Finite Group Databasebeta

← C11×#21513 #14598706

Subgroups — C11×#21513 #14598706

Order 2816.

1120 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic
2C2×C11×#442C211yesmaximal, characteristic, complemented
3C2×C4×C11×D8C211yesmaximal, characteristic, complemented
4C11×#2328C211yesmaximal, characteristic, complemented
5C11×#2275C211yesmaximal, characteristic, complemented
6C11×#1982C211yesmaximal, characteristic, complemented
7C11×#1949C211yesmaximal, characteristic, complemented
8C11×#1926C211yesmaximal, characteristic, complemented
9C11×#1925C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1804C211yesmaximal, characteristic, complemented
13C11×#1768C211yesmaximal, characteristic, complemented
14C11×#1762C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#127C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C11×#459C418yescomplemented
25C11×#442—24no—
26C4×C11×D8—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#106C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic
40C2×C4×C8×C11C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#386—21no—
44C11×#386—21no—
45C11×#386—21no—
46C11×#386—21no—
47C11×#382C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2211yescharacteristic
51C4×C11×C22⋊C4—21no—
52C4×C11×C22⋊C4—21no—
53C4×C11×C22⋊C4—21no—
54C11×#376C2211yescharacteristic
55C2×C11×#95—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C2×C11×D8—22no—
73C2×C11×D8—22no—
74C2×C11×D8—22no—
75C2×C11×D8—22no—
76C2×C11×D8C2×C414yescomplemented
77C2×C11×D8C2×C414yescomplemented
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×#127—22no—
83C11×#127C2×C414yescomplemented
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11C2×C414yescomplemented
93C4×D4×C11D414yescomplemented
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C11×#107—22no—
115C11×#106—22no—
116C11×C4⋊C8—22no—
117C11×C4⋊C8C2×C414yescomplemented
118C11×#102—22no—
119C11×#102—22no—
120C11×#102—22no—
121C11×#102—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102C2×C414yescomplemented
125C11×#102C2×C414yescomplemented
126C11×#97—22no—
127C4×C8×C11—22no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95D411yescharacteristic
134C11×#95D411yescharacteristic
135C11×#95D411yescharacteristic
136C11×#95D411yescharacteristic
137#21513C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
141C2×D4×C11—24no—
142C2×D4×C11—24no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—81no—
157C2×D4×C11—81no—
158C2×D4×C11—81no—
159C2×D4×C11—81no—
160C2×D4×C11C22×C412yes—
161C2×D4×C11C22×C412yes—
162C2×D4×C11C22×C412yes—
163C2×D4×C11C2×D412yes—
164C2×D4×C11#4112yes—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—24no—
169C22×C4×C11—24no—
170C22×C4×C11—24no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—81no—
176C22×C4×C11—81no—
177C22×C4×C11—81no—
178C22×C4×C11—81no—
179C22×C4×C11—81no—
180C22×C4×C11—81no—
181C22×C4×C11—81no—
182C22×C4×C11—81no—
183C22×C4×C11—81no—
184C22×C4×C11—81no—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2411yescharacteristic
192C11×D8—28no—
193C11×D8—28no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11C22×C412yes—
205C2×C8×C11C22×C412yes—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4C22×C412yes—
214C11×C4⋊C4C2×D412yes—
215C11×C4⋊C4#4112yes—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—24no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—81no—
222C11×C22⋊C4—81no—
223C11×C22⋊C4—81no—
224C11×C22⋊C4—81no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—81no—
228C42×C11—81no—
229C42×C11—81no—
230C42×C11C22×C412yes—
231C42×C11C2×D412yes—
232C42×C11#4112yes—
233C42×C11#4112yes—
234C2×#459C2×C1111yescharacteristic
235C2×#442C2×C1111yescharacteristic, complemented
236C2×C4×D8C2×C1111yescharacteristic, complemented
237#2328C2×C1111yescharacteristic, complemented
238#2275C2×C1111yescharacteristic, complemented
239#1982C2×C1111yescharacteristic, complemented
240#1949C2×C1111yescharacteristic, complemented
241#1926C2×C1111yescharacteristic, complemented
242#1925C2×C1111yescharacteristic, complemented
243#1879C2×C1111yescharacteristic, complemented
244#1879C2×C1111yescharacteristic, complemented
245#1804C2×C1111yescharacteristic, complemented
246#1768C2×C1111yescharacteristic, complemented
247#1762C2×C1111yescharacteristic, complemented
248C4×#102C2×C1111yescharacteristic, complemented
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11C22×D411yescharacteristic
271D4×C11—22no—
272D4×C11—22no—
273D4×C11—22no—
274D4×C11—22no—
275D4×C11—22no—
276D4×C11—22no—
277D4×C11—22no—
278D4×C11—41no—
279D4×C11—41no—
280D4×C11—41no—
281D4×C11—41no—
282D4×C11—84no—
283D4×C11—84no—
284D4×C11C4×D414yes—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—22no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
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×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—84no—
315C2×C4×C11—84no—
316C2×C4×C11—84no—
317C2×C4×C11—84no—
318C2×C4×C11—84no—
319C2×C4×C11C4×D412yes—
320C2×C4×C11C4×D412yes—
321C2×C4×C11#12112yes—
322C2×C4×C11#12112yes—
323C2×C4×C11C23×C411yescharacteristic
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4111yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11C2×#4111yescharacteristic
328C2×C4×C11C2×#4111yescharacteristic
329C8×C11—22no—
330C8×C11—22no—
331C8×C11—41no—
332C8×C11—41no—
333C22×D8C22×C1111yescharacteristic
334C22×D8C22×C1111yescharacteristic
335C2×#127C22×C1111yescharacteristic
336C2×C4×D4C22×C1111yescharacteristic
337C2×C4×D4C22×C1111yescharacteristic
338C2×C4×D4C22×C1111yescharacteristic
339C2×C4×D4C22×C1111yescharacteristic
340C2×C4×D4C22×C1111yescharacteristic
341#459C4×C1118yescomplemented
342#442—24no—
343C4×D8—24no—
344C2×#107C22×C1111yescharacteristic
345C2×#106C22×C1111yescharacteristic
346C2×C4⋊C8C22×C1111yescharacteristic
347C2×C4⋊C8C22×C1111yescharacteristic
348C2×#102C22×C1111yescharacteristic
349C2×#102C22×C1111yescharacteristic
350C2×#102C22×C1111yescharacteristic
351C2×#102C22×C1111yescharacteristic
352C2×#102C22×C1111yescharacteristic
353C2×#102C22×C1111yescharacteristic
354C2×#102C22×C1111yescharacteristic
355C2×#102C22×C1111yescharacteristic
356C2×#97C22×C1111yescharacteristic
357C2×C4×C8C22×C1111yescharacteristic
358#390C22×C1111yescharacteristic
359#390C22×C1111yescharacteristic
360#386—21no—
361#386—21no—
362#386—21no—
363#386—21no—
364#382C22×C1111yescharacteristic
365C4×C4⋊C4C22×C1111yescharacteristic
366C4×C4⋊C4C22×C1111yescharacteristic
367C4×C4⋊C4C22×C1111yescharacteristic
368C4×C22⋊C4—21no—
369C4×C22⋊C4—21no—
370C4×C22⋊C4—21no—
371#376C22×C1111yescharacteristic
372C2×#95—21no—
373#340C22×C1111yescharacteristic
374#340C22×C1111yescharacteristic
375#340C22×C1111yescharacteristic
376#340C22×C1111yescharacteristic
377#336C22×C1111yescharacteristic
378#336C22×C1111yescharacteristic
379C22×C11—24no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—42no—
389C22×C11—42no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—81no—
393C22×C11—81no—
394C22×C11—81no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11C2×C4×D411yescharacteristic
401C22×C11C2×#12111yescharacteristic
402C22×C11#52511yescharacteristic
403C22×C11#57611yescharacteristic
404C22×C11#57611yescharacteristic
405C22×C11#57611yescharacteristic
406C22×C11#57711yescharacteristic
407C4×C11—22no—
408C4×C11—22no—
409C4×C11—22no—
410C4×C11—22no—
411C4×C11—41no—
412C4×C11—41no—
413C4×C11—42no—
414C4×C11—42no—
415C4×C11—42no—
416C4×C11—81no—
417C4×C11—81no—
418C4×C11C2×C4×D411yescharacteristic
419C4×C11C4×#4111yescharacteristic
420C4×C11#52911yescharacteristic
421C4×C11#53211yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4C23×C1111yescharacteristic
425C22×D4C23×C1111yescharacteristic
426C22×D4C23×C1111yescharacteristic
427C23×C4—21no—
428C23×C4—21no—
429C23×C4—21no—
430C23×C4—21no—
431C23×C4—21no—
432C2×D8—22no—
433C2×D8—22no—
434C2×D8—22no—
435C2×D8—22no—
436C2×D8C2×C4×C1114yescomplemented
437C2×D8C2×C4×C1114yescomplemented
438C22×C8C23×C1111yescharacteristic
439C22×C8C23×C1111yescharacteristic
440C22×C8C23×C1111yescharacteristic
441C22×C8C23×C1111yescharacteristic
442#127—22no—
443#127C2×C4×C1114yescomplemented
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4C2×C4×C1114yescomplemented
453C4×D4D4×C1114yescomplemented
454C2×C4⋊C4C23×C1111yescharacteristic
455C2×C4⋊C4C23×C1111yescharacteristic
456C2×C4⋊C4C23×C1111yescharacteristic
457C2×C4⋊C4C23×C1111yescharacteristic
458C2×C4⋊C4C23×C1111yescharacteristic
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42C23×C1111yescharacteristic
472C2×C42C23×C1111yescharacteristic
473C2×C42C23×C1111yescharacteristic
474#107—22no—
475#106—22no—
476C4⋊C8—22no—
477C4⋊C8C2×C4×C1114yescomplemented
478#102—22no—
479#102—22no—
480#102—22no—
481#102—22no—
482#102—22no—
483#102—22no—
484#102C2×C4×C1114yescomplemented
485#102C2×C4×C1114yescomplemented
486#97—22no—
487C4×C8—22no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95D4×C1111yescharacteristic
494#95D4×C1111yescharacteristic
495#95D4×C1111yescharacteristic
496#95D4×C1111yescharacteristic
497C2×C11—44no—
498C2×C11—82no—
499C2×C11—82no—
500C2×C11C4×#12111yescharacteristic
501C2×C11#294611yescharacteristic
502C2×C11#294811yescharacteristic
503C2×C11#304111yescharacteristic
504C2×C11#304511yescharacteristic
505C2×C11#311911yescharacteristic
506C2×C11#312211yescharacteristic
507C24—21no—
508C24—21no—
509C24—21no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—81no—
526C2×D4—81no—
527C2×D4—81no—
528C2×D4—81no—
529C2×D4C22×C4×C1112yes—
530C2×D4C22×C4×C1112yes—
531C2×D4C22×C4×C1112yes—
532C2×D4C2×D4×C1112yes—
533C2×D4C11×#4112yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4C2×D4×C1111yescharacteristic
555C22×C4C2×D4×C1111yescharacteristic
556C22×C4C2×D4×C1111yescharacteristic
557C22×C4C2×D4×C1111yescharacteristic
558C22×C4C2×D4×C1111yescharacteristic
559C22×C4C2×D4×C1111yescharacteristic
560C22×C4C24×C1111yescharacteristic
561D8—28no—
562D8—28no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8C22×C4×C1112yes—
574C2×C8C22×C4×C1112yes—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4C22×C4×C1112yes—
583C4⋊C4C2×D4×C1112yes—
584C4⋊C4C11×#4112yes—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—81no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C42—21no—
595C42—21no—
596C42—81no—
597C42—81no—
598C42—81no—
599C42C22×C4×C1112yes—
600C42C2×D4×C1112yes—
601C42C11×#4112yes—
602C42C11×#4112yes—
603C11#2151311yescharacteristic, direct product factor, Sylow
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23C22×D4×C1111yescharacteristic
626D4—22no—
627D4—22no—
628D4—22no—
629D4—22no—
630D4—22no—
631D4—22no—
632D4—22no—
633D4—41no—
634D4—41no—
635D4—41no—
636D4—41no—
637D4—84no—
638D4—84no—
639D4C4×D4×C1114yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—84no—
670C2×C4—84no—
671C2×C4—84no—
672C2×C4—84no—
673C2×C4—84no—
674C2×C4C4×D4×C1112yes—
675C2×C4C4×D4×C1112yes—
676C2×C4C11×#12112yes—
677C2×C4C11×#12112yes—
678C2×C4C23×C4×C1111yescharacteristic
679C2×C4C22×D4×C1111yescharacteristic
680C2×C4C2×C11×#4111yescharacteristic
681C2×C4C2×C11×#4111yescharacteristic
682C2×C4C2×C11×#4111yescharacteristic
683C2×C4C2×C11×#4111yescharacteristic
684C8—22no—
685C8—22no—
686C8—41no—
687C8—41no—
688C22—24no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22C2×C4×D4×C1111yescharacteristic
710C22C2×C11×#12111yescharacteristic
711C22C11×#52511yescharacteristic
712C22C11×#57611yescharacteristic
713C22C11×#57611yescharacteristic
714C22C11×#57611yescharacteristic
715C22C11×#57711yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—41no—
723C4—41no—
724C4—42no—
725C4—81no—
726C4—81no—
727C4C2×C4×D4×C1111yescharacteristic
728C4C4×C11×#4111yescharacteristic
729C4C11×#52911yescharacteristic
730C4C11×#53211yescharacteristic
731C2—44no—
732C2—82no—
733C2—82no—
734C2C4×C11×#12111yescharacteristic
735C2C11×#294611yescharacteristic
736C2C11×#294811yescharacteristic
737C2C11×#304111yescharacteristic
738C2C11×#304511yescharacteristic
739C2C11×#311911yescharacteristic
740C2C11×#312211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#459C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#442C2semidirect
3. C2×C4×C11×D8C2semidirect
4. C11×#2328C2semidirect
5. C11×#2275C2semidirect
6. C11×#1982C2semidirect
7. C11×#1949C2semidirect
8. C11×#1926C2semidirect
9. C11×#1925C2semidirect
10. C11×#1879C2semidirect
11. C11×#1879C2semidirect
12. C11×#1804C2semidirect
13. C11×#1768C2semidirect
14. C11×#1762C2semidirect
15. C4×C11×#102C2semidirect
24. C11×#459C4semidirect
76. C2×C11×D8C2×C4semidirect
77. C2×C11×D8C2×C4semidirect
83. C11×#127C2×C4semidirect
92. C4×D4×C11C2×C4semidirect
93. C4×D4×C11D4semidirect
117. C11×C4⋊C8C2×C4semidirect
124. C11×#102C2×C4semidirect
125. C11×#102C2×C4semidirect
137. #21513C11direct (N × H)
235. C2×#442C2×C11semidirect
236. C2×C4×D8C2×C11semidirect
237. #2328C2×C11semidirect
238. #2275C2×C11semidirect
239. #1982C2×C11semidirect
240. #1949C2×C11semidirect
241. #1926C2×C11semidirect
242. #1925C2×C11semidirect
243. #1879C2×C11semidirect
244. #1879C2×C11semidirect
245. #1804C2×C11semidirect
246. #1768C2×C11semidirect
247. #1762C2×C11semidirect
248. C4×#102C2×C11semidirect
341. #459C4×C11semidirect
436. C2×D8C2×C4×C11semidirect
437. C2×D8C2×C4×C11semidirect
443. #127C2×C4×C11semidirect
452. C4×D4C2×C4×C11semidirect
453. C4×D4D4×C11semidirect
477. C4⋊C8C2×C4×C11semidirect
484. #102C2×C4×C11semidirect
485. #102C2×C4×C11semidirect
603. C11#21513direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C2×C11×#4422
C2×C4×C11×D82
C11×#23282
C11×#22752
C11×#19822
C11×#19492
C11×#19262
C11×#19252
C11×#18792
C11×#18042
C11×#17682
C11×#17622
C4×C11×#1022
#2151311