Finite Group Databasebeta

← #14684532

Subgroups — #14684532

Order 2816.

1586 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622285C211yesmaximal, characteristic
2C2×#10622283C211yesmaximal, characteristic, complemented
3C2×#10622603C211yesmaximal, characteristic, complemented
4#13066873C211yesmaximal, characteristic, complemented
5#13066867C211yesmaximal, characteristic, complemented
6#13066862C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic, complemented
11#13066858C211yesmaximal, characteristic, complemented
12#13066856C211yesmaximal, characteristic
13#13066856C211yesmaximal, characteristic
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C11×#1442C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
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
51#10622603—24no—
52#10622285C418yescomplemented
53#10622283—24no—
54C24×D11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×D44—41no—
70C22×D44—41no—
71C22×D44—41no—
72C22×D44—41no—
73C22×D44—41no—
74C22×D44—41no—
75C22×D44C2×C414yes—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—41no—
78C2×C11×C4⋊C4—41no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—41no—
88C2×(C2×D11)⋊C4—41no—
89C2×(C2×D11)⋊C4—41no—
90C2×(C2×D11)⋊C4—41no—
91C2×(C2×D11)⋊C4—41no—
92C2×(C2×D11)⋊C4—41no—
93C2×(C2×D11)⋊C4—41no—
94C2×(C2×D11)⋊C4—41no—
95C2×(C2×D11)⋊C4—41no—
96C2×(C2×D11)⋊C4—41no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4—41no—
99C2×(C2×D11)⋊C4—41no—
100C2×(C2×D11)⋊C4—41no—
101C2×(C2×D11)⋊C4—41no—
102C2×(C2×D11)⋊C4—41no—
103C2×(C2×D11)⋊C4—41no—
104C2×(C2×D11)⋊C4—41no—
105C2×(C2×D11)⋊C4—41no—
106C2×(C2×D11)⋊C4—41no—
107C2×(C2×D11)⋊C4—41no—
108C2×(C2×D11)⋊C4—41no—
109C2×(C2×D11)⋊C4—41no—
110C2×(C2×D11)⋊C4—41no—
111C2×(C2×D11)⋊C4C2×C414yes—
112C2×(C2×D11)⋊C4C2×C414yes—
113C2×(C2×D11)⋊C4C2×C414yes—
114C2×(C2×D11)⋊C4C2×C414yes—
115C2×C4⋊Dic11—22no—
116C2×C4⋊Dic11—41no—
117C2×C4⋊Dic11—41no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—41no—
120C2×Dic11⋊C4—41no—
121C2×Dic11⋊C4—41no—
122C2×Dic11⋊C4—41no—
123C2×Dic11⋊C4—41no—
124C2×Dic11⋊C4—41no—
125C2×Dic11⋊C4—41no—
126C2×Dic11⋊C4C2×C414yes—
127C2×C4×Dic11—41no—
128C2×C4×Dic11—41no—
129C2×C4×Dic11D414yescomplemented
130C11×#95—22no—
131C11×#95—41no—
132C11×#95—41no—
133C11×#95—41no—
134C11×#95—41no—
135C11×#95C2×C414yes—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146#14632—111nomaximal, Sylow
147C24×C11C2411yescharacteristic
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11C22×C412yes—
177C23×D11C22×C412yes—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
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—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11C22×C412yes—
224C22×C4×C11C22×C412yes—
225C22×C4×C11C22×C412yes—
226C22×C4×C11C2×D412yes—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
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×Dic11C22×C412yes—
265C22×Dic11C22×C412yes—
266C22×Dic11C2×D412yes—
267C22×Dic11C2×D412yes—
268C22×Dic11#4112yes—
269C2×D44—44no—
270C2×D44—44no—
271C2×D44—44no—
272C2×D44—44no—
273C2×D44—44no—
274C2×D44—44no—
275C2×D44—44no—
276C11×C4⋊C4—44no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—44no—
280(C2×D11)⋊C4—44no—
281(C2×D11)⋊C4—44no—
282(C2×D11)⋊C4—44no—
283(C2×D11)⋊C4—44no—
284(C2×D11)⋊C4—44no—
285(C2×D11)⋊C4—44no—
286(C2×D11)⋊C4—44no—
287(C2×D11)⋊C4—44no—
288(C2×D11)⋊C4—44no—
289C4⋊Dic11—44no—
290Dic11⋊C4—44no—
291Dic11⋊C4—44no—
292Dic11⋊C4—44no—
293C4×Dic11—44no—
294C2×#394—111no—
295C2×#388—111no—
296C2×#388—111no—
297#1442—111no—
298#1442D1111yescharacteristic, complemented
299#1441—111no—
300#1439—111no—
301#1439—111no—
302#1439—111no—
303#1439—111no—
304#1439—111no—
305#1439—111no—
306#1438—111no—
307#1438—111no—
308C4⋊#95—111no—
309C23×C11C23×C411yescharacteristic
310C23×C11C22×D411yescharacteristic
311C23×C11C2×#4111yescharacteristic
312C23×C11H(5,𝔽2)11yescharacteristic
313C23×C11H(5,𝔽2)11yescharacteristic
314C23×C11H(5,𝔽2)11yescharacteristic
315C23×C11H(5,𝔽2)11yescharacteristic
316C23×C11H(5,𝔽2)11yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C11H(5,𝔽2)11yescharacteristic
319C23×C11H(5,𝔽2)11yescharacteristic
320C23×C11H(5,𝔽2)11yescharacteristic
321C23×C112−1+411yescharacteristic
322C23×C112−1+411yescharacteristic
323C23×C112−1+411yescharacteristic
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—41no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11—41no—
355C22×D11—41no—
356C22×D11—41no—
357C22×D11—41no—
358C22×D11—41no—
359C22×D11—41no—
360C22×D11—41no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—41no—
367C22×D11—41no—
368C22×D11—41no—
369C22×D11—41no—
370C22×D11—41no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—41no—
375C22×D11—41no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11—41no—
462C2×Dic11—41no—
463C2×Dic11—41no—
464C2×Dic11—41no—
465C2×Dic11—41no—
466C2×Dic11—41no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
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×Dic11C4×D414yes—
485D44—416no—
486C23×D4—111no—
487C22×C4⋊C4—111no—
488C22×C4⋊C4—111no—
489C22×C4⋊C4—111no—
490C22×C4⋊C4—111no—
491C22×C4⋊C4C2×D1111yescharacteristic
492C22×C22⋊C4—111no—
493C22×C22⋊C4—111no—
494C22×C22⋊C4—111no—
495C22×C22⋊C4—111no—
496C22×C22⋊C4—111no—
497C22×C22⋊C4—111no—
498C22×C22⋊C4—111no—
499C22×C22⋊C4—111no—
500C22×C22⋊C4—111no—
501C22×C22⋊C4—111no—
502C22×C22⋊C4—111no—
503C22×C22⋊C4—111no—
504C22×C42—111no—
505#394—118no—
506#388—224no—
507#388—224no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
511C2×#95—111no—
512C2×#95—111no—
513C2×#95—111no—
514C2×#95—111no—
515C2×#95—111no—
516C2×#95—111no—
517C2×#95—111no—
518C2×#95C2×D1111yescharacteristic
519C2×#95C2×D1111yescharacteristic
520C2×#95C2×D1111yescharacteristic
521C2×#95C2×D1111yescharacteristic
522C2×#95C2×D1111yescharacteristic
523C2×#95C2×D1111yescharacteristic
524C22×C11C2×C4×D411yescharacteristic
525C22×C11#51811yescharacteristic
526C22×C11#51811yescharacteristic
527C22×C11#51811yescharacteristic
528C22×C11#52011yescharacteristic
529C22×C11#52011yescharacteristic
530C22×C11#52011yescharacteristic
531C22×C11#53411yescharacteristic
532C22×C11#53511yescharacteristic
533C22×C11#53511yescharacteristic
534C22×C11#53711yescharacteristic
535C22×C11#53711yescharacteristic
536C22×C11#53711yescharacteristic
537C22×C11#53811yescharacteristic
538C22×C11#53911yescharacteristic
539C22×C11#54011yescharacteristic
540C22×C11#54011yescharacteristic
541C22×C11#54211yescharacteristic
542C22×C11#54211yescharacteristic
543C22×C11#56011yescharacteristic
544C22×C11#56011yescharacteristic
545C22×C11#56011yescharacteristic
546C22×C11#56011yescharacteristic
547C22×C11#56011yescharacteristic
548C22×C11H(3,𝔽4)11yescharacteristic
549C22×C11H(3,𝔽4)11yescharacteristic
550C22×C11#56211yescharacteristic
551C22×C11#56211yescharacteristic
552C22×C11#56211yescharacteristic
553C22×C11#56211yescharacteristic
554C22×C11#56211yescharacteristic
555C22×C11#56211yescharacteristic
556C22×C11#56311yescharacteristic
557C22×C11#56311yescharacteristic
558C22×C11#56311yescharacteristic
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—42no—
562C2×D11—42no—
563C2×D11—42no—
564C2×D11—42no—
565C2×D11—42no—
566C2×D11—42no—
567C2×D11—42no—
568C2×D11—42no—
569C2×D11—42no—
570C2×D11—42no—
571C2×D11—42no—
572C2×D11—42no—
573C2×D11—81no—
574C2×D11—81no—
575C2×D11—81no—
576C2×D11—81no—
577C2×D11—81no—
578C2×D11—81no—
579C2×D11—81no—
580C2×D11—81no—
581C2×D11—81no—
582C2×D11—81no—
583C2×D11—81no—
584C2×D11—81no—
585C2×D11—81no—
586C2×D11—81no—
587C2×D11—81no—
588C2×D11—81no—
589C4×C11—42no—
590C4×C11—42no—
591C4×C11—42no—
592C4×C11—42no—
593C4×C11—81no—
594C4×C11—81no—
595C4×C11—81no—
596Dic11—24no—
597Dic11—42no—
598Dic11—42no—
599Dic11—81no—
600Dic11—81no—
601Dic11—81no—
602C25—111no—
603C25—111no—
604C22×D4—114no—
605C22×D4—441no—
606C22×D4—441no—
607C22×D4—441no—
608C22×D4—441no—
609C22×D4—441no—
610C22×D4—441no—
611C23×C4—111no—
612C23×C4—111no—
613C23×C4—111no—
614C23×C4—111no—
615C23×C4—111no—
616C23×C4—111no—
617C23×C4C22×D1111yescharacteristic
618C23×C4C22×D1111yescharacteristic
619C23×C4C22×D1111yescharacteristic
620C23×C4C22×D1111yescharacteristic
621C23×C4C22×D1111yescharacteristic
622C23×C4C22×D1111yescharacteristic
623C23×C4C22×D1111yescharacteristic
624C2×C4⋊C4—22no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—114no—
628C2×C4⋊C4—222no—
629C2×C4⋊C4—222no—
630C2×C4⋊C4—441no—
631C2×C4⋊C4—441no—
632C2×C4⋊C4—441no—
633C2×C4⋊C4—441no—
634C2×C4⋊C4—441no—
635C2×C4⋊C4—441no—
636C2×C4⋊C4—441no—
637C2×C4⋊C4—441no—
638C2×C4⋊C4—441no—
639C2×C22⋊C4—114no—
640C2×C22⋊C4—114no—
641C2×C22⋊C4—114no—
642C2×C22⋊C4—114no—
643C2×C22⋊C4—222no—
644C2×C22⋊C4—222no—
645C2×C22⋊C4—222no—
646C2×C22⋊C4—222no—
647C2×C22⋊C4—222no—
648C2×C22⋊C4—222no—
649C2×C22⋊C4—222no—
650C2×C22⋊C4—222no—
651C2×C22⋊C4—441no—
652C2×C22⋊C4—441no—
653C2×C22⋊C4—441no—
654C2×C22⋊C4—441no—
655C2×C22⋊C4—441no—
656C2×C22⋊C4—441no—
657C2×C22⋊C4—441no—
658C2×C22⋊C4—441no—
659C2×C22⋊C4—441no—
660C2×C22⋊C4—441no—
661C2×C22⋊C4—441no—
662C2×C22⋊C4—441no—
663C2×C22⋊C4—441no—
664C2×C22⋊C4—441no—
665C2×C22⋊C4—441no—
666C2×C22⋊C4—441no—
667C2×C22⋊C4—441no—
668C2×C22⋊C4—441no—
669C2×C22⋊C4—441no—
670C2×C22⋊C4—441no—
671C2×C22⋊C4—441no—
672C2×C22⋊C4—441no—
673C2×C22⋊C4—441no—
674C2×C22⋊C4—441no—
675C2×C42—114no—
676C2×C42—441no—
677C2×C42—441no—
678#95—22no—
679#95—41no—
680#95—41no—
681#95—41no—
682#95—41no—
683#95—222no—
684#95—222no—
685#95—222no—
686#95—441no—
687#95—441no—
688#95—441no—
689#95—441no—
690#95—441no—
691#95—441no—
692#95—441no—
693#95C4×D1114yes—
694C2×C11#232411yescharacteristic
695C2×C11#232411yescharacteristic
696C2×C11#232511yescharacteristic
697C2×C11#237511yescharacteristic
698C2×C11#237611yescharacteristic
699C2×C11#237611yescharacteristic
700C2×C11#237911yescharacteristic
701C2×C11#281311yescharacteristic
702C2×C11#281311yescharacteristic
703C2×C11#281911yescharacteristic
704C2×C11#282311yescharacteristic
705C2×C11#282811yescharacteristic
706C2×C11#283211yescharacteristic
707C2×C11#283711yescharacteristic
708C2×C11#283711yescharacteristic
709D11—82no—
710D11—82no—
711C24—112no—
712C24—112no—
713C24—221no—
714C24—221no—
715C24—221no—
716C24—221no—
717C24—221no—
718C24—221no—
719C24—221no—
720C24—221no—
721C24—221no—
722C24—221no—
723C24—221no—
724C24—221no—
725C24—221no—
726C24—221no—
727C24—221no—
728C24—221no—
729C24—221no—
730C24—221no—
731C24—221no—
732C24—221no—
733C24—221no—
734C24—221no—
735C24—221no—
736C24—221no—
737C24—221no—
738C24—221no—
739C24—221no—
740C24—221no—
741C24C23×D1111yescharacteristic
742C2×D4—444no—
743C2×D4—444no—
744C2×D4—444no—
745C2×D4—444no—
746C2×D4—444no—
747C2×D4—444no—
748C2×D4—444no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
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—112no—
795C22×C4—112no—
796C22×C4—112no—
797C22×C4—112no—
798C22×C4—112no—
799C22×C4—221no—
800C22×C4—221no—
801C22×C4—221no—
802C22×C4—221no—
803C22×C4—221no—
804C22×C4—221no—
805C22×C4—221no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—221no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
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×C4C2×C4×D1112yes—
837C22×C4C2×C4×D1112yes—
838C22×C4C2×C4×D1112yes—
839C22×C4D4×D1112yes—
840C4⋊C4—44no—
841C4⋊C4—444no—
842C4⋊C4—444no—
843C4⋊C4—444no—
844C4⋊C4—444no—
845C22⋊C4—228no—
846C22⋊C4—228no—
847C22⋊C4—444no—
848C22⋊C4—444no—
849C22⋊C4—444no—
850C22⋊C4—444no—
851C22⋊C4—444no—
852C22⋊C4—444no—
853C22⋊C4—444no—
854C22⋊C4—444no—
855C22⋊C4—444no—
856C22⋊C4—444no—
857C42—444no—
858C11#1463211yescharacteristic, complemented, Sylow
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23—222no—
864C23—222no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—441no—
874C23—441no—
875C23—441no—
876C23—441no—
877C23—441no—
878C23—441no—
879C23—441no—
880C23—441no—
881C23—441no—
882C23—441no—
883C23—441no—
884C23—441no—
885C23—441no—
886C23—441no—
887C23—441no—
888C23—441no—
889C23—441no—
890C23—441no—
891C23—441no—
892C23—441no—
893C23—441no—
894C23—441no—
895C23—441no—
896C23—441no—
897C23—441no—
898C23—441no—
899C23—441no—
900C23—441no—
901C23—441no—
902C23—441no—
903C23—441no—
904C23—441no—
905C23—441no—
906C23—441no—
907C23—441no—
908C23—441no—
909C23—441no—
910C23—441no—
911C23—441no—
912C23—441no—
913C23—441no—
914C23—441no—
915C23—441no—
916C23—441no—
917C23—441no—
918C23—441no—
919C23—441no—
920C23—441no—
921C23—441no—
922C23—441no—
923C23—441no—
924C23—441no—
925C23—441no—
926C23—441no—
927C23—441no—
928C23—441no—
929C23C22×C4×D1111yescharacteristic
930C23C2×D4×D1111yescharacteristic
931C23#6703711yescharacteristic
932C23#6703711yescharacteristic
933C23#6703711yescharacteristic
934C23#6704011yescharacteristic
935C23#6704011yescharacteristic
936C23#41×D1111yescharacteristic
937C23#6704211yescharacteristic
938C23#6704211yescharacteristic
939C23#6704211yescharacteristic
940C23#6704211yescharacteristic
941C23#6704211yescharacteristic
942C23#6704211yescharacteristic
943C23#6704311yescharacteristic
944D4—4416no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—114no—
995C2×C4—222no—
996C2×C4—222no—
997C2×C4—222no—
998C2×C4—222no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—441no—
1008C2×C4—441no—
1009C2×C4—441no—
1010C2×C4—441no—
1011C2×C4—441no—
1012C2×C4—441no—
1013C2×C4—441no—
1014C2×C4—441no—
1015C2×C4—441no—
1016C2×C4—441no—
1017C2×C4—441no—
1018C2×C4—441no—
1019C2×C4—441no—
1020C2×C4—441no—
1021C2×C4—441no—
1022C2×C4—441no—
1023C2×C4—441no—
1024C2×C4—441no—
1025C2×C4—441no—
1026C2×C4—441no—
1027C2×C4—441no—
1028C2×C4—441no—
1029C2×C4—441no—
1030C2×C4—441no—
1031C2×C4—441no—
1032C2×C4—441no—
1033C2×C4—441no—
1034C2×C4—441no—
1035C2×C4—441no—
1036C22—442no—
1037C22—442no—
1038C22—442no—
1039C22—442no—
1040C22—442no—
1041C22—442no—
1042C22—442no—
1043C22—442no—
1044C22—442no—
1045C22—442no—
1046C22—442no—
1047C22—442no—
1048C22—442no—
1049C22—442no—
1050C22—881no—
1051C22—881no—
1052C22—881no—
1053C22—881no—
1054C22—881no—
1055C22—881no—
1056C22—881no—
1057C22—881no—
1058C22—881no—
1059C22—881no—
1060C22—881no—
1061C22—881no—
1062C22—881no—
1063C22—881no—
1064C22—881no—
1065C22—881no—
1066C22#1062303511yescharacteristic
1067C22#1062305211yescharacteristic
1068C22#1062305411yescharacteristic
1069C22C4×D4×D1111yescharacteristic
1070C22#1062307611yescharacteristic
1071C22#1062307611yescharacteristic
1072C22#1062310511yescharacteristic
1073C22#1062312311yescharacteristic
1074C22#1062312811yescharacteristic
1075C22#1062315111yescharacteristic
1076C22#1062315111yescharacteristic
1077C22#1062316011yescharacteristic
1078C22#1062316011yescharacteristic
1079C22#1062317111yescharacteristic
1080C22#1062317811yescharacteristic
1081C22#1062317811yescharacteristic
1082C22#1062318411yescharacteristic
1083C22#1062319411yescharacteristic
1084C22#1062319411yescharacteristic
1085C22#1062319711yescharacteristic
1086C22#1062319811yescharacteristic
1087C22#1062320511yescharacteristic
1088C22#1062321411yescharacteristic
1089C22#1062321411yescharacteristic
1090C22#1062321511yescharacteristic
1091C22#1062322311yescharacteristic
1092C22#1062323011yescharacteristic
1093C22#1062323011yescharacteristic
1094C22#1062323111yescharacteristic
1095C22#1062323111yescharacteristic
1096C22#1062323511yescharacteristic
1097C22#1062324111yescharacteristic
1098C22#1062324211yescharacteristic
1099C22#1062324211yescharacteristic
1100C22#1062326611yescharacteristic
1101C4—42no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—224no—
1109C4—442no—
1110C4—442no—
1111C4—881no—
1112C4—881no—
1113C4—881no—
1114C2—882no—
1115C2—882no—
1116C2#1307130411yescharacteristic
1117C2#1307130811yescharacteristic
1118C2#1307131511yescharacteristic
1119C2#1307175611yescharacteristic
1120C2#1307176111yescharacteristic
1121C2#1307176311yescharacteristic
1122C2#1307178711yescharacteristic
1123C2#1307662111yescharacteristic
1124C2#1307662411yescharacteristic
1125C2#1307666411yescharacteristic
1126C2#1307669111yescharacteristic
1127C2#1307673711yescharacteristic
1128C2#1307678511yescharacteristic
1129C2#1307682711yescharacteristic
1130C2#1307683711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1442D11
hypocenterC11#14632
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#10622283C2semidirect
3. C2×#10622603C2semidirect
4. #13066873C2semidirect
5. #13066867C2semidirect
6. #13066862C2semidirect
7. #13066860C2semidirect
8. #13066860C2semidirect
9. #13066860C2semidirect
10. #13066860C2semidirect
11. #13066858C2semidirect
14. Dic11⋊#95C2semidirect
15. C11×#1442C2semidirect
52. #10622285C4semidirect
129. C2×C4×Dic11D4semidirect
298. #1442D11semidirect
858. C11#14632semidirect

Maximal subgroups

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

subgroupindex
C2×#106222852
C2×#106222832
C2×#106226032
#130668732
#130668672
#130668622
#130668602
#130668582
#130668562
Dic11⋊#952
C11×#14422
#1463211