C4×D43—22no—
303C2×C4×D43—24no—
304C2×C4×D43—28no—
305C2×C4×D43—24no—
306C2×C4×D43—24no—
307C2×C4×D43—24no—
308C2×C4×D43—44no—
309C2×C4×D43—82no—
310C2×C4×D43C2×D414yes—
311C2×C4×D43C2×D414yes—
312C2×C4×D43C2×D412yes—
313C2×C4×D43C2×D412yes—
314C2×C4×D43C2412yes—
315C2×C4×D43C2412yes—
316C2×Dic86—28no—
317C2×Dic86—28no—
318C2×Dic86—216no—
319C2×Dic86—264no—
320C2×Dic86—21no—
321C2×Dic86—21no—
322C2×Dic86—22no—
323C2×Dic86—22no—
324C2×Dic86—24no—
325C2×Dic86—28no—
326C2×Dic86—24no—
327C2×Dic86—24no—
328C2×Dic86—24no—
329C2×Dic86—28no—
330C2×Dic86—28no—
331C2×Dic86C2×D414yes—
332C2×Dic86C2×D414yes—
333C2×Dic86C2×D414yes—
334C2×Dic86C2412yes—
335C2×Dic86C2412yes—
336Q16×C43—28no—
337SD16×C43—28no—
338C2×C8×C43—22no—
339C2×C8×C43—22no—
340C2×C8×C43C2412yes—
341C2×C8×C43C2412yes—
342C4⋊C4×C43—24no—
343C4⋊C4×C43—21no—
344C4⋊C4×C43C2412yes—
345C22⋊C4×C43—24no—
346#10621885—28no—
347#10621885—28no—
348#10621884—28no—
349#10621882—28no—
350(C2×D43)⋊C4—24no—
351(C2×D43)⋊C4—24no—
352(C2×D43)⋊C4—24no—
353C4⋊Dic43—21no—
354C4⋊Dic43C2412yes—
355Dic43⋊C4—24no—
356Dic43⋊C4—24no—
357C2×C43⋊C8—22no—
358C2×C43⋊C8—22no—
359C2×C43⋊C8C2412yes—
360C2×C43⋊C8C2412yes—
361#10621873—28no—
362#10621873—28no—
363#10621872—28no—
364C8×D43—28no—
365C23×C43—22no—
366C23×C43—24no—
367C23×C43—22no—
368C23×C43—22no—
369C23×C43—22no—
370C23×C43—42no—
371C23×C43—42no—
372C23×C43C22×D412yes—
373C23×C43C22×D411yescharacteristic
374C22×D43—22no—
375C22×D43—22no—
376C22×D43—22no—
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—22no—
380C22×D43—42no—
381C22×D43—42no—
382C22×D43—42no—
383C22×D43#12014yes—
384C22×D43C22×D412yes—
385C22×D43C22×D412yes—
386Q8×C43—24no—
387Q8×C43—22no—
388Q8×C43—22no—
389Q8×C43—22no—
390Q8×C43—42no—
391Q8×C43C22×D414yes—
392D4×C43—216no—
393D4×C43—24no—
394D4×C43—22no—
395D4×C43C22×D414yes—
396C2×C4×C43—216no—
397C2×C4×C43—22no—
398C2×C4×C43—24no—
399C2×C4×C43—22no—
400C2×C4×C43—24no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—42no—
406C2×C4×C43—42no—
407C2×C4×C43C22×D412yes—
408C2×C4×C43C22×D411yescharacteristic
409C2×C4×C43C22×D412yes—
410C2×C4×C43C22×D412yes—
411C2×C4×C43C2511yescharacteristic
412C22⋊D43—216no—
413C22⋊D43—28no—
414C22⋊D43—216no—
415C22⋊D43—28no—
416C22⋊D43—84no—
417C2×Dic43—216no—
418C2×Dic43—216no—
419C2×Dic43—22no—
420C2×Dic43—24no—
421C2×Dic43—24no—
422C2×Dic43—22no—
423C2×Dic43—22no—
424C2×Dic43—216no—
425C2×Dic43—22no—
426C2×Dic43—42no—
427C2×Dic43#12014yes—
428C2×Dic43C22×D412yes—
429C2×Dic43C22×D412yes—
430D172—28no—
431D172—22no—
432D172—22no—
433D172—48no—
434D172—42no—
435D172—84no—
436C4×D43—216no—
437C4×D43—216no—
438C4×D43—24no—
439C4×D43—22no—
440C4×D43—22no—
441C4×D43—48no—
442C4×D43—84no—
443C4×D43#12018yes—
444C4×D43C22×D414yes—
445C4×D43C22×D414yes—
446Dic86—216no—
447Dic86—216no—
448Dic86—24no—
449Dic86—24no—
450Dic86—22no—
451Dic86—22no—
452Dic86—28no—
453Dic86—216no—
454Dic86C22×D414yes—
455Dic86C22×D414yes—
456C8×C43—22no—
457C8×C43—22no—
458C43⋊C8—22no—
459C43⋊C8—22no—
460C2×#3013—431nomaximal, Sylow
461C22×C43—24no—
462C22×C43—22no—
463C22×C43—22no—
464C22×C43—22no—
465C22×C43—44no—
466C22×C43—48no—
467C22×C43—42no—
468C22×C43—42no—
469C22×C43C2×#12012yes—
470C22×C43#57712yes—
471C22×C43#57812yes—
472C22×C43C23×D411yescharacteristic
473C2×D43—28no—
474C2×D43—22no—
475C2×D43—22no—
476C2×D43—22no—
477C2×D43—22no—
478C2×D43—22no—
479C2×D43—44no—
480C2×D43—42no—
481C2×D43—42no—
482C2×D43—42no—
483C2×D43—84no—
484C2×D43C2×#12014yes—
485C4×C43—22no—
486C4×C43—24no—
487C4×C43—42no—
488C4×C43—42no—
489C4×C43C2×#12012yes—
490C4×C43C23×D411yescharacteristic
491C4×C43C23×D411yescharacteristic
492Dic43—22no—
493Dic43—24no—
494Dic43—24no—
495Dic43—42no—
496Dic43C2×#12014yes—
497C22×2−1+4—431no—
498C22×#137—431no—
499C22×#135—431no—
500C2×#537—431no—
501#3013—4316no—
502C2×#452—431no—
503C2×#452D4311yescharacteristic, complemented
504C2×#449—431no—
505C2×#449—431no—
506C2×#451—431no—
507C2×#451—431no—
508C2×#448—431no—
509C2×#448—431no—
510C2×#417—431no—
511C22×#103—431no—
512C2×#408—431no—
513C2×C43—42no—
514C2×C43—44no—
515C2×C43#301314yescomplemented
516C2×C43C22×#12011yescharacteristic
517C2×C43C2×#57711yescharacteristic
518C2×C43C2×#57811yescharacteristic
519D43—24no—
520D43—42no—
521D43—82no—
522C2×2−1+4—438no—
523C2×2−1+4—868no—
524C2×2−1+4—868no—
525C2×2−1+4—864no—
526C22×#41—431no—
527C22×#41—431no—
528C22×#41—431no—
529C22×#41—431no—
530C22×#41—861no—
531C22×#41—861no—
532C22×#41—861no—
533C22×#41C2×D4311yescharacteristic
534C23×Q8—431no—
535C23×Q8—431no—
536C23×Q8—431no—
537C23×Q8—861no—
538C2×#137—438no—
539C2×#137—868no—
540C2×#135—438no—
541C2×#135—868no—
542C22×Q16—431no—
543C22×Q16—431no—
544C22×Q16C2×D4311yescharacteristic
545C22×SD16—431no—
546C22×SD16—431no—
547C22×SD16—431no—
548C22×SD16C2×D4311yescharacteristic
549C22×D8—431no—
550C22×M16—431no—
551C23×C8—431no—
552#537—438no—
553#537—864no—
554C2×C22⋊Q8—431no—
555C2×C22⋊Q8—861no—
556C2×C22⋊Q8C2×D4311yescharacteristic
557C2×#121—431no—
558C2×#121—431no—
559C2×#121—861no—
560C2×#121—861no—
561C2×#121—861no—
562C22×C4⋊C4—431no—
563#452—438no—
564#452C2×D4318yescomplemented
565#451—438no—
566#451—438no—
567#449—438no—
568#449—438no—
569#448—438no—
570#448—438no—
571#417—438no—
572C2×#103—431no—
573C2×#103—431no—
574C2×#103—431no—
575C2×#103—431no—
576C2×#103—431no—
577C2×#103—438no—
578C2×#103C2×D4311yescharacteristic
579C2×#102—431no—
580C2×#102C2×D4311yescharacteristic
581#408—438no—
582C2×C22⋊C8—431no—
583C2×C22⋊C8—431no—
584C2×C22⋊C8—431no—
585C2×C22⋊C8C2×D4311yescharacteristic
586C43C2×#301311yescharacteristic, complemented, Sylow
5872−1+4—8632no—
5882−1+4—8632no—
5892−1+4—8664no—
590C2×#41—24no—
591C2×#41—24no—
592C2×#41—22no—
593C2×#41—434no—
594C2×#41—434no—
595C2×#41—434no—
596C2×#41—438no—
597C2×#41—434no—
598C2×#41—434no—
599C2×#41—864no—
600C2×#41—864no—
601C2×#41—868no—
602C2×#41—8616no—
603C2×#41—862no—
604C2×#41—864no—
605C2×#41—862no—
606C2×#41—862no—
607C2×#41—864no—
608C2×#41—864no—
609C2×#41—868no—
610C2×#41—868no—
611C2×#41—864no—
612C2×#41—8616no—
613C2×#41—8616no—
614C2×#41—864no—
615C2×#41C22×D4314yes—
616C22×Q8—431no—
617C22×Q8—438no—
618C22×Q8—434no—
619C22×Q8—434no—
620C22×Q8—431no—
621C22×Q8—431no—
622C22×Q8—434no—
623C22×Q8—861no—
624C22×Q8—861no—
625C22×Q8—864no—
626C22×Q8—864no—
627C22×Q8—868no—
628C22×Q8—8616no—
629C22×Q8—862no—
630C22×Q8—864no—
631C22×Q8—862no—
632C22×Q8—864no—
633C22×Q8—864no—
634C22×Q8—861no—
635C22×Q8—862no—
636C22×Q8C22×D4311yescharacteristic
637C22×Q8C22×D4311yescharacteristic
638C22×D4—21no—
639C22×D4—431no—
640C22×D4—431no—
641C22×D4—431no—
642C22×D4—431no—
643C22×D4—861no—
644C22×D4—861no—
645C22×D4—861no—
646C22×D4—861no—
647C22×D4—861no—
648C22×D4C22×D4311yescharacteristic
649C23×C4—21no—
650C23×C4—431no—
651C23×C4—431no—
652C23×C4—861no—
653C23×C4—861no—
654C23×C4—861no—
655C23×C4—861no—
656C23×C4—861no—
657C23×C4—861no—
658C23×C4—861no—
659C23×C4C22×D4311yescharacteristic
660#137—8632no—
661#135—8632no—
662C2×Q16—24no—
663C2×Q16—434no—
664C2×Q16—434no—
665C2×Q16—864no—
666C2×Q16—864no—
667C2×Q16C22×D4314yes—
668C2×SD16—24no—
669C2×SD16—434no—
670C2×SD16—434no—
671C2×SD16—434no—
672C2×SD16—864no—
673C2×SD16—864no—
674C2×SD16—864no—
675C2×SD16C22×D4314yes—
676C2×D8—434no—
677C2×D8—864no—
678C2×M16—434no—
679C2×M16—864no—
680C22×C8—431no—
681C22×C8—431no—
682C22×C8—434no—
683C22×C8—864no—
684C22×C8C22×D4311yescharacteristic
685C22×C8C22×D4311yescharacteristic
686C22⋊Q8—22no—
687C22⋊Q8—434no—
688C22⋊Q8—868no—
689C22⋊Q8—862no—
690C22⋊Q8C22×D4314yes—
691#121—434no—
692#121—434no—
693#121—868no—
694#121—868no—
695#121—862no—
696#121—868no—
697#121—862no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—431no—
700C2×C4⋊C4—434no—
701C2×C4⋊C4—862no—
702C2×C4⋊C4—861no—
703C2×C4⋊C4—861no—
704C2×C4⋊C4C22×D4311yescharacteristic
705C2×C22⋊C4—21no—
706C2×C22⋊C4—861no—
707C2×C22⋊C4—861no—
708C2×C22⋊C4—861no—
709#103—434no—
710#103—434no—
711#103—434no—
712#103—434no—
713#103—434no—
714#103C22×D4314yes—
715#102—434no—
716#102C22×D4314yes—
717C22⋊C8—434no—
718C22⋊C8—434no—
719C22⋊C8—434no—
720C22⋊C8C22×D4314yes—
721C24—21no—
722C24—431no—
723C24—431no—
724C24—861no—
725C24D4×D4311yescharacteristic
726#41—216no—
727#41—28no—
728#41—28no—
729#41—4316no—
730#41—8616no—
731#41—868no—
732#41—868no—
733#41—8664no—
734#41—8616no—
735#41—868no—
736#41—868no—
737#41—868no—
738#41—868no—
739#41—8664no—
740#41—8664no—
741#41—8616no—
742#41—868no—
743#41—1728no—
744C2×Q8—22no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—22no—
748C2×Q8—22no—
749C2×Q8—434no—
750C2×Q8—4316no—
751C2×Q8—434no—
752C2×Q8—434no—
753C2×Q8—432no—
754C2×Q8—432no—
755C2×Q8—864no—
756C2×Q8—868no—
757C2×Q8—864no—
758C2×Q8—864no—
759C2×Q8—868no—
760C2×Q8—868no—
761C2×Q8—868no—
762C2×Q8—868no—
763C2×Q8—8664no—
764C2×Q8—8616no—
765C2×Q8—8616no—
766C2×Q8—868no—
767C2×Q8—868no—
768C2×Q8—8616no—
769C2×Q8—868no—
770C2×Q8—862no—
771C2×Q8—862no—
772C2×Q8—864no—
773C2×Q8—861no—
774C2×Q8—861no—
775C2×Q8D4×D4314yes—
776C2×Q8C23×D4312yes—
777C2×Q8C23×D4312yes—
778C2×D4—28no—
779C2×D4—24no—
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—434no—
783C2×D4—434no—
784C2×D4—434no—
785C2×D4—432no—
786C2×D4—864no—
787C2×D4—864no—
788C2×D4—864no—
789C2×D4—864no—
790C2×D4—864no—
791C2×D4—868no—
792C2×D4—864no—
793C2×D4—864no—
794C2×D4—868no—
795C2×D4—864no—
796C2×D4—862no—
797C2×D4—862no—
798C2×D4—861no—
799C2×D4—3442no—
800C2×D4—3442no—
801C2×D4—1724no—
802C2×D4D4×D4314yes—
803C2×D4C23×D4312yes—
804C22×C4—28no—
805C22×C4—21no—
806C22×C4—24no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—431no—
812C22×C4—432no—
813C22×C4—434no—
814C22×C4—434no—
815C22×C4—432no—
816C22×C4—431no—
817C22×C4—432no—
818C22×C4—432no—
819C22×C4—864no—
820C22×C4—868no—
821C22×C4—864no—
822C22×C4—864no—
823C22×C4—868no—
824C22×C4—864no—
825C22×C4—868no—
826C22×C4—864no—
827C22×C4—864no—
828C22×C4—868no—
829C22×C4—868no—
830C22×C4—864no—
831C22×C4—861no—
832C22×C4—861no—
833C22×C4—862no—
834C22×C4—862no—
835C22×C4—861no—
836C22×C4—3442no—
837C22×C4—1724no—
838C22×C4D4×D4312yes—
839C22×C4D4×D4311yescharacteristic
840C22×C4C23×D4312yes—
841C22×C4C23×D4311yescharacteristic
842Q16—28no—
843Q16—868no—
844Q16—868no—
845SD16—28no—
846SD16—868no—
847SD16—868no—
848SD16—868no—
849D8—868no—
850M16—868no—
851C2×C8—22no—
852C2×C8—22no—
853C2×C8—432no—
854C2×C8—432no—
855C2×C8—868no—
856C2×C8—862no—
857C2×C8—862no—
858C2×C8C23×D4312yes—
859C2×C8C23×D4312yes—
860C4⋊C4—24no—
861C4⋊C4—21no—
862C4⋊C4—432no—
863C4⋊C4—864no—
864C4⋊C4—864no—
865C4⋊C4—861no—
866C4⋊C4C23×D4312yes—
867C22⋊C4—24no—
868C22⋊C4—864no—
869C22⋊C4—864no—
870C22⋊C4—864no—
871C23—22no—
872C23—24no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—42no—
877C23—42no—
878C23—434no—
879C23—432no—
880C23—432no—
881C23—862no—
882C23—862no—
883C23—862no—
884C23—862no—
885C23—862no—
886C23—862no—
887C23—1722no—
888C23—1722no—
889C23—1722no—
890C23C2×D4×D4312yes—
891C23C2×D4×D4311yescharacteristic
892Q8—24no—
893Q8—22no—
894Q8—22no—
895Q8—22no—
896Q8—42no—
897Q8—434no—
898Q8—434no—
899Q8—868no—
900Q8—8616no—
901Q8—8616no—
902Q8—8616no—
903Q8—864no—
904Q8—864no—
905Q8—862no—
906Q8—862no—
907Q8C2×D4×D4314yes—
908D4—216no—
909D4—24no—
910D4—22no—
911D4—868no—
912D4—868no—
913D4—868no—
914D4—8616no—
915D4—8616no—
916D4—862no—
917D4—862no—
918D4—3444no—
919D4—3444no—
920D4—1728no—
921D4—1722no—
922D4C2×D4×D4314yes—
923C2×C4—216no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—434no—
935C2×C4—432no—
936C2×C4—438no—
937C2×C4—434no—
938C2×C4—434no—
939C2×C4—432no—
940C2×C4—8616no—
941C2×C4—8616no—
942C2×C4—8616no—
943C2×C4—8616no—
944C2×C4—8616no—
945C2×C4—862no—
946C2×C4—864no—
947C2×C4—864no—
948C2×C4—862no—
949C2×C4—862no—
950C2×C4—864no—
951C2×C4—862no—
952C2×C4—862no—
953C2×C4—862no—
954C2×C4—3444no—
955C2×C4—1728no—
956C2×C4—1722no—
957C2×C4C2×D4×D4312yes—
958C2×C4C2×D4×D4311yescharacteristic
959C2×C4C2×D4×D4312yes—
960C2×C4C2×D4×D4312yes—
961C2×C4C24×D4311yescharacteristic
962C8—22no—
963C8—22no—
964C8—862no—
965C8—862no—
966C22—22no—
967C22—24no—
968C22—22no—
969C22—22no—
970C22—42no—
971C22—42no—
972C22—44no—
973C22—48no—
974C22—434no—
975C22—862no—
976C22—862no—
977C22—868no—
978C22—862no—
979C22—862no—
980C22—862no—
981C22—3444no—
982C22—1722no—
983C22—1722no—
984C22—1722no—
985C22—1724no—
986C22#120×D4312yes—
987C22#1458370612yes—
988C22#1458371512yes—
989C22C22×D4×D4311yescharacteristic
990C4—22no—
991C4—24no—
992C4—42no—
993C4—42no—
994C4—434no—
995C4—862no—
996C4—864no—
997C4—864no—
998C4—1722no—
999C4#120×D4312yes—
1000C4C22×D4×D4311yescharacteristic
1001C4C22×D4×D4311yescharacteristic
1002C2—42no—
1003C2—44no—
1004C2—864no—
1005C2—3442no—
1006C2—1722no—
1007C2#1914391414yesdirect product factor
1008C2C2×#120×D4311yescharacteristic
1009C2C2×#1458370611yescharacteristic
1010C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
hypercenterC2×#452D43
hypocenterC43C2×#3013
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
1. C22×#13063372C2semidirect
2. C22×#13063357C2semidirect
3. C22×#13063346C2semidirect
4. C2×#14583479C2semidirect
5. #19143914C2direct (N × H)
6. C2×#14583058C2semidirect
7. C2×#14583045C2semidirect
8. C2×#14583044C2semidirect
9. C2×#14583054C2semidirect
10. C2×#14583053C2semidirect
11. C2×#14583040C2semidirect
12. C2×#14583039C2semidirect
13. C2×#14582897C2semidirect
14. C2×#103×D43C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#452C2semidirect
20. C2×#13063372C22semidirect
33. C2×#13063357C22semidirect
35. C2×#13063346C22semidirect
45. #14583479C22semidirect
54. #14583058C22semidirect
55. #14583054C22semidirect
56. #14583053C22semidirect
57. #14583045C22semidirect
58. #14583044C22semidirect
59. #14583040C22semidirect
60. #14583039C22semidirect
61. #14582897C22semidirect
67. #103×D43C22semidirect
69. #14582864C22semidirect
77. C43×#452C22semidirect
103. C2×#10621900D4semidirect
123. C2×Q8×D43D4semidirect
277. Q8×D43C2×D4semidirect
285. #10621900C2×D4semidirect
503. C2×#452D43semidirect
515. C2×C43#3013semidirect
564. #452C2×D43semidirect
586. C43C2×#3013semidirect
1007. C2#19143914direct (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×#130633572
C22×#130633462
C2×#145834792
#191439142
C2×#145830582
C2×#145830452
C2×#145830442
C2×#145830542
C2×#145830532
C2×#145830402
C2×#145830392
C2×#145828972
C2×#103×D432
C2×#145828642
C2×C43×#4522
C2×#301343