Finite Group Databasebeta

← #14804559

Subgroups — #14804559

Order 2816.

1052 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622664C211yesmaximal, characteristic, complemented
2C2×#10622654C211yesmaximal, characteristic, complemented
3C2×#10622667C211yesmaximal, characteristic, complemented
4C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
5#13073525C211yesmaximal, characteristic, complemented
6#13069809C211yesmaximal, characteristic, complemented
7#13069795C211yesmaximal, characteristic, complemented
8#13069624C211yesmaximal, characteristic, complemented
9#13069619C211yesmaximal, characteristic, complemented
10#13069428C211yesmaximal, characteristic, complemented
11#13069384C211yesmaximal, characteristic, complemented
12#13069045C211yesmaximal, characteristic, complemented
13#13069040C211yesmaximal, characteristic, complemented
14C4×#66874C211yesmaximal, characteristic, complemented
15C11×#2540C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C22×#4324C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27C23×C11⋊C8C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C11×#399—21no—
30C11×#392—21no—
31C11×#390—21no—
32C11×#390—21no—
33C4×C11×C4⋊C4C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37#10622835—21no—
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41#10622825C2211yescharacteristic
42#10622825C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622667—24no—
46#10622664—24no—
47#10622654—24no—
48D4×C11⋊C8—24no—
49#10622593—21no—
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54#10622557—21no—
55#10622557—21no—
56#10622549C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×C4×C11⋊C8C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11D411yescharacteristic
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×Dic22C2311yescharacteristic
71C11×#124—22no—
72C11×#124—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—41no—
76C11×C22⋊Q8—41no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#121—41no—
80C11×#121—41no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
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⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11—21no—
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11—21no—
102C2×#4326—22no—
103C2×#4326—22no—
104C2×#4326—41no—
105C2×#4324—22no—
106C2×#4324—22no—
107C2×#4324—41no—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111#66977—22no—
112#66977—22no—
113#66977—41no—
114#66977—41no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×C4×Dic11—21no—
119C22×C11⋊C8—22no—
120C22×C11⋊C8—22no—
121C22×C11⋊C8—22no—
122C22×C11⋊C8—22no—
123C22×C11⋊C8—41no—
124C22×C11⋊C8—41no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C4×Dic22—22no—
130C4×Dic22—22no—
131C11×#95—21no—
132#66899—22no—
133#66899—22no—
134#66899—41no—
135#66896—22no—
136#66896—22no—
137#66896—41no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C22⋊(C11⋊C8)—22no—
143C22⋊(C11⋊C8)—22no—
144#66874—22no—
145#66874D414yescomplemented
146#66872—22no—
147#66871—22no—
148C4⋊(C11⋊C8)D414yescomplemented
149C4×C11⋊C8—22no—
150#25389—111nomaximal, Sylow
151C24×C11—21no—
152C24×C11C2×D411yescharacteristic
153C24×C11C2×D411yescharacteristic
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11—81no—
174C2×D4×C11—81no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2411yescharacteristic
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22—21no—
204C2×Dic22C2×D412yes—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—42no—
209C11×C4⋊C4—42no—
210C11×C4⋊C4C2×D412yes—
211C11×C4⋊C4#4112yes—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C42×C11—81no—
221C42×C11C2×D412yes—
222C42×C11#4112yes—
223C22⋊Dic11—42no—
224C22⋊Dic11—42no—
225C22⋊Dic11—42no—
226C22⋊Dic11—42no—
227#4326—44no—
228#4324—44no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235Dic11⋊C4—42no—
236Dic11⋊C4—42no—
237Dic11⋊C4—42no—
238C4×Dic11—42no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—44no—
249C2×C11⋊C8—44no—
250C2×C11⋊C8C2×D412yes—
251C2×C11⋊C8C2×D412yes—
252C2×C11⋊C8C2×D412yes—
253C2×#467—111no—
254C2×#465—111no—
255C2×#464—111no—
256C2×C8×D4—111no—
257#2540D1111yescharacteristic
258#2536—111no—
259#2035—111no—
260#2033—111no—
261#2001—111no—
262#2000—111no—
263#1958—111no—
264#1949—111no—
265#1893—111no—
266#1892—111no—
267C4×#103—111no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11#13512yes—
288C23×C11#13512yes—
289C23×C11C22×D411yescharacteristic
290Q8×C11—41no—
291Q8×C11—41no—
292Q8×C11—41no—
293Q8×C11—41no—
294D4×C11—28no—
295D4×C11—41no—
296D4×C11—41no—
297D4×C11—41no—
298D4×C11—41no—
299D4×C11—84no—
300D4×C11—84no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11#12112yes—
329C2×C4×C11#12112yes—
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×Dic11—22no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348Dic22—22no—
349Dic22—22no—
350Dic22—41no—
351Dic22—41no—
352C11⋊C8—22no—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C11⋊C8—41no—
356C22×Q16—111no—
357C22×SD16—111no—
358C23×C8—111no—
359C23×C8—111no—
360C2×#124C2×D1111yescharacteristic
361C2×C22⋊Q8—111no—
362C2×C22⋊Q8—111no—
363C2×C22⋊Q8C2×D1111yescharacteristic
364C2×C22⋊Q8C2×D1111yescharacteristic
365C2×#121C2×D1111yescharacteristic
366C2×#121C2×D1111yescharacteristic
367C2×C4×Q8—111no—
368C2×C4×D4C2×D1111yescharacteristic
369#467—224no—
370#465—224no—
371#464—224no—
372C8×D4—224no—
373C2×#107—111no—
374C2×#106—111no—
375C2×C4⋊C8—111no—
376C2×#103—111no—
377C2×#103—111no—
378C2×#103—111no—
379C2×#103—111no—
380C2×#103—111no—
381C2×#102—111no—
382C2×#102—111no—
383C2×#102—111no—
384C2×C22⋊C8—111no—
385C2×C22⋊C8—111no—
386C2×C4×C8—111no—
387#399—21no—
388#398—221no—
389#394—221no—
390#392—21no—
391#390—21no—
392#390—21no—
393#388—221no—
394#388—221no—
395#382—111no—
396#380—111no—
397#380—111no—
398C4×C4⋊C4C2×D1111yescharacteristic
399#340—111no—
400#340—111no—
401#340—111no—
402#340—111no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11—81no—
423C22×C11—81no—
424C22×C11C2×#12111yescharacteristic
425C22×C11D4211yescharacteristic
426C22×C11#54611yescharacteristic
427C22×C11C2×#13511yescharacteristic
428C22×C11C2×#13511yescharacteristic
429C22×C11#57711yescharacteristic
430C22×C11#57811yescharacteristic
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—41no—
434C4×C11—41no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—81no—
438C4×C11#53211yescharacteristic
439C4×C11#54011yescharacteristic
440C4×C11D4211yescharacteristic
441C4×C11#55011yescharacteristic
442Dic11—42no—
443Dic11—81no—
444Dic11—81no—
445Dic11—81no—
446C22×Q8—111no—
447C22×Q8C22×D1111yescharacteristic
448C22×D4—21no—
449C22×D4—21no—
450C22×D4C22⋊D1111yescharacteristic
451C22×D4C22×D1111yescharacteristic
452C23×C4C22×D1111yescharacteristic
453C23×C4C22×D1111yescharacteristic
454C2×Q16—222no—
455C2×Q16—222no—
456C2×Q16—441no—
457C2×SD16—222no—
458C2×SD16—222no—
459C2×SD16—441no—
460C22×C8—111no—
461C22×C8—111no—
462C22×C8—111no—
463C22×C8—111no—
464C22×C8—222no—
465C22×C8—222no—
466C22×C8—222no—
467C22×C8—222no—
468C22×C8—441no—
469C22×C8—441no—
470#124—22no—
471#124—22no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—41no—
475C22⋊Q8—41no—
476C22⋊Q8—222no—
477C22⋊Q8—222no—
478C22⋊Q8—441no—
479C22⋊Q8—441no—
480#121—22no—
481#121—22no—
482#121—41no—
483#121—41no—
484C4×Q8—222no—
485C4×Q8—222no—
486C4×D4—22no—
487C4×D4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4C22⋊D1111yescharacteristic
497C2×C4⋊C4C22×D1111yescharacteristic
498C2×C4⋊C4C22×D1111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4C22⋊D1111yescharacteristic
510C2×C22⋊C4C22⋊D1111yescharacteristic
511C2×C42—21no—
512C2×C42—221no—
513C2×C42C22×D1111yescharacteristic
514#107—222no—
515#106—222no—
516C4⋊C8—114no—
517#103—114no—
518#103—222no—
519#103—222no—
520#103—222no—
521#103—441no—
522#102—222no—
523#102—222no—
524#102—441no—
525C22⋊C8—222no—
526C22⋊C8—222no—
527C4×C8—222no—
528#95—21no—
529#95—221no—
530#95—221no—
531#95—221no—
532#95—221no—
533C2×C11—42no—
534C2×C11—42no—
535C2×C11—161no—
536C2×C11#242811yescharacteristic
537C2×C11#305011yescharacteristic
538C2×C11#306311yescharacteristic
539C2×C11#328211yescharacteristic
540C2×C11#328511yescharacteristic
541C2×C11#329611yescharacteristic
542C2×C11#330011yescharacteristic
543C24—21no—
544C24C2×C22⋊D1111yescharacteristic
545C24C2×C22⋊D1111yescharacteristic
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—112no—
553C2×Q8—221no—
554C2×Q8—221no—
555C2×Q8—221no—
556C2×Q8—221no—
557C2×Q8—221no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—81no—
572C2×D4—81no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4C2×C22⋊D1111yescharacteristic
593C22×C4C2×C22⋊D1111yescharacteristic
594C22×C4C2×C22⋊D1111yescharacteristic
595C22×C4C2×C22⋊D1111yescharacteristic
596C22×C4C23×D1111yescharacteristic
597Q16—444no—
598SD16—444no—
599C2×C8—112no—
600C2×C8—112no—
601C2×C8—112no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8—221no—
611C2×C8—444no—
612C2×C8—444no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4—221no—
624C4⋊C4—442no—
625C4⋊C4—442no—
626C4⋊C4—442no—
627C4⋊C4D4×D1112yes—
628C4⋊C4#434112yes—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—442no—
638C22⋊C4—442no—
639C22⋊C4—442no—
640C22⋊C4—442no—
641C42—81no—
642C42—442no—
643C42D4×D1112yes—
644C42#434112yes—
645C11#2538911yescharacteristic, complemented, Sylow
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23#6700312yes—
666C23#6700312yes—
667C23C22×C22⋊D1111yescharacteristic
668Q8—41no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—222no—
673Q8—222no—
674Q8—441no—
675Q8—441no—
676D4—28no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—84no—
682D4—84no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—222no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4#6699212yes—
723C2×C4#6699212yes—
724C2×C4C2×D4×D1111yescharacteristic
725C2×C4C2×D4×D1111yescharacteristic
726C2×C4C2×#434111yescharacteristic
727C2×C4C2×#434111yescharacteristic
728C2×C4#6703711yescharacteristic
729C2×C4#6703711yescharacteristic
730C8—222no—
731C8—222no—
732C8—222no—
733C8—441no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22D4×C22⋊D1111yescharacteristic
756C22C2×#6699211yescharacteristic
757C22#1062333711yescharacteristic
758C22C2×#6700311yescharacteristic
759C22C2×#6700311yescharacteristic
760C22#1062336711yescharacteristic
761C22#1062336911yescharacteristic
762C4—22no—
763C4—22no—
764C4—41no—
765C4—41no—
766C4—42no—
767C4—42no—
768C4—81no—
769C4—442no—
770C4—881no—
771C4—881no—
772C4—881no—
773C4#1062324711yescharacteristic
774C4#1062324811yescharacteristic
775C4#1062324911yescharacteristic
776C4#1062325011yescharacteristic
777C2—42no—
778C2—42no—
779C2—161no—
780C2#1307220711yescharacteristic
781C2#1307819411yescharacteristic
782C2#1307830911yescharacteristic
783C2#1308031911yescharacteristic
784C2#1308035311yescharacteristic
785C2#1308045111yescharacteristic
786C2#1308050311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2540C2
socleC23×C11C22×D4
hypercenter#2540D11
hypocenterC11#25389
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#10622664C2semidirect
2. C2×#10622654C2semidirect
3. C2×#10622667C2semidirect
4. C2×D4×C11⋊C8C2semidirect
5. #13073525C2semidirect
6. #13069809C2semidirect
7. #13069795C2semidirect
8. #13069624C2semidirect
9. #13069619C2semidirect
10. #13069428C2semidirect
11. #13069384C2semidirect
12. #13069045C2semidirect
13. #13069040C2semidirect
14. C4×#66874C2semidirect
145. #66874D4semidirect
148. C4⋊(C11⋊C8)D4semidirect
645. C11#25389semidirect

Maximal subgroups

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

subgroupindex
C2×#106226642
C2×#106226542
C2×#106226672
C2×D4×C11⋊C82
#130735252
#130698092
#130697952
#130696242
#130696192
#130694282
#130693842
#130690452
#130690402
C4×#668742
C11×#25402
#2538911