Finite Group Databasebeta

← #14676107

Subgroups — #14676107

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic
3C2×#10622601C211yesmaximal, characteristic
4C2×#10622277C212yesmaximal, complemented
5#13066864C212yesmaximal, complemented
6#13066864C212yesmaximal, complemented
7#13066845C211yesmaximal, characteristic, complemented
8#13066845C211yesmaximal, characteristic, complemented
9(C2×D11)⋊#95C212yesmaximal, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C2×#66946—24no—
26C2×#66946—24no—
27C2×#66946C418yescomplemented
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38#10622601—24no—
39#10622552—24no—
40#10622277—28no—
41C24×D11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44C2×C414yes—
57C22×D44D414yes—
58C22×D44D414yes—
59C22×C4×D11—24no—
60C22×C4×D11—24no—
61C22×C4×D11—24no—
62C22×C4×D11—24no—
63C22×C4×D11—42no—
64C22×C4×D11—42no—
65C22×C4×D11C2×C418yes—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4C2×C414yes—
72C2×C42×C11—22no—
73C2×C42×C11—22no—
74C2×C42×C11—22no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4—42no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4C2×C418yes—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—22no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—22no—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11C2×C414yes—
99#66946—232no—
100C11×#95—24no—
101C11×#95—42no—
102C11⋊#95—22no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105C11⋊#95—22no—
106C11⋊#95—22no—
107C11⋊#95—42no—
108C11⋊#95—42no—
109C11⋊#95D414yescomplemented
110#13916—111nomaximal, Sylow
111C24×C11C2411yescharacteristic
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11C22×C414yes—
125C23×D11C2×D414yes—
126C23×D11C2×D414yes—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11C22×C414yes—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11#4112yes—
158C22×C4×C11#4112yes—
159C22×C4×C11#4112yes—
160C22×C4×C11#4112yes—
161C22×C4×C11#4112yes—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11C22×C412yes—
192C22×Dic11C22×C412yes—
193C22×Dic11C2×D412yes—
194C22×Dic11C2×D412yes—
195C22×Dic11#4112yes—
196C22×Dic11#4112yes—
197C2×D44—28no—
198C2×D44—28no—
199C2×D44—28no—
200C2×D44—28no—
201C2×D44—28no—
202C2×D44—28no—
203C2×D44C22⋊C4116yes—
204C2×C4×D11—216no—
205C2×C4×D11—216no—
206C2×C4×D11—48no—
207C2×C4×D11—48no—
208C2×C4×D11—48no—
209C2×C4×D11—48no—
210C2×C4×D11—48no—
211C11×C4⋊C4—28no—
212C11×C4⋊C4—44no—
213C42×C11—44no—
214(C2×D11)⋊C4—216no—
215(C2×D11)⋊C4—48no—
216(C2×D11)⋊C4—48no—
217(C2×D11)⋊C4—48no—
218(C2×D11)⋊C4—48no—
219C4⋊Dic11—44no—
220C4×Dic11—28no—
221C4×Dic11—44no—
222C22×C4×D4—111no—
223C2×#390—111no—
224C2×#390—111no—
225C2×#381—112no—
226#1440—112no—
227#1440—112no—
228C4⋊#95—111no—
229C4⋊#95—111no—
230C4⋊#95D1111yescharacteristic, complemented
231C22⋊#95—112no—
232C4×#95—111no—
233C23×C11C23×C411yescharacteristic
234C23×C11C22×D411yescharacteristic
235C23×C11C22×D411yescharacteristic
236C23×C11C22×D411yescharacteristic
237C23×C11C2×#4111yescharacteristic
238C23×C11C2×#4111yescharacteristic
239C23×C11C2×#4111yescharacteristic
240C23×C11C2×#4111yescharacteristic
241C23×C11C2×#4111yescharacteristic
242C23×C11C2×#4111yescharacteristic
243C23×C11C2×#4111yescharacteristic
244C23×C11H(5,𝔽2)11yescharacteristic
245C23×C11H(5,𝔽2)11yescharacteristic
246C23×C11H(5,𝔽2)11yescharacteristic
247C23×C112−1+411yescharacteristic
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—24no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11C2×C22⋊C418yes—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11C2×C22⋊C414yes—
312C2×C4×C11#11714yes—
313C2×C4×C11#11714yes—
314C2×C4×C11#12314yes—
315C2×C4×C11#12314yes—
316C2×C4×C11#12314yes—
317C2×C4×C11#12314yes—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11C4×D414yes—
353D44—232no—
354C4×D11—432no—
355C23×D4—111no—
356C24×C4—112no—
357C2×C4×D4—118no—
358C2×C4×D4—224no—
359C2×C4×D4—224no—
360C22×C4⋊C4—111no—
361C22×C4⋊C4C2×D1111yescharacteristic
362C22×C4⋊C4C2×D1111yescharacteristic
363C22×C22⋊C4—112no—
364C22×C22⋊C4—112no—
365C22×C22⋊C4—112no—
366C22×C22⋊C4—112no—
367C22×C22⋊C4—112no—
368C22×C42—111no—
369C22×C42—111no—
370C22×C42C2×D1111yescharacteristic
371#390—224no—
372#390—224no—
373#381—228no—
374C2×#95—111no—
375C2×#95—111no—
376C2×#95—111no—
377C2×#95—111no—
378C2×#95—112no—
379C2×#95—112no—
380C2×#95—112no—
381C2×#95—112no—
382C2×#95C2×D1112yes—
383C2×#95C2×D1112yes—
384C22×C11C22×C22⋊C411yescharacteristic
385C22×C11C2×#11711yescharacteristic
386C22×C11C2×#11711yescharacteristic
387C22×C11C2×C4×D411yescharacteristic
388C22×C11C4×#4111yescharacteristic
389C22×C11#51811yescharacteristic
390C22×C11#52011yescharacteristic
391C22×C11C2×#12311yescharacteristic
392C22×C11C2×#12311yescharacteristic
393C22×C11C2×#12311yescharacteristic
394C22×C11C2×#12311yescharacteristic
395C22×C11#52911yescharacteristic
396C22×C11#52911yescharacteristic
397C22×C11#53211yescharacteristic
398C22×C11#53211yescharacteristic
399C22×C11#54011yescharacteristic
400C22×C11#54011yescharacteristic
401C22×C11#54211yescharacteristic
402C22×C11#54211yescharacteristic
403C22×C11D4211yescharacteristic
404C22×C11D4211yescharacteristic
405C22×C11#54611yescharacteristic
406C22×C11#54611yescharacteristic
407C22×C11#54611yescharacteristic
408C22×C11#54611yescharacteristic
409C22×C11#54711yescharacteristic
410C22×C11#54711yescharacteristic
411C22×C11#54711yescharacteristic
412C22×C11#55011yescharacteristic
413C22×C11#55311yescharacteristic
414C22×C11#55311yescharacteristic
415C22×C11#55511yescharacteristic
416C22×C11#55611yescharacteristic
417C22×C11#55911yescharacteristic
418C22×C11#55911yescharacteristic
419C2×D11—28no—
420C2×D11—28no—
421C2×D11—28no—
422C2×D11—44no—
423C2×D11—44no—
424C2×D11—44no—
425C2×D11—44no—
426C2×D11—44no—
427C2×D11—44no—
428C2×D11—44no—
429C2×D11—44no—
430C2×D11—44no—
431C2×D11—44no—
432C2×D11—44no—
433C2×D11—44no—
434C4×C11—44no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—82no—
438C4×C11#38118yescomplemented
439Dic11—24no—
440Dic11—42no—
441Dic11—42no—
442Dic11—42no—
443Dic11—82no—
444C25—112no—
445C22×D4—114no—
446C22×D4—114no—
447C22×D4—114no—
448C22×D4—222no—
449C22×D4—222no—
450C22×D4—222no—
451C22×D4—222no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—118no—
457C23×C4—112no—
458C23×C4—224no—
459C23×C4—224no—
460C23×C4—224no—
461C23×C4—224no—
462C23×C4—442no—
463C23×C4—442no—
464C23×C4C22×D1112yes—
465C23×C4C22×D1112yes—
466C23×C4C22×D1111yescharacteristic
467C23×C4C22×D1111yescharacteristic
468C23×C4C22×D1111yescharacteristic
469C4×D4—2232no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—222no—
476C2×C4⋊C4—222no—
477C2×C4⋊C4—222no—
478C2×C4⋊C4C4×D1114yes—
479C2×C22⋊C4—118no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—224no—
482C2×C22⋊C4—224no—
483C2×C22⋊C4—224no—
484C2×C22⋊C4—224no—
485C2×C22⋊C4—224no—
486C2×C22⋊C4—224no—
487C2×C22⋊C4—224no—
488C2×C22⋊C4—224no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—442no—
491C2×C22⋊C4—442no—
492C2×C22⋊C4—442no—
493C2×C22⋊C4—442no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—114no—
498C2×C42—222no—
499C2×C42—222no—
500C2×C42—222no—
501C2×C42—222no—
502C2×C42—222no—
503#95—24no—
504#95—42no—
505#95—114no—
506#95—222no—
507#95—222no—
508#95—224no—
509#95—224no—
510#95—222no—
511#95—442no—
512#95—442no—
513C2×C11C2×#38111yescharacteristic
514C2×C11#229311yescharacteristic
515C2×C11#231911yescharacteristic
516C2×C11D4×C22⋊C411yescharacteristic
517C2×C11#233911yescharacteristic
518C2×C11#235411yescharacteristic
519C2×C11#235711yescharacteristic
520C2×C11#242011yescharacteristic
521C2×C11#242011yescharacteristic
522C2×C11#242211yescharacteristic
523C2×C11#242211yescharacteristic
524C2×C11#244511yescharacteristic
525C2×C11#244511yescharacteristic
526C2×C11#244711yescharacteristic
527C2×C11#244711yescharacteristic
528D11—48no—
529C24—114no—
530C24—114no—
531C24—114no—
532C24—222no—
533C24—222no—
534C24—222no—
535C24—222no—
536C24—222no—
537C24—222no—
538C24—222no—
539C24—222no—
540C24—222no—
541C24—222no—
542C24—222no—
543C24—222no—
544C24C23×D1111yescharacteristic
545C2×D4—1116no—
546C2×D4—228no—
547C2×D4—228no—
548C2×D4—228no—
549C2×D4—228no—
550C2×D4—228no—
551C2×D4—228no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—112no—
578C22×C4—112no—
579C22×C4—112no—
580C22×C4—112no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—2216no—
584C22×C4—2216no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—448no—
615C22×C4—448no—
616C22×C4—448no—
617C22×C4—448no—
618C22×C4—448no—
619C22×C4C2×C4×D1114yes—
620C22×C4C2×C4×D1112yes—
621C22×C4#433912yes—
622C22×C4#433912yes—
623C22×C4D4×D1112yes—
624C22×C4D4×D1112yes—
625C22×C4D4×D1112yes—
626C22×C4#434112yes—
627C22×C4#434312yes—
628C22×C4#434312yes—
629C4⋊C4—28no—
630C4⋊C4—44no—
631C4⋊C4—444no—
632C22⋊C4—2216no—
633C22⋊C4—448no—
634C22⋊C4—448no—
635C22⋊C4—448no—
636C22⋊C4—448no—
637C42—44no—
638C42—228no—
639C42—444no—
640C11#1391611yescharacteristic, complemented, Sylow
641C23—118no—
642C23—224no—
643C23—224no—
644C23—224no—
645C23—224no—
646C23—224no—
647C23—224no—
648C23—224no—
649C23—224no—
650C23—224no—
651C23—224no—
652C23—224no—
653C23—224no—
654C23—224no—
655C23—224no—
656C23—224no—
657C23—224no—
658C23—224no—
659C23—224no—
660C23—442no—
661C23—442no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23—442no—
669C23—442no—
670C23—442no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23—442no—
676C23C22×C4×D1111yescharacteristic
677C23C2×#433911yescharacteristic
678C23C2×#433911yescharacteristic
679C23C2×D4×D1111yescharacteristic
680C23C2×D4×D1111yescharacteristic
681C23C2×D4×D1111yescharacteristic
682C23C2×#434111yescharacteristic
683C23#6703711yescharacteristic
684C23C2×#434311yescharacteristic
685C23C2×#434311yescharacteristic
686C23#6704011yescharacteristic
687C23#41×D1111yescharacteristic
688C23#41×D1111yescharacteristic
689C23#6704211yescharacteristic
690C23#6704211yescharacteristic
691D4—2232no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—114no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—4432no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—441no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—442no—
750C2×C4—442no—
751C2×C4—442no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4#6692514yes—
757C2×C4C22⋊C4×D1114yes—
758C2×C4#6693614yes—
759C2×C4#6693614yes—
760C2×C4#6694514yes—
761C2×C4#6694714yes—
762C2×C4#6694714yes—
763C22—228no—
764C22—228no—
765C22—228no—
766C22—444no—
767C22—444no—
768C22—444no—
769C22—444no—
770C22—444no—
771C22—444no—
772C22—444no—
773C22—444no—
774C22—444no—
775C22—444no—
776C22—444no—
777C22—444no—
778C22C2×#6692511yescharacteristic
779C22C2×C22⋊C4×D1111yescharacteristic
780C22C2×#6693611yescharacteristic
781C22C2×#6693611yescharacteristic
782C22C2×#6694511yescharacteristic
783C22C2×#6694711yescharacteristic
784C22C2×#6694711yescharacteristic
785C22#1062303811yescharacteristic
786C22#1062304511yescharacteristic
787C22#1062306111yescharacteristic
788C22#1062306311yescharacteristic
789C22C4×D4×D1111yescharacteristic
790C22#1062307611yescharacteristic
791C22#1062308411yescharacteristic
792C22#1062309011yescharacteristic
793C22#1062309911yescharacteristic
794C22C4×#434311yescharacteristic
795C22#1062310511yescharacteristic
796C22#1062311611yescharacteristic
797C22#1062312711yescharacteristic
798C22#1062314011yescharacteristic
799C22#1062314311yescharacteristic
800C22#1062315011yescharacteristic
801C22#1062315511yescharacteristic
802C22#1062316111yescharacteristic
803C22#1062316211yescharacteristic
804C22#1062317411yescharacteristic
805C22#1062320711yescharacteristic
806C22#1062320711yescharacteristic
807C22#1062322211yescharacteristic
808C22#1062322911yescharacteristic
809C22#1062324811yescharacteristic
810C22#1062325611yescharacteristic
811C22#1062325711yescharacteristic
812C22#1062326411yescharacteristic
813C4—42no—
814C4—44no—
815C4—42no—
816C4—82no—
817C4—224no—
818C4—442no—
819C4—442no—
820C4—442no—
821C4—882no—
822C4#1062227718yescomplemented
823C2—448no—
824C2C2×#1062227711yescharacteristic
825C2#1307107411yescharacteristic
826C2#1307125511yescharacteristic
827C2#1307143711yescharacteristic
828C2#1307144511yescharacteristic
829C2#1307156111yescharacteristic
830C2#1307158511yescharacteristic
831C2#1307211011yescharacteristic
832C2#1307211111yescharacteristic
833C2#1307213211yescharacteristic
834C2#1307213311yescharacteristic
835C2#1307238311yescharacteristic
836C2#1307238411yescharacteristic
837C2#1307240511yescharacteristic
838C2#1307240611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#13916
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#10622277C2semidirect
5. #13066864C2semidirect
6. #13066864C2semidirect
7. #13066845C2semidirect
8. #13066845C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. C4×C11⋊#95C2semidirect
11. C11×C4⋊#95C2semidirect
27. C2×#66946C4semidirect
109. C11⋊#95D4semidirect
230. C4⋊#95D11semidirect
438. C4×C11#381semidirect
640. C11#13916semidirect
822. C4#10622277semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
C2×#106225522
C2×#106226012
C2×#106222772
#130668642
#130668452
(C2×D11)⋊#952
C4×C11⋊#952
C11×C4⋊#952
#1391611