Finite Group Databasebeta

← #26005146

Subgroups — #26005146

Order 11008.

11346 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583736C211yesmaximal, characteristic, complemented
2C2×#14583734C211yesmaximal, characteristic, complemented
3#19148388C211yesmaximal, characteristic, complemented
4#19148385C213yesmaximal, complemented
5#19148382C213yesmaximal, complemented
6#19148377C213yesmaximal, complemented
7#19148376C211yesmaximal, characteristic, complemented
8#19148370C213yesmaximal, complemented
9#19148369C211yesmaximal, characteristic, complemented
10#19148363C214yesmaximal, complemented
11#19148355C2112yesmaximal, complemented
12#19148084C214yesmaximal, complemented
13#19148079C2112yesmaximal, complemented
14#19147927C213yesmaximal, complemented
15#19147926C213yesmaximal, complemented
16C2×#14583448C213yesmaximal, complemented
17#532×D43C213yesmaximal, complemented
18C4×#41×D43C211yesmaximal, characteristic, complemented
19C43×#3500C211yesmaximal, characteristic, complemented
20#14583736—216no—
21#14583734—216no—
22C2×#13063373C2212yescomplemented
23C2×#13063373C2213yescomplemented
24C2×#13063372C2212yescomplemented
25C2×#13063372C2211yescharacteristic, complemented
26C2×#13063372C2213yescomplemented
27C2×#13063371C2216yescomplemented
28C2×#13063371C2211yescharacteristic, complemented
29C2×#13063371C2213yescomplemented
30C2×#13063370C2216yescomplemented
31C2×#13063370C2213yescomplemented
32C22×#10621902C2212yescomplemented
33C22×#10621902C2213yescomplemented
34C22×#10621900C2216yescomplemented
35C22×#10621900C2213yescomplemented
36C2×#41×D43C2211yescharacteristic
37C2×#41×D43C2216yescomplemented
38C2×#41×D43C2212yescomplemented
39C2×#41×D43C2213yescomplemented
40C2×#41×D43C2213yescomplemented
41#14583568C2214yescomplemented
42#14583567C22112yescomplemented
43Q8×C22⋊D43C2214yescomplemented
44#14583562C22112yescomplemented
45#14583561C2214yescomplemented
46#14583558C22112yescomplemented
47#14583557C22112yescomplemented
48#14583551C22112yescomplemented
49#14583548C22112yescomplemented
50#14583547C22124yescomplemented
51#14583545C22112yescomplemented
52#14583544C22112yescomplemented
53#14583542C22112yescomplemented
54#14583539C22124yescomplemented
55#14583538C22124yescomplemented
56#14583533C22112yescomplemented
57D4×C22⋊D43C22112yescomplemented
58#14583531C22124yescomplemented
59#14583479C22112yescomplemented
60#14583478C22112yescomplemented
61#14583475C2213yescomplemented
62#14583474C2216yescomplemented
63#14583473C2213yescomplemented
64#14583470C2213yescomplemented
65#14583469C2216yescomplemented
66#14583468C2213yescomplemented
67#14583467C2216yescomplemented
68#14583466C2213yescomplemented
69#14583463C2213yescomplemented
70#14583462C2216yescomplemented
71#14583460C22112yescomplemented
72#14583459C22112yescomplemented
73#14583450C2213yescomplemented
74#14583449C2213yescomplemented
75#14583448C22112yescomplemented
76#14583448C22112yescomplemented
77#14583448C2216yescomplemented
78#14583448C2216yescomplemented
79#14583448C2211yescharacteristic, complemented
80#14583448C2213yescomplemented
81#14583448C2216yescomplemented
82#14583447C2213yescomplemented
83#14583446C22112yescomplemented
84#14583445C2213yescomplemented
85#14583445C2213yescomplemented
86#14583444C22112yescomplemented
87C2×#13063323C2213yescomplemented
88C4⋊Q8×D43C2213yescomplemented
89C2×#13063321C2213yescomplemented
90#127×D43C2213yescomplemented
91C2×#13063313C2213yescomplemented
92#124×D43C2213yescomplemented
93#124×D43C2213yescomplemented
94#14583412C22112yescomplemented
95#14583409C22112yescomplemented
96#14583407C22112yescomplemented
97#14583405C22112yescomplemented
98C2×#13063298C22112yescomplemented
99#121×D43C22112yescomplemented
100#41×Dic43C2211yescharacteristic, complemented
101C4×#10621902C2212yescomplemented
102C4×#10621898C2213yescomplemented
103#14583367C2213yescomplemented
104C4×#10621900C2216yescomplemented
105C4×Q8×D43C2212yescomplemented
106C2×(C22⋊D43)⋊C4C22112yescomplemented
107C4×D4×D43C22112yescomplemented
108C4×D4×D43C2216yescomplemented
109#117×D43C2213yescomplemented
110C2×C42×D43C2213yescomplemented
111C2×2−1+4×C43C2211yescharacteristic, complemented
112C2×H(5,𝔽2)×C43C2211yescharacteristic, complemented
113C43×#548C2214yescomplemented
114C43×#546C22112yescomplemented
115C43×#536C2213yescomplemented
116C43×#535C2213yescomplemented
117C43×#532C2213yescomplemented
118C2×#124×C43C2213yescomplemented
119C4×#41×C43C2211yescharacteristic, complemented
120#13063373—216no—
121#13063373—224no—
122#13063372—28no—
123#13063372—216no—
124#13063372—224no—
125#13063371—28no—
126#13063371—248no—
127#13063371—224no—
128#13063370—248no—
129#13063370—224no—
130C2×#10621902—216no—
131C2×#10621902—224no—
132C2×#10621902C2312yes—
133C2×#10621902C2316yes—
134C2×#10621902C2313yes—
135C2×#10621902C2316yes—
136C2×#10621902C2316yes—
137C2×#10621902C2311yescharacteristic
138C2×#10621902C2316yes—
139C2×#10621902C2311yescharacteristic
140C2×#10621898C2316yes—
141C2×#10621898C2313yes—
142C2×#10621898C2313yes—
143C2×#10621898C2316yes—
144C2×#10621898C2316yes—
145C2×#10621898C2316yes—
146C2×#10621898C23112yes—
147C2×#10621898C2313yes—
148C2×#10621900—248no—
149C2×#10621900—224no—
150C2×#10621900C2316yes—
151C2×#10621900C2316yes—
152C2×#10621900C2316yes—
153C2×#10621900C2316yes—
154C2×#10621900C2311yescharacteristic
155C2×#10621900C2313yes—
156C2×#10621900C2316yes—
157C2×#10621900C2316yes—
158C2×#10621900C23112yes—
159C2×#10621900C2316yes—
160C2×#10621900C2313yes—
161#41×D43—216no—
162#41×D43—248no—
163#41×D43—224no—
164#41×D43—224no—
165#41×D43D4116yescomplemented
166C22×Dic86C2316yes—
167C22×Dic86C2313yes—
168C2×Q8×D43C2316yes—
169C2×Q8×D43C2312yes—
170C2×Q8×D43C2313yes—
171C2×Q8×D43C2313yes—
172C2×Q8×D43C2311yescharacteristic
173C22×D172C2316yes—
174C22×D172C2313yes—
175C22×D172C2316yes—
176C22×C22⋊D43C2316yes—
177C22×C22⋊D43C23112yes—
178C22×C22⋊D43C23112yes—
179C2×D4×D43C2316yes—
180C2×D4×D43C2316yes—
181C2×D4×D43C2313yes—
182C2×D4×D43C2313yes—
183C2×D4×D43C2316yes—
184C2×D4×D43C23112yes—
185C2×D4×D43C2316yes—
186C2×D4×D43C23112yes—
187C2×D4×D43C2313yes—
188C23×Dic43C2316yes—
189C22×C4×D43C2316yes—
190C22×C4×D43C2316yes—
191C22×C4×D43C2316yes—
192C22×C4×D43C2316yes—
193C22×C4×D43C2313yes—
194#13063325C2313yes—
195#13063324C23112yes—
196#13063323C23112yes—
197#13063323C2311yescharacteristic
198#13063323C2313yes—
199#13063323C2316yes—
200#13063322C2313yes—
201#13063321C23112yes—
202#13063321C23112yes—
203#13063321C2311yescharacteristic
204#13063321C2313yes—
205#13063321C2316yes—
206#13063314C2313yes—
207#13063314C2313yes—
208#13063313C23112yes—
209#13063313C2311yescharacteristic
210#13063313C2313yes—
211#13063313C2316yes—
212#13063312C2313yes—
213#13063312C2313yes—
214#13063311C23112yes—
215#13063311C23112yes—
216#13063310C23124yes—
217#13063309C23112yes—
218#13063308C23112yes—
219#13063307C23124yes—
220#13063306C23112yes—
221#13063305C23112yes—
222#13063304C23112yes—
223#13063303C23124yes—
224#13063302C23124yes—
225#13063301C23112yes—
226#13063300C23112yes—
227#13063300C23112yes—
228#13063299C23112yes—
229#13063299C23112yes—
230#13063298C23124yes—
231#13063298C2314yes—
232#13063298C23112yes—
233#13063298C23124yes—
234#13063298C23124yes—
235#13063298C23124yes—
236#13063297C23124yes—
237#13063297C23112yes—
238#13063297C23112yes—
239#13063296C23112yes—
240#13063296C23112yes—
241#13063295C23112yes—
242#13063295C23124yes—
243#13063294C23112yes—
244#13063293C23112yes—
245#13063293C23124yes—
246Q8×Dic43C2312yes—
247C4×Dic86C2316yes—
248#13063290C2316yes—
249C4×D172C23112yes—
250C4×D172C2316yes—
251D4×Dic43C2316yes—
252D4×Dic43C23112yes—
253#13063287C2316yes—
254#13063287C23112yes—
255C4×C22⋊D43C23112yes—
256C4×C22⋊D43C23112yes—
257C4×C22⋊D43C23112yes—
258(C22⋊D43)⋊C4C23124yes—
259(C22⋊D43)⋊C4C23124yes—
260(C22⋊D43)⋊C4C2314yes—
261(C22⋊D43)⋊C4C23112yes—
262(C22⋊D43)⋊C4C23112yes—
263(C22⋊D43)⋊C4C23124yes—
264#13063284C2313yes—
265#13063283C2316yes—
266#13063282C2316yes—
267#13063281C2316yes—
268C2×Dic43⋊C4C23112yes—
269C4⋊C4×D43C2316yes—
270C4⋊C4×D43C23112yes—
271C2×(C2×D43)⋊C4C23112yes—
272C22⋊C4×D43C2316yes—
273C22⋊C4×D43C23112yes—
274C22⋊C4×D43C23112yes—
275C2×C4×Dic43C2316yes—
276C2×C4×Dic43C2313yes—
277C42×D43C2311yescharacteristic
278C42×D43C2313yes—
279C42×D43C2316yes—
280C42×D43C2316yes—
281C42×D43C2313yes—
282C42×D43C2313yes—
2832−1+4×C43—28no—
284H(5,𝔽2)×C43—28no—
285C2×#41×C43C2312yes—
286C2×#41×C43C2313yes—
287C2×#41×C43C2313yes—
288C2×#41×C43C2316yes—
289C2×#41×C43C2311yescharacteristic
290C22×Q8×C43C2312yes—
291C22×Q8×C43C2313yes—
292C22×D4×C43C2313yes—
293C22×D4×C43C2316yes—
294C4⋊Q8×C43C2313yes—
295#127×C43C2313yes—
296#124×C43C23112yes—
297#124×C43C2313yes—
298#124×C43C2316yes—
299#124×C43C2311yescharacteristic
300#123×C43C23112yes—
301C22⋊Q8×C43C23112yes—
302#121×C43C23112yes—
303#121×C43C23112yes—
304#120×C43C23112yes—
305C4×Q8×C43C2312yes—
306C4×D4×C43C23112yes—
307C4×D4×C43C2316yes—
308#117×C43C2313yes—
309C2×C22⋊C4×C43C23112yes—
310C2×C42×C43C2313yes—
311C24×C43C2416yes—
312C23×D43C2416yes—
313C23×D43C2416yes—
314C23×D43C2416yes—
315C23×D43C2413yes—
316#41×C43—28no—
317#41×C43—224no—
318#41×C43—212no—
319#41×C43—212no—
320#41×C43C2×D418yescomplemented
321C2×Q8×C43—28no—
322C2×Q8×C43—212no—
323C2×Q8×C43C2416yes—
324C2×Q8×C43C2413yes—
325C2×Q8×C43C2411yescharacteristic
326C2×Q8×C43C2411yescharacteristic
327C2×D4×C43—224no—
328C2×D4×C43—212no—
329C2×D4×C43C2416yes—
330C2×D4×C43C2416yes—
331C2×D4×C43C2416yes—
332C2×D4×C43C2413yes—
333C2×D4×C43C2411yescharacteristic
334C2×D4×C43C24112yes—
335C2×D4×C43C2413yes—
336C22×C4×C43C2416yes—
337C22×C4×C43C2416yes—
338C22×C4×C43C2416yes—
339C22×C4×C43C2416yes—
340C22×C4×C43C2413yes—
341C2×C22⋊D43—248no—
342C2×C22⋊D43—224no—
343C2×C22⋊D43—424no—
344C2×C22⋊D43C24112yes—
345C2×C22⋊D43C2414yes—
346C2×C22⋊D43C24112yes—
347C2×C22⋊D43C2416yes—
348C2×C22⋊D43C2416yes—
349C2×C22⋊D43C2412yes—
350C2×C22⋊D43C2416yes—
351C2×C22⋊D43C2416yes—
352C2×C22⋊D43C2416yes—
353C2×C22⋊D43C24124yes—
354C2×C22⋊D43C2416yes—
355C22×Dic43—224no—
356C22×Dic43C2416yes—
357C22×Dic43C2416yes—
358C22×Dic43C2416yes—
359C22×Dic43C24112yes—
360C22×Dic43C2412yes—
361C22×Dic43C2413yes—
362#10621902—28no—
363#10621902—224no—
364#10621902—24no—
365#10621902—224no—
366#10621902—212no—
367#10621902—224no—
368#10621902—224no—
369#10621902C2×D418yescomplemented
370Q8×D43—28no—
371Q8×D43—212no—
372Q8×D43—212no—
373Q8×D43—224no—
374Q8×D43C2×D418yescomplemented
375#10621900—224no—
376#10621900—248no—
377#10621900—224no—
378#10621900—224no—
379#10621900—24no—
380#10621900—224no—
381#10621900—212no—
382#10621900—224no—
383#10621900—224no—
384#10621900—224no—
385#10621900C2×D4124yescomplemented
386D4×D43—224no—
387D4×D43—248no—
388D4×D43—224no—
389D4×D43—212no—
390D4×D43—212no—
391D4×D43—224no—
392D4×D43—224no—
393D4×D43—424no—
394D4×D43C2×D4124yescomplemented
395#10621898—212no—
396#10621898—212no—
397#10621898—248no—
398#10621898—224no—
399#10621898—224no—
400#10621898—224no—
401#10621898—224no—
402#10621898C2×D4124yescomplemented
403C2×D172—212no—
404C2×D172—224no—
405C2×D172—224no—
406C2×D172C24112yes—
407C2×D172C2416yes—
408C2×D172C2412yes—
409C2×D172C2416yes—
410C2×D172C2413yes—
411C2×D172C2411yescharacteristic
412C2×D172C24112yes—
413C2×D172C2413yes—
414C2×C4×D43—224no—
415C2×C4×D43—224no—
416C2×C4×D43—224no—
417C2×C4×D43—412no—
418C2×C4×D43C2×D4124yescomplemented
419C2×C4×D43C2412yes—
420C2×C4×D43C2416yes—
421C2×C4×D43C2416yes—
422C2×C4×D43C2416yes—
423C2×C4×D43C2416yes—
424C2×C4×D43C24112yes—
425C2×C4×D43C2412yes—
426C2×C4×D43C2416yes—
427C2×C4×D43C2416yes—
428C2×C4×D43C2416yes—
429C2×C4×D43C2416yes—
430C2×C4×D43C2411yescharacteristic
431C2×C4×D43C2413yes—
432C2×C4×D43C2413yes—
433C2×C4×D43C2413yes—
434C2×Dic86—212no—
435C2×Dic86—224no—
436C2×Dic86C2416yes—
437C2×Dic86C2416yes—
438C2×Dic86C2416yes—
439C2×Dic86C2411yescharacteristic
440C2×Dic86C2413yes—
441C2×Dic86C2413yes—
442C4⋊C4×C43C2416yes—
443C4⋊C4×C43C24112yes—
444C22⋊C4×C43C24112yes—
445C22⋊C4×C43C24124yes—
446C22⋊C4×C43C2416yes—
447C22⋊C4×C43C2414yes—
448C42×C43C2411yescharacteristic
449C42×C43C2413yes—
450C42×C43C2416yes—
451C22⋊Dic43C2416yes—
452C22⋊Dic43C24112yes—
453C22⋊Dic43C24112yes—
454(C2×D43)⋊C4C2414yes—
455(C2×D43)⋊C4C24112yes—
456(C2×D43)⋊C4C24112yes—
457(C2×D43)⋊C4C24112yes—
458(C2×D43)⋊C4C24112yes—
459(C2×D43)⋊C4C24124yes—
460C4⋊Dic43C2416yes—
461C4⋊Dic43C24112yes—
462Dic43⋊C4C2414yes—
463Dic43⋊C4C24112yes—
464Dic43⋊C4C24112yes—
465Dic43⋊C4C24124yes—
466C4×Dic43C2412yes—
467C4×Dic43C2411yescharacteristic
468C4×Dic43C2416yes—
469C4×Dic43C2413yes—
470C4×Dic43C2416yes—
471C4×Dic43C2416yes—
472C4×Dic43C2416yes—
473C23×C43—212no—
474C23×C43—412no—
475C23×C43C2512yes—
476C23×C43C2516yes—
477C23×C43C2513yes—
478C22×D43—212no—
479C22×D43—212no—
480C22×D43—212no—
481C22×D43—46no—
482C22×D43—412no—
483C22×D43—412no—
484C22×D43—412no—
485C22×D43C22×D4112yes—
486C22×D43C2516yes—
487C22×D43C2512yes—
488C22×D43C2513yes—
489C22×D43C2511yescharacteristic
490Q8×C43—22no—
491Q8×C43—26no—
492Q8×C43—212no—
493Q8×C43C22×D414yes—
494D4×C43—212no—
495D4×C43—212no—
496D4×C43—22no—
497D4×C43—26no—
498D4×C43—212no—
499D4×C43—412no—
500D4×C43C22×D4112yes—
501C2×C4×C43—212no—
502C2×C4×C43—212no—
503C2×C4×C43—212no—
504C2×C4×C43—46no—
505C2×C4×C43C22×D4112yes—
506C2×C4×C43C2512yes—
507C2×C4×C43C2516yes—
508C2×C4×C43C2516yes—
509C2×C4×C43C2512yes—
510C2×C4×C43C2511yescharacteristic
511C2×C4×C43C2513yes—
512C22⋊D43—212no—
513C22⋊D43—212no—
514C22⋊D43—24no—
515C22⋊D43—224no—
516C22⋊D43—212no—
517C22⋊D43—212no—
518C22⋊D43—212no—
519C22⋊D43—28no—
520C22⋊D43—224no—
521C22⋊D43—424no—
522C22⋊D43C22×D4124yes—
523C2×Dic43—212no—
524C2×Dic43—224no—
525C2×Dic43—24no—
526C2×Dic43—212no—
527C2×Dic43—212no—
528C2×Dic43C22×D4112yes—
529C2×Dic43C2516yes—
530C2×Dic43C2516yes—
531C2×Dic43C2512yes—
532C2×Dic43C2511yescharacteristic
533C2×Dic43C2513yes—
534C2×Dic43C2512yes—
535D172—224no—
536D172—212no—
537D172—24no—
538D172—26no—
539D172—212no—
540D172—22no—
541D172—412no—
542D172C22×D4112yes—
543C4×D43—212no—
544C4×D43—212no—
545C4×D43—212no—
546C4×D43—212no—
547C4×D43—24no—
548C4×D43—212no—
549C4×D43—224no—
550C4×D43—24no—
551C4×D43—212no—
552C4×D43—46no—
553C4×D43—46no—
554C4×D43C22×D4112yes—
555C4×D43C22×D414yes—
556C4×D43C22×D4112yes—
557C4×D43C22×D4112yes—
558Dic86—26no—
559Dic86—212no—
560Dic86—22no—
561Dic86—212no—
562Dic86—212no—
563Dic86C22×D4112yes—
564#62812—431nomaximal, Sylow
565C22×C43—26no—
566C22×C43—22no—
567C22×C43—26no—
568C22×C43—24no—
569C22×C43—212no—
570C22×C43—812no—
571C22×C43C23×D416yes—
572C22×C43C2611yescharacteristic
573C2×D43—26no—
574C2×D43—22no—
575C2×D43—26no—
576C2×D43—22no—
577C2×D43—24no—
578C2×D43—212no—
579C2×D43—412no—
580C2×D43—812no—
581C2×D43—812no—
582C2×D43—812no—
583C2×D43C23×D416yes—
584C2×D43C23×D412yes—
585C4×C43—22no—
586C4×C43—26no—
587C4×C43—22no—
588C4×C43—26no—
589C4×C43C23×D412yes—
590C4×C43C23×D416yes—
591Dic43—22no—
592Dic43—26no—
593Dic43—26no—
594Dic43C23×D416yes—
595Dic43C23×D412yes—
596Dic43#58514yescomplemented
597C2×#585—431no—
598C2×#585—431no—
599#3500—433no—
600#3500—433no—
601#3500—431no—
602#3500D4311yescharacteristic, complemented
603#3499—431no—
604#3499—433no—
605#3498—431no—
606#3498—433no—
607#3497—434no—
608#3496—4312no—
609D4×#41—434no—
610D4×#41—4312no—
611#3449—433no—
612#3449—433no—
613C2×#532—433no—
614C2×#532—433no—
615C2×C4×#41—431no—
616C2×C43—26no—
617C2×C43—42no—
618C2×C43—46no—
619C2×C43C24×D411yescharacteristic
620C2×C43C2×#58512yes—
621D43—22no—
622D43—26no—
623D43—46no—
624D43—42no—
625#585—8616no—
626#585—8616no—
627C2×2−1+4—432no—
628C2×2−1+4—433no—
629C2×2−1+4—431no—
630C2×2−1+4—432no—
631C2×2−1+4—433no—
632C2×2−1+4C2×D4311yescharacteristic, complemented
633C2×H(5,𝔽2)—436no—
634C2×H(5,𝔽2)—433no—
635C2×H(5,𝔽2)—431no—
636C2×H(5,𝔽2)—436no—
637C2×H(5,𝔽2)—433no—
638C2×H(5,𝔽2)C2×D4311yescharacteristic, complemented
639C22×#41—431no—
640C22×#41—433no—
641C22×#41—433no—
642C22×#41—432no—
643C22×#41—436no—
644C22×#41—433no—
645C22×#41—432no—
646C22×#41—433no—
647C22×#41—436no—
648#550—434no—
649#550—4312no—
650D4×Q8—434no—
651D4×Q8—4312no—
652#548—4312no—
653#548—434no—
654#548—4312no—
655#548C2×D4314yescomplemented
656#547—4312no—
657#547—4324no—
658#547—4312no—
659#546—4312no—
660#546—4324no—
661#546—4312no—
662#546—4312no—
663#546—4324no—
664#546C2×D43112yescomplemented
665D42—4312no—
666D42—4312no—
667D42—4324no—
668#537—4312no—
669#537—4312no—
670#536—433no—
671#536—433no—
672#536—436no—
673#536—436no—
674#536—433no—
675#536C2×D4313yescomplemented
676#535—433no—
677#535—433no—
678#535—436no—
679#535—436no—
680#535—433no—
681#535C2×D4313yescomplemented
682#534—4312no—
683#534—4312no—
684#532—433no—
685#532—433no—
686#532—433no—
687#532—433no—
688#532—431no—
689#532—433no—
690#532—436no—
691#532—4312no—
692#532—4312no—
693#532—436no—
694#532—436no—
695#532—4312no—
696#532—4312no—
697#532—433no—
698#532C2×D4313yescomplemented
699C2×C4⋊Q8—433no—
700C2×C4⋊Q8—433no—
701C2×#127—433no—
702C2×#127—433no—
703C2×#124—433no—
704C2×#124—433no—
705C2×#124—433no—
706C2×#124C2×D4313yescomplemented
707#525—4312no—
708#525—4312no—
709#525—4312no—
710#525—4312no—
711C2×#121—4312no—
712C2×#121—4312no—
713C4×#41—431no—
714C4×#41—432no—
715C4×#41—436no—
716C4×#41—433no—
717C4×#41—433no—
718C4×#41C2×D4311yescharacteristic, complemented
719C2×C4×Q8—432no—
720C2×C4×D4—436no—
721C2×C4×D4—4312no—
722C2×C4×D4—4312no—
723C2×#117—433no—
724C22×C42—433no—
725C43#6281211yescharacteristic, complemented, Sylow
7262−1+4—28no—
7272−1+4—8616no—
7282−1+4—8624no—
7292−1+4—8616no—
7302−1+4—8624no—
7312−1+4—868no—
732H(5,𝔽2)—28no—
733H(5,𝔽2)—8648no—
734H(5,𝔽2)—8624no—
735H(5,𝔽2)—8648no—
736H(5,𝔽2)—8624no—
737H(5,𝔽2)—868no—
738C2×#41—4316no—
739C2×#41—431no—
740C2×#41—436no—
741C2×#41—431no—
742C2×#41—433no—
743C2×#41—436no—
744C2×#41—436no—
745C2×#41—436no—
746C2×#41—432no—
747C2×#41—433no—
748C2×#41—436no—
749C2×#41—436no—
750C2×#41—436no—
751C2×#41—431no—
752C2×#41—433no—
753C2×#41—436no—
754C2×#41—436no—
755C2×#41—436no—
756C2×#41—4312no—
757C2×#41—436no—
758C2×#41—433no—
759C2×#41—433no—
760C2×#41—433no—
761C2×#41—436no—
762C2×#41—436no—
763C2×#41—436no—
764C2×#41—4312no—
765C2×#41—436no—
766C2×#41—8624no—
767C2×#41—8624no—
768C2×#41—8624no—
769C2×#41—8624no—
770C2×#41—8648no—
771C2×#41—8616no—
772C2×#41—8616no—
773C2×#41—8648no—
774C2×#41C22×D4313yes—
775C2×#41C22×D4313yes—
776C2×#41C22×D4316yes—
777C2×#41C22×D4312yes—
778C2×#41C22×D4311yescharacteristic
779C22×Q8—431no—
780C22×Q8—433no—
781C22×Q8—433no—
782C22×Q8—436no—
783C22×Q8—432no—
784C22×Q8—433no—
785C22×Q8—436no—
786C22×Q8C22×D4313yes—
787C22×Q8C22×D4312yes—
788C22×D4—433no—
789C22×D4—436no—
790C22×D4—4312no—
791C22×D4—4312no—
792C22×D4—436no—
793C22×D4—436no—
794C22×D4—433no—
795C22×D4—433no—
796C22×D4—4312no—
797C22×D4—436no—
798C22×D4—436no—
799C22×D4—4312no—
800C22×D4—436no—
801C22×D4—433no—
802C22×D4—436no—
803C22×D4C22×D4313yes—
804C22×D4C22×D4316yes—
805C23×C4—433no—
806C23×C4—436no—
807C23×C4—436no—
808C23×C4—436no—
809C23×C4—436no—
810C23×C4—436no—
811C4⋊Q8—431no—
812C4⋊Q8—433no—
813C4⋊Q8—436no—
814C4⋊Q8—4312no—
815C4⋊Q8—4312no—
816C4⋊Q8—433no—
817C4⋊Q8C22×D4313yes—
818#127—431no—
819#127—433no—
820#127—436no—
821#127—4312no—
822#127—4312no—
823#127—433no—
824#127C22×D4313yes—
825#124—433no—
826#124—433no—
827#124—433no—
828#124—433no—
829#124—4312no—
830#124—4312no—
831#124—431no—
832#124—433no—
833#124—436no—
834#124—4312no—
835#124C22×D4311yescharacteristic
836#124C22×D4313yes—
837#124C22×D4316yes—
838#124C22×D43112yes—
839#123—4312no—
840#123—4312no—
841#123—4324no—
842#123—4324no—
843#123—4312no—
844#123C22×D43112yes—
845C22⋊Q8—4312no—
846C22⋊Q8—4312no—
847C22⋊Q8—4324no—
848C22⋊Q8—4312no—
849C22⋊Q8—4324no—
850C22⋊Q8C22×D43112yes—
851#121—4312no—
852#121—4312no—
853#121—4312no—
854#121—4312no—
855#121—4324no—
856#121—4312no—
857#121—4312no—
858#121—4312no—
859#121—4312no—
860#121—434no—
861#121—4312no—
862#121—4324no—
863#121—4324no—
864#121—4324no—
865#121—4324no—
866#121C22×D43112yes—
867#121C22×D43112yes—
868#120—4312no—
869#120—4312no—
870#120—4324no—
871#120—4324no—
872#120—4312no—
873#120C22×D43112yes—
874C4×Q8—432no—
875C4×Q8—436no—
876C4×Q8—436no—
877C4×Q8C22×D4312yes—
878C4×D4—436no—
879C4×D4—4312no—
880C4×D4—4312no—
881C4×D4—4312no—
882C4×D4—4312no—
883C4×D4—436no—
884C4×D4—4312no—
885C4×D4—434no—
886C4×D4—4312no—
887C4×D4—4312no—
888C4×D4—4324no—
889C4×D4—4324no—
890C4×D4—4324no—
891C4×D4—436no—
892C4×D4—4312no—
893C4×D4C22×D4316yes—
894C4×D4C22×D43112yes—
895#117—433no—
896#117—436no—
897#117—436no—
898#117—436no—
899#117C22×D4313yes—
900C2×C4⋊C4—4312no—
901C2×C4⋊C4—436no—
902C2×C4⋊C4—4312no—
903C2×C22⋊C4—4312no—
904C2×C22⋊C4—436no—
905C2×C22⋊C4—4312no—
906C2×C22⋊C4—4312no—
907C2×C22⋊C4C22×D43112yes—
908C2×C42—436no—
909C2×C42—433no—
910C2×C42—433no—
911C2×C42—436no—
912C2×C42—436no—
913C2×C42—433no—
914C2×C42—433no—
915C2×C42—431no—
916C2×C42C22×D4313yes—
917C24—433no—
918C24—436no—
919C24—436no—
920C24—436no—
921C24C23×D4316yes—
922#41—28no—
923#41—224no—
924#41—212no—
925#41—212no—
926#41—438no—
927#41—4324no—
928#41—4324no—
929#41—8624no—
930#41—8624no—
931#41—8648no—
932#41—8624no—
933#41—8624no—
934#41—8624no—
935#41—8624no—
936#41—8612no—
937#41—864no—
938#41—8624no—
939#41—8624no—
940#41—8624no—
941#41—8612no—
942#41—864no—
943#41—8624no—
944#41—8624no—
945#41—8624no—
946#41—8648no—
947#41—8624no—
948#41—8624no—
949#41—868no—
950#41—8624no—
951#41—8612no—
952#41—8612no—
953#41D4×D4318yescomplemented
954C2×Q8—28no—
955C2×Q8—212no—
956C2×Q8—438no—
957C2×Q8—433no—
958C2×Q8—436no—
959C2×Q8—436no—
960C2×Q8—436no—
961C2×Q8—431no—
962C2×Q8—433no—
963C2×Q8—8624no—
964C2×Q8—8612no—
965C2×Q8—8612no—
966C2×Q8—8624no—
967C2×Q8—868no—
968C2×Q8—8612no—
969C2×Q8C23×D4316yes—
970C2×Q8C23×D4311yescharacteristic
971C2×Q8C23×D4313yes—
972C2×Q8C23×D4311yescharacteristic
973C2×D4—224no—
974C2×D4—212no—
975C2×D4—436no—
976C2×D4—4324no—
977C2×D4—434no—
978C2×D4—4312no—
979C2×D4—4312no—
980C2×D4—436no—
981C2×D4—436no—
982C2×D4—432no—
983C2×D4—436no—
984C2×D4—436no—
985C2×D4—436no—
986C2×D4—4324no—
987C2×D4—433no—
988C2×D4—4312no—
989C2×D4—432no—
990C2×D4—436no—
991C2×D4—436no—
992C2×D4—431no—
993C2×D4—433no—
994C2×D4—4312no—
995C2×D4—8624no—
996C2×D4—8624no—
997C2×D4—8612no—
998C2×D4—8612no—
999C2×D4—8648no—
1000C2×D4—8624no—
1001C2×D4—8624no—
1002C2×D4—8624no—
1003C2×D4—8648no—
1004C2×D4—8624no—
1005C2×D4—8624no—
1006C2×D4—8612no—
1007C2×D4—17224no—
1008C2×D4—17224no—
1009C2×D4C23×D4316yes—
1010C2×D4C23×D4316yes—
1011C2×D4C23×D4316yes—
1012C2×D4C23×D4311yescharacteristic
1013C2×D4C23×D4313yes—
1014C2×D4C23×D43112yes—
1015C2×D4C23×D4313yes—
1016C22×C4—433no—
1017C22×C4—4324no—
1018C22×C4—431no—
1019C22×C4—433no—
1020C22×C4—433no—
1021C22×C4—433no—
1022C22×C4—436no—
1023C22×C4—436no—
1024C22×C4—432no—
1025C22×C4—436no—
1026C22×C4—4312no—
1027C22×C4—432no—
1028C22×C4—436no—
1029C22×C4—436no—
1030C22×C4—436no—
1031C22×C4—432no—
1032C22×C4—436no—
1033C22×C4—4312no—
1034C22×C4—436no—
1035C22×C4—436no—
1036C22×C4—436no—
1037C22×C4—436no—
1038C22×C4—8624no—
1039C22×C4—8624no—
1040C22×C4—8624no—
1041C22×C4—8624no—
1042C22×C4—17212no—
1043C22×C4C23×D4316yes—
1044C22×C4C23×D4316yes—
1045C22×C4C23×D4316yes—
1046C22×C4C23×D4316yes—
1047C22×C4C23×D4313yes—
1048C4⋊C4—434no—
1049C4⋊C4—4312no—
1050C4⋊C4—4312no—
1051C4⋊C4—436no—
1052C4⋊C4—4324no—
1053C4⋊C4—4312no—
1054C4⋊C4C23×D4316yes—
1055C4⋊C4C23×D43112yes—
1056C22⋊C4—436no—
1057C22⋊C4—4312no—
1058C22⋊C4—4312no—
1059C22⋊C4—4312no—
1060C22⋊C4—434no—
1061C22⋊C4—4312no—
1062C22⋊C4—4312no—
1063C22⋊C4—4312no—
1064C22⋊C4—4324no—
1065C22⋊C4C23×D4314yes—
1066C22⋊C4C23×D43112yes—
1067C22⋊C4C23×D4316yes—
1068C22⋊C4C23×D43124yes—
1069C42—432no—
1070C42—431no—
1071C42—436no—
1072C42—433no—
1073C42—436no—
1074C42—436no—
1075C42—436no—
1076C42C23×D4311yescharacteristic
1077C42C23×D4313yes—
1078C42C23×D4316yes—
1079C23—212no—
1080C23—412no—
1081C23—433no—
1082C23—431no—
1083C23—4312no—
1084C23—432no—
1085C23—436no—
1086C23—8612no—
1087C23—8612no—
1088C23—8612no—
1089C23—17212no—
1090C23—17212no—
1091C23—17212no—
1092C23—1726no—
1093C23C24×D4312yes—
1094C23C24×D4316yes—
1095C23C24×D4313yes—
1096Q8—212no—
1097Q8—26no—
1098Q8—22no—
1099Q8—4312no—
1100Q8—8612no—
1101Q8—8612no—
1102Q8—8612no—
1103Q8—862no—
1104Q8—866no—
1105Q8C2×D4×D4314yes—
1106D4—212no—
1107D4—212no—
1108D4—212no—
1109D4—26no—
1110D4—22no—
1111D4—412no—
1112D4—4324no—
1113D4—4312no—
1114D4—864no—
1115D4—8612no—
1116D4—8624no—
1117D4—8612no—
1118D4—8612no—
1119D4—868no—
1120D4—8624no—
1121D4—864no—
1122D4—8612no—
1123D4—8624no—
1124D4—8612no—
1125D4—8612no—
1126D4—8612no—
1127D4—862no—
1128D4—866no—
1129D4—17212no—
1130D4—17224no—
1131D4C2×D4×D43112yes—
1132C2×C4—212no—
1133C2×C4—212no—
1134C2×C4—212no—
1135C2×C4—46no—
1136C2×C4—4312no—
1137C2×C4—432no—
1138C2×C4—431no—
1139C2×C4—433no—
1140C2×C4—434no—
1141C2×C4—4312no—
1142C2×C4—4312no—
1143C2×C4—4312no—
1144C2×C4—436no—
1145C2×C4—432no—
1146C2×C4—436no—
1147C2×C4—864no—
1148C2×C4—8612no—
1149C2×C4—8624no—
1150C2×C4—864no—
1151C2×C4—8612no—
1152C2×C4—8612no—
1153C2×C4—8612no—
1154C2×C4—864no—
1155C2×C4—8612no—
1156C2×C4—8624no—
1157C2×C4—8612no—
1158C2×C4—8612no—
1159C2×C4—8612no—
1160C2×C4—8612no—
1161C2×C4—1726no—
1162C2×C4—1726no—
1163C2×C4C2×D4×D43112yes—
1164C2×C4C24×D4312yes—
1165C2×C4C24×D4316yes—
1166C2×C4C24×D4312yes—
1167C2×C4C24×D4316yes—
1168C2×C4C24×D4311yescharacteristic
1169C2×C4C24×D4313yes—
1170C22—26no—
1171C22—22no—
1172C22—26no—
1173C22—24no—
1174C22—212no—
1175C22—812no—
1176C22—432no—
1177C22—436no—
1178C22—862no—
1179C22—866no—
1180C22—866no—
1181C22—862no—
1182C22—864no—
1183C22—8612no—
1184C22—34412no—
1185C22—34412no—
1186C22—34412no—
1187C22—17212no—
1188C22C22×D4×D4316yes—
1189C22C25×D4311yescharacteristic
1190C4—22no—
1191C4—26no—
1192C4—22no—
1193C4—26no—
1194C4—432no—
1195C4—436no—
1196C4—434no—
1197C4—862no—
1198C4—866no—
1199C4—866no—
1200C4C22×D4×D4316yes—
1201C4C22×D4×D4312yes—
1202C2—26no—
1203C2—46no—
1204C2—42no—
1205C2—866no—
1206C2—862no—
1207C2—1726no—
1208C2—1722no—
1209C2C23×D4×D4311yescharacteristic
1210C2#585×D4312yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3500C2
hypercenter#3500D43
hypocenterC43#62812
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3500

Complements

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

NH ≅ G/Ntype
1. C2×#14583736C2semidirect
2. C2×#14583734C2semidirect
3. #19148388C2semidirect
4. #19148385C2semidirect
5. #19148382C2semidirect
6. #19148377C2semidirect
7. #19148376C2semidirect
8. #19148370C2semidirect
9. #19148369C2semidirect
10. #19148363C2semidirect
11. #19148355C2semidirect
12. #19148084C2semidirect
13. #19148079C2semidirect
14. #19147927C2semidirect
15. #19147926C2semidirect
16. C2×#14583448C2semidirect
17. #532×D43C2semidirect
18. C4×#41×D43C2semidirect
19. C43×#3500C2semidirect
22. C2×#13063373C22semidirect
23. C2×#13063373C22semidirect
24. C2×#13063372C22semidirect
25. C2×#13063372C22semidirect
26. C2×#13063372C22semidirect
27. C2×#13063371C22semidirect
28. C2×#13063371C22semidirect
29. C2×#13063371C22semidirect
30. C2×#13063370C22semidirect
31. C2×#13063370C22semidirect
32. C22×#10621902C22semidirect
33. C22×#10621902C22semidirect
34. C22×#10621900C22semidirect
35. C22×#10621900C22semidirect
37. C2×#41×D43C22semidirect
38. C2×#41×D43C22semidirect
39. C2×#41×D43C22semidirect
40. C2×#41×D43C22semidirect
41. #14583568C22semidirect
42. #14583567C22semidirect
43. Q8×C22⋊D43C22semidirect
44. #14583562C22semidirect
45. #14583561C22semidirect
46. #14583558C22semidirect
47. #14583557C22semidirect
48. #14583551C22semidirect
49. #14583548C22semidirect
50. #14583547C22semidirect
51. #14583545C22semidirect
52. #14583544C22semidirect
53. #14583542C22semidirect
54. #14583539C22semidirect
55. #14583538C22semidirect
56. #14583533C22semidirect
57. D4×C22⋊D43C22semidirect
58. #14583531C22semidirect
59. #14583479C22semidirect
60. #14583478C22semidirect
61. #14583475C22semidirect
62. #14583474C22semidirect
63. #14583473C22semidirect
64. #14583470C22semidirect
65. #14583469C22semidirect
66. #14583468C22semidirect
67. #14583467C22semidirect
68. #14583466C22semidirect
69. #14583463C22semidirect
70. #14583462C22semidirect
71. #14583460C22semidirect
72. #14583459C22semidirect
73. #14583450C22semidirect
74. #14583449C22semidirect
75. #14583448C22semidirect
76. #14583448C22semidirect
77. #14583448C22semidirect
78. #14583448C22semidirect
79. #14583448C22semidirect
80. #14583448C22semidirect
81. #14583448C22semidirect
82. #14583447C22semidirect
83. #14583446C22semidirect
84. #14583445C22semidirect
85. #14583445C22semidirect
86. #14583444C22semidirect
87. C2×#13063323C22semidirect
88. C4⋊Q8×D43C22semidirect
89. C2×#13063321C22semidirect
90. #127×D43C22semidirect
91. C2×#13063313C22semidirect
92. #124×D43C22semidirect
93. #124×D43C22semidirect
94. #14583412C22semidirect
95. #14583409C22semidirect
96. #14583407C22semidirect
97. #14583405C22semidirect
98. C2×#13063298C22semidirect
99. #121×D43C22semidirect
100. #41×Dic43C22semidirect
101. C4×#10621902C22semidirect
102. C4×#10621898C22semidirect
103. #14583367C22semidirect
104. C4×#10621900C22semidirect
105. C4×Q8×D43C22semidirect
106. C2×(C22⋊D43)⋊C4C22semidirect
107. C4×D4×D43C22semidirect
108. C4×D4×D43C22semidirect
109. #117×D43C22semidirect
110. C2×C42×D43C22semidirect
111. C2×2−1+4×C43C22semidirect
112. C2×H(5,𝔽2)×C43C22semidirect
113. C43×#548C22semidirect
114. C43×#546C22semidirect
115. C43×#536C22semidirect
116. C43×#535C22semidirect
117. C43×#532C22semidirect
118. C2×#124×C43C22semidirect
119. C4×#41×C43C22semidirect
165. #41×D43D4semidirect
320. #41×C43C2×D4semidirect
369. #10621902C2×D4semidirect
374. Q8×D43C2×D4semidirect
385. #10621900C2×D4semidirect
394. D4×D43C2×D4semidirect
402. #10621898C2×D4semidirect
418. C2×C4×D43C2×D4semidirect
596. Dic43#585semidirect
602. #3500D43semidirect
632. C2×2−1+4C2×D43semidirect
638. C2×H(5,𝔽2)C2×D43semidirect
655. #548C2×D43semidirect
664. #546C2×D43semidirect
675. #536C2×D43semidirect
681. #535C2×D43semidirect
698. #532C2×D43semidirect
706. C2×#124C2×D43semidirect
718. C4×#41C2×D43semidirect
725. C43#62812semidirect
953. #41D4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145837362
C2×#145837342
#191483882
#191483852
#191483822
#191483772
#191483762
#191483702
#191483692
#191483632
#191483552
#191480842
#191480792
#191479272
#191479262
C2×#145834482
#532×D432
C4×#41×D432
C43×#35002
#6281243