Finite Group Databasebeta

← C11×#24790 #14601983

Subgroups — C11×#24790 #14601983

Order 2816.

1082 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#469C211yesmaximal, characteristic, complemented
2C2×C11×#466C211yesmaximal, characteristic, complemented
3C2×C11×#435C211yesmaximal, characteristic, complemented
4C2×C11×#428C211yesmaximal, characteristic, complemented
5C11×#2416C211yesmaximal, characteristic, complemented
6C11×#2414C211yesmaximal, characteristic, complemented
7C11×#2067C211yesmaximal, characteristic, complemented
8C11×#2065C211yesmaximal, characteristic, complemented
9C11×#2034C211yesmaximal, characteristic, complemented
10C11×#2033C211yesmaximal, characteristic, complemented
11C11×#1972C211yesmaximal, characteristic, complemented
12C11×#1943C211yesmaximal, characteristic, complemented
13C11×#1875C211yesmaximal, characteristic, complemented
14C11×#1874C211yesmaximal, characteristic, complemented
15C11×#1807C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×#121—21no—
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C11×#469—24no—
28C11×#466—24no—
29C11×#435—24no—
30C11×#428—24no—
31C2×C11×#107C2211yescharacteristic
32C2×C11×#107C2211yescharacteristic
33C2×C11×#106C2211yescharacteristic
34C2×C11×#106C2211yescharacteristic
35C2×C11×#106C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2211yescharacteristic
45C2×C11×#97C2211yescharacteristic
46C11×#396—21no—
47C11×#394—21no—
48C11×#394—21no—
49C11×#392—21no—
50C11×#390—21no—
51C11×#390C2211yescharacteristic
52C11×#390C2211yescharacteristic
53C11×#389C2211yescharacteristic
54C11×#389C2211yescharacteristic
55C11×#388—21no—
56C11×#386—21no—
57C11×#380C2211yescharacteristic
58C11×#380C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11D411yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C2×C11×D8—22no—
74C2×C11×D8—22no—
75C2×C11×D8—22no—
76C2×C11×M16—22no—
77C2×C11×M16—22no—
78C2×C11×M16D414yescomplemented
79C22×C8×C11—22no—
80C22×C8×C11—22no—
81C22×C8×C11—22no—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C11×#121—22no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—22no—
91C11×#121—22no—
92C11×#121—41no—
93C11×#121—41no—
94C11×#121—44no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C11×#117—22no—
98C11×#117—41no—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—41no—
104C2×C11×C4⋊C4D411yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4D411yescharacteristic
123C2×C11×C22⋊C4D411yescharacteristic
124C2×C42×C11—21no—
125C2×C42×C11C2311yescharacteristic
126C11×#107—22no—
127C11×#107D414yescomplemented
128C11×#106—22no—
129C11×#106—22no—
130C11×#106—22no—
131C11×C4⋊C8—22no—
132C11×#102—22no—
133C11×#102—22no—
134C11×#102—22no—
135C11×#102—22no—
136C11×#102—41no—
137C11×#102—41no—
138C11×C22⋊C8—22no—
139C11×C22⋊C8—22no—
140C11×#97—22no—
141C11×#95—21no—
142C11×#95—21no—
143C11×#95—21no—
144C11×#95—21no—
145#24790C1111yesmaximal, characteristic, direct product factor, Sylow
146C24×C11—21no—
147C24×C11—21no—
148C24×C11C2×D411yescharacteristic
149C24×C11C2×D411yescharacteristic
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—41no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11—81no—
174C2×D4×C11—81no—
175C2×D4×C11—81no—
176C2×D4×C11—81no—
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×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11—81no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D412yes—
201C22×C4×C11#4112yes—
202C22×C4×C11C2411yescharacteristic
203C11×D8—44no—
204C11×M16—28no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—44no—
214C2×C8×C11C2×D412yes—
215C2×C8×C11C2×D412yes—
216C2×C8×C11C2×D412yes—
217C2×C8×C11#4112yes—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—42no—
230C11×C4⋊C4—42no—
231C11×C4⋊C4—81no—
232C11×C4⋊C4C2×D412yes—
233C11×C4⋊C4C2×D412yes—
234C11×C22⋊C4—22no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—42no—
237C11×C22⋊C4—42no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4—42no—
240C11×C22⋊C4—42no—
241C11×C22⋊C4—42no—
242C11×C22⋊C4—42no—
243C11×C22⋊C4—42no—
244C11×C22⋊C4—81no—
245C11×C22⋊C4—81no—
246C11×C22⋊C4—81no—
247C42×C11—21no—
248C42×C11—21no—
249C42×C11—42no—
250C2×#469C2×C1111yescharacteristic, complemented
251C2×#466C2×C1111yescharacteristic, complemented
252C2×#435C2×C1111yescharacteristic, complemented
253C2×#428C2×C1111yescharacteristic, complemented
254#2416C2×C1111yescharacteristic, complemented
255#2414C2×C1111yescharacteristic, complemented
256#2067C2×C1111yescharacteristic, complemented
257#2065C2×C1111yescharacteristic, complemented
258#2034C2×C1111yescharacteristic, complemented
259#2033C2×C1111yescharacteristic, complemented
260#1972C2×C1111yescharacteristic, complemented
261#1943C2×C1111yescharacteristic, complemented
262#1875C2×C1111yescharacteristic, complemented
263#1874C2×C1111yescharacteristic, complemented
264#1807C2×C1111yescharacteristic, complemented
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
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—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11#12112yes—
292C23×C11AGL(1,ℤ/8)12yes—
293C23×C11C22×D411yescharacteristic
294D4×C11—44no—
295D4×C11—41no—
296D4×C11—41no—
297D4×C11—41no—
298D4×C11—41no—
299D4×C11—41no—
300D4×C11—41no—
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—84no—
304D4×C11—84no—
305D4×C11—84no—
306D4×C11—84no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—22no—
317C2×C4×C11—21no—
318C2×C4×C11—22no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—84no—
345C2×C4×C11#12112yes—
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C2×#4111yescharacteristic
349C2×C4×C11C2×#4111yescharacteristic
350C2×C4×C11H(5,𝔽2)11yescharacteristic
351C2×C4×C112−1+411yescharacteristic
352C8×C11—22no—
353C8×C11—41no—
354C8×C11—41no—
355C8×C11#12114yescomplemented
356C22×D8C22×C1111yescharacteristic
357C22×M16C22×C1111yescharacteristic
358C23×C8C22×C1111yescharacteristic
359C2×#121—21no—
360C2×#121C22×C1111yescharacteristic
361C2×#121C22×C1111yescharacteristic
362C2×#121C22×C1111yescharacteristic
363C2×#121C22×C1111yescharacteristic
364C2×C4×D4C22×C1111yescharacteristic
365C2×#117C22×C1111yescharacteristic
366C22×C4⋊C4C22×C1111yescharacteristic
367#469—24no—
368#466—24no—
369#435—24no—
370#428—24no—
371C2×#107C22×C1111yescharacteristic
372C2×#107C22×C1111yescharacteristic
373C2×#106C22×C1111yescharacteristic
374C2×#106C22×C1111yescharacteristic
375C2×#106C22×C1111yescharacteristic
376C2×C4⋊C8C22×C1111yescharacteristic
377C2×#102C22×C1111yescharacteristic
378C2×#102C22×C1111yescharacteristic
379C2×#102C22×C1111yescharacteristic
380C2×#102C22×C1111yescharacteristic
381C2×#102C22×C1111yescharacteristic
382C2×#102C22×C1111yescharacteristic
383C2×C22⋊C8C22×C1111yescharacteristic
384C2×C22⋊C8C22×C1111yescharacteristic
385C2×#97C22×C1111yescharacteristic
386#396—21no—
387#394—21no—
388#394—21no—
389#392—21no—
390#390—21no—
391#390C22×C1111yescharacteristic
392#390C22×C1111yescharacteristic
393#389C22×C1111yescharacteristic
394#389C22×C1111yescharacteristic
395#388—21no—
396#386—21no—
397#380C22×C1111yescharacteristic
398#380C22×C1111yescharacteristic
399#340C22×C1111yescharacteristic
400#340C22×C1111yescharacteristic
401#340C22×C1111yescharacteristic
402#340C22×C1111yescharacteristic
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×C11—81no—
425C22×C11—81no—
426C22×C11—81no—
427C22×C11—81no—
428C22×C11—81no—
429C22×C11—81no—
430C22×C11—81no—
431C22×C11C2×#12111yescharacteristic
432C22×C11D4211yescharacteristic
433C22×C11#54711yescharacteristic
434C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
435C22×C11#57511yescharacteristic
436C22×C11#57611yescharacteristic
437C22×C11#57711yescharacteristic
438C4×C11—22no—
439C4×C11—41no—
440C4×C11—42no—
441C4×C11—42no—
442C4×C11—41no—
443C4×C11—41no—
444C4×C11—81no—
445C4×C11—81no—
446C4×C11—81no—
447C4×C11—81no—
448C4×C11C2×#12111yescharacteristic
449C4×C11#53711yescharacteristic
450C4×C11#54811yescharacteristic
451C4×C11#55311yescharacteristic
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4D4×C1111yescharacteristic
457C22×D4C23×C1111yescharacteristic
458C22×D4C23×C1111yescharacteristic
459C23×C4—21no—
460C23×C4C23×C1111yescharacteristic
461C23×C4C23×C1111yescharacteristic
462C2×D8—22no—
463C2×D8—22no—
464C2×D8—22no—
465C2×M16—22no—
466C2×M16—22no—
467C2×M16D4×C1114yescomplemented
468C22×C8—22no—
469C22×C8—22no—
470C22×C8—22no—
471C22×C8C23×C1111yescharacteristic
472C22×C8C23×C1111yescharacteristic
473C22×C8C23×C1111yescharacteristic
474C22×C8C23×C1111yescharacteristic
475#121—22no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—41no—
482#121—41no—
483#121—44no—
484C4×D4—22no—
485C4×D4—22no—
486#117—22no—
487#117—41no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—41no—
493C2×C4⋊C4D4×C1111yescharacteristic
494C2×C4⋊C4C23×C1111yescharacteristic
495C2×C4⋊C4C23×C1111yescharacteristic
496C2×C4⋊C4C23×C1111yescharacteristic
497C2×C4⋊C4C23×C1111yescharacteristic
498C2×C4⋊C4C23×C1111yescharacteristic
499C2×C4⋊C4C23×C1111yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4D4×C1111yescharacteristic
512C2×C22⋊C4D4×C1111yescharacteristic
513C2×C42—21no—
514C2×C42C23×C1111yescharacteristic
515#107—22no—
516#107D4×C1114yescomplemented
517#106—22no—
518#106—22no—
519#106—22no—
520C4⋊C8—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529#97—22no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534C2×C11—42no—
535C2×C11—42no—
536C2×C11—161no—
537C2×C11—161no—
538C2×C11#241611yescharacteristic
539C2×C11#305511yescharacteristic
540C2×C11#306211yescharacteristic
541C2×C11#326411yescharacteristic
542C2×C11#327111yescharacteristic
543C2×C11#334511yescharacteristic
544C2×C11#334711yescharacteristic
545C24—21no—
546C24—21no—
547C24C2×D4×C1111yescharacteristic
548C24C2×D4×C1111yescharacteristic
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—81no—
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—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—81no—
595C22×C4C2×D4×C1111yescharacteristic
596C22×C4C2×D4×C1111yescharacteristic
597C22×C4C2×D4×C1111yescharacteristic
598C22×C4C2×D4×C1111yescharacteristic
599C22×C4C2×D4×C1112yes—
600C22×C4C11×#4112yes—
601C22×C4C24×C1111yescharacteristic
602D8—44no—
603M16—28no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—44no—
613C2×C8C2×D4×C1112yes—
614C2×C8C2×D4×C1112yes—
615C2×C8C2×D4×C1112yes—
616C2×C8C11×#4112yes—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—81no—
631C4⋊C4C2×D4×C1112yes—
632C4⋊C4C2×D4×C1112yes—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C42—21no—
647C42—21no—
648C42—42no—
649C11#2479011yescharacteristic, direct product factor, Sylow
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23C11×#12112yes—
677C23C11×AGL(1,ℤ/8)12yes—
678C23C22×D4×C1111yescharacteristic
679D4—44no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—84no—
689D4—84no—
690D4—84no—
691D4—84no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—84no—
730C2×C4C11×#12112yes—
731C2×C4C22×D4×C1111yescharacteristic
732C2×C4C22×D4×C1111yescharacteristic
733C2×C4C2×C11×#4111yescharacteristic
734C2×C4C2×C11×#4111yescharacteristic
735C2×C4C11×H(5,𝔽2)11yescharacteristic
736C2×C4C11×2−1+411yescharacteristic
737C8—22no—
738C8—41no—
739C8—41no—
740C8C11×#12114yescomplemented
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22C2×C11×#12111yescharacteristic
770C22D42×C1111yescharacteristic
771C22C11×#54711yescharacteristic
772C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
773C22C11×#57511yescharacteristic
774C22C11×#57611yescharacteristic
775C22C11×#57711yescharacteristic
776C4—22no—
777C4—41no—
778C4—42no—
779C4—42no—
780C4—41no—
781C4—41no—
782C4—81no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4C2×C11×#12111yescharacteristic
787C4C11×#53711yescharacteristic
788C4C11×#54811yescharacteristic
789C4C11×#55311yescharacteristic
790C2—42no—
791C2—42no—
792C2—161no—
793C2—161no—
794C2C11×#241611yescharacteristic
795C2C11×#305511yescharacteristic
796C2C11×#306211yescharacteristic
797C2C11×#326411yescharacteristic
798C2C11×#327111yescharacteristic
799C2C11×#334511yescharacteristic
800C2C11×#334711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#469C2semidirect
2. C2×C11×#466C2semidirect
3. C2×C11×#435C2semidirect
4. C2×C11×#428C2semidirect
5. C11×#2416C2semidirect
6. C11×#2414C2semidirect
7. C11×#2067C2semidirect
8. C11×#2065C2semidirect
9. C11×#2034C2semidirect
10. C11×#2033C2semidirect
11. C11×#1972C2semidirect
12. C11×#1943C2semidirect
13. C11×#1875C2semidirect
14. C11×#1874C2semidirect
15. C11×#1807C2semidirect
78. C2×C11×M16D4semidirect
127. C11×#107D4semidirect
145. #24790C11direct (N × H)
250. C2×#469C2×C11semidirect
251. C2×#466C2×C11semidirect
252. C2×#435C2×C11semidirect
253. C2×#428C2×C11semidirect
254. #2416C2×C11semidirect
255. #2414C2×C11semidirect
256. #2067C2×C11semidirect
257. #2065C2×C11semidirect
258. #2034C2×C11semidirect
259. #2033C2×C11semidirect
260. #1972C2×C11semidirect
261. #1943C2×C11semidirect
262. #1875C2×C11semidirect
263. #1874C2×C11semidirect
264. #1807C2×C11semidirect
355. C8×C11#121semidirect
467. C2×M16D4×C11semidirect
516. #107D4×C11semidirect
649. C11#24790direct (N × H)
740. C8C11×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4692
C2×C11×#4662
C2×C11×#4352
C2×C11×#4282
C11×#24162
C11×#24142
C11×#20672
C11×#20652
C11×#20342
C11×#20332
C11×#19722
C11×#19432
C11×#18752
C11×#18742
C11×#18072
#2479011