Finite Group Databasebeta

← #14769583

Subgroups — #14769583

Order 2816.

1406 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622797C211yesmaximal, characteristic, complemented
2C2×Q16×Dic11C211yesmaximal, characteristic, complemented
3#13071457C211yesmaximal, characteristic
4Q8×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13069499C211yesmaximal, characteristic, complemented
6#13069472C211yesmaximal, characteristic, complemented
7#13068973C211yesmaximal, characteristic, complemented
8#13068973C211yesmaximal, characteristic, complemented
9#13068959C211yesmaximal, characteristic, complemented
10#13068959C211yesmaximal, characteristic, complemented
11#13068649C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic
13#13068551C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C22×C11×#137C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C2×C11×#137—24no—
19C2×C11×#137—24no—
20C2×C11×#137C418yescomplemented
21C22×C11×Q16C2211yescharacteristic
22C22×C11×Q16C2211yescharacteristic
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C22×C11×M16C2211yescharacteristic
26C2×Q8×Dic11C2211yescharacteristic
27C2×Q8×Dic11C2211yescharacteristic
28C2×Q8×Dic11C2211yescharacteristic
29C2×Q8×Dic11C2211yescharacteristic
30#10622843—21no—
31#10622843—21no—
32#10622843C2211yescharacteristic
33#10622843C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40#10622834—21no—
41#10622834—21no—
42#10622834C2211yescharacteristic
43#10622834C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46#10622825—21no—
47#10622825—21no—
48#10622825C2211yescharacteristic
49#10622825C2211yescharacteristic
50C4×C22⋊Dic11—21no—
51C4×C22⋊Dic11—21no—
52C4×C22⋊Dic11C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622797—24no—
55Q16×Dic11—24no—
56C2×#66882C2211yescharacteristic
57C2×#66881C2211yescharacteristic
58C2×#66879C2211yescharacteristic
59C2×C8×Dic11C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622188C2211yescharacteristic
63#10622188C2211yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C2×C11×#41C2×C414yes—
70C22×Q8×C11—21no—
71C22×Q8×C11—22no—
72C22×Q8×C11—22no—
73C22×Q8×C11—22no—
74C22×Q8×C11—41no—
75C22×Q8×C11—41no—
76C22×Q8×C11C2×C414yes—
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C23×C4×C11—21no—
84C23×C4×C11C2311yescharacteristic
85C11×#137—232no—
86C2×C11×Q16—22no—
87C2×C11×Q16—22no—
88C2×C11×Q16C2×C414yes—
89C2×C11×Q16C2×C414yes—
90C2×C11×Q16D414yes—
91C2×C11×Q16D414yes—
92C2×C11×SD16—22no—
93C2×C11×SD16—22no—
94C2×C11×SD16—22no—
95C2×C11×SD16—22no—
96C2×C11×SD16C2×C414yes—
97C2×C11×SD16C2×C414yes—
98C2×C11×M16—22no—
99C2×C11×M16—22no—
100C2×C11×M16C2×C414yes—
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11D411yescharacteristic
110C2×C22⋊Dic11D411yescharacteristic
111Q8×Dic11—22no—
112Q8×Dic11—22no—
113Q8×Dic11—22no—
114Q8×Dic11—22no—
115Q8×Dic11—41no—
116Q8×Dic11—41no—
117Q8×Dic11—41no—
118Q8×Dic11—41no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4×Dic11—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11—21no—
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135#66899—22no—
136#66899—22no—
137#66899—22no—
138#66899—22no—
139#66899—41no—
140#66899—41no—
141#66896—41no—
142#66896—41no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149C11⋊#95D411yescharacteristic
150C11⋊#95D411yescharacteristic
151C22⋊(C11⋊C8)—22no—
152#66882—22no—
153#66881—22no—
154#66879—22no—
155C8×Dic11—22no—
156#22445—111nomaximal, Sylow
157C24×C11—21no—
158C24×C11C2×D411yescharacteristic
159C11×#41—28no—
160C11×#41—44no—
161C11×#41—44no—
162C11×#41—44no—
163C2×Q8×C11—24no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—28no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—42no—
177C2×Q8×C11—42no—
178C2×Q8×C11—44no—
179C2×Q8×C11—44no—
180C2×Q8×C11—44no—
181C2×Q8×C11C22×C412yes—
182C2×Q8×C11C22×C412yes—
183C2×Q8×C11C22×C412yes—
184C2×Q8×C11C2×D412yes—
185C2×Q8×C11C2×D412yes—
186C2×Q8×C11C2×D412yes—
187C2×Q8×C11C2×D412yes—
188C2×D4×C11—24no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—42no—
195C2×D4×C11—42no—
196C2×D4×C11C22×C412yes—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—24no—
204C22×C4×C11—21no—
205C22×C4×C11—24no—
206C22×C4×C11—42no—
207C22×C4×C11—42no—
208C22×C4×C11—42no—
209C22×C4×C11—42no—
210C22×C4×C11C22×C412yes—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11#4112yes—
213C22×C4×C11C2411yescharacteristic
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222C11×Q16—28no—
223C11×Q16C22⋊C4116yescomplemented
224C11×SD16—28no—
225C11×SD16—28no—
226C11×M16—28no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11C22×C412yes—
230C2×C8×C11C22×C412yes—
231C2×C8×C11C2×D412yes—
232C2×C8×C11C2×D412yes—
233C22⋊Dic11—22no—
234C22⋊Dic11—41no—
235C22⋊Dic11—42no—
236C22⋊Dic11—42no—
237C22⋊Dic11—42no—
238C22⋊Dic11—81no—
239C22⋊Dic11—81no—
240C22⋊Dic11—81no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—21no—
249C4⋊Dic11—42no—
250C4⋊Dic11—42no—
251C4⋊Dic11—42no—
252C4⋊Dic11—42no—
253C4×Dic11—21no—
254C4×Dic11—21no—
255C4×Dic11—21no—
256C4×Dic11—21no—
257C4×Dic11—42no—
258C4×Dic11—42no—
259C4×Dic11—42no—
260C4×Dic11—42no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C22×#137D1111yescharacteristic
268C2×#441—111no—
269C2×C4×Q16—111no—
270#2341—111no—
271Q8×C22⋊C4—111no—
272#1973—111no—
273#1968—111no—
274#1880—111no—
275#1880—111no—
276#1878—111no—
277#1878—111no—
278#1809—111no—
279#1788—111no—
280#1787—111no—
281#1753—111no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—22no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11C4×D412yes—
296C23×C11C22×D411yescharacteristic
297Q8×C11—22no—
298Q8×C11—22no—
299Q8×C11—22no—
300Q8×C11—22no—
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—48no—
306Q8×C11—41no—
307Q8×C11—41no—
308Q8×C11C2×C22⋊C414yes—
309Q8×C11C2×C22⋊C414yes—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—48no—
313D4×C11—41no—
314D4×C11—41no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—48no—
329C2×C4×C11—48no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11C4×D412yes—
333C2×C4×C11C23×C411yescharacteristic
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11#13712yescomplemented
363C8×C11—22no—
364C8×C11C2×C22⋊C414yes—
365C11⋊C8—41no—
366C11⋊C8—41no—
367C22×#41C2×D1111yescharacteristic
368C23×Q8C2×D1111yescharacteristic
369C2×#137—24no—
370C2×#137—24no—
371C2×#137Dic1118yescomplemented
372C22×Q16C2×D1111yescharacteristic
373C22×Q16C2×D1111yescharacteristic
374C22×SD16C2×D1111yescharacteristic
375C22×SD16C2×D1111yescharacteristic
376C22×M16C2×D1111yescharacteristic
377C2×C4×Q8—111no—
378C2×C4×Q8—111no—
379C2×C4×Q8—111no—
380C2×C4×Q8—111no—
381#441—224no—
382C4×Q16—224no—
383C2×#107—111no—
384C2×#106—111no—
385C2×#103—111no—
386C2×#103—111no—
387C2×#103—111no—
388C2×#103—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×C22⋊C8—111no—
394C2×#97—111no—
395C2×C4×C8—111no—
396#391—111no—
397#391—111no—
398#391—221no—
399#391—221no—
400#390—111no—
401#390—111no—
402#390—221no—
403#390—221no—
404#380—111no—
405#380—111no—
406#380—221no—
407#380—221no—
408C4×C22⋊C4—111no—
409C4×C22⋊C4—221no—
410C4×C22⋊C4—221no—
411#340—111no—
412#340—111no—
413#336—111no—
414#336—111no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—81no—
426C22×C11—81no—
427C22×C11—81no—
428C22×C11—81no—
429C22×C11C2×C4×D411yescharacteristic
430C22×C11D4211yescharacteristic
431C22×C11D4211yescharacteristic
432C22×C11C2×#13711yescharacteristic
433C22×C11#57511yescharacteristic
434C22×C11#57711yescharacteristic
435C22×C11#57811yescharacteristic
436C4×C11—22no—
437C4×C11—24no—
438C4×C11—24no—
439C4×C11—42no—
440C4×C11C22×C22⋊C411yescharacteristic
441C4×C11#51811yescharacteristic
442C4×C11#54611yescharacteristic
443C4×C11#54611yescharacteristic
444Dic11—22no—
445Dic11—41no—
446Dic11—41no—
447Dic11—41no—
448Dic11—81no—
449Dic11—81no—
450Dic11—81no—
451Dic11—81no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—41no—
456C2×#41—41no—
457C2×#41C2×Dic1114yes—
458C22×Q8—21no—
459C22×Q8—22no—
460C22×Q8—22no—
461C22×Q8—22no—
462C22×Q8—41no—
463C22×Q8—41no—
464C22×Q8C2×Dic1114yes—
465C22×Q8C22×D1111yescharacteristic
466C22×Q8C22×D1111yescharacteristic
467C22×Q8C22×D1111yescharacteristic
468C22×D4—21no—
469C22×D4C22×D1111yescharacteristic
470C23×C4—21no—
471C23×C4—21no—
472C23×C4C22×D1111yescharacteristic
473#137—232no—
474C2×Q16—22no—
475C2×Q16—22no—
476C2×Q16C2×Dic1114yes—
477C2×Q16C2×Dic1114yes—
478C2×Q16C22⋊D1114yes—
479C2×Q16C22⋊D1114yes—
480C2×SD16—22no—
481C2×SD16—22no—
482C2×SD16—22no—
483C2×SD16—22no—
484C2×SD16C2×Dic1114yes—
485C2×SD16C2×Dic1114yes—
486C2×M16—22no—
487C2×M16—22no—
488C2×M16C2×Dic1114yes—
489C22×C8—111no—
490C22×C8—111no—
491C22×C8C22×D1111yescharacteristic
492C22×C8C22×D1111yescharacteristic
493C4×Q8—222no—
494C4×Q8—222no—
495C4×Q8—222no—
496C4×Q8—222no—
497C4×Q8—441no—
498C4×Q8—441no—
499C4×Q8—441no—
500C4×Q8—441no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C22⋊C4—111no—
510C2×C22⋊C4—111no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C42—111no—
518C2×C42—111no—
519C2×C42—221no—
520C2×C42—221no—
521C2×C42—221no—
522C2×C42—221no—
523#107—222no—
524#106—222no—
525#103—222no—
526#103—222no—
527#103—222no—
528#103—222no—
529#103—441no—
530#103—441no—
531#102—441no—
532#102—441no—
533C22⋊C8—222no—
534#97—222no—
535C4×C8—222no—
536#95—111no—
537#95—111no—
538#95—221no—
539#95—221no—
540#95—221no—
541#95—221no—
542#95—221no—
543#95—221no—
544C2×C11—42no—
545C2×C11—82no—
546C2×C11D4×C22⋊C411yescharacteristic
547C2×C11C4×#13711yescharacteristic
548C2×C11#294711yescharacteristic
549C2×C11#327011yescharacteristic
550C2×C11#327111yescharacteristic
551C2×C11#327711yescharacteristic
552C2×C11#327811yescharacteristic
553C24—21no—
554C24D4×D1111yescharacteristic
555#41—28no—
556#41—44no—
557#41—44no—
558#41—44no—
559C2×Q8—24no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—28no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8C22×Dic1112yes—
578C2×Q8C22×Dic1112yes—
579C2×Q8C22×Dic1112yes—
580C2×Q8C2×C22⋊D1112yes—
581C2×Q8C2×C22⋊D1112yes—
582C2×Q8C2×C22⋊D1112yes—
583C2×Q8C2×C22⋊D1112yes—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4C22×Dic1112yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—111no—
609C22×C4—111no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4D4×D1111yescharacteristic
615C22×C4#434112yes—
616C22×C4C22×Dic1112yes—
617C22×C4C23×D1111yescharacteristic
618Q16—28no—
619Q16C22⋊Dic11116yescomplemented
620SD16—28no—
621SD16—28no—
622M16—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—221no—
630C2×C8—221no—
631C2×C8C22×Dic1112yes—
632C2×C8C22×Dic1112yes—
633C2×C8C2×C22⋊D1112yes—
634C2×C8C2×C22⋊D1112yes—
635C4⋊C4—221no—
636C4⋊C4—221no—
637C4⋊C4—221no—
638C4⋊C4—221no—
639C4⋊C4—221no—
640C4⋊C4—221no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—442no—
644C4⋊C4—442no—
645C4⋊C4—442no—
646C4⋊C4—442no—
647C22⋊C4—222no—
648C22⋊C4—442no—
649C22⋊C4—441no—
650C22⋊C4—442no—
651C22⋊C4—442no—
652C22⋊C4—881no—
653C22⋊C4—881no—
654C22⋊C4—881no—
655C42—221no—
656C42—221no—
657C42—221no—
658C42—221no—
659C42—442no—
660C42—442no—
661C42—442no—
662C42—442no—
663C11#2244511yescharacteristic, complemented, Sylow
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23D4×Dic1112yes—
678C23C2×D4×D1111yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—48no—
688Q8—41no—
689Q8—41no—
690Q8C2×C22⋊Dic1114yes—
691Q8C2×C22⋊Dic1114yes—
692D4—22no—
693D4—22no—
694D4—48no—
695D4—41no—
696D4—41no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—48no—
711C2×C4—48no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—112no—
715C2×C4—221no—
716C2×C4—221no—
717C2×C4—221no—
718C2×C4—221no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—221no—
722C2×C4—221no—
723C2×C4—221no—
724C2×C4—221no—
725C2×C4—221no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4D4×Dic1112yes—
739C2×C4C2×#434111yescharacteristic
740C2×C4#6703711yescharacteristic
741C2×C4#6703711yescharacteristic
742C2×C4C23×Dic1111yescharacteristic
743C2×C4C22×C22⋊D1111yescharacteristic
744C2×C4C22×C22⋊D1111yescharacteristic
745C8—22no—
746C8—441no—
747C8—441no—
748C8C2×C22⋊Dic1114yes—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22D11×#13711yescharacteristic
764C22#1062330811yescharacteristic
765C22#1062330911yescharacteristic
766C22#1062331011yescharacteristic
767C22C2×D4×Dic1111yescharacteristic
768C22D4×C22⋊D1111yescharacteristic
769C22D4×C22⋊D1111yescharacteristic
770C4—22no—
771C4—24no—
772C4—24no—
773C4—42no—
774C4—222no—
775C4—441no—
776C4—441no—
777C4—441no—
778C4—881no—
779C4—881no—
780C4—881no—
781C4—881no—
782C4#1062332911yescharacteristic
783C4#1062333711yescharacteristic
784C4#1062333711yescharacteristic
785C4C22×C22⋊Dic1111yescharacteristic
786C2—42no—
787C2—82no—
788C2D4×C22⋊Dic1111yescharacteristic
789C2#137×Dic1111yescharacteristic
790C2#1307746011yescharacteristic
791C2#1308018011yescharacteristic
792C2#1308019511yescharacteristic
793C2#1308026711yescharacteristic
794C2#1308027611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#137C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC22×#137D11
hypocenterC11#22445
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. C2×#10622797C2semidirect
2. C2×Q16×Dic11C2semidirect
4. Q8×C22⋊Dic11C2semidirect
5. #13069499C2semidirect
6. #13069472C2semidirect
7. #13068973C2semidirect
8. #13068973C2semidirect
9. #13068959C2semidirect
10. #13068959C2semidirect
11. #13068649C2semidirect
13. #13068551C2semidirect
14. #13068397C2semidirect
20. C2×C11×#137C4semidirect
223. C11×Q16C22⋊C4semidirect
362. C2×Dic11#137semidirect
371. C2×#137Dic11semidirect
619. Q16C22⋊Dic11semidirect
663. C11#22445semidirect

Maximal subgroups

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

subgroupindex
C2×#106227972
C2×Q16×Dic112
#130714572
Q8×C22⋊Dic112
#130694992
#130694722
#130689732
#130689592
#130686492
#130685562
#130685512
#130683972
C22×C11×#1372
#2244511