Finite Group Databasebeta

← C2×#13080243 #15628899

Subgroups — C2×#13080243 #15628899

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×#67004C211yesmaximal, characteristic, complemented
2C22×#66985C211yesmaximal, characteristic, complemented
3C2×#10623083C211yesmaximal, characteristic, complemented
4#13080243C2116yesmaximal, direct product factor
5C2×#10622672C211yesmaximal, characteristic, complemented
6C2×#10622665C211yesmaximal, characteristic, complemented
7C2×#10622652C211yesmaximal, characteristic, complemented
8C2×#10622667C211yesmaximal, characteristic, complemented
9C2×#10622629C211yesmaximal, characteristic, complemented
10C2×#10622660C211yesmaximal, characteristic, complemented
11C2×#10622851C211yesmaximal, characteristic, complemented
12C2×#10622653C211yesmaximal, characteristic, complemented
13C2×#10622831C211yesmaximal, characteristic, complemented
14C2×C4×#4324C211yesmaximal, characteristic, complemented
15C2×#10622625C211yesmaximal, characteristic, complemented
16C2×C11×#546C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C23×Dic22C2211yescharacteristic, complemented
21C11×#546—24no—
22C11×#546C2218yescomplemented
23C2×C11×#124C2211yescharacteristic
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121—21no—
27C2×C11×#121C2211yescharacteristic
28C2×C11×#120—21no—
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C22×C11×C22⋊C4—21no—
32C2×#67004—28no—
33C2×#67004C2218yescomplemented
34C22×#4326C2211yescharacteristic, complemented
35C22×#4326C2211yescharacteristic, complemented
36C22×#4325C2211yescharacteristic, complemented
37C2×#66992—21no—
38C22×#4324C2211yescharacteristic
39C22×#4324C2211yescharacteristic
40C22×#4324C2211yescharacteristic
41C22×#4324C2211yescharacteristic
42C2×#66985—28no—
43C2×#66985C2218yescomplemented
44C22×#4323C2211yescharacteristic
45C22×#4323C2211yescharacteristic
46C2×#66983C2211yescharacteristic, complemented
47C2×#66977C2211yescharacteristic
48C22×#4318C2211yescharacteristic
49C22×#4318C2211yescharacteristic, complemented
50#10623083—24no—
51#10623083C2218yescomplemented
52C2×#66949—21no—
53C2×#66938—21no—
54C2×(C22⋊D11)⋊C4—21no—
55C2×#66928C2211yescharacteristic, complemented
56C2×C4×Dic22C2211yescharacteristic, complemented
57#10622851C2218yescomplemented
58C2×#66899C2211yescharacteristic, complemented
59#10622831C2218yescomplemented
60C2×#66896C2211yescharacteristic
61C2×#66896C2211yescharacteristic
62C2×C22⋊(C11⋊C8)C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
64#10622672C2218yescomplemented
65#10622667C2218yescomplemented
66#10622665C2218yescomplemented
67#10622660C2218yescomplemented
68#10622653C2218yescomplemented
69#10622652C2218yescomplemented
70C4×#4324C2218yescomplemented
71#10622629C2218yescomplemented
72#10622625C2218yescomplemented
73C2×#66874C2211yescharacteristic, complemented
74C2×#66874C2211yescharacteristic, complemented
75C2×#66873C2211yescharacteristic, complemented
76C2×#66872C2211yescharacteristic, complemented
77C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
78C2×C4×C11⋊C8C2211yescharacteristic, complemented
79C25×C11—21no—
80C2×C11×#41—22no—
81C2×C11×#41—24no—
82C2×C11×#41—42no—
83C2×C11×#41C2314yes—
84C22×Q8×C11C2311yescharacteristic
85C22×D4×C11—24no—
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—22no—
90C22×D4×C11—42no—
91C22×D4×C11D411yescharacteristic
92C22×D4×C11C2311yescharacteristic
93C22×D4×C11C2314yes—
94C22×D4×C11C2311yescharacteristic
95C23×C4×C11—21no—
96C23×C4×C11—21no—
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C22×C22⋊D11—21no—
100C22×C22⋊D11—21no—
101C23×Dic11—21no—
102C2×#4339—22no—
103C2×#4339—24no—
104C2×#4339—42no—
105C2×#4339C2314yes—
106C22×D44C2311yescharacteristic
107C22×C4×D11—21no—
108C22×Dic22—24no—
109C22×Dic22—21no—
110C22×Dic22—22no—
111C22×Dic22—42no—
112C22×Dic22C2311yescharacteristic
113C22×Dic22C2311yescharacteristic
114C22×Dic22C2314yescomplemented
115C11×#124—22no—
116C11×#124C2314yes—
117C11×#123—28no—
118C11×C22⋊Q8—22no—
119C11×C22⋊Q8C2314yes—
120C11×#121—22no—
121C11×#121—28no—
122C11×#121C2314yes—
123C11×#120—28no—
124C4×D4×C11—22no—
125C4×D4×C11D414yes—
126C4×D4×C11C2314yes—
127C4×D4×C11C2314yes—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4D411yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—28no—
137C2×C11×C22⋊C4D411yescharacteristic
138C2×C11×C22⋊C4D411yescharacteristic
139C2×C42×C11C2311yescharacteristic
140C2×C22⋊Dic11—21no—
141#67004—232no—
142C2×#4326—24no—
143C2×#4326—24no—
144C2×#4326C2314yescomplemented
145C2×#4326C2314yescomplemented
146C2×#4325—42no—
147C2×#4325C2314yescomplemented
148#66992—28no—
149C2×#4324—24no—
150C2×#4324—24no—
151C2×#4324—42no—
152C2×#4324D418yescomplemented
153C2×#4324C2314yes—
154C2×#4324C2314yes—
155C2×#4324C2314yes—
156C2×#4324C2314yes—
157#66985—232no—
158C2×#4323—24no—
159C2×#4323—24no—
160C2×#4323C2314yes—
161C2×#4323C2314yes—
162#66983—22no—
163#66983C2314yescomplemented
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4—21no—
167C2×C4⋊Dic11C2311yescharacteristic
168#66977—22no—
169#66977C2314yes—
170C2×Dic11⋊C4—21no—
171C2×Dic11⋊C4—21no—
172C2×C4×Dic11—21no—
173C2×#4318—24no—
174C2×#4318—24no—
175C2×#4318C2314yes—
176C2×#4318C2314yescomplemented
177C22×C11⋊C8C2311yescharacteristic
178C22×C11⋊C8C2311yescharacteristic
179C22×C11⋊C8C2311yescharacteristic
180C22×C11⋊C8C2311yescharacteristic
181#66949—28no—
182#66938—28no—
183(C22⋊D11)⋊C4—28no—
184#66928—22no—
185#66928C2314yescomplemented
186C4×Dic22—22no—
187C4×Dic22C2314yescomplemented
188#66899C2314yescomplemented
189#66896C2314yes—
190#66896C2314yes—
191C22⋊(C11⋊C8)C2314yes—
192C22⋊(C11⋊C8)C2314yescomplemented
193#66874C2314yescomplemented
194#66874C2314yescomplemented
195#66873C2314yescomplemented
196#66872C2314yescomplemented
197C4⋊(C11⋊C8)C2314yescomplemented
198C4×C11⋊C8C2314yescomplemented
199C2×#3275—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11—21no—
202C24×C11—24no—
203C24×C11—44no—
204C24×C11—44no—
205C24×C11—82no—
206C24×C11C2×D411yescharacteristic
207C24×C11C2×D411yescharacteristic
208C23×D11—21no—
209C11×#41—28no—
210C11×#41—44no—
211C11×#41—48no—
212C2×Q8×C11—21no—
213C2×Q8×C11—22no—
214C2×Q8×C11—22no—
215C2×Q8×C11C2412yes—
216C2×D4×C11—28no—
217C2×D4×C11—24no—
218C2×D4×C11—24no—
219C2×D4×C11—21no—
220C2×D4×C11—22no—
221C2×D4×C11—24no—
222C2×D4×C11—21no—
223C2×D4×C11—22no—
224C2×D4×C11—22no—
225C2×D4×C11—44no—
226C2×D4×C11—48no—
227C2×D4×C11—42no—
228C2×D4×C11—44no—
229C2×D4×C11—44no—
230C2×D4×C11—82no—
231C2×D4×C11C2×D414yes—
232C2×D4×C11C2×D414yes—
233C2×D4×C11C2412yes—
234C2×D4×C11C2412yes—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—24no—
242C22×C4×C11—24no—
243C22×C4×C11—44no—
244C22×C4×C11—82no—
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D412yes—
251C22×C4×C11C2412yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2411yescharacteristic
254C2×C22⋊D11—24no—
255C2×C22⋊D11—24no—
256C2×C22⋊D11—44no—
257C2×C22⋊D11—44no—
258C22×Dic11—21no—
259C22×Dic11—24no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—44no—
263#4339—28no—
264#4339—44no—
265#4339—48no—
266C2×D44—21no—
267C2×D44—22no—
268C2×D44—22no—
269C2×D44C2412yes—
270C2×C4×D11—24no—
271C2×C4×D11—44no—
272C2×Dic22—28no—
273C2×Dic22—21no—
274C2×Dic22—22no—
275C2×Dic22—21no—
276C2×Dic22—24no—
277C2×Dic22—22no—
278C2×Dic22—22no—
279C2×Dic22—44no—
280C2×Dic22—48no—
281C2×Dic22—44no—
282C2×Dic22C2×D414yes—
283C2×Dic22C2412yes—
284C2×Dic22C2412yes—
285C11×C4⋊C4—24no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4C2×D414yes—
288C11×C4⋊C4C2412yes—
289C11×C22⋊C4—24no—
290C11×C22⋊C4—24no—
291C11×C22⋊C4—24no—
292C11×C22⋊C4—24no—
293C11×C22⋊C4—24no—
294C11×C22⋊C4C2×D414yes—
295C11×C22⋊C4C2×D414yes—
296C42×C11C2×D412yes—
297C42×C11C2412yes—
298C22⋊Dic11—24no—
299#4326—28no—
300#4326—28no—
301#4325—44no—
302#4324—28no—
303#4324—28no—
304#4324—44no—
305#4324C2×D4116yescomplemented
306#4323—28no—
307#4323—28no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—24no—
311C4⋊Dic11—21no—
312C4⋊Dic11C2412yes—
313Dic11⋊C4—24no—
314Dic11⋊C4—24no—
315C4×Dic11—24no—
316#4318—28no—
317#4318—28no—
318C2×C11⋊C8—22no—
319C2×C11⋊C8—22no—
320C2×C11⋊C8—22no—
321C2×C11⋊C8C2×D414yes—
322C2×C11⋊C8C2412yes—
323C2×C11⋊C8C2412yes—
324C2×C11⋊C8C2412yes—
325C2×C11⋊C8C2412yes—
326C22×#137—111no—
327C22×AGL(1,ℤ/8)—111no—
328C2×#548—111no—
329C2×#546D1111yescharacteristic, complemented
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×#448—111no—
339C2×#450—111no—
340C2×C4×SD16—111no—
341C2×#436—111no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—24no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—48no—
352C23×C11—48no—
353C23×C11—42no—
354C23×C11—42no—
355C23×C11—42no—
356C23×C11—42no—
357C23×C11—42no—
358C23×C11—84no—
359C23×C11—816no—
360C23×C11C22×D412yes—
361C23×C11C22×D412yes—
362C23×C11C22×D411yescharacteristic
363C22×D11—22no—
364C22×D11—42no—
365C22×D11—42no—
366C22×D11—42no—
367Q8×C11—22no—
368Q8×C11—22no—
369Q8×C11—42no—
370D4×C11—24no—
371D4×C11—22no—
372D4×C11—22no—
373D4×C11—22no—
374D4×C11—44no—
375D4×C11—48no—
376D4×C11—48no—
377D4×C11—42no—
378D4×C11—84no—
379D4×C11C22×D414yes—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—24no—
385C2×C4×C11—24no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—48no—
393C2×C4×C11—42no—
394C2×C4×C11—42no—
395C2×C4×C11—84no—
396C2×C4×C11C22×D412yes—
397C2×C4×C11C22×D412yes—
398C2×C4×C11C22×D412yes—
399C2×C4×C11C22×D412yes—
400C2×C4×C11C22×D412yes—
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11H(5,𝔽2)12yes—
403C2×C4×C11C2511yescharacteristic
404C22⋊D11—48no—
405C22⋊D11—48no—
406C2×Dic11—24no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—48no—
411C2×Dic11—42no—
412C2×Dic11—42no—
413D44—22no—
414D44—22no—
415D44—42no—
416C4×D11—48no—
417Dic22—24no—
418Dic22—22no—
419Dic22—22no—
420Dic22—22no—
421Dic22—48no—
422Dic22—42no—
423Dic22C22×D414yes—
424C11⋊C8—22no—
425C11⋊C8—22no—
426C11⋊C8—22no—
427C11⋊C8C22×D414yes—
428C22×#41—111no—
429C22×#41C2×D1111yescharacteristic
430C23×Q8—111no—
431C23×D4C2×D1111yescharacteristic
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×SD16—111no—
442C22×SD16—111no—
443C22×D8—111no—
444C22×D8—111no—
445C22×M16—111no—
446C22×M16—111no—
447#548—118no—
448#548—224no—
449#546—24no—
450#546C2×D1118yescomplemented
451C2×#124—111no—
452C2×#124—221no—
453C2×#124C2×D1111yescharacteristic
454C2×#123—21no—
455C2×C22⋊Q8—111no—
456C2×C22⋊Q8—221no—
457C2×C22⋊Q8C2×D1111yescharacteristic
458C2×#121—21no—
459C2×#121—111no—
460C2×#121—221no—
461C2×#121C2×D1111yescharacteristic
462C2×#120—21no—
463C2×C4×Q8—111no—
464C2×C4×D4—221no—
465C2×C4×D4C2×D1111yescharacteristic
466C2×C4×D4C2×D1111yescharacteristic
467C22×C22⋊C4—21no—
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#448—118no—
477C4×SD16—118no—
478#436—118no—
479C2×#106—111no—
480C2×C4⋊C8—111no—
481C2×#103—111no—
482C2×#103—111no—
483C2×#103—111no—
484C2×#102—111no—
485C2×#102—111no—
486C2×#102—111no—
487C2×C22⋊C8—111no—
488C2×C22⋊C8—111no—
489C2×C4×C8—111no—
490C22×C11—22no—
491C22×C11—22no—
492C22×C11—24no—
493C22×C11—22no—
494C22×C11—22no—
495C22×C11—22no—
496C22×C11—22no—
497C22×C11—44no—
498C22×C11—44no—
499C22×C11—48no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—816no—
506C22×C11—84no—
507C22×C11D4212yes—
508C22×C11#57512yes—
509C22×C11#57712yes—
510C22×C11C23×D411yescharacteristic
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—84no—
515C4×C11—22no—
516C4×C11—22no—
517C4×C11—22no—
518C4×C11—22no—
519C4×C11—42no—
520C4×C11—42no—
521C4×C11D4212yes—
522C4×C11C23×D411yescharacteristic
523C4×C11C2×H(5,𝔽2)11yescharacteristic
524Dic11—24no—
525Dic11—42no—
526Dic11—42no—
527C25—21no—
528C2×#41—22no—
529C2×#41—24no—
530C2×#41—42no—
531C2×#41—114no—
532C2×#41—224no—
533C2×#41—222no—
534C2×#41—442no—
535C2×#41C22×D1114yes—
536C22×Q8—111no—
537C22×Q8—111no—
538C22×Q8—114no—
539C22×Q8—224no—
540C22×Q8—221no—
541C22×Q8—222no—
542C22×Q8—442no—
543C22×Q8C22×D1111yescharacteristic
544C22×D4—24no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—42no—
550C22×D4—111no—
551C22×D4—221no—
552C22×D4—221no—
553C22×D4C22⋊D1111yescharacteristic
554C22×D4C22×D1111yescharacteristic
555C22×D4C22×D1114yes—
556C22×D4C22×D1111yescharacteristic
557C23×C4—21no—
558C23×C4—21no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4C22×D1111yescharacteristic
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—118no—
570C2×SD16—114no—
571C2×SD16—114no—
572C2×SD16—114no—
573C2×SD16—114no—
574C2×SD16—114no—
575C2×SD16—224no—
576C2×SD16—224no—
577C2×SD16—442no—
578C2×SD16—442no—
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×C8—111no—
590C22×C8—111no—
591#124—22no—
592#124—114no—
593#124—228no—
594#124—222no—
595#124C22×D1114yes—
596#123—28no—
597C22⋊Q8—22no—
598C22⋊Q8—114no—
599C22⋊Q8—222no—
600C22⋊Q8—228no—
601C22⋊Q8C22×D1114yes—
602#121—22no—
603#121—28no—
604#121—114no—
605#121—228no—
606#121—222no—
607#121C22×D1114yes—
608#120—28no—
609C4×Q8—114no—
610C4×Q8—222no—
611C4×D4—22no—
612C4×D4—228no—
613C4×D4C22⋊D1114yes—
614C4×D4C22×D1114yes—
615C4×D4C22×D1114yes—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—221no—
619C2×C4⋊C4—221no—
620C2×C4⋊C4C22⋊D1111yescharacteristic
621C2×C4⋊C4C22×D1111yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—28no—
628C2×C22⋊C4—221no—
629C2×C22⋊C4—221no—
630C2×C22⋊C4—221no—
631C2×C22⋊C4—221no—
632C2×C22⋊C4C22⋊D1111yescharacteristic
633C2×C22⋊C4C22⋊D1111yescharacteristic
634C2×C42—221no—
635C2×C42C22×D1111yescharacteristic
636#106—114no—
637C4⋊C8—114no—
638#103—114no—
639#103—114no—
640#103—114no—
641#102—114no—
642#102—114no—
643#102—114no—
644C22⋊C8—114no—
645C22⋊C8—114no—
646C4×C8—114no—
647C2×C11—42no—
648C2×C11—42no—
649C2×C11—44no—
650C2×C11—82no—
651C2×C11#327514yescomplemented
652C2×C11C2×D4211yescharacteristic
653C2×C11C2×#57511yescharacteristic
654C2×C11C2×#57711yescharacteristic
655D11—82no—
656C24—21no—
657C24—21no—
658C24—24no—
659C24—44no—
660C24—44no—
661C24—82no—
662C24—221no—
663C24C2×C22⋊D1111yescharacteristic
664C24C2×C22⋊D1111yescharacteristic
665#41—28no—
666#41—44no—
667#41—48no—
668#41—228no—
669#41—444no—
670#41—448no—
671C2×Q8—21no—
672C2×Q8—22no—
673C2×Q8—22no—
674C2×Q8—114no—
675C2×Q8—112no—
676C2×Q8—112no—
677C2×Q8—228no—
678C2×Q8—222no—
679C2×Q8—221no—
680C2×Q8—224no—
681C2×Q8—221no—
682C2×Q8—222no—
683C2×Q8—222no—
684C2×Q8—444no—
685C2×Q8—444no—
686C2×Q8—448no—
687C2×Q8C23×D1112yes—
688C2×D4—28no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—21no—
695C2×D4—24no—
696C2×D4—21no—
697C2×D4—44no—
698C2×D4—48no—
699C2×D4—42no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—82no—
703C2×D4—112no—
704C2×D4—224no—
705C2×D4—224no—
706C2×D4—222no—
707C2×D4—222no—
708C2×D4—221no—
709C2×D4—444no—
710C2×D4—444no—
711C2×D4D4×D1114yes—
712C2×D4C2×C22⋊D1114yes—
713C2×D4C23×D1112yes—
714C2×D4C23×D1112yes—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—44no—
724C22×C4—82no—
725C22×C4—221no—
726C22×C4—224no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—224no—
730C22×C4—444no—
731C22×C4—444no—
732C22×C4C2×C22⋊D1112yes—
733C22×C4C2×C22⋊D1112yes—
734C22×C4C2×C22⋊D1111yescharacteristic
735C22×C4C2×C22⋊D1111yescharacteristic
736C22×C4C2×C22⋊D1111yescharacteristic
737C22×C4C2×C22⋊D1111yescharacteristic
738C22×C4C23×D1112yes—
739C22×C4C23×D1112yes—
740C22×C4C23×D1111yescharacteristic
741Q16—228no—
742Q16—228no—
743SD16—1116no—
744SD16—228no—
745SD16—228no—
746SD16—444no—
747SD16—444no—
748D8—228no—
749D8—228no—
750M16—228no—
751M16—228no—
752C2×C8—114no—
753C2×C8—112no—
754C2×C8—112no—
755C2×C8—112no—
756C2×C8—112no—
757C2×C8—222no—
758C2×C8—222no—
759C2×C8—222no—
760C4⋊C4—24no—
761C4⋊C4—21no—
762C4⋊C4—112no—
763C4⋊C4—221no—
764C4⋊C4—224no—
765C4⋊C4—224no—
766C4⋊C4C2×C22⋊D1114yes—
767C4⋊C4C23×D1112yes—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—224no—
774C22⋊C4—224no—
775C22⋊C4—224no—
776C22⋊C4—224no—
777C22⋊C4C2×C22⋊D1114yes—
778C22⋊C4C2×C22⋊D1114yes—
779C42—224no—
780C42C2×C22⋊D1112yes—
781C42C23×D1112yes—
782C11C2×#327511yescharacteristic, complemented, Sylow
783C23—22no—
784C23—22no—
785C23—24no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—48no—
793C23—48no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—84no—
800C23—816no—
801C23—222no—
802C23—442no—
803C23—442no—
804C23—442no—
805C23C22×C22⋊D1112yes—
806C23C22×C22⋊D1112yes—
807C23C22×C22⋊D1111yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—42no—
811Q8—114no—
812Q8—224no—
813Q8—222no—
814Q8—222no—
815Q8—222no—
816Q8—448no—
817Q8—442no—
818D4—24no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—44no—
823D4—48no—
824D4—48no—
825D4—42no—
826D4—84no—
827D4—222no—
828D4—222no—
829D4—448no—
830D4—448no—
831D4—442no—
832D4C2×D4×D1114yes—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—48no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—84no—
849C2×C4—224no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—448no—
854C2×C4—448no—
855C2×C4—442no—
856C2×C4—442no—
857C2×C4C2×D4×D1112yes—
858C2×C4#6703712yes—
859C2×C4C22×C22⋊D1112yes—
860C2×C4C22×C22⋊D1112yes—
861C2×C4C22×C22⋊D1112yes—
862C2×C4C22×C22⋊D1112yes—
863C2×C4C22×C22⋊D1111yescharacteristic
864C2×C4C24×D1111yescharacteristic
865C8—114no—
866C8—222no—
867C8—222no—
868C8—222no—
869C22—22no—
870C22—22no—
871C22—24no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—44no—
877C22—44no—
878C22—48no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—816no—
885C22—84no—
886C22—442no—
887C22—442no—
888C22—442no—
889C22—884no—
890C22D4×C22⋊D1112yes—
891C22#1062335312yes—
892C22#1062336712yes—
893C22C23×C22⋊D1111yescharacteristic
894C4—22no—
895C4—22no—
896C4—22no—
897C4—22no—
898C4—42no—
899C4—42no—
900C4—224no—
901C4—442no—
902C4—442no—
903C4D4×C22⋊D1112yes—
904C4C22×D4×D1111yescharacteristic
905C4C2×#6703711yescharacteristic
906C2—42no—
907C2—42no—
908C2—44no—
909C2—82no—
910C2—882no—
911C2#1308024314yesdirect product factor
912C2C2×D4×C22⋊D1111yescharacteristic
913C2C2×#1062335311yescharacteristic
914C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#546C2
socleC23×C11C22×D4
hypercenterC2×#546D11
hypocenterC11C2×#3275
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C22×#67004C2semidirect
2. C22×#66985C2semidirect
3. C2×#10623083C2semidirect
4. #13080243C2direct (N × H)
5. C2×#10622672C2semidirect
6. C2×#10622665C2semidirect
7. C2×#10622652C2semidirect
8. C2×#10622667C2semidirect
9. C2×#10622629C2semidirect
10. C2×#10622660C2semidirect
11. C2×#10622851C2semidirect
12. C2×#10622653C2semidirect
13. C2×#10622831C2semidirect
14. C2×C4×#4324C2semidirect
15. C2×#10622625C2semidirect
16. C2×C11×#546C2semidirect
20. C23×Dic22C22semidirect
22. C11×#546C22semidirect
33. C2×#67004C22semidirect
34. C22×#4326C22semidirect
35. C22×#4326C22semidirect
36. C22×#4325C22semidirect
43. C2×#66985C22semidirect
46. C2×#66983C22semidirect
49. C22×#4318C22semidirect
51. #10623083C22semidirect
55. C2×#66928C22semidirect
56. C2×C4×Dic22C22semidirect
57. #10622851C22semidirect
58. C2×#66899C22semidirect
59. #10622831C22semidirect
63. C2×C22⋊(C11⋊C8)C22semidirect
64. #10622672C22semidirect
65. #10622667C22semidirect
66. #10622665C22semidirect
67. #10622660C22semidirect
68. #10622653C22semidirect
69. #10622652C22semidirect
70. C4×#4324C22semidirect
71. #10622629C22semidirect
72. #10622625C22semidirect
73. C2×#66874C22semidirect
74. C2×#66874C22semidirect
75. C2×#66873C22semidirect
76. C2×#66872C22semidirect
77. C2×C4⋊(C11⋊C8)C22semidirect
78. C2×C4×C11⋊C8C22semidirect
114. C22×Dic22C23semidirect
144. C2×#4326C23semidirect
145. C2×#4326C23semidirect
147. C2×#4325C23semidirect
152. C2×#4324D4semidirect
163. #66983C23semidirect
176. C2×#4318C23semidirect
185. #66928C23semidirect
187. C4×Dic22C23semidirect
188. #66899C23semidirect
192. C22⋊(C11⋊C8)C23semidirect
193. #66874C23semidirect
194. #66874C23semidirect
195. #66873C23semidirect
196. #66872C23semidirect
197. C4⋊(C11⋊C8)C23semidirect
198. C4×C11⋊C8C23semidirect
305. #4324C2×D4semidirect
329. C2×#546D11semidirect
450. #546C2×D11semidirect
651. C2×C11#3275semidirect
782. C11C2×#3275semidirect
911. C2#13080243direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C22×#669852
C2×#106230832
#130802432
C2×#106226722
C2×#106226652
C2×#106226522
C2×#106226672
C2×#106226292
C2×#106226602
C2×#106228512
C2×#106226532
C2×#106228312
C2×C4×#43242
C2×#106226252
C2×C11×#5462
C2×#327511