Finite Group Databasebeta

← #15624674

Subgroups — #15624674

Order 2816.

2208 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082285C211yesmaximal, characteristic, complemented
2#13081945C211yesmaximal, characteristic, complemented
3#13079528C212yesmaximal, complemented
4#13079518C212yesmaximal, complemented
5#13079470C212yesmaximal, complemented
6#13079470C212yesmaximal, complemented
7#13079458C212yesmaximal, complemented
8#13079432C212yesmaximal, complemented
9#13079409C212yesmaximal, complemented
10#13079383C212yesmaximal, complemented
11#13078586C211yesmaximal, characteristic, complemented
12#13078575C211yesmaximal, characteristic, complemented
13#13078557C211yesmaximal, characteristic, complemented
14#13078531C211yesmaximal, characteristic, complemented
15#13078307C211yesmaximal, characteristic, complemented
16#13078296C211yesmaximal, characteristic, complemented
17#13078264C211yesmaximal, characteristic, complemented
18#13078255C211yesmaximal, characteristic, complemented
19#13077895C211yesmaximal, characteristic, complemented
20#13077886C211yesmaximal, characteristic, complemented
21#13077861C211yesmaximal, characteristic, complemented
22C2×#10622347C211yesmaximal, characteristic, complemented
23C11×#2880C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C2×#67042C2211yescharacteristic
26C22×#4339C2211yescharacteristic, complemented
27C2×C11×#131C2211yescharacteristic, complemented
28C2×C11×#131C2211yescharacteristic, complemented
29#10623365—21no—
30#10623364C2211yescharacteristic
31#10623364C2212yescomplemented
32#10623364C2212yescomplemented
33#10623364C2212yescomplemented
34#10623363—21no—
35#10623363—21no—
36#10623361C2211yescharacteristic
37#10623361C2211yescharacteristic
38#10623361C2211yescharacteristic, complemented
39#10623361C2212yescomplemented
40#10623360—22no—
41#10623360—21no—
42#10623359—22no—
43#10623358C2211yescharacteristic
44#10623356C2211yescharacteristic
45#10623356C2211yescharacteristic, complemented
46#10623348—21no—
47#10623347—21no—
48#10623336—21no—
49#10623335—22no—
50D4×C22⋊D11—21no—
51D4×C22⋊D11—22no—
52#10623322C2211yescharacteristic
53#10623322C2212yescomplemented
54#10623322C2212yescomplemented
55#10623322C2212yescomplemented
56C2×#66983C2211yescharacteristic
57C2×#66983C2212yescomplemented
58C2×#66979C2211yescharacteristic, complemented
59C2×#66962C2211yescharacteristic, complemented
60C2×#66961C2211yescharacteristic, complemented
61C22×D88C2211yescharacteristic, complemented
62C22×#4314C2211yescharacteristic, complemented
63C11×#408C2211yescharacteristic
64C11×#408C2211yescharacteristic
65C11×#408C2212yescomplemented
66C11×#408C2212yescomplemented
67C11×#407C2211yescharacteristic, complemented
68C11×#407C2212yescomplemented
69C2×C11×C22⋊C8C2211yescharacteristic, complemented
70C2×C11×C22⋊C8C2212yescomplemented
71#10622750C2212yescomplemented
72#10622748C2212yescomplemented
73#10622748C2212yescomplemented
74#10622748C2212yescomplemented
75#10622747C2212yescomplemented
76#10622747C2212yescomplemented
77#10622747C2212yescomplemented
78#10622747C2212yescomplemented
79#10622744C2211yescharacteristic, complemented
80#10622744C2211yescharacteristic, complemented
81#10622744C2211yescharacteristic, complemented
82#10622734C2211yescharacteristic, complemented
83#10622734C2211yescharacteristic, complemented
84#10622733C2211yescharacteristic, complemented
85#10622729C2212yescomplemented
86#10622728C2212yescomplemented
87#10622728C2212yescomplemented
88#10622728C2212yescomplemented
89#10622727C2212yescomplemented
90#10622727C2212yescomplemented
91#10622727C2212yescomplemented
92#10622727C2212yescomplemented
93#10622726C2211yescharacteristic, complemented
94#10622726C2211yescharacteristic, complemented
95C2×#66885C2211yescharacteristic, complemented
96#10622719C2211yescharacteristic, complemented
97#10622719C2211yescharacteristic, complemented
98C2×#66880C2211yescharacteristic, complemented
99#10622350C2211yescharacteristic, complemented
100#10622350C2211yescharacteristic, complemented
101#10622350C2212yescomplemented
102#10622350C2212yescomplemented
103#10622350C2212yescomplemented
104#10622350C2212yescomplemented
105#10622349C2211yescharacteristic, complemented
106#10622349C2212yescomplemented
107#10622349C2212yescomplemented
108#10622348C2211yescharacteristic, complemented
109#10622348C2212yescomplemented
110#10622348C2212yescomplemented
111#10622347C2212yescomplemented
112#10622347C2212yescomplemented
113#10622347C2212yescomplemented
114#10622347C2212yescomplemented
115#10622347C2212yescomplemented
116#10622347C2212yescomplemented
117#10622347C2212yescomplemented
118#10622347C2212yescomplemented
119#10622346C2212yescomplemented
120#10622346C2212yescomplemented
121#10622346C2212yescomplemented
122#10622346C2212yescomplemented
123#10622345C2212yescomplemented
124#10622345C2212yescomplemented
125#10622344C2212yescomplemented
126#10622344C2212yescomplemented
127#10622336C2211yescharacteristic, complemented
128#10622336C2211yescharacteristic, complemented
129#10622336C2212yescomplemented
130#10622336C2212yescomplemented
131#10622335C2211yescharacteristic, complemented
132#10622335C2212yescomplemented
133#10622334C2211yescharacteristic, complemented
134#10622334C2212yescomplemented
135C2×C11×#41—42no—
136C2×C11×#41—42no—
137C2×C11×#41D412yes—
138C2×C11×#41D411yescharacteristic
139C2×C11×#41D411yescharacteristic
140C2×C11×#41C2311yescharacteristic
141C2×C11×#41C2311yescharacteristic
142C2×C11×#41C2312yes—
143C22×Q8×C11D411yescharacteristic
144C22×D4×C11D412yes—
145C22×D4×C11D411yescharacteristic
146C23×C4×C11C2311yescharacteristic
147C23×C4×C11C2312yes—
148C22×C22⋊D11—21no—
149C22×C22⋊D11—21no—
150C22×C22⋊D11—22no—
151#67042—42no—
152#67042—42no—
153C2×#4343—21no—
154C2×D4×D11—22no—
155C2×D4×D11—21no—
156C2×#4339—21no—
157C2×#4339—21no—
158C2×#4339—42no—
159C2×#4339—42no—
160C2×#4339C2311yescharacteristic
161C2×#4339C2312yes—
162C2×#4339C2312yes—
163C2×#4339C2312yes—
164C22×D44C2311yescharacteristic
165C22×D44C2311yescharacteristic
166C22×D44C2312yes—
167C22×C4×D11—21no—
168C22×Dic22C2311yescharacteristic
169C11×#131—42no—
170C11×#131—42no—
171C2×C11×M16C2311yescharacteristic
172C2×C11×M16C2311yescharacteristic
173C2×C11×M16C2312yes—
174C2×C11×M16C2312yes—
175C22×C8×C11C2311yescharacteristic
176C22×C8×C11C2311yescharacteristic
177C22×C8×C11C2312yes—
178C22×C8×C11C2312yes—
179#67006—21no—
180#67006—22no—
181#67006—22no—
182#67006—22no—
183C2×C22⋊Dic11—21no—
184#67000—21no—
185#67000—21no—
186#67000—21no—
187#67000—22no—
188#66999—22no—
189#66999—22no—
190#66999—21no—
191#66999—22no—
192Q8×Dic11—21no—
193#66997—21no—
194#66997—21no—
195#66993—21no—
196#66993—22no—
197#66993—21no—
198#66993—21no—
199#66992—22no—
200#66992—22no—
201#66992—22no—
202#66992—22no—
203#66992—22no—
204#66992—22no—
205#66992—22no—
206#66991—21no—
207#66991—22no—
208#66991—22no—
209#66991—22no—
210#66990—22no—
211#66990—22no—
212#66990—22no—
213#66990—22no—
214#66990—22no—
215#66989—21no—
216#66989—21no—
217#66988—22no—
218#66988—22no—
219D4×Dic11—22no—
220D4×Dic11—21no—
221#66983—21no—
222#66983—21no—
223#66983—22no—
224#66983—22no—
225#66983C2312yes—
226#66983C2312yes—
227#66983C2312yes—
228#66983C2312yes—
229#66983C2312yes—
230#66983C2312yes—
231#66983C2312yes—
232#66983C2311yescharacteristic
233#66983C2311yescharacteristic
234#66983C2312yes—
235#66983C2312yes—
236#66982—21no—
237#66982—22no—
238#66982—22no—
239#66982—22no—
240C4×C22⋊D11—21no—
241C4×C22⋊D11—21no—
242C4×C22⋊D11—22no—
243C4×C22⋊D11—22no—
244C4×C22⋊D11—22no—
245C4×C22⋊D11—22no—
246C4×C22⋊D11—22no—
247C4×C22⋊D11—22no—
248C2×(C2×D11)⋊C4—21no—
249C2×(C2×D11)⋊C4—22no—
250#66979—21no—
251#66979—21no—
252#66979C2311yescharacteristic
253#66979C2311yescharacteristic
254#66979C2311yescharacteristic
255#66979C2311yescharacteristic
256#66979C2311yescharacteristic
257#66979C2312yes—
258C2×C4⋊Dic11C2311yescharacteristic
259C2×C4⋊Dic11C2311yescharacteristic
260C2×C4⋊Dic11C2311yescharacteristic
261C2×C4⋊Dic11C2312yes—
262#66977C2312yes—
263#66977C2312yes—
264#66977C2312yes—
265#66977C2311yescharacteristic
266#66977C2311yescharacteristic
267#66977C2312yes—
268#66977C2312yes—
269C2×C4×Dic11—21no—
270#66962—42no—
271#66961—42no—
272C2×Dic44C2312yes—
273C2×D88—42no—
274C2×D88C2312yes—
275C2×D88C2312yes—
276C2×D88C2312yes—
277C2×#4314—42no—
278C2×#4314C2312yes—
279C2×#4314C2312yes—
280C2×#4314C2312yes—
281C2×#4314C2312yes—
282C11×C22⋊C8C2312yes—
283C11×C22⋊C8C2311yescharacteristic
284C11×C22⋊C8C2312yes—
285C11×C22⋊C8C2311yescharacteristic
286C11×C22⋊C8C2311yescharacteristic
287C11×C22⋊C8C2311yescharacteristic
288C11×C22⋊C8C2312yes—
289C11×C22⋊C8C2312yes—
290C11×C22⋊C8C2312yes—
291C11×C22⋊C8C2312yes—
292#66885C2312yes—
293#66885C2312yes—
294#66885C2311yescharacteristic
295#66885C2311yescharacteristic
296#66885C2311yescharacteristic
297#66885C2311yescharacteristic
298#66885C2312yes—
299#66885C2312yes—
300#66885C2312yes—
301#66885C2312yes—
302#66885C2312yes—
303#66885C2312yes—
304#66882C2311yescharacteristic
305#66882C2311yescharacteristic
306#66882C2312yes—
307#66882C2312yes—
308#66882C2311yescharacteristic
309#66882C2311yescharacteristic
310#66881C2311yescharacteristic
311#66881C2311yescharacteristic
312#66881C2312yes—
313#66881C2312yes—
314#66881C2311yescharacteristic
315#66881C2311yescharacteristic
316#66880C2311yescharacteristic
317#66880C2311yescharacteristic
318#66880C2311yescharacteristic
319#66880C2311yescharacteristic
320#66880C2312yes—
321#66880C2312yes—
322#66880C2312yes—
323#66880C2312yes—
324#60760—111nomaximal, Sylow
325C24×C11C2×D411yescharacteristic
326C24×C11C2×D412yes—
327C23×D11—22no—
328C23×D11—21no—
329C23×D11—21no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41—22no—
333C11×#41—22no—
334C11×#41—42no—
335C11×#41—42no—
336C11×#41—44no—
337C11×#41—42no—
338C11×#41—42no—
339C2×Q8×C11—42no—
340C2×Q8×C11C2×D411yescharacteristic
341C2×Q8×C11C2×D411yescharacteristic
342C2×Q8×C11C2×D412yes—
343C2×D4×C11—42no—
344C2×D4×C11—44no—
345C2×D4×C11C2×D412yes—
346C2×D4×C11C2×D411yescharacteristic
347C2×D4×C11C2×D412yes—
348C2×D4×C11C2×D411yescharacteristic
349C2×D4×C11C2×D412yes—
350C2×D4×C11C2×D412yes—
351C2×D4×C11C2×D412yes—
352C22×C4×C11—22no—
353C22×C4×C11—22no—
354C22×C4×C11—42no—
355C22×C4×C11—42no—
356C22×C4×C11C2×D411yescharacteristic
357C22×C4×C11C2×D411yescharacteristic
358C22×C4×C11C2×D411yescharacteristic
359C22×C4×C11C2×D412yes—
360C22×C4×C11C2×D412yes—
361C22×C4×C11C2×D412yes—
362C22×C4×C11C2412yes—
363C22×C4×C11C2411yescharacteristic
364C22×C4×C11C2411yescharacteristic
365C22×C4×C11C2412yes—
366C22×C4×C11C2411yescharacteristic
367C2×C22⋊D11—21no—
368C2×C22⋊D11—22no—
369C2×C22⋊D11—22no—
370C2×C22⋊D11—22no—
371C2×C22⋊D11—21no—
372C2×C22⋊D11—22no—
373C2×C22⋊D11—22no—
374C2×C22⋊D11—21no—
375C2×C22⋊D11—22no—
376C2×C22⋊D11—22no—
377C2×C22⋊D11—22no—
378C2×C22⋊D11—22no—
379C2×C22⋊D11—22no—
380C2×C22⋊D11—22no—
381C2×C22⋊D11—22no—
382C2×C22⋊D11—44no—
383C2×C22⋊D11—82no—
384C2×C22⋊D11—84no—
385C22×Dic11—21no—
386C22×Dic11—21no—
387C22×Dic11—21no—
388C22×Dic11—22no—
389C22×Dic11—21no—
390#4343—44no—
391D4×D11—48no—
392D4×D11—44no—
393#4339—22no—
394#4339—22no—
395#4339—42no—
396#4339—42no—
397#4339—42no—
398#4339—42no—
399#4339—42no—
400#4339—42no—
401#4339—44no—
402#4339—44no—
403C2×D44—22no—
404C2×D44—21no—
405C2×D44—21no—
406C2×D44—22no—
407C2×D44—22no—
408C2×D44—22no—
409C2×D44—22no—
410C2×D44—42no—
411C2×D44—42no—
412C2×D44C2412yes—
413C2×D44C2411yescharacteristic
414C2×D44C2412yes—
415C2×C4×D11—22no—
416C2×C4×D11—22no—
417C2×C4×D11—21no—
418C2×C4×D11—22no—
419C2×C4×D11—44no—
420C2×Dic22—21no—
421C2×Dic22—22no—
422C2×Dic22—22no—
423C2×Dic22C2412yes—
424C2×Dic22C2411yescharacteristic
425C11×M16—22no—
426C11×M16—22no—
427C11×M16—42no—
428C11×M16—42no—
429C2×C8×C11—22no—
430C2×C8×C11—22no—
431C2×C8×C11—42no—
432C2×C8×C11—42no—
433C2×C8×C11C2411yescharacteristic
434C2×C8×C11C2411yescharacteristic
435C2×C8×C11C2412yes—
436C2×C8×C11C2411yescharacteristic
437C2×C8×C11C2411yescharacteristic
438C2×C8×C11C2412yes—
439C22⋊Dic11—21no—
440C22⋊Dic11—22no—
441C22⋊Dic11—22no—
442C22⋊Dic11—22no—
443C22⋊Dic11—22no—
444C22⋊Dic11—22no—
445C22⋊Dic11—21no—
446C22⋊Dic11—21no—
447C22⋊Dic11—21no—
448C22⋊Dic11—21no—
449C22⋊Dic11—21no—
450C22⋊Dic11—22no—
451C22⋊Dic11—21no—
452(C2×D11)⋊C4—22no—
453(C2×D11)⋊C4—21no—
454(C2×D11)⋊C4—22no—
455(C2×D11)⋊C4—22no—
456(C2×D11)⋊C4—22no—
457(C2×D11)⋊C4—22no—
458(C2×D11)⋊C4—21no—
459(C2×D11)⋊C4—22no—
460(C2×D11)⋊C4—22no—
461(C2×D11)⋊C4—22no—
462(C2×D11)⋊C4—22no—
463C4⋊Dic11—21no—
464C4⋊Dic11—21no—
465C4⋊Dic11—22no—
466C4⋊Dic11—21no—
467C4⋊Dic11C2412yes—
468C4⋊Dic11C2411yescharacteristic
469C4⋊Dic11C2411yescharacteristic
470C4⋊Dic11C2411yescharacteristic
471C4⋊Dic11C2411yescharacteristic
472C4⋊Dic11C2411yescharacteristic
473C4⋊Dic11C2411yescharacteristic
474Dic11⋊C4—21no—
475Dic11⋊C4—22no—
476Dic11⋊C4—22no—
477Dic11⋊C4—22no—
478Dic11⋊C4—22no—
479Dic11⋊C4—22no—
480Dic11⋊C4—21no—
481C4×Dic11—21no—
482C4×Dic11—21no—
483C4×Dic11—21no—
484C4×Dic11—21no—
485C4×Dic11—22no—
486C4×Dic11—21no—
487Dic44—42no—
488D88—42no—
489D88—42no—
490D88—42no—
491#4314—42no—
492#4314—42no—
493#4314—42no—
494#4314—42no—
495#3488—111no—
496#3449—111no—
497#3204—112no—
498#3203—112no—
499#3198—112no—
500#3198—112no—
501#3197—112no—
502#3194—112no—
503#3191—112no—
504#3188—112no—
505#3097—111no—
506#3096—111no—
507#3094—111no—
508#3091—111no—
509#3063—111no—
510#3062—111no—
511#3058—111no—
512#3057—111no—
513#3009—111no—
514#3008—111no—
515#3005—111no—
516C2×#449—111no—
517#2880D1111yescharacteristic, complemented
518C23×C11—22no—
519C23×C11—41no—
520C23×C11—42no—
521C23×C11—42no—
522C23×C11—41no—
523C23×C11—42no—
524C23×C11C22×D412yes—
525C23×C11C22×D411yescharacteristic
526C23×C11C22×D412yes—
527C23×C11C22×D411yescharacteristic
528C23×C11C22×D411yescharacteristic
529C22×D11—22no—
530C22×D11—21no—
531C22×D11—22no—
532C22×D11—42no—
533C22×D11—44no—
534C22×D11—42no—
535C22×D11—81no—
536C22×D11—81no—
537C22×D11—81no—
538C22×D11—82no—
539C22×D11—81no—
540C22×D11—82no—
541Q8×C11—22no—
542Q8×C11—22no—
543Q8×C11—42no—
544D4×C11—24no—
545D4×C11—24no—
546D4×C11—22no—
547D4×C11—22no—
548D4×C11—42no—
549D4×C11—42no—
550D4×C11—42no—
551C2×C4×C11—22no—
552C2×C4×C11—22no—
553C2×C4×C11—22no—
554C2×C4×C11—22no—
555C2×C4×C11—22no—
556C2×C4×C11—22no—
557C2×C4×C11—22no—
558C2×C4×C11—21no—
559C2×C4×C11—21no—
560C2×C4×C11—21no—
561C2×C4×C11—21no—
562C2×C4×C11—42no—
563C2×C4×C11—42no—
564C2×C4×C11—42no—
565C2×C4×C11C22×D411yescharacteristic
566C2×C4×C11C22×D412yes—
567C2×C4×C11C22×D412yes—
568C2×C4×C11C22×D411yescharacteristic
569C2×C4×C11C22×D411yescharacteristic
570C2×C4×C11H(5,𝔽2)12yes—
571C2×C4×C11H(5,𝔽2)12yes—
572C2×C4×C11C2511yescharacteristic
573C22⋊D11—44no—
574C22⋊D11—44no—
575C22⋊D11—44no—
576C22⋊D11—42no—
577C22⋊D11—44no—
578C22⋊D11—42no—
579C22⋊D11—82no—
580C22⋊D11—82no—
581C22⋊D11—81no—
582C22⋊D11—82no—
583C22⋊D11—82no—
584C22⋊D11—82no—
585C22⋊D11—82no—
586C22⋊D11—82no—
587C22⋊D11—82no—
588C2×Dic11—21no—
589C2×Dic11—21no—
590C2×Dic11—21no—
591C2×Dic11—21no—
592C2×Dic11—21no—
593C2×Dic11—22no—
594C2×Dic11—21no—
595C2×Dic11—22no—
596C2×Dic11—21no—
597C2×Dic11—42no—
598C2×Dic11—81no—
599C2×Dic11—81no—
600C2×Dic11—81no—
601C2×Dic11—82no—
602D44—22no—
603D44—21no—
604D44—22no—
605D44—22no—
606D44—22no—
607D44—21no—
608D44—44no—
609D44—42no—
610D44—42no—
611C4×D11—44no—
612C4×D11—44no—
613C4×D11—44no—
614C4×D11—42no—
615Dic22—22no—
616Dic22—21no—
617Dic22—22no—
618Dic22—21no—
619Dic22—42no—
620C8×C11—21no—
621C8×C11—21no—
622C8×C11—22no—
623C8×C11—22no—
624C8×C11—21no—
625C8×C11—21no—
626C2×H(5,𝔽2)—111no—
627C22×#41—111no—
628C22×#41C2×D1111yescharacteristic
629C2×#137—111no—
630C2×AGL(1,ℤ/8)—111no—
631C22×SD16—111no—
632C22×D8—111no—
633C2×#131C2×D1111yescharacteristic, complemented
634C2×#131C2×D1111yescharacteristic, complemented
635#550—221no—
636#548—221no—
637#546—222no—
638#546—221no—
639D42—222no—
640D42—221no—
641#537—112no—
642#537—112no—
643#537—112no—
644#537—111no—
645#536—111no—
646#536—111no—
647#536—221no—
648#535—111no—
649#535—111no—
650#535—112no—
651#535—111no—
652#535—221no—
653#534—222no—
654#532—221no—
655#532—221no—
656#525—111no—
657#525—112no—
658#525—112no—
659#525—112no—
660#525—222no—
661C2×#121—111no—
662C2×#121—112no—
663#520—111no—
664C2×#117—111no—
665#485—111no—
666#485—111no—
667#485—112no—
668#485—112no—
669#484—111no—
670#484—112no—
671#483—111no—
672#483—112no—
673#482—111no—
674#482—111no—
675#482—112no—
676#482—112no—
677#482—112no—
678#482—112no—
679#481—111no—
680#481—112no—
681#481—112no—
682#480—111no—
683#480—112no—
684#480—112no—
685#470—112no—
686#469—112no—
687#469—112no—
688#469—112no—
689#468—112no—
690#468—112no—
691#468—112no—
692#468—112no—
693#467—112no—
694#466—112no—
695#466—112no—
696#466—112no—
697#465—112no—
698#465—112no—
699#465—112no—
700#465—112no—
701#452—112no—
702#452—112no—
703#452—112no—
704#452—112no—
705#450—112no—
706#450—112no—
707#449—112no—
708#449—112no—
709#449—112no—
710#449—112no—
711#449—112no—
712#449—112no—
713#449—112no—
714#449—112no—
715#447—112no—
716#447—112no—
717#428—111no—
718#428—111no—
719#427—111no—
720#427—111no—
721#419—111no—
722#418—111no—
723#418—111no—
724#418—111no—
725#416—111no—
726#416—111no—
727C2×#103—111no—
728C2×#102—111no—
729#408C2×D1111yescharacteristic
730#408C2×D1111yescharacteristic
731#408C2×D1112yescomplemented
732#408C2×D1112yescomplemented
733#407C2×D1111yescharacteristic, complemented
734#407C2×D1112yescomplemented
735C2×C22⋊C8C2×D1111yescharacteristic, complemented
736C2×C22⋊C8C2×D1112yescomplemented
737C22×C11—21no—
738C22×C11—21no—
739C22×C11—22no—
740C22×C11—21no—
741C22×C11—21no—
742C22×C11—22no—
743C22×C11—22no—
744C22×C11—21no—
745C22×C11—21no—
746C22×C11—22no—
747C22×C11—21no—
748C22×C11—21no—
749C22×C11—22no—
750C22×C11—22no—
751C22×C11—82no—
752C22×C11—84no—
753C22×C11#53412yes—
754C22×C11C23×D411yescharacteristic
755C2×D11—42no—
756C2×D11—41no—
757C2×D11—42no—
758C2×D11—42no—
759C2×D11—41no—
760C2×D11—42no—
761C2×D11—41no—
762C2×D11—42no—
763C2×D11—42no—
764C2×D11—84no—
765C2×D11—162no—
766C2×D11—164no—
767C4×C11—21no—
768C4×C11—21no—
769C4×C11—22no—
770C4×C11—22no—
771C4×C11#53412yes—
772C4×C11C2×H(5,𝔽2)11yescharacteristic
773C4×C11C2×H(5,𝔽2)11yescharacteristic
774Dic11—41no—
775Dic11—41no—
776Dic11—41no—
777Dic11—42no—
778Dic11—41no—
779Dic11—41no—
780Dic11—41no—
781Dic11—42no—
782Dic11—41no—
783H(5,𝔽2)—442no—
784H(5,𝔽2)—442no—
785C2×#41—42no—
786C2×#41—42no—
787C2×#41—111no—
788C2×#41—112no—
789C2×#41—112no—
790C2×#41—112no—
791C2×#41—221no—
792C2×#41—221no—
793C2×#41—221no—
794C2×#41—442no—
795C2×#41—442no—
796C2×#41D4412yes—
797C2×#41D4411yescharacteristic
798C2×#41D4411yescharacteristic
799C2×#41C22×D1111yescharacteristic
800C2×#41C22×D1111yescharacteristic
801C2×#41C22×D1112yes—
802C22×Q8—111no—
803C22×Q8D4411yescharacteristic
804C22×D4—111no—
805C22×D4—111no—
806C22×D4—112no—
807C22×D4—221no—
808C22×D4—221no—
809C22×D4—222no—
810C22×D4—222no—
811C22×D4—221no—
812C22×D4D4412yes—
813C22×D4D4411yescharacteristic
814C23×C4—221no—
815C23×C4C22×D1111yescharacteristic
816C23×C4C22×D1112yes—
817#137—442no—
818AGL(1,ℤ/8)—442no—
819C2×Q16—112no—
820C2×SD16—112no—
821C2×SD16—112no—
822C2×SD16—112no—
823C2×SD16—112no—
824C2×SD16—442no—
825C2×D8—112no—
826C2×D8—112no—
827C2×D8—112no—
828C2×D8—442no—
829#131—42no—
830#131—42no—
831C2×M16C22×D1111yescharacteristic
832C2×M16C22×D1111yescharacteristic
833C2×M16C22×D1112yes—
834C2×M16C22×D1112yes—
835C22×C8C22×D1111yescharacteristic
836C22×C8C22×D1111yescharacteristic
837C22×C8C22×D1112yes—
838C22×C8C22×D1112yes—
839C4⋊Q8—221no—
840C4⋊Q8—221no—
841#127—221no—
842#127—221no—
843#127—221no—
844#127—222no—
845#124—221no—
846#124—221no—
847#124—221no—
848#124—222no—
849#124—221no—
850#124—221no—
851#123—222no—
852#123—222no—
853#123—222no—
854#123—222no—
855#123—221no—
856#123—222no—
857C22⋊Q8—111no—
858C22⋊Q8—112no—
859C22⋊Q8—112no—
860C22⋊Q8—112no—
861C22⋊Q8—112no—
862C22⋊Q8—111no—
863C22⋊Q8—112no—
864C22⋊Q8—222no—
865C22⋊Q8—222no—
866C22⋊Q8—221no—
867C22⋊Q8—222no—
868#121—112no—
869#121—111no—
870#121—112no—
871#121—112no—
872#121—112no—
873#121—111no—
874#121—112no—
875#121—112no—
876#121—112no—
877#121—112no—
878#121—112no—
879#121—222no—
880#121—222no—
881#121—222no—
882#121—222no—
883#121—222no—
884#121—222no—
885#121—222no—
886#121—222no—
887#121—222no—
888#121—221no—
889#121—222no—
890#121—221no—
891#121—222no—
892#121—221no—
893#121—222no—
894#120—222no—
895#120—222no—
896#120—221no—
897#120—222no—
898#120—222no—
899#120—222no—
900#120—222no—
901#120—222no—
902#120—222no—
903C4×Q8—221no—
904C4×D4—222no—
905C4×D4—221no—
906C4×D4—222no—
907C4×D4—222no—
908C4×D4—222no—
909C4×D4—222no—
910C4×D4—221no—
911C4×D4—222no—
912C4×D4—221no—
913C4×D4—222no—
914#117—111no—
915#117—111no—
916#117—111no—
917#117—111no—
918#117—111no—
919#117—112no—
920#117—221no—
921#117—221no—
922C2×C4⋊C4—111no—
923C2×C4⋊C4—111no—
924C2×C4⋊C4—111no—
925C2×C4⋊C4—112no—
926C2×C22⋊C4—221no—
927C2×C22⋊C4—221no—
928C2×C22⋊C4—222no—
929C2×C42—221no—
930#107—111no—
931#107—111no—
932#107—111no—
933#107—111no—
934#107—112no—
935#107—112no—
936#106—111no—
937#106—111no—
938#106—111no—
939#106—111no—
940#106—112no—
941#106—112no—
942#103—112no—
943#103—112no—
944#103—111no—
945#103—111no—
946#103—111no—
947#103—111no—
948#103—112no—
949#103—112no—
950#102—112no—
951#102—112no—
952#102—111no—
953#102—111no—
954#102—111no—
955#102—111no—
956#102—112no—
957#102—112no—
958#102—112no—
959#102—112no—
960#102—112no—
961#102—112no—
962C22⋊C8C22×D1111yescharacteristic
963C22⋊C8C22×D1111yescharacteristic
964C22⋊C8C22×D1112yes—
965C22⋊C8C22×D1112yes—
966C22⋊C8C22×D1112yes—
967C22⋊C8C22×D1111yescharacteristic
968C22⋊C8C22×D1111yescharacteristic
969C22⋊C8C22×D1112yes—
970C22⋊C8C22×D1112yes—
971C22⋊C8C22×D1112yes—
972C2×C11—22no—
973C2×C11—42no—
974C2×C11—41no—
975C2×C11—42no—
976C2×C11—41no—
977C2×C11C2×#53411yescharacteristic
978C2×C11#358411yescharacteristic
979C2×C11#358511yescharacteristic
980D11—82no—
981D11—82no—
982D11—81no—
983C24—222no—
984C24—221no—
985C24—221no—
986C24C2×D4411yescharacteristic
987C24C2×D4412yes—
988#41—22no—
989#41—22no—
990#41—22no—
991#41—22no—
992#41—42no—
993#41—42no—
994#41—44no—
995#41—42no—
996#41—42no—
997#41—222no—
998#41—222no—
999#41—442no—
1000#41—442no—
1001#41—442no—
1002#41—442no—
1003#41—442no—
1004#41—442no—
1005#41—444no—
1006#41—444no—
1007#41—444no—
1008C2×Q8—42no—
1009C2×Q8—112no—
1010C2×Q8—111no—
1011C2×Q8—221no—
1012C2×Q8—222no—
1013C2×Q8—222no—
1014C2×Q8C2×D4411yescharacteristic
1015C2×Q8C2×D4411yescharacteristic
1016C2×Q8C2×D4412yes—
1017C2×D4—42no—
1018C2×D4—44no—
1019C2×D4—112no—
1020C2×D4—112no—
1021C2×D4—111no—
1022C2×D4—221no—
1023C2×D4—222no—
1024C2×D4—222no—
1025C2×D4—222no—
1026C2×D4—221no—
1027C2×D4—222no—
1028C2×D4—222no—
1029C2×D4—221no—
1030C2×D4—222no—
1031C2×D4—222no—
1032C2×D4—222no—
1033C2×D4—222no—
1034C2×D4—222no—
1035C2×D4—222no—
1036C2×D4—222no—
1037C2×D4—222no—
1038C2×D4—221no—
1039C2×D4—221no—
1040C2×D4—222no—
1041C2×D4—222no—
1042C2×D4—222no—
1043C2×D4—222no—
1044C2×D4—442no—
1045C2×D4—442no—
1046C2×D4—448no—
1047C2×D4—444no—
1048C2×D4—444no—
1049C2×D4—882no—
1050C2×D4—884no—
1051C2×D4C2×D4412yes—
1052C2×D4C2×D4411yescharacteristic
1053C2×D4C2×D4412yes—
1054C2×D4C2×D4411yescharacteristic
1055C2×D4C2×D4412yes—
1056C2×D4C2×D4412yes—
1057C2×D4C2×D4412yes—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—221no—
1063C22×C4—221no—
1064C22×C4—221no—
1065C22×C4—222no—
1066C22×C4—221no—
1067C22×C4—222no—
1068C22×C4—222no—
1069C22×C4—221no—
1070C22×C4—222no—
1071C22×C4—444no—
1072C22×C4C2×D4411yescharacteristic
1073C22×C4C2×D4411yescharacteristic
1074C22×C4C2×D4411yescharacteristic
1075C22×C4C2×D4412yes—
1076C22×C4C2×D4412yes—
1077C22×C4C2×D4412yes—
1078C22×C4C23×D1111yescharacteristic
1079C22×C4C23×D1112yes—
1080C22×C4C23×D1111yescharacteristic
1081C22×C4C23×D1112yes—
1082C22×C4C23×D1111yescharacteristic
1083Q16—442no—
1084SD16—442no—
1085SD16—442no—
1086SD16—442no—
1087SD16—442no—
1088D8—442no—
1089D8—442no—
1090D8—442no—
1091M16—22no—
1092M16—22no—
1093M16—42no—
1094M16—42no—
1095C2×C8—22no—
1096C2×C8—22no—
1097C2×C8—42no—
1098C2×C8—42no—
1099C2×C8C23×D1112yes—
1100C2×C8C23×D1111yescharacteristic
1101C2×C8C23×D1111yescharacteristic
1102C2×C8C23×D1112yes—
1103C2×C8C23×D1111yescharacteristic
1104C2×C8C23×D1111yescharacteristic
1105C4⋊C4—111no—
1106C4⋊C4—111no—
1107C4⋊C4—111no—
1108C4⋊C4—111no—
1109C4⋊C4—112no—
1110C4⋊C4—111no—
1111C4⋊C4—111no—
1112C4⋊C4—221no—
1113C4⋊C4—221no—
1114C4⋊C4—222no—
1115C4⋊C4—221no—
1116C4⋊C4—221no—
1117C4⋊C4—222no—
1118C4⋊C4—221no—
1119C4⋊C4—222no—
1120C4⋊C4—222no—
1121C4⋊C4—222no—
1122C4⋊C4—222no—
1123C22⋊C4—221no—
1124C22⋊C4—221no—
1125C22⋊C4—221no—
1126C22⋊C4—221no—
1127C22⋊C4—222no—
1128C22⋊C4—221no—
1129C22⋊C4—221no—
1130C22⋊C4—222no—
1131C22⋊C4—221no—
1132C22⋊C4—222no—
1133C22⋊C4—222no—
1134C22⋊C4—222no—
1135C22⋊C4—222no—
1136C22⋊C4—222no—
1137C22⋊C4—221no—
1138C22⋊C4—222no—
1139C22⋊C4—222no—
1140C22⋊C4—222no—
1141C22⋊C4—222no—
1142C22⋊C4—221no—
1143C22⋊C4—222no—
1144C22⋊C4—222no—
1145C22⋊C4—222no—
1146C22⋊C4—222no—
1147C42—221no—
1148C42—221no—
1149C42—221no—
1150C42—221no—
1151C42—222no—
1152C42—221no—
1153C11#6076011yescharacteristic, complemented, Sylow
1154C23—22no—
1155C23—42no—
1156C23—41no—
1157C23—42no—
1158C23—41no—
1159C23—42no—
1160C23—222no—
1161C23—222no—
1162C23—221no—
1163C23—444no—
1164C23—442no—
1165C23—442no—
1166C23—881no—
1167C23—881no—
1168C23—881no—
1169C23—882no—
1170C23—881no—
1171C23—882no—
1172C23C22×D4412yes—
1173C23C22×D4411yescharacteristic
1174C23C22×D4412yes—
1175C23C22×D4411yescharacteristic
1176C23C22×D4411yescharacteristic
1177Q8—22no—
1178Q8—22no—
1179Q8—42no—
1180Q8—222no—
1181Q8—221no—
1182Q8—222no—
1183Q8—221no—
1184Q8—442no—
1185D4—24no—
1186D4—24no—
1187D4—22no—
1188D4—22no—
1189D4—42no—
1190D4—42no—
1191D4—42no—
1192D4—222no—
1193D4—222no—
1194D4—221no—
1195D4—222no—
1196D4—222no—
1197D4—221no—
1198D4—444no—
1199D4—444no—
1200D4—444no—
1201D4—444no—
1202D4—444no—
1203D4—442no—
1204D4—442no—
1205D4—442no—
1206D4—442no—
1207D4—882no—
1208D4—882no—
1209D4—882no—
1210D4—882no—
1211D4—882no—
1212D4—882no—
1213D4—882no—
1214D4—881no—
1215D4—882no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—221no—
1231C2×C4—221no—
1232C2×C4—221no—
1233C2×C4—221no—
1234C2×C4—221no—
1235C2×C4—222no—
1236C2×C4—221no—
1237C2×C4—221no—
1238C2×C4—222no—
1239C2×C4—444no—
1240C2×C4—444no—
1241C2×C4—444no—
1242C2×C4—442no—
1243C2×C4—442no—
1244C2×C4—881no—
1245C2×C4—882no—
1246C2×C4—881no—
1247C2×C4—881no—
1248C2×C4C22×D4411yescharacteristic
1249C2×C4C22×D4412yes—
1250C2×C4C22×D4412yes—
1251C2×C4C22×D4411yescharacteristic
1252C2×C4C22×D4411yescharacteristic
1253C2×C4#6703712yes—
1254C2×C4#6703712yes—
1255C2×C4C24×D1111yescharacteristic
1256C8—21no—
1257C8—21no—
1258C8—21no—
1259C8—21no—
1260C8—22no—
1261C8—22no—
1262C22—21no—
1263C22—21no—
1264C22—21no—
1265C22—22no—
1266C22—21no—
1267C22—22no—
1268C22—21no—
1269C22—21no—
1270C22—22no—
1271C22—22no—
1272C22—21no—
1273C22—22no—
1274C22—22no—
1275C22—21no—
1276C22—82no—
1277C22—84no—
1278C22—442no—
1279C22—441no—
1280C22—442no—
1281C22—442no—
1282C22—442no—
1283C22—441no—
1284C22—442no—
1285C22—442no—
1286C22—441no—
1287C22—884no—
1288C22—1762no—
1289C22—1764no—
1290C22#1062302412yes—
1291C22C23×D4411yescharacteristic
1292C4—21no—
1293C4—21no—
1294C4—22no—
1295C4—22no—
1296C4—442no—
1297C4—441no—
1298C4—441no—
1299C4—441no—
1300C4—441no—
1301C4—442no—
1302C4—441no—
1303C4—441no—
1304C4—441no—
1305C4#1062302412yes—
1306C4C2×#6703711yescharacteristic
1307C4C2×#6703711yescharacteristic
1308C2—22no—
1309C2—41no—
1310C2—42no—
1311C2—41no—
1312C2—42no—
1313C2—882no—
1314C2—882no—
1315C2—881no—
1316C2C2×#1062302411yescharacteristic
1317C2#1308339011yescharacteristic
1318C2#1308339711yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2880C2
socleC22×C11C23×D4
hypercenter#2880D11
hypocenterC11#60760
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ #2880

Complements

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

NH ≅ G/Ntype
1. #13082285C2semidirect
2. #13081945C2semidirect
3. #13079528C2semidirect
4. #13079518C2semidirect
5. #13079470C2semidirect
6. #13079470C2semidirect
7. #13079458C2semidirect
8. #13079432C2semidirect
9. #13079409C2semidirect
10. #13079383C2semidirect
11. #13078586C2semidirect
12. #13078575C2semidirect
13. #13078557C2semidirect
14. #13078531C2semidirect
15. #13078307C2semidirect
16. #13078296C2semidirect
17. #13078264C2semidirect
18. #13078255C2semidirect
19. #13077895C2semidirect
20. #13077886C2semidirect
21. #13077861C2semidirect
22. C2×#10622347C2semidirect
23. C11×#2880C2semidirect
26. C22×#4339C22semidirect
27. C2×C11×#131C22semidirect
28. C2×C11×#131C22semidirect
31. #10623364C22semidirect
32. #10623364C22semidirect
33. #10623364C22semidirect
38. #10623361C22semidirect
39. #10623361C22semidirect
45. #10623356C22semidirect
53. #10623322C22semidirect
54. #10623322C22semidirect
55. #10623322C22semidirect
57. C2×#66983C22semidirect
58. C2×#66979C22semidirect
59. C2×#66962C22semidirect
60. C2×#66961C22semidirect
61. C22×D88C22semidirect
62. C22×#4314C22semidirect
65. C11×#408C22semidirect
66. C11×#408C22semidirect
67. C11×#407C22semidirect
68. C11×#407C22semidirect
69. C2×C11×C22⋊C8C22semidirect
70. C2×C11×C22⋊C8C22semidirect
71. #10622750C22semidirect
72. #10622748C22semidirect
73. #10622748C22semidirect
74. #10622748C22semidirect
75. #10622747C22semidirect
76. #10622747C22semidirect
77. #10622747C22semidirect
78. #10622747C22semidirect
79. #10622744C22semidirect
80. #10622744C22semidirect
81. #10622744C22semidirect
82. #10622734C22semidirect
83. #10622734C22semidirect
84. #10622733C22semidirect
85. #10622729C22semidirect
86. #10622728C22semidirect
87. #10622728C22semidirect
88. #10622728C22semidirect
89. #10622727C22semidirect
90. #10622727C22semidirect
91. #10622727C22semidirect
92. #10622727C22semidirect
93. #10622726C22semidirect
94. #10622726C22semidirect
95. C2×#66885C22semidirect
96. #10622719C22semidirect
97. #10622719C22semidirect
98. C2×#66880C22semidirect
99. #10622350C22semidirect
100. #10622350C22semidirect
101. #10622350C22semidirect
102. #10622350C22semidirect
103. #10622350C22semidirect
104. #10622350C22semidirect
105. #10622349C22semidirect
106. #10622349C22semidirect
107. #10622349C22semidirect
108. #10622348C22semidirect
109. #10622348C22semidirect
110. #10622348C22semidirect
111. #10622347C22semidirect
112. #10622347C22semidirect
113. #10622347C22semidirect
114. #10622347C22semidirect
115. #10622347C22semidirect
116. #10622347C22semidirect
117. #10622347C22semidirect
118. #10622347C22semidirect
119. #10622346C22semidirect
120. #10622346C22semidirect
121. #10622346C22semidirect
122. #10622346C22semidirect
123. #10622345C22semidirect
124. #10622345C22semidirect
125. #10622344C22semidirect
126. #10622344C22semidirect
127. #10622336C22semidirect
128. #10622336C22semidirect
129. #10622336C22semidirect
130. #10622336C22semidirect
131. #10622335C22semidirect
132. #10622335C22semidirect
133. #10622334C22semidirect
134. #10622334C22semidirect
517. #2880D11semidirect
633. C2×#131C2×D11semidirect
634. C2×#131C2×D11semidirect
731. #408C2×D11semidirect
732. #408C2×D11semidirect
733. #407C2×D11semidirect
734. #407C2×D11semidirect
735. C2×C22⋊C8C2×D11semidirect
736. C2×C22⋊C8C2×D11semidirect
1153. C11#60760semidirect

Maximal subgroups

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

subgroupindex
#130822852
#130819452
#130795282
#130795182
#130794702
#130794582
#130794322
#130794092
#130793832
#130785862
#130785752
#130785572
#130785312
#130783072
#130782962
#130782642
#130782552
#130778952
#130778862
#130778612
C2×#106223472
C11×#28802
#6076011