Finite Group Databasebeta

← #15617275

Subgroups — #15617275

Order 2816.

4812 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623453C211yesmaximal, characteristic
2C2×#10623276C212yesmaximal, complemented
3#13077097C214yesmaximal, complemented
4#13077096C214yesmaximal, complemented
5#13077093C214yesmaximal, complemented
6#13077092C214yesmaximal, complemented
7C2×#10622850C211yesmaximal, characteristic, complemented
8C2×#10622745C212yesmaximal, complemented
9D11×#413C218yesmaximal, complemented
10C2×C11×#413C211yesmaximal, characteristic, complemented
11C22×C11×#41C2211yescharacteristic
12#10623453—24no—
13#10623453—24no—
14#10623453—24no—
15#10623453—24no—
16C2×#67043C412yes—
17C2×#67043C2212yes—
18C2×#67042C412yes—
19C2×#67042C2212yes—
20C2×#41×D11C414yes—
21C2×#41×D11C2214yes—
22C2×#67040C2212yes—
23C2×#67037C414yes—
24C2×#67037C2212yes—
25C22×#4339C414yes—
26C22×#4339C2211yescharacteristic
27C22×#4339C2211yescharacteristic
28C22×C11×M16C2212yescomplemented
29C22×#4318C2212yescomplemented
30#10623276—24no—
31#10623276—24no—
32#10623276C2218yescomplemented
33#10623276C2218yescomplemented
34C2×#66960—24no—
35C2×M16×D11C2218yescomplemented
36C2×#66954—24no—
37C11×#413C2214yescomplemented
38C11×#413C2214yescomplemented
39C2×C11×#101C2212yescomplemented
40C2×C11×#100C2212yescomplemented
41#10622850C2214yescomplemented
42#10622850C2214yescomplemented
43C2×#66900C2212yescomplemented
44C2×#66897C2212yescomplemented
45C2×#66888C2214yescomplemented
46#10622745C2218yescomplemented
47#10622745C2218yescomplemented
48C2×#66887C2214yescomplemented
49#10622364C22116yescomplemented
50D11×#101C22116yescomplemented
51#10622358C22116yescomplemented
52D11×#100C22116yescomplemented
53C2×C11×#41—22no—
54C2×C11×#41—22no—
55C2×C11×#41—22no—
56C2×C11×#41—22no—
57C2×C11×#41C2×C412yes—
58C2×C11×#41C2×C412yes—
59C2×C11×#41C2312yes—
60C2×C11×#41C2312yes—
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2×C412yes—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11C2×C412yes—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C418yes—
67C22×C22⋊D11C2×C412yes—
68C22×C22⋊D11C2×C412yes—
69#67043—28no—
70#67043—28no—
71#67043—28no—
72#67043—28no—
73#67042—28no—
74#67042—28no—
75#67042—28no—
76#67042—28no—
77#41×D11—216no—
78#41×D11—216no—
79#41×D11—216no—
80#41×D11—216no—
81#67040—28no—
82#67040—28no—
83C2×#4343C2×C414yes—
84C2×#4343C2314yes—
85C2×Q8×D11C2×C414yes—
86C2×Q8×D11C2314yes—
87#67037—216no—
88#67037—216no—
89#67037—28no—
90#67037—28no—
91C2×#4341C2×C418yes—
92C2×#4341C2×C418yes—
93C2×#4341C2×C414yes—
94C2×#4341C2314yes—
95C2×D4×D11C2×C418yes—
96C2×D4×D11C2×C418yes—
97C2×D4×D11C2×C414yes—
98C2×D4×D11C2314yes—
99C2×#4339—22no—
100C2×#4339—22no—
101C2×#4339—22no—
102C2×#4339—22no—
103C2×#4339—28no—
104C2×#4339—28no—
105C2×#4339—28no—
106C2×#4339—28no—
107C2×#4339C2×C412yes—
108C2×#4339C2×C418yes—
109C2×#4339C2×C418yes—
110C2×#4339C2×C414yes—
111C2×#4339C2×C414yes—
112C2×#4339C2×C412yes—
113C2×#4339C2×C412yes—
114C2×#4339C2×C412yes—
115C2×#4339D414yes—
116C2×#4339D414yes—
117C2×#4339D414yes—
118C2×#4339D414yes—
119C2×#4339C2312yes—
120C2×#4339C2312yes—
121C2×#4339C2312yes—
122C2×#4339C2312yes—
123C22×D44C2×C414yes—
124C22×D44C2×C411yescharacteristic
125C22×D44C2311yescharacteristic
126C22×C4×D11C2×C418yes—
127C22×C4×D11C2×C412yes—
128C22×C4×D11C2312yes—
129C22×Dic22C2×C414yes—
130C22×Dic22C2×C411yescharacteristic
131C22×Dic22C2311yescharacteristic
132C2×C11×M16—22no—
133C2×C11×M16—22no—
134C2×C11×M16—22no—
135C2×C11×M16C2314yes—
136C2×C11×M16C2314yes—
137C2×C11×M16C2314yes—
138C22×C8×C11—22no—
139C2×#4318—22no—
140C2×#4318—22no—
141C2×#4318—22no—
142C2×#4318C2314yes—
143C2×#4318C2314yes—
144C2×#4318C2314yes—
145C22×C11⋊C8—22no—
146#66960—216no—
147#66960—216no—
148M16×D11—216no—
149M16×D11C23132yes—
150#66954—216no—
151#66954—216no—
152C2×#4313—28no—
153C2×C8×D11—28no—
154C11×#101C2318yes—
155C11×#100C2318yes—
156#66900C2318yes—
157#66897C2318yes—
158#66888C23116yes—
159#66887C23116yes—
160#60076—111nomaximal, Sylow
161C24×C11C22×C412yes—
162C24×C11C22×C411yescharacteristic
163C23×D11C22×C418yes—
164C23×D11C22×C412yes—
165C23×D11C22×C412yes—
166C11×#41—24no—
167C11×#41—24no—
168C11×#41—24no—
169C11×#41—24no—
170C11×#41—24no—
171C11×#41—24no—
172C11×#41—24no—
173C11×#41—24no—
174C2×Q8×C11—22no—
175C2×Q8×C11—22no—
176C2×Q8×C11C22×C412yes—
177C2×Q8×C11C2412yes—
178C2×D4×C11—24no—
179C2×D4×C11—24no—
180C2×D4×C11—22no—
181C2×D4×C11—22no—
182C2×D4×C11C22×C414yes—
183C2×D4×C11C22×C414yes—
184C2×D4×C11C22×C412yes—
185C2×D4×C11C2412yes—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11C22×C414yes—
191C22×C4×C11C22×C414yes—
192C22×C4×C11C22×C412yes—
193C22×C4×C11C22×C411yescharacteristic
194C22×C4×C11C22×C411yescharacteristic
195C22×C4×C11C22×C411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—216no—
204C2×C22⋊D11—216no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11C22⋊C418yes—
208C2×C22⋊D11C22⋊C418yes—
209C2×C22⋊D11C22×C414yes—
210C2×C22⋊D11C22×C418yes—
211C2×C22⋊D11C22×C418yes—
212C2×C22⋊D11C22×C414yes—
213C2×C22⋊D11C22×C414yes—
214C2×C22⋊D11C22×C414yes—
215C22×Dic11C22×C418yes—
216C22×Dic11C22×C412yes—
217C22×Dic11C22×C412yes—
218#4343—216no—
219#4343—216no—
220Q8×D11—216no—
221Q8×D11—216no—
222#4341—232no—
223#4341—232no—
224#4341—216no—
225#4341—216no—
226D4×D11—232no—
227D4×D11—216no—
228D4×D11—216no—
229D4×D11—232no—
230#4339—216no—
231#4339—216no—
232#4339—28no—
233#4339—28no—
234#4339—216no—
235#4339—216no—
236#4339—28no—
237#4339—28no—
238#4339—22no—
239#4339—22no—
240#4339—22no—
241#4339—22no—
242#4339—24no—
243#4339—24no—
244#4339—24no—
245#4339—24no—
246#4339—24no—
247#4339—24no—
248#4339C22⋊C414yes—
249#4339C22⋊C414yes—
250#4339C22⋊C414yes—
251#4339C22⋊C414yes—
252#4339C22⋊C418yes—
253#4339C22⋊C418yes—
254#4339C2×D418yes—
255#4339C2×D418yes—
256#4339C2×D418yes—
257#4339C2×D418yes—
258C2×D44—28no—
259C2×D44—28no—
260C2×D44—22no—
261C2×D44—22no—
262C2×D44C22⋊C414yes—
263C2×D44C22⋊C414yes—
264C2×D44C22×C412yes—
265C2×D44C22×C418yes—
266C2×D44C22×C412yes—
267C2×D44C22×C412yes—
268C2×D44C2412yes—
269C2×C4×D11—216no—
270C2×C4×D11—216no—
271C2×C4×D11—24no—
272C2×C4×D11—24no—
273C2×C4×D11C22×C414yes—
274C2×C4×D11C22×C418yes—
275C2×C4×D11C22×C418yes—
276C2×C4×D11C22×C414yes—
277C2×C4×D11C22×C414yes—
278C2×C4×D11C2×D418yes—
279C2×C4×D11C2×D418yes—
280C2×C4×D11C2414yes—
281C2×Dic22—28no—
282C2×Dic22—28no—
283C2×Dic22—22no—
284C2×Dic22—22no—
285C2×Dic22C22⋊C414yes—
286C2×Dic22C22⋊C414yes—
287C2×Dic22C22×C412yes—
288C2×Dic22C22×C418yes—
289C2×Dic22C22×C412yes—
290C2×Dic22C22×C412yes—
291C2×Dic22C2412yes—
292C11×M16—24no—
293C11×M16—24no—
294C11×M16—24no—
295C11×M16C2418yes—
296C2×C8×C11—24no—
297C2×C8×C11—24no—
298C2×C8×C11—24no—
299#4318—24no—
300#4318—24no—
301#4318—24no—
302#4318C2418yes—
303C2×C11⋊C8—24no—
304C2×C11⋊C8—24no—
305C2×C11⋊C8—24no—
306#4313—232no—
307C8×D11—232no—
308C2×#585—111no—
309C2×#568—112no—
310#2889—114no—
311#2889—114no—
312#2888—114no—
313#2888—114no—
314C2×#413—118no—
315C2×#413—111no—
316C2×#413—112no—
317C2×#413D1111yescharacteristic, complemented
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—81no—
321C23×C11—82no—
322C23×C11C2×C22⋊C412yes—
323C23×C11C2×C22⋊C412yes—
324C23×C11C23×C414yes—
325C23×C11C23×C411yescharacteristic
326C23×C11C23×C411yescharacteristic
327C23×C11C23×C411yescharacteristic
328C22×D11—24no—
329C22×D11—216no—
330C22×D11—82no—
331C22×D11—88no—
332C22×D11—82no—
333C22×D11C2×C22⋊C418yes—
334C22×D11C23×C414yes—
335C22×D11C23×C414yes—
336Q8×C11—24no—
337Q8×C11—24no—
338D4×C11—28no—
339D4×C11—28no—
340D4×C11—24no—
341D4×C11—24no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—24no—
345C2×C4×C11—24no—
346C2×C4×C11—24no—
347C2×C4×C11—24no—
348C2×C4×C11C2×C22⋊C412yes—
349C2×C4×C11C2×C22⋊C412yes—
350C2×C4×C11C2×C22⋊C412yes—
351C2×C4×C11C2×C22⋊C412yes—
352C2×C4×C11C2×C22⋊C411yescharacteristic
353C2×C4×C11C2×C22⋊C411yescharacteristic
354C2×C4×C11C2×C22⋊C411yescharacteristic
355C2×C4×C11C2×C22⋊C411yescharacteristic
356C2×C4×C11C23×C414yes—
357C2×C4×C11C23×C411yescharacteristic
358C2×C4×C11C23×C411yescharacteristic
359C2×C4×C11C23×C411yescharacteristic
360C2×C4×C11C22×D412yes—
361C2×C4×C11C22×D412yes—
362C2×C4×C11C22×D412yes—
363C2×C4×C11C22×D412yes—
364C2×C4×C11C22×D412yes—
365C2×C4×C11C22×D412yes—
366C2×C4×C11C2511yescharacteristic
367C22⋊D11—24no—
368C22⋊D11—24no—
369C22⋊D11—28no—
370C22⋊D11—216no—
371C22⋊D11—216no—
372C22⋊D11C2×C22⋊C418yes—
373C22⋊D11C2×C22⋊C418yes—
374C22⋊D11C2×C22⋊C4116yes—
375C2×Dic11—24no—
376C2×Dic11—216no—
377C2×Dic11C2×C22⋊C418yes—
378C2×Dic11C23×C414yes—
379C2×Dic11C23×C414yes—
380D44—216no—
381D44—22no—
382D44—22no—
383D44—24no—
384D44C2×C22⋊C414yes—
385D44C2×C22⋊C414yes—
386D44C2×C22⋊C418yes—
387C4×D11—216no—
388C4×D11—24no—
389C4×D11—24no—
390C4×D11—28no—
391C4×D11—216no—
392C4×D11C2×C22⋊C418yes—
393C4×D11C2×C22⋊C418yes—
394C4×D11C22×D4116yes—
395Dic22—22no—
396Dic22—22no—
397Dic22—24no—
398Dic22—216no—
399Dic22C2×C22⋊C414yes—
400Dic22C2×C22⋊C414yes—
401Dic22C2×C22⋊C418yes—
402C8×C11—28no—
403C11⋊C8—28no—
404#585—224no—
405#585—224no—
406#585—224no—
407#585—224no—
408C2×2−1+4—112no—
409C2×2−1+4—112no—
410C2×2−1+4—112no—
411C2×H(5,𝔽2)—112no—
412C2×H(5,𝔽2)—112no—
413C2×H(5,𝔽2)—112no—
414C2×H(5,𝔽2)—114no—
415C22×#41—114no—
416C22×#41—114no—
417C22×#41—111no—
418C22×#41—111no—
419C22×#41—114no—
420C22×#41C2×D1111yescharacteristic
421#568—118no—
422#568—118no—
423#568—224no—
424#568—224no—
425C2×#131—224no—
426C2×#131—224no—
427C22×M16—112no—
428C22×M16—118no—
429C22×M16C2×D1112yescomplemented
430#413—114no—
431#413—114no—
432#413—118no—
433#413—118no—
434#413—1116no—
435#413—1116no—
436#413C2×D1114yescomplemented
437#413C2×D1114yescomplemented
438C2×#101—112no—
439C2×#101—114no—
440C2×#101—1116no—
441C2×#101C2×D1112yescomplemented
442C2×#100—112no—
443C2×#100—114no—
444C2×#100—1116no—
445C2×#100C2×D1112yescomplemented
446C22×C11—24no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—44no—
453C22×C11—82no—
454C22×C11—82no—
455C22×C11C22×C22⋊C411yescharacteristic
456C22×C11C22×C22⋊C411yescharacteristic
457C22×C11C22×C22⋊C412yes—
458C22×C11C22×C22⋊C412yes—
459C22×C11C24×C411yescharacteristic
460C2×D11—24no—
461C2×D11—44no—
462C2×D11—48no—
463C2×D11—44no—
464C2×D11—816no—
465C2×D11—84no—
466C2×D11C22×C22⋊C418yes—
467C4×C11—24no—
468C4×C11C22×C22⋊C411yescharacteristic
469C4×C11C22×C22⋊C411yescharacteristic
470C4×C11C22×C22⋊C411yescharacteristic
471C4×C11C22×C22⋊C412yes—
472C4×C11C22×C22⋊C411yescharacteristic
473C4×C11C23×D412yes—
474Dic11—24no—
475Dic11C22×C22⋊C418yes—
4762−1+4—228no—
4772−1+4—228no—
4782−1+4—228no—
4792−1+4—228no—
4802−1+4—228no—
4812−1+4—228no—
482H(5,𝔽2)—2216no—
483H(5,𝔽2)—2216no—
484H(5,𝔽2)—228no—
485H(5,𝔽2)—228no—
486H(5,𝔽2)—228no—
487H(5,𝔽2)—228no—
488H(5,𝔽2)—228no—
489H(5,𝔽2)—228no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—114no—
495C2×#41—114no—
496C2×#41—118no—
497C2×#41—118no—
498C2×#41—114no—
499C2×#41—114no—
500C2×#41—112no—
501C2×#41—112no—
502C2×#41—118no—
503C2×#41—112no—
504C2×#41—114no—
505C2×#41—114no—
506C2×#41—118no—
507C2×#41—112no—
508C2×#41—114no—
509C2×#41—114no—
510C2×#41—114no—
511C2×#41—114no—
512C2×#41—112no—
513C2×#41—112no—
514C2×#41—112no—
515C2×#41—112no—
516C2×#41—228no—
517C2×#41—228no—
518C2×#41—228no—
519C2×#41—228no—
520C2×#41—2216no—
521C2×#41—2216no—
522C2×#41—2216no—
523C2×#41—2216no—
524C2×#41—222no—
525C2×#41—222no—
526C2×#41—222no—
527C2×#41—222no—
528C2×#41C4×D1112yes—
529C2×#41C4×D1112yes—
530C2×#41C22×D1112yes—
531C2×#41C22×D1112yes—
532C22×Q8—114no—
533C22×Q8—114no—
534C22×Q8—111no—
535C22×Q8—114no—
536C22×Q8—111no—
537C22×Q8C22×D1111yescharacteristic
538C22×D4—112no—
539C22×D4—118no—
540C22×D4—112no—
541C22×D4—118no—
542C22×D4—114no—
543C22×D4—118no—
544C22×D4—114no—
545C22×D4—111no—
546C22×D4—114no—
547C22×D4—111no—
548C22×D4C4×D1112yes—
549C22×D4C22×D1111yescharacteristic
550C23×C4—112no—
551C23×C4—118no—
552C23×C4—112no—
553C23×C4C4×D1112yes—
554C23×C4C22×D1111yescharacteristic
555#131—2216no—
556#131—2216no—
557#131—2216no—
558#131—2216no—
559C2×M16—22no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—114no—
563C2×M16—114no—
564C2×M16—114no—
565C2×M16—1132no—
566C2×M16—228no—
567C2×M16—2216no—
568C2×M16—222no—
569C2×M16—222no—
570C2×M16—222no—
571C2×M16C22×D1114yes—
572C2×M16C22×D1114yes—
573C2×M16C22×D1114yes—
574C22×C8—22no—
575C22×C8—228no—
576C22×C8—222no—
577#101—118no—
578#101—1116no—
579#101C22×D1118yes—
580#100—118no—
581#100—1116no—
582#100C22×D1118yes—
583C2×C11—21no—
584C2×C11—22no—
585C2×C11—22no—
586C2×C11—21no—
587C2×C11—21no—
588C2×C11—44no—
589C2×C11C23×C22⋊C411yescharacteristic
590D11—28no—
591D11—44no—
592C24—112no—
593C24—118no—
594C24—112no—
595C24C2×C4×D1112yes—
596C24C2×C4×D1111yescharacteristic
597#41—24no—
598#41—24no—
599#41—24no—
600#41—24no—
601#41—24no—
602#41—24no—
603#41—24no—
604#41—24no—
605#41—114no—
606#41—114no—
607#41—118no—
608#41—114no—
609#41—114no—
610#41—118no—
611#41—118no—
612#41—118no—
613#41—118no—
614#41—118no—
615#41—2216no—
616#41—2216no—
617#41—2216no—
618#41—2216no—
619#41—228no—
620#41—228no—
621#41—228no—
622#41—228no—
623#41—2232no—
624#41—2216no—
625#41—2216no—
626#41—2232no—
627#41—2216no—
628#41—2216no—
629#41—222no—
630#41—222no—
631#41—222no—
632#41—222no—
633#41—224no—
634#41—224no—
635#41—224no—
636#41—224no—
637#41—224no—
638#41—224no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—114no—
642C2×Q8—114no—
643C2×Q8—112no—
644C2×Q8—112no—
645C2×Q8—118no—
646C2×Q8—112no—
647C2×Q8—112no—
648C2×Q8—228no—
649C2×Q8—228no—
650C2×Q8—2216no—
651C2×Q8—2216no—
652C2×Q8—222no—
653C2×Q8—222no—
654C2×Q8C2×C4×D1112yes—
655C2×Q8C23×D1112yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—118no—
661C2×D4—118no—
662C2×D4—114no—
663C2×D4—114no—
664C2×D4—118no—
665C2×D4—118no—
666C2×D4—114no—
667C2×D4—114no—
668C2×D4—114no—
669C2×D4—114no—
670C2×D4—112no—
671C2×D4—112no—
672C2×D4—118no—
673C2×D4—112no—
674C2×D4—112no—
675C2×D4—228no—
676C2×D4—228no—
677C2×D4—2216no—
678C2×D4—2232no—
679C2×D4—2216no—
680C2×D4—2232no—
681C2×D4—2216no—
682C2×D4—2216no—
683C2×D4—224no—
684C2×D4—224no—
685C2×D4—222no—
686C2×D4—222no—
687C2×D4C2×C4×D1112yes—
688C2×D4C2×C4×D1114yes—
689C2×D4C2×C4×D1114yes—
690C2×D4C23×D1112yes—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—112no—
696C22×C4—114no—
697C22×C4—118no—
698C22×C4—118no—
699C22×C4—114no—
700C22×C4—118no—
701C22×C4—112no—
702C22×C4—114no—
703C22×C4—118no—
704C22×C4—118no—
705C22×C4—114no—
706C22×C4—2216no—
707C22×C4—2216no—
708C22×C4—224no—
709C22×C4—224no—
710C22×C4C2×C4×D1114yes—
711C22×C4C2×C4×D1114yes—
712C22×C4C2×C4×D1112yes—
713C22×C4C2×C4×D1111yescharacteristic
714C22×C4C2×C4×D1111yescharacteristic
715C22×C4C2×C4×D1111yescharacteristic
716C22×C4D4×D1112yes—
717C22×C4D4×D1112yes—
718C22×C4D4×D1112yes—
719C22×C4D4×D1112yes—
720C22×C4C23×D1111yescharacteristic
721C22×C4C23×D1111yescharacteristic
722C22×C4C23×D1111yescharacteristic
723M16—24no—
724M16—24no—
725M16—24no—
726M16—118no—
727M16—2232no—
728M16—224no—
729M16—224no—
730M16—224no—
731M16C23×D1118yes—
732C2×C8—24no—
733C2×C8—24no—
734C2×C8—24no—
735C2×C8—2232no—
736C2×C8—224no—
737C2×C8—224no—
738C2×C8—224no—
739C11#6007611yescharacteristic, complemented, Sylow
740C23—22no—
741C23—22no—
742C23—81no—
743C23—82no—
744C23—118no—
745C23—114no—
746C23—114no—
747C23—2216no—
748C23—224no—
749C23—882no—
750C23—882no—
751C23—888no—
752C23C22⋊C4×D1112yes—
753C23C22⋊C4×D1112yes—
754C23C22×C4×D1114yes—
755C23C22×C4×D1111yescharacteristic
756C23C22×C4×D1111yescharacteristic
757C23C22×C4×D1111yescharacteristic
758Q8—24no—
759Q8—24no—
760Q8—114no—
761Q8—114no—
762Q8—118no—
763Q8—2216no—
764Q8—222no—
765Q8—222no—
766Q8—224no—
767D4—28no—
768D4—28no—
769D4—24no—
770D4—24no—
771D4—118no—
772D4—118no—
773D4—1116no—
774D4—114no—
775D4—114no—
776D4—118no—
777D4—2216no—
778D4—2216no—
779D4—2216no—
780D4—224no—
781D4—224no—
782D4—228no—
783D4—222no—
784D4—222no—
785D4—224no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—118no—
793C2×C4—114no—
794C2×C4—118no—
795C2×C4—118no—
796C2×C4—1116no—
797C2×C4—114no—
798C2×C4—2216no—
799C2×C4—2216no—
800C2×C4—2216no—
801C2×C4—224no—
802C2×C4—224no—
803C2×C4—228no—
804C2×C4—224no—
805C2×C4C22⋊C4×D1111yescharacteristic
806C2×C4C22⋊C4×D1111yescharacteristic
807C2×C4C22⋊C4×D1112yes—
808C2×C4C22⋊C4×D1112yes—
809C2×C4C22⋊C4×D1112yes—
810C2×C4C22⋊C4×D1111yescharacteristic
811C2×C4C22⋊C4×D1111yescharacteristic
812C2×C4C22⋊C4×D1112yes—
813C2×C4C22×C4×D1114yes—
814C2×C4C22×C4×D1111yescharacteristic
815C2×C4C22×C4×D1111yescharacteristic
816C2×C4C22×C4×D1111yescharacteristic
817C2×C4C2×D4×D1112yes—
818C2×C4C2×D4×D1112yes—
819C2×C4C2×D4×D1112yes—
820C2×C4C2×D4×D1112yes—
821C2×C4C2×D4×D1112yes—
822C2×C4C2×D4×D1112yes—
823C2×C4C24×D1111yescharacteristic
824C8—28no—
825C8—228no—
826C22—24no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—44no—
833C22—82no—
834C22—82no—
835C22—118no—
836C22—224no—
837C22—444no—
838C22—448no—
839C22—444no—
840C22—884no—
841C22—8816no—
842C22C2×C22⋊C4×D1111yescharacteristic
843C22C2×C22⋊C4×D1111yescharacteristic
844C22C2×C22⋊C4×D1112yes—
845C22C2×C22⋊C4×D1112yes—
846C22C23×C4×D1111yescharacteristic
847C4—24no—
848C4—118no—
849C4—224no—
850C4C2×C22⋊C4×D1111yescharacteristic
851C4C2×C22⋊C4×D1111yescharacteristic
852C4C2×C22⋊C4×D1111yescharacteristic
853C4C2×C22⋊C4×D1112yes—
854C4C2×C22⋊C4×D1111yescharacteristic
855C4C22×D4×D1112yes—
856C2—21no—
857C2—21no—
858C2—21no—
859C2—22no—
860C2—22no—
861C2—44no—
862C2—228no—
863C2—444no—
864C2C22×C22⋊C4×D1111yescharacteristic
subgroupG/H
centerC4C2×C22⋊C4×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#413C2
socleC2×C11C23×C22⋊C4
prime radicalC2×#10623453C2
cosocleC2×C4×C11C25
hypercenterC2×#413D11
hypocenterC11#60076
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#10623276C2semidirect
3. #13077097C2semidirect
4. #13077096C2semidirect
5. #13077093C2semidirect
6. #13077092C2semidirect
7. C2×#10622850C2semidirect
8. C2×#10622745C2semidirect
9. D11×#413C2semidirect
10. C2×C11×#413C2semidirect
28. C22×C11×M16C22semidirect
29. C22×#4318C22semidirect
32. #10623276C22semidirect
33. #10623276C22semidirect
35. C2×M16×D11C22semidirect
37. C11×#413C22semidirect
38. C11×#413C22semidirect
39. C2×C11×#101C22semidirect
40. C2×C11×#100C22semidirect
41. #10622850C22semidirect
42. #10622850C22semidirect
43. C2×#66900C22semidirect
44. C2×#66897C22semidirect
45. C2×#66888C22semidirect
46. #10622745C22semidirect
47. #10622745C22semidirect
48. C2×#66887C22semidirect
49. #10622364C22semidirect
50. D11×#101C22semidirect
51. #10622358C22semidirect
52. D11×#100C22semidirect
317. C2×#413D11semidirect
429. C22×M16C2×D11semidirect
436. #413C2×D11semidirect
437. #413C2×D11semidirect
441. C2×#101C2×D11semidirect
445. C2×#100C2×D11semidirect
739. C11#60076semidirect

Maximal subgroups

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

subgroupindex
C2×#106234532
C2×#106232762
#130770972
#130770962
#130770932
#130770922
C2×#106228502
C2×#106227452
D11×#4132
C2×C11×#4132
#6007611