Finite Group Databasebeta

← #14677167

Subgroups — #14677167

Order 2816.

2474 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic
3C2×#10622570C211yesmaximal, characteristic
4C2×#10622585C211yesmaximal, characteristic, complemented
5C2×#10622602C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
7#13066862C211yesmaximal, characteristic, complemented
8#13066861C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066858C211yesmaximal, characteristic, complemented
11Dic11⋊#95C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13#13066839C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#385C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C2×C4×C22⋊D11—24no—
27C2×C4×C22⋊D11—24no—
28C2×C4×C22⋊D11—24no—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C11×#385—24no—
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
54C2×C11⋊#95C2211yescharacteristic
55#10622602—24no—
56C4⋊C4×Dic11—24no—
57#10622585—24no—
58#10622570—24no—
59#10622570C418yescomplemented
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—41no—
68C23×C4×C11—41no—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11C2×C414yes—
80C22×C22⋊D11D414yes—
81C22×C22⋊D11Q814yes—
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—41no—
95C22×C4×D11—41no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4—41no—
101C2×C11×C4⋊C4D414yescomplemented
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—41no—
107C2×C11×C22⋊C4C2×C414yescomplemented
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—22no—
112C2×C22⋊Dic11—22no—
113C2×C22⋊Dic11—41no—
114C2×C22⋊Dic11—41no—
115C2×C22⋊Dic11—41no—
116C2×C22⋊Dic11C2×C414yescomplemented
117C4×C22⋊D11—232no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4—41no—
131C2×(C2×D11)⋊C4C2×C414yescomplemented
132C2×(C2×D11)⋊C4C2×C414yescomplemented
133C2×C4⋊Dic11—22no—
134C2×C4⋊Dic11—22no—
135C2×C4⋊Dic11—22no—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—22no—
144C2×Dic11⋊C4—22no—
145C2×Dic11⋊C4—41no—
146C2×Dic11⋊C4C2×C414yescomplemented
147C2×Dic11⋊C4D414yes—
148C2×C4×Dic11—22no—
149C2×C4×Dic11—22no—
150C2×C4×Dic11—22no—
151C2×C4×Dic11—22no—
152C2×C4×Dic11—22no—
153C2×C4×Dic11—22no—
154C2×C4×Dic11—22no—
155C2×C4×Dic11C2×C414yescomplemented
156C2×C4×Dic11D414yes—
157C11×#95—22no—
158C11×#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—41no—
166C11⋊#95—41no—
167C11⋊#95—41no—
168C11⋊#95—41no—
169#14018—111nomaximal, Sylow
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11C22×C412yes—
183C24×C11C2×D412yes—
184C24×C11C2×Q812yes—
185C24×C11C2411yescharacteristic
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—21no—
196C23×D11—21no—
197C23×D11—21no—
198C23×D11C22×C412yes—
199C23×D11C2×D412yes—
200C23×D11C2×Q812yes—
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—28no—
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×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—44no—
236C22×C4×C11—44no—
237C22×C4×C11—44no—
238C22×C4×C11—44no—
239C22×C4×C11—44no—
240C22×C4×C11—44no—
241C22×C4×C11C22×C412yes—
242C22×C4×C11C22×C412yes—
243C22×C4×C11C2×D412yes—
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11#4112yes—
249C22×C4×C11#4112yes—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—28no—
255C2×C22⋊D11—28no—
256C2×C22⋊D11C4⋊C4116yescomplemented
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×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11C22×C412yes—
295C22×Dic11C22×C412yes—
296C22×Dic11C22×C412yes—
297C22×Dic11C2×D412yes—
298C22×Dic11C2×D412yes—
299C22×Dic11C2×D412yes—
300C22×Dic11C2×D412yes—
301C22×Dic11C2×D412yes—
302C22×Dic11C2×Q812yes—
303C22×Dic11#4112yes—
304C22×Dic11#4112yes—
305C22×Dic11#4112yes—
306C2×C4×D11—28no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
309C2×C4×D11—44no—
310C2×C4×D11—44no—
311C2×C4×D11—44no—
312C2×C4×D11—44no—
313C11×C4⋊C4—28no—
314C11×C4⋊C4—44no—
315C11×C22⋊C4—28no—
316C11×C22⋊C4—44no—
317C22⋊Dic11—28no—
318C22⋊Dic11—44no—
319C22⋊Dic11—44no—
320(C2×D11)⋊C4—28no—
321(C2×D11)⋊C4—28no—
322(C2×D11)⋊C4—44no—
323(C2×D11)⋊C4—44no—
324(C2×D11)⋊C4—44no—
325C4⋊Dic11—28no—
326Dic11⋊C4—28no—
327Dic11⋊C4—28no—
328Dic11⋊C4—44no—
329Dic11⋊C4—44no—
330C4×Dic11—28no—
331C4×Dic11—28no—
332C4×Dic11—44no—
333C22×C4×D4—111no—
334C2×#390—111no—
335C2×#390—111no—
336C2×#389—111no—
337C2×#385—111no—
338C2×#385D1111yescharacteristic, complemented
339C2×C4×C4⋊C4—111no—
340#1439—111no—
341#1439—111no—
342#1439—111no—
343#1439—111no—
344C4⋊#95—111no—
345C4⋊#95—111no—
346C22⋊#95—111no—
347C22⋊#95—111no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11C2×C4⋊C414yes—
383C23×C11C23×C411yescharacteristic
384C23×C11C22×D411yescharacteristic
385C23×C11C22×D411yescharacteristic
386C23×C11C22×D411yescharacteristic
387C23×C11C22×D411yescharacteristic
388C23×C11C22×Q811yescharacteristic
389C23×C11C2×#4111yescharacteristic
390C23×C11C2×#4111yescharacteristic
391C23×C11C2×#4111yescharacteristic
392C23×C11C2×#4111yescharacteristic
393C23×C11C2×#4111yescharacteristic
394C23×C11H(5,𝔽2)11yescharacteristic
395C23×C11H(5,𝔽2)11yescharacteristic
396C23×C11H(5,𝔽2)11yescharacteristic
397C23×C112−1+411yescharacteristic
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
422C22×D11—41no—
423C22×D11—41no—
424C22×D11—41no—
425C22×D11—41no—
426C22×D11—41no—
427C22×D11—41no—
428C22×D11—41no—
429C22×D11—41no—
430C22×D11—41no—
431C22×D11—41no—
432C22×D11C2×C4⋊C414yes—
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—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—416no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11C4×D414yescomplemented
475C2×C4×C11#12114yes—
476C22⋊D11—232no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
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—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
514C2×Dic11—41no—
515C2×Dic11—41no—
516C2×Dic11—41no—
517C2×Dic11—41no—
518C2×Dic11—41no—
519C2×Dic11C2×C4⋊C414yes—
520C2×Dic11C4×D414yes—
521C2×Dic11C4×D414yes—
522C2×Dic11#12014yes—
523C2×Dic11C22⋊Q814yes—
524C2×Dic11C22⋊Q814yes—
525C2×Dic11#12314yes—
526C4×D11—416no—
527C23×D4—111no—
528C24×C4—111no—
529C24×C4C2×D1111yescharacteristic
530C2×C4×D4—224no—
531C2×C4×D4—224no—
532C2×C4×D4—224no—
533C22×C4⋊C4—111no—
534C22×C4⋊C4—111no—
535C22×C4⋊C4—111no—
536C22×C4⋊C4—111no—
537C22×C4⋊C4—111no—
538C22×C4⋊C4C2×D1111yescharacteristic
539C22×C4⋊C4C2×D1111yescharacteristic
540C22×C22⋊C4—111no—
541C22×C22⋊C4—111no—
542C22×C22⋊C4—111no—
543C22×C22⋊C4—111no—
544C22×C22⋊C4—111no—
545C22×C22⋊C4—111no—
546C22×C22⋊C4—111no—
547C22×C22⋊C4—111no—
548C22×C22⋊C4C2×D1111yescharacteristic
549C22×C22⋊C4C2×D1111yescharacteristic
550C22×C42—111no—
551C22×C42—111no—
552C22×C42—111no—
553#390—118no—
554#390—224no—
555#389—224no—
556#385—24no—
557#385—224no—
558C4×C4⋊C4—224no—
559C2×#95—111no—
560C2×#95—111no—
561C2×#95—111no—
562C2×#95—111no—
563C2×#95—111no—
564C2×#95—111no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95—111no—
568C2×#95—111no—
569C2×#95C2×D1111yescharacteristic
570C2×#95C2×D1111yescharacteristic
571C22×C11—24no—
572C22×C11—24no—
573C22×C11—24no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—42no—
578C22×C11—42no—
579C22×C11—42no—
580C22×C11—42no—
581C22×C11—42no—
582C22×C11—42no—
583C22×C11—42no—
584C22×C11—42no—
585C22×C11—42no—
586C22×C11C22×C4⋊C411yescharacteristic
587C22×C11C2×C4×D411yescharacteristic
588C22×C11C2×C4×D411yescharacteristic
589C22×C11C2×C4×D411yescharacteristic
590C22×C11C4×#4111yescharacteristic
591C22×C11#51811yescharacteristic
592C22×C11#52011yescharacteristic
593C22×C11C2×#12011yescharacteristic
594C22×C11C2×#12111yescharacteristic
595C22×C11C2×C22⋊Q811yescharacteristic
596C22×C11C2×C22⋊Q811yescharacteristic
597C22×C11C2×#12311yescharacteristic
598C22×C11#52511yescharacteristic
599C22×C11#52911yescharacteristic
600C22×C11#53211yescharacteristic
601C22×C11#53511yescharacteristic
602C22×C11#53711yescharacteristic
603C22×C11#54011yescharacteristic
604C22×C11#54211yescharacteristic
605C22×C11D4211yescharacteristic
606C22×C11D4211yescharacteristic
607C22×C11#54611yescharacteristic
608C22×C11#54611yescharacteristic
609C22×C11#54611yescharacteristic
610C22×C11#54711yescharacteristic
611C22×C11#54811yescharacteristic
612C22×C11D4×Q811yescharacteristic
613C22×C11#55011yescharacteristic
614C22×C11#55011yescharacteristic
615C22×C11#55411yescharacteristic
616C22×C11#55411yescharacteristic
617C22×C11#55411yescharacteristic
618C22×C11#55611yescharacteristic
619C22×C11#55911yescharacteristic
620C22×C11#55911yescharacteristic
621C2×D11—24no—
622C2×D11—24no—
623C2×D11—24no—
624C2×D11—42no—
625C2×D11—42no—
626C2×D11—42no—
627C2×D11—42no—
628C2×D11—42no—
629C2×D11—42no—
630C2×D11—42no—
631C2×D11—42no—
632C2×D11—42no—
633C2×D11—42no—
634C2×D11—42no—
635C2×D11—42no—
636C4×C11—24no—
637C4×C11—24no—
638C4×C11—42no—
639C4×C11—42no—
640C4×C11—42no—
641C4×C11—81no—
642Dic11—42no—
643Dic11—42no—
644Dic11—42no—
645Dic11—42no—
646Dic11—42no—
647Dic11—81no—
648Dic11#38518yescomplemented
649C25—111no—
650C25C22×D1111yescharacteristic
651C22×D4—114no—
652C22×D4—114no—
653C22×D4—114no—
654C22×D4—222no—
655C22×D4—222no—
656C22×D4—222no—
657C22×D4—222no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—41no—
664C23×C4—41no—
665C23×C4—111no—
666C23×C4—111no—
667C23×C4—111no—
668C23×C4—111no—
669C23×C4—111no—
670C23×C4—111no—
671C23×C4—111no—
672C23×C4—222no—
673C23×C4—222no—
674C23×C4—222no—
675C23×C4—222no—
676C23×C4—222no—
677C23×C4—441no—
678C23×C4—441no—
679C23×C4C22×D1111yescharacteristic
680C23×C4C22×D1111yescharacteristic
681C23×C4C22×D1111yescharacteristic
682C23×C4C22×D1111yescharacteristic
683C23×C4C22×D1111yescharacteristic
684C23×C4C22×D1111yescharacteristic
685C4×D4—2232no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—114no—
692C2×C4⋊C4—114no—
693C2×C4⋊C4—222no—
694C2×C4⋊C4—222no—
695C2×C4⋊C4—222no—
696C2×C4⋊C4—222no—
697C2×C4⋊C4—222no—
698C2×C4⋊C4—222no—
699C2×C4⋊C4—222no—
700C2×C4⋊C4—222no—
701C2×C4⋊C4—222no—
702C2×C4⋊C4—222no—
703C2×C4⋊C4—222no—
704C2×C4⋊C4—222no—
705C2×C4⋊C4—441no—
706C2×C4⋊C4C22⋊D1114yescomplemented
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—114no—
713C2×C22⋊C4—114no—
714C2×C22⋊C4—114no—
715C2×C22⋊C4—222no—
716C2×C22⋊C4—222no—
717C2×C22⋊C4—222no—
718C2×C22⋊C4—222no—
719C2×C22⋊C4—222no—
720C2×C22⋊C4—222no—
721C2×C22⋊C4—222no—
722C2×C22⋊C4—222no—
723C2×C22⋊C4—222no—
724C2×C22⋊C4—222no—
725C2×C22⋊C4—222no—
726C2×C22⋊C4—222no—
727C2×C22⋊C4—222no—
728C2×C22⋊C4—222no—
729C2×C22⋊C4—441no—
730C2×C22⋊C4—441no—
731C2×C22⋊C4—441no—
732C2×C22⋊C4—441no—
733C2×C22⋊C4—441no—
734C2×C22⋊C4—441no—
735C2×C22⋊C4—441no—
736C2×C22⋊C4C4×D1114yescomplemented
737C2×C42—114no—
738C2×C42—114no—
739C2×C42—222no—
740C2×C42—222no—
741C2×C42—222no—
742C2×C42—222no—
743C2×C42—222no—
744C2×C42—222no—
745C2×C42—222no—
746#95—22no—
747#95—22no—
748#95—222no—
749#95—222no—
750#95—222no—
751#95—222no—
752#95—222no—
753#95—222no—
754#95—441no—
755#95—441no—
756#95—441no—
757#95—441no—
758C2×C11—44no—
759C2×C11C2×#38511yescharacteristic
760C2×C11C4×#12111yescharacteristic
761C2×C11#232411yescharacteristic
762C2×C11D4×C4⋊C411yescharacteristic
763C2×C11#234911yescharacteristic
764C2×C11#236611yescharacteristic
765C2×C11#236711yescharacteristic
766C2×C11#240711yescharacteristic
767C2×C11#240811yescharacteristic
768C2×C11#244511yescharacteristic
769C2×C11#244711yescharacteristic
770C2×C11#245211yescharacteristic
771C2×C11#245411yescharacteristic
772C2×C11#253811yescharacteristic
773C2×C11#258011yescharacteristic
774D11—44no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—112no—
788C24—112no—
789C24—112no—
790C24—221no—
791C24—221no—
792C24—221no—
793C24—221no—
794C24—221no—
795C24—221no—
796C24—221no—
797C24—221no—
798C24—221no—
799C24—221no—
800C24—221no—
801C24—221no—
802C24C2×C4×D1112yes—
803C24D4×D1112yes—
804C24Q8×D1112yes—
805C24C23×D1111yescharacteristic
806C2×D4—1116no—
807C2×D4—228no—
808C2×D4—228no—
809C2×D4—228no—
810C2×D4—228no—
811C2×D4—228no—
812C2×D4—228no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—28no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—112no—
854C22×C4—112no—
855C22×C4—112no—
856C22×C4—112no—
857C22×C4—112no—
858C22×C4—112no—
859C22×C4—112no—
860C22×C4—112no—
861C22×C4—112no—
862C22×C4—112no—
863C22×C4—112no—
864C22×C4—112no—
865C22×C4—228no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
879C22×C4—221no—
880C22×C4—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—221no—
888C22×C4—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—221no—
898C22×C4—221no—
899C22×C4—221no—
900C22×C4—221no—
901C22×C4—221no—
902C22×C4—221no—
903C22×C4—444no—
904C22×C4—444no—
905C22×C4—444no—
906C22×C4—444no—
907C22×C4—444no—
908C22×C4—444no—
909C22×C4C2×C4×D1112yes—
910C22×C4C2×C4×D1112yes—
911C22×C4#433912yes—
912C22×C4D4×D1112yes—
913C22×C4D4×D1112yes—
914C22×C4#434112yes—
915C22×C4C2×C22⋊D1112yes—
916C22×C4C2×C22⋊D1112yes—
917C22×C4C2×C22⋊D1112yes—
918C4⋊C4—28no—
919C4⋊C4—44no—
920C4⋊C4—228no—
921C4⋊C4—228no—
922C4⋊C4—228no—
923C4⋊C4—444no—
924C4⋊C4—444no—
925C22⋊C4—28no—
926C22⋊C4—44no—
927C22⋊C4—228no—
928C22⋊C4—228no—
929C22⋊C4—228no—
930C22⋊C4—444no—
931C22⋊C4—444no—
932C22⋊C4—444no—
933C22⋊C4—444no—
934C22⋊C4—444no—
935C42—228no—
936C42—228no—
937C42—444no—
938C11#1401811yescharacteristic, complemented, Sylow
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—114no—
974C23—222no—
975C23—222no—
976C23—222no—
977C23—222no—
978C23—222no—
979C23—222no—
980C23—222no—
981C23—222no—
982C23—222no—
983C23—222no—
984C23—222no—
985C23—222no—
986C23—222no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—441no—
993C23—441no—
994C23—441no—
995C23—441no—
996C23—441no—
997C23—441no—
998C23—441no—
999C23—441no—
1000C23—441no—
1001C23—441no—
1002C23—441no—
1003C23—441no—
1004C23—441no—
1005C23—441no—
1006C23—441no—
1007C23—441no—
1008C23C4⋊C4×D1114yes—
1009C23C22×C4×D1111yescharacteristic
1010C23C2×#433911yescharacteristic
1011C23C2×D4×D1111yescharacteristic
1012C23C2×D4×D1111yescharacteristic
1013C23C2×D4×D1111yescharacteristic
1014C23C2×#434111yescharacteristic
1015C23#6703711yescharacteristic
1016C23#6703711yescharacteristic
1017C23C2×Q8×D1111yescharacteristic
1018C23#6704011yescharacteristic
1019C23#41×D1111yescharacteristic
1020C23#41×D1111yescharacteristic
1021C23#41×D1111yescharacteristic
1022C23#6704211yescharacteristic
1023C23C22×C22⋊D1111yescharacteristic
1024D4—2232no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—416no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—114no—
1067C2×C4—114no—
1068C2×C4—114no—
1069C2×C4—114no—
1070C2×C4—114no—
1071C2×C4—114no—
1072C2×C4—114no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—4416no—
1089C2×C4—441no—
1090C2×C4—441no—
1091C2×C4—441no—
1092C2×C4—441no—
1093C2×C4—441no—
1094C2×C4—441no—
1095C2×C4—441no—
1096C2×C4—441no—
1097C2×C4—441no—
1098C2×C4—441no—
1099C2×C4—441no—
1100C2×C4—441no—
1101C2×C4—441no—
1102C2×C4—441no—
1103C2×C4—441no—
1104C2×C4—441no—
1105C2×C4—441no—
1106C2×C4—441no—
1107C2×C4—441no—
1108C2×C4—441no—
1109C2×C4—441no—
1110C2×C4—441no—
1111C2×C4—441no—
1112C2×C4—441no—
1113C2×C4—441no—
1114C2×C4—441no—
1115C2×C4—441no—
1116C2×C4C4×C22⋊D1114yescomplemented
1117C2×C4#6699214yes—
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—224no—
1134C22—224no—
1135C22—224no—
1136C22—442no—
1137C22—442no—
1138C22—442no—
1139C22—442no—
1140C22—442no—
1141C22—442no—
1142C22—442no—
1143C22—442no—
1144C22—442no—
1145C22—442no—
1146C22—442no—
1147C22—442no—
1148C22C2×C4⋊C4×D1111yescharacteristic
1149C22#1062303511yescharacteristic
1150C22#1062303811yescharacteristic
1151C22#1062304211yescharacteristic
1152C22C4×#434111yescharacteristic
1153C22#1062306911yescharacteristic
1154C22C4×D4×D1111yescharacteristic
1155C22C4×D4×D1111yescharacteristic
1156C22#1062307611yescharacteristic
1157C22#1062307811yescharacteristic
1158C22#1062308411yescharacteristic
1159C22#1062309011yescharacteristic
1160C22D11×#12011yescharacteristic
1161C22#1062312211yescharacteristic
1162C22#1062312211yescharacteristic
1163C22#1062312311yescharacteristic
1164C22D11×C22⋊Q811yescharacteristic
1165C22D11×C22⋊Q811yescharacteristic
1166C22#1062316011yescharacteristic
1167C22#1062316411yescharacteristic
1168C22#1062316611yescharacteristic
1169C22#1062316711yescharacteristic
1170C22#1062317111yescharacteristic
1171C22#1062317211yescharacteristic
1172C22D11×#12311yescharacteristic
1173C22#1062318511yescharacteristic
1174C22#1062319411yescharacteristic
1175C22#1062319511yescharacteristic
1176C22C2×C4×C22⋊D1111yescharacteristic
1177C22D4×C22⋊D1111yescharacteristic
1178C22D4×C22⋊D1111yescharacteristic
1179C22C2×#6699211yescharacteristic
1180C22Q8×C22⋊D1111yescharacteristic
1181C22#1062336311yescharacteristic
1182C22#1062336511yescharacteristic
1183C4—24no—
1184C4—24no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—81no—
1189C4—118no—
1190C4—442no—
1191C4—442no—
1192C4—442no—
1193C4—442no—
1194C4—442no—
1195C4—881no—
1196C2—44no—
1197C2—444no—
1198C2D11×#38511yescharacteristic
1199C2C4×#6699211yescharacteristic
1200C2#1307130811yescharacteristic
1201C2C4⋊C4×C22⋊D1111yescharacteristic
1202C2#1307152211yescharacteristic
1203C2#1307167811yescharacteristic
1204C2#1307168411yescharacteristic
1205C2#1307196011yescharacteristic
1206C2#1307196911yescharacteristic
1207C2#1307238011yescharacteristic
1208C2#1307240011yescharacteristic
1209C2#1307246511yescharacteristic
1210C2#1307248511yescharacteristic
1211C2#1307353511yescharacteristic
1212C2#1307397311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#385D11
hypocenterC11#14018
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#10622585C2semidirect
5. C2×#10622602C2semidirect
6. C2×C4⋊C4×Dic11C2semidirect
7. #13066862C2semidirect
8. #13066861C2semidirect
9. #13066859C2semidirect
10. #13066858C2semidirect
11. Dic11⋊#95C2semidirect
12. Dic11⋊#95C2semidirect
13. #13066839C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#385C2semidirect
59. #10622570C4semidirect
101. C2×C11×C4⋊C4D4semidirect
107. C2×C11×C22⋊C4C2×C4semidirect
116. C2×C22⋊Dic11C2×C4semidirect
131. C2×(C2×D11)⋊C4C2×C4semidirect
132. C2×(C2×D11)⋊C4C2×C4semidirect
146. C2×Dic11⋊C4C2×C4semidirect
155. C2×C4×Dic11C2×C4semidirect
256. C2×C22⋊D11C4⋊C4semidirect
338. C2×#385D11semidirect
474. C2×C4×C11C4×D4semidirect
648. Dic11#385semidirect
706. C2×C4⋊C4C22⋊D11semidirect
736. C2×C22⋊C4C4×D11semidirect
938. C11#14018semidirect
1116. C2×C4C4×C22⋊D11semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106225702
C2×#106225852
C2×#106226022
C2×C4⋊C4×Dic112
#130668622
#130668612
#130668592
#130668582
Dic11⋊#952
#130668392
(C2×D11)⋊#952
C2×C11×#3852
#1401811