Finite Group Databasebeta

← C11×#23403 #14600596

Subgroups — C11×#23403 #14600596

Order 2816.

1942 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×C11×#575C211yesmaximal, characteristic
2C2×C11×#536C211yesmaximal, characteristic, complemented
3C2×C11×#536C211yesmaximal, characteristic, complemented
4C2×C11×#421C211yesmaximal, characteristic, complemented
5C11×#2896C211yesmaximal, characteristic, complemented
6C22×C11×#101C211yesmaximal, characteristic, complemented
7C11×#2005C214yesmaximal, complemented
8C11×#2003C214yesmaximal, complemented
9C11×#1733C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×C11×#41C2211yescharacteristic
12C23×Q8×C11C2211yescharacteristic
13C11×#575—24no—
14C11×#575—24no—
15C2×C11×#137—21no—
16C2×C11×#137C2212yes—
17C2×C11×AGL(1,ℤ/8)—21no—
18C2×C11×AGL(1,ℤ/8)C2212yes—
19C2×C11×#135—22no—
20C22×C11×M16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C11×#536—22no—
23C11×#536—24no—
24C11×#536—22no—
25C11×#536—22no—
26C11×#536—24no—
27C11×#536C2214yes—
28C2×C11×C4⋊Q8—21no—
29C2×C11×C4⋊Q8C2212yescomplemented
30C2×C11×#124—21no—
31C2×C11×#124C2212yescomplemented
32C2×C11×#123—22no—
33C2×C11×#123—22no—
34C2×C11×C22⋊Q8—22no—
35C2×C11×C22⋊Q8—22no—
36C2×C11×#117C2211yescharacteristic
37C2×C11×#117C2211yescharacteristic
38C11×#421—24no—
39C2×C11×#104C2214yes—
40C11×#419C2212yescomplemented
41C11×#418C2212yescomplemented
42C11×#417—22no—
43C11×#416—22no—
44C2×C11×#101—24no—
45C2×C11×#101C2214yescomplemented
46C11×#339C2214yescomplemented
47C2×C11×#41—21no—
48C2×C11×#41—22no—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—21no—
52C2×C11×#41—22no—
53C2×C11×#41—21no—
54C2×C11×#41—21no—
55C2×C11×#41—22no—
56C2×C11×#41—22no—
57C2×C11×#41—22no—
58C2×C11×#41—22no—
59C2×C11×#41—22no—
60C2×C11×#41D412yes—
61C2×C11×#41D414yes—
62C2×C11×#41C2312yes—
63C22×Q8×C11—21no—
64C22×Q8×C11—21no—
65C22×Q8×C11—21no—
66C22×Q8×C11—22no—
67C22×Q8×C11—21no—
68C22×Q8×C11—22no—
69C22×Q8×C11—22no—
70C22×Q8×C11—22no—
71C22×Q8×C11D411yescharacteristic
72C22×Q8×C11D412yes—
73C22×Q8×C11C2311yescharacteristic
74C22×Q8×C11C2312yes—
75C22×D4×C11—21no—
76C22×D4×C11—21no—
77C22×D4×C11D411yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C23×C4×C11—21no—
81C23×C4×C11D412yes—
82C23×C4×C11C2311yescharacteristic
83C11×#137—28no—
84C11×#137—24no—
85C11×#137—24no—
86C11×AGL(1,ℤ/8)—28no—
87C11×AGL(1,ℤ/8)—24no—
88C11×AGL(1,ℤ/8)—24no—
89C11×#135—216no—
90C2×C11×Q16—22no—
91C2×C11×SD16—22no—
92C2×C11×SD16—22no—
93C2×C11×D8—22no—
94C2×C11×M16—21no—
95C2×C11×M16—22no—
96C2×C11×M16—21no—
97C2×C11×M16—22no—
98C2×C11×M16—22no—
99C2×C11×M16D414yes—
100C2×C11×M16C2312yes—
101C2×C11×M16C2312yes—
102C22×C8×C11—21no—
103C22×C8×C11—21no—
104C11×C4⋊Q8—24no—
105C11×C4⋊Q8—24no—
106C11×C4⋊Q8—24no—
107C11×C4⋊Q8—24no—
108C11×#124—24no—
109C11×#124—24no—
110C11×#124—24no—
111C11×#124—24no—
112C11×#123—216no—
113C11×#123—28no—
114C11×#123—28no—
115C11×C22⋊Q8—216no—
116C11×C22⋊Q8—28no—
117C11×C22⋊Q8—28no—
118C11×#117—21no—
119C11×#117—21no—
120C11×#117—22no—
121C11×#117D412yes—
122C11×#117D414yes—
123C11×#117C2312yes—
124C2×C11×C4⋊C4—24no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—24no—
127C2×C11×C4⋊C4D412yes—
128C2×C11×C22⋊C4—24no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—24no—
132C2×C42×C11—21no—
133C2×C42×C11C2312yes—
134C11×#104—28no—
135C11×#103—24no—
136C11×#102—24no—
137C11×#101—28no—
138#23403C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C11×#41—24no—
143C11×#41—24no—
144C11×#41—24no—
145C11×#41—24no—
146C11×#41—24no—
147C11×#41—24no—
148C11×#41—22no—
149C11×#41—22no—
150C11×#41—22no—
151C11×#41—22no—
152C11×#41—42no—
153C11×#41—42no—
154C11×#41—42no—
155C11×#41—42no—
156C11×#41—42no—
157C11×#41—42no—
158C11×#41—42no—
159C11×#41—42no—
160C2×Q8×C11—24no—
161C2×Q8×C11—22no—
162C2×Q8×C11—22no—
163C2×Q8×C11—21no—
164C2×Q8×C11—24no—
165C2×Q8×C11—22no—
166C2×Q8×C11—22no—
167C2×Q8×C11—22no—
168C2×Q8×C11—22no—
169C2×Q8×C11—22no—
170C2×Q8×C11—21no—
171C2×Q8×C11—22no—
172C2×Q8×C11—22no—
173C2×Q8×C11—22no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—42no—
179C2×Q8×C11—42no—
180C2×Q8×C11—42no—
181C2×Q8×C11—42no—
182C2×Q8×C11—42no—
183C2×Q8×C11—42no—
184C2×Q8×C11—42no—
185C2×Q8×C11—42no—
186C2×Q8×C11C2×D412yes—
187C2×Q8×C11C2×D412yes—
188C2×D4×C11—24no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—21no—
193C2×D4×C11—22no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—41no—
200C2×D4×C11—41no—
201C2×D4×C11—42no—
202C2×D4×C11—42no—
203C2×D4×C11—42no—
204C2×D4×C11C2×D412yes—
205C2×D4×C11C2×D412yes—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—21no—
209C22×C4×C11—24no—
210C22×C4×C11—22no—
211C22×C4×C11—24no—
212C22×C4×C11—22no—
213C22×C4×C11—21no—
214C22×C4×C11—24no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—41no—
218C22×C4×C11—41no—
219C22×C4×C11—42no—
220C22×C4×C11—42no—
221C22×C4×C11—42no—
222C22×C4×C11C2×D414yes—
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D412yes—
227C22×C4×C11C2×D412yes—
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D412yes—
231C22×C4×C11#4112yes—
232C22×C4×C11C2411yescharacteristic
233C11×Q16—28no—
234C11×SD16—28no—
235C11×SD16—28no—
236C11×D8—28no—
237C11×M16—24no—
238C11×M16—22no—
239C11×M16—22no—
240C11×M16—22no—
241C11×M16—42no—
242C11×M16C2×D414yes—
243C2×C8×C11—24no—
244C2×C8×C11—22no—
245C2×C8×C11—22no—
246C2×C8×C11—42no—
247C11×C4⋊C4—216no—
248C11×C4⋊C4—216no—
249C11×C4⋊C4—24no—
250C11×C4⋊C4—22no—
251C11×C4⋊C4C2×D414yes—
252C11×C22⋊C4—216no—
253C11×C22⋊C4—216no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—22no—
256C11×C22⋊C4—22no—
257C42×C11—22no—
258C42×C11—22no—
259C42×C11—22no—
260C42×C11C2×D414yes—
261C2×#575C2×C1111yescharacteristic
262C2×#536C2×C1111yescharacteristic, complemented
263C2×#536C2×C1111yescharacteristic, complemented
264C2×#421C2×C1111yescharacteristic, complemented
265#2896C2×C1111yescharacteristic, complemented
266C22×#101C2×C1111yescharacteristic, complemented
267#2005C2×C1114yescomplemented
268#2003C2×C1114yescomplemented
269#1733C2×C1111yescharacteristic, complemented
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—42no—
273C23×C11—44no—
274C23×C11—44no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—42no—
278C23×C11#12011yescharacteristic
279C23×C11#12011yescharacteristic
280C23×C11#12012yes—
281C23×C11#12112yes—
282C23×C11C22×D411yescharacteristic
283Q8×C11—22no—
284Q8×C11—22no—
285Q8×C11—22no—
286Q8×C11—22no—
287Q8×C11—42no—
288Q8×C11—42no—
289Q8×C11—42no—
290Q8×C11—41no—
291Q8×C11—42no—
292Q8×C11—41no—
293Q8×C11—44no—
294Q8×C11—44no—
295Q8×C11—42no—
296D4×C11—22no—
297D4×C11—22no—
298D4×C11—22no—
299D4×C11—22no—
300D4×C11—42no—
301D4×C11—42no—
302D4×C11—44no—
303D4×C11—44no—
304D4×C11—44no—
305D4×C11—41no—
306D4×C11—41no—
307D4×C11—42no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—22no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
313C2×C4×C11—22no—
314C2×C4×C11—24no—
315C2×C4×C11—44no—
316C2×C4×C11—44no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—44no—
320C2×C4×C11—44no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—44no—
325C2×C4×C11—44no—
326C2×C4×C11—44no—
327C2×C4×C11#12012yes—
328C2×C4×C11#12012yes—
329C2×C4×C11#12012yes—
330C2×C4×C11#12011yescharacteristic
331C2×C4×C11#12011yescharacteristic
332C2×C4×C11#12112yes—
333C2×C4×C11#12112yes—
334C2×C4×C11#12112yes—
335C2×C4×C11#12112yes—
336C2×C4×C11#12112yes—
337C2×C4×C11#12712yes—
338C2×C4×C11#12712yes—
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C2×#4111yescharacteristic
345C8×C11—24no—
346C8×C11—42no—
347C22×#41C22×C1111yescharacteristic
348C22×#41C22×C1111yescharacteristic
349C23×Q8C22×C1111yescharacteristic
350#575—24no—
351#575—24no—
352C2×#137—21no—
353C2×#137C22×C1112yes—
354C2×AGL(1,ℤ/8)—21no—
355C2×AGL(1,ℤ/8)C22×C1112yes—
356C2×#135—22no—
357C22×M16C22×C1111yescharacteristic
358C22×M16C22×C1111yescharacteristic
359#536—22no—
360#536—24no—
361#536—22no—
362#536—22no—
363#536—24no—
364#536C22×C1114yes—
365C2×C4⋊Q8—21no—
366C2×C4⋊Q8C22×C1112yescomplemented
367C2×#124—21no—
368C2×#124C22×C1112yescomplemented
369C2×#123—22no—
370C2×#123—22no—
371C2×C22⋊Q8—22no—
372C2×C22⋊Q8—22no—
373C2×#117C22×C1111yescharacteristic
374C2×#117C22×C1111yescharacteristic
375#421—24no—
376C2×#104C22×C1114yes—
377#419C22×C1112yescomplemented
378#418C22×C1112yescomplemented
379#417—22no—
380#416—22no—
381C2×#101—24no—
382C2×#101C22×C1114yescomplemented
383#339C22×C1114yescomplemented
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—42no—
388C22×C11—42no—
389C22×C11—44no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—44no—
393C22×C11—82no—
394C22×C11—84no—
395C22×C11—82no—
396C22×C11#39212yes—
397C22×C11#39212yes—
398C22×C11C2×#12011yescharacteristic
399C22×C11C2×#12011yescharacteristic
400C22×C11C2×#12111yescharacteristic
401C4×C11—44no—
402C4×C11—44no—
403C4×C11—42no—
404C4×C11—42no—
405C4×C11—44no—
406C4×C11#39212yes—
407C4×C11#39212yes—
408C4×C11C2×#12011yescharacteristic
409C4×C11C2×#12111yescharacteristic
410C4×C11C2×#12111yescharacteristic
411C4×C11C2×#12711yescharacteristic
412C2×#41—21no—
413C2×#41—22no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—22no—
418C2×#41—22no—
419C2×#41—22no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—22no—
423C2×#41—22no—
424C2×#41—22no—
425C2×#41D4×C1112yes—
426C2×#41D4×C1114yes—
427C2×#41C23×C1112yes—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—22no—
432C22×Q8—21no—
433C22×Q8—22no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8D4×C1111yescharacteristic
437C22×Q8D4×C1112yes—
438C22×Q8C23×C1111yescharacteristic
439C22×Q8C23×C1112yes—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4D4×C1111yescharacteristic
443C22×D4C23×C1111yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C23×C4D4×C1112yes—
447C23×C4C23×C1111yescharacteristic
448#137—28no—
449#137—24no—
450#137—24no—
451AGL(1,ℤ/8)—28no—
452AGL(1,ℤ/8)—24no—
453AGL(1,ℤ/8)—24no—
454#135—216no—
455C2×Q16—22no—
456C2×SD16—22no—
457C2×SD16—22no—
458C2×D8—22no—
459C2×M16—21no—
460C2×M16—22no—
461C2×M16—21no—
462C2×M16—22no—
463C2×M16—22no—
464C2×M16D4×C1114yes—
465C2×M16C23×C1112yes—
466C2×M16C23×C1112yes—
467C22×C8—21no—
468C22×C8—21no—
469C4⋊Q8—24no—
470C4⋊Q8—24no—
471C4⋊Q8—24no—
472C4⋊Q8—24no—
473#124—24no—
474#124—24no—
475#124—24no—
476#124—24no—
477#123—28no—
478#123—216no—
479#123—28no—
480C22⋊Q8—216no—
481C22⋊Q8—28no—
482C22⋊Q8—28no—
483#117—21no—
484#117—21no—
485#117—22no—
486#117D4×C1112yes—
487#117D4×C1114yes—
488#117C23×C1112yes—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4D4×C1112yes—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—24no—
497C2×C42—21no—
498C2×C42C23×C1112yes—
499#104—28no—
500#103—24no—
501#102—24no—
502#101—28no—
503C2×C11—21no—
504C2×C11—21no—
505C2×C11—22no—
506C2×C11—22no—
507C2×C11—82no—
508C2×C11—82no—
509C2×C11C2×#39211yescharacteristic
510C2×C11#302012yes—
511C24—21no—
512C24—21no—
513C24C2×D4×C1111yescharacteristic
514#41—24no—
515#41—24no—
516#41—24no—
517#41—24no—
518#41—24no—
519#41—24no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—42no—
525#41—42no—
526#41—42no—
527#41—42no—
528#41—42no—
529#41—42no—
530#41—42no—
531#41—42no—
532C2×Q8—22no—
533C2×Q8—24no—
534C2×Q8—22no—
535C2×Q8—21no—
536C2×Q8—24no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—42no—
551C2×Q8—42no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8—42no—
555C2×Q8—42no—
556C2×Q8—42no—
557C2×Q8—42no—
558C2×Q8C2×D4×C1112yes—
559C2×Q8C2×D4×C1112yes—
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4C2×D4×C1112yes—
577C2×D4C2×D4×C1112yes—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4C2×D4×C1114yes—
595C22×C4C2×D4×C1111yescharacteristic
596C22×C4C2×D4×C1111yescharacteristic
597C22×C4C2×D4×C1111yescharacteristic
598C22×C4C2×D4×C1112yes—
599C22×C4C2×D4×C1112yes—
600C22×C4C2×D4×C1111yescharacteristic
601C22×C4C2×D4×C1111yescharacteristic
602C22×C4C2×D4×C1112yes—
603C22×C4C11×#4112yes—
604C22×C4C24×C1111yescharacteristic
605Q16—28no—
606SD16—28no—
607SD16—28no—
608D8—28no—
609M16—24no—
610M16—22no—
611M16—22no—
612M16—22no—
613M16—42no—
614M16C2×D4×C1114yes—
615C2×C8—24no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—42no—
619C4⋊C4—216no—
620C4⋊C4—216no—
621C4⋊C4—24no—
622C4⋊C4—22no—
623C4⋊C4C2×D4×C1114yes—
624C22⋊C4—216no—
625C22⋊C4—216no—
626C22⋊C4—22no—
627C22⋊C4—24no—
628C22⋊C4—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42C2×D4×C1114yes—
633C11#2340311yescharacteristic, direct product factor, Sylow
634C23—22no—
635C23—22no—
636C23—42no—
637C23—44no—
638C23—44no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23C11×#12011yescharacteristic
643C23C11×#12011yescharacteristic
644C23C11×#12012yes—
645C23C11×#12112yes—
646C23C22×D4×C1111yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—22no—
650Q8—22no—
651Q8—42no—
652Q8—42no—
653Q8—42no—
654Q8—41no—
655Q8—44no—
656Q8—44no—
657Q8—42no—
658Q8—42no—
659Q8—41no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—42no—
665D4—42no—
666D4—44no—
667D4—44no—
668D4—44no—
669D4—41no—
670D4—42no—
671D4—41no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—42no—
691C2×C4C11×#12012yes—
692C2×C4C11×#12012yes—
693C2×C4C11×#12011yescharacteristic
694C2×C4C11×#12011yescharacteristic
695C2×C4C11×#12012yes—
696C2×C4C11×#12112yes—
697C2×C4C11×#12112yes—
698C2×C4C11×#12112yes—
699C2×C4C11×#12112yes—
700C2×C4C11×#12112yes—
701C2×C4C11×#12712yes—
702C2×C4C11×#12712yes—
703C2×C4C22×D4×C1111yescharacteristic
704C2×C4C22×D4×C1111yescharacteristic
705C2×C4C22×D4×C1111yescharacteristic
706C2×C4C22×D4×C1111yescharacteristic
707C2×C4C22×D4×C1111yescharacteristic
708C2×C4C2×C11×#4111yescharacteristic
709C8—24no—
710C8—42no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—44no—
720C22—82no—
721C22—84no—
722C22—82no—
723C22C11×#39212yes—
724C22C11×#39212yes—
725C22C2×C11×#12011yescharacteristic
726C22C2×C11×#12011yescharacteristic
727C22C2×C11×#12111yescharacteristic
728C4—44no—
729C4—44no—
730C4—42no—
731C4—42no—
732C4—44no—
733C4C11×#39212yes—
734C4C11×#39212yes—
735C4C2×C11×#12011yescharacteristic
736C4C2×C11×#12111yescharacteristic
737C4C2×C11×#12111yescharacteristic
738C4C2×C11×#12711yescharacteristic
739C2—21no—
740C2—21no—
741C2—22no—
742C2—22no—
743C2—82no—
744C2—82no—
745C2C2×C11×#39211yescharacteristic
746C2C11×#302012yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#536C2semidirect
3. C2×C11×#536C2semidirect
4. C2×C11×#421C2semidirect
5. C11×#2896C2semidirect
6. C22×C11×#101C2semidirect
7. C11×#2005C2semidirect
8. C11×#2003C2semidirect
9. C11×#1733C2semidirect
29. C2×C11×C4⋊Q8C22semidirect
31. C2×C11×#124C22semidirect
40. C11×#419C22semidirect
41. C11×#418C22semidirect
45. C2×C11×#101C22semidirect
46. C11×#339C22semidirect
138. #23403C11direct (N × H)
262. C2×#536C2×C11semidirect
263. C2×#536C2×C11semidirect
264. C2×#421C2×C11semidirect
265. #2896C2×C11semidirect
266. C22×#101C2×C11semidirect
267. #2005C2×C11semidirect
268. #2003C2×C11semidirect
269. #1733C2×C11semidirect
366. C2×C4⋊Q8C22×C11semidirect
368. C2×#124C22×C11semidirect
377. #419C22×C11semidirect
378. #418C22×C11semidirect
382. C2×#101C22×C11semidirect
383. #339C22×C11semidirect
633. C11#23403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5752
C2×C11×#5362
C2×C11×#4212
C11×#28962
C22×C11×#1012
C11×#20052
C11×#20032
C11×#17332
#2340311