Finite Group Databasebeta

← C4×#10622836 #14675557

Subgroups — C4×#10622836 #14675557

Order 2816.

3502 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C212yesmaximal, complemented
2C2×#10622836C211yesmaximal, characteristic
3C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic11C212yesmaximal, complemented
5#13066879C211yesmaximal, characteristic, complemented
6#13066859C212yesmaximal, complemented
7#13066858C211yesmaximal, characteristic, complemented
8#13066857C211yesmaximal, characteristic, complemented
9#13066855C212yesmaximal, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C22×C4×D4×C11C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2212yes—
14C23×C22⋊D11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C2×C4×D4×C11—28no—
17C2×C4×D4×C11—24no—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C2×C4×C22⋊D11—28no—
25C2×C4×C22⋊D11—28no—
26C2×C4×C22⋊D11—28no—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2212yes—
33#10622836C418yesdirect product factor
34C4×C22⋊Dic11—28no—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C4×(C2×D11)⋊C4—24no—
43C25×C11C2312yes—
44C24×D11C2311yescharacteristic
45C22×D4×C11—24no—
46C22×D4×C11—24no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11C2×C414yescomplemented
50C23×C4×C11—24no—
51C23×C4×C11—24no—
52C23×C4×C11—24no—
53C23×C4×C11—24no—
54C23×C4×C11—24no—
55C23×C4×C11—24no—
56C23×C4×C11D418yescomplemented
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—24no—
62C22×C22⋊D11—24no—
63C22×C22⋊D11—24no—
64C22×C22⋊D11—24no—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—24no—
67C22×C22⋊D11C2×C418yescomplemented
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2312yes—
73C22×C4×D11—22no—
74C22×C4×D11—24no—
75C22×C4×D11—24no—
76C22×C4×D11—22no—
77C22×C4×D11D414yescomplemented
78C4×D4×C11—232no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—24no—
84C2×C42×C11—24no—
85C2×C42×C11D414yescomplemented
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11—24no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—24no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—24no—
93C2×C22⋊Dic11—24no—
94C2×C22⋊Dic11C2×C418yescomplemented
95C4×C22⋊D11—264no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—24no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4C2×C414yescomplemented
105C2×Dic11⋊C4—24no—
106C2×Dic11⋊C4—24no—
107C2×Dic11⋊C4—24no—
108C2×C4×Dic11—24no—
109C2×C4×Dic11—24no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—24no—
112C2×C4×Dic11D418yescomplemented
113C11⋊#95—22no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—24no—
117C11⋊#95—24no—
118C11⋊#95—24no—
119C11⋊#95C2×C414yescomplemented
120C4×#392—111nomaximal, Sylow
121C24×C11—22no—
122C24×C11—22no—
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×C11C22×C414yes—
134C24×C11C2×D414yes—
135C24×C11#4114yes—
136C24×C11C2411yescharacteristic
137C23×D11—21no—
138C23×D11—22no—
139C23×D11—22no—
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11C22×C412yes—
146C23×D11C2×D412yes—
147C23×D11#4112yes—
148C2×D4×C11—28no—
149C2×D4×C11—28no—
150C2×D4×C11—216no—
151C2×D4×C11—216no—
152C2×D4×C11—28no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—216no—
166C22×C4×C11—216no—
167C22×C4×C11—216no—
168C22×C4×C11—48no—
169C22×C4×C11—48no—
170C22×C4×C11—48no—
171C22×C4×C11—48no—
172C22×C4×C11C22×C412yes—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D414yes—
178C22×C4×C11C2×D414yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11#4112yes—
181C22×C4×C11#4112yes—
182C2×C22⋊D11—216no—
183C2×C22⋊D11—216no—
184C2×C22⋊D11—216no—
185C2×C22⋊D11—216no—
186C2×C22⋊D11—216no—
187C2×C22⋊D11—216no—
188C2×C22⋊D11—216no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—21no—
211C22×Dic11C22×C412yes—
212C22×Dic11C22×C414yes—
213C22×Dic11C2×D414yes—
214C22×Dic11C2×D412yes—
215C22×Dic11C2×D414yes—
216C22×Dic11#4112yes—
217C22×Dic11#4114yes—
218C2×C4×D11—216no—
219C2×C4×D11—28no—
220C2×C4×D11—44no—
221C2×C4×D11—48no—
222C2×C4×D11—44no—
223C11×C4⋊C4—28no—
224C11×C22⋊C4—216no—
225C42×C11—28no—
226C22⋊Dic11—216no—
227C22⋊Dic11—216no—
228C22⋊Dic11—216no—
229(C2×D11)⋊C4—28no—
230(C2×D11)⋊C4—216no—
231(C2×D11)⋊C4—28no—
232Dic11⋊C4—216no—
233C4×Dic11—216no—
234C4×Dic11—44no—
235C22×C4×D4—112no—
236C22×C4×D4D1111yescharacteristic, complemented
237C2×#392—111no—
238C2×C4×C22⋊C4—111no—
239C2×C4×C22⋊C4—112no—
240#1444—111no—
241#1439—111no—
242#1439—112no—
243#1438—111no—
244#1438—112no—
245C4×#95—111no—
246C23×C11—24no—
247C23×C11—24no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—24no—
255C23×C11—24no—
256C23×C11—24no—
257C23×C11—24no—
258C23×C11—24no—
259C23×C11—24no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—24no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11—42no—
274C23×C11—42no—
275C23×C11—42no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11C4×D418yescomplemented
281C23×C11C23×C411yescharacteristic
282C23×C11C22×D411yescharacteristic
283C23×C11C22×D412yes—
284C23×C11C22×D412yes—
285C23×C11C22×D411yescharacteristic
286C23×C11C2×#4112yes—
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4111yescharacteristic
289C23×C11C2×#4111yescharacteristic
290C23×C11C2×#4112yes—
291C23×C11C2×#4111yescharacteristic
292C22×D11—22no—
293C22×D11—24no—
294C22×D11—24no—
295C22×D11—22no—
296C22×D11—24no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—24no—
300C22×D11—24no—
301C22×D11—24no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—41no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—41no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—41no—
311C22×D11—42no—
312C22×D11—41no—
313C22×D11—42no—
314C22×D11C4×D414yescomplemented
315D4×C11—232no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—24no—
320C2×C4×C11—24no—
321C2×C4×C11—22no—
322C2×C4×C11—24no—
323C2×C4×C11—24no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—432no—
333C2×C4×C11C4×D414yescomplemented
334C2×C4×C11#12018yes—
335C2×C4×C11#12014yes—
336C2×C4×C11#12114yes—
337C2×C4×C11#12118yes—
338C2×C4×C11#12714yes—
339C22⋊D11—264no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—22no—
347C2×Dic11—24no—
348C2×Dic11—24no—
349C2×Dic11—24no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—24no—
353C2×Dic11—24no—
354C2×Dic11—24no—
355C2×Dic11—41no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11—41no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11—41no—
367C2×Dic11—42no—
368C2×Dic11C4×D418yescomplemented
369C4×D11—416no—
370C23×D4—112no—
371C23×D4C2×D1111yescharacteristic
372C24×C4—111no—
373C24×C4C2×D1112yes—
374C2×C4×D4—28no—
375C2×C4×D4—24no—
376C2×C4×D4—228no—
377C2×C4×D4—228no—
378C2×C4×D4—228no—
379C22×C4⋊C4—112no—
380C22×C4⋊C4C2×D1111yescharacteristic
381C22×C22⋊C4—112no—
382C22×C22⋊C4—111no—
383C22×C22⋊C4—112no—
384C22×C22⋊C4—112no—
385C22×C22⋊C4—112no—
386C22×C22⋊C4—111no—
387C22×C22⋊C4C2×D1112yes—
388C22×C42—112no—
389C22×C42—111no—
390C22×C42C2×D1111yescharacteristic
391#392—118no—
392C4×C22⋊C4—228no—
393C4×C22⋊C4—224no—
394C2×#95—111no—
395C2×#95—112no—
396C2×#95—111no—
397C2×#95—112no—
398C2×#95—111no—
399C2×#95—112no—
400C2×#95—111no—
401C22×C11—28no—
402C22×C11—28no—
403C22×C11—28no—
404C22×C11—44no—
405C22×C11—44no—
406C22×C11—44no—
407C22×C11—44no—
408C22×C11—44no—
409C22×C11—44no—
410C22×C11—44no—
411C22×C11—44no—
412C22×C11—44no—
413C22×C11—44no—
414C22×C11—44no—
415C22×C11—44no—
416C22×C11C2×C4×D411yescharacteristic
417C22×C11C2×C4×D412yes—
418C22×C11C2×C4×D412yes—
419C22×C11C2×C4×D411yescharacteristic
420C22×C11C4×#4111yescharacteristic
421C22×C11C2×#12012yes—
422C22×C11C2×#12011yescharacteristic
423C22×C11C2×#12111yescharacteristic
424C22×C11C2×#12112yes—
425C22×C11#52512yes—
426C22×C11#52511yescharacteristic
427C22×C11#52512yes—
428C22×C11#52512yes—
429C22×C11#52512yes—
430C22×C11#52512yes—
431C22×C11#52511yescharacteristic
432C22×C11#52912yes—
433C22×C11#52911yescharacteristic
434C22×C11C2×#12711yescharacteristic
435C22×C11#53212yes—
436C22×C11#53211yescharacteristic
437C22×C11#53211yescharacteristic
438C22×C11#53212yes—
439C2×D11—28no—
440C2×D11—24no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—44no—
445C2×D11—42no—
446C2×D11—44no—
447C2×D11—42no—
448C2×D11—42no—
449C2×D11—44no—
450C4×C11—24no—
451C4×C11—44no—
452C4×C11—42no—
453C4×C11#39218yescomplemented
454Dic11—28no—
455Dic11—42no—
456Dic11—42no—
457Dic11—44no—
458Dic11—42no—
459C25—111no—
460C25C22×D1112yes—
461C22×D4—24no—
462C22×D4—24no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—118no—
466C22×D4—224no—
467C22×D4—224no—
468C22×D4—224no—
469C22×D4—224no—
470C22×D4—224no—
471C22×D4—224no—
472C22×D4C4×D1114yescomplemented
473C23×C4—24no—
474C23×C4—24no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—112no—
480C23×C4—111no—
481C23×C4—112no—
482C23×C4—111no—
483C23×C4—111no—
484C23×C4—114no—
485C23×C4—224no—
486C23×C4—222no—
487C23×C4—224no—
488C23×C4—222no—
489C23×C4C22⋊D1118yescomplemented
490C23×C4C22×D1111yescharacteristic
491C23×C4C22×D1112yes—
492C23×C4C22×D1111yescharacteristic
493C23×C4C22×D1111yescharacteristic
494C4×D4—232no—
495C4×D4—2264no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4—224no—
500C2×C4⋊C4—224no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—118no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—224no—
507C2×C22⋊C4—222no—
508C2×C22⋊C4—224no—
509C2×C22⋊C4—222no—
510C2×C22⋊C4—224no—
511C2×C22⋊C4—224no—
512C2×C22⋊C4—224no—
513C2×C22⋊C4—224no—
514C2×C22⋊C4—224no—
515C2×C22⋊C4—224no—
516C2×C22⋊C4—224no—
517C2×C22⋊C4—224no—
518C2×C22⋊C4—222no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—222no—
521C2×C22⋊C4—222no—
522C2×C42—24no—
523C2×C42—118no—
524C2×C42—224no—
525C2×C42—224no—
526C2×C42—224no—
527C2×C42—222no—
528C2×C42C22⋊D1114yescomplemented
529#95—114no—
530#95—224no—
531#95—224no—
532#95—224no—
533#95—222no—
534#95—222no—
535#95—222no—
536C2×C11—48no—
537C2×C11C4×#12012yes—
538C2×C11C4×#12011yescharacteristic
539C2×C11C4×#12111yescharacteristic
540C2×C11C4×#12112yes—
541C2×C11C4×#12711yescharacteristic
542C2×C11C2×#39211yescharacteristic
543C2×C11#238811yescharacteristic
544C2×C11#238812yes—
545C2×C11#239211yescharacteristic
546C2×C11#239212yes—
547C2×C11#239711yescharacteristic
548D11—44no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—112no—
562C24—112no—
563C24—112no—
564C24—221no—
565C24—222no—
566C24—222no—
567C24—221no—
568C24—221no—
569C24—222no—
570C24—221no—
571C24—222no—
572C24C2×C4×D1114yes—
573C24#433914yes—
574C24C2×C22⋊D1114yes—
575C24C23×D1111yescharacteristic
576C2×D4—28no—
577C2×D4—216no—
578C2×D4—28no—
579C2×D4—216no—
580C2×D4—28no—
581C2×D4—2216no—
582C2×D4—2216no—
583C2×D4—2216no—
584C2×D4—2216no—
585C2×D4—2216no—
586C2×D4—2216no—
587C2×D4—2216no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—216no—
601C22×C4—216no—
602C22×C4—216no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—114no—
608C22×C4—114no—
609C22×C4—114no—
610C22×C4—112no—
611C22×C4—114no—
612C22×C4—112no—
613C22×C4—112no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—221no—
620C22×C4—222no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—221no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—221no—
631C22×C4—221no—
632C22×C4—221no—
633C22×C4—221no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—2216no—
637C22×C4—228no—
638C22×C4—448no—
639C22×C4—444no—
640C22×C4—444no—
641C22×C4C2×C4×D1112yes—
642C22×C4#433912yes—
643C22×C4D4×D1112yes—
644C22×C4D4×D1114yes—
645C22×C4#434112yes—
646C22×C4C2×C22⋊D1112yes—
647C22×C4C2×C22⋊D1114yes—
648C22×C4C2×C22⋊D1112yes—
649C22×C4C2×C22⋊D1114yes—
650C22×C4C2×C22⋊D1112yes—
651C4⋊C4—28no—
652C4⋊C4—2216no—
653C22⋊C4—216no—
654C22⋊C4—2216no—
655C22⋊C4—228no—
656C22⋊C4—2216no—
657C22⋊C4—2216no—
658C22⋊C4—2216no—
659C22⋊C4—228no—
660C42—28no—
661C42—2216no—
662C42—444no—
663C11C4×#39211yescharacteristic, complemented, Sylow
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—114no—
699C23—222no—
700C23—224no—
701C23—222no—
702C23—224no—
703C23—224no—
704C23—222no—
705C23—224no—
706C23—224no—
707C23—222no—
708C23—222no—
709C23—222no—
710C23—224no—
711C23—441no—
712C23—442no—
713C23—442no—
714C23—442no—
715C23—442no—
716C23—441no—
717C23—442no—
718C23—442no—
719C23—441no—
720C23—441no—
721C23C4×C22⋊D1118yescomplemented
722C23C22×C4×D1111yescharacteristic
723C23C2×#433912yes—
724C23C2×#433911yescharacteristic
725C23C2×D4×D1111yescharacteristic
726C23C2×D4×D1112yes—
727C23C2×#434111yescharacteristic
728C23#41×D1111yescharacteristic
729C23#41×D1112yes—
730C23#41×D1111yescharacteristic
731C23C22×C22⋊D1112yes—
732C23C22×C22⋊D1111yescharacteristic
733D4—232no—
734D4—2264no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—432no—
752C2×C4—118no—
753C2×C4—224no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—222no—
760C2×C4—224no—
761C2×C4—224no—
762C2×C4—224no—
763C2×C4—222no—
764C2×C4—224no—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—222no—
768C2×C4—441no—
769C2×C4—442no—
770C2×C4—442no—
771C2×C4—442no—
772C2×C4—442no—
773C2×C4—441no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4—442no—
777C2×C4—442no—
778C2×C4—441no—
779C2×C4—442no—
780C2×C4—441no—
781C2×C4—4416no—
782C2×C4C4×C22⋊D1114yescomplemented
783C2×C4#6699018yes—
784C2×C4#6699114yes—
785C2×C4#6699218yes—
786C2×C4#6699314yes—
787C2×C4#6700614yes—
788C22—28no—
789C22—28no—
790C22—28no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—44no—
803C22—228no—
804C22—224no—
805C22—442no—
806C22—444no—
807C22—442no—
808C22—442no—
809C22—442no—
810C22—442no—
811C22—444no—
812C22—442no—
813C22—444no—
814C22C4×#434111yescharacteristic
815C22#1062306912yes—
816C22C4×D4×D1111yescharacteristic
817C22C4×D4×D1112yes—
818C22#1062307812yes—
819C22#1062307812yes—
820C22#1062307812yes—
821C22#1062307911yescharacteristic
822C22#1062307912yes—
823C22#1062308811yescharacteristic
824C22C2×C4×C22⋊D1112yes—
825C22C2×C4×C22⋊D1111yescharacteristic
826C22#1062332211yescharacteristic
827C22#1062332212yes—
828C22C2×#6699012yes—
829C22C2×#6699111yescharacteristic
830C22C2×#6699212yes—
831C22C2×#6699311yescharacteristic
832C22#1062335912yes—
833C22#1062335911yescharacteristic
834C22#1062336312yes—
835C22#1062336311yescharacteristic
836C22C2×#6700611yescharacteristic
837C4—24no—
838C4—44no—
839C4—42no—
840C4—228no—
841C4—442no—
842C4—442no—
843C4—442no—
844C4—444no—
845C4#1062283618yesdirect product factor
846C2—48no—
847C2—444no—
848C2C4×#6699012yes—
849C2C4×#6700611yescharacteristic
850C2C4×#6699111yescharacteristic
851C2C4×#6699212yes—
852C2C4×#6699311yescharacteristic
853C2C2×#1062283611yescharacteristic
854C2#1307182911yescharacteristic
855C2#1307183112yes—
856C2#1307185411yescharacteristic
857C2#1307185812yes—
858C2#1307189511yescharacteristic
subgroupG/H
centerC23×C4C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC22×C4×D4D11
hypocenterC11C4×#392
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D11C2semidirect
3. C2×C4×(C2×D11)⋊C4C2semidirect
4. C2×C4×C22⋊Dic11C2semidirect
5. #13066879C2semidirect
6. #13066859C2semidirect
7. #13066858C2semidirect
8. #13066857C2semidirect
9. #13066855C2semidirect
10. C4×C11⋊#95C2semidirect
11. C22×C4×D4×C11C2semidirect
33. #10622836C4direct (N × H)
49. C22×D4×C11C2×C4semidirect
56. C23×C4×C11D4semidirect
67. C22×C22⋊D11C2×C4semidirect
77. C22×C4×D11D4semidirect
85. C2×C42×C11D4semidirect
94. C2×C22⋊Dic11C2×C4semidirect
104. C2×(C2×D11)⋊C4C2×C4semidirect
112. C2×C4×Dic11D4semidirect
119. C11⋊#95C2×C4semidirect
236. C22×C4×D4D11semidirect
280. C23×C11C4×D4semidirect
314. C22×D11C4×D4semidirect
333. C2×C4×C11C4×D4semidirect
368. C2×Dic11C4×D4semidirect
453. C4×C11#392semidirect
472. C22×D4C4×D11semidirect
489. C23×C4C22⋊D11semidirect
528. C2×C42C22⋊D11semidirect
663. C11C4×#392semidirect
721. C23C4×C22⋊D11semidirect
782. C2×C4C4×C22⋊D11semidirect
845. C4#10622836direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106228362
C2×C4×(C2×D11)⋊C42
C2×C4×C22⋊Dic112
#130668792
#130668592
#130668582
#130668572
#130668552
C4×C11⋊#952
C22×C4×D4×C112
C4×#39211