Finite Group Databasebeta

← C2×#13080138 #15628767

Subgroups — C2×#13080138 #15628767

Order 2816.

2914 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×#66967C211yesmaximal, characteristic, complemented
2C22×#66957C211yesmaximal, characteristic, complemented
3C2×#10623162C211yesmaximal, characteristic, complemented
4C2×#10623143C211yesmaximal, characteristic, complemented
5#13080138C2116yesmaximal, direct product factor
6C2×#10622780C211yesmaximal, characteristic, complemented
7C2×#10622481C211yesmaximal, characteristic, complemented
8C2×#10622400C211yesmaximal, characteristic, complemented
9C2×#10622431C211yesmaximal, characteristic, complemented
10C2×#10622423C211yesmaximal, characteristic, complemented
11C2×#10622660C211yesmaximal, characteristic, complemented
12C2×#10622650C211yesmaximal, characteristic, complemented
13C2×#10622389C211yesmaximal, characteristic, complemented
14C2×#10622482C211yesmaximal, characteristic, complemented
15C2×#10622724C211yesmaximal, characteristic, complemented
16C2×C11×#465C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×#4339C2211yescharacteristic, complemented
21C22×C11×SD16C2211yescharacteristic
22C23×C8×C11C2211yescharacteristic, complemented
23C2×C11×C22⋊Q8C2211yescharacteristic, complemented
24C2×C11×#121C2211yescharacteristic
25C2×#66997C2211yescharacteristic, complemented
26C22×#4326C2211yescharacteristic, complemented
27C22×#4325C2211yescharacteristic
28C2×#66991—21no—
29C2×#66990—21no—
30C2×#66989C2211yescharacteristic
31C22×#4324C2211yescharacteristic
32C22×#4323C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×#66967—28no—
35C2×#66967C2218yescomplemented
36C22×Dic44C2211yescharacteristic, complemented
37C2×#66957—28no—
38C2×#66957C2218yescomplemented
39C22×D88C2211yescharacteristic
40C22×#4314C2211yescharacteristic
41C22×#4314C2211yescharacteristic, complemented
42C22×#4313C2211yescharacteristic
43#10623162—24no—
44#10623162C2218yescomplemented
45#10623143—24no—
46#10623143C2218yescomplemented
47C2×#66950C2211yescharacteristic
48C2×#66950C2211yescharacteristic
49C2×#66947—21no—
50C2×#66946C2211yescharacteristic
51C2×#66946C2211yescharacteristic, complemented
52C2×C4⋊C4×D11—21no—
53C2×#66937—21no—
54C2×#66936—21no—
55C2×#66936—21no—
56C2×C22⋊C4×D11—21no—
57C11×#465C2218yescomplemented
58C2×C11×#106C2211yescharacteristic, complemented
59C2×C11×#103C2211yescharacteristic, complemented
60C2×C11×#102C2211yescharacteristic
61C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
62#10622780C2218yescomplemented
63#10622724C2218yescomplemented
64C2×(C2×D11)⋊C8C2211yescharacteristic
65C2×#66879C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67#10622660C2218yescomplemented
68#10622650C2218yescomplemented
69C2×#66874C2211yescharacteristic, complemented
70C2×#66874C2211yescharacteristic, complemented
71C2×#66873C2211yescharacteristic
72C2×#66873C2211yescharacteristic, complemented
73#10622482C2218yescomplemented
74#10622481C2218yescomplemented
75#10622431C2218yescomplemented
76#10622423C2218yescomplemented
77#10622400C2218yescomplemented
78#10622389C2218yescomplemented
79C24×D11—21no—
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11—21no—
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C22×C22⋊D11D411yescharacteristic
88C2×#4343—22no—
89C2×#4343—24no—
90C2×#4343—42no—
91C2×#4343C2314yes—
92C2×D4×D11—24no—
93C2×D4×D11—22no—
94C2×D4×D11—42no—
95C2×D4×D11C2314yes—
96C2×#4339—22no—
97C2×#4339—22no—
98C2×#4339—24no—
99C2×#4339—24no—
100C2×#4339—42no—
101C2×#4339—42no—
102C2×#4339C2314yes—
103C2×#4339C2314yescomplemented
104C22×D44—21no—
105C22×D44C2311yescharacteristic
106C22×D44C2311yescharacteristic
107C22×C4×D11—21no—
108C22×C4×D11—21no—
109C22×C4×D11—21no—
110C22×C4×D11—21no—
111C22×C4×D11—21no—
112C22×C4×D11C2311yescharacteristic
113C22×Dic22C2311yescharacteristic
114C22×Dic22C2311yescharacteristic
115C2×C11×SD16—24no—
116C2×C11×SD16C2314yes—
117C22×C8×C11—24no—
118C22×C8×C11C2311yescharacteristic
119C22×C8×C11C2311yescharacteristic
120C22×C8×C11C2314yescomplemented
121C11×C22⋊Q8—22no—
122C11×C22⋊Q8C2314yescomplemented
123C11×#121—22no—
124C11×#121C2314yes—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4—21no—
130C2×C22⋊Dic11—21no—
131C2×C22⋊Dic11—21no—
132C2×C22⋊Dic11D411yescharacteristic
133#66997—22no—
134#66997C2314yescomplemented
135C2×#4326—42no—
136C2×#4326C2314yescomplemented
137C2×#4325—24no—
138C2×#4325C2314yes—
139#66991—28no—
140#66990—28no—
141#66989—22no—
142#66989C2314yes—
143C2×#4324—42no—
144C2×#4324C2314yes—
145C2×#4323—24no—
146C2×#4323C2314yes—
147C4×C22⋊D11D414yes—
148C4×C22⋊D11C2314yes—
149C2×(C2×D11)⋊C4—21no—
150C2×(C2×D11)⋊C4—21no—
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4—21no—
153C2×(C2×D11)⋊C4D411yescharacteristic
154C2×C4⋊Dic11—21no—
155C2×C4⋊Dic11—21no—
156C2×Dic11⋊C4—21no—
157C2×Dic11⋊C4—21no—
158C2×Dic11⋊C4D411yescharacteristic
159C2×C4×Dic11C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2311yescharacteristic
162#66967—232no—
163C2×Dic44—24no—
164C2×Dic44C2314yescomplemented
165#66957—232no—
166C2×D88D418yescomplemented
167C2×D88C2314yes—
168C2×#4314—24no—
169C2×#4314—24no—
170C2×#4314C2314yes—
171C2×#4314C2314yescomplemented
172C2×#4313—24no—
173C2×#4313C2314yes—
174#66950—22no—
175#66950—22no—
176#66950C2314yes—
177#66950C2314yes—
178#66947—28no—
179#66946—22no—
180#66946—22no—
181#66946C2314yes—
182#66946C2314yescomplemented
183C4⋊C4×D11—28no—
184#66937—28no—
185#66936—28no—
186#66936—28no—
187C22⋊C4×D11—28no—
188C11×#106C2314yescomplemented
189C11×#103C2314yescomplemented
190C11×#102C2314yes—
191C22⋊(C11⋊C8)C2314yescomplemented
192(C2×D11)⋊C8C2314yes—
193#66879C2314yescomplemented
194Dic11⋊C8C2314yescomplemented
195#66874C2314yescomplemented
196#66874C2314yescomplemented
197#66873C2314yes—
198#66873C2314yescomplemented
199C2×#3267—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—22no—
211C2×Q8×C11—22no—
212C2×Q8×C11C2412yes—
213C2×D4×C11—24no—
214C2×D4×C11—22no—
215C2×D4×C11—21no—
216C2×D4×C11—22no—
217C2×D4×C11—82no—
218C2×D4×C11C2412yes—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2411yescharacteristic
228C2×C22⋊D11—24no—
229C2×C22⋊D11—24no—
230C2×C22⋊D11—24no—
231C2×C22⋊D11—42no—
232C2×C22⋊D11—44no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—44no—
235C2×C22⋊D11C2×D414yes—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11C2×D411yescharacteristic
239C22×Dic11C2×D411yescharacteristic
240C22×Dic11C2×D411yescharacteristic
241#4343—28no—
242#4343—44no—
243#4343—48no—
244D4×D11—28no—
245D4×D11—44no—
246D4×D11—48no—
247#4339—28no—
248#4339—28no—
249#4339—44no—
250#4339—44no—
251#4339—48no—
252#4339—48no—
253C2×D44—24no—
254C2×D44—21no—
255C2×D44—21no—
256C2×D44—22no—
257C2×D44—22no—
258C2×D44—44no—
259C2×D44C2×D414yes—
260C2×D44C2×D414yes—
261C2×D44C2412yes—
262C2×D44C2412yes—
263C2×C4×D11—24no—
264C2×C4×D11—24no—
265C2×C4×D11—24no—
266C2×C4×D11—22no—
267C2×C4×D11—24no—
268C2×C4×D11—24no—
269C2×C4×D11—22no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11—44no—
274C2×C4×D11—82no—
275C2×C4×D11C2×D412yes—
276C2×C4×D11C2412yes—
277C2×Dic22—22no—
278C2×Dic22—22no—
279C2×Dic22—21no—
280C2×Dic22—21no—
281C2×Dic22—22no—
282C2×Dic22—22no—
283C2×Dic22C2412yes—
284C2×Dic22C2412yes—
285C11×SD16—28no—
286C2×C8×C11—28no—
287C2×C8×C11—22no—
288C2×C8×C11C2×D414yes—
289C2×C8×C11C2412yes—
290C2×C8×C11C2412yes—
291C11×C4⋊C4—24no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—21no—
294C11×C4⋊C4C2412yes—
295C11×C4⋊C4C2412yes—
296C11×C22⋊C4—24no—
297C11×C22⋊C4—24no—
298C22⋊Dic11—24no—
299C22⋊Dic11—24no—
300C22⋊Dic11C2×D414yes—
301#4326—44no—
302#4325—28no—
303#4324—44no—
304#4323—28no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4C2×D414yes—
310C4⋊Dic11—24no—
311C4⋊Dic11—24no—
312Dic11⋊C4—24no—
313Dic11⋊C4—24no—
314Dic11⋊C4C2×D414yes—
315C4×Dic11C2×D412yes—
316C4×Dic11C2412yes—
317C2×C11⋊C8—22no—
318C2×C11⋊C8—22no—
319C2×C11⋊C8C2412yes—
320C2×C11⋊C8C2412yes—
321Dic44—28no—
322D88C2×D4116yescomplemented
323#4314—28no—
324#4314—28no—
325#4313—28no—
326C22×AGL(1,ℤ/8)—111no—
327C22×#135—111no—
328C2×#547—111no—
329C2×#546—111no—
330#3267—1116no—
331C2×#497—111no—
332C2×#470—111no—
333C2×#465D1111yescharacteristic, complemented
334C2×#463—111no—
335C2×#461—111no—
336C2×#452—111no—
337C2×#452—111no—
338C2×#449—111no—
339C2×#450—111no—
340C2×#442—111no—
341C2×#435—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—24no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—48no—
359C22×D11—48no—
360C22×D11—42no—
361C22×D11—42no—
362C22×D11—42no—
363C22×D11—42no—
364C22×D11—84no—
365C22×D11—816no—
366C22×D11C22×D412yes—
367Q8×C11—22no—
368Q8×C11—22no—
369Q8×C11—42no—
370D4×C11—22no—
371D4×C11—22no—
372D4×C11—42no—
373D4×C11—84no—
374C2×C4×C11—22no—
375C2×C4×C11—24no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—42no—
382C2×C4×C11—42no—
383C2×C4×C11—42no—
384C2×C4×C11C22×D412yes—
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D412yes—
387C2×C4×C11H(5,𝔽2)12yes—
388C2×C4×C11C2511yescharacteristic
389C22⋊D11—44no—
390C22⋊D11—48no—
391C22⋊D11—48no—
392C22⋊D11—48no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—42no—
399C2×Dic11—42no—
400C2×Dic11C22×D412yes—
401C2×Dic11C22×D412yes—
402C2×Dic11C22×D412yes—
403D44—24no—
404D44—24no—
405D44—22no—
406D44—22no—
407D44—48no—
408D44C22×D414yes—
409D44C22×D414yes—
410C4×D11—24no—
411C4×D11—22no—
412C4×D11—22no—
413C4×D11—48no—
414C4×D11—48no—
415C4×D11—48no—
416C4×D11—48no—
417C4×D11—84no—
418Dic22—22no—
419Dic22—22no—
420Dic22—22no—
421Dic22—22no—
422Dic22—42no—
423Dic22—42no—
424C8×C11—22no—
425C8×C11C22×D414yes—
426C11⋊C8—22no—
427C11⋊C8—22no—
428C22×#41—111no—
429C22×#41—111no—
430C22×#41—111no—
431C23×D4—111no—
432C2×AGL(1,ℤ/8)—118no—
433C2×AGL(1,ℤ/8)—228no—
434C2×#135—118no—
435C2×#135—228no—
436C22×Q16—111no—
437C22×Q16—111no—
438C22×SD16—111no—
439C22×SD16—111no—
440C22×SD16—111no—
441C22×SD16—111no—
442C22×SD16C2×D1111yescharacteristic
443C22×D8—111no—
444C22×D8—111no—
445C22×M16—111no—
446C23×C8C2×D1111yescharacteristic, complemented
447#547—118no—
448#547—224no—
449#546—118no—
450#546—224no—
451C2×C4⋊Q8—111no—
452C2×#124—111no—
453C2×#123—221no—
454C2×#123—221no—
455C2×#123—221no—
456C2×C22⋊Q8—111no—
457C2×C22⋊Q8—111no—
458C2×C22⋊Q8C2×D1111yescharacteristic, complemented
459C2×#121—221no—
460C2×#121—221no—
461C2×#121C2×D1111yescharacteristic
462C2×#120—221no—
463C2×C4×D4—111no—
464C2×C4×D4—111no—
465C2×C4×D4—111no—
466C22×C4⋊C4—221no—
467C22×C22⋊C4—221no—
468#497—118no—
469#470—118no—
470#465C2×D1118yescomplemented
471#463—118no—
472#461—118no—
473#452—118no—
474#452—118no—
475#450—118no—
476#449—118no—
477#442—118no—
478#435—118no—
479C2×#106C2×D1111yescharacteristic, complemented
480C2×C4⋊C8—111no—
481C2×#103—111no—
482C2×#103—111no—
483C2×#103C2×D1111yescharacteristic, complemented
484C2×#102—111no—
485C2×#102—111no—
486C2×#102C2×D1111yescharacteristic
487C2×C22⋊C8—111no—
488C2×C22⋊C8—111no—
489C2×#97—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—24no—
504C2×D11—22no—
505C2×D11—22no—
506C2×D11—22no—
507C2×D11—44no—
508C2×D11—48no—
509C2×D11—48no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—816no—
515C4×C11—22no—
516C4×C11—42no—
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—114no—
531C2×#41—224no—
532C2×#41—224no—
533C2×#41—222no—
534C2×#41—222no—
535C2×#41—222no—
536C2×#41—224no—
537C2×#41—442no—
538C2×#41—442no—
539C2×#41—442no—
540C22×Q8—111no—
541C22×Q8—111no—
542C22×Q8C22×D1111yescharacteristic
543C22×D4—21no—
544C22×D4—111no—
545C22×D4—114no—
546C22×D4—111no—
547C22×D4—111no—
548C22×D4—221no—
549C22×D4—222no—
550C22×D4—221no—
551C22×D4—224no—
552C22×D4—221no—
553C22×D4—221no—
554C22×D4—442no—
555C22×D4C22×D1111yescharacteristic
556C23×C4—111no—
557C23×C4—221no—
558C23×C4—221no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4—221no—
562C23×C4C22×D1111yescharacteristic
563AGL(1,ℤ/8)—2232no—
564#135—2232no—
565C2×Q16—114no—
566C2×Q16—114no—
567C2×Q16—224no—
568C2×Q16—442no—
569C2×SD16—24no—
570C2×SD16—114no—
571C2×SD16—114no—
572C2×SD16—114no—
573C2×SD16—114no—
574C2×SD16—224no—
575C2×SD16—224no—
576C2×SD16—224no—
577C2×SD16—442no—
578C2×SD16C22×D1114yes—
579C2×D8—114no—
580C2×D8—118no—
581C2×D8—114no—
582C2×D8—224no—
583C2×M16—114no—
584C2×M16—224no—
585C22×C8—24no—
586C22×C8—111no—
587C22×C8—111no—
588C22×C8C22×D1111yescharacteristic
589C22×C8C22×D1111yescharacteristic
590C22×C8C22×D1114yescomplemented
591C4⋊Q8—114no—
592C4⋊Q8—222no—
593#124—114no—
594#124—222no—
595#123—228no—
596#123—228no—
597#123—228no—
598C22⋊Q8—22no—
599C22⋊Q8—114no—
600C22⋊Q8—114no—
601C22⋊Q8—222no—
602C22⋊Q8—222no—
603C22⋊Q8C22×D1114yescomplemented
604#121—22no—
605#121—228no—
606#121—228no—
607#121C22×D1114yes—
608#120—228no—
609C4×D4—114no—
610C4×D4—114no—
611C4×D4—114no—
612C4×D4—114no—
613C4×D4—222no—
614C4×D4—222no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—228no—
618C2×C4⋊C4—221no—
619C2×C4⋊C4—221no—
620C2×C4⋊C4—221no—
621C2×C4⋊C4—221no—
622C2×C4⋊C4C22×D1111yescharacteristic
623C2×C4⋊C4C22×D1111yescharacteristic
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—111no—
627C2×C22⋊C4—111no—
628C2×C22⋊C4—228no—
629C2×C22⋊C4—221no—
630C2×C22⋊C4—221no—
631C2×C22⋊C4—221no—
632C2×C22⋊C4—221no—
633C2×C22⋊C4—221no—
634C2×C22⋊C4—221no—
635C2×C42—111no—
636#106C22×D1114yescomplemented
637C4⋊C8—114no—
638#103—114no—
639#103—114no—
640#103C22×D1114yescomplemented
641#102—114no—
642#102—114no—
643#102C22×D1114yes—
644C22⋊C8—114no—
645C22⋊C8—114no—
646#97—114no—
647C2×C11—42no—
648C2×C11—82no—
649C2×C11#326714yescomplemented
650C2×C11C2×D4211yescharacteristic
651C2×C11C2×#57511yescharacteristic
652C2×C11C2×#57711yescharacteristic
653D11—42no—
654D11—44no—
655D11—44no—
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—228no—
668#41—444no—
669#41—444no—
670#41—448no—
671#41—448no—
672#41—444no—
673#41—448no—
674C2×Q8—21no—
675C2×Q8—22no—
676C2×Q8—22no—
677C2×Q8—112no—
678C2×Q8—112no—
679C2×Q8—221no—
680C2×Q8—221no—
681C2×Q8—222no—
682C2×Q8—222no—
683C2×Q8—222no—
684C2×Q8—222no—
685C2×Q8C23×D1112yes—
686C2×D4—24no—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—22no—
690C2×D4—82no—
691C2×D4—114no—
692C2×D4—114no—
693C2×D4—114no—
694C2×D4—112no—
695C2×D4—112no—
696C2×D4—224no—
697C2×D4—224no—
698C2×D4—228no—
699C2×D4—224no—
700C2×D4—224no—
701C2×D4—221no—
702C2×D4—221no—
703C2×D4—222no—
704C2×D4—222no—
705C2×D4—444no—
706C2×D4—444no—
707C2×D4—448no—
708C2×D4—442no—
709C2×D4—444no—
710C2×D4—444no—
711C2×D4—444no—
712C2×D4C23×D1112yes—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—111no—
719C22×C4—111no—
720C22×C4—111no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—224no—
724C22×C4—224no—
725C22×C4—224no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—224no—
731C22×C4—224no—
732C22×C4—444no—
733C22×C4—444no—
734C22×C4—444no—
735C22×C4—444no—
736C22×C4—882no—
737C22×C4D4×D1112yes—
738C22×C4D4×D1111yescharacteristic
739C22×C4C23×D1112yes—
740C22×C4C23×D1111yescharacteristic
741Q16—228no—
742Q16—444no—
743SD16—28no—
744SD16—228no—
745SD16—228no—
746SD16—228no—
747SD16—444no—
748D8—1116no—
749D8—228no—
750M16—228no—
751C2×C8—22no—
752C2×C8—28no—
753C2×C8—112no—
754C2×C8—112no—
755C2×C8—222no—
756C2×C8—222no—
757C2×C8D4×D1114yes—
758C2×C8C23×D1112yes—
759C2×C8C23×D1112yes—
760C4⋊C4—24no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—114no—
764C4⋊C4—224no—
765C4⋊C4—224no—
766C4⋊C4—224no—
767C4⋊C4—224no—
768C4⋊C4C23×D1112yes—
769C4⋊C4C23×D1112yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—114no—
773C22⋊C4—114no—
774C22⋊C4—224no—
775C22⋊C4—224no—
776C22⋊C4—224no—
777C22⋊C4—224no—
778C22⋊C4—224no—
779C22⋊C4—224no—
780C42—112no—
781C42—112no—
782C11C2×#326711yescharacteristic, 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—224no—
796C23—222no—
797C23—222no—
798C23—448no—
799C23—448no—
800C23—442no—
801C23—442no—
802C23—442no—
803C23—442no—
804C23—884no—
805C23—8816no—
806C23C2×D4×D1112yes—
807C23C2×D4×D1111yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—42no—
811Q8—222no—
812Q8—222no—
813Q8—222no—
814Q8—222no—
815Q8—442no—
816Q8—442no—
817D4—22no—
818D4—22no—
819D4—42no—
820D4—84no—
821D4—114no—
822D4—114no—
823D4—224no—
824D4—224no—
825D4—222no—
826D4—222no—
827D4—448no—
828D4—444no—
829D4—448no—
830D4—448no—
831D4—448no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—112no—
843C2×C4—112no—
844C2×C4—112no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—222no—
848C2×C4—224no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—448no—
854C2×C4—448no—
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#6704212yes—
864C2×C4C24×D1111yescharacteristic
865C8—22no—
866C8—222no—
867C8—222no—
868C8C2×D4×D1114yes—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—84no—
877C22—222no—
878C22—224no—
879C22—224no—
880C22—222no—
881C22—222no—
882C22—444no—
883C22—448no—
884C22—448no—
885C22—442no—
886C22—442no—
887C22—442no—
888C22—442no—
889C22—8816no—
890C22#1062314012yes—
891C22#1062329312yes—
892C22#1062329912yes—
893C22C22×D4×D1111yescharacteristic
894C4—22no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—222no—
899C4—222no—
900C4—222no—
901C4—442no—
902C4—442no—
903C4#1062314012yes—
904C4C22×D4×D1111yescharacteristic
905C4C2×#6704211yescharacteristic
906C2—42no—
907C2—82no—
908C2—442no—
909C2—444no—
910C2—444no—
911C2#1308013814yesdirect product factor
912C2C2×#1062314011yescharacteristic
913C2C2×#1062329911yescharacteristic
914C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
hypercenterC2×#465D11
hypocenterC11C2×#3267
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C22×#66967C2semidirect
2. C22×#66957C2semidirect
3. C2×#10623162C2semidirect
4. C2×#10623143C2semidirect
5. #13080138C2direct (N × H)
6. C2×#10622780C2semidirect
7. C2×#10622481C2semidirect
8. C2×#10622400C2semidirect
9. C2×#10622431C2semidirect
10. C2×#10622423C2semidirect
11. C2×#10622660C2semidirect
12. C2×#10622650C2semidirect
13. C2×#10622389C2semidirect
14. C2×#10622482C2semidirect
15. C2×#10622724C2semidirect
16. C2×C11×#465C2semidirect
20. C22×#4339C22semidirect
22. C23×C8×C11C22semidirect
23. C2×C11×C22⋊Q8C22semidirect
25. C2×#66997C22semidirect
26. C22×#4326C22semidirect
35. C2×#66967C22semidirect
36. C22×Dic44C22semidirect
38. C2×#66957C22semidirect
41. C22×#4314C22semidirect
44. #10623162C22semidirect
46. #10623143C22semidirect
51. C2×#66946C22semidirect
57. C11×#465C22semidirect
58. C2×C11×#106C22semidirect
59. C2×C11×#103C22semidirect
61. C2×C22⋊(C11⋊C8)C22semidirect
62. #10622780C22semidirect
63. #10622724C22semidirect
65. C2×#66879C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. #10622660C22semidirect
68. #10622650C22semidirect
69. C2×#66874C22semidirect
70. C2×#66874C22semidirect
72. C2×#66873C22semidirect
73. #10622482C22semidirect
74. #10622481C22semidirect
75. #10622431C22semidirect
76. #10622423C22semidirect
77. #10622400C22semidirect
78. #10622389C22semidirect
103. C2×#4339C23semidirect
120. C22×C8×C11C23semidirect
122. C11×C22⋊Q8C23semidirect
134. #66997C23semidirect
136. C2×#4326C23semidirect
164. C2×Dic44C23semidirect
166. C2×D88D4semidirect
171. C2×#4314C23semidirect
182. #66946C23semidirect
188. C11×#106C23semidirect
189. C11×#103C23semidirect
191. C22⋊(C11⋊C8)C23semidirect
193. #66879C23semidirect
194. Dic11⋊C8C23semidirect
195. #66874C23semidirect
196. #66874C23semidirect
198. #66873C23semidirect
322. D88C2×D4semidirect
333. C2×#465D11semidirect
446. C23×C8C2×D11semidirect
458. C2×C22⋊Q8C2×D11semidirect
470. #465C2×D11semidirect
479. C2×#106C2×D11semidirect
483. C2×#103C2×D11semidirect
590. C22×C8C22×D11semidirect
603. C22⋊Q8C22×D11semidirect
636. #106C22×D11semidirect
640. #103C22×D11semidirect
649. C2×C11#3267semidirect
782. C11C2×#3267semidirect
911. C2#13080138direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669672
C22×#669572
C2×#106231622
C2×#106231432
#130801382
C2×#106227802
C2×#106224812
C2×#106224002
C2×#106224312
C2×#106224232
C2×#106226602
C2×#106226502
C2×#106223892
C2×#106224822
C2×#106227242
C2×C11×#4652
C2×#326711