Finite Group Databasebeta

← #15617375

Subgroups — #15617375

Order 2816.

4852 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623453C211yesmaximal, characteristic
2C2×#10623276C211yesmaximal, characteristic, complemented
3#13081817C211yesmaximal, characteristic, complemented
4#13077162C218yesmaximal, complemented
5#13077160C218yesmaximal, complemented
6C2×#10622618C211yesmaximal, characteristic, complemented
7C2×#10622849C211yesmaximal, characteristic, complemented
8C2×#10622752C211yesmaximal, characteristic, complemented
9D11×#421C218yesmaximal, complemented
10C2×C11×#421C211yesmaximal, characteristic, complemented
11C22×C11×#41C2211yescharacteristic
12#10623453—22no—
13#10623453—22no—
14#10623453—22no—
15#10623453—22no—
16#10623453C414yescomplemented
17#10623453C414yescomplemented
18#10623453C2214yes—
19#10623453C2214yes—
20C2×#67043—21no—
21C2×#67043C412yescomplemented
22C2×#67042—21no—
23C2×#67042C412yescomplemented
24C2×#41×D11—22no—
25C2×#41×D11C2214yes—
26C2×#67040C412yescomplemented
27C2×#67037—22no—
28C2×#67037C412yescomplemented
29C22×#4339—22no—
30C22×#4339C2211yescharacteristic
31C22×#4339C2211yescharacteristic
32C22×C11×M16C2211yescharacteristic, complemented
33C2×C11×#117C2211yescharacteristic, complemented
34C2×#66979C2211yescharacteristic, complemented
35C22×#4318C2211yescharacteristic, complemented
36#10623276—22no—
37#10623276—22no—
38#10623276C2214yescomplemented
39#10623276C2214yescomplemented
40C2×#66960—22no—
41C2×M16×D11C2214yescomplemented
42C2×#66954—22no—
43#10623054—22no—
44#10623053C2214yescomplemented
45#10623052—21no—
46D11×#117C2214yescomplemented
47#10623047—21no—
48#10623035—22no—
49#10623017—22no—
50C4×#4339C2214yescomplemented
51C11×#421C2214yescomplemented
52C11×#421C2214yescomplemented
53C2×C11×#104C2214yescomplemented
54#10622849C2214yescomplemented
55#10622849C2214yescomplemented
56C2×#66901C2214yescomplemented
57#10622752C2214yescomplemented
58#10622752C2214yescomplemented
59C2×#66889C2214yescomplemented
60#10622618C2214yescomplemented
61#10622618C2214yescomplemented
62C2×#66869C2214yescomplemented
63#10622434C22132yescomplemented
64D11×#104C22132yescomplemented
65C2×C11×#41—21no—
66C2×C11×#41—21no—
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×C11×#41—21no—
70C2×C11×#41—21no—
71C2×C11×#41C2×C412yescomplemented
72C2×C11×#41C2×C412yescomplemented
73C2×C11×#41C2×C412yescomplemented
74C2×C11×#41C2312yes—
75C2×C11×#41C2312yes—
76C2×C11×#41C2312yes—
77C22×Q8×C11C2×C411yescharacteristic, complemented
78C22×D4×C11—21no—
79C22×D4×C11C2×C411yescharacteristic, complemented
80C23×C4×C11—21no—
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11D412yes—
85#67043—24no—
86#67043—24no—
87#67043—24no—
88#67043—24no—
89#67043—24no—
90#67043—24no—
91#67043C2×C418yescomplemented
92#67043C2×C418yescomplemented
93#67042—24no—
94#67042—24no—
95#67042—24no—
96#67042—24no—
97#67042—24no—
98#67042—24no—
99#67042C2×C418yescomplemented
100#67042C2×C418yescomplemented
101#41×D11—28no—
102#41×D11—28no—
103#41×D11—28no—
104#41×D11—28no—
105#41×D11—28no—
106#41×D11—28no—
107#41×D11C2×C4116yescomplemented
108#41×D11C23116yes—
109#67040—24no—
110#67040—24no—
111#67040C2×C418yescomplemented
112#67040C2×C418yescomplemented
113C2×#4343—22no—
114C2×#4343C2×C414yescomplemented
115C2×Q8×D11—22no—
116C2×Q8×D11C2×C414yescomplemented
117#67037—28no—
118#67037—28no—
119#67037—28no—
120#67037—28no—
121#67037—24no—
122#67037—24no—
123#67037C2×C418yescomplemented
124#67037C2×C418yescomplemented
125C2×#4341—24no—
126C2×#4341—24no—
127C2×#4341—22no—
128C2×#4341C2×C414yescomplemented
129C2×D4×D11—24no—
130C2×D4×D11—24no—
131C2×D4×D11—22no—
132C2×D4×D11C2×C414yescomplemented
133C2×#4339—21no—
134C2×#4339—21no—
135C2×#4339—21no—
136C2×#4339—21no—
137C2×#4339—21no—
138C2×#4339—21no—
139C2×#4339—24no—
140C2×#4339—28no—
141C2×#4339—28no—
142C2×#4339—28no—
143C2×#4339—28no—
144C2×#4339—22no—
145C2×#4339—24no—
146C2×#4339—22no—
147C2×#4339C2×C412yes—
148C2×#4339C2×C412yes—
149C2×#4339C2×C412yes—
150C2×#4339C2×C412yes—
151C2×#4339C2×C412yescomplemented
152C2×#4339C2×C412yescomplemented
153C2×#4339C2×C412yescomplemented
154C2×#4339D412yes—
155C2×#4339D412yes—
156C2×#4339D412yes—
157C2×#4339D412yes—
158C2×#4339D412yes—
159C2×#4339D412yes—
160C2×#4339C2312yes—
161C2×#4339C2312yes—
162C2×#4339C2312yes—
163C2×#4339C2312yes—
164C2×#4339C2312yes—
165C22×D44—22no—
166C22×D44C2×C411yescharacteristic, complemented
167C22×D44D411yescharacteristic
168C22×C4×D11—21no—
169C22×C4×D11—24no—
170C22×C4×D11C2312yes—
171C22×Dic22—22no—
172C22×Dic22C2×C411yescharacteristic, complemented
173C22×Dic22D411yescharacteristic
174C2×C11×M16—21no—
175C2×C11×M16—21no—
176C2×C11×M16—21no—
177C2×C11×M16C2312yes—
178C2×C11×M16C2312yescomplemented
179C2×C11×M16C2312yescomplemented
180C22×C8×C11—21no—
181C11×#117—21no—
182C11×#117—21no—
183C11×#117C2312yes—
184C11×#117C2312yescomplemented
185C2×C11×C4⋊C4—21no—
186C2×C11×C22⋊C4—21no—
187C2×C42×C11C2312yescomplemented
188C2×C22⋊Dic11—21no—
189C4×C22⋊D11—28no—
190#66979—21no—
191#66979—21no—
192#66979C2312yes—
193#66979C2312yescomplemented
194C2×C4⋊Dic11—21no—
195C2×C4×Dic11C2312yescomplemented
196C2×#4318—21no—
197C2×#4318—21no—
198C2×#4318—21no—
199C2×#4318C2312yes—
200C2×#4318C2312yescomplemented
201C2×#4318C2312yescomplemented
202C22×C11⋊C8—21no—
203#66960—28no—
204#66960—28no—
205M16×D11—28no—
206M16×D11C23116yescomplemented
207#66954—28no—
208#66954—28no—
209C2×#4313—24no—
210C2×C8×D11—24no—
211#66946—24no—
212#66945—24no—
213C4⋊C4×D11—24no—
214#66940—24no—
215(C22⋊D11)⋊C4—28no—
216C22⋊C4×D11—24no—
217#66930—24no—
218C4×D44—24no—
219#66925C2318yescomplemented
220C42×D11C2318yescomplemented
221C4×Dic22—24no—
222C11×#104C23116yescomplemented
223#66901C23116yescomplemented
224#66889C23116yescomplemented
225#66869C23116yescomplemented
226#60093—111nomaximal, Sylow
227C24×C11—21no—
228C24×C11C2×D411yescharacteristic
229C23×D11—21no—
230C23×D11—24no—
231C23×D11C2×D412yes—
232C11×#41—22no—
233C11×#41—22no—
234C11×#41—22no—
235C11×#41—22no—
236C11×#41—22no—
237C11×#41—22no—
238C11×#41—22no—
239C11×#41—22no—
240C11×#41—22no—
241C11×#41—22no—
242C11×#41—22no—
243C11×#41—22no—
244C11×#41C22×C414yes—
245C11×#41C22×C414yes—
246C11×#41C22×C414yes—
247C11×#41C2414yes—
248C2×Q8×C11—21no—
249C2×Q8×C11—21no—
250C2×Q8×C11—21no—
251C2×Q8×C11C22×C412yes—
252C2×Q8×C11C22×C412yes—
253C2×Q8×C11C22×C412yes—
254C2×D4×C11—22no—
255C2×D4×C11—22no—
256C2×D4×C11—22no—
257C2×D4×C11—22no—
258C2×D4×C11—22no—
259C2×D4×C11—22no—
260C2×D4×C11—21no—
261C2×D4×C11—21no—
262C2×D4×C11—21no—
263C2×D4×C11C22×C412yes—
264C2×D4×C11C22×C412yes—
265C2×D4×C11C22×C412yes—
266C22×C4×C11—21no—
267C22×C4×C11—22no—
268C22×C4×C11—22no—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—22no—
274C22×C4×C11C22×C411yescharacteristic
275C22×C4×C11C22×C411yescharacteristic
276C22×C4×C11C22×C411yescharacteristic
277C22×C4×C11C22×C411yescharacteristic
278C22×C4×C11C2×D411yescharacteristic
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2×D411yescharacteristic
283C22×C4×C11C2×D411yescharacteristic
284C22×C4×C11C2×D411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C2×C22⋊D11—216no—
289C2×C22⋊D11—216no—
290C2×C22⋊D11—24no—
291C2×C22⋊D11—22no—
292C2×C22⋊D11—22no—
293C2×C22⋊D11—22no—
294C2×C22⋊D11—22no—
295C2×C22⋊D11—22no—
296C2×C22⋊D11—22no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11C22⋊C414yes—
299C2×C22⋊D11C22⋊C414yes—
300C2×C22⋊D11C22⋊C414yes—
301C2×C22⋊D11C22⋊C414yes—
302C2×C22⋊D11C2×D414yes—
303C2×C22⋊D11C2×D414yes—
304C22×Dic11—24no—
305C22×Dic11—21no—
306C22×Dic11—22no—
307C22×Dic11C2×D412yes—
308#4343—28no—
309#4343—28no—
310#4343—28no—
311#4343C22×C4116yes—
312Q8×D11—28no—
313Q8×D11—28no—
314Q8×D11—28no—
315Q8×D11C22×C4116yes—
316#4341—216no—
317#4341—216no—
318#4341—216no—
319#4341—216no—
320#4341—28no—
321#4341—28no—
322#4341—28no—
323#4341C22×C4116yes—
324D4×D11—216no—
325D4×D11—216no—
326D4×D11—28no—
327D4×D11—28no—
328D4×D11—28no—
329D4×D11—216no—
330D4×D11—216no—
331D4×D11C22×C4116yes—
332#4339—216no—
333#4339—216no—
334#4339—28no—
335#4339—28no—
336#4339—216no—
337#4339—216no—
338#4339—28no—
339#4339—28no—
340#4339—22no—
341#4339—22no—
342#4339—22no—
343#4339—22no—
344#4339—22no—
345#4339—22no—
346#4339—22no—
347#4339—22no—
348#4339—22no—
349#4339—22no—
350#4339—22no—
351#4339—22no—
352#4339C22⋊C414yes—
353#4339C22⋊C414yes—
354#4339C22⋊C414yes—
355#4339C22⋊C414yes—
356#4339C22⋊C414yes—
357#4339C22⋊C414yes—
358#4339C22⋊C414yes—
359#4339C22⋊C414yes—
360#4339C22×C414yes—
361#4339C22×C414yes—
362#4339C22×C414yes—
363#4339C22×C414yes—
364#4339C22×C414yes—
365#4339C22×C414yes—
366#4339C22×C414yes—
367#4339C2×D414yes—
368#4339C2×D414yes—
369#4339C2×D414yes—
370#4339C2×D414yes—
371#4339C2414yes—
372C2×D44—28no—
373C2×D44—28no—
374C2×D44—24no—
375C2×D44—21no—
376C2×D44—21no—
377C2×D44—21no—
378C2×D44C22⋊C412yes—
379C2×D44C22⋊C412yes—
380C2×D44C22⋊C412yes—
381C2×D44C22⋊C412yes—
382C2×D44C22×C412yes—
383C2×D44C22×C412yes—
384C2×D44C22×C412yes—
385C2×D44C2×D412yes—
386C2×D44C2×D412yes—
387C2×C4×D11—24no—
388C2×C4×D11—216no—
389C2×C4×D11—216no—
390C2×C4×D11—24no—
391C2×C4×D11—28no—
392C2×C4×D11—22no—
393C2×C4×D11—22no—
394C2×C4×D11—22no—
395C2×C4×D11—22no—
396C2×C4×D11—22no—
397C2×C4×D11—22no—
398C2×C4×D11C22×C414yes—
399C2×C4×D11C22×C414yes—
400C2×C4×D11C2×D414yes—
401C2×C4×D11C2×D414yes—
402C2×C4×D11C2×D414yes—
403C2×C4×D11C2414yes—
404C2×Dic22—24no—
405C2×Dic22—28no—
406C2×Dic22—28no—
407C2×Dic22—21no—
408C2×Dic22—21no—
409C2×Dic22—21no—
410C2×Dic22C22⋊C412yes—
411C2×Dic22C22⋊C412yes—
412C2×Dic22C22⋊C412yes—
413C2×Dic22C22⋊C412yes—
414C2×Dic22C22×C412yes—
415C2×Dic22C22×C412yes—
416C2×Dic22C22×C412yes—
417C2×Dic22C2×D412yes—
418C2×Dic22C2×D412yes—
419C11×M16—22no—
420C11×M16—22no—
421C11×M16—22no—
422C11×M16C2414yes—
423C2×C8×C11—22no—
424C2×C8×C11—22no—
425C2×C8×C11—22no—
426C11×C4⋊C4—22no—
427C11×C4⋊C4—22no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4—22no—
430C42×C11—22no—
431C42×C11C2414yes—
432C22⋊Dic11—22no—
433C22⋊Dic11—22no—
434(C2×D11)⋊C4—28no—
435C4⋊Dic11—22no—
436C4⋊Dic11—22no—
437Dic11⋊C4—28no—
438C4×Dic11—28no—
439C4×Dic11—22no—
440C4×Dic11C2414yes—
441#4318—22no—
442#4318—22no—
443#4318—22no—
444#4318C2414yes—
445C2×C11⋊C8—22no—
446C2×C11⋊C8—22no—
447C2×C11⋊C8—22no—
448#4313—216no—
449C8×D11—216no—
450C2×#585—111no—
451C2×#568—111no—
452#3428—111no—
453#2901—118no—
454#2901—118no—
455C2×#421—118no—
456C2×#421—111no—
457C2×#421—111no—
458C2×#421—111no—
459C2×#421D1111yescharacteristic, complemented
460C23×C11—22no—
461C23×C11—22no—
462C23×C11—22no—
463C23×C11—81no—
464C23×C11—82no—
465C23×C11C2×C22⋊C411yescharacteristic
466C23×C11C2×C22⋊C411yescharacteristic
467C23×C11C2×C22⋊C411yescharacteristic
468C23×C11C2×C22⋊C411yescharacteristic
469C23×C11C22×D411yescharacteristic
470C23×C11C22×D411yescharacteristic
471C23×C11C22×D411yescharacteristic
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—216no—
476C22×D11—82no—
477C22×D11—88no—
478C22×D11—82no—
479C22×D11C2×C22⋊C414yes—
480C22×D11C2×C22⋊C414yes—
481C22×D11C22×D414yes—
482Q8×C11—22no—
483Q8×C11—22no—
484Q8×C11—22no—
485Q8×C11C23×C414yes—
486D4×C11—24no—
487D4×C11—24no—
488D4×C11—24no—
489D4×C11—24no—
490D4×C11—22no—
491D4×C11—22no—
492D4×C11—22no—
493D4×C11C23×C414yes—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—24no—
498C2×C4×C11—24no—
499C2×C4×C11—24no—
500C2×C4×C11—24no—
501C2×C4×C11—24no—
502C2×C4×C11—82no—
503C2×C4×C11C2×C22⋊C411yescharacteristic
504C2×C4×C11C2×C22⋊C411yescharacteristic
505C2×C4×C11C2×C22⋊C411yescharacteristic
506C2×C4×C11C2×C22⋊C411yescharacteristic
507C2×C4×C11C2×C22⋊C411yescharacteristic
508C2×C4×C11C2×C22⋊C411yescharacteristic
509C2×C4×C11C2×C22⋊C411yescharacteristic
510C2×C4×C11C2×C22⋊C411yescharacteristic
511C2×C4×C11C2×C22⋊C411yescharacteristic
512C2×C4×C11C2×C22⋊C411yescharacteristic
513C2×C4×C11C2×C22⋊C411yescharacteristic
514C2×C4×C11C2×C22⋊C411yescharacteristic
515C2×C4×C11C23×C411yescharacteristic
516C2×C4×C11C23×C411yescharacteristic
517C2×C4×C11C23×C411yescharacteristic
518C2×C4×C11C23×C411yescharacteristic
519C2×C4×C11C23×C411yescharacteristic
520C2×C4×C11C23×C411yescharacteristic
521C2×C4×C11C22×D411yescharacteristic
522C2×C4×C11C22×D411yescharacteristic
523C2×C4×C11C22×D411yescharacteristic
524C2×C4×C11C22×D411yescharacteristic
525C2×C4×C11C22×D411yescharacteristic
526C2×C4×C11C22×D411yescharacteristic
527C2×C4×C11C22×D411yescharacteristic
528C2×C4×C11C22×D411yescharacteristic
529C2×C4×C11C22×D411yescharacteristic
530C2×C4×C11C2511yescharacteristic
531C22⋊D11—24no—
532C22⋊D11—24no—
533C22⋊D11—24no—
534C22⋊D11—24no—
535C22⋊D11—216no—
536C22⋊D11—216no—
537C22⋊D11C2×C22⋊C418yes—
538C22⋊D11C2×C22⋊C418yes—
539C22⋊D11C2×C22⋊C418yes—
540C22⋊D11C2×C22⋊C418yes—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—216no—
545C2×Dic11—24no—
546C2×Dic11—82no—
547C2×Dic11C2×C22⋊C414yes—
548C2×Dic11C2×C22⋊C414yes—
549C2×Dic11C22×D414yes—
550D44—216no—
551D44—22no—
552D44—22no—
553D44—22no—
554D44C2×C22⋊C414yes—
555D44C2×C22⋊C414yes—
556D44C2×C22⋊C414yes—
557D44C2×C22⋊C414yes—
558D44C23×C414yes—
559C4×D11—216no—
560C4×D11—24no—
561C4×D11—24no—
562C4×D11—24no—
563C4×D11—24no—
564C4×D11—216no—
565C4×D11—88no—
566C4×D11C2×C22⋊C418yes—
567C4×D11C2×C22⋊C418yes—
568C4×D11C23×C418yes—
569C4×D11C22×D418yes—
570Dic22—22no—
571Dic22—22no—
572Dic22—22no—
573Dic22—216no—
574Dic22C2×C22⋊C414yes—
575Dic22C2×C22⋊C414yes—
576Dic22C2×C22⋊C414yes—
577Dic22C2×C22⋊C414yes—
578Dic22C23×C414yes—
579C8×C11—24no—
580C11⋊C8—24no—
581#585—114no—
582#585—114no—
583#585—114no—
584#585—114no—
585#585—222no—
586#585—222no—
587#585—222no—
588#585—222no—
589C2×2−1+4—112no—
590C2×2−1+4—112no—
591C2×2−1+4—221no—
592C2×H(5,𝔽2)—112no—
593C2×H(5,𝔽2)—112no—
594C2×H(5,𝔽2)—222no—
595C2×H(5,𝔽2)—221no—
596C22×#41—111no—
597C22×#41—114no—
598C22×#41—111no—
599C22×#41—222no—
600C22×#41—222no—
601C22×#41C2×D1111yescharacteristic
602#568—114no—
603#568—114no—
604#568—222no—
605#568—222no—
606C2×#131—222no—
607C2×#131—222no—
608C22×M16—111no—
609C22×M16—114no—
610C22×M16C2×D1111yescharacteristic, complemented
611#520—222no—
612#520—222no—
613#519—221no—
614#518—222no—
615#518—221no—
616C4×#41—114no—
617C4×#41—114no—
618C2×#117—111no—
619C2×#117—114no—
620C2×#117C2×D1111yescharacteristic, complemented
621#421—114no—
622#421—114no—
623#421—114no—
624#421—114no—
625#421—114no—
626#421—114no—
627#421—1132no—
628#421C2×D1114yescomplemented
629#421C2×D1114yescomplemented
630C2×#104—114no—
631C2×#104—114no—
632C2×#104—114no—
633C2×#104—1132no—
634C2×#104C2×D1114yescomplemented
635C22×C11—24no—
636C22×C11—41no—
637C22×C11—41no—
638C22×C11—41no—
639C22×C11—41no—
640C22×C11—41no—
641C22×C11—41no—
642C22×C11—41no—
643C22×C11—44no—
644C22×C11—82no—
645C22×C11—82no—
646C22×C11C22×C22⋊C411yescharacteristic
647C22×C11C22×C22⋊C411yescharacteristic
648C22×C11C22×C22⋊C411yescharacteristic
649C22×C11C22×C22⋊C411yescharacteristic
650C22×C11C22×C22⋊C411yescharacteristic
651C22×C11C22×C22⋊C411yescharacteristic
652C22×C11C23×D411yescharacteristic
653C2×D11—24no—
654C2×D11—44no—
655C2×D11—44no—
656C2×D11—44no—
657C2×D11—44no—
658C2×D11—816no—
659C2×D11—82no—
660C2×D11—82no—
661C2×D11C22×C22⋊C418yes—
662C4×C11—24no—
663C4×C11—44no—
664C4×C11C22×C22⋊C411yescharacteristic
665C4×C11C22×C22⋊C411yescharacteristic
666C4×C11C22×C22⋊C411yescharacteristic
667C4×C11C22×C22⋊C411yescharacteristic
668C4×C11C22×C22⋊C411yescharacteristic
669C4×C11C22×C22⋊C411yescharacteristic
670C4×C11C24×C411yescharacteristic
671C4×C11C23×D411yescharacteristic
672Dic11—24no—
673Dic11—44no—
674Dic11C22×C22⋊C418yes—
6752−1+4—118no—
6762−1+4—118no—
6772−1+4—118no—
6782−1+4—118no—
6792−1+4—224no—
6802−1+4—224no—
6812−1+4—224no—
6822−1+4—224no—
6832−1+4—224no—
6842−1+4—224no—
6852−1+4—224no—
6862−1+4—224no—
687H(5,𝔽2)—118no—
688H(5,𝔽2)—118no—
689H(5,𝔽2)—118no—
690H(5,𝔽2)—118no—
691H(5,𝔽2)—228no—
692H(5,𝔽2)—228no—
693H(5,𝔽2)—228no—
694H(5,𝔽2)—228no—
695H(5,𝔽2)—224no—
696H(5,𝔽2)—224no—
697H(5,𝔽2)—224no—
698H(5,𝔽2)—224no—
699H(5,𝔽2)—224no—
700H(5,𝔽2)—224no—
701H(5,𝔽2)—224no—
702H(5,𝔽2)—224no—
703C2×#41—21no—
704C2×#41—21no—
705C2×#41—21no—
706C2×#41—21no—
707C2×#41—21no—
708C2×#41—21no—
709C2×#41—112no—
710C2×#41—112no—
711C2×#41—112no—
712C2×#41—112no—
713C2×#41—112no—
714C2×#41—112no—
715C2×#41—112no—
716C2×#41—112no—
717C2×#41—112no—
718C2×#41—112no—
719C2×#41—112no—
720C2×#41—112no—
721C2×#41—1116no—
722C2×#41—1116no—
723C2×#41—114no—
724C2×#41—114no—
725C2×#41—112no—
726C2×#41—112no—
727C2×#41—112no—
728C2×#41—112no—
729C2×#41—112no—
730C2×#41—112no—
731C2×#41—224no—
732C2×#41—224no—
733C2×#41—222no—
734C2×#41—222no—
735C2×#41—228no—
736C2×#41—228no—
737C2×#41—228no—
738C2×#41—228no—
739C2×#41—224no—
740C2×#41—228no—
741C2×#41—228no—
742C2×#41—224no—
743C2×#41—222no—
744C2×#41—222no—
745C2×#41—228no—
746C2×#41—228no—
747C2×#41—228no—
748C2×#41—228no—
749C2×#41—221no—
750C2×#41—221no—
751C2×#41—221no—
752C2×#41—221no—
753C2×#41—221no—
754C2×#41—221no—
755C2×#41C4×D1112yescomplemented
756C2×#41C4×D1112yescomplemented
757C2×#41C4×D1112yescomplemented
758C2×#41C22×D1112yes—
759C2×#41C22×D1112yes—
760C2×#41C22×D1112yes—
761C22×Q8—111no—
762C22×Q8—114no—
763C22×Q8—111no—
764C22×Q8—222no—
765C22×Q8—222no—
766C22×Q8C4×D1111yescharacteristic, complemented
767C22×D4—21no—
768C22×D4—112no—
769C22×D4—114no—
770C22×D4—111no—
771C22×D4—111no—
772C22×D4—222no—
773C22×D4—224no—
774C22×D4—222no—
775C22×D4—224no—
776C22×D4—224no—
777C22×D4—221no—
778C22×D4C4×D1111yescharacteristic, complemented
779C23×C4—21no—
780C23×C4—112no—
781C23×C4—224no—
782C23×C4—221no—
783C23×C4C22×D1111yescharacteristic
784#131—228no—
785#131—228no—
786#131—228no—
787#131—228no—
788C2×M16—21no—
789C2×M16—21no—
790C2×M16—21no—
791C2×M16—112no—
792C2×M16—112no—
793C2×M16—112no—
794C2×M16—1116no—
795C2×M16—224no—
796C2×M16—228no—
797C2×M16—221no—
798C2×M16—221no—
799C2×M16—221no—
800C2×M16C22×D1112yes—
801C2×M16C22×D1112yescomplemented
802C2×M16C22×D1112yescomplemented
803C22×C8—21no—
804C22×C8—224no—
805C22×C8—221no—
806C4×Q8—224no—
807C4×Q8—224no—
808C4×D4—224no—
809C4×D4—228no—
810C4×D4—224no—
811C4×D4—228no—
812#117—21no—
813#117—21no—
814#117—112no—
815#117—112no—
816#117—118no—
817#117—224no—
818#117—224no—
819#117—221no—
820#117—221no—
821#117C22×D1112yes—
822#117C22×D1112yescomplemented
823C2×C4⋊C4—21no—
824C2×C4⋊C4—224no—
825C2×C4⋊C4—221no—
826C2×C22⋊C4—21no—
827C2×C22⋊C4—224no—
828C2×C22⋊C4—221no—
829C2×C42—112no—
830C2×C42—118no—
831C2×C42C22×D1112yescomplemented
832#104—1116no—
833#104—1116no—
834#104—1116no—
835#104C22×D11116yescomplemented
836C2×C11—21no—
837C2×C11—21no—
838C2×C11—21no—
839C2×C11—21no—
840C2×C11—21no—
841C2×C11—21no—
842C2×C11—21no—
843C2×C11—44no—
844C2×C11C23×C22⋊C411yescharacteristic
845D11—28no—
846D11—44no—
847C24—21no—
848C24—112no—
849C24—224no—
850C24—221no—
851C24D4×D1111yescharacteristic
852#41—22no—
853#41—22no—
854#41—22no—
855#41—22no—
856#41—22no—
857#41—22no—
858#41—22no—
859#41—22no—
860#41—22no—
861#41—22no—
862#41—22no—
863#41—22no—
864#41—114no—
865#41—114no—
866#41—114no—
867#41—114no—
868#41—114no—
869#41—114no—
870#41—114no—
871#41—114no—
872#41—114no—
873#41—114no—
874#41—114no—
875#41—114no—
876#41—114no—
877#41—114no—
878#41—114no—
879#41—114no—
880#41—1116no—
881#41—1116no—
882#41—114no—
883#41—114no—
884#41—114no—
885#41—114no—
886#41—2216no—
887#41—2216no—
888#41—2216no—
889#41—2216no—
890#41—228no—
891#41—228no—
892#41—228no—
893#41—228no—
894#41—2216no—
895#41—2216no—
896#41—228no—
897#41—228no—
898#41—2216no—
899#41—2216no—
900#41—228no—
901#41—228no—
902#41—228no—
903#41—228no—
904#41—222no—
905#41—222no—
906#41—222no—
907#41—222no—
908#41—222no—
909#41—222no—
910#41—222no—
911#41—222no—
912#41—222no—
913#41—222no—
914#41—222no—
915#41—222no—
916#41C2×C4×D1114yes—
917#41C2×C4×D1114yes—
918#41C2×C4×D1114yes—
919#41C23×D1114yes—
920C2×Q8—21no—
921C2×Q8—21no—
922C2×Q8—21no—
923C2×Q8—112no—
924C2×Q8—112no—
925C2×Q8—112no—
926C2×Q8—112no—
927C2×Q8—112no—
928C2×Q8—112no—
929C2×Q8—1116no—
930C2×Q8—112no—
931C2×Q8—112no—
932C2×Q8—112no—
933C2×Q8—224no—
934C2×Q8—228no—
935C2×Q8—228no—
936C2×Q8—228no—
937C2×Q8—228no—
938C2×Q8—228no—
939C2×Q8—221no—
940C2×Q8—221no—
941C2×Q8—221no—
942C2×Q8C2×C4×D1112yes—
943C2×Q8C2×C4×D1112yes—
944C2×Q8C2×C4×D1112yes—
945C2×D4—22no—
946C2×D4—22no—
947C2×D4—22no—
948C2×D4—22no—
949C2×D4—22no—
950C2×D4—22no—
951C2×D4—21no—
952C2×D4—21no—
953C2×D4—21no—
954C2×D4—114no—
955C2×D4—114no—
956C2×D4—114no—
957C2×D4—114no—
958C2×D4—114no—
959C2×D4—114no—
960C2×D4—1116no—
961C2×D4—112no—
962C2×D4—112no—
963C2×D4—112no—
964C2×D4—112no—
965C2×D4—112no—
966C2×D4—112no—
967C2×D4—112no—
968C2×D4—112no—
969C2×D4—112no—
970C2×D4—228no—
971C2×D4—228no—
972C2×D4—224no—
973C2×D4—228no—
974C2×D4—224no—
975C2×D4—2216no—
976C2×D4—2216no—
977C2×D4—228no—
978C2×D4—228no—
979C2×D4—2216no—
980C2×D4—2216no—
981C2×D4—2216no—
982C2×D4—2216no—
983C2×D4—224no—
984C2×D4—222no—
985C2×D4—222no—
986C2×D4—222no—
987C2×D4—222no—
988C2×D4—222no—
989C2×D4—222no—
990C2×D4—221no—
991C2×D4—221no—
992C2×D4—221no—
993C2×D4C2×C4×D1112yes—
994C2×D4C2×C4×D1112yes—
995C2×D4C2×C4×D1112yes—
996C22×C4—21no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—112no—
1005C22×C4—114no—
1006C22×C4—114no—
1007C22×C4—114no—
1008C22×C4—114no—
1009C22×C4—114no—
1010C22×C4—114no—
1011C22×C4—224no—
1012C22×C4—2216no—
1013C22×C4—2216no—
1014C22×C4—224no—
1015C22×C4—228no—
1016C22×C4—224no—
1017C22×C4—221no—
1018C22×C4—222no—
1019C22×C4—222no—
1020C22×C4—222no—
1021C22×C4—222no—
1022C22×C4—222no—
1023C22×C4—222no—
1024C22×C4—222no—
1025C22×C4C2×C4×D1111yescharacteristic
1026C22×C4C2×C4×D1111yescharacteristic
1027C22×C4C2×C4×D1111yescharacteristic
1028C22×C4C2×C4×D1111yescharacteristic
1029C22×C4D4×D1111yescharacteristic
1030C22×C4D4×D1111yescharacteristic
1031C22×C4D4×D1111yescharacteristic
1032C22×C4D4×D1111yescharacteristic
1033C22×C4D4×D1111yescharacteristic
1034C22×C4D4×D1111yescharacteristic
1035C22×C4D4×D1111yescharacteristic
1036C22×C4C23×D1111yescharacteristic
1037C22×C4C23×D1111yescharacteristic
1038C22×C4C23×D1111yescharacteristic
1039M16—22no—
1040M16—22no—
1041M16—22no—
1042M16—114no—
1043M16—2216no—
1044M16—222no—
1045M16—222no—
1046M16—222no—
1047M16C23×D1114yes—
1048C2×C8—22no—
1049C2×C8—22no—
1050C2×C8—22no—
1051C2×C8—2216no—
1052C2×C8—222no—
1053C2×C8—222no—
1054C2×C8—222no—
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—228no—
1058C4⋊C4—222no—
1059C4⋊C4—222no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—228no—
1063C22⋊C4—222no—
1064C22⋊C4—222no—
1065C42—22no—
1066C42—114no—
1067C42—228no—
1068C42—222no—
1069C42C23×D1114yes—
1070C11#6009311yescharacteristic, complemented, Sylow
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—81no—
1075C23—82no—
1076C23—114no—
1077C23—114no—
1078C23—114no—
1079C23—2216no—
1080C23—222no—
1081C23—222no—
1082C23—222no—
1083C23—882no—
1084C23—882no—
1085C23—888no—
1086C23C22⋊C4×D1111yescharacteristic
1087C23C22⋊C4×D1111yescharacteristic
1088C23C22⋊C4×D1111yescharacteristic
1089C23C22⋊C4×D1111yescharacteristic
1090C23C2×D4×D1111yescharacteristic
1091C23C2×D4×D1111yescharacteristic
1092C23C2×D4×D1111yescharacteristic
1093Q8—22no—
1094Q8—22no—
1095Q8—22no—
1096Q8—114no—
1097Q8—114no—
1098Q8—114no—
1099Q8—114no—
1100Q8—114no—
1101Q8—2216no—
1102Q8—222no—
1103Q8—222no—
1104Q8—222no—
1105Q8C22×C4×D1114yes—
1106D4—24no—
1107D4—24no—
1108D4—24no—
1109D4—24no—
1110D4—22no—
1111D4—22no—
1112D4—22no—
1113D4—118no—
1114D4—118no—
1115D4—118no—
1116D4—118no—
1117D4—114no—
1118D4—114no—
1119D4—114no—
1120D4—114no—
1121D4—114no—
1122D4—2216no—
1123D4—2216no—
1124D4—2216no—
1125D4—224no—
1126D4—224no—
1127D4—224no—
1128D4—224no—
1129D4—222no—
1130D4—222no—
1131D4—222no—
1132D4C22×C4×D1114yes—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—82no—
1142C2×C4—114no—
1143C2×C4—114no—
1144C2×C4—114no—
1145C2×C4—118no—
1146C2×C4—118no—
1147C2×C4—118no—
1148C2×C4—118no—
1149C2×C4—2216no—
1150C2×C4—2216no—
1151C2×C4—2216no—
1152C2×C4—222no—
1153C2×C4—222no—
1154C2×C4—222no—
1155C2×C4—224no—
1156C2×C4—224no—
1157C2×C4—224no—
1158C2×C4—224no—
1159C2×C4—224no—
1160C2×C4—888no—
1161C2×C4—882no—
1162C2×C4C22⋊C4×D1111yescharacteristic
1163C2×C4C22⋊C4×D1111yescharacteristic
1164C2×C4C22⋊C4×D1111yescharacteristic
1165C2×C4C22⋊C4×D1111yescharacteristic
1166C2×C4C22⋊C4×D1111yescharacteristic
1167C2×C4C22⋊C4×D1111yescharacteristic
1168C2×C4C22⋊C4×D1111yescharacteristic
1169C2×C4C22⋊C4×D1111yescharacteristic
1170C2×C4C22⋊C4×D1111yescharacteristic
1171C2×C4C22⋊C4×D1111yescharacteristic
1172C2×C4C22⋊C4×D1111yescharacteristic
1173C2×C4C22⋊C4×D1111yescharacteristic
1174C2×C4C22×C4×D1111yescharacteristic
1175C2×C4C22×C4×D1111yescharacteristic
1176C2×C4C22×C4×D1111yescharacteristic
1177C2×C4C22×C4×D1111yescharacteristic
1178C2×C4C22×C4×D1111yescharacteristic
1179C2×C4C22×C4×D1111yescharacteristic
1180C2×C4C2×D4×D1111yescharacteristic
1181C2×C4C2×D4×D1111yescharacteristic
1182C2×C4C2×D4×D1111yescharacteristic
1183C2×C4C2×D4×D1111yescharacteristic
1184C2×C4C2×D4×D1111yescharacteristic
1185C2×C4C2×D4×D1111yescharacteristic
1186C2×C4C2×D4×D1111yescharacteristic
1187C2×C4C2×D4×D1111yescharacteristic
1188C2×C4C2×D4×D1111yescharacteristic
1189C2×C4C24×D1111yescharacteristic
1190C8—24no—
1191C8—224no—
1192C22—24no—
1193C22—41no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—44no—
1201C22—82no—
1202C22—82no—
1203C22—118no—
1204C22—224no—
1205C22—444no—
1206C22—444no—
1207C22—444no—
1208C22—444no—
1209C22—882no—
1210C22—882no—
1211C22—8816no—
1212C22C2×C22⋊C4×D1111yescharacteristic
1213C22C2×C22⋊C4×D1111yescharacteristic
1214C22C2×C22⋊C4×D1111yescharacteristic
1215C22C2×C22⋊C4×D1111yescharacteristic
1216C22C2×C22⋊C4×D1111yescharacteristic
1217C22C2×C22⋊C4×D1111yescharacteristic
1218C22C22×D4×D1111yescharacteristic
1219C4—24no—
1220C4—44no—
1221C4—118no—
1222C4—224no—
1223C4—444no—
1224C4C2×C22⋊C4×D1111yescharacteristic
1225C4C2×C22⋊C4×D1111yescharacteristic
1226C4C2×C22⋊C4×D1111yescharacteristic
1227C4C2×C22⋊C4×D1111yescharacteristic
1228C4C2×C22⋊C4×D1111yescharacteristic
1229C4C2×C22⋊C4×D1111yescharacteristic
1230C4C23×C4×D1111yescharacteristic
1231C4C22×D4×D1111yescharacteristic
1232C2—21no—
1233C2—21no—
1234C2—21no—
1235C2—21no—
1236C2—21no—
1237C2—21no—
1238C2—21no—
1239C2—44no—
1240C2—228no—
1241C2—444no—
1242C2C22×C22⋊C4×D1111yescharacteristic
subgroupG/H
centerC4C22×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#421C2
socleC2×C11C23×C22⋊C4
prime radicalC2×#10623453C2
cosocleC2×C4×C11C25
hypercenterC2×#421D11
hypocenterC11#60093
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#10623276C2semidirect
3. #13081817C2semidirect
4. #13077162C2semidirect
5. #13077160C2semidirect
6. C2×#10622618C2semidirect
7. C2×#10622849C2semidirect
8. C2×#10622752C2semidirect
9. D11×#421C2semidirect
10. C2×C11×#421C2semidirect
16. #10623453C4semidirect
17. #10623453C4semidirect
21. C2×#67043C4semidirect
23. C2×#67042C4semidirect
26. C2×#67040C4semidirect
28. C2×#67037C4semidirect
32. C22×C11×M16C22semidirect
33. C2×C11×#117C22semidirect
34. C2×#66979C22semidirect
35. C22×#4318C22semidirect
38. #10623276C22semidirect
39. #10623276C22semidirect
41. C2×M16×D11C22semidirect
44. #10623053C22semidirect
46. D11×#117C22semidirect
50. C4×#4339C22semidirect
51. C11×#421C22semidirect
52. C11×#421C22semidirect
53. C2×C11×#104C22semidirect
54. #10622849C22semidirect
55. #10622849C22semidirect
56. C2×#66901C22semidirect
57. #10622752C22semidirect
58. #10622752C22semidirect
59. C2×#66889C22semidirect
60. #10622618C22semidirect
61. #10622618C22semidirect
62. C2×#66869C22semidirect
63. #10622434C22semidirect
64. D11×#104C22semidirect
71. C2×C11×#41C2×C4semidirect
72. C2×C11×#41C2×C4semidirect
73. C2×C11×#41C2×C4semidirect
77. C22×Q8×C11C2×C4semidirect
79. C22×D4×C11C2×C4semidirect
91. #67043C2×C4semidirect
92. #67043C2×C4semidirect
99. #67042C2×C4semidirect
100. #67042C2×C4semidirect
107. #41×D11C2×C4semidirect
111. #67040C2×C4semidirect
112. #67040C2×C4semidirect
114. C2×#4343C2×C4semidirect
116. C2×Q8×D11C2×C4semidirect
123. #67037C2×C4semidirect
124. #67037C2×C4semidirect
128. C2×#4341C2×C4semidirect
132. C2×D4×D11C2×C4semidirect
151. C2×#4339C2×C4semidirect
152. C2×#4339C2×C4semidirect
153. C2×#4339C2×C4semidirect
166. C22×D44C2×C4semidirect
172. C22×Dic22C2×C4semidirect
178. C2×C11×M16C23semidirect
179. C2×C11×M16C23semidirect
184. C11×#117C23semidirect
187. C2×C42×C11C23semidirect
193. #66979C23semidirect
195. C2×C4×Dic11C23semidirect
200. C2×#4318C23semidirect
201. C2×#4318C23semidirect
206. M16×D11C23semidirect
219. #66925C23semidirect
220. C42×D11C23semidirect
222. C11×#104C23semidirect
223. #66901C23semidirect
224. #66889C23semidirect
225. #66869C23semidirect
459. C2×#421D11semidirect
610. C22×M16C2×D11semidirect
620. C2×#117C2×D11semidirect
628. #421C2×D11semidirect
629. #421C2×D11semidirect
634. C2×#104C2×D11semidirect
755. C2×#41C4×D11semidirect
756. C2×#41C4×D11semidirect
757. C2×#41C4×D11semidirect
766. C22×Q8C4×D11semidirect
778. C22×D4C4×D11semidirect
801. C2×M16C22×D11semidirect
802. C2×M16C22×D11semidirect
822. #117C22×D11semidirect
831. C2×C42C22×D11semidirect
835. #104C22×D11semidirect
1070. C11#60093semidirect

Maximal subgroups

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

subgroupindex
C2×#106234532
C2×#106232762
#130818172
#130771622
#130771602
C2×#106226182
C2×#106228492
C2×#106227522
D11×#4212
C2×C11×#4212
#6009311