Finite Group Databasebeta

← #15624638

Subgroups — #15624638

Order 2816.

2186 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082286C211yesmaximal, characteristic
2D11×#536C211yesmaximal, characteristic, complemented
3#13079505C212yesmaximal, complemented
4#13079503C212yesmaximal, complemented
5#13079487C212yesmaximal, complemented
6#13079487C212yesmaximal, complemented
7#13079450C212yesmaximal, complemented
8#13079421C212yesmaximal, complemented
9#13079401C212yesmaximal, complemented
10#13079372C212yesmaximal, complemented
11#13078585C211yesmaximal, characteristic, complemented
12#13078558C211yesmaximal, characteristic, complemented
13#13078533C211yesmaximal, characteristic, complemented
14#13078308C211yesmaximal, characteristic, complemented
15#13078305C211yesmaximal, characteristic, complemented
16#13078258C211yesmaximal, characteristic, complemented
17#13078256C211yesmaximal, characteristic, complemented
18#13077895C211yesmaximal, characteristic, complemented
19#13077891C211yesmaximal, characteristic, complemented
20#13077852C211yesmaximal, characteristic, complemented
21C2×#10622419C211yesmaximal, characteristic, complemented
22#13077064C211yesmaximal, characteristic, complemented
23C11×#3097C211yesmaximal, characteristic, complemented
24C2×#67042C2211yescharacteristic
25C2×#41×D11C2211yescharacteristic
26C22×Q8×D11C2211yescharacteristic, complemented
27C11×#536C2211yescharacteristic
28C11×#520C2211yescharacteristic
29#10623356C2211yescharacteristic
30#10623347C2211yescharacteristic, complemented
31C2×#66995C2211yescharacteristic, complemented
32C22×#4325C2211yescharacteristic, complemented
33C2×#66962C2211yescharacteristic, complemented
34C2×#66960C2211yescharacteristic, complemented
35C22×#4314C2211yescharacteristic, complemented
36C2×#66954C2211yescharacteristic, complemented
37#10623255—21no—
38D11×C4⋊Q8—21no—
39#10623206—21no—
40D11×#124—21no—
41D11×#123—22no—
42#10623179—22no—
43#10623159C2212yescomplemented
44#10623159C2212yescomplemented
45D11×C22⋊Q8C2212yescomplemented
46D11×C22⋊Q8C2212yescomplemented
47#10623108—21no—
48#10623107—21no—
49#10623085—22no—
50#10623085—21no—
51D4×D44—22no—
52D4×D44—21no—
53#10623057C2211yescharacteristic, complemented
54#10623056C2212yes—
55#10623056C2211yescharacteristic
56#10623055C2211yescharacteristic
57#10623055C2212yes—
58D11×#117C2211yescharacteristic, complemented
59#10623041C2211yescharacteristic
60#10623041C2212yes—
61C2×#66948C2211yescharacteristic
62C2×#66948C2212yes—
63C11×#485C2212yescomplemented
64C11×#485C2212yescomplemented
65C11×#484C2212yescomplemented
66C11×#483C2212yescomplemented
67C11×#428C2211yescharacteristic, complemented
68C11×#427C2211yescharacteristic, complemented
69C11×#419C2211yescharacteristic, complemented
70C2×C11×#103C2211yescharacteristic, complemented
71C11×#408C2211yescharacteristic
72#10622847C2211yescharacteristic
73#10622744C2211yescharacteristic, complemented
74#10622739C2211yescharacteristic, complemented
75#10622726C2211yescharacteristic, complemented
76C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
77#10622660C2212yescomplemented
78#10622660C2212yescomplemented
79#10622659C2212yescomplemented
80#10622659C2212yescomplemented
81#10622617C2211yescharacteristic, complemented
82#10622615C2211yescharacteristic, complemented
83#10622614C2211yescharacteristic, complemented
84#10622611C2211yescharacteristic, complemented
85#10622609C2212yescomplemented
86#10622609C2212yescomplemented
87#10622584C2212yescomplemented
88#10622583C2212yescomplemented
89C2×#66874C2211yescharacteristic, complemented
90#10622577C2211yescharacteristic, complemented
91#10622501C2211yescharacteristic, complemented
92#10622500C2212yescomplemented
93#10622499C2212yescomplemented
94#10622499C2212yescomplemented
95#10622499C2212yescomplemented
96#10622498C2211yescharacteristic, complemented
97#10622498C2212yescomplemented
98#10622497C2211yescharacteristic, complemented
99#10622495C2211yescharacteristic, complemented
100#10622495C2212yescomplemented
101#10622481C2212yescomplemented
102#10622480C2211yescharacteristic, complemented
103#10622479C2211yescharacteristic, complemented
104#10622479C2212yescomplemented
105#10622477C2212yescomplemented
106#10622477C2212yescomplemented
107#10622477C2212yescomplemented
108#10622476C2211yescharacteristic, complemented
109#10622476C2212yescomplemented
110#10622475C2211yescharacteristic, complemented
111#10622429C2212yescomplemented
112#10622426C2212yescomplemented
113#10622425C2212yescomplemented
114#10622425C2212yescomplemented
115#10622425C2212yescomplemented
116#10622421C2212yescomplemented
117#10622421C2212yescomplemented
118#10622420C2212yescomplemented
119#10622420C2212yescomplemented
120#10622420C2212yescomplemented
121#10622419C2212yescomplemented
122#10622419C2212yescomplemented
123#10622419C2212yescomplemented
124#10622419C2212yescomplemented
125#10622419C2212yescomplemented
126#10622419C2212yescomplemented
127#10622346C2212yescomplemented
128#10622346C2212yescomplemented
129#10622344C2212yescomplemented
130#10622344C2212yescomplemented
131#10622340C2212yescomplemented
132#10622340C2212yescomplemented
133#10622339C2212yescomplemented
134D11×C22⋊C8C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136C22×Q8×C11C2311yescharacteristic
137#67042—42no—
138#67042—42no—
139#41×D11—42no—
140#41×D11—42no—
141C2×#4343—21no—
142C2×#4343D411yescharacteristic
143C2×Q8×D11—21no—
144C2×Q8×D11—21no—
145C2×Q8×D11—42no—
146C2×Q8×D11—42no—
147C2×Q8×D11D411yescharacteristic
148C2×Q8×D11C2312yes—
149C2×Q8×D11C2312yes—
150C2×#4341D412yes—
151C2×#4341D411yescharacteristic
152C2×D4×D11—22no—
153C2×D4×D11—21no—
154C2×D4×D11D412yes—
155C2×D4×D11D411yescharacteristic
156C2×#4339C2311yescharacteristic
157C2×#4339C2312yes—
158C2×#4339C2311yescharacteristic
159C2×#4339C2312yes—
160C22×D44—21no—
161C22×D44—22no—
162C22×D44C2311yescharacteristic
163C22×D44C2312yes—
164C22×C4×D11—21no—
165C22×C4×D11C2311yescharacteristic
166C22×C4×D11C2312yes—
167C22×Dic22—21no—
168C22×Dic22C2311yescharacteristic
169C2×C11×M16C2311yescharacteristic
170C22×C8×C11C2311yescharacteristic
171C11×C4⋊Q8—21no—
172C11×#124—21no—
173C11×#123—22no—
174C11×C22⋊Q8C2312yes—
175C11×C22⋊Q8C2312yes—
176C4×Q8×C11—21no—
177C4×D4×C11—22no—
178C4×D4×C11—21no—
179C11×#117C2311yescharacteristic
180C11×#117C2312yes—
181C11×#117C2311yescharacteristic
182C2×C11×C4⋊C4C2311yescharacteristic
183C2×C11×C4⋊C4C2312yes—
184#67000—21no—
185#66999C2312yes—
186#66999C2312yes—
187#66997—21no—
188#66997—21no—
189C2×#4326C2312yes—
190#66995—42no—
191C2×#4325—42no—
192C2×#4325C2312yes—
193C2×#4325C2312yes—
194C2×#4325C2312yes—
195#66989—21no—
196#66988—22no—
197#66983—22no—
198#66983—22no—
199#66983—22no—
200#66982—22no—
201C2×(C2×D11)⋊C4—21no—
202C2×(C2×D11)⋊C4—22no—
203#66979C2311yescharacteristic
204#66977C2312yes—
205#66977C2312yes—
206C2×#4318C2311yescharacteristic
207C22×C11⋊C8C2311yescharacteristic
208#66962—42no—
209#66960—42no—
210C2×Dic44C2312yes—
211C2×#4314—42no—
212C2×#4314C2312yes—
213C2×#4314C2312yes—
214C2×#4314C2312yes—
215#66954—42no—
216C2×#4313C2312yes—
217C2×#4313C2312yes—
218C2×C8×D11C2312yes—
219C2×C8×D11C2312yes—
220#66950—21no—
221#66950—22no—
222#66950C2311yescharacteristic
223#66950C2312yes—
224#66950C2312yes—
225#66950C2311yescharacteristic
226#66950C2312yes—
227#66949—22no—
228#66949—22no—
229#66948—21no—
230#66948—22no—
231#66948—21no—
232#66948—22no—
233#66948—21no—
234#66948—22no—
235#66948C2311yescharacteristic
236#66948C2312yes—
237#66948C2312yes—
238#66948C2312yes—
239#66948C2312yes—
240#66948C2312yes—
241#66948C2311yescharacteristic
242#66947—22no—
243#66947—22no—
244#66945C2311yescharacteristic
245#66945C2311yescharacteristic
246C4⋊C4×D11—22no—
247C4⋊C4×D11—22no—
248C4⋊C4×D11C2311yescharacteristic
249C4⋊C4×D11C2311yescharacteristic
250#66941—22no—
251#66941—22no—
252#66939—22no—
253#66939—21no—
254#66939—22no—
255#66938—22no—
256#66938—22no—
257#66936—22no—
258#66936—22no—
259#66935—21no—
260#66935—22no—
261#66935—22no—
262#66935—22no—
263#66935—22no—
264C22⋊C4×D11—21no—
265C22⋊C4×D11—22no—
266C22⋊C4×D11—22no—
267#66931—22no—
268#66931—22no—
269#66930—21no—
270#66928—21no—
271#66928—21no—
272#66928—22no—
273#66927—21no—
274#66927—22no—
275C4×D44—21no—
276C4×D44—22no—
277C4×D44—21no—
278C4×D44—22no—
279#66925—21no—
280C42×D11—21no—
281#66922—21no—
282C11×#107C2312yes—
283C11×#107C2311yescharacteristic
284C11×#107C2311yescharacteristic
285C11×#106C2311yescharacteristic
286C11×#106C2311yescharacteristic
287C11×#106C2312yes—
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#103C2312yes—
291C11×#103C2312yes—
292C11×C22⋊C8C2312yes—
293C11×C22⋊C8C2312yes—
294C22⋊(C11⋊C8)C2312yes—
295C22⋊(C11⋊C8)C2312yes—
296#66885C2311yescharacteristic
297#66885C2311yescharacteristic
298#66885C2312yes—
299#66885C2312yes—
300(C2×D11)⋊C8C2311yescharacteristic
301(C2×D11)⋊C8C2311yescharacteristic
302(C2×D11)⋊C8C2311yescharacteristic
303(C2×D11)⋊C8C2311yescharacteristic
304(C2×D11)⋊C8C2312yes—
305(C2×D11)⋊C8C2312yes—
306#66880C2311yescharacteristic
307#66880C2311yescharacteristic
308#66874C2311yescharacteristic
309#66874C2312yes—
310#66874C2312yes—
311#66874C2312yes—
312#66874C2311yescharacteristic
313#66874C2312yes—
314#66873C2311yescharacteristic
315#66873C2312yes—
316#66873C2312yes—
317#66873C2311yescharacteristic
318#66872C2311yescharacteristic
319#66872C2312yes—
320#66872C2311yescharacteristic
321#66871C2312yes—
322#66871C2311yescharacteristic
323#66871C2311yescharacteristic
324#60758—111nomaximal, Sylow
325C23×D11—22no—
326C23×D11—21no—
327C23×D11C2×D411yescharacteristic
328C23×D11C2×D412yes—
329C11×#41—22no—
330C11×#41—22no—
331C2×Q8×C11—21no—
332C2×Q8×C11—22no—
333C2×Q8×C11—22no—
334C2×Q8×C11C2×D411yescharacteristic
335C2×Q8×C11C2412yes—
336C2×D4×C11C2×D412yes—
337C2×D4×C11C2×D411yescharacteristic
338C22×C4×C11—21no—
339C22×C4×C11—22no—
340C22×C4×C11—21no—
341C22×C4×C11C2412yes—
342C22×C4×C11C2411yescharacteristic
343C2×C22⋊D11—22no—
344C2×C22⋊D11—21no—
345C2×C22⋊D11C2×D412yes—
346C2×C22⋊D11C2×D412yes—
347C2×C22⋊D11C2×D412yes—
348C22×Dic11—21no—
349C22×Dic11C2×D411yescharacteristic
350C22×Dic11C2×D412yes—
351#4343—42no—
352#4343—44no—
353Q8×D11—42no—
354Q8×D11—42no—
355Q8×D11—42no—
356Q8×D11—42no—
357Q8×D11—42no—
358Q8×D11—44no—
359Q8×D11—44no—
360#4341—42no—
361#4341—44no—
362D4×D11—44no—
363D4×D11—42no—
364D4×D11—48no—
365D4×D11—44no—
366#4339—22no—
367#4339—22no—
368#4339—22no—
369#4339—22no—
370#4339—42no—
371#4339—42no—
372#4339—42no—
373#4339—42no—
374C2×D44—21no—
375C2×D44—22no—
376C2×D44—22no—
377C2×D44—21no—
378C2×D44—22no—
379C2×D44—22no—
380C2×D44—22no—
381C2×D44—22no—
382C2×D44—21no—
383C2×D44—22no—
384C2×D44—22no—
385C2×D44—42no—
386C2×D44—42no—
387C2×D44—82no—
388C2×D44—84no—
389C2×D44C2×D411yescharacteristic
390C2×D44C2×D412yes—
391C2×D44C2412yes—
392C2×D44C2411yescharacteristic
393C2×C4×D11—21no—
394C2×C4×D11—21no—
395C2×C4×D11—22no—
396C2×C4×D11—22no—
397C2×C4×D11—22no—
398C2×C4×D11—21no—
399C2×C4×D11—22no—
400C2×C4×D11—22no—
401C2×C4×D11—42no—
402C2×C4×D11—42no—
403C2×C4×D11—44no—
404C2×C4×D11C2×D411yescharacteristic
405C2×C4×D11C2×D411yescharacteristic
406C2×C4×D11C2×D412yes—
407C2×C4×D11C2×D412yes—
408C2×C4×D11C2411yescharacteristic
409C2×C4×D11C2411yescharacteristic
410C2×C4×D11C2412yes—
411C2×Dic22—22no—
412C2×Dic22—22no—
413C2×Dic22—21no—
414C2×Dic22—22no—
415C2×Dic22—22no—
416C2×Dic22—44no—
417C2×Dic22C2×D411yescharacteristic
418C2×Dic22C2×D412yes—
419C2×Dic22C2412yes—
420C2×Dic22C2411yescharacteristic
421C11×M16—22no—
422C2×C8×C11—22no—
423C2×C8×C11C2411yescharacteristic
424C2×C8×C11C2411yescharacteristic
425C2×C8×C11C2412yes—
426C11×C4⋊C4—22no—
427C11×C4⋊C4—22no—
428C11×C4⋊C4—22no—
429C11×C4⋊C4—21no—
430C11×C4⋊C4C2412yes—
431C11×C4⋊C4C2411yescharacteristic
432C11×C4⋊C4C2411yescharacteristic
433C11×C4⋊C4C2411yescharacteristic
434C11×C4⋊C4C2411yescharacteristic
435C11×C22⋊C4—21no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—22no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—21no—
440C42×C11—21no—
441C42×C11—22no—
442C42×C11—21no—
443C22⋊Dic11—21no—
444C22⋊Dic11—22no—
445C22⋊Dic11—22no—
446#4326—42no—
447#4325—42no—
448#4325—42no—
449#4325—42no—
450(C2×D11)⋊C4—21no—
451(C2×D11)⋊C4—22no—
452(C2×D11)⋊C4—21no—
453(C2×D11)⋊C4—22no—
454(C2×D11)⋊C4—22no—
455(C2×D11)⋊C4—22no—
456(C2×D11)⋊C4—22no—
457(C2×D11)⋊C4—21no—
458(C2×D11)⋊C4—21no—
459(C2×D11)⋊C4—21no—
460(C2×D11)⋊C4—22no—
461(C2×D11)⋊C4—21no—
462(C2×D11)⋊C4—22no—
463(C2×D11)⋊C4—22no—
464(C2×D11)⋊C4—22no—
465(C2×D11)⋊C4—22no—
466C4⋊Dic11—22no—
467C4⋊Dic11—22no—
468C4⋊Dic11—21no—
469C4⋊Dic11—21no—
470C4⋊Dic11—22no—
471C4⋊Dic11C2411yescharacteristic
472C4⋊Dic11C2411yescharacteristic
473Dic11⋊C4—21no—
474Dic11⋊C4—21no—
475Dic11⋊C4—22no—
476Dic11⋊C4—22no—
477Dic11⋊C4—22no—
478Dic11⋊C4—22no—
479C4×Dic11—21no—
480C4×Dic11—21no—
481C4×Dic11—21no—
482#4318—22no—
483C2×C11⋊C8—22no—
484C2×C11⋊C8C2411yescharacteristic
485C2×C11⋊C8C2412yes—
486C2×C11⋊C8C2411yescharacteristic
487Dic44—42no—
488#4314—42no—
489#4314—42no—
490#4314—42no—
491#4313—42no—
492#4313—42no—
493C8×D11—42no—
494C8×D11—42no—
495#3488—111no—
496C2×#536—111no—
497#3201—112no—
498#3201—112no—
499#3200—112no—
500#3200—112no—
501#3196—112no—
502#3193—112no—
503#3190—112no—
504#3187—112no—
505#3097—111no—
506#3097D1111yescharacteristic, complemented
507#3094—111no—
508#3091—111no—
509#3063—111no—
510#3063—111no—
511#3057—111no—
512#3057—111no—
513#3009—111no—
514#3009—111no—
515#3004—111no—
516C2×#448—111no—
517#2880—111no—
518C23×C11C22×D412yes—
519C23×C11C22×D411yescharacteristic
520C22×D11—22no—
521C22×D11—22no—
522C22×D11—24no—
523C22×D11—21no—
524C22×D11—22no—
525C22×D11—41no—
526C22×D11—42no—
527C22×D11—42no—
528C22×D11—44no—
529C22×D11—42no—
530C22×D11—81no—
531C22×D11—82no—
532C22×D11—81no—
533C22×D11—82no—
534C22×D11C22×D412yes—
535C22×D11C22×D411yescharacteristic
536C22×D11C22×D411yescharacteristic
537Q8×C11—22no—
538Q8×C11—22no—
539Q8×C11—22no—
540Q8×C11—42no—
541D4×C11—24no—
542D4×C11—22no—
543C2×C4×C11—22no—
544C2×C4×C11—22no—
545C2×C4×C11—21no—
546C2×C4×C11—21no—
547C2×C4×C11—22no—
548C2×C4×C11—21no—
549C2×C4×C11—21no—
550C2×C4×C11—22no—
551C2×C4×C11—42no—
552C2×C4×C11—81no—
553C2×C4×C11—82no—
554C2×C4×C11C22×D412yes—
555C2×C4×C11C22×D411yescharacteristic
556C2×C4×C11H(5,𝔽2)12yes—
557C2×C4×C11H(5,𝔽2)12yes—
558C2×C4×C11C2511yescharacteristic
559C22⋊D11—24no—
560C22⋊D11—42no—
561C22⋊D11—42no—
562C22⋊D11—44no—
563C22⋊D11—42no—
564C2×Dic11—22no—
565C2×Dic11—21no—
566C2×Dic11—21no—
567C2×Dic11—22no—
568C2×Dic11—21no—
569C2×Dic11—42no—
570C2×Dic11—42no—
571C2×Dic11C22×D411yescharacteristic
572C2×Dic11C22×D412yes—
573C2×Dic11C22×D411yescharacteristic
574D44—22no—
575D44—22no—
576D44—21no—
577D44—22no—
578D44—21no—
579D44—42no—
580D44—44no—
581D44—44no—
582D44—42no—
583D44—42no—
584D44—81no—
585D44—82no—
586D44—82no—
587D44—82no—
588D44—82no—
589C4×D11—22no—
590C4×D11—22no—
591C4×D11—22no—
592C4×D11—22no—
593C4×D11—21no—
594C4×D11—21no—
595C4×D11—21no—
596C4×D11—21no—
597C4×D11—42no—
598C4×D11—42no—
599C4×D11—44no—
600C4×D11—42no—
601C4×D11—44no—
602C4×D11—44no—
603C4×D11—42no—
604C4×D11—42no—
605Dic22—22no—
606Dic22—22no—
607Dic22—22no—
608Dic22—21no—
609Dic22—21no—
610Dic22—42no—
611Dic22—44no—
612Dic22—44no—
613Dic22—42no—
614C8×C11—21no—
615C8×C11—22no—
616C8×C11—21no—
617C11⋊C8—21no—
618C11⋊C8—22no—
619C11⋊C8—21no—
620C2×H(5,𝔽2)—111no—
621C22×#41—111no—
622C23×Q8—111no—
623C2×#137—111no—
624C2×#137—111no—
625C22×SD16—111no—
626C22×SD16—111no—
627C2×#131—111no—
628C2×#131—111no—
629#550—221no—
630#548—221no—
631#546—222no—
632#546—221no—
633D42—222no—
634D42—221no—
635#537—112no—
636#537—111no—
637#536—111no—
638#536—111no—
639#536—112no—
640#536—112no—
641#536—111no—
642#536—222no—
643#536—221no—
644#536—221no—
645#536C2×D1111yescharacteristic
646#535—112no—
647#535—111no—
648C2×C4⋊Q8—221no—
649C2×#124—221no—
650#525—111no—
651#525—112no—
652C2×#123—222no—
653C2×C22⋊Q8—112no—
654C2×C22⋊Q8—112no—
655C2×#121—111no—
656C2×#121—112no—
657#520C2×D1111yescharacteristic
658C2×#117—111no—
659#485—112no—
660#485—112no—
661#485—111no—
662#485—111no—
663#485C2×D1112yescomplemented
664#485C2×D1112yescomplemented
665#484—112no—
666#484—111no—
667#484C2×D1112yescomplemented
668#483—112no—
669#483—111no—
670#483C2×D1112yescomplemented
671#482—111no—
672#482—112no—
673#482—111no—
674#482—112no—
675#481—111no—
676#481—112no—
677#480—111no—
678#480—112no—
679#470—112no—
680#470—112no—
681#468—112no—
682#468—112no—
683#468—112no—
684#468—112no—
685#468—112no—
686#468—112no—
687#467—112no—
688#467—112no—
689#465—112no—
690#465—112no—
691#465—112no—
692#465—112no—
693#465—112no—
694#465—112no—
695#452—112no—
696#452—112no—
697#452—112no—
698#452—112no—
699#451—112no—
700#451—112no—
701#450—112no—
702#450—112no—
703#450—112no—
704#450—112no—
705#448—112no—
706#448—112no—
707#448—112no—
708#448—112no—
709#448—112no—
710#448—112no—
711#428—111no—
712#428C2×D1111yescharacteristic, complemented
713#427—111no—
714#427C2×D1111yescharacteristic, complemented
715#419—111no—
716#419C2×D1111yescharacteristic, complemented
717#418—111no—
718#418—111no—
719#416—111no—
720#416—111no—
721C2×#103—111no—
722C2×#103C2×D1111yescharacteristic, complemented
723#408—111no—
724#408—112no—
725#408—112no—
726#408C2×D1111yescharacteristic
727#407—111no—
728#407—112no—
729C2×C22⋊C8—111no—
730C2×C22⋊C8—112no—
731C22×C11—21no—
732C22×C11—21no—
733C22×C11—22no—
734C22×C11—22no—
735C22×C11—22no—
736C22×C11#53412yes—
737C22×C11C23×D411yescharacteristic
738C2×D11—21no—
739C2×D11—21no—
740C2×D11—21no—
741C2×D11—22no—
742C2×D11—21no—
743C2×D11—22no—
744C2×D11—21no—
745C2×D11—22no—
746C2×D11—44no—
747C2×D11—42no—
748C2×D11—41no—
749C2×D11—41no—
750C2×D11—42no—
751C2×D11—42no—
752C2×D11—41no—
753C2×D11—84no—
754C2×D11—162no—
755C2×D11—164no—
756C2×D11#57712yes—
757C4×C11—22no—
758C4×C11—41no—
759C4×C11—41no—
760C4×C11—42no—
761C4×C11—42no—
762C4×C11—41no—
763C4×C11—41no—
764C4×C11#53412yes—
765C4×C11C2×H(5,𝔽2)11yescharacteristic
766C4×C11C2×H(5,𝔽2)11yescharacteristic
767Dic11—22no—
768Dic11—21no—
769Dic11—21no—
770Dic11—41no—
771Dic11—42no—
772Dic11—41no—
773Dic11—41no—
774H(5,𝔽2)—442no—
775H(5,𝔽2)—442no—
776C2×#41—111no—
777C2×#41—112no—
778C2×#41—111no—
779C2×#41—111no—
780C2×#41—112no—
781C2×#41—111no—
782C2×#41—112no—
783C2×#41—221no—
784C2×#41—442no—
785C2×#41—442no—
786C2×#41C22×D1111yescharacteristic
787C22×Q8—111no—
788C22×Q8—112no—
789C22×Q8—112no—
790C22×Q8—111no—
791C22×Q8—221no—
792C22×Q8—221no—
793C22×Q8—221no—
794C22×Q8—442no—
795C22×Q8—442no—
796C22×Q8C22×D1111yescharacteristic
797C22×D4—112no—
798C22×D4—111no—
799C22×D4—111no—
800C22×D4—112no—
801C22×D4—221no—
802C22×D4—222no—
803C22×D4—222no—
804C22×D4—221no—
805C23×C4—111no—
806C23×C4—112no—
807C23×C4—221no—
808#137—442no—
809#137—442no—
810C2×Q16—112no—
811C2×Q16—112no—
812C2×SD16—112no—
813C2×SD16—112no—
814C2×SD16—112no—
815C2×SD16—112no—
816C2×SD16—112no—
817C2×SD16—112no—
818C2×SD16—442no—
819C2×SD16—442no—
820#131—442no—
821#131—442no—
822C2×M16—111no—
823C2×M16—112no—
824C2×M16—112no—
825C2×M16C22×D1111yescharacteristic
826C22×C8—111no—
827C22×C8—112no—
828C22×C8—112no—
829C22×C8C22×D1111yescharacteristic
830C4⋊Q8—21no—
831C4⋊Q8—221no—
832C4⋊Q8—222no—
833C4⋊Q8—222no—
834C4⋊Q8—221no—
835C4⋊Q8—221no—
836#127—221no—
837#127—222no—
838#124—21no—
839#124—221no—
840#124—221no—
841#124—222no—
842#124—222no—
843#124—222no—
844#124—221no—
845#124—221no—
846#123—22no—
847#123—221no—
848#123—222no—
849#123—222no—
850#123—222no—
851#123—222no—
852#123—222no—
853#123—222no—
854#123—222no—
855#123—222no—
856C22⋊Q8—112no—
857C22⋊Q8—112no—
858C22⋊Q8—112no—
859C22⋊Q8—112no—
860C22⋊Q8—112no—
861C22⋊Q8—112no—
862C22⋊Q8—111no—
863C22⋊Q8—111no—
864C22⋊Q8—112no—
865C22⋊Q8—222no—
866C22⋊Q8—222no—
867C22⋊Q8—222no—
868C22⋊Q8—222no—
869C22⋊Q8—221no—
870C22⋊Q8—222no—
871C22⋊Q8C22×D1112yes—
872C22⋊Q8C22×D1112yes—
873#121—112no—
874#121—111no—
875#121—112no—
876#121—112no—
877#121—112no—
878#121—111no—
879#121—112no—
880#121—221no—
881#121—222no—
882#121—221no—
883#121—222no—
884#121—221no—
885#121—222no—
886#121—222no—
887#121—222no—
888#121—222no—
889#120—222no—
890#120—222no—
891#120—222no—
892#120—221no—
893#120—222no—
894C4×Q8—21no—
895C4×D4—22no—
896C4×D4—21no—
897C4×D4—221no—
898C4×D4—222no—
899C4×D4—221no—
900C4×D4—222no—
901#117—111no—
902#117—111no—
903#117—111no—
904#117—221no—
905#117—221no—
906#117C22×D1111yescharacteristic
907#117C22×D1111yescharacteristic
908#117C22×D1112yes—
909C2×C4⋊C4—111no—
910C2×C4⋊C4—111no—
911C2×C4⋊C4—222no—
912C2×C4⋊C4—222no—
913C2×C4⋊C4C22×D1111yescharacteristic
914C2×C4⋊C4C22×D1112yes—
915C2×C22⋊C4—221no—
916C2×C22⋊C4—222no—
917C2×C22⋊C4—222no—
918C2×C22⋊C4—221no—
919C2×C22⋊C4—222no—
920C2×C42—221no—
921#107—111no—
922#107—111no—
923#107—112no—
924#107C22×D1111yescharacteristic
925#107C22×D1111yescharacteristic
926#107C22×D1112yes—
927#106—111no—
928#106—111no—
929#106—112no—
930#106C22×D1111yescharacteristic
931#106C22×D1111yescharacteristic
932#106C22×D1112yes—
933#103—111no—
934#103—111no—
935#103—112no—
936#103—112no—
937#103—111no—
938#103—111no—
939#103—112no—
940#103—112no—
941#103C22×D1112yes—
942#103C22×D1112yes—
943#103C22×D1112yes—
944#103C22×D1112yes—
945#102—111no—
946#102—111no—
947#102—112no—
948#102—112no—
949#102—111no—
950#102—111no—
951#102—112no—
952#102—112no—
953C22⋊C8—112no—
954C22⋊C8—112no—
955C22⋊C8—111no—
956C22⋊C8—111no—
957C22⋊C8—112no—
958C22⋊C8—111no—
959C22⋊C8—111no—
960C22⋊C8—112no—
961C22⋊C8C22×D1112yes—
962C22⋊C8C22×D1112yes—
963C2×C11—22no—
964C2×C11—42no—
965C2×C11C2×#53411yescharacteristic
966C2×C11C2×#57711yescharacteristic
967C2×C11#358611yescharacteristic
968D11—22no—
969D11—41no—
970D11—42no—
971D11—82no—
972D11—81no—
973C24—111no—
974C24—112no—
975C24—222no—
976C24—221no—
977#41—22no—
978#41—22no—
979#41—222no—
980#41—222no—
981#41—222no—
982#41—222no—
983#41—442no—
984#41—442no—
985#41—442no—
986#41—442no—
987#41—444no—
988#41—442no—
989#41—442no—
990#41—444no—
991C2×Q8—21no—
992C2×Q8—22no—
993C2×Q8—22no—
994C2×Q8—111no—
995C2×Q8—112no—
996C2×Q8—112no—
997C2×Q8—111no—
998C2×Q8—222no—
999C2×Q8—222no—
1000C2×Q8—221no—
1001C2×Q8—222no—
1002C2×Q8—222no—
1003C2×Q8—444no—
1004C2×Q8—442no—
1005C2×Q8—442no—
1006C2×Q8—442no—
1007C2×Q8—442no—
1008C2×Q8—442no—
1009C2×Q8—444no—
1010C2×Q8—444no—
1011C2×Q8D4×D1111yescharacteristic
1012C2×Q8C23×D1112yes—
1013C2×D4—112no—
1014C2×D4—112no—
1015C2×D4—112no—
1016C2×D4—111no—
1017C2×D4—112no—
1018C2×D4—112no—
1019C2×D4—111no—
1020C2×D4—221no—
1021C2×D4—222no—
1022C2×D4—222no—
1023C2×D4—221no—
1024C2×D4—222no—
1025C2×D4—222no—
1026C2×D4—222no—
1027C2×D4—222no—
1028C2×D4—221no—
1029C2×D4—222no—
1030C2×D4—221no—
1031C2×D4—222no—
1032C2×D4—222no—
1033C2×D4—442no—
1034C2×D4—442no—
1035C2×D4—442no—
1036C2×D4—444no—
1037C2×D4—448no—
1038C2×D4—444no—
1039C2×D4—882no—
1040C2×D4—884no—
1041C2×D4D4×D1112yes—
1042C2×D4D4×D1111yescharacteristic
1043C22×C4—21no—
1044C22×C4—22no—
1045C22×C4—21no—
1046C22×C4—111no—
1047C22×C4—112no—
1048C22×C4—111no—
1049C22×C4—111no—
1050C22×C4—111no—
1051C22×C4—111no—
1052C22×C4—112no—
1053C22×C4—112no—
1054C22×C4—112no—
1055C22×C4—221no—
1056C22×C4—221no—
1057C22×C4—222no—
1058C22×C4—222no—
1059C22×C4—222no—
1060C22×C4—222no—
1061C22×C4—221no—
1062C22×C4—222no—
1063C22×C4—221no—
1064C22×C4—442no—
1065C22×C4—442no—
1066C22×C4—444no—
1067C22×C4C23×D1112yes—
1068C22×C4C23×D1111yescharacteristic
1069Q16—442no—
1070Q16—442no—
1071SD16—442no—
1072SD16—442no—
1073SD16—442no—
1074SD16—442no—
1075SD16—442no—
1076SD16—442no—
1077M16—22no—
1078M16—222no—
1079M16—442no—
1080M16—442no—
1081C2×C8—22no—
1082C2×C8—112no—
1083C2×C8—111no—
1084C2×C8—111no—
1085C2×C8—222no—
1086C2×C8—442no—
1087C2×C8—442no—
1088C2×C8C23×D1112yes—
1089C2×C8C23×D1111yescharacteristic
1090C2×C8C23×D1111yescharacteristic
1091C4⋊C4—22no—
1092C4⋊C4—22no—
1093C4⋊C4—22no—
1094C4⋊C4—21no—
1095C4⋊C4—111no—
1096C4⋊C4—111no—
1097C4⋊C4—221no—
1098C4⋊C4—221no—
1099C4⋊C4—222no—
1100C4⋊C4—222no—
1101C4⋊C4—222no—
1102C4⋊C4—222no—
1103C4⋊C4—221no—
1104C4⋊C4—221no—
1105C4⋊C4—222no—
1106C4⋊C4—222no—
1107C4⋊C4—222no—
1108C4⋊C4C23×D1111yescharacteristic
1109C4⋊C4C23×D1111yescharacteristic
1110C4⋊C4C23×D1112yes—
1111C4⋊C4C23×D1111yescharacteristic
1112C4⋊C4C23×D1111yescharacteristic
1113C22⋊C4—21no—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—22no—
1117C22⋊C4—21no—
1118C22⋊C4—222no—
1119C22⋊C4—221no—
1120C22⋊C4—222no—
1121C22⋊C4—222no—
1122C22⋊C4—222no—
1123C22⋊C4—221no—
1124C22⋊C4—222no—
1125C22⋊C4—221no—
1126C22⋊C4—221no—
1127C22⋊C4—222no—
1128C22⋊C4—222no—
1129C22⋊C4—222no—
1130C22⋊C4—222no—
1131C22⋊C4—221no—
1132C22⋊C4—222no—
1133C22⋊C4—221no—
1134C22⋊C4—221no—
1135C22⋊C4—222no—
1136C22⋊C4—222no—
1137C42—21no—
1138C42—22no—
1139C42—21no—
1140C42—221no—
1141C42—221no—
1142C42—221no—
1143C11#6075811yescharacteristic, complemented, Sylow
1144C23—111no—
1145C23—112no—
1146C23—111no—
1147C23—222no—
1148C23—224no—
1149C23—222no—
1150C23—222no—
1151C23—221no—
1152C23—441no—
1153C23—442no—
1154C23—442no—
1155C23—444no—
1156C23—442no—
1157C23—881no—
1158C23—882no—
1159C23—881no—
1160C23—882no—
1161C23C2×D4×D1112yes—
1162C23C2×D4×D1111yescharacteristic
1163Q8—22no—
1164Q8—22no—
1165Q8—22no—
1166Q8—42no—
1167Q8—222no—
1168Q8—222no—
1169Q8—222no—
1170Q8—221no—
1171Q8—221no—
1172Q8—442no—
1173Q8—444no—
1174Q8—444no—
1175Q8—442no—
1176D4—24no—
1177D4—22no—
1178D4—224no—
1179D4—222no—
1180D4—222no—
1181D4—222no—
1182D4—221no—
1183D4—221no—
1184D4—442no—
1185D4—444no—
1186D4—444no—
1187D4—442no—
1188D4—442no—
1189D4—442no—
1190D4—444no—
1191D4—442no—
1192D4—442no—
1193D4—882no—
1194D4—882no—
1195D4—882no—
1196D4—881no—
1197D4—882no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—42no—
1207C2×C4—81no—
1208C2×C4—82no—
1209C2×C4—111no—
1210C2×C4—112no—
1211C2×C4—111no—
1212C2×C4—222no—
1213C2×C4—222no—
1214C2×C4—222no—
1215C2×C4—222no—
1216C2×C4—222no—
1217C2×C4—221no—
1218C2×C4—221no—
1219C2×C4—221no—
1220C2×C4—221no—
1221C2×C4—221no—
1222C2×C4—221no—
1223C2×C4—221no—
1224C2×C4—222no—
1225C2×C4—442no—
1226C2×C4—442no—
1227C2×C4—444no—
1228C2×C4—442no—
1229C2×C4—444no—
1230C2×C4—444no—
1231C2×C4—442no—
1232C2×C4—442no—
1233C2×C4—442no—
1234C2×C4—442no—
1235C2×C4C2×D4×D1112yes—
1236C2×C4C2×D4×D1111yescharacteristic
1237C2×C4#6704212yes—
1238C2×C4#6704212yes—
1239C2×C4C24×D1111yescharacteristic
1240C8—21no—
1241C8—21no—
1242C8—22no—
1243C8—221no—
1244C8—221no—
1245C8—222no—
1246C22—21no—
1247C22—21no—
1248C22—22no—
1249C22—22no—
1250C22—22no—
1251C22—112no—
1252C22—221no—
1253C22—221no—
1254C22—221no—
1255C22—222no—
1256C22—221no—
1257C22—222no—
1258C22—221no—
1259C22—222no—
1260C22—444no—
1261C22—442no—
1262C22—441no—
1263C22—442no—
1264C22—441no—
1265C22—442no—
1266C22—441no—
1267C22—884no—
1268C22—1762no—
1269C22—1764no—
1270C22#1062318412yes—
1271C22C22×D4×D1111yescharacteristic
1272C4—22no—
1273C4—41no—
1274C4—41no—
1275C4—42no—
1276C4—42no—
1277C4—41no—
1278C4—41no—
1279C4—221no—
1280C4—221no—
1281C4—222no—
1282C4—441no—
1283C4—441no—
1284C4—442no—
1285C4—441no—
1286C4#1062318412yes—
1287C4C2×#6704211yescharacteristic
1288C4C2×#6704211yescharacteristic
1289C2—22no—
1290C2—42no—
1291C2—222no—
1292C2—441no—
1293C2—442no—
1294C2—882no—
1295C2—881no—
1296C2C2×#1062318411yescharacteristic
1297C2D11×#57711yescharacteristic
1298C2#1308340111yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3097C2
socleC22×C11C23×D4
prime radical#13082286C2
hypercenter#3097D11
hypocenterC11#60758
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3097

Complements

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

NH ≅ G/Ntype
2. D11×#536C2semidirect
3. #13079505C2semidirect
4. #13079503C2semidirect
5. #13079487C2semidirect
6. #13079487C2semidirect
7. #13079450C2semidirect
8. #13079421C2semidirect
9. #13079401C2semidirect
10. #13079372C2semidirect
11. #13078585C2semidirect
12. #13078558C2semidirect
13. #13078533C2semidirect
14. #13078308C2semidirect
15. #13078305C2semidirect
16. #13078258C2semidirect
17. #13078256C2semidirect
18. #13077895C2semidirect
19. #13077891C2semidirect
20. #13077852C2semidirect
21. C2×#10622419C2semidirect
22. #13077064C2semidirect
23. C11×#3097C2semidirect
26. C22×Q8×D11C22semidirect
30. #10623347C22semidirect
31. C2×#66995C22semidirect
32. C22×#4325C22semidirect
33. C2×#66962C22semidirect
34. C2×#66960C22semidirect
35. C22×#4314C22semidirect
36. C2×#66954C22semidirect
43. #10623159C22semidirect
44. #10623159C22semidirect
45. D11×C22⋊Q8C22semidirect
46. D11×C22⋊Q8C22semidirect
53. #10623057C22semidirect
58. D11×#117C22semidirect
63. C11×#485C22semidirect
64. C11×#485C22semidirect
65. C11×#484C22semidirect
66. C11×#483C22semidirect
67. C11×#428C22semidirect
68. C11×#427C22semidirect
69. C11×#419C22semidirect
70. C2×C11×#103C22semidirect
73. #10622744C22semidirect
74. #10622739C22semidirect
75. #10622726C22semidirect
76. C2×(C2×D11)⋊C8C22semidirect
77. #10622660C22semidirect
78. #10622660C22semidirect
79. #10622659C22semidirect
80. #10622659C22semidirect
81. #10622617C22semidirect
82. #10622615C22semidirect
83. #10622614C22semidirect
84. #10622611C22semidirect
85. #10622609C22semidirect
86. #10622609C22semidirect
87. #10622584C22semidirect
88. #10622583C22semidirect
89. C2×#66874C22semidirect
90. #10622577C22semidirect
91. #10622501C22semidirect
92. #10622500C22semidirect
93. #10622499C22semidirect
94. #10622499C22semidirect
95. #10622499C22semidirect
96. #10622498C22semidirect
97. #10622498C22semidirect
98. #10622497C22semidirect
99. #10622495C22semidirect
100. #10622495C22semidirect
101. #10622481C22semidirect
102. #10622480C22semidirect
103. #10622479C22semidirect
104. #10622479C22semidirect
105. #10622477C22semidirect
106. #10622477C22semidirect
107. #10622477C22semidirect
108. #10622476C22semidirect
109. #10622476C22semidirect
110. #10622475C22semidirect
111. #10622429C22semidirect
112. #10622426C22semidirect
113. #10622425C22semidirect
114. #10622425C22semidirect
115. #10622425C22semidirect
116. #10622421C22semidirect
117. #10622421C22semidirect
118. #10622420C22semidirect
119. #10622420C22semidirect
120. #10622420C22semidirect
121. #10622419C22semidirect
122. #10622419C22semidirect
123. #10622419C22semidirect
124. #10622419C22semidirect
125. #10622419C22semidirect
126. #10622419C22semidirect
127. #10622346C22semidirect
128. #10622346C22semidirect
129. #10622344C22semidirect
130. #10622344C22semidirect
131. #10622340C22semidirect
132. #10622340C22semidirect
133. #10622339C22semidirect
134. D11×C22⋊C8C22semidirect
506. #3097D11semidirect
663. #485C2×D11semidirect
664. #485C2×D11semidirect
667. #484C2×D11semidirect
670. #483C2×D11semidirect
712. #428C2×D11semidirect
714. #427C2×D11semidirect
716. #419C2×D11semidirect
722. C2×#103C2×D11semidirect
1143. C11#60758semidirect

Maximal subgroups

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

subgroupindex
#130822862
D11×#5362
#130795052
#130795032
#130794872
#130794502
#130794212
#130794012
#130793722
#130785852
#130785582
#130785332
#130783082
#130783052
#130782582
#130782562
#130778952
#130778912
#130778522
C2×#106224192
#130770642
C11×#30972
#6075811