Finite Group Databasebeta

← #15631022

Subgroups — #15631022

Order 2816.

2074 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082258C211yesmaximal, characteristic, complemented
2#13080766C212yesmaximal, complemented
3#13080706C212yesmaximal, complemented
4#13080646C212yesmaximal, complemented
5#13080586C212yesmaximal, complemented
6#13080538C212yesmaximal, complemented
7#13080527C212yesmaximal, complemented
8#13080460C212yesmaximal, complemented
9#13080445C212yesmaximal, complemented
10#13078986C211yesmaximal, characteristic, complemented
11#13078585C211yesmaximal, characteristic, complemented
12#13078547C211yesmaximal, characteristic, complemented
13#13078441C211yesmaximal, characteristic, complemented
14#13078309C211yesmaximal, characteristic, complemented
15#13078194C211yesmaximal, characteristic, complemented
16#13078166C211yesmaximal, characteristic, complemented
17#13077917C211yesmaximal, characteristic, complemented
18#13077856C211yesmaximal, characteristic, complemented
19#13077444C211yesmaximal, characteristic, complemented
20#13077311C211yesmaximal, characteristic, complemented
21#13077139C211yesmaximal, characteristic, complemented
22C2×#10622615C211yesmaximal, characteristic, complemented
23C11×#3493C211yesmaximal, characteristic, complemented
24C2×#67042C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C11×#556—21no—
27C11×#556C2212yescomplemented
28C11×#555—21no—
29C11×#555C2212yescomplemented
30C11×#553—21no—
31C11×#553C2212yescomplemented
32C11×#552—21no—
33C11×#552C2212yescomplemented
34C11×#544C2211yescharacteristic, complemented
35C11×#538—22no—
36C11×#537C2211yescharacteristic
37C11×#529—22no—
38C11×#525C2211yescharacteristic
39C11×#525C2211yescharacteristic, complemented
40C11×#520C2211yescharacteristic
41C11×#520C2211yescharacteristic, complemented
42C2×C11×#117C2211yescharacteristic, complemented
43#10623356C2211yescharacteristic
44C2×#67004C2211yescharacteristic, complemented
45C2×#67003C2211yescharacteristic
46C2×#67002C2211yescharacteristic
47C2×#67001C2211yescharacteristic
48#10623322C2211yescharacteristic
49C23×C11⋊C8C2211yescharacteristic, complemented
50D11×#123—22no—
51#10623162—21no—
52#10623162—21no—
53#10623143—21no—
54#10623143—21no—
55#10623120—22no—
56#10623082C2212yes—
57#10623082C2212yes—
58#10623081C2212yes—
59#10623081C2212yes—
60#10623057C2211yescharacteristic
61#10623052C2211yescharacteristic
62#10622847C2211yescharacteristic
63#10622846C2211yescharacteristic, complemented
64#10622820C2211yescharacteristic, complemented
65#10622706C2212yescomplemented
66#10622702C2212yescomplemented
67#10622700C2212yescomplemented
68#10622697C2212yescomplemented
69#10622682C2212yescomplemented
70#10622681C2212yescomplemented
71#10622679C2212yescomplemented
72#10622679C2212yescomplemented
73#10622665C2212yescomplemented
74#10622664C2212yescomplemented
75#10622664C2211yescharacteristic, complemented
76#10622664C2211yescharacteristic, complemented
77#10622661C2211yescharacteristic, complemented
78#10622661C2211yescharacteristic, complemented
79#10622660C2212yescomplemented
80#10622660C2212yescomplemented
81#10622660C2212yescomplemented
82#10622659C2212yescomplemented
83#10622655C2212yescomplemented
84#10622654C2211yescharacteristic, complemented
85#10622654C2212yescomplemented
86#10622654C2211yescharacteristic, complemented
87#10622651C2211yescharacteristic, complemented
88#10622651C2211yescharacteristic, complemented
89#10622650C2212yescomplemented
90#10622650C2212yescomplemented
91#10622650C2212yescomplemented
92#10622649C2212yescomplemented
93#10622644C2212yescomplemented
94#10622641C2212yescomplemented
95#10622639C2212yescomplemented
96C4×#4325C2212yescomplemented
97#10622632C2212yescomplemented
98#10622629C2212yescomplemented
99#10622627C2212yescomplemented
100C4×#4323C2212yescomplemented
101#10622624C2212yescomplemented
102#10622624C2212yescomplemented
103D4×C11⋊C8C2212yescomplemented
104D4×C11⋊C8C2212yescomplemented
105#10622617C2211yescharacteristic, complemented
106#10622616C2212yescomplemented
107#10622616C2212yescomplemented
108#10622615C2211yescharacteristic
109#10622615C2212yescomplemented
110#10622615C2212yescomplemented
111#10622615C2212yescomplemented
112#10622615C2212yescomplemented
113#10622615C2212yescomplemented
114#10622614C2211yescharacteristic
115#10622614C2212yescomplemented
116#10622612C2211yescharacteristic, complemented
117#10622611C2211yescharacteristic, complemented
118#10622610C2211yescharacteristic, complemented
119#10622609C2212yescomplemented
120#10622609C2212yescomplemented
121#10622609C2212yescomplemented
122#10622609C2212yescomplemented
123#10622584C2212yescomplemented
124#10622583C2212yescomplemented
125C2×#66874C2211yescharacteristic, complemented
126C2×#66874C2211yescharacteristic, complemented
127#10622579C2211yescharacteristic
128#10622579C2211yescharacteristic
129#10622579C2212yescomplemented
130C2×#66873C2211yescharacteristic
131C2×#66873C2211yescharacteristic
132C2×#66873C2212yescomplemented
133#10622577C2211yescharacteristic, complemented
134#10622577C2211yescharacteristic, complemented
135C2×C11×#41C2311yescharacteristic
136C2×C11×#41C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C22×C22⋊D11—21no—
139#67042—24no—
140#67042—42no—
141C2×#4343—21no—
142C2×D4×D11—22no—
143C2×D4×D11—21no—
144C2×#4339—21no—
145C2×#4339—21no—
146C2×#4339—24no—
147C2×#4339—42no—
148C2×#4339C2311yescharacteristic
149C2×#4339C2312yes—
150C2×#4339C2312yes—
151C2×#4339C2312yes—
152C22×D44C2312yes—
153C22×D44C2311yescharacteristic
154C22×C4×D11—21no—
155C22×Dic22C2311yescharacteristic
156C11×C4⋊Q8—21no—
157C11×C4⋊Q8C2312yes—
158C11×#126—22no—
159C11×#126—22no—
160C11×#126—22no—
161C11×#126—22no—
162C11×#125—22no—
163C11×#125—21no—
164C11×#125C2312yes—
165C11×#124—22no—
166C11×#124—22no—
167C11×#124—22no—
168C11×#123—22no—
169C11×#123—21no—
170C11×#123—22no—
171C11×#123D412yes—
172C11×C22⋊Q8—21no—
173C11×C22⋊Q8—22no—
174C11×C22⋊Q8D411yescharacteristic
175C11×C22⋊Q8D411yescharacteristic
176C11×C22⋊Q8C2311yescharacteristic
177C11×C22⋊Q8C2311yescharacteristic
178C11×C22⋊Q8C2312yes—
179C11×#121—22no—
180C11×#121—21no—
181C11×#121—22no—
182C11×#121—22no—
183C11×#121D411yescharacteristic
184C11×#121D411yescharacteristic
185C11×#121C2311yescharacteristic
186C11×#121C2311yescharacteristic
187C11×#121C2312yes—
188C11×#120—21no—
189C11×#120D412yes—
190C4×Q8×C11—21no—
191C4×Q8×C11—22no—
192C4×Q8×C11C2312yes—
193C4×D4×C11—22no—
194C4×D4×C11—21no—
195C4×D4×C11—21no—
196C4×D4×C11—21no—
197C4×D4×C11—22no—
198C4×D4×C11—22no—
199C4×D4×C11C2312yes—
200C4×D4×C11C2312yes—
201C4×D4×C11C2312yes—
202C11×#117—21no—
203C11×#117—21no—
204C11×#117—21no—
205C11×#117—22no—
206C11×#117—22no—
207C11×#117C2312yes—
208C11×#117C2312yes—
209C11×#117C2312yes—
210C11×#117C2311yescharacteristic
211C11×#117C2311yescharacteristic
212C2×C11×C4⋊C4—21no—
213C2×C11×C4⋊C4C2311yescharacteristic
214C2×C11×C4⋊C4C2311yescharacteristic
215C2×C11×C4⋊C4C2312yes—
216C2×C11×C22⋊C4—21no—
217C2×C42×C11—21no—
218#67006—21no—
219#67004—42no—
220#67003—42no—
221#67002—24no—
222#67001—42no—
223#66997—21no—
224C2×#4326C2311yescharacteristic
225C2×#4326C2312yes—
226C2×#4325C2312yes—
227C2×#4325C2311yescharacteristic
228#66991—22no—
229#66991—22no—
230#66990—22no—
231#66990—22no—
232#66989—21no—
233#66988—22no—
234C2×#4324C2311yescharacteristic
235C2×#4324C2312yes—
236C2×#4323C2312yes—
237C2×#4323C2311yescharacteristic
238#66983C2311yescharacteristic
239#66983C2311yescharacteristic
240#66982—21no—
241C4×C22⋊D11—21no—
242C4×C22⋊D11—21no—
243#66979C2311yescharacteristic
244#66977C2311yescharacteristic
245#66977C2311yescharacteristic
246#66977C2312yes—
247#66977C2312yes—
248C2×#4318C2311yescharacteristic
249C2×#4318C2311yescharacteristic
250C2×#4318C2312yes—
251C22×C11⋊C8—42no—
252C22×C11⋊C8C2311yescharacteristic
253C22×C11⋊C8C2311yescharacteristic
254C22×C11⋊C8C2311yescharacteristic
255C22×C11⋊C8C2311yescharacteristic
256C22×C11⋊C8C2311yescharacteristic
257C22×C11⋊C8C2311yescharacteristic
258C22×C11⋊C8C2312yes—
259#66950—21no—
260#66950—21no—
261#66947—22no—
262#66947—22no—
263#66946—21no—
264#66946—21no—
265C4⋊C4×D11—22no—
266C4⋊C4×D11—22no—
267#66939—22no—
268#66937—22no—
269#66937—22no—
270#66936—22no—
271#66936—22no—
272#66936—22no—
273#66936—22no—
274C22⋊C4×D11—22no—
275C22⋊C4×D11—22no—
276C22⋊C4×D11—22no—
277#66928C2312yes—
278C4×D44C2312yes—
279C4×D44C2312yes—
280#66922C2312yes—
281#66899C2311yescharacteristic
282#66899C2311yescharacteristic
283#66896C2311yescharacteristic
284#66896C2311yescharacteristic
285C22⋊(C11⋊C8)C2312yes—
286C22⋊(C11⋊C8)C2312yes—
287C22⋊(C11⋊C8)C2312yes—
288C22⋊(C11⋊C8)C2312yes—
289#66874C2312yes—
290#66874C2312yes—
291#66874C2311yescharacteristic
292#66874C2312yes—
293#66874C2312yes—
294#66874C2312yes—
295#66874C2312yes—
296#66874C2312yes—
297#66874C2312yes—
298#66874C2311yescharacteristic
299#66873C2312yes—
300#66873C2312yes—
301#66873C2312yes—
302#66873C2312yes—
303#66873C2311yescharacteristic
304#66873C2312yes—
305#66873C2312yes—
306#66873C2312yes—
307#66873C2312yes—
308#66873C2311yescharacteristic
309#66872C2312yes—
310#66872C2312yes—
311#66872C2311yescharacteristic
312#66872C2311yescharacteristic
313#66871C2312yes—
314#66871C2312yes—
315#66871C2311yescharacteristic
316#66871C2311yescharacteristic
317C4⋊(C11⋊C8)C2312yes—
318C4⋊(C11⋊C8)C2312yes—
319#66867C2312yes—
320C4×C11⋊C8C2312yes—
321#61169—111nomaximal, Sylow
322C24×C11C2×D411yescharacteristic
323C23×D11—21no—
324C23×D11—22no—
325C11×#41—22no—
326C11×#41—22no—
327C11×#41—22no—
328C11×#41—22no—
329C2×Q8×C11—22no—
330C2×Q8×C11C2×D411yescharacteristic
331C2×Q8×C11C2411yescharacteristic
332C2×D4×C11—21no—
333C2×D4×C11—21no—
334C2×D4×C11—21no—
335C2×D4×C11—22no—
336C2×D4×C11C2×D412yes—
337C2×D4×C11C2×D411yescharacteristic
338C2×D4×C11C2×D412yes—
339C2×D4×C11C2×D412yes—
340C2×D4×C11C2411yescharacteristic
341C22×C4×C11—22no—
342C22×C4×C11—22no—
343C22×C4×C11—21no—
344C22×C4×C11—21no—
345C22×C4×C11—22no—
346C22×C4×C11—21no—
347C22×C4×C11—22no—
348C22×C4×C11C2×D411yescharacteristic
349C22×C4×C11C2×D411yescharacteristic
350C22×C4×C11C2×D411yescharacteristic
351C22×C4×C11C2411yescharacteristic
352C22×C4×C11C2411yescharacteristic
353C22×C4×C11C2412yes—
354C22×C4×C11C2411yescharacteristic
355C2×C22⋊D11—22no—
356C2×C22⋊D11—22no—
357C2×C22⋊D11—22no—
358C2×C22⋊D11—21no—
359C2×C22⋊D11—21no—
360C2×C22⋊D11—21no—
361C2×C22⋊D11—44no—
362C22×Dic11—21no—
363#4343—44no—
364D4×D11—48no—
365D4×D11—44no—
366#4339—24no—
367#4339—24no—
368#4339—24no—
369#4339—22no—
370#4339—22no—
371#4339—42no—
372#4339—42no—
373#4339—42no—
374#4339—44no—
375#4339—44no—
376C2×D44—24no—
377C2×D44—21no—
378C2×D44—22no—
379C2×D44—22no—
380C2×D44—42no—
381C2×D44#4114yes—
382C2×D44C2411yescharacteristic
383C2×D44C2412yes—
384C2×C4×D11—22no—
385C2×C4×D11—22no—
386C2×C4×D11—22no—
387C2×C4×D11—21no—
388C2×C4×D11—22no—
389C2×C4×D11—22no—
390C2×C4×D11—44no—
391C2×Dic22—21no—
392C2×Dic22—22no—
393C2×Dic22—22no—
394C2×Dic22C2411yescharacteristic
395C2×Dic22C2412yes—
396C11×C4⋊C4—21no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4—22no—
400C11×C4⋊C4—21no—
401C11×C4⋊C4—22no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4C2×D412yes—
407C11×C4⋊C4C2×D412yes—
408C11×C4⋊C4C2×D411yescharacteristic
409C11×C4⋊C4C2×D411yescharacteristic
410C11×C4⋊C4C2412yes—
411C11×C4⋊C4C2411yescharacteristic
412C11×C4⋊C4C2412yes—
413C11×C4⋊C4C2411yescharacteristic
414C11×C22⋊C4—22no—
415C11×C22⋊C4—22no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—21no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—21no—
420C11×C22⋊C4—21no—
421C11×C22⋊C4—21no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—21no—
425C11×C22⋊C4C2×D412yes—
426C11×C22⋊C4C2×D412yes—
427C11×C22⋊C4C2×D412yes—
428C11×C22⋊C4C2×D412yes—
429C11×C22⋊C4C2×D412yes—
430C42×C11—22no—
431C42×C11—22no—
432C42×C11—22no—
433C42×C11—22no—
434C42×C11—21no—
435C42×C11C2412yes—
436C22⋊Dic11—21no—
437C22⋊Dic11—22no—
438C22⋊Dic11—22no—
439C22⋊Dic11—21no—
440C22⋊Dic11—21no—
441#4326—41no—
442#4326—42no—
443#4325—24no—
444#4325—41no—
445#4324—41no—
446#4324—42no—
447#4323—24no—
448#4323—41no—
449(C2×D11)⋊C4—22no—
450(C2×D11)⋊C4—22no—
451(C2×D11)⋊C4—22no—
452(C2×D11)⋊C4—22no—
453(C2×D11)⋊C4—21no—
454(C2×D11)⋊C4—21no—
455C4⋊Dic11—22no—
456C4⋊Dic11—22no—
457C4⋊Dic11C2411yescharacteristic
458C4⋊Dic11C2411yescharacteristic
459Dic11⋊C4—21no—
460Dic11⋊C4—21no—
461Dic11⋊C4—22no—
462Dic11⋊C4—22no—
463C4×Dic11—21no—
464#4318—22no—
465#4318—22no—
466#4318—42no—
467C2×C11⋊C8—22no—
468C2×C11⋊C8—22no—
469C2×C11⋊C8—41no—
470C2×C11⋊C8—41no—
471C2×C11⋊C8—41no—
472C2×C11⋊C8—41no—
473C2×C11⋊C8—42no—
474C2×C11⋊C8C2411yescharacteristic
475C2×C11⋊C8C2412yes—
476C2×C11⋊C8C2411yescharacteristic
477C2×C11⋊C8C2411yescharacteristic
478C2×C11⋊C8C2412yes—
479C2×C11⋊C8C2411yescharacteristic
480#3493D1111yescharacteristic, complemented
481#3485—111no—
482#3319—112no—
483#3315—112no—
484#3311—112no—
485#3307—112no—
486#3303—112no—
487#3302—112no—
488#3297—112no—
489#3296—112no—
490#3137—111no—
491#3097—111no—
492#3093—111no—
493#3081—111no—
494#3063—111no—
495#3050—111no—
496#3046—111no—
497#3012—111no—
498#3005—111no—
499#2946—111no—
500#2929—111no—
501#2897—111no—
502C2×#416—111no—
503C23×C11—22no—
504C23×C11—21no—
505C23×C11—41no—
506C23×C11—41no—
507C23×C11C22×D412yes—
508C23×C11C22×D411yescharacteristic
509C23×C11C22×D411yescharacteristic
510C23×C11C22×D411yescharacteristic
511C22×D11—22no—
512C22×D11—24no—
513C22×D11—21no—
514C22×D11—44no—
515C22×D11—81no—
516C22×D11—81no—
517C22×D11—82no—
518C22×D11—82no—
519Q8×C11—22no—
520Q8×C11—21no—
521Q8×C11—21no—
522Q8×C11—82no—
523D4×C11—24no—
524D4×C11—22no—
525D4×C11—21no—
526D4×C11—21no—
527D4×C11—42no—
528D4×C11—42no—
529D4×C11—42no—
530D4×C11—81no—
531D4×C11—82no—
532D4×C11—81no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—21no—
538C2×C4×C11—21no—
539C2×C4×C11—21no—
540C2×C4×C11—21no—
541C2×C4×C11—22no—
542C2×C4×C11—22no—
543C2×C4×C11—21no—
544C2×C4×C11—21no—
545C2×C4×C11—22no—
546C2×C4×C11—21no—
547C2×C4×C11—42no—
548C2×C4×C11—82no—
549C2×C4×C11—81no—
550C2×C4×C11—82no—
551C2×C4×C11—81no—
552C2×C4×C11C22×D412yes—
553C2×C4×C11C22×D411yescharacteristic
554C2×C4×C11C22×D411yescharacteristic
555C2×C4×C11C22×D412yes—
556C2×C4×C11C22×D412yes—
557C2×C4×C11C22×D411yescharacteristic
558C2×C4×C11C2×#4112yes—
559C2×C4×C11H(5,𝔽2)12yes—
560C2×C4×C11C2511yescharacteristic
561C22⋊D11—44no—
562C22⋊D11—44no—
563C22⋊D11—44no—
564C22⋊D11—42no—
565C22⋊D11—81no—
566C22⋊D11—81no—
567C2×Dic11—21no—
568C2×Dic11—21no—
569C2×Dic11—21no—
570C2×Dic11—22no—
571C2×Dic11—42no—
572D44—24no—
573D44—21no—
574D44—22no—
575D44—21no—
576D44—44no—
577D44C2×#4114yes—
578C4×D11—44no—
579C4×D11—44no—
580C4×D11—44no—
581C4×D11—42no—
582C4×D11—82no—
583C4×D11—82no—
584Dic22—22no—
585Dic22—21no—
586Dic22—22no—
587Dic22—21no—
588Dic22—42no—
589C11⋊C8—22no—
590C11⋊C8—21no—
591C11⋊C8—21no—
592C11⋊C8—21no—
593C11⋊C8—21no—
594C11⋊C8—22no—
595C2×H(5,𝔽2)—111no—
596C22×#41—111no—
597C2×#137—111no—
598C2×AGL(1,ℤ/8)—111no—
599C2×#135—111no—
600C2×#131—111no—
601C23×C8—111no—
602#556—21no—
603#556C2×D1112yescomplemented
604#555—21no—
605#555C2×D1112yescomplemented
606#553—21no—
607#553C2×D1112yescomplemented
608#552—21no—
609#552C2×D1112yescomplemented
610#547—112no—
611#547—112no—
612#547—221no—
613#547—221no—
614#546—112no—
615#546—112no—
616#546—221no—
617#546—221no—
618#544C2×D1111yescharacteristic, complemented
619#538—22no—
620#537C2×D1111yescharacteristic
621#536—111no—
622#536—111no—
623#534—222no—
624#529—22no—
625#525—111no—
626#525C2×D1111yescharacteristic
627#525C2×D1111yescharacteristic, complemented
628C2×#123—222no—
629#520C2×D1111yescharacteristic
630#520C2×D1111yescharacteristic, complemented
631#518—111no—
632C2×#117C2×D1111yescharacteristic, complemented
633#491—112no—
634#489—112no—
635#488—112no—
636#487—112no—
637#485—112no—
638#485—112no—
639#485—112no—
640#485—112no—
641#484—112no—
642#483—112no—
643#482—112no—
644#482—112no—
645#478—112no—
646#478—112no—
647#476—112no—
648#474—112no—
649#470—112no—
650#468—112no—
651#467—112no—
652#467—111no—
653#467—111no—
654#466—111no—
655#466—111no—
656#465—111no—
657#465—111no—
658#465—112no—
659#465—111no—
660#465—111no—
661#464—112no—
662#463—112no—
663#462—112no—
664#461—112no—
665#452—112no—
666#452—112no—
667#452—112no—
668#450—112no—
669#449—112no—
670#449—112no—
671#449—112no—
672#447—112no—
673#442—112no—
674#440—112no—
675C4×SD16—112no—
676C4×D8—112no—
677#435—112no—
678#435—112no—
679C8×D4—112no—
680C8×D4—112no—
681#428—111no—
682#428—111no—
683#427—111no—
684#424—111no—
685#419—111no—
686#418—111no—
687#418—112no—
688#417—111no—
689#417—111no—
690#417—112no—
691#416—111no—
692#416—111no—
693#416—112no—
694#416—112no—
695#416—112no—
696#416—112no—
697#416—112no—
698C2×#103—111no—
699C2×#103—111no—
700C2×#102—111no—
701C2×#102—111no—
702C2×#102—112no—
703#408—111no—
704#407—111no—
705#405—111no—
706C22×C11—21no—
707C22×C11—21no—
708C22×C11—22no—
709C22×C11—21no—
710C22×C11—21no—
711C22×C11—22no—
712C22×C11—21no—
713C22×C11—21no—
714C22×C11—21no—
715C22×C11—21no—
716C22×C11—22no—
717C22×C11—44no—
718C22×C11—41no—
719C22×C11—41no—
720C22×C11—41no—
721C22×C11#54612yes—
722C22×C11C23×D411yescharacteristic
723C2×D11—24no—
724C2×D11—42no—
725C2×D11—42no—
726C2×D11—41no—
727C2×D11—41no—
728C2×D11—41no—
729C2×D11—84no—
730C2×D11—164no—
731C4×C11—22no—
732C4×C11—22no—
733C4×C11—21no—
734C4×C11—21no—
735C4×C11—22no—
736C4×C11—42no—
737C4×C11—41no—
738C4×C11—42no—
739C4×C11—41no—
740C4×C11—41no—
741C4×C11#54612yes—
742C4×C11C22×#4111yescharacteristic
743C4×C11C2×H(5,𝔽2)11yescharacteristic
744Dic11—41no—
745Dic11—41no—
746Dic11—42no—
747Dic11—41no—
748H(5,𝔽2)—224no—
749H(5,𝔽2)—442no—
750C2×#41—111no—
751C2×#41—112no—
752C2×#41—112no—
753C2×#41—112no—
754C2×#41—224no—
755C2×#41—221no—
756C2×#41—221no—
757C2×#41—221no—
758C2×#41—442no—
759C2×#41C22×D1111yescharacteristic
760C2×#41C22×D1111yescharacteristic
761C22×Q8—111no—
762C22×D4—111no—
763C22×D4—112no—
764C22×D4—221no—
765C22×D4—222no—
766C22×D4—221no—
767C23×C4—221no—
768C23×C4C22×D1111yescharacteristic
769#137—442no—
770AGL(1,ℤ/8)—224no—
771#135—442no—
772C2×Q16—111no—
773C2×Q16—112no—
774C2×SD16—112no—
775C2×SD16—111no—
776C2×SD16—111no—
777C2×SD16—112no—
778C2×D8—112no—
779C2×D8—111no—
780#131—442no—
781C2×M16—111no—
782C2×M16—111no—
783C2×M16—112no—
784C22×C8—111no—
785C22×C8—111no—
786C22×C8—111no—
787C22×C8—111no—
788C22×C8—111no—
789C22×C8—111no—
790C22×C8—112no—
791C22×C8—442no—
792C4⋊Q8—21no—
793C4⋊Q8—112no—
794C4⋊Q8—221no—
795C4⋊Q8C22×D1112yes—
796#126—22no—
797#126—22no—
798#126—22no—
799#126—22no—
800#125—22no—
801#125—21no—
802#125C22×D1112yes—
803#124—22no—
804#124—22no—
805#124—22no—
806#124—112no—
807#124—221no—
808#123—22no—
809#123—21no—
810#123—22no—
811#123—222no—
812#123—221no—
813#123—222no—
814#123—222no—
815#123—222no—
816#123—222no—
817#123—222no—
818#123—222no—
819#123—222no—
820#123C22⋊D1112yes—
821C22⋊Q8—21no—
822C22⋊Q8—22no—
823C22⋊Q8—111no—
824C22⋊Q8—111no—
825C22⋊Q8—112no—
826C22⋊Q8—112no—
827C22⋊Q8—221no—
828C22⋊Q8—221no—
829C22⋊Q8C22⋊D1111yescharacteristic
830C22⋊Q8C22⋊D1111yescharacteristic
831C22⋊Q8C22×D1111yescharacteristic
832C22⋊Q8C22×D1111yescharacteristic
833C22⋊Q8C22×D1112yes—
834#121—22no—
835#121—21no—
836#121—22no—
837#121—22no—
838#121—111no—
839#121—111no—
840#121—222no—
841#121—222no—
842#121—222no—
843#121—222no—
844#121C22⋊D1111yescharacteristic
845#121C22⋊D1111yescharacteristic
846#121C22×D1111yescharacteristic
847#121C22×D1111yescharacteristic
848#121C22×D1112yes—
849#120—21no—
850#120—221no—
851#120—222no—
852#120—222no—
853#120C22⋊D1112yes—
854C4×Q8—21no—
855C4×Q8—22no—
856C4×Q8C22×D1112yes—
857C4×D4—22no—
858C4×D4—21no—
859C4×D4—21no—
860C4×D4—21no—
861C4×D4—22no—
862C4×D4—22no—
863C4×D4—112no—
864C4×D4—112no—
865C4×D4—221no—
866C4×D4—221no—
867C4×D4—221no—
868C4×D4—221no—
869C4×D4C22×D1112yes—
870C4×D4C22×D1112yes—
871C4×D4C22×D1112yes—
872#117—21no—
873#117—21no—
874#117—21no—
875#117—22no—
876#117—22no—
877#117—111no—
878#117C22×D1112yes—
879#117C22×D1112yes—
880#117C22×D1111yescharacteristic
881#117C22×D1112yes—
882#117C22×D1111yescharacteristic
883C2×C4⋊C4—21no—
884C2×C4⋊C4—222no—
885C2×C4⋊C4—222no—
886C2×C4⋊C4C22×D1111yescharacteristic
887C2×C4⋊C4C22×D1111yescharacteristic
888C2×C4⋊C4C22×D1112yes—
889C2×C22⋊C4—21no—
890C2×C22⋊C4—222no—
891C2×C22⋊C4—222no—
892C2×C22⋊C4—222no—
893C2×C42—21no—
894#107—111no—
895#107—111no—
896#107—112no—
897#107—112no—
898#106—111no—
899#106—111no—
900#106—112no—
901#106—112no—
902C4⋊C8—112no—
903C4⋊C8—112no—
904#103—111no—
905#103—111no—
906#103—112no—
907#103—112no—
908#103—112no—
909#103—112no—
910#103—111no—
911#103—112no—
912#103—111no—
913#103—112no—
914#103—112no—
915#103—112no—
916#102—111no—
917#102—111no—
918#102—112no—
919#102—111no—
920#102—112no—
921#102—112no—
922#102—112no—
923#102—112no—
924#102—112no—
925#102—112no—
926#102—111no—
927#102—112no—
928C22⋊C8—112no—
929C22⋊C8—112no—
930C22⋊C8—112no—
931C22⋊C8—112no—
932#97—112no—
933C4×C8—112no—
934C2×C11—22no—
935C2×C11—42no—
936C2×C11—41no—
937C2×C11—41no—
938C2×C11—81no—
939C2×C11C2×#54611yescharacteristic
940C2×C11#358411yescharacteristic
941C2×C11#358411yescharacteristic
942D11—44no—
943D11—81no—
944C24—221no—
945C24—222no—
946C24C2×C22⋊D1111yescharacteristic
947#41—22no—
948#41—22no—
949#41—22no—
950#41—22no—
951#41—224no—
952#41—224no—
953#41—224no—
954#41—222no—
955#41—222no—
956#41—442no—
957#41—442no—
958#41—442no—
959#41—444no—
960#41—444no—
961#41—444no—
962C2×Q8—22no—
963C2×Q8—112no—
964C2×Q8—111no—
965C2×Q8—221no—
966C2×Q8—222no—
967C2×Q8—222no—
968C2×Q8C2×C22⋊D1111yescharacteristic
969C2×Q8C23×D1111yescharacteristic
970C2×D4—21no—
971C2×D4—21no—
972C2×D4—21no—
973C2×D4—22no—
974C2×D4—114no—
975C2×D4—112no—
976C2×D4—111no—
977C2×D4—224no—
978C2×D4—222no—
979C2×D4—222no—
980C2×D4—221no—
981C2×D4—222no—
982C2×D4—221no—
983C2×D4—221no—
984C2×D4—222no—
985C2×D4—221no—
986C2×D4—222no—
987C2×D4—442no—
988C2×D4—444no—
989C2×D4—448no—
990C2×D4—444no—
991C2×D4C2×C22⋊D1112yes—
992C2×D4C2×C22⋊D1111yescharacteristic
993C2×D4C2×C22⋊D1112yes—
994C2×D4C2×C22⋊D1112yes—
995C2×D4C23×D1111yescharacteristic
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—22no—
1001C22×C4—21no—
1002C22×C4—22no—
1003C22×C4—221no—
1004C22×C4—222no—
1005C22×C4—222no—
1006C22×C4—222no—
1007C22×C4—221no—
1008C22×C4—222no—
1009C22×C4—222no—
1010C22×C4—444no—
1011C22×C4C2×C22⋊D1111yescharacteristic
1012C22×C4C2×C22⋊D1111yescharacteristic
1013C22×C4C2×C22⋊D1111yescharacteristic
1014C22×C4C23×D1112yes—
1015C22×C4C23×D1111yescharacteristic
1016C22×C4C23×D1111yescharacteristic
1017C22×C4C23×D1111yescharacteristic
1018Q16—441no—
1019Q16—442no—
1020SD16—224no—
1021SD16—441no—
1022SD16—442no—
1023SD16—441no—
1024D8—224no—
1025D8—441no—
1026M16—222no—
1027M16—222no—
1028M16—442no—
1029C2×C8—111no—
1030C2×C8—112no—
1031C2×C8—111no—
1032C2×C8—112no—
1033C2×C8—111no—
1034C2×C8—111no—
1035C2×C8—222no—
1036C2×C8—222no—
1037C2×C8—441no—
1038C2×C8—441no—
1039C2×C8—441no—
1040C2×C8—441no—
1041C2×C8—442no—
1042C4⋊C4—21no—
1043C4⋊C4—22no—
1044C4⋊C4—21no—
1045C4⋊C4—22no—
1046C4⋊C4—21no—
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—21no—
1050C4⋊C4—22no—
1051C4⋊C4—22no—
1052C4⋊C4—111no—
1053C4⋊C4—111no—
1054C4⋊C4—221no—
1055C4⋊C4—221no—
1056C4⋊C4—222no—
1057C4⋊C4—222no—
1058C4⋊C4—222no—
1059C4⋊C4—222no—
1060C4⋊C4C2×C22⋊D1111yescharacteristic
1061C4⋊C4C2×C22⋊D1112yes—
1062C4⋊C4C2×C22⋊D1112yes—
1063C4⋊C4C2×C22⋊D1111yescharacteristic
1064C4⋊C4C23×D1112yes—
1065C4⋊C4C23×D1111yescharacteristic
1066C4⋊C4C23×D1112yes—
1067C4⋊C4C23×D1111yescharacteristic
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—21no—
1072C22⋊C4—22no—
1073C22⋊C4—21no—
1074C22⋊C4—21no—
1075C22⋊C4—21no—
1076C22⋊C4—22no—
1077C22⋊C4—22no—
1078C22⋊C4—21no—
1079C22⋊C4—221no—
1080C22⋊C4—222no—
1081C22⋊C4—222no—
1082C22⋊C4—221no—
1083C22⋊C4—221no—
1084C22⋊C4—221no—
1085C22⋊C4—221no—
1086C22⋊C4—222no—
1087C22⋊C4—222no—
1088C22⋊C4—222no—
1089C22⋊C4—222no—
1090C22⋊C4C2×C22⋊D1112yes—
1091C22⋊C4C2×C22⋊D1112yes—
1092C22⋊C4C2×C22⋊D1112yes—
1093C22⋊C4C2×C22⋊D1112yes—
1094C22⋊C4C2×C22⋊D1112yes—
1095C42—22no—
1096C42—22no—
1097C42—22no—
1098C42—22no—
1099C42—21no—
1100C42—221no—
1101C42C23×D1112yes—
1102C11#6116911yescharacteristic, complemented, Sylow
1103C23—22no—
1104C23—21no—
1105C23—41no—
1106C23—41no—
1107C23—222no—
1108C23—224no—
1109C23—221no—
1110C23—444no—
1111C23—881no—
1112C23—881no—
1113C23—882no—
1114C23—882no—
1115C23C22×C22⋊D1111yescharacteristic
1116C23C22×C22⋊D1111yescharacteristic
1117C23C22×C22⋊D1112yes—
1118C23C22×C22⋊D1111yescharacteristic
1119Q8—22no—
1120Q8—21no—
1121Q8—21no—
1122Q8—82no—
1123Q8—222no—
1124Q8—221no—
1125Q8—222no—
1126Q8—221no—
1127Q8—442no—
1128D4—24no—
1129D4—22no—
1130D4—21no—
1131D4—21no—
1132D4—42no—
1133D4—42no—
1134D4—42no—
1135D4—81no—
1136D4—82no—
1137D4—81no—
1138D4—114no—
1139D4—224no—
1140D4—221no—
1141D4—222no—
1142D4—221no—
1143D4—444no—
1144D4—444no—
1145D4—444no—
1146D4—444no—
1147D4—442no—
1148D4—881no—
1149D4—881no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—42no—
1165C2×C4—82no—
1166C2×C4—81no—
1167C2×C4—82no—
1168C2×C4—81no—
1169C2×C4—221no—
1170C2×C4—221no—
1171C2×C4—222no—
1172C2×C4—221no—
1173C2×C4—444no—
1174C2×C4—444no—
1175C2×C4—444no—
1176C2×C4—442no—
1177C2×C4—442no—
1178C2×C4—882no—
1179C2×C4—882no—
1180C2×C4#41×D1112yes—
1181C2×C4#6704212yes—
1182C2×C4C22×C22⋊D1111yescharacteristic
1183C2×C4C22×C22⋊D1111yescharacteristic
1184C2×C4C22×C22⋊D1112yes—
1185C2×C4C22×C22⋊D1112yes—
1186C2×C4C22×C22⋊D1112yes—
1187C2×C4C22×C22⋊D1111yescharacteristic
1188C2×C4C24×D1111yescharacteristic
1189C8—222no—
1190C8—221no—
1191C8—221no—
1192C8—221no—
1193C8—221no—
1194C8—222no—
1195C22—21no—
1196C22—21no—
1197C22—21no—
1198C22—21no—
1199C22—22no—
1200C22—22no—
1201C22—21no—
1202C22—21no—
1203C22—22no—
1204C22—21no—
1205C22—21no—
1206C22—44no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—224no—
1211C22—442no—
1212C22—442no—
1213C22—441no—
1214C22—441no—
1215C22—441no—
1216C22—884no—
1217C22—1764no—
1218C22#1062336012yes—
1219C22C23×C22⋊D1111yescharacteristic
1220C4—21no—
1221C4—21no—
1222C4—22no—
1223C4—22no—
1224C4—22no—
1225C4—41no—
1226C4—42no—
1227C4—41no—
1228C4—42no—
1229C4—41no—
1230C4—441no—
1231C4—442no—
1232C4—441no—
1233C4—441no—
1234C4#1062336012yes—
1235C4C2×#41×D1111yescharacteristic
1236C4C2×#6704211yescharacteristic
1237C2—22no—
1238C2—41no—
1239C2—41no—
1240C2—42no—
1241C2—81no—
1242C2—444no—
1243C2—881no—
1244C2C2×#1062336011yescharacteristic
1245C2#1308338711yescharacteristic
1246C2#1308338711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3493C2
socleC22×C11C23×D4
hypercenter#3493D11
hypocenterC11#61169
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #525 ◁ #3493

Complements

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

NH ≅ G/Ntype
1. #13082258C2semidirect
2. #13080766C2semidirect
3. #13080706C2semidirect
4. #13080646C2semidirect
5. #13080586C2semidirect
6. #13080538C2semidirect
7. #13080527C2semidirect
8. #13080460C2semidirect
9. #13080445C2semidirect
10. #13078986C2semidirect
11. #13078585C2semidirect
12. #13078547C2semidirect
13. #13078441C2semidirect
14. #13078309C2semidirect
15. #13078194C2semidirect
16. #13078166C2semidirect
17. #13077917C2semidirect
18. #13077856C2semidirect
19. #13077444C2semidirect
20. #13077311C2semidirect
21. #13077139C2semidirect
22. C2×#10622615C2semidirect
23. C11×#3493C2semidirect
27. C11×#556C22semidirect
29. C11×#555C22semidirect
31. C11×#553C22semidirect
33. C11×#552C22semidirect
34. C11×#544C22semidirect
39. C11×#525C22semidirect
41. C11×#520C22semidirect
42. C2×C11×#117C22semidirect
44. C2×#67004C22semidirect
49. C23×C11⋊C8C22semidirect
63. #10622846C22semidirect
64. #10622820C22semidirect
65. #10622706C22semidirect
66. #10622702C22semidirect
67. #10622700C22semidirect
68. #10622697C22semidirect
69. #10622682C22semidirect
70. #10622681C22semidirect
71. #10622679C22semidirect
72. #10622679C22semidirect
73. #10622665C22semidirect
74. #10622664C22semidirect
75. #10622664C22semidirect
76. #10622664C22semidirect
77. #10622661C22semidirect
78. #10622661C22semidirect
79. #10622660C22semidirect
80. #10622660C22semidirect
81. #10622660C22semidirect
82. #10622659C22semidirect
83. #10622655C22semidirect
84. #10622654C22semidirect
85. #10622654C22semidirect
86. #10622654C22semidirect
87. #10622651C22semidirect
88. #10622651C22semidirect
89. #10622650C22semidirect
90. #10622650C22semidirect
91. #10622650C22semidirect
92. #10622649C22semidirect
93. #10622644C22semidirect
94. #10622641C22semidirect
95. #10622639C22semidirect
96. C4×#4325C22semidirect
97. #10622632C22semidirect
98. #10622629C22semidirect
99. #10622627C22semidirect
100. C4×#4323C22semidirect
101. #10622624C22semidirect
102. #10622624C22semidirect
103. D4×C11⋊C8C22semidirect
104. D4×C11⋊C8C22semidirect
105. #10622617C22semidirect
106. #10622616C22semidirect
107. #10622616C22semidirect
109. #10622615C22semidirect
110. #10622615C22semidirect
111. #10622615C22semidirect
112. #10622615C22semidirect
113. #10622615C22semidirect
115. #10622614C22semidirect
116. #10622612C22semidirect
117. #10622611C22semidirect
118. #10622610C22semidirect
119. #10622609C22semidirect
120. #10622609C22semidirect
121. #10622609C22semidirect
122. #10622609C22semidirect
123. #10622584C22semidirect
124. #10622583C22semidirect
125. C2×#66874C22semidirect
126. C2×#66874C22semidirect
129. #10622579C22semidirect
132. C2×#66873C22semidirect
133. #10622577C22semidirect
134. #10622577C22semidirect
480. #3493D11semidirect
603. #556C2×D11semidirect
605. #555C2×D11semidirect
607. #553C2×D11semidirect
609. #552C2×D11semidirect
618. #544C2×D11semidirect
627. #525C2×D11semidirect
630. #520C2×D11semidirect
632. C2×#117C2×D11semidirect
1102. C11#61169semidirect

Maximal subgroups

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

subgroupindex
#130822582
#130807662
#130807062
#130806462
#130805862
#130805382
#130805272
#130804602
#130804452
#130789862
#130785852
#130785472
#130784412
#130783092
#130781942
#130781662
#130779172
#130778562
#130774442
#130773112
#130771392
C2×#106226152
C11×#34932
#6116911