Finite Group Databasebeta

← C2×C11×#1902 #14598186

Subgroups — C2×C11×#1902 #14598186

Order 2816.

1654 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#137C211yesmaximal, characteristic
2C2×C11×#568C211yesmaximal, characteristic
3C2×C11×#421C211yesmaximal, characteristic
4C2×C11×#419C211yesmaximal, characteristic, complemented
5C22×C11×#101C211yesmaximal, characteristic, complemented
6C11×#1902C218yesmaximal, direct product factor
7C2×C11×#344C211yesmaximal, characteristic, complemented
8C2×C11×#338C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic
11C2×C11×#137—22no—
12C2×C11×#137—22no—
13C2×C11×#137—22no—
14C2×C11×#137—22no—
15C2×C11×#137C414yescomplemented
16C2×C11×#137C2214yes—
17C22×C11×Q16C412yescomplemented
18C22×C11×SD16C412yescomplemented
19C11×#568—22no—
20C11×#568—22no—
21C11×#568—22no—
22C11×#568C2214yes—
23C2×C11×#131—22no—
24C2×C11×#131—22no—
25C22×C11×M16—22no—
26C22×C11×M16C2211yescharacteristic
27C22×C11×M16C2211yescharacteristic
28C22×C11×M16C2211yescharacteristic
29C22×C11×M16C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C11×#421—22no—
32C11×#421C2214yes—
33C2×C11×#104—22no—
34C11×#419—22no—
35C11×#419C2214yescomplemented
36C2×C11×#103—22no—
37C2×C11×#101—22no—
38C2×C11×#101—22no—
39C2×C11×#101C2214yescomplemented
40C11×#344C2214yescomplemented
41C11×#338C2214yescomplemented
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41C2×C412yes—
49C2×C11×#41D412yes—
50C2×C11×#41D412yes—
51C2×C11×#41D412yes—
52C2×C11×#41D412yes—
53C2×C11×#41C2312yes—
54C22×Q8×C11—21no—
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C22×Q8×C11—21no—
58C22×Q8×C11—21no—
59C22×Q8×C11—21no—
60C22×Q8×C11—21no—
61C22×Q8×C11—21no—
62C22×Q8×C11—21no—
63C22×Q8×C11—21no—
64C22×Q8×C11—21no—
65C22×Q8×C11C2×C412yes—
66C22×Q8×C11C2×C412yes—
67C22×Q8×C11C2×C411yescharacteristic
68C22×Q8×C11C2312yes—
69C22×D4×C11—21no—
70C22×D4×C11C2×C411yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C11×#137—28no—
75C11×#137—28no—
76C11×#137—28no—
77C11×#137—28no—
78C2×C11×Q16—24no—
79C2×C11×Q16—24no—
80C2×C11×Q16C2×C418yescomplemented
81C2×C11×SD16—24no—
82C2×C11×SD16—24no—
83C2×C11×SD16C2×C418yescomplemented
84C11×#131—28no—
85C11×#131—28no—
86C11×#131—28no—
87C11×#131—28no—
88C2×C11×M16—24no—
89C2×C11×M16—28no—
90C2×C11×M16—21no—
91C2×C11×M16—21no—
92C2×C11×M16—21no—
93C2×C11×M16—21no—
94C2×C11×M16—21no—
95C2×C11×M16—21no—
96C2×C11×M16—21no—
97C2×C11×M16—21no—
98C2×C11×M16—21no—
99C2×C11×M16—21no—
100C2×C11×M16—21no—
101C2×C11×M16—28no—
102C2×C11×M16—21no—
103C2×C11×M16—21no—
104C2×C11×M16—21no—
105C2×C11×M16—21no—
106C2×C11×M16—21no—
107C2×C11×M16C2×C412yes—
108C2×C11×M16D412yes—
109C2×C11×M16D412yes—
110C2×C11×M16D412yes—
111C2×C11×M16C2312yes—
112C2×C11×M16C2312yes—
113C2×C11×M16C2312yes—
114C2×C11×M16C2312yes—
115C22×C8×C11—24no—
116C22×C8×C11—21no—
117C22×C8×C11—21no—
118C22×C8×C11C2×C412yes—
119C22×C8×C11D412yes—
120C11×#117—21no—
121C11×#117—21no—
122C11×#117—21no—
123C11×#117C2312yes—
124C2×C11×C4⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C42×C11—21no—
127C11×#104—28no—
128C11×#103—28no—
129C11×#101—28no—
130C2×#1902C1111yesmaximal, characteristic, direct product factor, Sylow
131C24×C11—21no—
132C24×C11#4111yescharacteristic
133C11×#41—22no—
134C11×#41—22no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—22no—
141C11×#41—22no—
142C11×#41—22no—
143C11×#41—22no—
144C11×#41—22no—
145C11×#41C22⋊C414yes—
146C11×#41C22⋊C414yes—
147C11×#41C2×D414yes—
148C11×#41C2×D414yes—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—22no—
153C2×Q8×C11—22no—
154C2×Q8×C11—22no—
155C2×Q8×C11—22no—
156C2×Q8×C11—22no—
157C2×Q8×C11—22no—
158C2×Q8×C11—22no—
159C2×Q8×C11—22no—
160C2×Q8×C11—22no—
161C2×Q8×C11—22no—
162C2×Q8×C11—22no—
163C2×Q8×C11—22no—
164C2×Q8×C11—22no—
165C2×Q8×C11—22no—
166C2×Q8×C11—22no—
167C2×Q8×C11—41no—
168C2×Q8×C11—41no—
169C2×Q8×C11—41no—
170C2×Q8×C11—41no—
171C2×Q8×C11—41no—
172C2×Q8×C11—41no—
173C2×Q8×C11—41no—
174C2×Q8×C11—41no—
175C2×Q8×C11—41no—
176C2×Q8×C11—41no—
177C2×Q8×C11—41no—
178C2×Q8×C11—41no—
179C2×Q8×C11C22⋊C412yes—
180C2×Q8×C11C22⋊C412yes—
181C2×Q8×C11C22×C414yes—
182C2×Q8×C11C22×C412yes—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11C22⋊C412yes—
193C2×D4×C11C22⋊C412yes—
194C2×D4×C11C22×C412yes—
195C22×C4×C11—21no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—41no—
206C22×C4×C11—41no—
207C22×C4×C11—41no—
208C22×C4×C11—41no—
209C22×C4×C11—41no—
210C22×C4×C11C22×C411yescharacteristic
211C22×C4×C11C22×C411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11#4111yescharacteristic
221C22×C4×C11#4111yescharacteristic
222C22×C4×C11#4111yescharacteristic
223C22×C4×C11C2411yescharacteristic
224C11×Q16—216no—
225C11×SD16—216no—
226C11×M16—216no—
227C11×M16—22no—
228C11×M16—22no—
229C11×M16—22no—
230C11×M16—22no—
231C11×M16—22no—
232C11×M16—22no—
233C11×M16—22no—
234C11×M16—22no—
235C11×M16—22no—
236C11×M16—22no—
237C11×M16—22no—
238C11×M16—22no—
239C11×M16—22no—
240C11×M16—41no—
241C11×M16—41no—
242C11×M16C2×D414yes—
243C2×C8×C11—216no—
244C2×C8×C11—22no—
245C2×C8×C11—22no—
246C2×C8×C11—22no—
247C2×C8×C11—22no—
248C2×C8×C11—22no—
249C2×C8×C11—22no—
250C2×C8×C11—22no—
251C2×C8×C11—22no—
252C2×C8×C11—41no—
253C2×C8×C11—41no—
254C2×C8×C11C22×C414yes—
255C2×C8×C11C2×D414yes—
256C11×C4⋊C4—22no—
257C11×C4⋊C4—41no—
258C11×C22⋊C4—22no—
259C11×C22⋊C4—41no—
260C42×C11—22no—
261C42×C11—41no—
262C22×#137C2×C1111yescharacteristic
263C2×#568C2×C1111yescharacteristic
264C2×#421C2×C1111yescharacteristic
265C2×#419C2×C1111yescharacteristic, complemented
266C22×#101C2×C1111yescharacteristic, complemented
267#1902C2×C1118yesdirect product factor
268C2×#344C2×C1111yescharacteristic, complemented
269C2×#338C2×C1111yescharacteristic, complemented
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—42no—
274C23×C11—82no—
275C23×C11C4×D411yescharacteristic
276C23×C11C4×D411yescharacteristic
277C23×C11#12111yescharacteristic
278C23×C11#12111yescharacteristic
279C23×C11#12311yescharacteristic
280C23×C11#12311yescharacteristic
281C23×C11C2×#4111yescharacteristic
282Q8×C11—22no—
283Q8×C11—22no—
284Q8×C11—22no—
285Q8×C11—24no—
286Q8×C11—24no—
287Q8×C11—42no—
288Q8×C11—42no—
289Q8×C11—42no—
290Q8×C11—42no—
291Q8×C11—42no—
292Q8×C11—42no—
293Q8×C11C2×C22⋊C414yes—
294D4×C11—24no—
295D4×C11—24no—
296D4×C11—24no—
297D4×C11—24no—
298D4×C11—22no—
299D4×C11—22no—
300D4×C11—22no—
301D4×C11C2×C22⋊C414yes—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—82no—
318C2×C4×C11C2×C22⋊C411yescharacteristic
319C2×C4×C11C2×C22⋊C411yescharacteristic
320C2×C4×C11C2×C22⋊C411yescharacteristic
321C2×C4×C11C2×C22⋊C411yescharacteristic
322C2×C4×C11C4×D411yescharacteristic
323C2×C4×C11C4×D411yescharacteristic
324C2×C4×C11C4×D411yescharacteristic
325C2×C4×C11C4×D411yescharacteristic
326C2×C4×C11C4×D411yescharacteristic
327C2×C4×C11C4×D411yescharacteristic
328C2×C4×C11#12011yescharacteristic
329C2×C4×C11#12011yescharacteristic
330C2×C4×C11#12011yescharacteristic
331C2×C4×C11#12011yescharacteristic
332C2×C4×C11#12111yescharacteristic
333C2×C4×C11#12111yescharacteristic
334C2×C4×C11#12111yescharacteristic
335C2×C4×C11#12111yescharacteristic
336C2×C4×C11#12111yescharacteristic
337C2×C4×C11#12111yescharacteristic
338C2×C4×C11#12311yescharacteristic
339C2×C4×C11#12311yescharacteristic
340C2×C4×C11C23×C411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C2×#4111yescharacteristic
346C8×C11—24no—
347C8×C11—24no—
348C8×C11—24no—
349C8×C11—42no—
350C22×#41C22×C1111yescharacteristic
351C23×Q8C22×C1111yescharacteristic
352C2×#137—22no—
353C2×#137—22no—
354C2×#137—22no—
355C2×#137—22no—
356C2×#137C4×C1114yescomplemented
357C2×#137C22×C1114yes—
358C22×Q16C4×C1112yescomplemented
359C22×SD16C4×C1112yescomplemented
360#568—22no—
361#568—22no—
362#568—22no—
363#568C22×C1114yes—
364C2×#131—22no—
365C2×#131—22no—
366C22×M16—22no—
367C22×M16C22×C1111yescharacteristic
368C22×M16C22×C1111yescharacteristic
369C22×M16C22×C1111yescharacteristic
370C22×M16C22×C1111yescharacteristic
371C2×#117C22×C1111yescharacteristic
372#421—22no—
373#421C22×C1114yes—
374C2×#104—22no—
375#419—22no—
376#419C22×C1114yescomplemented
377C2×#103—22no—
378C2×#101—22no—
379C2×#101—22no—
380C2×#101C22×C1114yescomplemented
381#344C22×C1114yescomplemented
382#338C22×C1114yescomplemented
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—24no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—44no—
392C22×C11—82no—
393C22×C11—82no—
394C22×C11#38611yescharacteristic
395C22×C11#38611yescharacteristic
396C22×C11#38611yescharacteristic
397C22×C11#38611yescharacteristic
398C22×C11C2×C4×D411yescharacteristic
399C22×C11C2×#12111yescharacteristic
400C22×C11C2×#12311yescharacteristic
401C4×C11—24no—
402C4×C11—44no—
403C4×C11—82no—
404C4×C11#38611yescharacteristic
405C4×C11#38611yescharacteristic
406C4×C11#38611yescharacteristic
407C4×C11#38611yescharacteristic
408C4×C11C22×C22⋊C411yescharacteristic
409C4×C11C2×C4×D411yescharacteristic
410C4×C11C2×#12011yescharacteristic
411C4×C11C2×#12111yescharacteristic
412C2×#41—21no—
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41C2×C4×C1112yes—
419C2×#41D4×C1112yes—
420C2×#41D4×C1112yes—
421C2×#41D4×C1112yes—
422C2×#41D4×C1112yes—
423C2×#41C23×C1112yes—
424C22×Q8—21no—
425C22×Q8—21no—
426C22×Q8—21no—
427C22×Q8—21no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—21no—
432C22×Q8—21no—
433C22×Q8—21no—
434C22×Q8—21no—
435C22×Q8C2×C4×C1112yes—
436C22×Q8C2×C4×C1112yes—
437C22×Q8C2×C4×C1111yescharacteristic
438C22×Q8C23×C1112yes—
439C22×D4—21no—
440C22×D4C2×C4×C1111yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4C23×C1111yescharacteristic
444#137—28no—
445#137—28no—
446#137—28no—
447#137—28no—
448C2×Q16—24no—
449C2×Q16—24no—
450C2×Q16C2×C4×C1118yescomplemented
451C2×SD16—24no—
452C2×SD16—24no—
453C2×SD16C2×C4×C1118yescomplemented
454#131—28no—
455#131—28no—
456#131—28no—
457#131—28no—
458C2×M16—24no—
459C2×M16—28no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16—28no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16C2×C4×C1112yes—
478C2×M16D4×C1112yes—
479C2×M16D4×C1112yes—
480C2×M16D4×C1112yes—
481C2×M16C23×C1112yes—
482C2×M16C23×C1112yes—
483C2×M16C23×C1112yes—
484C2×M16C23×C1112yes—
485C22×C8—24no—
486C22×C8—21no—
487C22×C8—21no—
488C22×C8C2×C4×C1112yes—
489C22×C8D4×C1112yes—
490#117—21no—
491#117—21no—
492#117—21no—
493#117C23×C1112yes—
494C2×C4⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C42—21no—
497#104—28no—
498#103—28no—
499#101—28no—
500C2×C11—21no—
501C2×C11—21no—
502C2×C11—21no—
503C2×C11—21no—
504C2×C11—21no—
505C2×C11—21no—
506C2×C11—44no—
507C2×C11#190212yesdirect product factor
508C2×C11C2×#38611yescharacteristic
509C24—21no—
510C24C11×#4111yescharacteristic
511#41—22no—
512#41—22no—
513#41—22no—
514#41—22no—
515#41—22no—
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41C11×C22⋊C414yes—
524#41C11×C22⋊C414yes—
525#41C2×D4×C1114yes—
526#41C2×D4×C1114yes—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8C11×C22⋊C412yes—
558C2×Q8C11×C22⋊C412yes—
559C2×Q8C22×C4×C1114yes—
560C2×Q8C22×C4×C1112yes—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4C11×C22⋊C412yes—
571C2×D4C11×C22⋊C412yes—
572C2×D4C22×C4×C1112yes—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4C22×C4×C1111yescharacteristic
589C22×C4C22×C4×C1111yescharacteristic
590C22×C4C2×D4×C1111yescharacteristic
591C22×C4C2×D4×C1111yescharacteristic
592C22×C4C2×D4×C1111yescharacteristic
593C22×C4C2×D4×C1111yescharacteristic
594C22×C4C2×D4×C1111yescharacteristic
595C22×C4C2×D4×C1111yescharacteristic
596C22×C4C2×D4×C1111yescharacteristic
597C22×C4C2×D4×C1111yescharacteristic
598C22×C4C11×#4111yescharacteristic
599C22×C4C11×#4111yescharacteristic
600C22×C4C11×#4111yescharacteristic
601C22×C4C24×C1111yescharacteristic
602Q16—216no—
603SD16—216no—
604M16—216no—
605M16—22no—
606M16—22no—
607M16—22no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—22no—
612M16—22no—
613M16—22no—
614M16—22no—
615M16—22no—
616M16—22no—
617M16—22no—
618M16—41no—
619M16—41no—
620M16C2×D4×C1114yes—
621C2×C8—216no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8C22×C4×C1114yes—
633C2×C8C2×D4×C1114yes—
634C4⋊C4—22no—
635C4⋊C4—41no—
636C22⋊C4—22no—
637C22⋊C4—41no—
638C42—22no—
639C42—41no—
640C11C2×#190211yescharacteristic, direct product factor, Sylow
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—82no—
646C23C4×D4×C1111yescharacteristic
647C23C4×D4×C1111yescharacteristic
648C23C11×#12111yescharacteristic
649C23C11×#12111yescharacteristic
650C23C11×#12311yescharacteristic
651C23C11×#12311yescharacteristic
652C23C2×C11×#4111yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—24no—
657Q8—24no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8C2×C11×C22⋊C414yes—
665D4—24no—
666D4—24no—
667D4—24no—
668D4—24no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4C2×C11×C22⋊C414yes—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—82no—
689C2×C4C2×C11×C22⋊C411yescharacteristic
690C2×C4C2×C11×C22⋊C411yescharacteristic
691C2×C4C2×C11×C22⋊C411yescharacteristic
692C2×C4C2×C11×C22⋊C411yescharacteristic
693C2×C4C4×D4×C1111yescharacteristic
694C2×C4C4×D4×C1111yescharacteristic
695C2×C4C4×D4×C1111yescharacteristic
696C2×C4C4×D4×C1111yescharacteristic
697C2×C4C4×D4×C1111yescharacteristic
698C2×C4C4×D4×C1111yescharacteristic
699C2×C4C11×#12011yescharacteristic
700C2×C4C11×#12011yescharacteristic
701C2×C4C11×#12011yescharacteristic
702C2×C4C11×#12011yescharacteristic
703C2×C4C11×#12111yescharacteristic
704C2×C4C11×#12111yescharacteristic
705C2×C4C11×#12111yescharacteristic
706C2×C4C11×#12111yescharacteristic
707C2×C4C11×#12111yescharacteristic
708C2×C4C11×#12111yescharacteristic
709C2×C4C11×#12311yescharacteristic
710C2×C4C11×#12311yescharacteristic
711C2×C4C23×C4×C1111yescharacteristic
712C2×C4C22×D4×C1111yescharacteristic
713C2×C4C22×D4×C1111yescharacteristic
714C2×C4C22×D4×C1111yescharacteristic
715C2×C4C22×D4×C1111yescharacteristic
716C2×C4C2×C11×#4111yescharacteristic
717C8—24no—
718C8—24no—
719C8—24no—
720C8—42no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—24no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—44no—
730C22—82no—
731C22—82no—
732C22C11×#38611yescharacteristic
733C22C11×#38611yescharacteristic
734C22C11×#38611yescharacteristic
735C22C11×#38611yescharacteristic
736C22C2×C4×D4×C1111yescharacteristic
737C22C2×C11×#12111yescharacteristic
738C22C2×C11×#12311yescharacteristic
739C4—24no—
740C4—44no—
741C4—82no—
742C4C11×#38611yescharacteristic
743C4C11×#38611yescharacteristic
744C4C11×#38611yescharacteristic
745C4C11×#38611yescharacteristic
746C4C22×C11×C22⋊C411yescharacteristic
747C4C2×C4×D4×C1111yescharacteristic
748C4C2×C11×#12011yescharacteristic
749C4C2×C11×#12111yescharacteristic
750C2—21no—
751C2—21no—
752C2—21no—
753C2—21no—
754C2—21no—
755C2—21no—
756C2—44no—
757C2C11×#190212yesdirect product factor
758C2C2×C11×#38611yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C11×#419C2semidirect
5. C22×C11×#101C2semidirect
6. C11×#1902C2direct (N × H)
7. C2×C11×#344C2semidirect
8. C2×C11×#338C2semidirect
15. C2×C11×#137C4semidirect
17. C22×C11×Q16C4semidirect
18. C22×C11×SD16C4semidirect
35. C11×#419C22semidirect
39. C2×C11×#101C22semidirect
40. C11×#344C22semidirect
41. C11×#338C22semidirect
80. C2×C11×Q16C2×C4semidirect
83. C2×C11×SD16C2×C4semidirect
130. C2×#1902C11direct (N × H)
265. C2×#419C2×C11semidirect
266. C22×#101C2×C11semidirect
267. #1902C2×C11direct (N × H)
268. C2×#344C2×C11semidirect
269. C2×#338C2×C11semidirect
356. C2×#137C4×C11semidirect
358. C22×Q16C4×C11semidirect
359. C22×SD16C4×C11semidirect
376. #419C22×C11semidirect
380. C2×#101C22×C11semidirect
381. #344C22×C11semidirect
382. #338C22×C11semidirect
450. C2×Q16C2×C4×C11semidirect
453. C2×SD16C2×C4×C11semidirect
507. C2×C11#1902direct (N × H)
640. C11C2×#1902direct (N × H)
757. C2C11×#1902direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1372
C2×C11×#5682
C2×C11×#4212
C2×C11×#4192
C22×C11×#1012
C11×#19022
C2×C11×#3442
C2×C11×#3382
C2×#190211