Finite Group Databasebeta

← C2×#13080250 #15628906

Subgroups — C2×#13080250 #15628906

Order 2816.

2902 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic, complemented
2C22×#66967C211yesmaximal, characteristic, complemented
3C2×#10623348C211yesmaximal, characteristic, complemented
4C2×#10623143C211yesmaximal, characteristic, complemented
5#13080250C2116yesmaximal, direct product factor
6C2×#10622781C211yesmaximal, characteristic, complemented
7C2×#10622429C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic, complemented
9C2×#10622779C211yesmaximal, characteristic, complemented
10C2×#10622432C211yesmaximal, characteristic, complemented
11C2×#10622423C211yesmaximal, characteristic, complemented
12C2×#10622347C211yesmaximal, characteristic, complemented
13C2×#10622782C211yesmaximal, characteristic, complemented
14C2×#10622401C211yesmaximal, characteristic, complemented
15C2×#10622342C211yesmaximal, characteristic, complemented
16C2×C11×#448C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic, complemented
18C22×#4343C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C22×#4339C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C22×C11×SD16C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24#10623348—24no—
25#10623348C2218yescomplemented
26C2×#67000—21no—
27C2×#67000C2211yescharacteristic, complemented
28C2×#66999—21no—
29C2×#66999C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic, complemented
31C22×#4326C2211yescharacteristic, complemented
32C22×#4326C2211yescharacteristic, complemented
33C2×#66995—28no—
34C2×#66995C2218yescomplemented
35C22×#4325C2211yescharacteristic
36C22×#4325C2211yescharacteristic
37C2×#66991—21no—
38C2×#66990—21no—
39C2×#66989C2211yescharacteristic
40C22×#4323C2211yescharacteristic
41C2×#66983—21no—
42C2×#66983C2211yescharacteristic, complemented
43C2×C4×C22⋊D11—21no—
44C2×C4×C22⋊D11C2211yescharacteristic
45C22×#4318C2211yescharacteristic, complemented
46C2×#66967—28no—
47C2×#66967C2218yescomplemented
48C22×D88C2211yescharacteristic
49C22×#4314C2211yescharacteristic, complemented
50C22×#4313C2211yescharacteristic
51#10623143—24no—
52#10623143C2218yescomplemented
53C2×#66950C2211yescharacteristic
54C2×#66946C2211yescharacteristic
55C2×#66936—21no—
56C2×C22⋊C4×D11—21no—
57C11×#448C2218yescomplemented
58C2×C11×#103C2211yescharacteristic, complemented
59C2×C11×#103C2211yescharacteristic, complemented
60C2×C11×C22⋊C8C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic
62#10622782C2218yescomplemented
63#10622781C2218yescomplemented
64#10622779C2218yescomplemented
65C2×#66885C2211yescharacteristic
66C2×(C2×D11)⋊C8C2211yescharacteristic
67C2×#66880C2211yescharacteristic, complemented
68C2×Dic11⋊C8C2211yescharacteristic, complemented
69C2×C8×Dic11C2211yescharacteristic, complemented
70#10622652C2218yescomplemented
71C2×#66873C2211yescharacteristic, complemented
72C2×#66872C2211yescharacteristic, complemented
73#10622432C2218yescomplemented
74#10622429C2218yescomplemented
75#10622423C2218yescomplemented
76#10622401C2218yescomplemented
77#10622347C2218yescomplemented
78#10622342C2218yescomplemented
79C24×D11—21no—
80C22×Q8×C11—21no—
81C22×Q8×C11—22no—
82C22×Q8×C11—24no—
83C22×Q8×C11—42no—
84C22×Q8×C11C2311yescharacteristic
85C22×Q8×C11C2311yescharacteristic
86C22×Q8×C11C2314yescomplemented
87C22×D4×C11—21no—
88C22×D4×C11C2311yescharacteristic
89C23×C4×C11—21no—
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11D411yescharacteristic
95C2×#4343—22no—
96C2×#4343—24no—
97C2×#4343—42no—
98C2×#4343C2314yes—
99C2×D4×D11—24no—
100C2×D4×D11—22no—
101C2×D4×D11—42no—
102C2×D4×D11C2314yes—
103C2×#4339—22no—
104C2×#4339—24no—
105C2×#4339—42no—
106C2×#4339C2314yes—
107C22×D44—21no—
108C22×D44C2311yescharacteristic
109C22×D44C2311yescharacteristic
110C22×C4×D11—21no—
111C22×C4×D11—21no—
112C22×C4×D11—21no—
113C22×C4×D11C2311yescharacteristic
114C22×Dic22C2311yescharacteristic
115C2×C11×SD16—24no—
116C2×C11×SD16—42no—
117C2×C11×SD16C2314yes—
118C2×C11×SD16C2314yes—
119C22×C8×C11C2311yescharacteristic
120C22×C8×C11C2311yescharacteristic
121C11×#121—22no—
122C11×#121C2314yes—
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127C2×C22⋊Dic11D411yescharacteristic
128#67000—28no—
129#67000—22no—
130#67000C2314yescomplemented
131#66999—22no—
132#66999—28no—
133#66999C2314yes—
134Q8×Dic11—22no—
135Q8×Dic11C2314yescomplemented
136C2×#4326—24no—
137C2×#4326—24no—
138C2×#4326C2314yescomplemented
139C2×#4326C2314yescomplemented
140#66995—232no—
141C2×#4325—24no—
142C2×#4325D418yescomplemented
143C2×#4325C2314yes—
144C2×#4325C2314yes—
145#66991—28no—
146#66990—28no—
147#66989—22no—
148#66989C2314yes—
149C2×#4323—24no—
150C2×#4323C2314yes—
151#66983—22no—
152#66983—28no—
153#66983C2314yescomplemented
154C4×C22⋊D11—28no—
155C4×C22⋊D11D414yes—
156C4×C22⋊D11C2314yes—
157C2×(C2×D11)⋊C4—21no—
158C2×(C2×D11)⋊C4—21no—
159C2×(C2×D11)⋊C4—21no—
160C2×(C2×D11)⋊C4—21no—
161C2×(C2×D11)⋊C4—21no—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4D411yescharacteristic
164C2×C4⋊Dic11—21no—
165C2×C4⋊Dic11—21no—
166C2×C4⋊Dic11C2311yescharacteristic
167C2×Dic11⋊C4—21no—
168C2×Dic11⋊C4D411yescharacteristic
169C2×C4×Dic11—21no—
170C2×C4×Dic11C2311yescharacteristic
171C2×#4318—24no—
172C2×#4318C2314yescomplemented
173C22×C11⋊C8C2311yescharacteristic
174C22×C11⋊C8C2311yescharacteristic
175#66967—232no—
176C2×D88—24no—
177C2×D88C2314yes—
178C2×#4314—42no—
179C2×#4314C2314yescomplemented
180C2×#4313—24no—
181C2×#4313C2314yes—
182#66950—22no—
183#66950C2314yes—
184#66946—22no—
185#66946C2314yes—
186#66936—28no—
187C22⋊C4×D11—28no—
188C11×#103C2314yescomplemented
189C11×#103C2314yescomplemented
190C11×C22⋊C8C2314yescomplemented
191#66896C2314yes—
192#66885C2314yes—
193(C2×D11)⋊C8C2314yes—
194#66880C2314yescomplemented
195Dic11⋊C8C2314yescomplemented
196C8×Dic11C2314yescomplemented
197#66873C2314yescomplemented
198#66872C2314yescomplemented
199C2×#3275—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—24no—
205C23×D11—44no—
206C23×D11—44no—
207C23×D11—82no—
208C23×D11C2×D411yescharacteristic
209C2×Q8×C11—21no—
210C2×Q8×C11—21no—
211C2×Q8×C11—24no—
212C2×Q8×C11—22no—
213C2×Q8×C11—28no—
214C2×Q8×C11—22no—
215C2×Q8×C11—22no—
216C2×Q8×C11—44no—
217C2×Q8×C11—44no—
218C2×Q8×C11—48no—
219C2×Q8×C11C2×D414yes—
220C2×Q8×C11C2412yes—
221C2×Q8×C11C2412yes—
222C2×D4×C11—24no—
223C2×D4×C11—22no—
224C2×D4×C11—21no—
225C2×D4×C11—22no—
226C2×D4×C11—82no—
227C2×D4×C11C2412yes—
228C22×C4×C11—21no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—24no—
234C22×C4×C11—44no—
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2412yes—
238C22×C4×C11C2411yescharacteristic
239C2×C22⋊D11—24no—
240C2×C22⋊D11—24no—
241C2×C22⋊D11—24no—
242C2×C22⋊D11—42no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11C2×D414yes—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11C2×D411yescharacteristic
250C22×Dic11C2×D411yescharacteristic
251C22×Dic11C2×D411yescharacteristic
252#4343—28no—
253#4343—44no—
254#4343—48no—
255D4×D11—28no—
256D4×D11—44no—
257D4×D11—48no—
258#4339—28no—
259#4339—44no—
260#4339—48no—
261C2×D44—24no—
262C2×D44—21no—
263C2×D44—21no—
264C2×D44—22no—
265C2×D44—22no—
266C2×D44—22no—
267C2×D44—44no—
268C2×D44C2×D414yes—
269C2×D44C2412yes—
270C2×D44C2412yes—
271C2×C4×D11—24no—
272C2×C4×D11—24no—
273C2×C4×D11—22no—
274C2×C4×D11—24no—
275C2×C4×D11—22no—
276C2×C4×D11—44no—
277C2×C4×D11—44no—
278C2×C4×D11—82no—
279C2×C4×D11C2×D412yes—
280C2×C4×D11C2412yes—
281C2×Dic22—22no—
282C2×Dic22—21no—
283C2×Dic22—22no—
284C2×Dic22C2412yes—
285C11×SD16—28no—
286C11×SD16—44no—
287C2×C8×C11—22no—
288C2×C8×C11—22no—
289C2×C8×C11C2412yes—
290C2×C8×C11C2412yes—
291C11×C4⋊C4—21no—
292C11×C4⋊C4C2412yes—
293C11×C22⋊C4—24no—
294C22⋊Dic11—24no—
295C22⋊Dic11—24no—
296C22⋊Dic11C2×D414yes—
297#4326—28no—
298#4326—28no—
299#4325—28no—
300#4325C2×D4116yescomplemented
301#4323—28no—
302(C2×D11)⋊C4—24no—
303(C2×D11)⋊C4—24no—
304(C2×D11)⋊C4—24no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4C2×D414yes—
309C4⋊Dic11—24no—
310C4⋊Dic11—24no—
311C4⋊Dic11—21no—
312C4⋊Dic11C2412yes—
313Dic11⋊C4—24no—
314Dic11⋊C4C2×D414yes—
315C4×Dic11—24no—
316C4×Dic11C2×D412yes—
317C4×Dic11C2412yes—
318#4318—28no—
319C2×C11⋊C8—22no—
320C2×C11⋊C8C2×D414yes—
321C2×C11⋊C8C2412yes—
322C2×C11⋊C8C2412yes—
323D88—28no—
324#4314—44no—
325#4313—28no—
326C22×#137—111no—
327C22×AGL(1,ℤ/8)—111no—
328C2×#548—111no—
329C2×#546—111no—
330#3275—1116no—
331C2×#495—111no—
332C2×#470—111no—
333C2×#469—111no—
334C2×#464—111no—
335C2×#463—111no—
336C2×#452—111no—
337C2×#449—111no—
338C2×#448D1111yescharacteristic, complemented
339C2×#450—111no—
340C2×C4×SD16—111no—
341C2×#436—111no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—42no—
347C23×C11—42no—
348C23×C11—42no—
349C23×C11C22×D412yes—
350C23×C11C22×D411yescharacteristic
351C22×D11—22no—
352C22×D11—24no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—48no—
358C22×D11—48no—
359C22×D11—42no—
360C22×D11—42no—
361C22×D11—42no—
362C22×D11—42no—
363C22×D11—42no—
364C22×D11—84no—
365C22×D11—816no—
366C22×D11C22×D412yes—
367Q8×C11—24no—
368Q8×C11—22no—
369Q8×C11—22no—
370Q8×C11—22no—
371Q8×C11—48no—
372Q8×C11—42no—
373Q8×C11C22×D414yes—
374D4×C11—22no—
375D4×C11—22no—
376D4×C11—42no—
377D4×C11—84no—
378C2×C4×C11—22no—
379C2×C4×C11—24no—
380C2×C4×C11—22no—
381C2×C4×C11—24no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—48no—
387C2×C4×C11—42no—
388C2×C4×C11—42no—
389C2×C4×C11C22×D412yes—
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D412yes—
392C2×C4×C11H(5,𝔽2)12yes—
393C2×C4×C11C2511yescharacteristic
394C22⋊D11—44no—
395C22⋊D11—48no—
396C22⋊D11—48no—
397C22⋊D11—48no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—42no—
404C2×Dic11—42no—
405C2×Dic11C22×D412yes—
406C2×Dic11C22×D412yes—
407C2×Dic11C22×D412yes—
408D44—24no—
409D44—22no—
410D44—22no—
411D44—22no—
412D44—48no—
413D44—42no—
414D44C22×D414yes—
415C4×D11—24no—
416C4×D11—22no—
417C4×D11—22no—
418C4×D11—48no—
419C4×D11—48no—
420C4×D11—84no—
421Dic22—22no—
422Dic22—22no—
423Dic22—42no—
424C8×C11—22no—
425C8×C11—22no—
426C11⋊C8—22no—
427C11⋊C8C22×D414yes—
428C22×#41—111no—
429C22×#41—111no—
430C23×Q8C2×D1111yescharacteristic, complemented
431C23×D4—111no—
432C2×#137—118no—
433C2×#137—228no—
434C2×AGL(1,ℤ/8)—118no—
435C2×AGL(1,ℤ/8)—228no—
436C22×Q16—111no—
437C22×Q16—111no—
438C22×SD16—111no—
439C22×SD16—111no—
440C22×SD16—111no—
441C22×SD16C2×D1111yescharacteristic
442C22×SD16C2×D1111yescharacteristic
443C22×D8—111no—
444C22×D8—111no—
445C22×M16—111no—
446C22×M16—111no—
447#548—118no—
448#548—224no—
449#546—118no—
450#546—224no—
451C2×#124—111no—
452C2×#124—111no—
453C2×#124—221no—
454C2×#123—221no—
455C2×C22⋊Q8—111no—
456C2×C22⋊Q8—111no—
457C2×C22⋊Q8—221no—
458C2×#121—111no—
459C2×#121—221no—
460C2×#121—221no—
461C2×#121C2×D1111yescharacteristic
462C2×#120—221no—
463C2×C4×Q8—111no—
464C2×C4×D4—111no—
465C2×C4×D4—111no—
466C2×C4×D4—221no—
467C22×C22⋊C4—221no—
468#495—118no—
469#470—118no—
470#469—118no—
471#464—118no—
472#463—118no—
473#452—118no—
474#450—118no—
475#449—118no—
476#448C2×D1118yescomplemented
477C4×SD16—118no—
478#436—118no—
479C2×#106—111no—
480C2×C4⋊C8—111no—
481C2×#103—111no—
482C2×#103C2×D1111yescharacteristic, complemented
483C2×#103C2×D1111yescharacteristic, complemented
484C2×#102—111no—
485C2×#102—111no—
486C2×#102—111no—
487C2×C22⋊C8—111no—
488C2×C22⋊C8C2×D1111yescharacteristic, complemented
489C2×C4×C8—111no—
490C22×C11—22no—
491C22×C11—22no—
492C22×C11—22no—
493C22×C11—44no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—84no—
498C22×C11D4212yes—
499C22×C11#57512yes—
500C22×C11#57712yes—
501C22×C11C23×D411yescharacteristic
502C2×D11—24no—
503C2×D11—22no—
504C2×D11—22no—
505C2×D11—22no—
506C2×D11—44no—
507C2×D11—48no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—816no—
514C2×D11—84no—
515C4×C11—22no—
516C4×C11—24no—
517C4×C11—42no—
518C4×C11—42no—
519C4×C11D4212yes—
520C4×C11C23×D411yescharacteristic
521C4×C11C2×H(5,𝔽2)11yescharacteristic
522Dic11—22no—
523Dic11—22no—
524Dic11—22no—
525Dic11—42no—
526Dic11—42no—
527C25—221no—
528C2×#41—114no—
529C2×#41—114no—
530C2×#41—224no—
531C2×#41—222no—
532C2×#41—222no—
533C2×#41—224no—
534C2×#41—442no—
535C2×#41—442no—
536C22×Q8—21no—
537C22×Q8—22no—
538C22×Q8—24no—
539C22×Q8—42no—
540C22×Q8—111no—
541C22×Q8C22×D1111yescharacteristic
542C22×Q8C22×D1111yescharacteristic
543C22×Q8C22×D1114yescomplemented
544C22×D4—21no—
545C22×D4—111no—
546C22×D4—114no—
547C22×D4—111no—
548C22×D4—111no—
549C22×D4—221no—
550C22×D4—222no—
551C22×D4—221no—
552C22×D4—224no—
553C22×D4—221no—
554C22×D4—221no—
555C22×D4—442no—
556C22×D4C22×D1111yescharacteristic
557C23×C4—21no—
558C23×C4—111no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4—221no—
562C23×C4C22×D1111yescharacteristic
563#137—2232no—
564AGL(1,ℤ/8)—2232no—
565C2×Q16—114no—
566C2×Q16—114no—
567C2×Q16—224no—
568C2×Q16—224no—
569C2×SD16—24no—
570C2×SD16—42no—
571C2×SD16—118no—
572C2×SD16—114no—
573C2×SD16—114no—
574C2×SD16—114no—
575C2×SD16—224no—
576C2×SD16—442no—
577C2×SD16C22×D1114yes—
578C2×SD16C22×D1114yes—
579C2×D8—114no—
580C2×D8—114no—
581C2×D8—224no—
582C2×D8—224no—
583C2×M16—114no—
584C2×M16—114no—
585C2×M16—224no—
586C2×M16—224no—
587C22×C8—111no—
588C22×C8—111no—
589C22×C8C22×D1111yescharacteristic
590C22×C8C22×D1111yescharacteristic
591#124—114no—
592#124—114no—
593#124—222no—
594#124—222no—
595#124—228no—
596#123—228no—
597C22⋊Q8—114no—
598C22⋊Q8—114no—
599C22⋊Q8—222no—
600C22⋊Q8—228no—
601C22⋊Q8—222no—
602#121—22no—
603#121—114no—
604#121—228no—
605#121—228no—
606#121—222no—
607#121C22×D1114yes—
608#120—228no—
609C4×Q8—114no—
610C4×Q8—222no—
611C4×D4—114no—
612C4×D4—114no—
613C4×D4—114no—
614C4×D4—222no—
615C4×D4—228no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—221no—
619C2×C4⋊C4—221no—
620C2×C4⋊C4—221no—
621C2×C4⋊C4C22×D1111yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—111no—
624C2×C22⋊C4—111no—
625C2×C22⋊C4—228no—
626C2×C22⋊C4—221no—
627C2×C22⋊C4—221no—
628C2×C22⋊C4—221no—
629C2×C22⋊C4—221no—
630C2×C22⋊C4—221no—
631C2×C22⋊C4—221no—
632C2×C22⋊C4—221no—
633C2×C22⋊C4—221no—
634C2×C42—111no—
635C2×C42—221no—
636#106—114no—
637C4⋊C8—114no—
638#103—114no—
639#103C22×D1114yescomplemented
640#103C22×D1114yescomplemented
641#102—114no—
642#102—114no—
643#102—114no—
644C22⋊C8—114no—
645C22⋊C8C22×D1114yescomplemented
646C4×C8—114no—
647C2×C11—42no—
648C2×C11—82no—
649C2×C11#327514yescomplemented
650C2×C11C2×D4211yescharacteristic
651C2×C11C2×#57511yescharacteristic
652C2×C11C2×#57711yescharacteristic
653D11—42no—
654D11—44no—
655D11—82no—
656C24—21no—
657C24—111no—
658C24—224no—
659C24—221no—
660C24—221no—
661C24—444no—
662C24—444no—
663C24—882no—
664C24D4×D1111yescharacteristic
665#41—228no—
666#41—228no—
667#41—444no—
668#41—448no—
669#41—444no—
670#41—448no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—24no—
674C2×Q8—22no—
675C2×Q8—28no—
676C2×Q8—22no—
677C2×Q8—22no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—48no—
681C2×Q8—112no—
682C2×Q8—221no—
683C2×Q8—222no—
684C2×Q8—222no—
685C2×Q8D4×D1114yes—
686C2×Q8C23×D1112yes—
687C2×Q8C23×D1112yes—
688C2×D4—24no—
689C2×D4—22no—
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—82no—
693C2×D4—114no—
694C2×D4—114no—
695C2×D4—112no—
696C2×D4—112no—
697C2×D4—224no—
698C2×D4—224no—
699C2×D4—228no—
700C2×D4—224no—
701C2×D4—224no—
702C2×D4—221no—
703C2×D4—222no—
704C2×D4—221no—
705C2×D4—222no—
706C2×D4—222no—
707C2×D4—444no—
708C2×D4—444no—
709C2×D4—448no—
710C2×D4—442no—
711C2×D4—444no—
712C2×D4—444no—
713C2×D4—444no—
714C2×D4C23×D1112yes—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—44no—
722C22×C4—111no—
723C22×C4—111no—
724C22×C4—111no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—224no—
728C22×C4—224no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—224no—
734C22×C4—444no—
735C22×C4—444no—
736C22×C4—882no—
737C22×C4D4×D1112yes—
738C22×C4D4×D1111yescharacteristic
739C22×C4C23×D1112yes—
740C22×C4C23×D1111yescharacteristic
741Q16—228no—
742Q16—228no—
743SD16—28no—
744SD16—44no—
745SD16—1116no—
746SD16—228no—
747SD16—444no—
748D8—228no—
749D8—228no—
750M16—228no—
751M16—228no—
752C2×C8—22no—
753C2×C8—22no—
754C2×C8—114no—
755C2×C8—112no—
756C2×C8—112no—
757C2×C8—222no—
758C2×C8C23×D1112yes—
759C2×C8C23×D1112yes—
760C4⋊C4—21no—
761C4⋊C4—114no—
762C4⋊C4—112no—
763C4⋊C4—224no—
764C4⋊C4—224no—
765C4⋊C4—224no—
766C4⋊C4—221no—
767C4⋊C4C23×D1112yes—
768C22⋊C4—24no—
769C22⋊C4—114no—
770C22⋊C4—114no—
771C22⋊C4—224no—
772C22⋊C4—224no—
773C22⋊C4—224no—
774C22⋊C4—224no—
775C22⋊C4—224no—
776C22⋊C4—224no—
777C22⋊C4—224no—
778C22⋊C4—224no—
779C42—112no—
780C42—112no—
781C42—224no—
782C11C2×#327511yescharacteristic, complemented, Sylow
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—112no—
791C23—222no—
792C23—222no—
793C23—222no—
794C23—224no—
795C23—222no—
796C23—222no—
797C23—448no—
798C23—448no—
799C23—442no—
800C23—442no—
801C23—442no—
802C23—442no—
803C23—442no—
804C23—884no—
805C23—8816no—
806C23C2×D4×D1112yes—
807C23C2×D4×D1111yescharacteristic
808Q8—24no—
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—48no—
813Q8—42no—
814Q8—222no—
815Q8—222no—
816Q8—442no—
817Q8C2×D4×D1114yes—
818D4—22no—
819D4—22no—
820D4—42no—
821D4—84no—
822D4—114no—
823D4—224no—
824D4—222no—
825D4—222no—
826D4—222no—
827D4—448no—
828D4—444no—
829D4—448no—
830D4—448no—
831D4—448no—
832D4—442no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—48no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—112no—
845C2×C4—112no—
846C2×C4—112no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—224no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—448no—
856C2×C4—448no—
857C2×C4—442no—
858C2×C4—442no—
859C2×C4—884no—
860C2×C4C2×D4×D1112yes—
861C2×C4C2×D4×D1111yescharacteristic
862C2×C4C2×D4×D1112yes—
863C2×C4#6703712yes—
864C2×C4C24×D1111yescharacteristic
865C8—22no—
866C8—22no—
867C8—114no—
868C8—222no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—84no—
877C22—222no—
878C22—224no—
879C22—222no—
880C22—222no—
881C22—444no—
882C22—448no—
883C22—442no—
884C22—442no—
885C22—442no—
886C22—442no—
887C22—442no—
888C22—8816no—
889C22—884no—
890C22#1062312112yes—
891C22#1062329312yes—
892C22#1062330812yes—
893C22C22×D4×D1111yescharacteristic
894C4—22no—
895C4—24no—
896C4—42no—
897C4—42no—
898C4—222no—
899C4—222no—
900C4—222no—
901C4—442no—
902C4—442no—
903C4#1062312112yes—
904C4C22×D4×D1111yescharacteristic
905C4C2×#6703711yescharacteristic
906C2—42no—
907C2—82no—
908C2—442no—
909C2—444no—
910C2—882no—
911C2#1308025014yesdirect product factor
912C2C2×#1062312111yescharacteristic
913C2C2×#1062330811yescharacteristic
914C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#448C2
socleC23×C11C22×D4
hypercenterC2×#448D11
hypocenterC11C2×#3275
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C22×#66995C2semidirect
2. C22×#66967C2semidirect
3. C2×#10623348C2semidirect
4. C2×#10623143C2semidirect
5. #13080250C2direct (N × H)
6. C2×#10622781C2semidirect
7. C2×#10622429C2semidirect
8. C2×#10622652C2semidirect
9. C2×#10622779C2semidirect
10. C2×#10622432C2semidirect
11. C2×#10622423C2semidirect
12. C2×#10622347C2semidirect
13. C2×#10622782C2semidirect
14. C2×#10622401C2semidirect
15. C2×#10622342C2semidirect
16. C2×C11×#448C2semidirect
17. C23×Q8×C11C22semidirect
25. #10623348C22semidirect
27. C2×#67000C22semidirect
30. C2×Q8×Dic11C22semidirect
31. C22×#4326C22semidirect
32. C22×#4326C22semidirect
34. C2×#66995C22semidirect
42. C2×#66983C22semidirect
45. C22×#4318C22semidirect
47. C2×#66967C22semidirect
49. C22×#4314C22semidirect
52. #10623143C22semidirect
57. C11×#448C22semidirect
58. C2×C11×#103C22semidirect
59. C2×C11×#103C22semidirect
60. C2×C11×C22⋊C8C22semidirect
62. #10622782C22semidirect
63. #10622781C22semidirect
64. #10622779C22semidirect
67. C2×#66880C22semidirect
68. C2×Dic11⋊C8C22semidirect
69. C2×C8×Dic11C22semidirect
70. #10622652C22semidirect
71. C2×#66873C22semidirect
72. C2×#66872C22semidirect
73. #10622432C22semidirect
74. #10622429C22semidirect
75. #10622423C22semidirect
76. #10622401C22semidirect
77. #10622347C22semidirect
78. #10622342C22semidirect
86. C22×Q8×C11C23semidirect
130. #67000C23semidirect
135. Q8×Dic11C23semidirect
138. C2×#4326C23semidirect
139. C2×#4326C23semidirect
142. C2×#4325D4semidirect
153. #66983C23semidirect
172. C2×#4318C23semidirect
179. C2×#4314C23semidirect
188. C11×#103C23semidirect
189. C11×#103C23semidirect
190. C11×C22⋊C8C23semidirect
194. #66880C23semidirect
195. Dic11⋊C8C23semidirect
196. C8×Dic11C23semidirect
197. #66873C23semidirect
198. #66872C23semidirect
300. #4325C2×D4semidirect
338. C2×#448D11semidirect
430. C23×Q8C2×D11semidirect
476. #448C2×D11semidirect
482. C2×#103C2×D11semidirect
483. C2×#103C2×D11semidirect
488. C2×C22⋊C8C2×D11semidirect
543. C22×Q8C22×D11semidirect
639. #103C22×D11semidirect
640. #103C22×D11semidirect
645. C22⋊C8C22×D11semidirect
649. C2×C11#3275semidirect
782. C11C2×#3275semidirect
911. C2#13080250direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669952
C22×#669672
C2×#106233482
C2×#106231432
#130802502
C2×#106227812
C2×#106224292
C2×#106226522
C2×#106227792
C2×#106224322
C2×#106224232
C2×#106223472
C2×#106227822
C2×#106224012
C2×#106223422
C2×C11×#4482
C2×#327511