Finite Group Databasebeta

← C2×#13080120 #15628748

Subgroups — C2×#13080120 #15628748

Order 2816.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×D11C211yesmaximal, characteristic, complemented
2C2×Q8×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×#10623360C211yesmaximal, characteristic
4#13080120C2116yesmaximal, direct product factor
5C2×#10622803C211yesmaximal, characteristic, complemented
6C2×#10622747C211yesmaximal, characteristic, complemented
7C2×#10622801C211yesmaximal, characteristic, complemented
8C2×#10622798C211yesmaximal, characteristic, complemented
9C2×#10622775C211yesmaximal, characteristic, complemented
10C2×#10622852C211yesmaximal, characteristic, complemented
11C2×#10622799C211yesmaximal, characteristic, complemented
12C2×#10622840C211yesmaximal, characteristic, complemented
13C2×#10622782C211yesmaximal, characteristic, complemented
14C2×#10622777C211yesmaximal, characteristic, complemented
15C2×#10622740C211yesmaximal, characteristic, complemented
16C22×C11×#137C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic, complemented
19C22×Q8×D11C2211yescharacteristic
20C22×D4×D11C2211yescharacteristic
21C2×C11×#137—28no—
22C2×C11×#137C2218yescomplemented
23C22×C11×Q16C2211yescharacteristic, complemented
24C22×C11×Q16C2211yescharacteristic, complemented
25C22×C11×SD16C2211yescharacteristic
26C22×C11×SD16C2211yescharacteristic
27C22×C11×M16C2211yescharacteristic, complemented
28#10623360—24no—
29#10623360C2218yes—
30Q8×C22⋊D11—24no—
31Q8×C22⋊D11C2218yescomplemented
32C2×#67000C2211yescharacteristic
33C2×#66999—21no—
34C2×#66999C2211yescharacteristic
35C2×#66999C2211yescharacteristic
36C2×Q8×Dic11C2211yescharacteristic, complemented
37C2×#66997—21no—
38C2×#66997C2211yescharacteristic, complemented
39C22×#4326C2211yescharacteristic, complemented
40C22×#4325C2211yescharacteristic
41C22×#4325C2211yescharacteristic
42C2×#66992—21no—
43C2×#66990—21no—
44C2×D4×Dic11C2211yescharacteristic
45C22×#4324C2211yescharacteristic
46C2×#66983C2211yescharacteristic
47C2×#66982—21no—
48C2×C4×C22⋊D11—21no—
49C2×C4×C22⋊D11C2211yescharacteristic
50C22×(C2×D11)⋊C4—21no—
51C2×#66977—21no—
52C2×#66977C2211yescharacteristic, complemented
53C2×SD16×D11—28no—
54C2×SD16×D11C2218yescomplemented
55C22×#4314C2211yescharacteristic
56C22×C8×D11C2211yescharacteristic
57#10622852C2218yescomplemented
58#10622840C2218yescomplemented
59C2×#66899C2211yescharacteristic, complemented
60C2×#66899C2211yescharacteristic, complemented
61C2×#66899C2211yescharacteristic, complemented
62C2×#66896C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
64#10622803C2218yescomplemented
65#10622801C2218yescomplemented
66#10622799C2218yescomplemented
67#10622798C2218yescomplemented
68#10622782C2218yescomplemented
69#10622777C2218yescomplemented
70#10622775C2218yescomplemented
71#10622747C2218yescomplemented
72#10622740C2218yescomplemented
73C2×#66885C2211yescharacteristic
74C2×(C2×D11)⋊C8C2211yescharacteristic
75C2×#66882C2211yescharacteristic, complemented
76C2×#66880C2211yescharacteristic, complemented
77C2×#66879C2211yescharacteristic, complemented
78C2×Dic11⋊C8C2211yescharacteristic, complemented
79C24×D11—21no—
80C2×C11×#41—22no—
81C2×C11×#41—24no—
82C2×C11×#41—42no—
83C2×C11×#41C2314yes—
84C22×Q8×C11—21no—
85C22×Q8×C11—22no—
86C22×Q8×C11—24no—
87C22×Q8×C11—42no—
88C22×Q8×C11C2311yescharacteristic
89C22×Q8×C11C2311yescharacteristic
90C22×Q8×C11C2311yescharacteristic
91C22×Q8×C11C2314yescomplemented
92C22×D4×C11—21no—
93C22×D4×C11C2311yescharacteristic
94C23×C4×C11—21no—
95C23×C4×C11—21no—
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—21no—
98C22×C22⋊D11—21no—
99C22×C22⋊D11D411yescharacteristic
100C23×Dic11—21no—
101C2×Q8×D11—22no—
102C2×Q8×D11—24no—
103C2×Q8×D11—42no—
104C2×Q8×D11C2314yes—
105C2×D4×D11—24no—
106C2×D4×D11—22no—
107C2×D4×D11—42no—
108C2×D4×D11C2314yes—
109C22×D44C2311yescharacteristic
110C22×C4×D11—21no—
111C22×C4×D11C2311yescharacteristic
112C22×Dic22—21no—
113C22×Dic22C2311yescharacteristic
114C11×#137—232no—
115C2×C11×Q16—24no—
116C2×C11×Q16—24no—
117C2×C11×Q16C2314yescomplemented
118C2×C11×Q16C2314yescomplemented
119C2×C11×SD16—24no—
120C2×C11×SD16D418yescomplemented
121C2×C11×SD16C2314yes—
122C2×C11×SD16C2314yes—
123C2×C11×M16—24no—
124C2×C11×M16C2314yescomplemented
125C22×C8×C11C2311yescharacteristic
126C22×C8×C11C2311yescharacteristic
127C2×C22⋊Dic11—21no—
128C2×C22⋊Dic11—21no—
129C2×C22⋊Dic11D411yescharacteristic
130#67000—22no—
131#67000C2314yes—
132#66999—22no—
133#66999—22no—
134#66999—28no—
135#66999C2314yes—
136#66999C2314yes—
137Q8×Dic11—22no—
138Q8×Dic11C2314yescomplemented
139#66997—28no—
140#66997—22no—
141#66997C2314yescomplemented
142C2×#4326—42no—
143C2×#4326C2314yescomplemented
144C2×#4325—24no—
145C2×#4325—42no—
146C2×#4325C2314yes—
147C2×#4325C2314yes—
148#66992—28no—
149#66990—28no—
150D4×Dic11—22no—
151D4×Dic11C2314yes—
152C2×#4324—24no—
153C2×#4324C2314yes—
154#66983—22no—
155#66983C2314yes—
156#66982—28no—
157C4×C22⋊D11—28no—
158C4×C22⋊D11D414yes—
159C4×C22⋊D11C2314yes—
160C2×(C2×D11)⋊C4—21no—
161C2×(C2×D11)⋊C4—21no—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4—21no—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4—28no—
166C2×(C2×D11)⋊C4D411yescharacteristic
167C2×C4⋊Dic11—21no—
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2311yescharacteristic
170#66977—22no—
171#66977—28no—
172#66977C2314yescomplemented
173C2×Dic11⋊C4—21no—
174C2×Dic11⋊C4—21no—
175C2×Dic11⋊C4—21no—
176C2×Dic11⋊C4—21no—
177C2×Dic11⋊C4—21no—
178C2×Dic11⋊C4D411yescharacteristic
179C2×C4×Dic11—21no—
180C2×C4×Dic11C2311yescharacteristic
181C22×C11⋊C8C2311yescharacteristic
182C22×C11⋊C8C2311yescharacteristic
183SD16×D11—232no—
184C2×#4314—24no—
185C2×#4314C2314yes—
186C2×C8×D11—24no—
187C2×C8×D11C2314yes—
188#66899C2314yescomplemented
189#66899C2314yescomplemented
190#66899C2314yescomplemented
191#66896C2314yes—
192C22⋊(C11⋊C8)C2314yescomplemented
193#66885C2314yes—
194(C2×D11)⋊C8C2314yes—
195#66882C2314yescomplemented
196#66880C2314yescomplemented
197#66879C2314yescomplemented
198Dic11⋊C8C2314yescomplemented
199C2×#3266—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C23×D11—24no—
204C23×D11—44no—
205C23×D11—44no—
206C23×D11—82no—
207C23×D11C2×D411yescharacteristic
208C11×#41—28no—
209C11×#41—44no—
210C11×#41—48no—
211C2×Q8×C11—21no—
212C2×Q8×C11—21no—
213C2×Q8×C11—24no—
214C2×Q8×C11—21no—
215C2×Q8×C11—22no—
216C2×Q8×C11—28no—
217C2×Q8×C11—22no—
218C2×Q8×C11—22no—
219C2×Q8×C11—22no—
220C2×Q8×C11—22no—
221C2×Q8×C11—44no—
222C2×Q8×C11—44no—
223C2×Q8×C11—48no—
224C2×Q8×C11C2×D414yes—
225C2×Q8×C11C2412yes—
226C2×Q8×C11C2412yes—
227C2×Q8×C11C2412yes—
228C2×D4×C11—24no—
229C2×D4×C11—21no—
230C2×D4×C11—22no—
231C2×D4×C11—44no—
232C2×D4×C11C2×D414yes—
233C2×D4×C11C2412yes—
234C22×C4×C11—21no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—24no—
240C22×C4×C11—24no—
241C22×C4×C11—44no—
242C22×C4×C11—44no—
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2411yescharacteristic
247C2×C22⋊D11—24no—
248C2×C22⋊D11—24no—
249C2×C22⋊D11—24no—
250C2×C22⋊D11—44no—
251C2×C22⋊D11—82no—
252C2×C22⋊D11C2×D414yes—
253C22×Dic11—24no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—82no—
258C22×Dic11C2×D411yescharacteristic
259C22×Dic11C2×D411yescharacteristic
260C22×Dic11C2×D411yescharacteristic
261Q8×D11—28no—
262Q8×D11—44no—
263Q8×D11—48no—
264D4×D11—28no—
265D4×D11—44no—
266D4×D11—48no—
267C2×D44—21no—
268C2×D44—22no—
269C2×D44—22no—
270C2×D44C2412yes—
271C2×C4×D11—24no—
272C2×C4×D11—22no—
273C2×C4×D11—22no—
274C2×C4×D11—44no—
275C2×C4×D11C2×D412yes—
276C2×C4×D11C2412yes—
277C2×Dic22—24no—
278C2×Dic22—22no—
279C2×Dic22—21no—
280C2×Dic22—22no—
281C2×Dic22—44no—
282C2×Dic22C2412yes—
283C11×Q16—28no—
284C11×Q16—28no—
285C11×SD16—28no—
286C11×SD16C2×D4116yescomplemented
287C11×M16—28no—
288C2×C8×C11—22no—
289C2×C8×C11C2×D414yes—
290C2×C8×C11C2412yes—
291C2×C8×C11C2412yes—
292C22⋊Dic11—24no—
293C22⋊Dic11—24no—
294C22⋊Dic11C2×D414yes—
295#4326—44no—
296#4325—28no—
297#4325—44no—
298#4324—28no—
299(C2×D11)⋊C4—24no—
300(C2×D11)⋊C4—24no—
301(C2×D11)⋊C4—24no—
302(C2×D11)⋊C4—24no—
303(C2×D11)⋊C4—24no—
304(C2×D11)⋊C4C2×D414yes—
305C4⋊Dic11—24no—
306C4⋊Dic11—21no—
307C4⋊Dic11—21no—
308C4⋊Dic11C2412yes—
309C4⋊Dic11C2412yes—
310Dic11⋊C4—24no—
311Dic11⋊C4—24no—
312Dic11⋊C4—24no—
313Dic11⋊C4—24no—
314Dic11⋊C4—24no—
315Dic11⋊C4C2×D414yes—
316C4×Dic11—24no—
317C4×Dic11C2×D412yes—
318C4×Dic11C2412yes—
319C2×C11⋊C8—22no—
320C2×C11⋊C8—22no—
321C2×C11⋊C8C2412yes—
322C2×C11⋊C8C2412yes—
323#4314—28no—
324C8×D11—28no—
325C22×#137D1111yescharacteristic, complemented
326C23×SD16—111no—
327C2×D4×Q8—111no—
328C2×#546—111no—
329#3266—1116no—
330C2×#497—111no—
331C2×#468—111no—
332C2×#467—111no—
333C2×#464—111no—
334C2×#461—111no—
335C2×#452—111no—
336C2×#451—111no—
337C2×#448—111no—
338C2×#450—111no—
339C2×#440—111no—
340C2×#435—111no—
341C23×C11—24no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—42no—
347C23×C11—42no—
348C23×C11C22×D412yes—
349C23×C11C22×D411yescharacteristic
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—48no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—42no—
357C22×D11—48no—
358C22×D11—84no—
359C22×D11—816no—
360C22×D11#13714yescomplemented
361C22×D11C22×D412yes—
362Q8×C11—24no—
363Q8×C11—22no—
364Q8×C11—22no—
365Q8×C11—22no—
366Q8×C11—22no—
367Q8×C11—22no—
368Q8×C11—48no—
369Q8×C11—42no—
370Q8×C11—42no—
371Q8×C11C22×D414yes—
372D4×C11—24no—
373D4×C11—22no—
374D4×C11—48no—
375D4×C11C22×D414yes—
376C2×C4×C11—24no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—24no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—48no—
385C2×C4×C11—48no—
386C2×C4×C11—42no—
387C2×C4×C11—42no—
388C2×C4×C11C22×D412yes—
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D412yes—
391C2×C4×C11H(5,𝔽2)12yes—
392C2×C4×C11C2511yescharacteristic
393C22⋊D11—28no—
394C22⋊D11—48no—
395C22⋊D11—84no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—42no—
403C2×Dic11—42no—
404C2×Dic11—42no—
405C2×Dic11—84no—
406C2×Dic11C22×D412yes—
407C2×Dic11C22×D412yes—
408C2×Dic11C22×D412yes—
409D44—22no—
410D44—22no—
411D44—42no—
412C4×D11—24no—
413C4×D11—22no—
414C4×D11—22no—
415C4×D11—48no—
416Dic22—22no—
417Dic22—22no—
418Dic22—48no—
419Dic22—42no—
420C8×C11—22no—
421C8×C11C22×D414yes—
422C11⋊C8—22no—
423C11⋊C8—22no—
424C22×#41C2×D1111yescharacteristic
425C23×Q8—111no—
426C23×Q8C2×D1111yescharacteristic, complemented
427C23×D4—111no—
428C2×#137—28no—
429C2×#137C2×D1118yescomplemented
430C22×Q16—111no—
431C22×Q16C2×D1111yescharacteristic, complemented
432C22×Q16C2×D1111yescharacteristic, complemented
433C22×SD16—111no—
434C22×SD16—111no—
435C22×SD16—111no—
436C22×SD16—118no—
437C22×SD16—111no—
438C22×SD16—228no—
439C22×SD16C2×D1111yescharacteristic
440C22×SD16C2×D1111yescharacteristic
441C22×M16C2×D1111yescharacteristic, complemented
442C23×C8—111no—
443D4×Q8—118no—
444D4×Q8—224no—
445#546—118no—
446#546—224no—
447C2×C4⋊Q8—111no—
448C2×C4⋊Q8—221no—
449C2×#124—111no—
450C2×#123—221no—
451C2×C22⋊Q8—111no—
452C2×C22⋊Q8—111no—
453C2×C22⋊Q8—111no—
454C2×C22⋊Q8—221no—
455C2×C22⋊Q8—221no—
456C2×#121—111no—
457C2×#121—221no—
458C2×#120—221no—
459C2×C4×Q8—111no—
460C2×C4×D4—111no—
461C2×C4×D4—111no—
462C2×C4×D4—221no—
463C22×C22⋊C4—221no—
464#497—118no—
465#468—118no—
466#467—118no—
467#464—118no—
468#461—118no—
469#452—118no—
470#451—118no—
471#450—118no—
472#448—118no—
473#440—118no—
474#435—118no—
475C2×#107—111no—
476C2×C4⋊C8—111no—
477C2×#103—111no—
478C2×#103—111no—
479C2×#103—111no—
480C2×#103—111no—
481C2×#102—111no—
482C2×#102—111no—
483C2×C22⋊C8—111no—
484C2×C22⋊C8—111no—
485C2×#97—111no—
486C22×C11—22no—
487C22×C11—24no—
488C22×C11—22no—
489C22×C11—22no—
490C22×C11—48no—
491C22×C11—44no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11D4212yes—
495C22×C11C2×#13712yes—
496C22×C11#57712yes—
497C22×C11C23×D411yescharacteristic
498C2×D11—22no—
499C2×D11—28no—
500C2×D11—22no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—816no—
505C2×D11—84no—
506C2×D11C2×#13714yescomplemented
507C4×C11—22no—
508C4×C11—24no—
509C4×C11—42no—
510C4×C11—42no—
511C4×C11D4212yes—
512C4×C11C23×D411yescharacteristic
513C4×C11C2×H(5,𝔽2)11yescharacteristic
514Dic11—22no—
515Dic11—22no—
516Dic11—22no—
517Dic11—42no—
518Dic11—42no—
519Dic11—42no—
520C25—221no—
521C2×#41—22no—
522C2×#41—24no—
523C2×#41—42no—
524C2×#41C22×D1114yes—
525C22×Q8—21no—
526C22×Q8—22no—
527C22×Q8—24no—
528C22×Q8—42no—
529C22×Q8—114no—
530C22×Q8—111no—
531C22×Q8—221no—
532C22×Q8—222no—
533C22×Q8—224no—
534C22×Q8—442no—
535C22×Q8C22×D1111yescharacteristic
536C22×Q8C22×D1111yescharacteristic
537C22×Q8C22×D1111yescharacteristic
538C22×Q8C22×D1114yescomplemented
539C22×D4—21no—
540C22×D4—111no—
541C22×D4—114no—
542C22×D4—111no—
543C22×D4—222no—
544C22×D4—221no—
545C22×D4—224no—
546C22×D4—221no—
547C22×D4—442no—
548C22×D4C22×D1111yescharacteristic
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—111no—
552C23×C4—221no—
553C23×C4—221no—
554C23×C4C22×D1111yescharacteristic
555#137—232no—
556C2×Q16—24no—
557C2×Q16—24no—
558C2×Q16—114no—
559C2×Q16—442no—
560C2×Q16C22×D1114yescomplemented
561C2×Q16C22×D1114yescomplemented
562C2×SD16—24no—
563C2×SD16—114no—
564C2×SD16—114no—
565C2×SD16—114no—
566C2×SD16—114no—
567C2×SD16—224no—
568C2×SD16—224no—
569C2×SD16—2232no—
570C2×SD16—224no—
571C2×SD16—442no—
572C2×SD16C22⋊D1118yescomplemented
573C2×SD16C22×D1114yes—
574C2×SD16C22×D1114yes—
575C2×M16—24no—
576C2×M16C22×D1114yescomplemented
577C22×C8—111no—
578C22×C8—111no—
579C22×C8—114no—
580C22×C8—224no—
581C22×C8C22×D1111yescharacteristic
582C22×C8C22×D1111yescharacteristic
583C4⋊Q8—114no—
584C4⋊Q8—222no—
585C4⋊Q8—228no—
586#124—114no—
587#124—222no—
588#123—228no—
589C22⋊Q8—114no—
590C22⋊Q8—114no—
591C22⋊Q8—114no—
592C22⋊Q8—228no—
593C22⋊Q8—228no—
594C22⋊Q8—222no—
595C22⋊Q8—222no—
596C22⋊Q8—222no—
597#121—114no—
598#121—228no—
599#121—222no—
600#120—228no—
601C4×Q8—114no—
602C4×Q8—222no—
603C4×D4—114no—
604C4×D4—114no—
605C4×D4—114no—
606C4×D4—222no—
607C4×D4—228no—
608C2×C4⋊C4—111no—
609C2×C4⋊C4—111no—
610C2×C4⋊C4—111no—
611C2×C4⋊C4—221no—
612C2×C4⋊C4—221no—
613C2×C4⋊C4—221no—
614C2×C4⋊C4—221no—
615C2×C4⋊C4—221no—
616C2×C4⋊C4—221no—
617C2×C22⋊C4—111no—
618C2×C22⋊C4—111no—
619C2×C22⋊C4—228no—
620C2×C22⋊C4—221no—
621C2×C22⋊C4—221no—
622C2×C22⋊C4—221no—
623C2×C22⋊C4—221no—
624C2×C22⋊C4—221no—
625C2×C22⋊C4—221no—
626C2×C22⋊C4—221no—
627C2×C42—111no—
628C2×C42—221no—
629#107—114no—
630C4⋊C8—114no—
631#103—114no—
632#103—114no—
633#103—114no—
634#103—114no—
635#102—114no—
636#102—114no—
637C22⋊C8—114no—
638C22⋊C8—114no—
639#97—114no—
640C2×C11—44no—
641C2×C11—42no—
642C2×C11#326614yescomplemented
643C2×C11C2×D4211yescharacteristic
644C2×C11C22×#13711yescharacteristic
645C2×C11C2×#57711yescharacteristic
646D11—24no—
647D11—82no—
648C24—21no—
649C24—111no—
650C24—224no—
651C24—221no—
652C24—444no—
653C24—444no—
654C24—882no—
655C24D4×D1111yescharacteristic
656#41—28no—
657#41—44no—
658#41—48no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—24no—
663C2×Q8—22no—
664C2×Q8—28no—
665C2×Q8—22no—
666C2×Q8—22no—
667C2×Q8—22no—
668C2×Q8—22no—
669C2×Q8—44no—
670C2×Q8—44no—
671C2×Q8—48no—
672C2×Q8—112no—
673C2×Q8—224no—
674C2×Q8—221no—
675C2×Q8—228no—
676C2×Q8—222no—
677C2×Q8—222no—
678C2×Q8—444no—
679C2×Q8—444no—
680C2×Q8—448no—
681C2×Q8C2×C22⋊D1114yes—
682C2×Q8C23×D1112yes—
683C2×Q8C23×D1112yes—
684C2×Q8C23×D1112yes—
685C2×D4—24no—
686C2×D4—21no—
687C2×D4—22no—
688C2×D4—44no—
689C2×D4—114no—
690C2×D4—112no—
691C2×D4—224no—
692C2×D4—224no—
693C2×D4—228no—
694C2×D4—224no—
695C2×D4—221no—
696C2×D4—222no—
697C2×D4—222no—
698C2×D4—444no—
699C2×D4—448no—
700C2×D4—444no—
701C2×D4—882no—
702C2×D4C2×C22⋊D1114yes—
703C2×D4C23×D1112yes—
704C22×C4—21no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—24no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—24no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—111no—
714C22×C4—111no—
715C22×C4—111no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—224no—
719C22×C4—224no—
720C22×C4—222no—
721C22×C4—222no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—444no—
726C22×C4—882no—
727C22×C4D4×D1112yes—
728C22×C4D4×D1111yescharacteristic
729C22×C4C23×D1112yes—
730C22×C4C23×D1111yescharacteristic
731Q16—28no—
732Q16—28no—
733Q16—444no—
734SD16—28no—
735SD16—228no—
736SD16—228no—
737SD16—228no—
738SD16—444no—
739SD16C2×C22⋊D11116yescomplemented
740M16—28no—
741C2×C8—22no—
742C2×C8—112no—
743C2×C8—112no—
744C2×C8—222no—
745C2×C8—222no—
746C2×C8—228no—
747C2×C8C2×C22⋊D1114yes—
748C2×C8C23×D1112yes—
749C2×C8C23×D1112yes—
750C4⋊C4—114no—
751C4⋊C4—112no—
752C4⋊C4—112no—
753C4⋊C4—224no—
754C4⋊C4—224no—
755C4⋊C4—224no—
756C4⋊C4—224no—
757C4⋊C4—224no—
758C4⋊C4—221no—
759C4⋊C4—221no—
760C4⋊C4—224no—
761C22⋊C4—114no—
762C22⋊C4—114no—
763C22⋊C4—224no—
764C22⋊C4—224no—
765C22⋊C4—224no—
766C22⋊C4—224no—
767C22⋊C4—224no—
768C22⋊C4—224no—
769C22⋊C4—224no—
770C42—112no—
771C42—112no—
772C42—224no—
773C11C2×#326611yescharacteristic, complemented, Sylow
774C23—22no—
775C23—22no—
776C23—22no—
777C23—24no—
778C23—22no—
779C23—42no—
780C23—42no—
781C23—114no—
782C23—112no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—448no—
787C23—448no—
788C23—442no—
789C23—442no—
790C23—442no—
791C23—884no—
792C23—8816no—
793C23C2×D4×D1112yes—
794C23C2×D4×D1111yescharacteristic
795Q8—24no—
796Q8—22no—
797Q8—22no—
798Q8—22no—
799Q8—22no—
800Q8—22no—
801Q8—48no—
802Q8—42no—
803Q8—42no—
804Q8—222no—
805Q8—222no—
806Q8—448no—
807Q8—442no—
808Q8C22×C22⋊D1114yes—
809D4—24no—
810D4—22no—
811D4—48no—
812D4—228no—
813D4—222no—
814D4—222no—
815D4—448no—
816D4—442no—
817D4—884no—
818D4C22×C22⋊D1114yes—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—48no—
828C2×C4—48no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—112no—
832C2×C4—112no—
833C2×C4—112no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—224no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—448no—
844C2×C4—442no—
845C2×C4—442no—
846C2×C4—442no—
847C2×C4—884no—
848C2×C4C2×D4×D1112yes—
849C2×C4C2×D4×D1111yescharacteristic
850C2×C4#6703712yes—
851C2×C4C22×C22⋊D1112yes—
852C2×C4C24×D1111yescharacteristic
853C8—22no—
854C8—222no—
855C8—222no—
856C8C22×C22⋊D1114yes—
857C22—22no—
858C22—24no—
859C22—22no—
860C22—22no—
861C22—44no—
862C22—48no—
863C22—42no—
864C22—42no—
865C22—114no—
866C22—228no—
867C22—222no—
868C22—222no—
869C22—442no—
870C22—442no—
871C22—442no—
872C22—8816no—
873C22—884no—
874C22D11×#13712yes—
875C22#1062330912yes—
876C22D4×C22⋊D1112yes—
877C22C22×D4×D1111yescharacteristic
878C4—22no—
879C4—24no—
880C4—42no—
881C4—42no—
882C4—222no—
883C4—222no—
884C4—222no—
885C4—442no—
886C4—442no—
887C4—442no—
888C4D4×C22⋊D1112yes—
889C4C2×#6703711yescharacteristic
890C4C23×C22⋊D1111yescharacteristic
891C2—42no—
892C2—44no—
893C2—224no—
894C2—882no—
895C2#1308012014yesdirect product factor
896C2C2×D4×C22⋊D1111yescharacteristic
897C2C2×D11×#13711yescharacteristic
898C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#137C2
socleC23×C11C22×D4
prime radicalC2×#10623360C2
hypercenterC22×#137D11
hypocenterC11C2×#3266
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×SD16×D11C2semidirect
2. C2×Q8×C22⋊D11C2semidirect
4. #13080120C2direct (N × H)
5. C2×#10622803C2semidirect
6. C2×#10622747C2semidirect
7. C2×#10622801C2semidirect
8. C2×#10622798C2semidirect
9. C2×#10622775C2semidirect
10. C2×#10622852C2semidirect
11. C2×#10622799C2semidirect
12. C2×#10622840C2semidirect
13. C2×#10622782C2semidirect
14. C2×#10622777C2semidirect
15. C2×#10622740C2semidirect
16. C22×C11×#137C2semidirect
18. C23×Q8×C11C22semidirect
22. C2×C11×#137C22semidirect
23. C22×C11×Q16C22semidirect
24. C22×C11×Q16C22semidirect
27. C22×C11×M16C22semidirect
31. Q8×C22⋊D11C22semidirect
36. C2×Q8×Dic11C22semidirect
38. C2×#66997C22semidirect
39. C22×#4326C22semidirect
52. C2×#66977C22semidirect
54. C2×SD16×D11C22semidirect
57. #10622852C22semidirect
58. #10622840C22semidirect
59. C2×#66899C22semidirect
60. C2×#66899C22semidirect
61. C2×#66899C22semidirect
63. C2×C22⋊(C11⋊C8)C22semidirect
64. #10622803C22semidirect
65. #10622801C22semidirect
66. #10622799C22semidirect
67. #10622798C22semidirect
68. #10622782C22semidirect
69. #10622777C22semidirect
70. #10622775C22semidirect
71. #10622747C22semidirect
72. #10622740C22semidirect
75. C2×#66882C22semidirect
76. C2×#66880C22semidirect
77. C2×#66879C22semidirect
78. C2×Dic11⋊C8C22semidirect
91. C22×Q8×C11C23semidirect
117. C2×C11×Q16C23semidirect
118. C2×C11×Q16C23semidirect
120. C2×C11×SD16D4semidirect
124. C2×C11×M16C23semidirect
138. Q8×Dic11C23semidirect
141. #66997C23semidirect
143. C2×#4326C23semidirect
172. #66977C23semidirect
188. #66899C23semidirect
189. #66899C23semidirect
190. #66899C23semidirect
192. C22⋊(C11⋊C8)C23semidirect
195. #66882C23semidirect
196. #66880C23semidirect
197. #66879C23semidirect
198. Dic11⋊C8C23semidirect
286. C11×SD16C2×D4semidirect
325. C22×#137D11semidirect
360. C22×D11#137semidirect
426. C23×Q8C2×D11semidirect
429. C2×#137C2×D11semidirect
431. C22×Q16C2×D11semidirect
432. C22×Q16C2×D11semidirect
441. C22×M16C2×D11semidirect
506. C2×D11C2×#137semidirect
538. C22×Q8C22×D11semidirect
560. C2×Q16C22×D11semidirect
561. C2×Q16C22×D11semidirect
572. C2×SD16C22⋊D11semidirect
576. C2×M16C22×D11semidirect
642. C2×C11#3266semidirect
739. SD16C2×C22⋊D11semidirect
773. C11C2×#3266semidirect
895. C2#13080120direct (N × H)

Maximal subgroups

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

subgroupindex
C22×SD16×D112
C2×Q8×C22⋊D112
C2×#106233602
#130801202
C2×#106228032
C2×#106227472
C2×#106228012
C2×#106227982
C2×#106227752
C2×#106228522
C2×#106227992
C2×#106228402
C2×#106227822
C2×#106227772
C2×#106227402
C22×C11×#1372
C2×#326611