Finite Group Databasebeta

← #14677092

Subgroups — #14677092

Order 2816.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622570C211yesmaximal, characteristic
2C2×#10622283C211yesmaximal, characteristic, complemented
3C2×#10622553C211yesmaximal, characteristic, complemented
4C2×#10622557C211yesmaximal, characteristic, complemented
5C2×#10622826C211yesmaximal, characteristic
6C2×#10622825C211yesmaximal, characteristic, complemented
7#13066880C211yesmaximal, characteristic, complemented
8#13066863C211yesmaximal, characteristic, complemented
9#13066862C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic
11#13066854C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13#13066849C211yesmaximal, characteristic, complemented
14C4×C11⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C4×C11×C22⋊C4—24no—
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40#10622826C418yescomplemented
41#10622825—24no—
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622570—24no—
55#10622557—24no—
56#10622553—24no—
57#10622283—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—41no—
65C23×C4×C11—41no—
66C23×C4×C11C2×C414yes—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—41no—
78C22×C22⋊D11—41no—
79C22×C22⋊D11C2×C414yes—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4D414yes—
93C2×C42×C11—22no—
94C2×C42×C11—22no—
95C2×C42×C11—22no—
96C2×C42×C11—22no—
97C2×C42×C11—41no—
98C2×C42×C11—41no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—41no—
106C2×C22⋊Dic11—41no—
107C2×C22⋊Dic11C2×C414yes—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4—41no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4C2×C414yes—
125C2×(C2×D11)⋊C4C2×C414yes—
126C2×C4⋊Dic11—22no—
127C2×C4⋊Dic11—22no—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11—22no—
130C2×C4⋊Dic11—41no—
131C2×C4⋊Dic11—41no—
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—41no—
137C2×Dic11⋊C4—41no—
138C2×C4×Dic11—22no—
139C2×C4×Dic11—22no—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—22no—
143C2×C4×Dic11—41no—
144C11×#95—22no—
145C11×#95D414yescomplemented
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—41no—
155C11⋊#95C2×C414yes—
156C11⋊#95C2×C414yes—
157C11⋊#95D414yescomplemented
158#14012—111nomaximal, Sylow
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11C22×C412yes—
172C24×C11C2×D412yes—
173C24×C11#4112yes—
174C24×C11C2411yescharacteristic
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11C22×C412yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—28no—
221C22×C4×C11—28no—
222C22×C4×C11—44no—
223C22×C4×C11—44no—
224C22×C4×C11—44no—
225C22×C4×C11—44no—
226C22×C4×C11—44no—
227C22×C4×C11C22×C412yes—
228C22×C4×C11C22×C412yes—
229C22×C4×C11C2×D412yes—
230C22×C4×C11C2×D412yes—
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11#4112yes—
236C22×C4×C11#4112yes—
237C22×C4×C11#4112yes—
238C22×C4×C11#4112yes—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11C22×C412yes—
289C22×Dic11C22×C412yes—
290C22×Dic11C22×C412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11#4112yes—
294C22×Dic11#4112yes—
295C11×C22⋊C4—28no—
296C11×C22⋊C4—28no—
297C42×C11—44no—
298C42×C11—44no—
299C22⋊Dic11—28no—
300C22⋊Dic11—44no—
301C22⋊Dic11—44no—
302(C2×D11)⋊C4—28no—
303(C2×D11)⋊C4—28no—
304(C2×D11)⋊C4—44no—
305(C2×D11)⋊C4—44no—
306(C2×D11)⋊C4—44no—
307(C2×D11)⋊C4—44no—
308C4⋊Dic11—44no—
309C4⋊Dic11—44no—
310Dic11⋊C4—44no—
311Dic11⋊C4—44no—
312C4×Dic11—44no—
313C4×Dic11—44no—
314C2×#390—111no—
315C2×#388—111no—
316C2×#388—111no—
317C2×#388—111no—
318C2×#386—111no—
319C2×#380—111no—
320C2×C4×C22⋊C4D1111yescharacteristic, complemented
321#1444—111no—
322#1440—111no—
323#1439—111no—
324#1438—111no—
325#1437—111no—
326#1436—111no—
327#1436—111no—
328C4×#95—111no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11C4×D414yes—
364C23×C11C23×C411yescharacteristic
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C23×C11C2×#4111yescharacteristic
369C23×C11C2×#4111yescharacteristic
370C23×C11C2×#4111yescharacteristic
371C23×C11C2×#4111yescharacteristic
372C23×C11C2×#4111yescharacteristic
373C23×C11C2×#4111yescharacteristic
374C23×C11C2×#4111yescharacteristic
375C23×C11H(5,𝔽2)11yescharacteristic
376C23×C11H(5,𝔽2)11yescharacteristic
377C23×C11H(5,𝔽2)11yescharacteristic
378C23×C112−1+411yescharacteristic
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—416no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11C4×D414yes—
455C2×C4×C11C4×D414yes—
456C2×C4×C11#12114yes—
457C22⋊D11—416no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11#11714yes—
507C23×D4—111no—
508C24×C4C2×D1111yescharacteristic
509C22×C4⋊C4—111no—
510C22×C4⋊C4—111no—
511C22×C4⋊C4—111no—
512C22×C4⋊C4—111no—
513C22×C22⋊C4—111no—
514C22×C22⋊C4—111no—
515C22×C22⋊C4—111no—
516C22×C22⋊C4—111no—
517C22×C22⋊C4—111no—
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4C2×D1111yescharacteristic
523C22×C22⋊C4C2×D1111yescharacteristic
524C22×C42—111no—
525C22×C42—111no—
526C22×C42C2×D1111yescharacteristic
527C22×C42C2×D1111yescharacteristic
528#390—224no—
529#388—224no—
530#388—224no—
531#388—224no—
532#386—118no—
533#380—224no—
534C4×C22⋊C4—24no—
535C2×#95—111no—
536C2×#95—111no—
537C2×#95—111no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95—111no—
547C2×#95C2×D1111yescharacteristic
548C2×#95C2×D1111yescharacteristic
549C22×C11—24no—
550C22×C11—24no—
551C22×C11—24no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11C2×#11711yescharacteristic
565C22×C11C2×C4×D411yescharacteristic
566C22×C11C2×C4×D411yescharacteristic
567C22×C11C2×C4×D411yescharacteristic
568C22×C11C4×#4111yescharacteristic
569C22×C11#51811yescharacteristic
570C22×C11#52011yescharacteristic
571C22×C11C2×#12111yescharacteristic
572C22×C11#52511yescharacteristic
573C22×C11#52911yescharacteristic
574C22×C11#52911yescharacteristic
575C22×C11#52911yescharacteristic
576C22×C11#53211yescharacteristic
577C22×C11#53211yescharacteristic
578C22×C11#53211yescharacteristic
579C22×C11#53811yescharacteristic
580C22×C11#53911yescharacteristic
581C22×C11#54011yescharacteristic
582C22×C11#54211yescharacteristic
583C22×C11D4211yescharacteristic
584C22×C11D4211yescharacteristic
585C22×C11#54611yescharacteristic
586C22×C11#54611yescharacteristic
587C22×C11#54611yescharacteristic
588C22×C11#54611yescharacteristic
589C22×C11#54711yescharacteristic
590C22×C11#54711yescharacteristic
591C22×C11#54811yescharacteristic
592C22×C11#55011yescharacteristic
593C22×C11#55111yescharacteristic
594C22×C11#55111yescharacteristic
595C22×C11#55111yescharacteristic
596C22×C11#55311yescharacteristic
597C22×C11#55511yescharacteristic
598C22×C11#55611yescharacteristic
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C2×D11—42no—
606C2×D11—81no—
607C2×D11—81no—
608C2×D11—81no—
609C2×D11—81no—
610C2×D11—81no—
611C2×D11—81no—
612C2×D11—81no—
613C2×D11—81no—
614C4×C11—24no—
615C4×C11—24no—
616C4×C11—24no—
617C4×C11—42no—
618C4×C11—42no—
619C4×C11—42no—
620Dic11—24no—
621Dic11—42no—
622Dic11—42no—
623Dic11—42no—
624Dic11—42no—
625Dic11—81no—
626Dic11—81no—
627C25—111no—
628C25C22×D1111yescharacteristic
629C22×D4—114no—
630C22×D4—222no—
631C22×D4—222no—
632C22×D4—222no—
633C22×D4—222no—
634C22×D4—441no—
635C22×D4—441no—
636C23×C4—22no—
637C23×C4—22no—
638C23×C4—22no—
639C23×C4—22no—
640C23×C4—41no—
641C23×C4—41no—
642C23×C4—111no—
643C23×C4—111no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—111no—
647C23×C4—111no—
648C23×C4—111no—
649C23×C4C4×D1114yes—
650C23×C4C22×D1111yescharacteristic
651C23×C4C22×D1111yescharacteristic
652C23×C4C22×D1111yescharacteristic
653C23×C4C22×D1111yescharacteristic
654C23×C4C22×D1111yescharacteristic
655C23×C4C22×D1111yescharacteristic
656C2×C4⋊C4—222no—
657C2×C4⋊C4—222no—
658C2×C4⋊C4—222no—
659C2×C4⋊C4—222no—
660C2×C4⋊C4—222no—
661C2×C4⋊C4—222no—
662C2×C4⋊C4—222no—
663C2×C4⋊C4—222no—
664C2×C4⋊C4—441no—
665C2×C4⋊C4—441no—
666C2×C4⋊C4—441no—
667C2×C4⋊C4—441no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—114no—
674C2×C22⋊C4—114no—
675C2×C22⋊C4—114no—
676C2×C22⋊C4—222no—
677C2×C22⋊C4—222no—
678C2×C22⋊C4—222no—
679C2×C22⋊C4—222no—
680C2×C22⋊C4—222no—
681C2×C22⋊C4—222no—
682C2×C22⋊C4—222no—
683C2×C22⋊C4—222no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4—222no—
687C2×C22⋊C4—222no—
688C2×C22⋊C4—222no—
689C2×C22⋊C4—222no—
690C2×C22⋊C4—222no—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—441no—
695C2×C22⋊C4—441no—
696C2×C22⋊C4—441no—
697C2×C22⋊C4—441no—
698C2×C22⋊C4—441no—
699C2×C22⋊C4—441no—
700C2×C22⋊C4D4414yes—
701C2×C42—22no—
702C2×C42—22no—
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—41no—
706C2×C42—41no—
707C2×C42—222no—
708C2×C42—222no—
709C2×C42—222no—
710C2×C42—222no—
711C2×C42—222no—
712C2×C42—441no—
713#95—22no—
714#95—114no—
715#95—114no—
716#95—114no—
717#95—222no—
718#95—222no—
719#95—222no—
720#95—222no—
721#95—222no—
722#95—222no—
723#95—222no—
724#95—222no—
725#95—441no—
726#95C22⋊D1114yescomplemented
727C2×C11—44no—
728C2×C11#229311yescharacteristic
729C2×C11C4×#12111yescharacteristic
730C2×C11#233511yescharacteristic
731C2×C11#234211yescharacteristic
732C2×C11#235411yescharacteristic
733C2×C11#235811yescharacteristic
734C2×C11#236111yescharacteristic
735C2×C11#242511yescharacteristic
736C2×C11#242811yescharacteristic
737C2×C11#246111yescharacteristic
738C2×C11#246711yescharacteristic
739C2×C11#252111yescharacteristic
740C2×C11#253111yescharacteristic
741C2×C11#255511yescharacteristic
742C2×C11#256011yescharacteristic
743D11—82no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—112no—
757C24—221no—
758C24—221no—
759C24—221no—
760C24—221no—
761C24—221no—
762C24—221no—
763C24—221no—
764C24—221no—
765C24—221no—
766C24—221no—
767C24—221no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24C2×C4×D1112yes—
772C24C2×D4412yes—
773C24#433912yes—
774C24C23×D1111yescharacteristic
775C2×D4—228no—
776C2×D4—228no—
777C2×D4—444no—
778C2×D4—444no—
779C2×D4—444no—
780C2×D4—444no—
781C2×D4—444no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—112no—
820C22×C4—112no—
821C22×C4—112no—
822C22×C4—112no—
823C22×C4—112no—
824C22×C4—112no—
825C22×C4—112no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4C2×C4×D1112yes—
869C22×C4C2×C4×D1112yes—
870C22×C4C2×D4412yes—
871C22×C4C2×D4412yes—
872C22×C4#433912yes—
873C22×C4#433912yes—
874C22×C4#433912yes—
875C22×C4D4×D1112yes—
876C22×C4#434112yes—
877C22×C4C2×C22⋊D1112yes—
878C22×C4C2×C22⋊D1112yes—
879C22×C4C2×C22⋊D1112yes—
880C4⋊C4—444no—
881C4⋊C4—444no—
882C4⋊C4—444no—
883C4⋊C4—444no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—228no—
887C22⋊C4—228no—
888C22⋊C4—228no—
889C22⋊C4—444no—
890C22⋊C4—444no—
891C22⋊C4—444no—
892C22⋊C4—444no—
893C22⋊C4—444no—
894C22⋊C4—444no—
895C42—44no—
896C42—44no—
897C42—444no—
898C42—444no—
899C11#1401211yescharacteristic, complemented, Sylow
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—441no—
942C23—441no—
943C23—441no—
944C23—441no—
945C23—441no—
946C23—441no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23—441no—
955C23—441no—
956C23—441no—
957C23—441no—
958C23—441no—
959C23—441no—
960C23—441no—
961C23—441no—
962C23—441no—
963C23—441no—
964C23—441no—
965C23—441no—
966C23—441no—
967C23—441no—
968C23—441no—
969C23C4×D4414yes—
970C23C22×C4×D1111yescharacteristic
971C23C22×D4411yescharacteristic
972C23C2×#433911yescharacteristic
973C23C2×#433911yescharacteristic
974C23C2×#433911yescharacteristic
975C23C2×#433911yescharacteristic
976C23C2×D4×D1111yescharacteristic
977C23C2×#434111yescharacteristic
978C23#6703711yescharacteristic
979C23#6703711yescharacteristic
980C23#41×D1111yescharacteristic
981C23#41×D1111yescharacteristic
982C23#6704211yescharacteristic
983C23#6704311yescharacteristic
984C23C22×C22⋊D1111yescharacteristic
985D4—4416no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—416no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—114no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—222no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—222no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4—441no—
1061C2×C4—441no—
1062C2×C4—441no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4(C22⋊D11)⋊C414yes—
1076C2×C4C4×C22⋊D1114yes—
1077C2×C4#6698314yes—
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—442no—
1094C22—442no—
1095C22—442no—
1096C22—442no—
1097C22—442no—
1098C22—442no—
1099C22—442no—
1100C22—881no—
1101C22—881no—
1102C22—881no—
1103C22—881no—
1104C22—881no—
1105C22—881no—
1106C22—881no—
1107C22—881no—
1108C22C2×C4×D4411yescharacteristic
1109C22C4×#433911yescharacteristic
1110C22#1062300811yescharacteristic
1111C22#1062301011yescharacteristic
1112C22C2×(C22⋊D11)⋊C411yescharacteristic
1113C22#1062301711yescharacteristic
1114C22#1062302111yescharacteristic
1115C22#1062302611yescharacteristic
1116C22D11×#11711yescharacteristic
1117C22#1062305411yescharacteristic
1118C22#1062306311yescharacteristic
1119C22#1062306411yescharacteristic
1120C22#1062306911yescharacteristic
1121C22#1062306911yescharacteristic
1122C22#1062307911yescharacteristic
1123C22#1062307911yescharacteristic
1124C22D4×D4411yescharacteristic
1125C22#1062308311yescharacteristic
1126C22#1062308511yescharacteristic
1127C22#1062308511yescharacteristic
1128C22#1062308611yescharacteristic
1129C22#1062308711yescharacteristic
1130C22#1062308711yescharacteristic
1131C22#1062309111yescharacteristic
1132C22#1062309211yescharacteristic
1133C22#1062309311yescharacteristic
1134C22#1062309511yescharacteristic
1135C22#1062309611yescharacteristic
1136C22C2×C4×C22⋊D1111yescharacteristic
1137C22C2×#6698311yescharacteristic
1138C22#1062332211yescharacteristic
1139C22D4×C22⋊D1111yescharacteristic
1140C22#1062333711yescharacteristic
1141C22#1062335511yescharacteristic
1142C22#1062336511yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—24no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—224no—
1150C4—442no—
1151C4—442no—
1152C4—442no—
1153C4—442no—
1154C4—881no—
1155C4—881no—
1156C2—44no—
1157C2—882no—
1158C2#1307107911yescharacteristic
1159C2C4×#6698311yescharacteristic
1160C2#1307140611yescharacteristic
1161C2#1307146811yescharacteristic
1162C2#1307156611yescharacteristic
1163C2#1307159511yescharacteristic
1164C2#1307163011yescharacteristic
1165C2#1307216111yescharacteristic
1166C2#1307219811yescharacteristic
1167C2#1307257711yescharacteristic
1168C2#1307266111yescharacteristic
1169C2#1307331911yescharacteristic
1170C2#1307346311yescharacteristic
1171C2#1307368511yescharacteristic
1172C2#1307376011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#14012
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622283C2semidirect
3. C2×#10622553C2semidirect
4. C2×#10622557C2semidirect
6. C2×#10622825C2semidirect
7. #13066880C2semidirect
8. #13066863C2semidirect
9. #13066862C2semidirect
11. #13066854C2semidirect
12. #13066850C2semidirect
13. #13066849C2semidirect
14. C4×C11⋊#95C2semidirect
15. C2×C4×C11×C22⋊C4C2semidirect
40. #10622826C4semidirect
145. C11×#95D4semidirect
157. C11⋊#95D4semidirect
320. C2×C4×C22⋊C4D11semidirect
726. #95C22⋊D11semidirect
899. C11#14012semidirect

Maximal subgroups

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

subgroupindex
C2×#106225702
C2×#106222832
C2×#106225532
C2×#106225572
C2×#106228262
C2×#106228252
#130668802
#130668632
#130668622
#130668552
#130668542
#130668502
#130668492
C4×C11⋊#952
C2×C4×C11×C22⋊C42
#1401211