Finite Group Databasebeta

← #14800970

Subgroups — #14800970

Order 2816.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622655C211yesmaximal, characteristic, complemented
2C2×#10622831C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic, complemented
4C2×#10622828C211yesmaximal, characteristic, complemented
5#13072045C211yesmaximal, characteristic, complemented
6#13070004C211yesmaximal, characteristic, complemented
7#13069933C211yesmaximal, characteristic, complemented
8#13069802C211yesmaximal, characteristic, complemented
9#13069619C211yesmaximal, characteristic, complemented
10#13069469C211yesmaximal, characteristic, complemented
11#13069302C211yesmaximal, characteristic, complemented
12#13069055C211yesmaximal, characteristic, complemented
13#13069047C211yesmaximal, characteristic, complemented
14#13068813C211yesmaximal, characteristic, complemented
15C11×#2408C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#120—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic, complemented
26C22×#4318C2211yescharacteristic
27C22×#4318C2211yescharacteristic, complemented
28C11×#394—21no—
29C11×#392—21no—
30C11×#390C2211yescharacteristic
31C11×#390C2211yescharacteristic
32C11×#380C2211yescharacteristic
33C11×#379—21no—
34#10622835—21no—
35#10622831—24no—
36#10622828—24no—
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825C2211yescharacteristic, complemented
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
46#10622655—24no—
47#10622625—24no—
48#10622585—21no—
49C2×#66874C2211yescharacteristic, complemented
50C2×#66874C2211yescharacteristic, complemented
51C2×#66872C2211yescharacteristic, complemented
52C2×#66871C2211yescharacteristic, complemented
53#10622565—21no—
54#10622558—21no—
55#10622542C2211yescharacteristic, complemented
56#10622541C2211yescharacteristic, complemented
57C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58C2×C4×C11⋊C8C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63C25×C11—21no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—21no—
67C22×D4×C11—21no—
68C22×D4×C11—22no—
69C22×D4×C11—21no—
70C22×D4×C11—22no—
71C22×D4×C11—41no—
72C22×D4×C11—41no—
73C22×D4×C11D411yescharacteristic
74C22×D4×C11C2311yescharacteristic
75C22×D4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×Dic22C2311yescharacteristic
79C11×#121—22no—
80C11×#121—22no—
81C11×#121—41no—
82C11×#121—41no—
83C11×#120—44no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C22⋊Dic11—21no—
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×#4324—22no—
104C2×#4324—22no—
105C2×#4324—22no—
106C2×#4324—22no—
107C2×#4324—41no—
108C2×#4324—41no—
109#66979—22no—
110#66979—41no—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114#66977—22no—
115#66977—22no—
116#66977—22no—
117#66977—41no—
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×C4×Dic11—21no—
122C2×#4318—22no—
123C2×#4318—22no—
124C2×#4318—22no—
125C2×#4318—22no—
126C2×#4318—41no—
127C2×#4318—41no—
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C11×#95—21no—
133#66896—22no—
134#66896—22no—
135#66896—22no—
136#66896—22no—
137#66896—22no—
138#66896D414yescomplemented
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C22⋊(C11⋊C8)—22no—
144C22⋊(C11⋊C8)D414yescomplemented
145#66874—22no—
146#66874—41no—
147#66872—41no—
148#66871—22no—
149C4⋊(C11⋊C8)—22no—
150C4×C11⋊C8—22no—
151#25136—111nomaximal, Sylow
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—42no—
155C24×C11—42no—
156C24×C11—42no—
157C24×C11—42no—
158C24×C11—42no—
159C24×C11—81no—
160C24×C11—81no—
161C24×C11C2×D411yescharacteristic
162C24×C11C2×D411yescharacteristic
163C2×D4×C11—28no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—44no—
177C2×D4×C11—44no—
178C2×D4×C11—41no—
179C2×D4×C11—42no—
180C2×D4×C11—42no—
181C2×D4×C11—44no—
182C2×D4×C11—42no—
183C2×D4×C11—42no—
184C2×D4×C11—42no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11—81no—
188C2×D4×C11—81no—
189C2×D4×C11C2×D412yes—
190C2×D4×C11#4112yes—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
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×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11#4112yes—
209C22×C4×C11C2411yescharacteristic
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22—21no—
220C11×C4⋊C4—22no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—81no—
233C11×C22⋊C4—81no—
234C42×C11—21no—
235C42×C11—21no—
236C22⋊Dic11—42no—
237C22⋊Dic11—42no—
238C22⋊Dic11—42no—
239C22⋊Dic11—42no—
240#4324—44no—
241#4324—44no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11C2×D412yes—
248Dic11⋊C4—42no—
249Dic11⋊C4—42no—
250Dic11⋊C4—42no—
251C4×Dic11—42no—
252#4318—44no—
253#4318—44no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8C2×D412yes—
264C2×C11⋊C8C2×D412yes—
265C2×C11⋊C8C2×D412yes—
266C2×#468—111no—
267C2×#450—111no—
268C2×#436—111no—
269C2×#418—111no—
270#2415—111no—
271#2408D1111yescharacteristic
272#2067—111no—
273#2055—111no—
274#2034—111no—
275#2000—111no—
276#1968—111no—
277#1934—111no—
278#1895—111no—
279#1894—111no—
280#1854—111no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—48no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—84no—
310C23×C11—84no—
311C23×C11—84no—
312C23×C11—84no—
313C23×C11—84no—
314C23×C11—84no—
315C23×C11#12112yes—
316C23×C11C22×D411yescharacteristic
317D4×C11—22no—
318D4×C11—22no—
319D4×C11—22no—
320D4×C11—22no—
321D4×C11—44no—
322D4×C11—48no—
323D4×C11—41no—
324D4×C11—41no—
325D4×C11—41no—
326D4×C11—41no—
327D4×C11—84no—
328D4×C11—84no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11#12112yes—
354C2×C4×C11AGL(1,ℤ/8)12yes—
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C2×#4111yescharacteristic
358C2×C4×C11C2×#4111yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C2×C4×C11H(5,𝔽2)11yescharacteristic
361C2×Dic11—22no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373Dic22—41no—
374Dic22—41no—
375Dic22—41no—
376Dic22—41no—
377C11⋊C8—22no—
378C11⋊C8—22no—
379C11⋊C8—22no—
380C11⋊C8—41no—
381C23×D4C2×D1111yescharacteristic
382C22×SD16—111no—
383C22×SD16—111no—
384C22×M16—111no—
385C22×M16—111no—
386C2×C22⋊Q8—111no—
387C2×C22⋊Q8—111no—
388C2×#121C2×D1111yescharacteristic
389C2×#121C2×D1111yescharacteristic
390C2×#120—21no—
391C2×C4×D4C2×D1111yescharacteristic
392C2×#117—111no—
393#468—224no—
394#450—224no—
395#436—224no—
396C2×#107—111no—
397C2×#106—111no—
398C2×C4⋊C8—111no—
399#418—224no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#102—111no—
403C2×#102—111no—
404C2×#102—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×C22⋊C8—111no—
409C2×C22⋊C8—111no—
410C2×C4×C8—111no—
411#397—221no—
412#394—21no—
413#394—221no—
414#392—21no—
415#391—111no—
416#390C2×D1111yescharacteristic
417#390C2×D1111yescharacteristic
418#389—111no—
419#389—221no—
420#388—221no—
421#380—111no—
422#380C2×D1111yescharacteristic
423#379—21no—
424#340—111no—
425#340—111no—
426#340—111no—
427#340—111no—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—41no—
432C22×C11—41no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—42no—
437C22×C11—42no—
438C22×C11—41no—
439C22×C11—42no—
440C22×C11—41no—
441C22×C11—42no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11—41no—
445C22×C11—42no—
446C22×C11—41no—
447C22×C11—42no—
448C22×C11—816no—
449C22×C11—81no—
450C22×C11—81no—
451C22×C11—81no—
452C22×C11—81no—
453C22×C11—81no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11C2×#12111yescharacteristic
458C22×C11D4211yescharacteristic
459C22×C11#54611yescharacteristic
460C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
461C22×C11#57511yescharacteristic
462C22×C11#57711yescharacteristic
463C22×C11#57711yescharacteristic
464C4×C11—22no—
465C4×C11—22no—
466C4×C11—41no—
467C4×C11—41no—
468C4×C11—81no—
469C4×C11—81no—
470C4×C11#52511yescharacteristic
471C4×C11#53811yescharacteristic
472C4×C11D4211yescharacteristic
473C4×C11#54611yescharacteristic
474Dic11—42no—
475Dic11—81no—
476Dic11—81no—
477Dic11—81no—
478C25—21no—
479C22×Q8—111no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—22no—
485C22×D4—22no—
486C22×D4—21no—
487C22×D4—41no—
488C22×D4—41no—
489C22×D4C22⋊D1111yescharacteristic
490C22×D4C22×D1111yescharacteristic
491C22×D4C22×D1111yescharacteristic
492C23×C4C22×D1111yescharacteristic
493C23×C4C22×D1111yescharacteristic
494C2×SD16—222no—
495C2×SD16—222no—
496C2×SD16—222no—
497C2×SD16—222no—
498C2×SD16—441no—
499C2×SD16—441no—
500C2×M16—222no—
501C2×M16—222no—
502C2×M16—222no—
503C2×M16—222no—
504C2×M16—441no—
505C2×M16—441no—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8—111no—
509C22×C8—111no—
510C22⋊Q8—222no—
511C22⋊Q8—222no—
512C22⋊Q8—222no—
513C22⋊Q8—441no—
514#121—22no—
515#121—22no—
516#121—41no—
517#121—41no—
518#120—44no—
519C4×D4—22no—
520C4×D4—22no—
521#117—222no—
522#117—441no—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—221no—
527C2×C4⋊C4—221no—
528C2×C4⋊C4—221no—
529C2×C4⋊C4C22⋊D1111yescharacteristic
530C2×C4⋊C4C22×D1111yescharacteristic
531C2×C4⋊C4C22×D1111yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4C22⋊D1111yescharacteristic
544C2×C22⋊C4C22⋊D1111yescharacteristic
545C2×C42—221no—
546C2×C42C22×D1111yescharacteristic
547#107—222no—
548#106—441no—
549C4⋊C8—222no—
550#103—222no—
551#103—441no—
552#102—114no—
553#102—222no—
554#102—222no—
555#102—222no—
556#102—222no—
557#102—222no—
558C22⋊C8—114no—
559C22⋊C8—222no—
560C4×C8—222no—
561#95—21no—
562#95—221no—
563#95—221no—
564#95—221no—
565#95—221no—
566C2×C11—42no—
567C2×C11—81no—
568C2×C11—82no—
569C2×C11—82no—
570C2×C11#242411yescharacteristic
571C2×C11#305511yescharacteristic
572C2×C11#305711yescharacteristic
573C2×C11#327211yescharacteristic
574C2×C11#327511yescharacteristic
575C2×C11#332311yescharacteristic
576C2×C11#332411yescharacteristic
577C24—21no—
578C24—21no—
579C24—42no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—81no—
585C24—81no—
586C24C2×C22⋊D1111yescharacteristic
587C24C2×C22⋊D1111yescharacteristic
588C2×Q8—221no—
589C2×Q8—221no—
590C2×Q8—221no—
591C2×Q8—221no—
592C2×Q8—221no—
593C2×Q8—221no—
594C2×D4—28no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—44no—
608C2×D4—44no—
609C2×D4—41no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4D4×D1112yes—
621C2×D4#434112yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—221no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4D4×D1112yes—
639C22×C4#434112yes—
640C22×C4C2×C22⋊D1111yescharacteristic
641C22×C4C2×C22⋊D1111yescharacteristic
642C22×C4C2×C22⋊D1111yescharacteristic
643C22×C4C2×C22⋊D1111yescharacteristic
644C22×C4C23×D1111yescharacteristic
645SD16—444no—
646SD16—444no—
647M16—444no—
648M16—444no—
649C2×C8—112no—
650C2×C8—112no—
651C2×C8—112no—
652C2×C8—221no—
653C2×C8—221no—
654C2×C8—221no—
655C2×C8—221no—
656C2×C8—221no—
657C2×C8—221no—
658C2×C8—221no—
659C2×C8—221no—
660C2×C8—221no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—112no—
667C4⋊C4—221no—
668C4⋊C4—221no—
669C4⋊C4—221no—
670C4⋊C4—221no—
671C4⋊C4—221no—
672C4⋊C4—442no—
673C4⋊C4—442no—
674C4⋊C4—442no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—442no—
685C22⋊C4—442no—
686C22⋊C4—442no—
687C22⋊C4—442no—
688C42—21no—
689C42—21no—
690C42—442no—
691C11#2513611yescharacteristic, complemented, Sylow
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—22no—
700C23—21no—
701C23—21no—
702C23—22no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#6699212yes—
727C23C22×C22⋊D1111yescharacteristic
728Q8—441no—
729Q8—441no—
730Q8—441no—
731Q8—441no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—48no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—84no—
743D4—84no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—222no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4—441no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4#6698512yes—
781C2×C4#6699212yes—
782C2×C4C2×D4×D1111yescharacteristic
783C2×C4C2×D4×D1111yescharacteristic
784C2×C4C2×#434111yescharacteristic
785C2×C4C2×#434111yescharacteristic
786C2×C4#6703711yescharacteristic
787C2×C4#6703711yescharacteristic
788C8—222no—
789C8—222no—
790C8—222no—
791C8—441no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—41no—
811C22—41no—
812C22—816no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22C2×#6698511yescharacteristic
822C22D4×C22⋊D1111yescharacteristic
823C22C2×#6699211yescharacteristic
824C22#1062333711yescharacteristic
825C22#1062335311yescharacteristic
826C22#1062336711yescharacteristic
827C22#1062336711yescharacteristic
828C4—22no—
829C4—22no—
830C4—41no—
831C4—41no—
832C4—81no—
833C4—81no—
834C4—442no—
835C4—881no—
836C4—881no—
837C4—881no—
838C4#1062311711yescharacteristic
839C4#1062312111yescharacteristic
840C4#1062312211yescharacteristic
841C4#1062312411yescharacteristic
842C2—42no—
843C2—81no—
844C2—82no—
845C2—82no—
846C2#1307215611yescharacteristic
847C2#1307823111yescharacteristic
848C2#1307825211yescharacteristic
849C2#1308021211yescharacteristic
850C2#1308024311yescharacteristic
851C2#1308083211yescharacteristic
852C2#1308084711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2408C2
socleC23×C11C22×D4
hypercenter#2408D11
hypocenterC11#25136
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C2×#10622655C2semidirect
2. C2×#10622831C2semidirect
3. C2×#10622625C2semidirect
4. C2×#10622828C2semidirect
5. #13072045C2semidirect
6. #13070004C2semidirect
7. #13069933C2semidirect
8. #13069802C2semidirect
9. #13069619C2semidirect
10. #13069469C2semidirect
11. #13069302C2semidirect
12. #13069055C2semidirect
13. #13069047C2semidirect
14. #13068813C2semidirect
25. C2×#66977C22semidirect
27. C22×#4318C22semidirect
43. #10622825C22semidirect
45. C2×C22⋊(C11⋊C8)C22semidirect
49. C2×#66874C22semidirect
50. C2×#66874C22semidirect
51. C2×#66872C22semidirect
52. C2×#66871C22semidirect
55. #10622542C22semidirect
56. #10622541C22semidirect
57. C2×C4⋊(C11⋊C8)C22semidirect
58. C2×C4×C11⋊C8C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
138. #66896D4semidirect
144. C22⋊(C11⋊C8)D4semidirect
691. C11#25136semidirect

Maximal subgroups

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

subgroupindex
C2×#106226552
C2×#106228312
C2×#106226252
C2×#106228282
#130720452
#130700042
#130699332
#130698022
#130696192
#130694692
#130693022
#130690552
#130690472
#130688132
C11×#24082
#2513611