Finite Group Databasebeta

← C2×C11×#2414 #14611903

Subgroups — C2×C11×#2414 #14611903

Order 2816.

4174 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#121C211yesmaximal, characteristic, complemented
2C22×C11×#121C211yesmaximal, characteristic, complemented
3C22×C4×D4×C11C211yesmaximal, characteristic, complemented
4C22×C11×#117C211yesmaximal, characteristic, complemented
5C11×#2414C2116yesmaximal, direct product factor
6C2×C11×#394C212yesmaximal, complemented
7C2×C11×#392C212yesmaximal, complemented
8C2×C11×#390C212yesmaximal, complemented
9C2×C11×#390C211yesmaximal, characteristic, complemented
10C2×C11×#389C211yesmaximal, characteristic, complemented
11C2×C11×#388C212yesmaximal, complemented
12C2×C11×#380C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C23×D4×C11C2212yes—
16C23×D4×C11C2212yes—
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C2×C11×#121—28no—
20C2×C11×#121—28no—
21C2×C11×#121C2218yescomplemented
22C2×C11×#121C2218yescomplemented
23C2×C4×D4×C11—28no—
24C2×C4×D4×C11C2218yescomplemented
25C2×C11×#117—28no—
26C2×C11×#117C2218yescomplemented
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C4⋊C4C2212yes—
31C22×C11×C4⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2212yes—
33C22×C11×C22⋊C4C2212yes—
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2212yes—
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2212yes—
38C22×C11×C22⋊C4C2212yes—
39C22×C11×C22⋊C4C2212yes—
40C22×C42×C11C2212yes—
41C22×C42×C11C2211yescharacteristic
42C11×#394C22116yescomplemented
43C11×#392C22116yescomplemented
44C11×#390C22116yescomplemented
45C11×#390C2218yescomplemented
46C11×#389C2218yescomplemented
47C11×#388C22116yescomplemented
48C11×#380C2218yescomplemented
49C2×C11×#95C2212yes—
50C2×C11×#95C2212yes—
51C25×C11C2312yes—
52C25×C11C2311yescharacteristic
53C25×C11C2311yescharacteristic
54C22×D4×C11—24no—
55C22×D4×C11—24no—
56C22×D4×C11—28no—
57C22×D4×C11—28no—
58C22×D4×C11—28no—
59C22×D4×C11—24no—
60C22×D4×C11—24no—
61C22×D4×C11—24no—
62C22×D4×C11—24no—
63C22×D4×C11—44no—
64C22×D4×C11—44no—
65C22×D4×C11—44no—
66C22×D4×C11C2314yes—
67C22×D4×C11C2314yes—
68C22×D4×C11C2318yes—
69C22×D4×C11C2318yes—
70C23×C4×C11—24no—
71C23×C4×C11—24no—
72C23×C4×C11—24no—
73C23×C4×C11—24no—
74C23×C4×C11—24no—
75C23×C4×C11D418yescomplemented
76C23×C4×C11C2314yes—
77C23×C4×C11C2312yes—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2312yes—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2312yes—
83C23×C4×C11C2314yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C11×#121—232no—
87C11×#121—232no—
88C4×D4×C11—232no—
89C11×#117—232no—
90C2×C11×C4⋊C4—24no—
91C2×C11×C4⋊C4—24no—
92C2×C11×C4⋊C4—24no—
93C2×C11×C4⋊C4—44no—
94C2×C11×C4⋊C4D418yescomplemented
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C4⋊C4C2318yes—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C22⋊C4—24no—
101C2×C11×C22⋊C4—28no—
102C2×C11×C22⋊C4—24no—
103C2×C11×C22⋊C4—28no—
104C2×C11×C22⋊C4—28no—
105C2×C11×C22⋊C4—28no—
106C2×C11×C22⋊C4—44no—
107C2×C11×C22⋊C4—44no—
108C2×C11×C22⋊C4C2318yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2318yes—
112C2×C11×C22⋊C4C2318yes—
113C2×C11×C22⋊C4C2318yes—
114C2×C11×C22⋊C4C2318yes—
115C2×C11×C22⋊C4C2318yes—
116C2×C42×C11—28no—
117C2×C42×C11—24no—
118C2×C42×C11C2318yes—
119C2×C42×C11C2314yes—
120C11×#95C2318yes—
121C11×#95C2318yes—
122C2×#2414C1111yesmaximal, characteristic, direct product factor, Sylow
123C24×C11—22no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11—22no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11—24no—
136C24×C11—24no—
137C24×C11—24no—
138C24×C11—24no—
139C24×C11—24no—
140C24×C11—24no—
141C24×C11—24no—
142C24×C11C2×D414yes—
143C24×C11#4114yes—
144C24×C11C2414yes—
145C24×C11C2412yes—
146C24×C11C2412yes—
147C24×C11C2411yescharacteristic
148C2×D4×C11—232no—
149C2×D4×C11—28no—
150C2×D4×C11—28no—
151C2×D4×C11—216no—
152C2×D4×C11—216no—
153C2×D4×C11—216no—
154C2×D4×C11—28no—
155C2×D4×C11—28no—
156C2×D4×C11—28no—
157C2×D4×C11—28no—
158C2×D4×C11—48no—
159C2×D4×C11—48no—
160C2×D4×C11—48no—
161C2×D4×C11—432no—
162C2×D4×C11—432no—
163C2×D4×C11—416no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—24no—
169C22×C4×C11—24no—
170C22×C4×C11—232no—
171C22×C4×C11—28no—
172C22×C4×C11—28no—
173C22×C4×C11—22no—
174C22×C4×C11—24no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—24no—
178C22×C4×C11—24no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—22no—
184C22×C4×C11—24no—
185C22×C4×C11—28no—
186C22×C4×C11—28no—
187C22×C4×C11—28no—
188C22×C4×C11—416no—
189C22×C4×C11C2×D418yes—
190C22×C4×C11C2×D414yes—
191C22×C4×C11C2×D414yes—
192C22×C4×C11C2×D414yes—
193C22×C4×C11C2×D4116yescomplemented
194C22×C4×C11#4114yes—
195C22×C4×C11#4114yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2414yes—
198C22×C4×C11C2414yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2414yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C11×C4⋊C4—28no—
205C11×C4⋊C4—28no—
206C11×C4⋊C4—28no—
207C11×C4⋊C4—48no—
208C11×C4⋊C4C2×D4116yescomplemented
209C11×C22⋊C4—28no—
210C11×C22⋊C4—216no—
211C11×C22⋊C4—28no—
212C11×C22⋊C4—216no—
213C11×C22⋊C4—216no—
214C11×C22⋊C4—216no—
215C11×C22⋊C4—48no—
216C11×C22⋊C4—48no—
217C42×C11—216no—
218C42×C11—28no—
219C22×#121C2×C1111yescharacteristic, complemented
220C22×#121C2×C1111yescharacteristic, complemented
221C22×C4×D4C2×C1111yescharacteristic, complemented
222C22×#117C2×C1111yescharacteristic, complemented
223#2414C2×C11116yesdirect product factor
224C2×#394C2×C1112yescomplemented
225C2×#392C2×C1112yescomplemented
226C2×#390C2×C1111yescharacteristic, complemented
227C2×#390C2×C1112yescomplemented
228C2×#389C2×C1111yescharacteristic, complemented
229C2×#388C2×C1112yescomplemented
230C2×#380C2×C1111yescharacteristic, complemented
231C23×C11—28no—
232C23×C11—28no—
233C23×C11—28no—
234C23×C11—28no—
235C23×C11—28no—
236C23×C11—28no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—24no—
255C23×C11—24no—
256C23×C11—44no—
257C23×C11—44no—
258C23×C11—44no—
259C23×C11—44no—
260C23×C11—44no—
261C23×C11—44no—
262C23×C11—44no—
263C23×C11—44no—
264C23×C11—48no—
265C23×C11—48no—
266C23×C11—48no—
267C23×C11—48no—
268C23×C11—48no—
269C23×C11—48no—
270C23×C11—48no—
271C23×C11C22×D414yes—
272C23×C11C22×D412yes—
273C23×C11C22×D412yes—
274C23×C11C2×#4114yes—
275C23×C11C2×#4112yes—
276C23×C11C2×#4112yes—
277C23×C11C2×#4112yes—
278C23×C11H(5,𝔽2)12yes—
279C23×C11H(5,𝔽2)12yes—
280C23×C11C2511yescharacteristic
281D4×C11—232no—
282D4×C11—432no—
283D4×C11—432no—
284D4×C11—416no—
285C2×C4×C11—28no—
286C2×C4×C11—28no—
287C2×C4×C11—216no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—232no—
295C2×C4×C11—22no—
296C2×C4×C11—24no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—22no—
306C2×C4×C11—24no—
307C2×C4×C11—44no—
308C2×C4×C11—44no—
309C2×C4×C11—48no—
310C2×C4×C11—48no—
311C2×C4×C11—416no—
312C2×C4×C11#121116yes—
313C2×C4×C11C22×D418yes—
314C2×C4×C11C22×D414yes—
315C2×C4×C11C22×D414yes—
316C2×C4×C11C22×D414yes—
317C2×C4×C11C2×#4114yes—
318C2×C4×C11C2×#4114yes—
319C23×D4C22×C1111yescharacteristic
320C23×D4C22×C1111yescharacteristic
321C23×D4C22×C1112yes—
322C23×D4C22×C1112yes—
323C24×C4C22×C1111yescharacteristic
324C24×C4C22×C1111yescharacteristic
325C2×#121—28no—
326C2×#121—28no—
327C2×#121C22×C1118yescomplemented
328C2×#121C22×C1118yescomplemented
329C2×C4×D4—28no—
330C2×C4×D4C22×C1118yescomplemented
331C2×#117—28no—
332C2×#117C22×C1118yescomplemented
333C22×C4⋊C4C22×C1111yescharacteristic
334C22×C4⋊C4C22×C1111yescharacteristic
335C22×C4⋊C4C22×C1111yescharacteristic
336C22×C4⋊C4C22×C1112yes—
337C22×C4⋊C4C22×C1111yescharacteristic
338C22×C22⋊C4C22×C1112yes—
339C22×C22⋊C4C22×C1112yes—
340C22×C22⋊C4C22×C1111yescharacteristic
341C22×C22⋊C4C22×C1112yes—
342C22×C22⋊C4C22×C1111yescharacteristic
343C22×C22⋊C4C22×C1112yes—
344C22×C22⋊C4C22×C1112yes—
345C22×C22⋊C4C22×C1112yes—
346C22×C42C22×C1112yes—
347C22×C42C22×C1111yescharacteristic
348#394C22×C11116yescomplemented
349#392C22×C11116yescomplemented
350#390C22×C11116yescomplemented
351#390C22×C1118yescomplemented
352#389C22×C1118yescomplemented
353#388C22×C11116yescomplemented
354#380C22×C1118yescomplemented
355C2×#95C22×C1112yes—
356C2×#95C22×C1112yes—
357C22×C11—24no—
358C22×C11—24no—
359C22×C11—24no—
360C22×C11—24no—
361C22×C11—24no—
362C22×C11—24no—
363C22×C11—42no—
364C22×C11—416no—
365C22×C11—416no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—44no—
374C22×C11—44no—
375C22×C11—44no—
376C22×C11—44no—
377C22×C11—44no—
378C22×C11—44no—
379C22×C11—44no—
380C22×C11—816no—
381C22×C11C2×#12114yes—
382C22×C11#52514yes—
383C22×C11#53514yes—
384C22×C11#54614yes—
385C22×C11#55014yes—
386C22×C11#55314yes—
387C22×C11#55514yes—
388C22×C11C23×D411yescharacteristic
389C22×C11C23×D411yescharacteristic
390C22×C11C22×#4111yescharacteristic
391C22×C11C22×#4111yescharacteristic
392C22×C11C22×#4111yescharacteristic
393C22×C11C2×H(5,𝔽2)11yescharacteristic
394C22×C11C2×H(5,𝔽2)11yescharacteristic
395C4×C11—24no—
396C4×C11—24no—
397C4×C11—28no—
398C4×C11—42no—
399C4×C11—42no—
400C4×C11—44no—
401C4×C11—44no—
402C4×C11C2×#12118yes—
403C25C23×C1112yes—
404C25C23×C1111yescharacteristic
405C25C23×C1111yescharacteristic
406C22×D4—24no—
407C22×D4—24no—
408C22×D4—28no—
409C22×D4—28no—
410C22×D4—28no—
411C22×D4—24no—
412C22×D4—24no—
413C22×D4—24no—
414C22×D4—24no—
415C22×D4—44no—
416C22×D4—44no—
417C22×D4—44no—
418C22×D4C23×C1114yes—
419C22×D4C23×C1114yes—
420C22×D4C23×C1118yes—
421C22×D4C23×C1118yes—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—24no—
426C23×C4—24no—
427C23×C4D4×C1118yescomplemented
428C23×C4C23×C1111yescharacteristic
429C23×C4C23×C1112yes—
430C23×C4C23×C1111yescharacteristic
431C23×C4C23×C1112yes—
432C23×C4C23×C1114yes—
433C23×C4C23×C1111yescharacteristic
434C23×C4C23×C1112yes—
435C23×C4C23×C1114yes—
436C23×C4C23×C1111yescharacteristic
437C23×C4C23×C1111yescharacteristic
438#121—232no—
439#121—232no—
440C4×D4—232no—
441#117—232no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—44no—
446C2×C4⋊C4D4×C1118yescomplemented
447C2×C4⋊C4C23×C1114yes—
448C2×C4⋊C4C23×C1114yes—
449C2×C4⋊C4C23×C1114yes—
450C2×C4⋊C4C23×C1118yes—
451C2×C4⋊C4C23×C1114yes—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—28no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—28no—
456C2×C22⋊C4—28no—
457C2×C22⋊C4—28no—
458C2×C22⋊C4—44no—
459C2×C22⋊C4—44no—
460C2×C22⋊C4C23×C1118yes—
461C2×C22⋊C4C23×C1114yes—
462C2×C22⋊C4C23×C1114yes—
463C2×C22⋊C4C23×C1118yes—
464C2×C22⋊C4C23×C1118yes—
465C2×C22⋊C4C23×C1118yes—
466C2×C22⋊C4C23×C1118yes—
467C2×C22⋊C4C23×C1118yes—
468C2×C42—28no—
469C2×C42—24no—
470C2×C42C23×C1118yes—
471C2×C42C23×C1114yes—
472#95C23×C1118yes—
473#95C23×C1118yes—
474C2×C11—44no—
475C2×C11—44no—
476C2×C11—84no—
477C2×C11#241418yesdirect product factor
478C2×C11C22×#12111yescharacteristic
479C2×C11C2×#52511yescharacteristic
480C2×C11C2×#53511yescharacteristic
481C2×C11C2×#54611yescharacteristic
482C2×C11C2×#55011yescharacteristic
483C2×C11C2×#55311yescharacteristic
484C2×C11C2×#55511yescharacteristic
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—24no—
498C24—24no—
499C24—24no—
500C24—24no—
501C24—24no—
502C24—24no—
503C24—24no—
504C24C2×D4×C1114yes—
505C24C11×#4114yes—
506C24C24×C1114yes—
507C24C24×C1112yes—
508C24C24×C1112yes—
509C24C24×C1111yescharacteristic
510C2×D4—232no—
511C2×D4—28no—
512C2×D4—28no—
513C2×D4—216no—
514C2×D4—216no—
515C2×D4—216no—
516C2×D4—28no—
517C2×D4—28no—
518C2×D4—28no—
519C2×D4—28no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—48no—
523C2×D4—432no—
524C2×D4—432no—
525C2×D4—416no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—232no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—416no—
551C22×C4C2×D4×C1118yes—
552C22×C4C2×D4×C1114yes—
553C22×C4C2×D4×C1114yes—
554C22×C4C2×D4×C1114yes—
555C22×C4C2×D4×C11116yescomplemented
556C22×C4C11×#4114yes—
557C22×C4C11×#4114yes—
558C22×C4C24×C1112yes—
559C22×C4C24×C1114yes—
560C22×C4C24×C1114yes—
561C22×C4C24×C1112yes—
562C22×C4C24×C1114yes—
563C22×C4C24×C1112yes—
564C22×C4C24×C1112yes—
565C22×C4C24×C1112yes—
566C4⋊C4—28no—
567C4⋊C4—28no—
568C4⋊C4—28no—
569C4⋊C4—48no—
570C4⋊C4C2×D4×C11116yescomplemented
571C22⋊C4—28no—
572C22⋊C4—216no—
573C22⋊C4—28no—
574C22⋊C4—216no—
575C22⋊C4—216no—
576C22⋊C4—216no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C42—216no—
580C42—28no—
581C11C2×#241411yescharacteristic, direct product factor, Sylow
582C23—28no—
583C23—28no—
584C23—28no—
585C23—28no—
586C23—28no—
587C23—28no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23—48no—
616C23—48no—
617C23—48no—
618C23—48no—
619C23—48no—
620C23—48no—
621C23—48no—
622C23C22×D4×C1114yes—
623C23C22×D4×C1112yes—
624C23C22×D4×C1112yes—
625C23C2×C11×#4114yes—
626C23C2×C11×#4112yes—
627C23C2×C11×#4112yes—
628C23C2×C11×#4112yes—
629C23C11×H(5,𝔽2)12yes—
630C23C11×H(5,𝔽2)12yes—
631C23C25×C1111yescharacteristic
632D4—232no—
633D4—432no—
634D4—432no—
635D4—416no—
636C2×C4—28no—
637C2×C4—28no—
638C2×C4—216no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—232no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—48no—
661C2×C4—48no—
662C2×C4—416no—
663C2×C4C11×#121116yes—
664C2×C4C22×D4×C1118yes—
665C2×C4C22×D4×C1114yes—
666C2×C4C22×D4×C1114yes—
667C2×C4C22×D4×C1114yes—
668C2×C4C2×C11×#4114yes—
669C2×C4C2×C11×#4114yes—
670C22—24no—
671C22—24no—
672C22—24no—
673C22—24no—
674C22—24no—
675C22—24no—
676C22—42no—
677C22—416no—
678C22—416no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—44no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—816no—
694C22C2×C11×#12114yes—
695C22C11×#52514yes—
696C22C11×#53514yes—
697C22C11×#54614yes—
698C22C11×#55014yes—
699C22C11×#55314yes—
700C22C11×#55514yes—
701C22C23×D4×C1111yescharacteristic
702C22C23×D4×C1111yescharacteristic
703C22C22×C11×#4111yescharacteristic
704C22C22×C11×#4111yescharacteristic
705C22C22×C11×#4111yescharacteristic
706C22C2×C11×H(5,𝔽2)11yescharacteristic
707C22C2×C11×H(5,𝔽2)11yescharacteristic
708C4—24no—
709C4—24no—
710C4—28no—
711C4—42no—
712C4—44no—
713C4—42no—
714C4—44no—
715C4C2×C11×#12118yes—
716C2—44no—
717C2—44no—
718C2—84no—
719C2C11×#241418yesdirect product factor
720C2C22×C11×#12111yescharacteristic
721C2C2×C11×#52511yescharacteristic
722C2C2×C11×#53511yescharacteristic
723C2C2×C11×#54611yescharacteristic
724C2C2×C11×#55011yescharacteristic
725C2C2×C11×#55311yescharacteristic
726C2C2×C11×#55511yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#121C2semidirect
2. C22×C11×#121C2semidirect
3. C22×C4×D4×C11C2semidirect
4. C22×C11×#117C2semidirect
5. C11×#2414C2direct (N × H)
6. C2×C11×#394C2semidirect
7. C2×C11×#392C2semidirect
8. C2×C11×#390C2semidirect
9. C2×C11×#390C2semidirect
10. C2×C11×#389C2semidirect
11. C2×C11×#388C2semidirect
12. C2×C11×#380C2semidirect
21. C2×C11×#121C22semidirect
22. C2×C11×#121C22semidirect
24. C2×C4×D4×C11C22semidirect
26. C2×C11×#117C22semidirect
42. C11×#394C22semidirect
43. C11×#392C22semidirect
44. C11×#390C22semidirect
45. C11×#390C22semidirect
46. C11×#389C22semidirect
47. C11×#388C22semidirect
48. C11×#380C22semidirect
75. C23×C4×C11D4semidirect
94. C2×C11×C4⋊C4D4semidirect
122. C2×#2414C11direct (N × H)
193. C22×C4×C11C2×D4semidirect
208. C11×C4⋊C4C2×D4semidirect
219. C22×#121C2×C11semidirect
220. C22×#121C2×C11semidirect
221. C22×C4×D4C2×C11semidirect
222. C22×#117C2×C11semidirect
223. #2414C2×C11direct (N × H)
224. C2×#394C2×C11semidirect
225. C2×#392C2×C11semidirect
226. C2×#390C2×C11semidirect
227. C2×#390C2×C11semidirect
228. C2×#389C2×C11semidirect
229. C2×#388C2×C11semidirect
230. C2×#380C2×C11semidirect
327. C2×#121C22×C11semidirect
328. C2×#121C22×C11semidirect
330. C2×C4×D4C22×C11semidirect
332. C2×#117C22×C11semidirect
348. #394C22×C11semidirect
349. #392C22×C11semidirect
350. #390C22×C11semidirect
351. #390C22×C11semidirect
352. #389C22×C11semidirect
353. #388C22×C11semidirect
354. #380C22×C11semidirect
427. C23×C4D4×C11semidirect
446. C2×C4⋊C4D4×C11semidirect
477. C2×C11#2414direct (N × H)
555. C22×C4C2×D4×C11semidirect
570. C4⋊C4C2×D4×C11semidirect
581. C11C2×#2414direct (N × H)
719. C2C11×#2414direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1212
C22×C4×D4×C112
C22×C11×#1172
C11×#24142
C2×C11×#3942
C2×C11×#3922
C2×C11×#3902
C2×C11×#3892
C2×C11×#3882
C2×C11×#3802
C2×#241411