Finite Group Databasebeta

← #14804513

Subgroups — #14804513

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622426C211yesmaximal, characteristic, complemented
2C2×#10622795C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D11C211yesmaximal, characteristic
4#13073566C211yesmaximal, characteristic
5#13073535C211yesmaximal, characteristic
6#13069821C211yesmaximal, characteristic, complemented
7#13069816C211yesmaximal, characteristic, complemented
8#13069624C211yesmaximal, characteristic, complemented
9#13069623C211yesmaximal, characteristic, complemented
10#13069416C211yesmaximal, characteristic, complemented
11#13069371C211yesmaximal, characteristic, complemented
12#13069039C211yesmaximal, characteristic, complemented
13#13069036C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C2×C11×#467C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×#66997C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C2×#66977C2211yescharacteristic
27C22×C8×D11C2211yescharacteristic
28C2×#66950C2211yescharacteristic
29C11×#467—24no—
30C2×C11×#107C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36#10622825C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38#10622795—24no—
39C8×C22⋊D11—24no—
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C2×Dic11⋊C8C2211yescharacteristic
44C2×C8×Dic11C2211yescharacteristic
45#10622607—21no—
46#10622605—21no—
47#10622600C2211yescharacteristic
48#10622589—21no—
49#10622589C2211yescharacteristic
50C4⋊C4×Dic11C2211yescharacteristic
51#10622585—21no—
52C2×#66874C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54#10622570—21no—
55#10622570—21no—
56#10622562—21no—
57#10622561—21no—
58#10622426—24no—
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11D411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×Dic22C2311yescharacteristic
69C2×C11×Q16—22no—
70C2×C11×Q16—22no—
71C2×C11×Q16—41no—
72C22×C8×C11—22no—
73C22×C8×C11—22no—
74C22×C8×C11—41no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—41no—
80C11×C22⋊Q8—41no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11D411yescharacteristic
90#66999—22no—
91#66999—22no—
92#66999—41no—
93#66999—41no—
94Q8×Dic11—22no—
95Q8×Dic11—22no—
96#66997—22no—
97#66997—22no—
98C2×#4326—22no—
99C2×#4326—22no—
100C2×#4326—41no—
101C4×C22⋊D11—22no—
102C4×C22⋊D11—22no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4D411yescharacteristic
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113#66977—22no—
114#66977—41no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4D411yescharacteristic
123C2×C4×Dic11—21no—
124C2×C4×Dic11—21no—
125C2×C4×Dic11C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C2×C8×D11—22no—
129C2×C8×D11—22no—
130C2×C8×D11—41no—
131#66950—22no—
132#66950—41no—
133C11×#107—22no—
134C11×#103—22no—
135C11×#103D414yescomplemented
136#66899—22no—
137#66899—22no—
138#66899—41no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C22⋊(C11⋊C8)—22no—
143(C2×D11)⋊C8—22no—
144#66880—22no—
145#66880—22no—
146Dic11⋊C8D414yes—
147C8×Dic11—22no—
148#66874—41no—
149#66871—22no—
150#25386—111nomaximal, Sylow
151C24×C11C2×D411yescharacteristic
152C23×D11C2×D411yescharacteristic
153C2×Q8×C11—21no—
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×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11C2×D412yes—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C2×C22⋊D11—22no—
178C2×C22⋊D11—22no—
179C2×C22⋊D11Q1614yescomplemented
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×Dic22—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C11×Q16—44no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—44no—
205C2×C8×C11C2×D412yes—
206C2×C8×C11C2×D412yes—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4C2×D412yes—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C22⋊Dic11—22no—
216C22⋊Dic11—42no—
217C22⋊Dic11—81no—
218#4326—44no—
219(C2×D11)⋊C4—22no—
220(C2×D11)⋊C4—42no—
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⋊Dic11#4112yes—
232Dic11⋊C4—22no—
233Dic11⋊C4—42no—
234Dic11⋊C4—42no—
235Dic11⋊C4—42no—
236Dic11⋊C4—42no—
237Dic11⋊C4—42no—
238Dic11⋊C4—42no—
239Dic11⋊C4—81no—
240C4×Dic11—42no—
241C4×Dic11—42no—
242C4×Dic11C2×D412yes—
243C4×Dic11#4112yes—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8C2×D412yes—
250C8×D11—44no—
251C2×#467—111no—
252C2×#467D1111yescharacteristic, complemented
253C2×#462—111no—
254C2×C8×D4—111no—
255#2542—111no—
256#2538—111no—
257#2036—111no—
258#2036—111no—
259#2001—111no—
260#2001—111no—
261#1956—111no—
262#1947—111no—
263#1892—111no—
264#1892—111no—
265C4×#103—111no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11C2×Q1612yes—
273C23×C11C22×D411yescharacteristic
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11C2×Q1612yes—
281Q8×C11—22no—
282Q8×C11—22no—
283Q8×C11—41no—
284Q8×C11—41no—
285Q8×C11—41no—
286Q8×C11—41no—
287Q8×C11—41no—
288Q8×C11—41no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
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—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11C22×D411yescharacteristic
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11H(5,𝔽2)11yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C22⋊D11—28no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—22no—
320C2×Dic11—21no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11#12112yes—
333C2×Dic11#12112yes—
334C2×Dic11C2×Q1612yes—
335C2×Dic11#13512yes—
336C4×D11—41no—
337C4×D11—41no—
338C4×D11—41no—
339C4×D11—41no—
340Dic22—41no—
341Dic22—41no—
342Dic22—41no—
343Dic22—41no—
344C8×C11—22no—
345C8×C11—22no—
346C11⋊C8—22no—
347C11⋊C8—41no—
348C22×Q16—111no—
349C22×Q16C2×D1111yescharacteristic
350C23×C8—111no—
351C23×C8C2×D1111yescharacteristic
352C2×C4⋊Q8—111no—
353C2×C22⋊Q8—111no—
354C2×C22⋊Q8—111no—
355C2×C22⋊Q8—111no—
356C2×C22⋊Q8—111no—
357C2×C22⋊Q8C2×D1111yescharacteristic
358C2×C22⋊Q8C2×D1111yescharacteristic
359C2×C4×Q8—111no—
360C2×C4×D4—111no—
361#467—24no—
362#467—224no—
363#462—224no—
364C8×D4—224no—
365C2×#107—111no—
366C2×#107C2×D1111yescharacteristic
367C2×C4⋊C8—111no—
368C2×#103—111no—
369C2×#103—111no—
370C2×#103—111no—
371C2×#103—111no—
372C2×#103—111no—
373C2×#103—111no—
374C2×#103C2×D1111yescharacteristic
375C2×#103C2×D1111yescharacteristic
376C2×C22⋊C8—111no—
377C2×C22⋊C8—111no—
378C2×C4×C8—111no—
379#399—221no—
380#399—221no—
381#396—221no—
382#396—221no—
383#390—221no—
384#390—221no—
385#389—221no—
386#384—111no—
387#384—221no—
388#380—111no—
389#380—111no—
390C4×C4⋊C4—111no—
391#340—111no—
392#340—111no—
393#340—111no—
394#340—111no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11C2×#12111yescharacteristic
403C22×C11D4211yescharacteristic
404C22×C11#54611yescharacteristic
405C22×C11C22×Q1611yescharacteristic
406C22×C11C2×#13511yescharacteristic
407C22×C11#57711yescharacteristic
408C22×C11#57811yescharacteristic
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11—41no—
413C2×D11—41no—
414C2×D11—41no—
415C2×D11—41no—
416C4×C11—41no—
417C4×C11—42no—
418C4×C11—42no—
419C4×C11—81no—
420C4×C11—81no—
421C4×C11#53211yescharacteristic
422C4×C11#54011yescharacteristic
423C4×C11D4211yescharacteristic
424C4×C11#55011yescharacteristic
425Dic11—22no—
426Dic11—41no—
427Dic11—42no—
428Dic11—81no—
429Dic11—81no—
430Dic11—81no—
431Dic11#46714yescomplemented
432C22×Q8—111no—
433C22×Q8C22×D1111yescharacteristic
434C22×Q8C22×D1111yescharacteristic
435C22×D4—111no—
436C23×C4—111no—
437C23×C4C22×D1111yescharacteristic
438C2×Q16—22no—
439C2×Q16—22no—
440C2×Q16—41no—
441C2×Q16—222no—
442C2×Q16—222no—
443C2×Q16—441no—
444C22×C8—22no—
445C22×C8—22no—
446C22×C8—41no—
447C22×C8—111no—
448C22×C8—111no—
449C22×C8—222no—
450C22×C8—222no—
451C22×C8—441no—
452C22×C8C22×D1111yescharacteristic
453C22×C8C22×D1111yescharacteristic
454C4⋊Q8—222no—
455C4⋊Q8—222no—
456C22⋊Q8—22no—
457C22⋊Q8—22no—
458C22⋊Q8—41no—
459C22⋊Q8—41no—
460C22⋊Q8—222no—
461C22⋊Q8—222no—
462C22⋊Q8—222no—
463C22⋊Q8—222no—
464C22⋊Q8—441no—
465C22⋊Q8—441no—
466C22⋊Q8—441no—
467C22⋊Q8—441no—
468C4×Q8—222no—
469C4×Q8—222no—
470C4×D4—222no—
471C4×D4—222no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—111no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4—221no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—111no—
492C2×C22⋊C4—111no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C42—111no—
500C2×C42—221no—
501C2×C42—221no—
502#107—22no—
503#107—222no—
504C4⋊C8—114no—
505#103—22no—
506#103—222no—
507#103—222no—
508#103—222no—
509#103—222no—
510#103—441no—
511#103—441no—
512#103C22⋊D1114yescomplemented
513C22⋊C8—222no—
514C22⋊C8—222no—
515C4×C8—222no—
516#95—221no—
517#95—221no—
518#95—221no—
519C2×C11—42no—
520C2×C11#242811yescharacteristic
521C2×C11C2×#46711yescharacteristic
522C2×C11#306311yescharacteristic
523C2×C11#328411yescharacteristic
524C2×C11D4×Q1611yescharacteristic
525C2×C11#329911yescharacteristic
526C2×C11#330211yescharacteristic
527D11—42no—
528C24—111no—
529C24D4×D1111yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—221no—
542C2×Q8—221no—
543C2×Q8—221no—
544C2×Q8—221no—
545C2×Q8—221no—
546C2×Q8—221no—
547C2×Q8C2×C22⋊D1112yes—
548C2×D4—114no—
549C2×D4—222no—
550C2×D4—222no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—111no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4D4×D1111yescharacteristic
575C22×C4C23×D1111yescharacteristic
576Q16—44no—
577Q16—444no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—44no—
583C2×C8—112no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—444no—
590C2×C8D4×D1112yes—
591C2×C8C2×C22⋊D1112yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—112no—
598C4⋊C4—222no—
599C4⋊C4—221no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—442no—
605C4⋊C4—442no—
606C4⋊C4—442no—
607C4⋊C4—442no—
608C4⋊C4—442no—
609C4⋊C4—442no—
610C4⋊C4—442no—
611C4⋊C4—442no—
612C4⋊C4—881no—
613C4⋊C4C2×C22⋊D1112yes—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—222no—
617C22⋊C4—222no—
618C22⋊C4—442no—
619C22⋊C4—442no—
620C22⋊C4—442no—
621C22⋊C4—442no—
622C22⋊C4—881no—
623C22⋊C4—881no—
624C42—112no—
625C42—112no—
626C42—442no—
627C42—442no—
628C11#2538611yescharacteristic, complemented, Sylow
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—112no—
636C23—221no—
637C23—221no—
638C23—221no—
639C23—221no—
640C23—221no—
641C23—221no—
642C23Q16×D1112yes—
643C23C2×D4×D1111yescharacteristic
644Q8—22no—
645Q8—22no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—441no—
653Q8—441no—
654Q8—441no—
655Q8—441no—
656D4—228no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—112no—
679C2×C4—112no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—222no—
685C2×C4—221no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4C2×D4×D1111yescharacteristic
702C2×C4#6703711yescharacteristic
703C2×C4#6703711yescharacteristic
704C2×C4#41×D1111yescharacteristic
705C2×C4#41×D1111yescharacteristic
706C2×C4C22×C22⋊D1111yescharacteristic
707C8—22no—
708C8—22no—
709C8—222no—
710C8—441no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—222no—
719C22—222no—
720C22—222no—
721C22—441no—
722C22—441no—
723C22—441no—
724C22—441no—
725C22D11×#12111yescharacteristic
726C22#1062314111yescharacteristic
727C22C2×Q16×D1111yescharacteristic
728C22#1062329711yescharacteristic
729C22D11×#13511yescharacteristic
730C22#1062330111yescharacteristic
731C22D4×C22⋊D1111yescharacteristic
732C4—42no—
733C4—41no—
734C4—42no—
735C4—81no—
736C4—81no—
737C4—114no—
738C4—222no—
739C4—441no—
740C4—442no—
741C4—881no—
742C4—881no—
743C4—881no—
744C4#1062313011yescharacteristic
745C4#1062314611yescharacteristic
746C4D4×C22⋊D1111yescharacteristic
747C4#1062336311yescharacteristic
748C2—42no—
749C2—442no—
750C2#1307220111yescharacteristic
751C2D11×#46711yescharacteristic
752C2#1307830611yescharacteristic
753C2#1308034011yescharacteristic
754C2Q16×C22⋊D1111yescharacteristic
755C2#1308048711yescharacteristic
756C2#1308052811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#467C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenterC2×#467D11
hypocenterC11#25386
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#10622426C2semidirect
2. C2×#10622795C2semidirect
6. #13069821C2semidirect
7. #13069816C2semidirect
8. #13069624C2semidirect
9. #13069623C2semidirect
10. #13069416C2semidirect
11. #13069371C2semidirect
12. #13069039C2semidirect
13. #13069036C2semidirect
14. #103×Dic11C2semidirect
15. C2×C11×#467C2semidirect
135. C11×#103D4semidirect
179. C2×C22⋊D11Q16semidirect
252. C2×#467D11semidirect
431. Dic11#467semidirect
512. #103C22⋊D11semidirect
628. C11#25386semidirect

Maximal subgroups

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

subgroupindex
C2×#106224262
C2×#106227952
C2×C8×C22⋊D112
#130735662
#130735352
#130698212
#130698162
#130696242
#130696232
#130694162
#130693712
#130690392
#130690362
#103×Dic112
C2×C11×#4672
#2538611