Finite Group Databasebeta

← #14676955

Subgroups — #14676955

Order 2816.

1838 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622570C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic
3C2×#10622570C211yesmaximal, characteristic
4C2×#10622263C211yesmaximal, characteristic, complemented
5C2×#10622262C211yesmaximal, characteristic, complemented
6#13066864C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066863C211yesmaximal, characteristic, complemented
9#13066853C211yesmaximal, characteristic, complemented
10#13066853C211yesmaximal, characteristic, complemented
11#13066852C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
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#10622570—24no—
52#10622570—24no—
53#10622570C418yescomplemented
54#10622263—24no—
55#10622262—24no—
56C25×C11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—22no—
65C22×C22⋊D11—22no—
66C22×C22⋊D11—22no—
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11C2×C414yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—41no—
82C2×C11×C22⋊C4—41no—
83C2×C11×C22⋊C4—41no—
84C2×C11×C22⋊C4—41no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4C2×C414yes—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—41no—
93C2×C22⋊Dic11—41no—
94C2×C22⋊Dic11—41no—
95C2×C22⋊Dic11C2×C414yes—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
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)⋊C4—41no—
112C2×(C2×D11)⋊C4C2×C414yes—
113C2×(C2×D11)⋊C4C2×C414yes—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×Dic11⋊C4C2×C414yes—
122C2×Dic11⋊C4D414yes—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—22no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130C2×C4×Dic11—22no—
131C2×C4×Dic11—22no—
132C2×C4×Dic11—41no—
133C2×C4×Dic11—41no—
134C2×C4×Dic11—41no—
135C2×C4×Dic11—41no—
136C2×C4×Dic11C2×C414yes—
137C2×C4×Dic11D414yes—
138C11×#95—22no—
139C11×#95—22no—
140C11×#95—22no—
141C11×#95—41no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95—41no—
152#14002—111nomaximal, Sylow
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
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×C11C22×C412yes—
168C24×C11C2411yescharacteristic
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
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×D11C22×C412yes—
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×C11C22×C412yes—
222C22×C4×C11C22×C412yes—
223C22×C4×C11C2×D412yes—
224C22×C4×C11C2×D412yes—
225C22×C4×C11#4112yes—
226C2×C22⋊D11—28no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—44no—
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×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11C22×C412yes—
269C22×Dic11C22×C412yes—
270C22×Dic11C22×C412yes—
271C22×Dic11C2×D412yes—
272C22×Dic11C2×D412yes—
273C22×Dic11C2×D412yes—
274C22×Dic11C2×D412yes—
275C22×Dic11#4112yes—
276C22×Dic11#4112yes—
277C22×Dic11#4112yes—
278C22×Dic11#4112yes—
279C22×Dic11#4112yes—
280C22×Dic11#4112yes—
281C22×Dic11#4112yes—
282C11×C22⋊C4—44no—
283C11×C22⋊C4—44no—
284C11×C22⋊C4—44no—
285C22⋊Dic11—44no—
286C22⋊Dic11—44no—
287C22⋊Dic11—44no—
288(C2×D11)⋊C4—44no—
289(C2×D11)⋊C4—44no—
290(C2×D11)⋊C4—44no—
291(C2×D11)⋊C4—44no—
292(C2×D11)⋊C4—44no—
293(C2×D11)⋊C4—44no—
294Dic11⋊C4—28no—
295Dic11⋊C4—28no—
296Dic11⋊C4—44no—
297C4×Dic11—28no—
298C4×Dic11—28no—
299C4×Dic11—44no—
300C4×Dic11—44no—
301C4×Dic11—44no—
302C2×#390—111no—
303C2×#390—111no—
304C2×#390—111no—
305C2×#382—111no—
306C2×C4×C4⋊C4—111no—
307#1440—111no—
308#1440—111no—
309#1440—111no—
310#1440D1111yescharacteristic, complemented
311#1437—111no—
312#1437—111no—
313#1437—111no—
314#1437—111no—
315C4⋊#95—111no—
316C4×#95—111no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11C23×C411yescharacteristic
353C23×C11C22×D411yescharacteristic
354C23×C11C22×D411yescharacteristic
355C23×C11C2×#4111yescharacteristic
356C23×C11C2×#4111yescharacteristic
357C23×C11C2×#4111yescharacteristic
358C23×C11C2×#4111yescharacteristic
359C23×C11C2×#4111yescharacteristic
360C23×C11C2×#4111yescharacteristic
361C23×C11C2×#4111yescharacteristic
362C23×C11C2×#4111yescharacteristic
363C23×C11H(5,𝔽2)11yescharacteristic
364C23×C11H(5,𝔽2)11yescharacteristic
365C23×C11H(5,𝔽2)11yescharacteristic
366C23×C11H(5,𝔽2)11yescharacteristic
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
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—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
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×C4×C11—41no—
444C22⋊D11—416no—
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—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
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×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11#11714yes—
487C2×Dic11C4×D414yes—
488C2×Dic11C4×D414yes—
489C2×Dic11#12114yes—
490C2×Dic11#12314yes—
491C2×Dic11#12414yes—
492C2×Dic11#12414yes—
493C2×Dic11#12614yes—
494C23×D4—111no—
495C22×C4⋊C4—111no—
496C22×C4⋊C4—111no—
497C22×C4⋊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×C22⋊C4—111no—
505C22×C22⋊C4—111no—
506C22×C22⋊C4—111no—
507C22×C22⋊C4C2×D1111yescharacteristic
508C22×C22⋊C4C2×D1111yescharacteristic
509C22×C22⋊C4C2×D1111yescharacteristic
510C22×C42—111no—
511C22×C42—111no—
512C22×C42—111no—
513C22×C42—111no—
514C22×C42—111no—
515#390—118no—
516#390—224no—
517#390—224no—
518#382—224no—
519C4×C4⋊C4—224no—
520C2×#95—111no—
521C2×#95—111no—
522C2×#95—111no—
523C2×#95—111no—
524C2×#95—111no—
525C2×#95—111no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95C2×D1111yescharacteristic
531C2×#95C2×D1111yescharacteristic
532C2×#95C2×D1111yescharacteristic
533C2×#95C2×D1111yescharacteristic
534C22×C11—42no—
535C22×C11—42no—
536C22×C11—42no—
537C22×C11—42no—
538C22×C11—42no—
539C22×C11—42no—
540C22×C11—42no—
541C22×C11—81no—
542C22×C11—81no—
543C22×C11—81no—
544C22×C11—81no—
545C22×C11—81no—
546C22×C11—81no—
547C22×C11—81no—
548C22×C11—81no—
549C22×C11C2×#11711yescharacteristic
550C22×C11C2×C4×D411yescharacteristic
551C22×C11C2×C4×D411yescharacteristic
552C22×C11C4×#4111yescharacteristic
553C22×C11C4×#4111yescharacteristic
554C22×C11#51811yescharacteristic
555C22×C11#51811yescharacteristic
556C22×C11C2×#12111yescharacteristic
557C22×C11C2×#12311yescharacteristic
558C22×C11C2×#12411yescharacteristic
559C22×C11C2×#12411yescharacteristic
560C22×C11C2×#12611yescharacteristic
561C22×C11#52911yescharacteristic
562C22×C11#52911yescharacteristic
563C22×C11#53211yescharacteristic
564C22×C11#53511yescharacteristic
565C22×C11#53511yescharacteristic
566C22×C11#54011yescharacteristic
567C22×C11#54011yescharacteristic
568C22×C11#54611yescharacteristic
569C22×C11#54611yescharacteristic
570C22×C11#55011yescharacteristic
571C22×C11#55011yescharacteristic
572C22×C11#55311yescharacteristic
573C22×C11#55311yescharacteristic
574C22×C11#55311yescharacteristic
575C22×C11#55311yescharacteristic
576C22×C11#55311yescharacteristic
577C22×C11#55311yescharacteristic
578C22×C11#55511yescharacteristic
579C22×C11#55511yescharacteristic
580C22×C11#55911yescharacteristic
581C22×C11#55911yescharacteristic
582C22×C11#55911yescharacteristic
583C22×C11#55911yescharacteristic
584C2×D11—42no—
585C2×D11—42no—
586C2×D11—42no—
587C2×D11—42no—
588C2×D11—42no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—81no—
592C2×D11—81no—
593C2×D11—81no—
594C2×D11—81no—
595C2×D11—81no—
596C2×D11—81no—
597C2×D11—81no—
598C2×D11—81no—
599C4×C11—42no—
600C4×C11—42no—
601C4×C11—42no—
602C4×C11—42no—
603C4×C11—42no—
604C4×C11—81no—
605Dic11—24no—
606Dic11—42no—
607Dic11—42no—
608Dic11—42no—
609Dic11—42no—
610Dic11—81no—
611Dic11#38818yes—
612C25—111no—
613C25C22×D1111yescharacteristic
614C22×D4—114no—
615C22×D4—222no—
616C22×D4—222no—
617C22×D4—222no—
618C22×D4—222no—
619C22×D4—222no—
620C22×D4—222no—
621C23×C4—111no—
622C23×C4—111no—
623C23×C4—111no—
624C23×C4—111no—
625C23×C4—111no—
626C23×C4—111no—
627C23×C4—111no—
628C23×C4C22×D1111yescharacteristic
629C23×C4C22×D1111yescharacteristic
630C23×C4C22×D1111yescharacteristic
631C23×C4C22×D1111yescharacteristic
632C23×C4C22×D1111yescharacteristic
633C23×C4C22×D1111yescharacteristic
634C2×C4⋊C4—114no—
635C2×C4⋊C4—114no—
636C2×C4⋊C4—222no—
637C2×C4⋊C4—222no—
638C2×C4⋊C4—222no—
639C2×C4⋊C4—222no—
640C2×C4⋊C4—222no—
641C2×C4⋊C4—222no—
642C2×C4⋊C4—222no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—41no—
647C2×C22⋊C4—41no—
648C2×C22⋊C4—41no—
649C2×C22⋊C4—41no—
650C2×C22⋊C4—41no—
651C2×C22⋊C4—114no—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—222no—
655C2×C22⋊C4—222no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4—222no—
658C2×C22⋊C4—222no—
659C2×C22⋊C4—222no—
660C2×C22⋊C4—222no—
661C2×C22⋊C4—222no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4—222no—
664C2×C22⋊C4—222no—
665C2×C22⋊C4—222no—
666C2×C22⋊C4—222no—
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×C22⋊C4—441no—
676C2×C22⋊C4—441no—
677C2×C22⋊C4—441no—
678C2×C22⋊C4C4×D1114yes—
679C2×C42—114no—
680C2×C42—114no—
681C2×C42—222no—
682C2×C42—222no—
683C2×C42—222no—
684C2×C42—222no—
685C2×C42—222no—
686C2×C42—222no—
687C2×C42—222no—
688C2×C42—222no—
689C2×C42—222no—
690C2×C42—441no—
691C2×C42—441no—
692C2×C42—441no—
693C2×C42—441no—
694#95—22no—
695#95—22no—
696#95—22no—
697#95—41no—
698#95—222no—
699#95—222no—
700#95—222no—
701#95—222no—
702#95—222no—
703#95—222no—
704#95—222no—
705#95—441no—
706#95—441no—
707#95—441no—
708C2×C11—82no—
709C2×C11C2×#38811yescharacteristic
710C2×C11C4×#12411yescharacteristic
711C2×C11#232811yescharacteristic
712C2×C11#235711yescharacteristic
713C2×C11#235711yescharacteristic
714C2×C11#236311yescharacteristic
715C2×C11#236311yescharacteristic
716C2×C11#249011yescharacteristic
717C2×C11#249011yescharacteristic
718C2×C11#250011yescharacteristic
719C2×C11#250411yescharacteristic
720C2×C11#251311yescharacteristic
721C2×C11#251311yescharacteristic
722C2×C11#254411yescharacteristic
723C2×C11#254811yescharacteristic
724D11—82no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—112no—
740C24—221no—
741C24—221no—
742C24—221no—
743C24—221no—
744C24—221no—
745C24—221no—
746C24—221no—
747C24—221no—
748C24—221no—
749C24—221no—
750C24—221no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24C2×C4×D1112yes—
755C24C23×D1111yescharacteristic
756C2×D4—228no—
757C2×D4—228no—
758C2×D4—228no—
759C2×D4—444no—
760C2×D4—444no—
761C2×D4—444no—
762C2×D4—444no—
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—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—112no—
801C22×C4—112no—
802C22×C4—112no—
803C22×C4—112no—
804C22×C4—112no—
805C22×C4—112no—
806C22×C4—112no—
807C22×C4—112no—
808C22×C4—112no—
809C22×C4—112no—
810C22×C4—112no—
811C22×C4—112no—
812C22×C4—112no—
813C22×C4—112no—
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×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×C4C2×C4×D1112yes—
850C22×C4C2×C4×D1112yes—
851C22×C4D4×D1112yes—
852C22×C4D4×D1112yes—
853C22×C4#434112yes—
854C4⋊C4—228no—
855C4⋊C4—228no—
856C4⋊C4—444no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—444no—
861C22⋊C4—444no—
862C22⋊C4—444no—
863C22⋊C4—444no—
864C22⋊C4—444no—
865C22⋊C4—444no—
866C22⋊C4—444no—
867C22⋊C4—444no—
868C22⋊C4—444no—
869C42—228no—
870C42—228no—
871C42—444no—
872C42—444no—
873C42—444no—
874C11#1400211yescharacteristic, complemented, Sylow
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—222no—
911C23—222no—
912C23—222no—
913C23—222no—
914C23—222no—
915C23—222no—
916C23—222no—
917C23—441no—
918C23—441no—
919C23—441no—
920C23—441no—
921C23—441no—
922C23—441no—
923C23—441no—
924C23—441no—
925C23—441no—
926C23—441no—
927C23—441no—
928C23—441no—
929C23—441no—
930C23—441no—
931C23—441no—
932C23—441no—
933C23—441no—
934C23—441no—
935C23—441no—
936C23—441no—
937C23—441no—
938C23—441no—
939C23—441no—
940C23—441no—
941C23—441no—
942C23—441no—
943C23—441no—
944C23—441no—
945C23C22×C4×D1111yescharacteristic
946C23C2×D4×D1111yescharacteristic
947C23C2×D4×D1111yescharacteristic
948C23C2×#434111yescharacteristic
949C23#6703711yescharacteristic
950C23#6703711yescharacteristic
951C23#6703711yescharacteristic
952C23#41×D1111yescharacteristic
953C23#41×D1111yescharacteristic
954C23#41×D1111yescharacteristic
955C23#41×D1111yescharacteristic
956C23#41×D1111yescharacteristic
957C23#41×D1111yescharacteristic
958C23#41×D1111yescharacteristic
959C23#6704211yescharacteristic
960D4—4416no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
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—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—114no—
1004C2×C4—114no—
1005C2×C4—114no—
1006C2×C4—114no—
1007C2×C4—114no—
1008C2×C4—114no—
1009C2×C4—114no—
1010C2×C4—114no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—441no—
1030C2×C4—441no—
1031C2×C4—441no—
1032C2×C4—441no—
1033C2×C4—441no—
1034C2×C4—441no—
1035C2×C4—441no—
1036C2×C4—441no—
1037C2×C4—441no—
1038C2×C4—441no—
1039C2×C4—441no—
1040C2×C4—441no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—442no—
1068C22—442no—
1069C22—442no—
1070C22—442no—
1071C22—442no—
1072C22—442no—
1073C22—442no—
1074C22—881no—
1075C22—881no—
1076C22—881no—
1077C22—881no—
1078C22—881no—
1079C22—881no—
1080C22—881no—
1081C22—881no—
1082C22#1062301711yescharacteristic
1083C22D11×#11711yescharacteristic
1084C22#1062305311yescharacteristic
1085C22C4×#434111yescharacteristic
1086C22C4×D4×D1111yescharacteristic
1087C22C4×D4×D1111yescharacteristic
1088C22#1062307611yescharacteristic
1089C22#1062312211yescharacteristic
1090C22#1062312311yescharacteristic
1091C22#1062312711yescharacteristic
1092C22#1062313011yescharacteristic
1093C22#1062313011yescharacteristic
1094C22#1062313211yescharacteristic
1095C22D11×#12111yescharacteristic
1096C22#1062313811yescharacteristic
1097C22#1062314611yescharacteristic
1098C22#1062314711yescharacteristic
1099C22#1062318011yescharacteristic
1100C22D11×#12311yescharacteristic
1101C22#1062318511yescharacteristic
1102C22#1062319211yescharacteristic
1103C22#1062319211yescharacteristic
1104C22#1062319211yescharacteristic
1105C22#1062319411yescharacteristic
1106C22#1062319511yescharacteristic
1107C22#1062319511yescharacteristic
1108C22#1062319511yescharacteristic
1109C22#1062320111yescharacteristic
1110C22D11×#12411yescharacteristic
1111C22D11×#12411yescharacteristic
1112C22#1062321211yescharacteristic
1113C22D11×#12611yescharacteristic
1114C22#1062323711yescharacteristic
1115C22#1062324011yescharacteristic
1116C22#1062324011yescharacteristic
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—81no—
1123C4—118no—
1124C4—224no—
1125C4—442no—
1126C4—442no—
1127C4—442no—
1128C4—442no—
1129C4—881no—
1130C2—82no—
1131C2—882no—
1132C2D11×#38811yescharacteristic
1133C2#1307115711yescharacteristic
1134C2#1307133711yescharacteristic
1135C2#1307158411yescharacteristic
1136C2#1307158611yescharacteristic
1137C2#1307164911yescharacteristic
1138C2#1307165711yescharacteristic
1139C2#1307296111yescharacteristic
1140C2#1307296311yescharacteristic
1141C2#1307307311yescharacteristic
1142C2#1307310311yescharacteristic
1143C2#1307320611yescharacteristic
1144C2#1307320811yescharacteristic
1145C2#1307358211yescharacteristic
1146C2#1307361411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1440D11
hypocenterC11#14002
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
4. C2×#10622263C2semidirect
5. C2×#10622262C2semidirect
6. #13066864C2semidirect
7. #13066864C2semidirect
8. #13066863C2semidirect
9. #13066853C2semidirect
10. #13066853C2semidirect
11. #13066852C2semidirect
12. #13066852C2semidirect
13. Dic11⋊#95C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1440C2semidirect
53. #10622570C4semidirect
310. #1440D11semidirect
874. C11#14002semidirect

Maximal subgroups

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

subgroupindex
C2×#106225702
C2×#106222632
C2×#106222622
#130668642
#130668632
#130668532
#130668522
Dic11⋊#952
#95×Dic112
C11×#14402
#1400211