Finite Group Databasebeta

← #15620444

Subgroups — #15620444

Order 2816.

4764 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C212yesmaximal, complemented
2#13081945C211yesmaximal, characteristic, complemented
3#13077995C214yesmaximal, complemented
4#13077988C214yesmaximal, complemented
5#13077980C214yesmaximal, complemented
6#13077973C214yesmaximal, complemented
7#13077965C218yesmaximal, complemented
8C2×#10622849C212yesmaximal, complemented
9C2×#10622850C211yesmaximal, characteristic, complemented
10C2×C11×#585C211yesmaximal, characteristic, complemented
11C11×#585—22no—
12C11×#585—22no—
13C11×#585—24no—
14C11×#585—24no—
15C11×#585C2214yes—
16C11×#585C2214yescomplemented
17C2×C11×2−1+4—22no—
18C2×C11×2−1+4C2212yescomplemented
19C2×C11×H(5,𝔽2)—22no—
20C2×C11×H(5,𝔽2)—22no—
21C2×C11×H(5,𝔽2)C2212yescomplemented
22C22×C11×#41—24no—
23C22×C11×#41—22no—
24C22×C11×#41C2212yes—
25C22×C11×#41C2211yescharacteristic
26C22×#4339C2211yescharacteristic, complemented
27#10623364—22no—
28#10623363C2214yescomplemented
29#10623361C2212yescomplemented
30#10623359—22no—
31#10623356C2212yescomplemented
32C2×#67004C2214yescomplemented
33#10623353—24no—
34#10623353—24no—
35#10623353C2218yescomplemented
36#10623353C2218yescomplemented
37C2×#67003—24no—
38C2×#67002C2214yescomplemented
39#10623347C2212yescomplemented
40C2×#66995—22no—
41#10623336C2212yescomplemented
42#10623335—22no—
43C2×#66985—22no—
44#10623322—22no—
45C2×#66979C2211yescharacteristic, complemented
46C22×#4318C2212yescomplemented
47#10622859C22116yescomplemented
48#10622858C22116yescomplemented
49#10622855C22116yescomplemented
50#10622854C22116yescomplemented
51#10622850C2214yescomplemented
52#10622850C2214yescomplemented
53#10622849C2218yescomplemented
54#10622849C2218yescomplemented
55C2×#66901C2218yescomplemented
56C2×#66900C2212yescomplemented
57C2×#66897C2212yescomplemented
58C11×2−1+4—28no—
59C11×2−1+4—28no—
60C11×2−1+4—28no—
61C11×2−1+4—28no—
62C11×2−1+4—28no—
63C11×2−1+4—24no—
64C11×2−1+4C2318yes—
65C11×H(5,𝔽2)—28no—
66C11×H(5,𝔽2)—28no—
67C11×H(5,𝔽2)—216no—
68C11×H(5,𝔽2)—28no—
69C11×H(5,𝔽2)—28no—
70C11×H(5,𝔽2)—28no—
71C11×H(5,𝔽2)—28no—
72C11×H(5,𝔽2)—28no—
73C11×H(5,𝔽2)—24no—
74C11×H(5,𝔽2)C2318yes—
75C2×C11×#41—24no—
76C2×C11×#41—28no—
77C2×C11×#41—24no—
78C2×C11×#41—216no—
79C2×C11×#41—216no—
80C2×C11×#41—28no—
81C2×C11×#41—28no—
82C2×C11×#41—216no—
83C2×C11×#41—216no—
84C2×C11×#41—24no—
85C2×C11×#41—24no—
86C2×C11×#41—22no—
87C2×C11×#41—22no—
88C2×C11×#41—24no—
89C2×C11×#41—28no—
90C2×C11×#41—28no—
91C2×C11×#41—22no—
92C2×C11×#41—22no—
93C2×C11×#41—22no—
94C2×C11×#41—22no—
95C2×C11×#41—22no—
96C2×C11×#41—22no—
97C2×C11×#41—22no—
98C2×C11×#41—22no—
99C2×C11×#41D412yes—
100C2×C11×#41D412yes—
101C2×C11×#41D414yescomplemented
102C2×C11×#41D414yescomplemented
103C2×C11×#41D414yescomplemented
104C2×C11×#41C2314yes—
105C2×C11×#41C2314yes—
106C2×C11×#41C2314yes—
107C2×C11×#41C2312yes—
108C2×C11×#41C2312yes—
109C22×Q8×C11—22no—
110C22×Q8×C11—24no—
111C22×Q8×C11D412yescomplemented
112C22×Q8×C11C2311yescharacteristic
113C22×D4×C11—28no—
114C22×D4×C11—22no—
115C22×D4×C11—24no—
116C22×D4×C11—22no—
117C22×D4×C11—24no—
118C22×D4×C11D412yes—
119C22×D4×C11D412yescomplemented
120C22×D4×C11C2311yescharacteristic
121C23×C4×C11—24no—
122C23×C4×C11—22no—
123C23×C4×C11D412yes—
124C23×C4×C11C2311yescharacteristic
125C22×C22⋊D11—21no—
126C2×#4339—21no—
127C2×#4339—21no—
128C2×#4339—22no—
129C2×#4339—22no—
130C2×#4339—22no—
131C2×#4339—22no—
132C2×#4339C2312yes—
133C2×#4339C2312yescomplemented
134C22×D44C2311yescharacteristic, complemented
135C22×C4×D11—21no—
136C22×Dic22C2311yescharacteristic, complemented
137#67006—24no—
138C2×C22⋊Dic11—21no—
139#67004—28no—
140#67004C23116yescomplemented
141#67003—216no—
142#67003—216no—
143#67002—28no—
144#67002C23116yescomplemented
145#67000C2314yescomplemented
146#66999—24no—
147#66997C2314yescomplemented
148C2×#4326—24no—
149#66995—28no—
150#66995—28no—
151C2×#4325—24no—
152#66993C2314yescomplemented
153#66992—28no—
154#66991—24no—
155#66990—24no—
156#66989C2314yescomplemented
157#66988—24no—
158C2×#4324—24no—
159#66985—28no—
160#66985—28no—
161C2×#4323—24no—
162#66983—24no—
163#66982—24no—
164C4×C22⋊D11—28no—
165#66979—21no—
166#66979—21no—
167#66979C2312yes—
168#66979C2312yescomplemented
169C2×C4⋊Dic11—21no—
170#66977—24no—
171C2×C4×Dic11C2312yescomplemented
172C2×#4318—22no—
173C2×#4318—22no—
174C2×#4318—22no—
175C2×#4318C2314yes—
176C2×#4318C2314yescomplemented
177C2×#4318C2314yescomplemented
178C22×C11⋊C8—22no—
179#66901C23132yescomplemented
180#66900C2318yescomplemented
181#66897C2318yescomplemented
182#60387—111nomaximal, Sylow
183C24×C11—24no—
184C24×C11—22no—
185C24×C11C2×D412yes—
186C24×C11C2×D411yescharacteristic
187C23×D11—21no—
188C11×#41—216no—
189C11×#41—216no—
190C11×#41—232no—
191C11×#41—232no—
192C11×#41—216no—
193C11×#41—216no—
194C11×#41—216no—
195C11×#41—216no—
196C11×#41—216no—
197C11×#41—216no—
198C11×#41—216no—
199C11×#41—24no—
200C11×#41—24no—
201C11×#41—24no—
202C11×#41—24no—
203C11×#41—24no—
204C11×#41—24no—
205C11×#41—24no—
206C11×#41—24no—
207C11×#41—24no—
208C11×#41—24no—
209C11×#41—24no—
210C11×#41—24no—
211C11×#41—24no—
212C11×#41—24no—
213C11×#41—216no—
214C11×#41—24no—
215C11×#41—24no—
216C11×#41—24no—
217C11×#41—24no—
218C11×#41—24no—
219C11×#41—24no—
220C11×#41C2×D418yes—
221C11×#41C2×D418yes—
222C11×#41C2×D418yes—
223C11×#41C2418yes—
224C2×Q8×C11—24no—
225C2×Q8×C11—216no—
226C2×Q8×C11—28no—
227C2×Q8×C11—28no—
228C2×Q8×C11—216no—
229C2×Q8×C11—22no—
230C2×Q8×C11—22no—
231C2×Q8×C11—22no—
232C2×Q8×C11—22no—
233C2×Q8×C11—22no—
234C2×Q8×C11C2×D414yes—
235C2×Q8×C11C2×D414yes—
236C2×Q8×C11C2×D414yes—
237C2×Q8×C11C2×D412yes—
238C2×Q8×C11C2412yes—
239C2×D4×C11—28no—
240C2×D4×C11—24no—
241C2×D4×C11—216no—
242C2×D4×C11—232no—
243C2×D4×C11—232no—
244C2×D4×C11—216no—
245C2×D4×C11—28no—
246C2×D4×C11—28no—
247C2×D4×C11—24no—
248C2×D4×C11—24no—
249C2×D4×C11—24no—
250C2×D4×C11—24no—
251C2×D4×C11—24no—
252C2×D4×C11—24no—
253C2×D4×C11—216no—
254C2×D4×C11—24no—
255C2×D4×C11—24no—
256C2×D4×C11—216no—
257C2×D4×C11—22no—
258C2×D4×C11—22no—
259C2×D4×C11—22no—
260C2×D4×C11—22no—
261C2×D4×C11—22no—
262C2×D4×C11C2×D414yes—
263C2×D4×C11C2×D412yes—
264C2×D4×C11C2×D414yes—
265C2×D4×C11C2×D414yes—
266C2×D4×C11C2×D414yes—
267C2×D4×C11C2×D414yes—
268C2×D4×C11C2412yes—
269C22×C4×C11—24no—
270C22×C4×C11—28no—
271C22×C4×C11—216no—
272C22×C4×C11—216no—
273C22×C4×C11—22no—
274C22×C4×C11—24no—
275C22×C4×C11—22no—
276C22×C4×C11—24no—
277C22×C4×C11—24no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—24no—
282C22×C4×C11—24no—
283C22×C4×C11—24no—
284C22×C4×C11C2×D414yes—
285C22×C4×C11C2×D414yes—
286C22×C4×C11C2×D412yes—
287C22×C4×C11C2×D411yescharacteristic
288C22×C4×C11C2×D411yescharacteristic
289C22×C4×C11C2×D411yescharacteristic
290C22×C4×C11C2×D412yes—
291C22×C4×C11C2×D412yes—
292C22×C4×C11C2×D412yes—
293C22×C4×C11C2×D412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C2×C22⋊D11—22no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—28no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11—42no—
302C22×Dic11—21no—
303C22×Dic11—22no—
304#4339—24no—
305#4339—24no—
306#4339—24no—
307#4339—24no—
308#4339—41no—
309#4339—41no—
310#4339—41no—
311#4339—41no—
312#4339—42no—
313#4339—42no—
314C2×D44—21no—
315C2×D44—22no—
316C2×D44—22no—
317C2×D44C2412yes—
318C2×C4×D11—22no—
319C2×C4×D11—22no—
320C2×C4×D11—42no—
321C2×C4×D11—42no—
322C2×Dic22—22no—
323C2×Dic22—22no—
324C2×Dic22—21no—
325C2×Dic22C2412yes—
326C22⋊Dic11—28no—
327C22⋊Dic11—22no—
328C22⋊Dic11—22no—
329#4326—216no—
330#4325—216no—
331#4324—216no—
332#4323—216no—
333(C2×D11)⋊C4—28no—
334C4⋊Dic11—22no—
335C4⋊Dic11—22no—
336Dic11⋊C4—28no—
337C4×Dic11—22no—
338C4×Dic11C2414yes—
339#4318—24no—
340#4318—24no—
341#4318—24no—
342#4318C2418yes—
343C2×C11⋊C8—24no—
344C2×C11⋊C8—24no—
345C2×C11⋊C8—24no—
346C2×#585D1111yescharacteristic, complemented
347C2×#575—112no—
348#3449—111no—
349#3022—114no—
350#3021—114no—
351#3020—114no—
352#3019—114no—
353#3018—118no—
354C2×#421—112no—
355C2×#413—111no—
356C23×C11—216no—
357C23×C11—22no—
358C23×C11—24no—
359C23×C11—22no—
360C23×C11—24no—
361C23×C11—24no—
362C23×C11—81no—
363C23×C11—82no—
364C23×C11—84no—
365C23×C11—88no—
366C23×C11#12012yes—
367C23×C11#12012yes—
368C23×C11C22×D414yes—
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C22×D11—22no—
373C22×D11—42no—
374C22×D11—82no—
375Q8×C11—216no—
376Q8×C11—24no—
377Q8×C11—24no—
378Q8×C11—24no—
379Q8×C11—24no—
380Q8×C11—24no—
381Q8×C11C22×D418yes—
382D4×C11—232no—
383D4×C11—216no—
384D4×C11—28no—
385D4×C11—28no—
386D4×C11—28no—
387D4×C11—28no—
388D4×C11—28no—
389D4×C11—28no—
390D4×C11—24no—
391D4×C11—24no—
392D4×C11—24no—
393D4×C11—24no—
394D4×C11—24no—
395D4×C11C22×D418yes—
396C2×C4×C11—216no—
397C2×C4×C11—232no—
398C2×C4×C11—24no—
399C2×C4×C11—22no—
400C2×C4×C11—24no—
401C2×C4×C11—24no—
402C2×C4×C11—22no—
403C2×C4×C11—28no—
404C2×C4×C11—28no—
405C2×C4×C11—24no—
406C2×C4×C11—24no—
407C2×C4×C11—28no—
408C2×C4×C11—24no—
409C2×C4×C11—24no—
410C2×C4×C11—28no—
411C2×C4×C11#12012yes—
412C2×C4×C11#12012yes—
413C2×C4×C11#12011yescharacteristic
414C2×C4×C11#12011yescharacteristic
415C2×C4×C11#12012yes—
416C2×C4×C11#12011yescharacteristic
417C2×C4×C11#12011yescharacteristic
418C2×C4×C11#12012yes—
419C2×C4×C11C22×D414yes—
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C22×D412yes—
424C2×C4×C11C22×D412yes—
425C2×C4×C11C22×D412yes—
426C2×C4×C11C22×D412yes—
427C2×C4×C11C22×D412yes—
428C2×C4×C11C22×D412yes—
429C2×C4×C11C2511yescharacteristic
430C22⋊D11—42no—
431C22⋊D11—44no—
432C22⋊D11—42no—
433C22⋊D11—88no—
434C2×Dic11—24no—
435C2×Dic11—22no—
436C2×Dic11—42no—
437C2×Dic11—82no—
438D44—24no—
439D44—41no—
440D44—41no—
441C4×D11—42no—
442C4×D11—44no—
443C4×D11—42no—
444Dic22—24no—
445Dic22—41no—
446Dic22—41no—
447C11⋊C8—28no—
448#585—22no—
449#585—22no—
450#585—24no—
451#585—24no—
452#585C2×D1114yes—
453#585C2×D1114yescomplemented
454C2×2−1+4—22no—
455C2×2−1+4C2×D1112yescomplemented
456C2×H(5,𝔽2)—22no—
457C2×H(5,𝔽2)—22no—
458C2×H(5,𝔽2)C2×D1112yescomplemented
459C22×#41—24no—
460C22×#41—22no—
461C22×#41—111no—
462C22×#41C2×D1112yes—
463C22×#41C2×D1111yescharacteristic
464#575—118no—
465#575—118no—
466#575—224no—
467#575—224no—
468C2×#137—114no—
469C2×#137—222no—
470C2×AGL(1,ℤ/8)—114no—
471C2×AGL(1,ℤ/8)—222no—
472C2×#135—224no—
473C22×M16—112no—
474#537—222no—
475#536—112no—
476#536—112no—
477#535—112no—
478#535—112no—
479#534—222no—
480#532—114no—
481#525—222no—
482#525—222no—
483C2×#117—111no—
484#456—1116no—
485#455—1116no—
486#454—1116no—
487#453—1116no—
488#421—118no—
489#421—118no—
490C2×#104—118no—
491#413—114no—
492#413—114no—
493C2×#101—112no—
494C2×#100—112no—
495C22×C11—24no—
496C22×C11—28no—
497C22×C11—41no—
498C22×C11—42no—
499C22×C11—41no—
500C22×C11—42no—
501C22×C11—41no—
502C22×C11—44no—
503C22×C11—44no—
504C22×C11—48no—
505C22×C11—82no—
506C22×C11—84no—
507C22×C11—84no—
508C22×C11—816no—
509C22×C11C2×#12011yescharacteristic
510C22×C11C2×#12012yes—
511C22×C11C2×#12012yes—
512C22×C11C2×#12011yescharacteristic
513C22×C11C23×D411yescharacteristic
514C2×D11—44no—
515C2×D11—42no—
516C2×D11—84no—
517C4×C11—28no—
518C4×C11—24no—
519C4×C11C2×#12011yescharacteristic
520C4×C11C2×#12011yescharacteristic
521C4×C11C2×#12012yes—
522C4×C11C2×#12011yescharacteristic
523C4×C11C2×#12011yescharacteristic
524C4×C11C23×D412yes—
525Dic11—44no—
526Dic11—42no—
5272−1+4—28no—
5282−1+4—28no—
5292−1+4—28no—
5302−1+4—28no—
5312−1+4—28no—
5322−1+4—24no—
5332−1+4C22×D1118yes—
534H(5,𝔽2)—28no—
535H(5,𝔽2)—28no—
536H(5,𝔽2)—216no—
537H(5,𝔽2)—28no—
538H(5,𝔽2)—28no—
539H(5,𝔽2)—28no—
540H(5,𝔽2)—28no—
541H(5,𝔽2)—28no—
542H(5,𝔽2)—24no—
543H(5,𝔽2)C22×D1118yes—
544C2×#41—24no—
545C2×#41—28no—
546C2×#41—24no—
547C2×#41—216no—
548C2×#41—216no—
549C2×#41—28no—
550C2×#41—28no—
551C2×#41—216no—
552C2×#41—216no—
553C2×#41—24no—
554C2×#41—24no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—24no—
558C2×#41—28no—
559C2×#41—28no—
560C2×#41—22no—
561C2×#41—22no—
562C2×#41—22no—
563C2×#41—22no—
564C2×#41—22no—
565C2×#41—22no—
566C2×#41—22no—
567C2×#41—22no—
568C2×#41—112no—
569C2×#41—112no—
570C2×#41—221no—
571C2×#41—221no—
572C2×#41—222no—
573C2×#41—222no—
574C2×#41—222no—
575C2×#41—222no—
576C2×#41C22⋊D1112yes—
577C2×#41C22⋊D1112yes—
578C2×#41C22⋊D1114yescomplemented
579C2×#41C22⋊D1114yescomplemented
580C2×#41C22⋊D1114yescomplemented
581C2×#41C22×D1114yes—
582C2×#41C22×D1114yes—
583C2×#41C22×D1114yes—
584C2×#41C22×D1112yes—
585C2×#41C22×D1112yes—
586C22×Q8—22no—
587C22×Q8—24no—
588C22×Q8—111no—
589C22×Q8C22⋊D1112yescomplemented
590C22×Q8C22×D1111yescharacteristic
591C22×D4—28no—
592C22×D4—22no—
593C22×D4—24no—
594C22×D4—22no—
595C22×D4—24no—
596C22×D4—111no—
597C22×D4—221no—
598C22×D4C22⋊D1112yes—
599C22×D4C22⋊D1112yescomplemented
600C22×D4C22×D1111yescharacteristic
601C23×C4—24no—
602C23×C4—22no—
603C23×C4—221no—
604C23×C4C22⋊D1112yes—
605C23×C4C22×D1111yescharacteristic
606#137—1116no—
607#137—228no—
608#137—228no—
609#137—228no—
610AGL(1,ℤ/8)—1116no—
611AGL(1,ℤ/8)—228no—
612AGL(1,ℤ/8)—228no—
613AGL(1,ℤ/8)—228no—
614#135—2216no—
615#135—2216no—
616C2×Q16—224no—
617C2×SD16—224no—
618C2×SD16—224no—
619C2×D8—224no—
620C2×M16—114no—
621C2×M16—114no—
622C2×M16—114no—
623C2×M16—222no—
624C2×M16—222no—
625C2×M16—222no—
626C22×C8—222no—
627C4⋊Q8—114no—
628#127—114no—
629#124—114no—
630#124—114no—
631#123—224no—
632#123—224no—
633C22⋊Q8—224no—
634C22⋊Q8—224no—
635#121—224no—
636#121—228no—
637#121—224no—
638#120—224no—
639#120—224no—
640C4×D4—228no—
641#117—112no—
642#117—112no—
643#117—221no—
644#117—221no—
645C2×C4⋊C4—221no—
646C2×C22⋊C4—221no—
647C2×C42—112no—
648#104—1132no—
649#101—118no—
650#100—118no—
651C2×C11—21no—
652C2×C11—22no—
653C2×C11—21no—
654C2×C11—22no—
655C2×C11—21no—
656C2×C11—44no—
657C2×C11—48no—
658C2×C11C22×#12011yescharacteristic
659D11—82no—
660C24—24no—
661C24—22no—
662C24—221no—
663C24C2×C22⋊D1112yes—
664C24C2×C22⋊D1111yescharacteristic
665#41—216no—
666#41—216no—
667#41—232no—
668#41—232no—
669#41—216no—
670#41—216no—
671#41—216no—
672#41—216no—
673#41—216no—
674#41—216no—
675#41—216no—
676#41—24no—
677#41—24no—
678#41—24no—
679#41—24no—
680#41—24no—
681#41—24no—
682#41—24no—
683#41—24no—
684#41—24no—
685#41—24no—
686#41—24no—
687#41—24no—
688#41—24no—
689#41—24no—
690#41—216no—
691#41—24no—
692#41—24no—
693#41—24no—
694#41—24no—
695#41—24no—
696#41—24no—
697#41—224no—
698#41—224no—
699#41—224no—
700#41—224no—
701#41—441no—
702#41—441no—
703#41—442no—
704#41—442no—
705#41—441no—
706#41—441no—
707#41C2×C22⋊D1118yes—
708#41C2×C22⋊D1118yes—
709#41C2×C22⋊D1118yes—
710#41C23×D1118yes—
711C2×Q8—24no—
712C2×Q8—216no—
713C2×Q8—28no—
714C2×Q8—28no—
715C2×Q8—216no—
716C2×Q8—22no—
717C2×Q8—22no—
718C2×Q8—22no—
719C2×Q8—22no—
720C2×Q8—22no—
721C2×Q8—112no—
722C2×Q8—221no—
723C2×Q8—222no—
724C2×Q8—222no—
725C2×Q8C2×C22⋊D1114yes—
726C2×Q8C2×C22⋊D1114yes—
727C2×Q8C2×C22⋊D1114yes—
728C2×Q8C2×C22⋊D1112yes—
729C2×Q8C23×D1112yes—
730C2×D4—28no—
731C2×D4—24no—
732C2×D4—216no—
733C2×D4—232no—
734C2×D4—232no—
735C2×D4—216no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—216no—
745C2×D4—24no—
746C2×D4—24no—
747C2×D4—216no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—22no—
752C2×D4—22no—
753C2×D4—112no—
754C2×D4—222no—
755C2×D4—222no—
756C2×D4—228no—
757C2×D4—222no—
758C2×D4—222no—
759C2×D4—221no—
760C2×D4—442no—
761C2×D4—442no—
762C2×D4C2×C22⋊D1114yes—
763C2×D4C2×C22⋊D1112yes—
764C2×D4C2×C22⋊D1114yes—
765C2×D4C2×C22⋊D1114yes—
766C2×D4C2×C22⋊D1114yes—
767C2×D4C2×C22⋊D1114yes—
768C2×D4C23×D1112yes—
769C22×C4—24no—
770C22×C4—28no—
771C22×C4—216no—
772C22×C4—216no—
773C22×C4—22no—
774C22×C4—24no—
775C22×C4—22no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—221no—
785C22×C4—222no—
786C22×C4—222no—
787C22×C4—222no—
788C22×C4—442no—
789C22×C4—442no—
790C22×C4C2×C22⋊D1114yes—
791C22×C4C2×C22⋊D1114yes—
792C22×C4C2×C22⋊D1112yes—
793C22×C4C2×C22⋊D1111yescharacteristic
794C22×C4C2×C22⋊D1111yescharacteristic
795C22×C4C2×C22⋊D1111yescharacteristic
796C22×C4C2×C22⋊D1112yes—
797C22×C4C2×C22⋊D1112yes—
798C22×C4C2×C22⋊D1112yes—
799C22×C4C2×C22⋊D1112yes—
800C22×C4C23×D1111yescharacteristic
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1111yescharacteristic
803Q16—2216no—
804SD16—2216no—
805SD16—2216no—
806D8—2216no—
807M16—118no—
808M16—224no—
809M16—224no—
810M16—224no—
811C2×C8—224no—
812C2×C8—224no—
813C2×C8—224no—
814C4⋊C4—222no—
815C4⋊C4—222no—
816C4⋊C4—228no—
817C22⋊C4—222no—
818C22⋊C4—222no—
819C22⋊C4—228no—
820C22⋊C4—228no—
821C42—114no—
822C42—222no—
823C11#6038711yescharacteristic, complemented, Sylow
824C23—216no—
825C23—22no—
826C23—24no—
827C23—22no—
828C23—24no—
829C23—24no—
830C23—81no—
831C23—82no—
832C23—84no—
833C23—88no—
834C23—222no—
835C23—442no—
836C23—882no—
837C23#6700612yes—
838C23#6700612yes—
839C23C22×C22⋊D1114yes—
840C23C22×C22⋊D1111yescharacteristic
841C23C22×C22⋊D1111yescharacteristic
842C23C22×C22⋊D1111yescharacteristic
843Q8—216no—
844Q8—24no—
845Q8—24no—
846Q8—24no—
847Q8—24no—
848Q8—24no—
849Q8—224no—
850Q8—441no—
851Q8—441no—
852Q8C22×C22⋊D1118yes—
853D4—232no—
854D4—216no—
855D4—28no—
856D4—28no—
857D4—28no—
858D4—28no—
859D4—28no—
860D4—28no—
861D4—24no—
862D4—24no—
863D4—24no—
864D4—24no—
865D4—24no—
866D4—224no—
867D4—442no—
868D4—442no—
869D4—444no—
870D4—441no—
871D4—441no—
872D4—888no—
873D4C22×C22⋊D1118yes—
874C2×C4—216no—
875C2×C4—232no—
876C2×C4—24no—
877C2×C4—22no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—22no—
881C2×C4—28no—
882C2×C4—24no—
883C2×C4—28no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—28no—
887C2×C4—24no—
888C2×C4—28no—
889C2×C4—224no—
890C2×C4—222no—
891C2×C4—442no—
892C2×C4—442no—
893C2×C4—444no—
894C2×C4—442no—
895C2×C4—882no—
896C2×C4#6700611yescharacteristic
897C2×C4#6700612yes—
898C2×C4#6700611yescharacteristic
899C2×C4#6700612yes—
900C2×C4#6700612yes—
901C2×C4#6700611yescharacteristic
902C2×C4#6700612yes—
903C2×C4#6700611yescharacteristic
904C2×C4C22×C22⋊D1114yes—
905C2×C4C22×C22⋊D1111yescharacteristic
906C2×C4C22×C22⋊D1111yescharacteristic
907C2×C4C22×C22⋊D1111yescharacteristic
908C2×C4C22×C22⋊D1112yes—
909C2×C4C22×C22⋊D1112yes—
910C2×C4C22×C22⋊D1112yes—
911C2×C4C22×C22⋊D1112yes—
912C2×C4C22×C22⋊D1112yes—
913C2×C4C22×C22⋊D1112yes—
914C2×C4C24×D1111yescharacteristic
915C8—228no—
916C22—24no—
917C22—28no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—42no—
923C22—44no—
924C22—44no—
925C22—48no—
926C22—84no—
927C22—84no—
928C22—82no—
929C22—816no—
930C22—444no—
931C22—442no—
932C22—884no—
933C22C2×#6700611yescharacteristic
934C22C2×#6700612yes—
935C22C2×#6700612yes—
936C22C2×#6700611yescharacteristic
937C22C23×C22⋊D1111yescharacteristic
938C4—28no—
939C4—24no—
940C4—444no—
941C4—442no—
942C4C2×#6700611yescharacteristic
943C4C2×#6700612yes—
944C4C2×#6700611yescharacteristic
945C4C2×#6700611yescharacteristic
946C4C2×#6700611yescharacteristic
947C4C23×C22⋊D1112yes—
948C2—21no—
949C2—21no—
950C2—22no—
951C2—22no—
952C2—21no—
953C2—44no—
954C2—48no—
955C2—882no—
956C2C22×#6700611yescharacteristic
subgroupG/H
centerC4C2×#67006
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#585C2
socleC2×C11C22×#120
hypercenterC2×#585D11
hypocenterC11#60387
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#585

Complements

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

NH ≅ G/Ntype
1. C2×#10623353C2semidirect
2. #13081945C2semidirect
3. #13077995C2semidirect
4. #13077988C2semidirect
5. #13077980C2semidirect
6. #13077973C2semidirect
7. #13077965C2semidirect
8. C2×#10622849C2semidirect
9. C2×#10622850C2semidirect
10. C2×C11×#585C2semidirect
16. C11×#585C22semidirect
18. C2×C11×2−1+4C22semidirect
21. C2×C11×H(5,𝔽2)C22semidirect
26. C22×#4339C22semidirect
28. #10623363C22semidirect
29. #10623361C22semidirect
31. #10623356C22semidirect
32. C2×#67004C22semidirect
35. #10623353C22semidirect
36. #10623353C22semidirect
38. C2×#67002C22semidirect
39. #10623347C22semidirect
41. #10623336C22semidirect
45. C2×#66979C22semidirect
46. C22×#4318C22semidirect
47. #10622859C22semidirect
48. #10622858C22semidirect
49. #10622855C22semidirect
50. #10622854C22semidirect
51. #10622850C22semidirect
52. #10622850C22semidirect
53. #10622849C22semidirect
54. #10622849C22semidirect
55. C2×#66901C22semidirect
56. C2×#66900C22semidirect
57. C2×#66897C22semidirect
101. C2×C11×#41D4semidirect
102. C2×C11×#41D4semidirect
103. C2×C11×#41D4semidirect
111. C22×Q8×C11D4semidirect
119. C22×D4×C11D4semidirect
133. C2×#4339C23semidirect
134. C22×D44C23semidirect
136. C22×Dic22C23semidirect
140. #67004C23semidirect
144. #67002C23semidirect
145. #67000C23semidirect
147. #66997C23semidirect
152. #66993C23semidirect
156. #66989C23semidirect
168. #66979C23semidirect
171. C2×C4×Dic11C23semidirect
176. C2×#4318C23semidirect
177. C2×#4318C23semidirect
179. #66901C23semidirect
180. #66900C23semidirect
181. #66897C23semidirect
346. C2×#585D11semidirect
453. #585C2×D11semidirect
455. C2×2−1+4C2×D11semidirect
458. C2×H(5,𝔽2)C2×D11semidirect
578. C2×#41C22⋊D11semidirect
579. C2×#41C22⋊D11semidirect
580. C2×#41C22⋊D11semidirect
589. C22×Q8C22⋊D11semidirect
599. C22×D4C22⋊D11semidirect
823. C11#60387semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
#130819452
#130779952
#130779882
#130779802
#130779732
#130779652
C2×#106228492
C2×#106228502
C2×C11×#5852
#6038711