Finite Group Databasebeta

← #26005147

Subgroups — #26005147

Order 11008.

11346 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583735C212yesmaximal, complemented
2#19148387C214yesmaximal, complemented
3#19148384C214yesmaximal, complemented
4#19148377C214yesmaximal, complemented
5#19148370C214yesmaximal, complemented
6#19148364C214yesmaximal, complemented
7#19148358C214yesmaximal, complemented
8#19148356C218yesmaximal, complemented
9#19148078C2116yesmaximal, complemented
10#19147928C211yesmaximal, characteristic, complemented
11#19147922C214yesmaximal, complemented
12C2×#14583445C212yesmaximal, complemented
13#532×D43C214yesmaximal, complemented
14C2×#14583367C211yesmaximal, characteristic, complemented
15C43×#3449C211yesmaximal, characteristic, complemented
16#14583735—232no—
17C2×#13063373C2214yescomplemented
18C2×#13063372C2214yescomplemented
19C2×#13063372C2214yescomplemented
20C2×#13063371C2214yescomplemented
21C2×#13063371C2214yescomplemented
22C2×#13063370C2218yescomplemented
23C2×#13063370C2214yescomplemented
24C22×#10621898C2211yescharacteristic
25C22×#10621898C2218yescomplemented
26C22×#10621898C2212yescomplemented
27C2×#41×D43C2218yescomplemented
28C2×#41×D43C2218yescomplemented
29#14583567C22116yescomplemented
30#14583562C22116yescomplemented
31#14583559C22116yescomplemented
32#14583555C22116yescomplemented
33#14583551C22116yescomplemented
34#14583547C22132yescomplemented
35#14583546C22116yescomplemented
36#14583541C22132yescomplemented
37#14583540C22116yescomplemented
38#14583536C22132yescomplemented
39#14583533C22116yescomplemented
40#14583531C22132yescomplemented
41#14583480C2214yescomplemented
42#14583476C22116yescomplemented
43#14583475C2214yescomplemented
44#14583474C2218yescomplemented
45#14583469C2218yescomplemented
46#14583468C2214yescomplemented
47#14583467C2218yescomplemented
48#14583462C2218yescomplemented
49#14583461C2214yescomplemented
50#14583457C22116yescomplemented
51#14583450C2214yescomplemented
52#14583449C2214yescomplemented
53#14583448C2218yescomplemented
54#14583447C2214yescomplemented
55#14583446C22116yescomplemented
56#14583445C2218yescomplemented
57#14583445C2218yescomplemented
58#14583445C2214yescomplemented
59#14583445C2214yescomplemented
60#14583445C2214yescomplemented
61#14583445C2214yescomplemented
62#14583444C22116yescomplemented
63C2×#13063323C2212yescomplemented
64C4⋊Q8×D43C2214yescomplemented
65C2×#13063321C2212yescomplemented
66#127×D43C2214yescomplemented
67C2×#13063314C2212yescomplemented
68C2×#13063312C2212yescomplemented
69#124×D43C2218yescomplemented
70#14583411C2218yescomplemented
71#14583408C22132yescomplemented
72C2×#13063297C2218yescomplemented
73#121×D43C22116yescomplemented
74#14583367C2218yescomplemented
75#14583367C2214yescomplemented
76#14583367C2214yescomplemented
77C2×#13063290C2212yescomplemented
78C2×#13063287C2212yescomplemented
79C2×C4×C22⋊D43C2218yescomplemented
80C2×(C22⋊D43)⋊C4C2214yescomplemented
81C4×D4×D43C22116yescomplemented
82C2×#13063282C2212yescomplemented
83C22×C4×Dic43C2211yescharacteristic, complemented
84C2×C42×D43C2212yescomplemented
85C22×#41×C43C2212yescomplemented
86C43×#537C2214yescomplemented
87C43×#536C2214yescomplemented
88C43×#535C2214yescomplemented
89C43×#534C2214yescomplemented
90C43×#532C2214yescomplemented
91C43×#525C2218yescomplemented
92C2×#117×C43C2211yescharacteristic, complemented
93#13063373—232no—
94#13063372—232no—
95#13063372—232no—
96#13063371—232no—
97#13063371—232no—
98#13063370—264no—
99#13063370—232no—
100C2×#10621902C2318yes—
101C2×#10621902C2318yes—
102C2×#10621898—216no—
103C2×#10621898—264no—
104C2×#10621898D4116yescomplemented
105C2×#10621898C2318yes—
106C2×#10621898C23116yes—
107C2×#10621898C2314yes—
108C2×#10621898C2314yes—
109C2×#10621898C2314yes—
110C2×#10621898C2314yes—
111C2×#10621898C23116yes—
112C2×#10621898C2318yes—
113C2×#10621898C2314yes—
114C2×#10621898C2314yes—
115C2×#10621900C2318yes—
116C2×#10621900C23116yes—
117C2×#10621900C2318yes—
118C2×#10621900C23116yes—
119#41×D43—264no—
120#41×D43—264no—
121C22×Dic86C2318yes—
122C22×Dic86C2312yes—
123C22×Dic86C2311yescharacteristic
124C2×Q8×D43C2318yes—
125C2×Q8×D43C2318yes—
126C22×D172C2312yes—
127C22×D172C2318yes—
128C22×D172C2311yescharacteristic
129C22×C22⋊D43C2314yes—
130C22×C22⋊D43C23116yes—
131C22×C22⋊D43C2318yes—
132C22×C22⋊D43C2312yes—
133C2×D4×D43C23116yes—
134C2×D4×D43C2318yes—
135C2×D4×D43C23116yes—
136C2×D4×D43C2318yes—
137C2×D4×D43C23116yes—
138C23×Dic43C2312yes—
139C22×C4×D43C23116yes—
140C22×C4×D43C2314yes—
141C22×C4×D43C2314yes—
142C22×C4×D43C2312yes—
143#13063325C2314yes—
144#13063324C23116yes—
145#13063323C2318yes—
146#13063323C2314yes—
147#13063323C2314yes—
148#13063322C2314yes—
149#13063321C23116yes—
150#13063321C2318yes—
151#13063321C2314yes—
152#13063321C2314yes—
153#13063314C2318yes—
154#13063314C2314yes—
155#13063314C2314yes—
156#13063313C2318yes—
157#13063312C2318yes—
158#13063312C2314yes—
159#13063312C2314yes—
160#13063311C23132yes—
161#13063310C23132yes—
162#13063309C23116yes—
163#13063307C23132yes—
164#13063305C23116yes—
165#13063303C23132yes—
166#13063302C23132yes—
167#13063300C23116yes—
168#13063300C23116yes—
169#13063299C23116yes—
170#13063298C23132yes—
171#13063298C23132yes—
172#13063297C23132yes—
173#13063297C23116yes—
174#13063297C23116yes—
175#13063297C23116yes—
176#13063297C23116yes—
177#13063296C23116yes—
178#13063295C23132yes—
179#13063295C23116yes—
180#13063293C23132yes—
181#13063290C2318yes—
182#13063290C2318yes—
183C4×D172C23116yes—
184D4×Dic43C23116yes—
185#13063287C23116yes—
186#13063287C2318yes—
187#13063287C2318yes—
188C4×C22⋊D43C23116yes—
189C4×C22⋊D43C23116yes—
190C4×C22⋊D43C23116yes—
191C4×C22⋊D43C23116yes—
192(C22⋊D43)⋊C4C23132yes—
193(C22⋊D43)⋊C4C23116yes—
194(C22⋊D43)⋊C4C23116yes—
195#13063282C2318yes—
196#13063282C2318yes—
197C2×Dic43⋊C4C2314yes—
198C2×Dic43⋊C4C2318yes—
199C4⋊C4×D43C23116yes—
200C2×C22⋊Dic43C2318yes—
201C2×(C2×D43)⋊C4C2314yes—
202C2×(C2×D43)⋊C4C2318yes—
203C22⋊C4×D43C23132yes—
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2314yes—
206C2×C4×Dic43C2311yescharacteristic
207C2×C4×Dic43C2314yes—
208C2×C4×Dic43C2312yes—
209C2×C4×Dic43C2312yes—
210C2×C4×Dic43C2312yes—
211C42×D43C2318yes—
212C42×D43C2314yes—
213C42×D43C2314yes—
214C2×#41×C43—216no—
215C2×#41×C43C2314yes—
216C2×#41×C43C2314yes—
217C2×#41×C43C2314yes—
218C2×#41×C43C2314yes—
219C22×Q8×C43C2312yes—
220C22×D4×C43C2314yes—
221C22×D4×C43C2312yes—
222C23×C4×C43C2314yes—
223C23×C4×C43C2311yescharacteristic
224C4⋊Q8×C43C2314yes—
225#127×C43C2314yes—
226#124×C43C2318yes—
227#123×C43C23116yes—
228C22⋊Q8×C43C23116yes—
229#121×C43C23116yes—
230#121×C43C23116yes—
231#120×C43C23116yes—
232C4×D4×C43C23116yes—
233#117×C43C2314yes—
234#117×C43C2314yes—
235C2×C4⋊C4×C43C2312yes—
236C2×C22⋊C4×C43C2312yes—
237C2×C42×C43C2312yes—
238C24×C43C2414yes—
239C24×C43C2411yescharacteristic
240C23×D43C24116yes—
241C23×D43C2414yes—
242C23×D43C2412yes—
243#41×C43—216no—
244#41×C43—216no—
245#41×C43—216no—
246#41×C43—216no—
247C2×Q8×C43—28no—
248C2×Q8×C43C2414yes—
249C2×Q8×C43C2414yes—
250C2×D4×C43—28no—
251C2×D4×C43—216no—
252C2×D4×C43C2418yes—
253C2×D4×C43C2418yes—
254C2×D4×C43C2414yes—
255C2×D4×C43C2414yes—
256C2×D4×C43C24116yes—
257C22×C4×C43—216no—
258C22×C4×C43C2×D418yescomplemented
259C22×C4×C43C2418yes—
260C22×C4×C43C2418yes—
261C22×C4×C43C2414yes—
262C22×C4×C43C2414yes—
263C22×C4×C43C2411yescharacteristic
264C22×C4×C43C2411yescharacteristic
265C22×C4×C43C2412yes—
266C22×C4×C43C2412yes—
267C2×C22⋊D43—264no—
268C2×C22⋊D43—216no—
269C2×C22⋊D43—416no—
270C2×C22⋊D43C2×D4116yescomplemented
271C2×C22⋊D43C24116yes—
272C2×C22⋊D43C24116yes—
273C2×C22⋊D43C2418yes—
274C2×C22⋊D43C2418yes—
275C2×C22⋊D43C24116yes—
276C2×C22⋊D43C24116yes—
277C2×C22⋊D43C2418yes—
278C22×Dic43—44no—
279C22×Dic43C2412yes—
280C22×Dic43C2414yes—
281C22×Dic43C2414yes—
282C22×Dic43C24116yes—
283C22×Dic43C2414yes—
284C22×Dic43C2412yes—
285C22×Dic43C2412yes—
286#10621902—232no—
287#10621902—232no—
288Q8×D43—232no—
289Q8×D43—232no—
290#10621900—264no—
291#10621900—264no—
292#10621900—232no—
293#10621900—232no—
294D4×D43—264no—
295D4×D43—232no—
296D4×D43—232no—
297D4×D43—264no—
298D4×D43—432no—
299#10621898—216no—
300#10621898—216no—
301#10621898—216no—
302#10621898—216no—
303#10621898—264no—
304#10621898—232no—
305#10621898—264no—
306#10621898—232no—
307#10621898C2×D4132yescomplemented
308#10621898C2×D4132yescomplemented
309C2×D172—28no—
310C2×D172—232no—
311C2×D172C2×D418yescomplemented
312C2×D172C24116yes—
313C2×D172C2414yes—
314C2×D172C2414yes—
315C2×D172C24116yes—
316C2×D172C2414yes—
317C2×C4×D43—216no—
318C2×C4×D43—264no—
319C2×C4×D43—48no—
320C2×C4×D43C2×D4116yescomplemented
321C2×C4×D43C2418yes—
322C2×C4×D43C24116yes—
323C2×C4×D43C24116yes—
324C2×C4×D43C2418yes—
325C2×C4×D43C2418yes—
326C2×C4×D43C2418yes—
327C2×C4×D43C2414yes—
328C2×C4×D43C2414yes—
329C2×Dic86—28no—
330C2×Dic86—232no—
331C2×Dic86C2×D418yescomplemented
332C2×Dic86C24116yes—
333C2×Dic86C2414yes—
334C2×Dic86C2414yes—
335C2×Dic86C2414yes—
336C4⋊C4×C43C2418yes—
337C4⋊C4×C43C24116yes—
338C22⋊C4×C43C2418yes—
339C22⋊C4×C43C24132yes—
340C42×C43C2414yes—
341C42×C43C2414yes—
342C22⋊Dic43C24116yes—
343C22⋊Dic43C24116yes—
344(C2×D43)⋊C4C24116yes—
345(C2×D43)⋊C4C24132yes—
346(C2×D43)⋊C4C24116yes—
347(C2×D43)⋊C4C24116yes—
348C4⋊Dic43C24116yes—
349Dic43⋊C4C24116yes—
350Dic43⋊C4C24116yes—
351Dic43⋊C4C24116yes—
352C4×Dic43C2412yes—
353C4×Dic43C2411yescharacteristic
354C4×Dic43C2411yescharacteristic
355C4×Dic43C2418yes—
356C4×Dic43C2418yes—
357C4×Dic43C2412yes—
358C4×Dic43C2412yes—
359C4×Dic43C2414yes—
360C4×Dic43C2414yes—
361C23×C43—28no—
362C23×C43—42no—
363C23×C43—48no—
364C23×C43C22×D414yes—
365C23×C43C2518yes—
366C23×C43C2512yes—
367C23×C43C2511yescharacteristic
368C22×D43—28no—
369C22×D43—232no—
370C22×D43—44no—
371C22×D43—432no—
372C22×D43—48no—
373C22×D43C22×D418yes—
374C22×D43C2518yes—
375C22×D43C2514yes—
376Q8×C43—28no—
377Q8×C43—28no—
378D4×C43—216no—
379D4×C43—216no—
380D4×C43—28no—
381D4×C43—28no—
382D4×C43—416no—
383C2×C4×C43—28no—
384C2×C4×C43—216no—
385C2×C4×C43—216no—
386C2×C4×C43—44no—
387C2×C4×C43C22×D418yes—
388C2×C4×C43C22×D414yes—
389C2×C4×C43C22×D418yes—
390C2×C4×C43C22×D414yes—
391C2×C4×C43C2518yes—
392C2×C4×C43C2518yes—
393C2×C4×C43C2511yescharacteristic
394C2×C4×C43C2512yes—
395C2×C4×C43C2511yescharacteristic
396C22⋊D43—216no—
397C22⋊D43—216no—
398C22⋊D43—232no—
399C22⋊D43—232no—
400C22⋊D43—232no—
401C22⋊D43—416no—
402C22⋊D43C22×D4132yes—
403C2×Dic43—28no—
404C2×Dic43—232no—
405C2×Dic43—24no—
406C2×Dic43—28no—
407C2×Dic43—44no—
408C2×Dic43—42no—
409C2×Dic43C22×D418yes—
410C2×Dic43C2512yes—
411C2×Dic43C2514yes—
412C2×Dic43C2518yes—
413C2×Dic43C2514yes—
414C2×Dic43C2512yes—
415D172—232no—
416D172—28no—
417D172—28no—
418D172—416no—
419D172C22×D4116yes—
420C4×D43—232no—
421C4×D43—216no—
422C4×D43—216no—
423C4×D43—232no—
424C4×D43—216no—
425C4×D43—48no—
426C4×D43C22×D4116yes—
427C4×D43C22×D4116yes—
428Dic86—28no—
429Dic86—28no—
430Dic86—232no—
431Dic86C22×D4116yes—
432#62812—431nomaximal, Sylow
433C22×C43—24no—
434C22×C43—22no—
435C22×C43—28no—
436C22×C43—216no—
437C22×C43—44no—
438C22×C43—88no—
439C22×C43C23×D414yes—
440C22×C43C23×D412yes—
441C22×C43C2611yescharacteristic
442C2×D43—28no—
443C2×D43—28no—
444C2×D43—216no—
445C2×D43—48no—
446C2×D43—832no—
447C2×D43—88no—
448C2×D43C23×D418yes—
449C4×C43—28no—
450C4×C43—28no—
451C4×C43C23×D412yes—
452C4×C43C23×D414yes—
453C4×C43C23×D412yes—
454Dic43—28no—
455Dic43—22no—
456Dic43—24no—
457Dic43C23×D418yes—
458Dic43#58514yescomplemented
459C2×#585—432no—
460#3500—434no—
461#3500—434no—
462#3499—434no—
463#3498—434no—
464#3497—434no—
465#3496—434no—
466#3496—438no—
467D4×#41—4316no—
468#3449—434no—
469#3449—431no—
470#3449D4311yescharacteristic, complemented
471C2×#532—432no—
472C2×#532—434no—
473C2×C4×#41—431no—
474C2×C43—22no—
475C2×C43—24no—
476C2×C43—48no—
477C2×C43C24×D411yescharacteristic
478C2×C43C2×#58512yes—
479D43—28no—
480D43—48no—
481#585—8632no—
482C2×2−1+4—434no—
483C2×2−1+4—434no—
484C2×2−1+4—434no—
485C2×H(5,𝔽2)—434no—
486C2×H(5,𝔽2)—434no—
487C2×H(5,𝔽2)—438no—
488C2×H(5,𝔽2)—434no—
489C22×#41—438no—
490C22×#41—438no—
491C22×#41—431no—
492C22×#41—432no—
493C22×#41—438no—
494C22×#41C2×D4312yescomplemented
495#550—4316no—
496D4×Q8—4316no—
497#548—4316no—
498#548—4316no—
499#547—4332no—
500#547—4316no—
501#546—4332no—
502#546—4316no—
503#546—4316no—
504#546—4332no—
505D42—4316no—
506D42—4332no—
507#537—4316no—
508#537—434no—
509#537C2×D4314yescomplemented
510#536—438no—
511#536—438no—
512#536—434no—
513#536C2×D4314yescomplemented
514#535—438no—
515#535—438no—
516#535—434no—
517#535C2×D4314yescomplemented
518#534—4316no—
519#534—434no—
520#534C2×D4314yescomplemented
521#532—434no—
522#532—434no—
523#532—438no—
524#532—438no—
525#532—434no—
526#532—434no—
527#532—434no—
528#532—434no—
529#532—438no—
530#532—4316no—
531#532—4316no—
532#532—434no—
533#532C2×D4314yescomplemented
534C2×C4⋊Q8—432no—
535C2×C4⋊Q8—434no—
536C2×#127—432no—
537C2×#127—434no—
538C2×#124—432no—
539C2×#124—432no—
540C2×#124—438no—
541#525—4332no—
542#525—438no—
543#525C2×D4318yescomplemented
544C2×#121—438no—
545C2×#121—4316no—
546C4×#41—438no—
547C4×#41—434no—
548C4×#41—434no—
549C2×C4×Q8—432no—
550C2×C4×D4—438no—
551C2×C4×D4—4316no—
552C2×C4×D4—432no—
553C2×C4×D4—434no—
554C2×#117—432no—
555C2×#117C2×D4311yescharacteristic, complemented
556C22×C42—431no—
557C22×C42—432no—
558C43#6281211yescharacteristic, complemented, Sylow
5592−1+4—8632no—
5602−1+4—8632no—
5612−1+4—8632no—
562H(5,𝔽2)—8664no—
563H(5,𝔽2)—8632no—
564H(5,𝔽2)—8632no—
565H(5,𝔽2)—8632no—
566C2×#41—216no—
567C2×#41—438no—
568C2×#41—438no—
569C2×#41—438no—
570C2×#41—4316no—
571C2×#41—4316no—
572C2×#41—438no—
573C2×#41—4316no—
574C2×#41—434no—
575C2×#41—434no—
576C2×#41—4316no—
577C2×#41—434no—
578C2×#41—434no—
579C2×#41—434no—
580C2×#41—434no—
581C2×#41—438no—
582C2×#41—4316no—
583C2×#41—438no—
584C2×#41—8664no—
585C2×#41—8664no—
586C2×#41—8664no—
587C2×#41—8616no—
588C2×#41C22×D4314yes—
589C2×#41C22×D4314yes—
590C2×#41C22×D4314yes—
591C2×#41C22×D4314yes—
592C22×Q8—438no—
593C22×Q8—438no—
594C22×Q8—431no—
595C22×Q8—432no—
596C22×Q8—438no—
597C22×Q8C22×D4312yes—
598C22×D4—432no—
599C22×D4—434no—
600C22×D4—4316no—
601C22×D4—438no—
602C22×D4—4316no—
603C22×D4—438no—
604C22×D4—4316no—
605C22×D4—438no—
606C22×D4—4316no—
607C22×D4—431no—
608C22×D4—432no—
609C22×D4—438no—
610C22×D4C22×D4314yes—
611C22×D4C22×D4312yes—
612C23×C4—432no—
613C23×C4—432no—
614C23×C4—4316no—
615C23×C4—434no—
616C23×C4—434no—
617C23×C4C22×D4314yes—
618C23×C4C22×D4311yescharacteristic
619C4⋊Q8—434no—
620C4⋊Q8—434no—
621C4⋊Q8—438no—
622C4⋊Q8—4316no—
623C4⋊Q8—434no—
624C4⋊Q8C22×D4314yes—
625#127—434no—
626#127—434no—
627#127—4316no—
628#127—438no—
629#127—434no—
630#127C22×D4314yes—
631#124—434no—
632#124—434no—
633#124—438no—
634#124—434no—
635#124—434no—
636#124—438no—
637#124—4332no—
638#124—438no—
639#124C22×D4318yes—
640#123—4332no—
641#123—4332no—
642#123—4316no—
643#123C22×D43116yes—
644C22⋊Q8—4332no—
645C22⋊Q8—4316no—
646C22⋊Q8—4332no—
647C22⋊Q8C22×D43116yes—
648#121—4316no—
649#121—4316no—
650#121—4316no—
651#121—4316no—
652#121—4316no—
653#121—4332no—
654#121—4316no—
655#121—4316no—
656#121—4316no—
657#121—4332no—
658#121—4332no—
659#121C22×D43116yes—
660#121C22×D43116yes—
661#120—4332no—
662#120—4332no—
663#120—4316no—
664#120C22×D43116yes—
665C4×Q8—438no—
666C4×Q8—438no—
667C4×D4—4316no—
668C4×D4—4316no—
669C4×D4—4316no—
670C4×D4—4316no—
671C4×D4—4316no—
672C4×D4—438no—
673C4×D4—438no—
674C4×D4—4316no—
675C4×D4—4316no—
676C4×D4—4316no—
677C4×D4—4332no—
678C4×D4—4316no—
679C4×D4C22×D43116yes—
680#117—438no—
681#117—438no—
682#117C22×D4314yes—
683#117C22×D4314yes—
684C2×C4⋊C4—434no—
685C2×C4⋊C4—438no—
686C2×C4⋊C4—4316no—
687C2×C4⋊C4C22×D4312yes—
688C2×C22⋊C4—438no—
689C2×C22⋊C4—434no—
690C2×C22⋊C4—438no—
691C2×C22⋊C4—4332no—
692C2×C22⋊C4C22×D4312yes—
693C2×C42—431no—
694C2×C42—434no—
695C2×C42—434no—
696C2×C42—432no—
697C2×C42—432no—
698C2×C42—432no—
699C2×C42—431no—
700C2×C42—438no—
701C2×C42—434no—
702C2×C42—434no—
703C2×C42C22×D4312yes—
704C24—432no—
705C24—4316no—
706C24—434no—
707C24C23×D4314yes—
708C24C23×D4311yescharacteristic
709#41—216no—
710#41—216no—
711#41—216no—
712#41—216no—
713#41—4332no—
714#41—4332no—
715#41—8664no—
716#41—8664no—
717#41—8632no—
718#41—8632no—
719#41—8664no—
720#41—8632no—
721#41—8632no—
722#41—8664no—
723#41—8632no—
724#41—8632no—
725#41—8616no—
726#41—8616no—
727#41—8616no—
728#41—8616no—
729C2×Q8—28no—
730C2×Q8—438no—
731C2×Q8—434no—
732C2×Q8—4316no—
733C2×Q8—434no—
734C2×Q8—434no—
735C2×Q8—8632no—
736C2×Q8—8632no—
737C2×Q8—8632no—
738C2×Q8—868no—
739C2×Q8C23×D4314yes—
740C2×Q8C23×D4314yes—
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—4316no—
744C2×D4—438no—
745C2×D4—4316no—
746C2×D4—4316no—
747C2×D4—438no—
748C2×D4—438no—
749C2×D4—4316no—
750C2×D4—4316no—
751C2×D4—438no—
752C2×D4—434no—
753C2×D4—4316no—
754C2×D4—434no—
755C2×D4—434no—
756C2×D4—4316no—
757C2×D4—8632no—
758C2×D4—8632no—
759C2×D4—8664no—
760C2×D4—8632no—
761C2×D4—8664no—
762C2×D4—8664no—
763C2×D4—8616no—
764C2×D4—868no—
765C2×D4—17232no—
766C2×D4—17216no—
767C2×D4C23×D4318yes—
768C2×D4C23×D4318yes—
769C2×D4C23×D4314yes—
770C2×D4C23×D4314yes—
771C2×D4C23×D43116yes—
772C22×C4—216no—
773C22×C4—432no—
774C22×C4—4316no—
775C22×C4—434no—
776C22×C4—434no—
777C22×C4—432no—
778C22×C4—434no—
779C22×C4—434no—
780C22×C4—4316no—
781C22×C4—434no—
782C22×C4—432no—
783C22×C4—438no—
784C22×C4—4316no—
785C22×C4—4316no—
786C22×C4—438no—
787C22×C4—438no—
788C22×C4—438no—
789C22×C4—8664no—
790C22×C4—8616no—
791C22×C4—1728no—
792C22×C4—1724no—
793C22×C4D4×D4318yescomplemented
794C22×C4C23×D4314yes—
795C22×C4C23×D4318yes—
796C22×C4C23×D4318yes—
797C22×C4C23×D4314yes—
798C22×C4C23×D4311yescharacteristic
799C22×C4C23×D4312yes—
800C22×C4C23×D4311yescharacteristic
801C22×C4C23×D4312yes—
802C4⋊C4—4316no—
803C4⋊C4—4316no—
804C4⋊C4—4316no—
805C4⋊C4—4316no—
806C4⋊C4C23×D43116yes—
807C4⋊C4C23×D4318yes—
808C22⋊C4—4316no—
809C22⋊C4—4316no—
810C22⋊C4—4316no—
811C22⋊C4—4316no—
812C22⋊C4—4316no—
813C22⋊C4—4332no—
814C22⋊C4C23×D43132yes—
815C22⋊C4C23×D4318yes—
816C42—431no—
817C42—431no—
818C42—432no—
819C42—438no—
820C42—434no—
821C42—438no—
822C42—434no—
823C42—432no—
824C42—432no—
825C42C23×D4314yes—
826C42C23×D4314yes—
827C23—28no—
828C23—42no—
829C23—48no—
830C23—434no—
831C23—438no—
832C23—438no—
833C23—8632no—
834C23—868no—
835C23—1728no—
836C23—17232no—
837C23—1724no—
838C23C2×D4×D4314yes—
839C23C24×D4318yes—
840C23C24×D4312yes—
841C23C24×D4311yescharacteristic
842Q8—28no—
843Q8—28no—
844Q8—4316no—
845Q8—8632no—
846Q8—868no—
847Q8—868no—
848D4—216no—
849D4—216no—
850D4—28no—
851D4—28no—
852D4—416no—
853D4—4332no—
854D4—4316no—
855D4—8632no—
856D4—8632no—
857D4—8632no—
858D4—8632no—
859D4—8616no—
860D4—8616no—
861D4—868no—
862D4—868no—
863D4—17216no—
864D4—17216no—
865C2×C4—28no—
866C2×C4—216no—
867C2×C4—216no—
868C2×C4—44no—
869C2×C4—438no—
870C2×C4—432no—
871C2×C4—434no—
872C2×C4—4316no—
873C2×C4—4316no—
874C2×C4—432no—
875C2×C4—434no—
876C2×C4—438no—
877C2×C4—8632no—
878C2×C4—8616no—
879C2×C4—8632no—
880C2×C4—8632no—
881C2×C4—864no—
882C2×C4—868no—
883C2×C4—868no—
884C2×C4—8616no—
885C2×C4—8616no—
886C2×C4—1728no—
887C2×C4—1724no—
888C2×C4—1722no—
889C2×C4C2×D4×D4318yes—
890C2×C4C2×D4×D4314yes—
891C2×C4C2×D4×D4318yes—
892C2×C4C2×D4×D4314yes—
893C2×C4C24×D4318yes—
894C2×C4C24×D4318yes—
895C2×C4C24×D4311yescharacteristic
896C2×C4C24×D4312yes—
897C2×C4C24×D4311yescharacteristic
898C22—22no—
899C22—24no—
900C22—28no—
901C22—216no—
902C22—44no—
903C22—88no—
904C22—438no—
905C22—868no—
906C22—868no—
907C22—8616no—
908C22—3448no—
909C22—34432no—
910C22—1728no—
911C22C22×D4×D4314yes—
912C22C22×D4×D4312yes—
913C22C25×D4311yescharacteristic
914C4—28no—
915C4—28no—
916C4—438no—
917C4—434no—
918C4—868no—
919C4—862no—
920C4—864no—
921C4C22×D4×D4312yes—
922C4C22×D4×D4314yes—
923C4C22×D4×D4312yes—
924C2—24no—
925C2—22no—
926C2—48no—
927C2—868no—
928C2—1728no—
929C2C23×D4×D4311yescharacteristic
930C2#585×D4312yes—
subgroupG/H
centerC2×C4C24×D43
commutator, socle, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC43×#3449C2
hypercenter#3449D43
hypocenterC43#62812
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#14583735C2semidirect
2. #19148387C2semidirect
3. #19148384C2semidirect
4. #19148377C2semidirect
5. #19148370C2semidirect
6. #19148364C2semidirect
7. #19148358C2semidirect
8. #19148356C2semidirect
9. #19148078C2semidirect
10. #19147928C2semidirect
11. #19147922C2semidirect
12. C2×#14583445C2semidirect
13. #532×D43C2semidirect
14. C2×#14583367C2semidirect
15. C43×#3449C2semidirect
17. C2×#13063373C22semidirect
18. C2×#13063372C22semidirect
19. C2×#13063372C22semidirect
20. C2×#13063371C22semidirect
21. C2×#13063371C22semidirect
22. C2×#13063370C22semidirect
23. C2×#13063370C22semidirect
25. C22×#10621898C22semidirect
26. C22×#10621898C22semidirect
27. C2×#41×D43C22semidirect
28. C2×#41×D43C22semidirect
29. #14583567C22semidirect
30. #14583562C22semidirect
31. #14583559C22semidirect
32. #14583555C22semidirect
33. #14583551C22semidirect
34. #14583547C22semidirect
35. #14583546C22semidirect
36. #14583541C22semidirect
37. #14583540C22semidirect
38. #14583536C22semidirect
39. #14583533C22semidirect
40. #14583531C22semidirect
41. #14583480C22semidirect
42. #14583476C22semidirect
43. #14583475C22semidirect
44. #14583474C22semidirect
45. #14583469C22semidirect
46. #14583468C22semidirect
47. #14583467C22semidirect
48. #14583462C22semidirect
49. #14583461C22semidirect
50. #14583457C22semidirect
51. #14583450C22semidirect
52. #14583449C22semidirect
53. #14583448C22semidirect
54. #14583447C22semidirect
55. #14583446C22semidirect
56. #14583445C22semidirect
57. #14583445C22semidirect
58. #14583445C22semidirect
59. #14583445C22semidirect
60. #14583445C22semidirect
61. #14583445C22semidirect
62. #14583444C22semidirect
63. C2×#13063323C22semidirect
64. C4⋊Q8×D43C22semidirect
65. C2×#13063321C22semidirect
66. #127×D43C22semidirect
67. C2×#13063314C22semidirect
68. C2×#13063312C22semidirect
69. #124×D43C22semidirect
70. #14583411C22semidirect
71. #14583408C22semidirect
72. C2×#13063297C22semidirect
73. #121×D43C22semidirect
74. #14583367C22semidirect
75. #14583367C22semidirect
76. #14583367C22semidirect
77. C2×#13063290C22semidirect
78. C2×#13063287C22semidirect
79. C2×C4×C22⋊D43C22semidirect
80. C2×(C22⋊D43)⋊C4C22semidirect
81. C4×D4×D43C22semidirect
82. C2×#13063282C22semidirect
83. C22×C4×Dic43C22semidirect
84. C2×C42×D43C22semidirect
85. C22×#41×C43C22semidirect
86. C43×#537C22semidirect
87. C43×#536C22semidirect
88. C43×#535C22semidirect
89. C43×#534C22semidirect
90. C43×#532C22semidirect
91. C43×#525C22semidirect
92. C2×#117×C43C22semidirect
104. C2×#10621898D4semidirect
258. C22×C4×C43C2×D4semidirect
270. C2×C22⋊D43C2×D4semidirect
307. #10621898C2×D4semidirect
308. #10621898C2×D4semidirect
311. C2×D172C2×D4semidirect
320. C2×C4×D43C2×D4semidirect
331. C2×Dic86C2×D4semidirect
458. Dic43#585semidirect
470. #3449D43semidirect
494. C22×#41C2×D43semidirect
509. #537C2×D43semidirect
513. #536C2×D43semidirect
517. #535C2×D43semidirect
520. #534C2×D43semidirect
533. #532C2×D43semidirect
543. #525C2×D43semidirect
555. C2×#117C2×D43semidirect
558. C43#62812semidirect
793. C22×C4D4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145837352
#191483872
#191483842
#191483772
#191483702
#191483642
#191483582
#191483562
#191480782
#191479282
#191479222
C2×#145834452
#532×D432
C2×#145833672
C43×#34492
#6281243