Finite Group Databasebeta

← #14774045

Subgroups — #14774045

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622840C211yesmaximal, characteristic
2C2×#10622430C211yesmaximal, characteristic, complemented
3#13071632C211yesmaximal, characteristic
4Q8×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13069494C211yesmaximal, characteristic, complemented
6#13069303C211yesmaximal, characteristic, complemented
7#13069260C211yesmaximal, characteristic, complemented
8#13069044C211yesmaximal, characteristic
9#13068969C211yesmaximal, characteristic, complemented
10#13068947C211yesmaximal, characteristic, complemented
11#13068868C211yesmaximal, characteristic, complemented
12#13068804C211yesmaximal, characteristic, complemented
13#13068448C211yesmaximal, characteristic, complemented
14#13068392C211yesmaximal, characteristic, complemented
15C22×C11×#103C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×C4×C22⋊D11—21no—
25C2×#66946C2211yescharacteristic
26C2×C11×#103—24no—
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31#10622843—21no—
32#10622843—21no—
33#10622843C2211yescharacteristic
34#10622843C2211yescharacteristic
35#10622840C418yescomplemented
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38#10622826—21no—
39#10622825—21no—
40#10622825C2211yescharacteristic
41C4×C22⋊Dic11—21no—
42C4×C22⋊Dic11C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C2×#66879C2211yescharacteristic
47C2×#66879C2211yescharacteristic
48#10622603—21no—
49#10622602—21no—
50#10622601C2211yescharacteristic
51C4⋊C4×Dic11C2211yescharacteristic
52#10622586C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54C2×#66871C2211yescharacteristic
55#10622430—24no—
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11—21no—
63C22×Q8×C11—22no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—41no—
67C22×Q8×C11—41no—
68C22×Q8×C11C2×C414yescomplemented
69C22×Q8×C11C2311yescharacteristic
70C22×Q8×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C22×C22⋊D11—21no—
75C22×D44C2311yescharacteristic
76C22×C4×D11—21no—
77C22×C8×C11—22no—
78C22×C8×C11—22no—
79C22×C8×C11—41no—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—41no—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11D411yescharacteristic
89C2×C22⋊Dic11D411yescharacteristic
90Q8×Dic11—22no—
91Q8×Dic11—22no—
92Q8×Dic11—41no—
93Q8×Dic11—41no—
94C2×#4325—22no—
95C2×#4325—22no—
96C2×#4325—41no—
97C2×#4325—41no—
98C2×#4325C2×C414yescomplemented
99C2×#4325C2×C414yescomplemented
100#66983—22no—
101#66983C2×C414yes—
102C4×C22⋊D11—44no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×Dic11⋊C4—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11—21no—
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120#66946—22no—
121#66946—41no—
122C11×#103—22no—
123C11×#103—22no—
124C11×#103—22no—
125C11×#103D414yescomplemented
126#66899C2×C414yescomplemented
127#66899C2×C414yescomplemented
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95D411yescharacteristic
136C11⋊#95D411yescharacteristic
137C22⋊(C11⋊C8)C2×C414yescomplemented
138#66885—22no—
139#66885—41no—
140#66879—22no—
141#66879—41no—
142#66871—22no—
143#66871—41no—
144#22855—111nomaximal, Sylow
145C24×C11C2×D411yescharacteristic
146C23×D11—21no—
147C2×Q8×C11—24no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—28no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—42no—
158C2×Q8×C11—42no—
159C2×Q8×C11—44no—
160C2×Q8×C11—44no—
161C2×Q8×C11—44no—
162C2×Q8×C11C22×C412yes—
163C2×Q8×C11C22×C412yes—
164C2×Q8×C11C2×D412yes—
165C2×Q8×C11#4112yes—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—24no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—81no—
180C22×C4×C11C22×C412yes—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11#4112yes—
183C22×C4×C11C2411yescharacteristic
184C2×C22⋊D11—24no—
185C2×C22⋊D11—42no—
186C2×C22⋊D11—42no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11C2×D411yescharacteristic
191C22×Dic11C2×D411yescharacteristic
192C22×Dic11C2×D411yescharacteristic
193C22×Dic11C2×D411yescharacteristic
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44C22×C412yes—
200C2×C4×D11—42no—
201C2×C4×D11—42no—
202C2×C4×D11—81no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—44no—
209C2×C8×C11C2×D412yes—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4C2×D412yes—
215C22⋊Dic11—22no—
216C22⋊Dic11—22no—
217C22⋊Dic11—42no—
218#4325—28no—
219#4325—44no—
220(C2×D11)⋊C4—24no—
221(C2×D11)⋊C4—42no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—81no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—42no—
230C4⋊Dic11—42no—
231C4⋊Dic11C22×C412yes—
232Dic11⋊C4—42no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—21no—
237C4×Dic11—42no—
238C4×Dic11—42no—
239C4×Dic11—42no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8C22×C412yes—
245C2×C11⋊C8C22×C412yes—
246C2×#448—111no—
247C2×#440—111no—
248C22×#103D1111yescharacteristic, complemented
249#2361—111no—
250Q8×C22⋊C4—111no—
251#1973—111no—
252#1935—111no—
253#1928—111no—
254#1893—111no—
255#1880—111no—
256#1877—111no—
257#1863—111no—
258#1852—111no—
259#1763—111no—
260#1752—111no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11C4×D412yes—
266C23×C11AGL(1,ℤ/8)12yes—
267C23×C11#13712yes—
268C23×C11C22×D411yescharacteristic
269C22×D11—22no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276Q8×C11—22no—
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—22no—
280Q8×C11—22no—
281Q8×C11—48no—
282Q8×C11—41no—
283Q8×C11—41no—
284Q8×C11C4×D414yescomplemented
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—48no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—84no—
305C2×C4×C11C4×D412yes—
306C2×C4×C11C23×C411yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C22⋊D11—48no—
313C2×Dic11—22no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334D44—22no—
335D44—22no—
336D44—41no—
337D44—41no—
338C4×D11—84no—
339C8×C11—22no—
340C8×C11—41no—
341C11⋊C8—22no—
342C11⋊C8—22no—
343C23×Q8C2×D1111yescharacteristic
344C22×SD16—111no—
345C22×SD16—111no—
346C23×C8C2×D1111yescharacteristic
347C2×#121—111no—
348C2×C4×Q8—111no—
349C2×C4×Q8—111no—
350C2×C4×D4—111no—
351C2×C4×D4—221no—
352C22×C4⋊C4C2×D1111yescharacteristic
353#448—118no—
354#440—224no—
355C2×#107—111no—
356C2×#107—111no—
357C2×#103—24no—
358C2×#103—111no—
359C2×#103—111no—
360C2×#103C2×D1111yescharacteristic
361C2×#103C2×D1111yescharacteristic
362C2×#103C2×D1111yescharacteristic
363C2×#103C2×D1111yescharacteristic
364C2×#102—111no—
365C2×#102—111no—
366C2×C22⋊C8—111no—
367C2×#97—111no—
368C2×#97—111no—
369#391—111no—
370#391—111no—
371#391—221no—
372#391—221no—
373#390—111no—
374#389—111no—
375#388—221no—
376#386—221no—
377#385—221no—
378#380—111no—
379#380—221no—
380C4×C4⋊C4—111no—
381C4×C22⋊C4—111no—
382C4×C22⋊C4—221no—
383#340—111no—
384#340—111no—
385#340—111no—
386#340—111no—
387#336—111no—
388#336—111no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11#44014yescomplemented
396C22×C11C2×C4×D411yescharacteristic
397C22×C11D4211yescharacteristic
398C22×C11#54611yescharacteristic
399C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C11C2×#13711yescharacteristic
401C22×C11#57711yescharacteristic
402C22×C11#57811yescharacteristic
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—81no—
407C2×D11—81no—
408C2×D11—81no—
409C2×D11—81no—
410C4×C11—22no—
411C4×C11—24no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11—81no—
415C4×C11C2×C4×D411yescharacteristic
416C4×C11#51811yescharacteristic
417C4×C11#54611yescharacteristic
418C4×C11#55111yescharacteristic
419Dic11—42no—
420Dic11—41no—
421Dic11—41no—
422Dic11—41no—
423Dic11—41no—
424Dic11—81no—
425Dic11—81no—
426C22×Q8—21no—
427C22×Q8—22no—
428C22×Q8—22no—
429C22×Q8—22no—
430C22×Q8—41no—
431C22×Q8—41no—
432C22×Q8C4×D1114yescomplemented
433C22×Q8C22×D1111yescharacteristic
434C22×Q8C22×D1111yescharacteristic
435C22×D4—111no—
436C22×D4—221no—
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—221no—
440C23×C4C22×D1111yescharacteristic
441C2×SD16—114no—
442C2×SD16—114no—
443C2×SD16—222no—
444C2×SD16—222no—
445C2×SD16—441no—
446C2×SD16—441no—
447C22×C8—22no—
448C22×C8—22no—
449C22×C8—41no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8C22×D1111yescharacteristic
453C22×C8C22×D1111yescharacteristic
454#121—114no—
455#121—222no—
456C4×Q8—222no—
457C4×Q8—222no—
458C4×Q8—441no—
459C4×Q8—441no—
460C4×D4—222no—
461C4×D4—441no—
462C4×D4—444no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—41no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4C22×D1111yescharacteristic
473C2×C4⋊C4C22×D1111yescharacteristic
474C2×C22⋊C4—111no—
475C2×C22⋊C4—111no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C42—111no—
482C2×C42—111no—
483C2×C42—221no—
484C2×C42—221no—
485C2×C42—221no—
486#107—222no—
487#107—441no—
488#103—22no—
489#103—22no—
490#103—22no—
491#103—114no—
492#103—114no—
493#103C22⋊D1114yescomplemented
494#102—222no—
495#102—441no—
496C22⋊C8—114no—
497#97—222no—
498#97—441no—
499#95—111no—
500#95—111no—
501#95—221no—
502#95—221no—
503#95—221no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95—221no—
508C2×C11—24no—
509C2×C11#235811yescharacteristic
510C2×C11C2×#44011yescharacteristic
511C2×C11#294711yescharacteristic
512C2×C11#326511yescharacteristic
513C2×C11#327011yescharacteristic
514C2×C11#330811yescharacteristic
515C2×C11#332011yescharacteristic
516D11—82no—
517C24—221no—
518C24D4×D1111yescharacteristic
519C2×Q8—24no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—28no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—42no—
530C2×Q8—42no—
531C2×Q8—44no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8C2×C4×D1112yes—
535C2×Q8C2×C4×D1112yes—
536C2×Q8#433912yes—
537C2×Q8C2×C22⋊D1112yes—
538C2×D4—112no—
539C2×D4—224no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—221no—
543C2×D4—221no—
544C2×D4—221no—
545C2×D4—442no—
546C2×D4—442no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—81no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—111no—
564C22×C4—111no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—442no—
569C22×C4—442no—
570C22×C4—881no—
571C22×C4C2×C4×D1112yes—
572C22×C4D4×D1111yescharacteristic
573C22×C4#434112yes—
574C22×C4C23×D1111yescharacteristic
575SD16—228no—
576SD16—444no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—44no—
583C2×C8—112no—
584C2×C8—112no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8C2×C22⋊D1112yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—42no—
594C4⋊C4—112no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—442no—
601C4⋊C4—442no—
602C4⋊C4—442no—
603C4⋊C4C2×C22⋊D1112yes—
604C22⋊C4—222no—
605C22⋊C4—222no—
606C22⋊C4—224no—
607C22⋊C4—442no—
608C22⋊C4—442no—
609C22⋊C4—442no—
610C22⋊C4—881no—
611C42—221no—
612C42—221no—
613C42—221no—
614C42—221no—
615C42—442no—
616C42—442no—
617C42—442no—
618C11#2285511yescharacteristic, complemented, Sylow
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—222no—
624C23—441no—
625C23—441no—
626C23—441no—
627C23—441no—
628C23—441no—
629C23—441no—
630C23(C22⋊D11)⋊C412yes—
631C23#6696712yes—
632C23#6697112yes—
633C23C2×D4×D1111yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8C4×C22⋊D1114yescomplemented
643D4—222no—
644D4—222no—
645D4—448no—
646D4—441no—
647D4—441no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—48no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—222no—
669C2×C4—221no—
670C2×C4—221no—
671C2×C4—221no—
672C2×C4—221no—
673C2×C4—221no—
674C2×C4—221no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—884no—
690C2×C4(C22⋊D11)⋊C412yes—
691C2×C4C22×C4×D1111yescharacteristic
692C2×C4C2×#433911yescharacteristic
693C2×C4C2×#434111yescharacteristic
694C2×C4#6703711yescharacteristic
695C2×C4#6703711yescharacteristic
696C2×C4C22×C22⋊D1111yescharacteristic
697C8—22no—
698C8—41no—
699C8—222no—
700C8—222no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—442no—
708C22—442no—
709C22—442no—
710C22—881no—
711C22—881no—
712C22—881no—
713C22—881no—
714C22#1062243014yescomplemented
715C22C2×(C22⋊D11)⋊C411yescharacteristic
716C22#1062302111yescharacteristic
717C22C2×#6696711yescharacteristic
718C22#1062329311yescharacteristic
719C22C2×#6697111yescharacteristic
720C22#1062329711yescharacteristic
721C22D4×C22⋊D1111yescharacteristic
722C4—22no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—81no—
727C4—441no—
728C4—441no—
729C4—441no—
730C4—442no—
731C4—441no—
732C4—881no—
733C4—881no—
734C4#1062301711yescharacteristic
735C4#1062302611yescharacteristic
736C4C2×C4×C22⋊D1111yescharacteristic
737C4#1062333711yescharacteristic
738C2—24no—
739C2—882no—
740C2#1307159511yescharacteristic
741C2C2×#1062243011yescharacteristic
742C2#1307745311yescharacteristic
743C2#1308011111yescharacteristic
744C2#1308018611yescharacteristic
745C2#1308060311yescharacteristic
746C2#1308078311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenterC22×#103D11
hypocenterC11#22855
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C2×#10622430C2semidirect
4. Q8×C22⋊Dic11C2semidirect
5. #13069494C2semidirect
6. #13069303C2semidirect
7. #13069260C2semidirect
9. #13068969C2semidirect
10. #13068947C2semidirect
11. #13068868C2semidirect
12. #13068804C2semidirect
13. #13068448C2semidirect
14. #13068392C2semidirect
15. C22×C11×#103C2semidirect
35. #10622840C4semidirect
68. C22×Q8×C11C2×C4semidirect
98. C2×#4325C2×C4semidirect
99. C2×#4325C2×C4semidirect
125. C11×#103D4semidirect
126. #66899C2×C4semidirect
127. #66899C2×C4semidirect
137. C22⋊(C11⋊C8)C2×C4semidirect
248. C22×#103D11semidirect
284. Q8×C11C4×D4semidirect
395. C22×C11#440semidirect
432. C22×Q8C4×D11semidirect
493. #103C22⋊D11semidirect
618. C11#22855semidirect
642. Q8C4×C22⋊D11semidirect
714. C22#10622430semidirect

Maximal subgroups

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

subgroupindex
C2×#106228402
C2×#106224302
#130716322
Q8×C22⋊Dic112
#130694942
#130693032
#130692602
#130690442
#130689692
#130689472
#130688682
#130688042
#130684482
#130683922
C22×C11×#1032
#2285511