Finite Group Databasebeta

← C2×#13082105 #15660734

Subgroups — C2×#13082105 #15660734

Order 2816.

12314 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4343C211yesmaximal, characteristic, complemented
2C22×#41×D11C211yesmaximal, characteristic, complemented
3#13082105C2132yesmaximal, direct product factor
4C2×#10623365C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D11C211yesmaximal, characteristic, complemented
6C2×#10623107C211yesmaximal, characteristic, complemented
7C2×#10623162C213yesmaximal, complemented
8C2×#10623081C213yesmaximal, complemented
9C2×#10623207C213yesmaximal, complemented
10C2×#10623140C213yesmaximal, complemented
11C2×#10623199C213yesmaximal, complemented
12C2×#10623158C213yesmaximal, complemented
13C2×#10623137C213yesmaximal, complemented
14C2×C4×#4343C211yesmaximal, characteristic, complemented
15C2×C4×D4×D11C213yesmaximal, complemented
16C2×C11×#548C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic, complemented
18C23×Q8×C11C2211yescharacteristic, complemented
19C2×#41×D11—216no—
20C2×#41×D11C22116yescomplemented
21C22×#4343—216no—
22C22×#4343C2211yescharacteristic
23C22×#4343C2213yescomplemented
24C22×#4343C2213yescomplemented
25C22×#4343C2211yescharacteristic, complemented
26C22×#4343C22116yescomplemented
27C22×Q8×D11C2211yescharacteristic, complemented
28C22×#4341C2213yescomplemented
29C22×D4×D11C2213yes—
30C22×D4×D11C2213yescomplemented
31C22×#4339C2213yescomplemented
32C23×D44C2213yescomplemented
33C23×C4×D11C2213yescomplemented
34C23×C4×D11C2213yescomplemented
35C11×#548C22116yescomplemented
36C2×C11×#124C2213yescomplemented
37C2×C11×C22⋊Q8C2213yescomplemented
38C2×C11×#121C2213yescomplemented
39C2×C4×Q8×C11C2211yescharacteristic, complemented
40C2×C4×D4×C11C2213yescomplemented
41#10623365C22116yescomplemented
42Q8×C22⋊D11C22116yescomplemented
43C2×#66999C2213yescomplemented
44C2×Q8×Dic11C2211yescharacteristic, complemented
45C2×#66997C2213yescomplemented
46C2×#66993C2213yescomplemented
47C2×#66991C2213yescomplemented
48C2×#66990C2216yescomplemented
49C2×D4×Dic11C2213yescomplemented
50C2×#66983C2213yescomplemented
51C2×C4×C22⋊D11C2213yes—
52C2×C4×C22⋊D11C2213yescomplemented
53C2×#66977C2213yescomplemented
54#10623207C22148yescomplemented
55#10623199C22148yescomplemented
56#10623162C22148yescomplemented
57#10623158C22148yescomplemented
58#10623140C22148yescomplemented
59#10623137C22148yescomplemented
60#10623107C22116yescomplemented
61C4×#4343C22116yescomplemented
62#10623081C22148yescomplemented
63C4×D4×D11C22148yescomplemented
64C2×#66950C2213yescomplemented
65C2×#66948C2213yescomplemented
66C2×#66947C2216yescomplemented
67C2×#66946C2213yescomplemented
68C2×#66946C2213yescomplemented
69C2×#66945C2213yescomplemented
70C2×C4⋊C4×D11C2213yescomplemented
71C2×#66937C2216yescomplemented
72C2×#66937C2216yescomplemented
73C2×#66936C2216yescomplemented
74C2×#66935C2216yescomplemented
75C2×(C22⋊D11)⋊C4C2211yescharacteristic
76C2×(C22⋊D11)⋊C4C2216yescomplemented
77C2×(C22⋊D11)⋊C4C2213yescomplemented
78C2×C22⋊C4×D11C2213yescomplemented
79C2×C22⋊C4×D11C2213yescomplemented
80C2×#66928C2213yescomplemented
81C2×C4×D44C2213yescomplemented
82C2×C4×D44C2213yescomplemented
83C2×C42×D11C2213yescomplemented
84C24×D11C2313yes—
85C24×D11C2313yes—
86C2×C11×#41—28no—
87C2×C11×#41C2318yescomplemented
88C22×Q8×C11—28no—
89C22×Q8×C11C2313yes—
90C22×Q8×C11C2311yescharacteristic
91C22×Q8×C11C2318yescomplemented
92C22×D4×C11C2313yes—
93C22×D4×C11C2313yes—
94C23×C4×C11C2313yes—
95C23×C4×C11C2313yes—
96C22×C22⋊D11C2313yes—
97C22×C22⋊D11C2316yes—
98C22×C22⋊D11C2316yes—
99C22×C22⋊D11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2313yes—
102#41×D11—2128no—
103C2×#4343—28no—
104C2×#4343—2128no—
105C2×#4343—224no—
106C2×#4343—224no—
107C2×#4343D4116yescomplemented
108C2×#4343C2318yes—
109C2×#4343C2318yescomplemented
110C2×#4343C23124yescomplemented
111C2×#4343C23124yescomplemented
112C2×Q8×D11—28no—
113C2×Q8×D11C2318yescomplemented
114C2×#4341—224no—
115C2×#4341C23124yescomplemented
116C2×D4×D11—224no—
117C2×D4×D11—224no—
118C2×D4×D11C23124yes—
119C2×D4×D11C23124yescomplemented
120C2×#4339—224no—
121C2×#4339C23124yescomplemented
122C22×D44—224no—
123C22×D44C2313yes—
124C22×D44C2313yes—
125C22×D44C2316yes—
126C22×D44C2313yes—
127C22×D44C23124yescomplemented
128C22×C4×D11—224no—
129C22×C4×D11—224no—
130C22×C4×D11C2313yes—
131C22×C4×D11C2313yes—
132C22×C4×D11C2313yes—
133C22×C4×D11C2313yes—
134C22×C4×D11C2313yes—
135C22×C4×D11C2311yescharacteristic
136C22×C4×D11C2313yes—
137C22×C4×D11C2313yes—
138C22×C4×D11C2313yes—
139C22×C4×D11C23124yescomplemented
140C22×C4×D11C23124yescomplemented
141C22×Dic22C2313yes—
142C11×#124C23124yescomplemented
143C11×C22⋊Q8C23124yescomplemented
144C11×#121C23124yescomplemented
145C4×Q8×C11C2318yescomplemented
146C4×D4×C11C23124yescomplemented
147C2×C11×C4⋊C4C2313yes—
148C2×C11×C4⋊C4C2313yes—
149C2×C11×C22⋊C4C2311yescharacteristic
150C2×C11×C22⋊C4C2313yes—
151C2×C11×C22⋊C4C2316yes—
152C2×C42×C11C2313yes—
153C2×C22⋊Dic11C2313yes—
154C2×C22⋊Dic11C2313yes—
155#66999C23124yescomplemented
156Q8×Dic11C2318yescomplemented
157#66997C23124yescomplemented
158#66993C23124yescomplemented
159#66991C23124yescomplemented
160#66990C23148yescomplemented
161D4×Dic11C23124yescomplemented
162#66983C23124yescomplemented
163C4×C22⋊D11C23124yes—
164C4×C22⋊D11C23124yescomplemented
165C2×(C2×D11)⋊C4C2311yescharacteristic
166C2×(C2×D11)⋊C4C2313yes—
167C2×(C2×D11)⋊C4C2316yes—
168C2×(C2×D11)⋊C4C2316yes—
169C2×(C2×D11)⋊C4C2313yes—
170C2×(C2×D11)⋊C4C2313yes—
171C2×C4⋊Dic11C2313yes—
172C2×C4⋊Dic11C2313yes—
173#66977C23124yescomplemented
174C2×Dic11⋊C4C2311yescharacteristic
175C2×Dic11⋊C4C2316yes—
176C2×Dic11⋊C4C2313yes—
177C2×C4×Dic11C2311yescharacteristic
178C2×C4×Dic11C2313yes—
179C2×C4×Dic11C2313yes—
180#66950C23124yescomplemented
181#66948C23124yescomplemented
182#66947C23148yescomplemented
183#66946C23124yescomplemented
184#66946C23124yescomplemented
185#66945C23124yescomplemented
186C4⋊C4×D11C23124yescomplemented
187#66937C23148yescomplemented
188#66937C23148yescomplemented
189#66936C23148yescomplemented
190#66935C23148yescomplemented
191(C22⋊D11)⋊C4C2318yes—
192(C22⋊D11)⋊C4C23124yescomplemented
193(C22⋊D11)⋊C4C23148yescomplemented
194C22⋊C4×D11C23124yescomplemented
195C22⋊C4×D11C23124yescomplemented
196#66928C23124yescomplemented
197C4×D44C23124yescomplemented
198C4×D44C23124yescomplemented
199C42×D11C23124yescomplemented
200C2×D4×#41—111nomaximal, Sylow
201C24×C11C2413yes—
202C24×C11C2411yescharacteristic
203C23×D11—212no—
204C23×D11—212no—
205C23×D11—212no—
206C23×D11—212no—
207C23×D11—46no—
208C23×D11—46no—
209C23×D11C2413yes—
210C23×D11C24112yes—
211C23×D11C24112yes—
212C23×D11C2413yes—
213C23×D11C2411yescharacteristic
214C11×#41—232no—
215C2×Q8×C11—232no—
216C2×Q8×C11—212no—
217C2×Q8×C11C2×D418yescomplemented
218C2×Q8×C11C24112yes—
219C2×Q8×C11C2414yes—
220C2×D4×C11—212no—
221C2×D4×C11—212no—
222C2×D4×C11C24112yes—
223C2×D4×C11C24112yes—
224C22×C4×C11—212no—
225C22×C4×C11—212no—
226C22×C4×C11C2413yes—
227C22×C4×C11C2411yescharacteristic
228C22×C4×C11C2413yes—
229C22×C4×C11C2411yescharacteristic
230C22×C4×C11C24112yes—
231C22×C4×C11C24112yes—
232C22×C4×C11C2413yes—
233C2×C22⋊D11—212no—
234C2×C22⋊D11—224no—
235C2×C22⋊D11—412no—
236C2×C22⋊D11#4118yescomplemented
237C2×C22⋊D11C24112yes—
238C2×C22⋊D11C24124yes—
239C2×C22⋊D11C24124yes—
240C2×C22⋊D11C2414yes—
241C22×Dic11—24no—
242C22×Dic11—212no—
243C22×Dic11C2414yes—
244C22×Dic11C24112yes—
245C22×Dic11C2413yes—
246C22×Dic11C2413yes—
247C22×Dic11C2411yescharacteristic
248C22×Dic11C2411yescharacteristic
249C22×Dic11C2411yescharacteristic
250#4343—296no—
251#4343—296no—
252#4343—232no—
253#4343C2×D4164yescomplemented
254Q8×D11—232no—
255#4341—296no—
256D4×D11—296no—
257D4×D11—296no—
258#4339—296no—
259C2×D44—296no—
260C2×D44—224no—
261C2×D44—212no—
262C2×D44—212no—
263C2×D44C2×D4124yescomplemented
264C2×D44C24112yes—
265C2×D44C24112yes—
266C2×D44C24124yes—
267C2×D44C24112yes—
268C2×C4×D11—24no—
269C2×C4×D11—212no—
270C2×C4×D11—212no—
271C2×C4×D11—296no—
272C2×C4×D11—296no—
273C2×C4×D11—212no—
274C2×C4×D11—212no—
275C2×C4×D11—212no—
276C2×C4×D11—212no—
277C2×C4×D11—46no—
278C2×C4×D11C2×D4124yescomplemented
279C2×C4×D11C24112yes—
280C2×C4×D11C24112yes—
281C2×C4×D11C24112yes—
282C2×C4×D11C24112yes—
283C2×C4×D11C24112yes—
284C2×C4×D11C2414yes—
285C2×C4×D11C24112yes—
286C2×C4×D11C24112yes—
287C2×C4×D11C24112yes—
288C2×Dic22—212no—
289C2×Dic22C24112yes—
290C11×C4⋊C4C24112yes—
291C11×C4⋊C4C24112yes—
292C11×C22⋊C4C2414yes—
293C11×C22⋊C4C24112yes—
294C11×C22⋊C4C24124yes—
295C42×C11C24112yes—
296C22⋊Dic11C24112yes—
297C22⋊Dic11C24112yes—
298(C2×D11)⋊C4C2414yes—
299(C2×D11)⋊C4C24112yes—
300(C2×D11)⋊C4C24124yes—
301(C2×D11)⋊C4C24124yes—
302(C2×D11)⋊C4C24112yes—
303(C2×D11)⋊C4C24112yes—
304C4⋊Dic11C24112yes—
305C4⋊Dic11C24112yes—
306Dic11⋊C4C2414yes—
307Dic11⋊C4C24124yes—
308Dic11⋊C4C24112yes—
309C4×Dic11C2414yes—
310C4×Dic11C24112yes—
311C4×Dic11C24112yes—
312C23×#41—111no—
313C23×#41—111no—
314D4×#41—1132no—
315C2×#550—111no—
316C2×D4×Q8—111no—
317C2×#548—111no—
318C2×#548D1111yescharacteristic, complemented
319C2×#547—113no—
320C2×#546—113no—
321C2×#546—113no—
322C2×D42—113no—
323C2×#532—113no—
324C2×#525—113no—
325C2×#525—113no—
326C2×C4×#41—111no—
327C22×C4×D4—113no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—26no—
331C23×C11—26no—
332C23×C11—26no—
333C23×C11C2×#4114yescomplemented
334C23×C11C2516yes—
335C23×C11C2512yes—
336C23×C11C2511yescharacteristic
337C22×D11—22no—
338C22×D11—26no—
339C22×D11—26no—
340C22×D11—22no—
341C22×D11—26no—
342C22×D11—26no—
343C22×D11—224no—
344C22×D11—26no—
345C22×D11—224no—
346C22×D11—224no—
347C22×D11—224no—
348C22×D11—412no—
349C22×D11—412no—
350C22×D11—448no—
351C22×D11—448no—
352C22×D11C22×D4112yes—
353C22×D11C2×#4114yescomplemented
354C22×D11C2516yes—
355C22×D11C2516yes—
356C22×D11C2512yes—
357Q8×C11—224no—
358Q8×C11C22×D4116yescomplemented
359D4×C11—224no—
360D4×C11—224no—
361C2×C4×C11—22no—
362C2×C4×C11—26no—
363C2×C4×C11—26no—
364C2×C4×C11—22no—
365C2×C4×C11—224no—
366C2×C4×C11—224no—
367C2×C4×C11C22×D4112yes—
368C2×C4×C11C2516yes—
369C2×C4×C11C2512yes—
370C2×C4×C11C2516yes—
371C2×C4×C11C2512yes—
372C2×C4×C11C2516yes—
373C22⋊D11—248no—
374C22⋊D11—224no—
375C22⋊D11—424no—
376C22⋊D11C2×#41116yescomplemented
377C2×Dic11—26no—
378C2×Dic11—22no—
379C2×Dic11—26no—
380C2×Dic11—28no—
381C2×Dic11—224no—
382C2×Dic11C22×D414yes—
383C2×Dic11C2×#4114yescomplemented
384C2×Dic11C2516yes—
385C2×Dic11C2516yes—
386C2×Dic11C2512yes—
387C2×Dic11C2512yes—
388C2×Dic11C2512yes—
389D44—248no—
390D44—224no—
391D44—224no—
392D44C22×D4148yescomplemented
393C4×D11—224no—
394C4×D11—224no—
395C4×D11—224no—
396C4×D11—224no—
397C4×D11—28no—
398C4×D11—224no—
399C4×D11—224no—
400C4×D11—412no—
401C4×D11C22×D4148yescomplemented
402Dic22—224no—
403C22×#41—1116no—
404C22×#41—111no—
405C22×#41—113no—
406C22×#41—113no—
407C22×#41—111no—
408C22×#41—1116no—
409C22×#41—113no—
410C22×#41—113no—
411C22×#41—2216no—
412C22×#41—2216no—
413C22×#41C2×D1111yescharacteristic, complemented
414C23×Q8—111no—
415C23×Q8C2×D1111yescharacteristic, complemented
416C23×D4—113no—
417C23×D4—113no—
418C23×D4—113no—
419C24×C4—113no—
420C24×C4—113no—
421#550—1116no—
422D4×Q8—1116no—
423#548—1116no—
424#548C2×D11116yescomplemented
425#547—1148no—
426#546—1148no—
427#546—1148no—
428D42—1148no—
429#532—1148no—
430C2×C4⋊Q8—113no—
431C2×#127—113no—
432C2×#124—113no—
433C2×#124C2×D1113yescomplemented
434#525—1148no—
435#525—1148no—
436C2×#123—116no—
437C2×#123—116no—
438C2×C22⋊Q8—113no—
439C2×C22⋊Q8—113no—
440C2×C22⋊Q8—113no—
441C2×C22⋊Q8C2×D1113yescomplemented
442C2×#121—113no—
443C2×#121—113no—
444C2×#121—113no—
445C2×#121—116no—
446C2×#121—116no—
447C2×#121C2×D1113yescomplemented
448C2×#120—116no—
449C2×#120—116no—
450C4×#41—1116no—
451C2×C4×Q8—111no—
452C2×C4×Q8C2×D1111yescharacteristic, complemented
453C2×C4×D4—113no—
454C2×C4×D4—113no—
455C2×C4×D4—113no—
456C2×C4×D4—1148no—
457C2×C4×D4—113no—
458C2×C4×D4—113no—
459C2×C4×D4—111no—
460C2×C4×D4—113no—
461C2×C4×D4—116no—
462C2×C4×D4—113no—
463C2×C4×D4—113no—
464C2×C4×D4C2×D1113yescomplemented
465C2×#117—113no—
466C22×C4⋊C4—113no—
467C22×C22⋊C4—113no—
468C22×C22⋊C4—113no—
469C22×C42—113no—
470C22×C11—22no—
471C22×C11—22no—
472C22×C11—28no—
473C22×C11—26no—
474C22×C11—26no—
475C22×C11—26no—
476C22×C11—412no—
477C22×C11C23×D412yes—
478C22×C11C22×#4112yes—
479C22×C11C22×#4114yescomplemented
480C22×C11#58512yes—
481C22×C11C2611yescharacteristic
482C2×D11—22no—
483C2×D11—26no—
484C2×D11—22no—
485C2×D11—26no—
486C2×D11—28no—
487C2×D11—224no—
488C2×D11—26no—
489C2×D11—26no—
490C2×D11—26no—
491C2×D11—448no—
492C2×D11—448no—
493C2×D11—412no—
494C2×D11C23×D4112yes—
495C2×D11C22×#4114yescomplemented
496C4×C11—22no—
497C4×C11—26no—
498C4×C11—26no—
499C4×C11—22no—
500C4×C11C23×D4112yes—
501Dic11—26no—
502Dic11—22no—
503Dic11—26no—
504Dic11C23×D414yes—
505Dic11C22×#4114yescomplemented
506C25—113no—
507C25—113no—
508C2×#41—28no—
509C2×#41—1116no—
510C2×#41—118no—
511C2×#41—1124no—
512C2×#41—1124no—
513C2×#41—118no—
514C2×#41—1124no—
515C2×#41—1124no—
516C2×#41—2224no—
517C2×#41—2224no—
518C2×#41—2224no—
519C2×#41—2224no—
520C2×#41—22128no—
521C2×#41—22128no—
522C2×#41—228no—
523C2×#41C22×D1118yescomplemented
524C22×Q8—28no—
525C22×Q8—118no—
526C22×Q8—113no—
527C22×Q8—228no—
528C22×Q8C22×D1113yes—
529C22×Q8C22×D1111yescharacteristic
530C22×Q8C22×D1118yescomplemented
531C22×D4—111no—
532C22×D4—113no—
533C22×D4—116no—
534C22×D4—116no—
535C22×D4—1124no—
536C22×D4—1124no—
537C22×D4—113no—
538C22×D4—113no—
539C22×D4—116no—
540C22×D4—113no—
541C22×D4—1124no—
542C22×D4—2224no—
543C22×D4—2224no—
544C22×D4—2224no—
545C22×D4C22×D1113yes—
546C22×D4C22×D1113yes—
547C23×C4—113no—
548C23×C4—111no—
549C23×C4—113no—
550C23×C4—113no—
551C23×C4—113no—
552C23×C4—113no—
553C23×C4—111no—
554C23×C4—113no—
555C23×C4—113no—
556C23×C4—113no—
557C23×C4—1124no—
558C23×C4—1124no—
559C23×C4—113no—
560C23×C4—2224no—
561C23×C4—2224no—
562C23×C4C22×D1113yes—
563C23×C4C22×D1113yes—
564C4⋊Q8—1124no—
565#127—1124no—
566#124—1124no—
567#124C22×D11124yescomplemented
568#123—1148no—
569#123—1148no—
570C22⋊Q8—1124no—
571C22⋊Q8—1124no—
572C22⋊Q8—1124no—
573C22⋊Q8C22×D11124yescomplemented
574#121—1124no—
575#121—1124no—
576#121—1124no—
577#121—1148no—
578#121—1148no—
579#121C22×D11124yescomplemented
580#120—1148no—
581#120—1148no—
582C4×Q8—118no—
583C4×Q8C22×D1118yescomplemented
584C4×D4—1124no—
585C4×D4—1124no—
586C4×D4—1124no—
587C4×D4—1124no—
588C4×D4—1124no—
589C4×D4—118no—
590C4×D4—1124no—
591C4×D4—1148no—
592C4×D4—1124no—
593C4×D4—1124no—
594C4×D4C22×D11124yescomplemented
595#117—1124no—
596C2×C4⋊C4—111no—
597C2×C4⋊C4—113no—
598C2×C4⋊C4—113no—
599C2×C4⋊C4—113no—
600C2×C4⋊C4—116no—
601C2×C4⋊C4—1124no—
602C2×C4⋊C4C22×D1113yes—
603C2×C4⋊C4C22×D1113yes—
604C2×C22⋊C4—113no—
605C2×C22⋊C4—113no—
606C2×C22⋊C4—111no—
607C2×C22⋊C4—113no—
608C2×C22⋊C4—113no—
609C2×C22⋊C4—113no—
610C2×C22⋊C4—116no—
611C2×C22⋊C4—116no—
612C2×C22⋊C4—1124no—
613C2×C22⋊C4—1124no—
614C2×C22⋊C4C22×D1111yescharacteristic
615C2×C22⋊C4C22×D1113yes—
616C2×C22⋊C4C22×D1116yes—
617C2×C42—113no—
618C2×C42—111no—
619C2×C42—113no—
620C2×C42—1124no—
621C2×C42C22×D1113yes—
622C2×C11—24no—
623C2×C11—46no—
624C2×C11D4×#4114yescomplemented
625C2×C11C24×D411yescharacteristic
626C2×C11C23×#4111yescharacteristic
627C2×C11C2×#58511yescharacteristic
628D11—24no—
629D11—212no—
630D11—46no—
631C24—111no—
632C24—113no—
633C24—113no—
634C24—1112no—
635C24—1112no—
636C24—2212no—
637C24—2212no—
638C24—2212no—
639C24—2212no—
640C24—446no—
641C24—446no—
642C24C23×D1113yes—
643C24C23×D1111yescharacteristic
644#41—232no—
645#41—1164no—
646#41—2296no—
647#41—2296no—
648#41—2296no—
649#41—2296no—
650#41—2232no—
651C2×Q8—232no—
652C2×Q8—212no—
653C2×Q8—1112no—
654C2×Q8—2232no—
655C2×Q8—2212no—
656C2×Q8D4×D1118yescomplemented
657C2×Q8C23×D11112yes—
658C2×Q8C23×D1114yes—
659C2×D4—212no—
660C2×D4—212no—
661C2×D4—118no—
662C2×D4—114no—
663C2×D4—1112no—
664C2×D4—1124no—
665C2×D4—1124no—
666C2×D4—1124no—
667C2×D4—1112no—
668C2×D4—1112no—
669C2×D4—1124no—
670C2×D4—1112no—
671C2×D4—2296no—
672C2×D4—2224no—
673C2×D4—2212no—
674C2×D4—2212no—
675C2×D4—2296no—
676C2×D4—2296no—
677C2×D4—2224no—
678C2×D4—2212no—
679C2×D4—4412no—
680C2×D4C23×D11112yes—
681C2×D4C23×D11112yes—
682C22×C4—212no—
683C22×C4—212no—
684C22×C4—111no—
685C22×C4—111no—
686C22×C4—1124no—
687C22×C4—1112no—
688C22×C4—114no—
689C22×C4—1112no—
690C22×C4—113no—
691C22×C4—111no—
692C22×C4—113no—
693C22×C4—1112no—
694C22×C4—1112no—
695C22×C4—1112no—
696C22×C4—114no—
697C22×C4—1112no—
698C22×C4—1112no—
699C22×C4—1112no—
700C22×C4—1112no—
701C22×C4—224no—
702C22×C4—2212no—
703C22×C4—2296no—
704C22×C4—2296no—
705C22×C4—2212no—
706C22×C4—2212no—
707C22×C4—2212no—
708C22×C4—224no—
709C22×C4—2212no—
710C22×C4—2212no—
711C22×C4—2212no—
712C22×C4—446no—
713C22×C4C23×D11112yes—
714C22×C4C23×D11112yes—
715C22×C4C23×D1111yescharacteristic
716C22×C4C23×D1113yes—
717C22×C4C23×D1111yescharacteristic
718C22×C4C23×D1113yes—
719C22×C4C23×D1113yes—
720C4⋊C4—114no—
721C4⋊C4—1112no—
722C4⋊C4—1112no—
723C4⋊C4—1112no—
724C4⋊C4—1124no—
725C4⋊C4C23×D11112yes—
726C4⋊C4C23×D11112yes—
727C22⋊C4—1112no—
728C22⋊C4—1112no—
729C22⋊C4—114no—
730C22⋊C4—1112no—
731C22⋊C4—1112no—
732C22⋊C4—1112no—
733C22⋊C4—1124no—
734C22⋊C4—1124no—
735C22⋊C4C23×D1114yes—
736C22⋊C4C23×D11112yes—
737C22⋊C4C23×D11124yes—
738C42—114no—
739C42—1112no—
740C42—1112no—
741C42C23×D11112yes—
742C11C2×D4×#4111yescharacteristic, complemented, Sylow
743C23—22no—
744C23—22no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—1112no—
749C23—114no—
750C23—112no—
751C23—116no—
752C23—116no—
753C23—2224no—
754C23—2224no—
755C23—2224no—
756C23—222no—
757C23—226no—
758C23—226no—
759C23—222no—
760C23—226no—
761C23—226no—
762C23—2224no—
763C23—226no—
764C23—4412no—
765C23—4412no—
766C23—4448no—
767C23—4448no—
768C23#41×D1114yescomplemented
769C23C24×D1116yes—
770C23C24×D1112yes—
771C23C24×D1111yescharacteristic
772Q8—224no—
773Q8—2224no—
774Q8C2×D4×D11116yescomplemented
775D4—224no—
776D4—224no—
777D4—1116no—
778D4—1148no—
779D4—2248no—
780D4—2224no—
781D4—2224no—
782D4—2248no—
783D4—2224no—
784D4—4424no—
785C2×C4—22no—
786C2×C4—26no—
787C2×C4—26no—
788C2×C4—22no—
789C2×C4—224no—
790C2×C4—224no—
791C2×C4—114no—
792C2×C4—114no—
793C2×C4—112no—
794C2×C4—112no—
795C2×C4—1148no—
796C2×C4—116no—
797C2×C4—112no—
798C2×C4—116no—
799C2×C4—228no—
800C2×C4—2224no—
801C2×C4—2224no—
802C2×C4—2224no—
803C2×C4—2224no—
804C2×C4—228no—
805C2×C4—2224no—
806C2×C4—222no—
807C2×C4—226no—
808C2×C4—226no—
809C2×C4—2224no—
810C2×C4—2224no—
811C2×C4—4412no—
812C2×C4C2×D4×D11112yes—
813C2×C4C24×D1112yes—
814C2×C4C24×D1116yes—
815C2×C4C24×D1112yes—
816C2×C4C24×D1116yes—
817C2×C4C24×D1116yes—
818C22—22no—
819C22—22no—
820C22—28no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—1112no—
826C22—114no—
827C22—222no—
828C22—226no—
829C22—226no—
830C22—222no—
831C22—228no—
832C22—2224no—
833C22—226no—
834C22—226no—
835C22—226no—
836C22—4448no—
837C22—4448no—
838C22—4412no—
839C22C22×D4×D1112yes—
840C22C2×#41×D1112yes—
841C22C2×#41×D1114yescomplemented
842C22#1062345712yes—
843C22C25×D1111yescharacteristic
844C4—22no—
845C4—26no—
846C4—26no—
847C4—22no—
848C4—114no—
849C4—114no—
850C4—222no—
851C4—226no—
852C4—226no—
853C4C22×D4×D11112yes—
854C2—24no—
855C2—46no—
856C2—224no—
857C2—2212no—
858C2—446no—
859C2#1308210514yesdirect product factor
860C2C23×D4×D1111yescharacteristic
861C2C22×#41×D1111yescharacteristic
862C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#548C2
socleC23×C11C25
hypercenterC2×#548D11
hypocenterC11C2×D4×#41
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C23×#4343C2semidirect
2. C22×#41×D11C2semidirect
3. #13082105C2direct (N × H)
4. C2×#10623365C2semidirect
5. C2×Q8×C22⋊D11C2semidirect
6. C2×#10623107C2semidirect
7. C2×#10623162C2semidirect
8. C2×#10623081C2semidirect
9. C2×#10623207C2semidirect
10. C2×#10623140C2semidirect
11. C2×#10623199C2semidirect
12. C2×#10623158C2semidirect
13. C2×#10623137C2semidirect
14. C2×C4×#4343C2semidirect
15. C2×C4×D4×D11C2semidirect
16. C2×C11×#548C2semidirect
17. C22×C11×#41C22semidirect
18. C23×Q8×C11C22semidirect
20. C2×#41×D11C22semidirect
23. C22×#4343C22semidirect
24. C22×#4343C22semidirect
25. C22×#4343C22semidirect
26. C22×#4343C22semidirect
27. C22×Q8×D11C22semidirect
28. C22×#4341C22semidirect
30. C22×D4×D11C22semidirect
31. C22×#4339C22semidirect
32. C23×D44C22semidirect
33. C23×C4×D11C22semidirect
34. C23×C4×D11C22semidirect
35. C11×#548C22semidirect
36. C2×C11×#124C22semidirect
37. C2×C11×C22⋊Q8C22semidirect
38. C2×C11×#121C22semidirect
39. C2×C4×Q8×C11C22semidirect
40. C2×C4×D4×C11C22semidirect
41. #10623365C22semidirect
42. Q8×C22⋊D11C22semidirect
43. C2×#66999C22semidirect
44. C2×Q8×Dic11C22semidirect
45. C2×#66997C22semidirect
46. C2×#66993C22semidirect
47. C2×#66991C22semidirect
48. C2×#66990C22semidirect
49. C2×D4×Dic11C22semidirect
50. C2×#66983C22semidirect
52. C2×C4×C22⋊D11C22semidirect
53. C2×#66977C22semidirect
54. #10623207C22semidirect
55. #10623199C22semidirect
56. #10623162C22semidirect
57. #10623158C22semidirect
58. #10623140C22semidirect
59. #10623137C22semidirect
60. #10623107C22semidirect
61. C4×#4343C22semidirect
62. #10623081C22semidirect
63. C4×D4×D11C22semidirect
64. C2×#66950C22semidirect
65. C2×#66948C22semidirect
66. C2×#66947C22semidirect
67. C2×#66946C22semidirect
68. C2×#66946C22semidirect
69. C2×#66945C22semidirect
70. C2×C4⋊C4×D11C22semidirect
71. C2×#66937C22semidirect
72. C2×#66937C22semidirect
73. C2×#66936C22semidirect
74. C2×#66935C22semidirect
76. C2×(C22⋊D11)⋊C4C22semidirect
77. C2×(C22⋊D11)⋊C4C22semidirect
78. C2×C22⋊C4×D11C22semidirect
79. C2×C22⋊C4×D11C22semidirect
80. C2×#66928C22semidirect
81. C2×C4×D44C22semidirect
82. C2×C4×D44C22semidirect
83. C2×C42×D11C22semidirect
87. C2×C11×#41C23semidirect
91. C22×Q8×C11C23semidirect
107. C2×#4343D4semidirect
109. C2×#4343C23semidirect
110. C2×#4343C23semidirect
111. C2×#4343C23semidirect
113. C2×Q8×D11C23semidirect
115. C2×#4341C23semidirect
119. C2×D4×D11C23semidirect
121. C2×#4339C23semidirect
127. C22×D44C23semidirect
139. C22×C4×D11C23semidirect
140. C22×C4×D11C23semidirect
142. C11×#124C23semidirect
143. C11×C22⋊Q8C23semidirect
144. C11×#121C23semidirect
145. C4×Q8×C11C23semidirect
146. C4×D4×C11C23semidirect
155. #66999C23semidirect
156. Q8×Dic11C23semidirect
157. #66997C23semidirect
158. #66993C23semidirect
159. #66991C23semidirect
160. #66990C23semidirect
161. D4×Dic11C23semidirect
162. #66983C23semidirect
164. C4×C22⋊D11C23semidirect
173. #66977C23semidirect
180. #66950C23semidirect
181. #66948C23semidirect
182. #66947C23semidirect
183. #66946C23semidirect
184. #66946C23semidirect
185. #66945C23semidirect
186. C4⋊C4×D11C23semidirect
187. #66937C23semidirect
188. #66937C23semidirect
189. #66936C23semidirect
190. #66935C23semidirect
192. (C22⋊D11)⋊C4C23semidirect
193. (C22⋊D11)⋊C4C23semidirect
194. C22⋊C4×D11C23semidirect
195. C22⋊C4×D11C23semidirect
196. #66928C23semidirect
197. C4×D44C23semidirect
198. C4×D44C23semidirect
199. C42×D11C23semidirect
217. C2×Q8×C11C2×D4semidirect
236. C2×C22⋊D11#41semidirect
253. #4343C2×D4semidirect
263. C2×D44C2×D4semidirect
278. C2×C4×D11C2×D4semidirect
318. C2×#548D11semidirect
333. C23×C11C2×#41semidirect
353. C22×D11C2×#41semidirect
358. Q8×C11C22×D4semidirect
376. C22⋊D11C2×#41semidirect
383. C2×Dic11C2×#41semidirect
392. D44C22×D4semidirect
401. C4×D11C22×D4semidirect
413. C22×#41C2×D11semidirect
415. C23×Q8C2×D11semidirect
424. #548C2×D11semidirect
433. C2×#124C2×D11semidirect
441. C2×C22⋊Q8C2×D11semidirect
447. C2×#121C2×D11semidirect
452. C2×C4×Q8C2×D11semidirect
464. C2×C4×D4C2×D11semidirect
479. C22×C11C22×#41semidirect
495. C2×D11C22×#41semidirect
505. Dic11C22×#41semidirect
523. C2×#41C22×D11semidirect
530. C22×Q8C22×D11semidirect
567. #124C22×D11semidirect
573. C22⋊Q8C22×D11semidirect
579. #121C22×D11semidirect
583. C4×Q8C22×D11semidirect
594. C4×D4C22×D11semidirect
624. C2×C11D4×#41semidirect
656. C2×Q8D4×D11semidirect
742. C11C2×D4×#41semidirect
768. C23#41×D11semidirect
774. Q8C2×D4×D11semidirect
841. C22C2×#41×D11semidirect
859. C2#13082105direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43432
C22×#41×D112
#130821052
C2×#106233652
C2×Q8×C22⋊D112
C2×#106231072
C2×#106231622
C2×#106230812
C2×#106232072
C2×#106231402
C2×#106231992
C2×#106231582
C2×#106231372
C2×C4×#43432
C2×C4×D4×D112
C2×C11×#5482
C2×D4×#4111