Finite Group Databasebeta

← #14677254

Subgroups — #14677254

Order 2816.

2358 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3C2×#10622259C211yesmaximal, characteristic, complemented
4C2×#10622570C211yesmaximal, characteristic
5C2×#10622570C211yesmaximal, characteristic
6#13066862C211yesmaximal, characteristic, complemented
7#13066861C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066854C211yesmaximal, characteristic, complemented
11#13066853C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C2×#66938—24no—
40C2×#66938—24no—
41C2×#66938C418yescomplemented
42C2×C4×Dic22—24no—
43C2×C4×Dic22—24no—
44C2×C4×Dic22—24no—
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
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622570—24no—
58#10622570—24no—
59#10622259—24no—
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11C2×C414yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C22×Dic22—22no—
83C22×Dic22—22no—
84C22×Dic22—22no—
85C22×Dic22—22no—
86C22×Dic22C2×C414yes—
87C22×Dic22D414yes—
88C22×Dic22D414yes—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—41no—
97C2×C11×C22⋊C4C2×C414yes—
98C2×C42×C11—22no—
99C2×C42×C11—22no—
100C2×C42×C11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—22no—
106C2×C22⋊Dic11—41no—
107C2×C22⋊Dic11—41no—
108C2×C22⋊Dic11—41no—
109C2×C22⋊Dic11C2×C414yes—
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—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—41no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4C2×C414yes—
127C2×(C2×D11)⋊C4C2×C414yes—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11—22no—
130C2×C4⋊Dic11—22no—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4D414yes—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—22no—
143C2×C4×Dic11—22no—
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147C2×C4×Dic11—22no—
148C2×C4×Dic11—22no—
149C2×C4×Dic11—22no—
150C2×C4×Dic11C2×C414yes—
151C2×C4×Dic11D414yes—
152#66938—232no—
153C4×Dic22—232no—
154C11×#95—22no—
155C11×#95—22no—
156C11×#95—41no—
157C11⋊#95—22no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—41no—
164C11⋊#95—41no—
165C11⋊#95—41no—
166#14026—111nomaximal, Sylow
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
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×C11C22×C412yes—
182C24×C11C2411yescharacteristic
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
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×D11C22×C412yes—
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×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×C11C22×C412yes—
232C22×C4×C11C22×C412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11#4112yes—
238C22×C4×C11#4112yes—
239C22×C4×C11#4112yes—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—28no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11—44no—
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×Dic11C22×C412yes—
283C22×Dic11C22×C412yes—
284C22×Dic11C22×C412yes—
285C22×Dic11C2×D412yes—
286C22×Dic11C2×D412yes—
287C22×Dic11C2×D412yes—
288C22×Dic11C2×D412yes—
289C22×Dic11C2×D412yes—
290C22×Dic11C2×D412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11#4112yes—
294C22×Dic11#4112yes—
295C22×Dic11#4112yes—
296C2×Dic22—28no—
297C2×Dic22—28no—
298C2×Dic22—28no—
299C2×Dic22—28no—
300C2×Dic22—28no—
301C2×Dic22—28no—
302C2×Dic22C22⋊C4116yescomplemented
303C11×C22⋊C4—28no—
304C11×C22⋊C4—44no—
305C11×C22⋊C4—44no—
306C42×C11—28no—
307C22⋊Dic11—28no—
308C22⋊Dic11—44no—
309C22⋊Dic11—44no—
310(C2×D11)⋊C4—28no—
311(C2×D11)⋊C4—28no—
312(C2×D11)⋊C4—44no—
313(C2×D11)⋊C4—44no—
314(C2×D11)⋊C4—44no—
315(C2×D11)⋊C4—44no—
316C4⋊Dic11—28no—
317Dic11⋊C4—28no—
318Dic11⋊C4—28no—
319Dic11⋊C4—44no—
320C4×Dic11—28no—
321C4×Dic11—28no—
322C4×Dic11—28no—
323C4×Dic11—44no—
324C22×#124—111no—
325C22×C4×Q8—111no—
326C2×#391—111no—
327C2×#390—111no—
328C2×#390—111no—
329#1439—111no—
330#1439—111no—
331#1439—111no—
332#1439—111no—
333#1437—111no—
334#1437—111no—
335#1437—111no—
336#1437D1111yescharacteristic, complemented
337C4⋊#95—111no—
338C4×#95—111no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—41no—
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×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
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×C11C23×C411yescharacteristic
375C23×C11C22×D411yescharacteristic
376C23×C11C22×D411yescharacteristic
377C23×C11C22×D411yescharacteristic
378C23×C11C22×D411yescharacteristic
379C23×C11C2×#4111yescharacteristic
380C23×C11C2×#4111yescharacteristic
381C23×C11C2×#4111yescharacteristic
382C23×C11C2×#4111yescharacteristic
383C23×C11C2×#4111yescharacteristic
384C23×C11C2×#4111yescharacteristic
385C23×C11H(5,𝔽2)11yescharacteristic
386C23×C11H(5,𝔽2)11yescharacteristic
387C23×C112−1+411yescharacteristic
388C23×C112−1+411yescharacteristic
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
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—
414C22×D11—41no—
415C22×D11—41no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
422C22×D11—41no—
423C22×D11—41no—
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—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
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×C11—41no—
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×C11C2×C22⋊C414yes—
465C2×C4×C11#12414yescomplemented
466C22⋊D11—416no—
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—22no—
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—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—41no—
507C2×Dic11—41no—
508C2×Dic11C2×C22⋊C414yes—
509C2×Dic11C2×C22⋊C414yes—
510C2×Dic11C4×D414yes—
511C2×Dic11C4×D414yes—
512C2×Dic11#12014yes—
513C2×Dic11#12114yes—
514C2×Dic11#12114yes—
515C2×Dic11#12314yes—
516Dic22—232no—
517C23×Q8—111no—
518C23×D4—111no—
519C2×#124—118no—
520C2×#124—224no—
521C2×#124—224no—
522C2×C4×Q8—224no—
523C2×C4×Q8—224no—
524C2×C4×Q8—224no—
525C22×C4⋊C4—111no—
526C22×C4⋊C4—111no—
527C22×C4⋊C4—111no—
528C22×C4⋊C4—111no—
529C22×C22⋊C4—111no—
530C22×C22⋊C4—111no—
531C22×C22⋊C4—111no—
532C22×C22⋊C4—111no—
533C22×C22⋊C4—111no—
534C22×C22⋊C4—111no—
535C22×C22⋊C4—111no—
536C22×C22⋊C4—111no—
537C22×C22⋊C4—111no—
538C22×C22⋊C4C2×D1111yescharacteristic
539C22×C22⋊C4C2×D1111yescharacteristic
540C22×C22⋊C4C2×D1111yescharacteristic
541C22×C42—111no—
542C22×C42—111no—
543C22×C42—111no—
544C22×C42—111no—
545C22×C42C2×D1111yescharacteristic
546#391—224no—
547#390—224no—
548#390—224no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95—111no—
552C2×#95—111no—
553C2×#95—111no—
554C2×#95—111no—
555C2×#95—111no—
556C2×#95—111no—
557C2×#95—111no—
558C2×#95C2×D1111yescharacteristic
559C2×#95C2×D1111yescharacteristic
560C2×#95C2×D1111yescharacteristic
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—81no—
569C22×C11—81no—
570C22×C11—81no—
571C22×C11—81no—
572C22×C11—81no—
573C22×C11—81no—
574C22×C11—81no—
575C22×C11—81no—
576C22×C11C22×C22⋊C411yescharacteristic
577C22×C11C2×C4×D411yescharacteristic
578C22×C11C2×C4×D411yescharacteristic
579C22×C11C4×#4111yescharacteristic
580C22×C11C4×#4111yescharacteristic
581C22×C11#52011yescharacteristic
582C22×C11#52011yescharacteristic
583C22×C11C2×#12011yescharacteristic
584C22×C11C2×#12111yescharacteristic
585C22×C11C2×#12111yescharacteristic
586C22×C11C2×#12311yescharacteristic
587C22×C11C2×#12411yescharacteristic
588C22×C11#52911yescharacteristic
589C22×C11#52911yescharacteristic
590C22×C11#53211yescharacteristic
591C22×C11#53511yescharacteristic
592C22×C11#53611yescharacteristic
593C22×C11#54211yescharacteristic
594C22×C11#54211yescharacteristic
595C22×C11#54611yescharacteristic
596C22×C11#54611yescharacteristic
597C22×C11#54811yescharacteristic
598C22×C11#54811yescharacteristic
599C22×C11#54811yescharacteristic
600C22×C11#54811yescharacteristic
601C22×C11#54811yescharacteristic
602C22×C11#54811yescharacteristic
603C22×C11#55011yescharacteristic
604C22×C11#55011yescharacteristic
605C22×C11#55011yescharacteristic
606C22×C11#55011yescharacteristic
607C22×C11#55611yescharacteristic
608C22×C11#55611yescharacteristic
609C22×C11#55911yescharacteristic
610C22×C11#55911yescharacteristic
611C2×D11—42no—
612C2×D11—42no—
613C2×D11—42no—
614C2×D11—42no—
615C2×D11—42no—
616C2×D11—42no—
617C2×D11—42no—
618C2×D11—81no—
619C2×D11—81no—
620C2×D11—81no—
621C2×D11—81no—
622C2×D11—81no—
623C2×D11—81no—
624C2×D11—81no—
625C2×D11—81no—
626C4×C11—24no—
627C4×C11—24no—
628C4×C11—42no—
629C4×C11—42no—
630C4×C11—42no—
631C4×C11—81no—
632Dic11—24no—
633Dic11—42no—
634Dic11—42no—
635Dic11—42no—
636Dic11—42no—
637Dic11—81no—
638Dic11#38618yes—
639C25—111no—
640C25C22×D1111yescharacteristic
641C22×Q8—114no—
642C22×Q8—114no—
643C22×Q8—114no—
644C22×Q8—222no—
645C22×Q8—222no—
646C22×Q8—222no—
647C22×Q8—222no—
648C22×D4—114no—
649C22×D4—222no—
650C22×D4—222no—
651C22×D4—222no—
652C22×D4—222no—
653C22×D4—222no—
654C22×D4—222no—
655C23×C4—111no—
656C23×C4—111no—
657C23×C4—111no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—111no—
662C23×C4C22×D1111yescharacteristic
663C23×C4C22×D1111yescharacteristic
664C23×C4C22×D1111yescharacteristic
665C23×C4C22×D1111yescharacteristic
666C23×C4C22×D1111yescharacteristic
667C23×C4C22×D1111yescharacteristic
668#124—2232no—
669C4×Q8—2232no—
670C2×C4⋊C4—114no—
671C2×C4⋊C4—222no—
672C2×C4⋊C4—222no—
673C2×C4⋊C4—222no—
674C2×C4⋊C4—222no—
675C2×C4⋊C4—222no—
676C2×C4⋊C4—222no—
677C2×C4⋊C4—222no—
678C2×C4⋊C4—222no—
679C2×C4⋊C4—222no—
680C2×C4⋊C4—222no—
681C2×C4⋊C4—222no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—114no—
691C2×C22⋊C4—114no—
692C2×C22⋊C4—114no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—222no—
695C2×C22⋊C4—222no—
696C2×C22⋊C4—222no—
697C2×C22⋊C4—222no—
698C2×C22⋊C4—222no—
699C2×C22⋊C4—222no—
700C2×C22⋊C4—222no—
701C2×C22⋊C4—222no—
702C2×C22⋊C4—222no—
703C2×C22⋊C4—222no—
704C2×C22⋊C4—222no—
705C2×C22⋊C4—222no—
706C2×C22⋊C4—222no—
707C2×C22⋊C4—222no—
708C2×C22⋊C4—222no—
709C2×C22⋊C4—222no—
710C2×C22⋊C4—441no—
711C2×C22⋊C4—441no—
712C2×C22⋊C4—441no—
713C2×C22⋊C4—441no—
714C2×C22⋊C4—441no—
715C2×C22⋊C4—441no—
716C2×C22⋊C4—441no—
717C2×C22⋊C4C4×D1114yes—
718C2×C42—22no—
719C2×C42—22no—
720C2×C42—22no—
721C2×C42—114no—
722C2×C42—114no—
723C2×C42—222no—
724C2×C42—222no—
725C2×C42—222no—
726C2×C42—222no—
727C2×C42—222no—
728C2×C42—222no—
729C2×C42—222no—
730C2×C42—222no—
731C2×C42—222no—
732C2×C42—222no—
733#95—22no—
734#95—22no—
735#95—41no—
736#95—222no—
737#95—222no—
738#95—222no—
739#95—222no—
740#95—222no—
741#95—222no—
742#95—441no—
743#95—441no—
744#95—441no—
745C2×C11—82no—
746C2×C11C2×#38611yescharacteristic
747C2×C11C4×#12411yescharacteristic
748C2×C11#232611yescharacteristic
749C2×C11#234111yescharacteristic
750C2×C11#234111yescharacteristic
751C2×C11#236711yescharacteristic
752C2×C11#236711yescharacteristic
753C2×C11#242611yescharacteristic
754C2×C11#242611yescharacteristic
755C2×C11#243111yescharacteristic
756C2×C11#243611yescharacteristic
757C2×C11#244811yescharacteristic
758C2×C11#244811yescharacteristic
759C2×C11#254511yescharacteristic
760C2×C11#254811yescharacteristic
761D11—82no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—112no—
777C24—221no—
778C24—221no—
779C24—221no—
780C24—221no—
781C24—221no—
782C24—221no—
783C24—221no—
784C24—221no—
785C24—221no—
786C24—221no—
787C24—221no—
788C24—221no—
789C24—221no—
790C24—221no—
791C24C2×C4×D1112yes—
792C24C23×D1111yescharacteristic
793C2×Q8—1116no—
794C2×Q8—228no—
795C2×Q8—228no—
796C2×Q8—228no—
797C2×Q8—228no—
798C2×Q8—228no—
799C2×Q8—228no—
800C2×D4—228no—
801C2×D4—228no—
802C2×D4—228no—
803C2×D4—444no—
804C2×D4—444no—
805C2×D4—444no—
806C2×D4—444no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
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—21no—
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—112no—
841C22×C4—112no—
842C22×C4—112no—
843C22×C4—112no—
844C22×C4—112no—
845C22×C4—112no—
846C22×C4—112no—
847C22×C4—112no—
848C22×C4—112no—
849C22×C4—112no—
850C22×C4—112no—
851C22×C4—112no—
852C22×C4—112no—
853C22×C4—112no—
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×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×C4C2×C4×D1112yes—
890C22×C4C2×C4×D1112yes—
891C22×C4#433912yes—
892C22×C4#433912yes—
893C22×C4D4×D1112yes—
894C22×C4D4×D1112yes—
895C22×C4D4×D1112yes—
896C22×C4D4×D1112yes—
897C22×C4#434112yes—
898C4⋊C4—228no—
899C4⋊C4—228no—
900C4⋊C4—228no—
901C4⋊C4—444no—
902C22⋊C4—28no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—228no—
906C22⋊C4—228no—
907C22⋊C4—228no—
908C22⋊C4—444no—
909C22⋊C4—444no—
910C22⋊C4—444no—
911C22⋊C4—444no—
912C22⋊C4—444no—
913C22⋊C4—444no—
914C42—28no—
915C42—228no—
916C42—228no—
917C42—228no—
918C42—444no—
919C11#1402611yescharacteristic, complemented, Sylow
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—222no—
956C23—222no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—441no—
963C23—441no—
964C23—441no—
965C23—441no—
966C23—441no—
967C23—441no—
968C23—441no—
969C23—441no—
970C23—441no—
971C23—441no—
972C23—441no—
973C23—441no—
974C23—441no—
975C23—441no—
976C23—441no—
977C23—441no—
978C23—441no—
979C23—441no—
980C23—441no—
981C23—441no—
982C23—441no—
983C23—441no—
984C23—441no—
985C23—441no—
986C23—441no—
987C23—441no—
988C23—441no—
989C23—441no—
990C23C22×C4×D1111yescharacteristic
991C23C2×#433911yescharacteristic
992C23C2×#433911yescharacteristic
993C23C2×D4×D1111yescharacteristic
994C23C2×D4×D1111yescharacteristic
995C23C2×D4×D1111yescharacteristic
996C23C2×D4×D1111yescharacteristic
997C23C2×#434111yescharacteristic
998C23#6703711yescharacteristic
999C23#41×D1111yescharacteristic
1000C23#41×D1111yescharacteristic
1001C23#41×D1111yescharacteristic
1002C23#6704211yescharacteristic
1003C23#6704311yescharacteristic
1004C23#6704311yescharacteristic
1005Q8—2232no—
1006D4—4416no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—114no—
1048C2×C4—114no—
1049C2×C4—114no—
1050C2×C4—114no—
1051C2×C4—114no—
1052C2×C4—114no—
1053C2×C4—114no—
1054C2×C4—114no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—441no—
1077C2×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—441no—
1086C2×C4—441no—
1087C2×C4—441no—
1088C2×C4—441no—
1089C2×C4—441no—
1090C2×C4—441no—
1091C2×C4—441no—
1092C2×C4—441no—
1093C2×C4—441no—
1094C2×C4—441no—
1095C2×C4—441no—
1096C2×C4C22⋊C4×D1114yes—
1097C2×C4#6693814yescomplemented
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—442no—
1114C22—442no—
1115C22—442no—
1116C22—442no—
1117C22—442no—
1118C22—442no—
1119C22—442no—
1120C22—881no—
1121C22—881no—
1122C22—881no—
1123C22—881no—
1124C22—881no—
1125C22—881no—
1126C22—881no—
1127C22—881no—
1128C22C4×#433911yescharacteristic
1129C22C2×C22⋊C4×D1111yescharacteristic
1130C22#1062302111yescharacteristic
1131C22C2×#6693811yescharacteristic
1132C22#1062305411yescharacteristic
1133C22#1062305911yescharacteristic
1134C22#1062306411yescharacteristic
1135C22C4×#434111yescharacteristic
1136C22#1062306911yescharacteristic
1137C22C4×D4×D1111yescharacteristic
1138C22C4×D4×D1111yescharacteristic
1139C22#1062307711yescharacteristic
1140C22#1062307911yescharacteristic
1141C22#1062308311yescharacteristic
1142C22#1062308311yescharacteristic
1143C22#1062308311yescharacteristic
1144C22#1062308411yescharacteristic
1145C22#1062308411yescharacteristic
1146C22#1062309011yescharacteristic
1147C22D11×#12011yescharacteristic
1148C22#1062312911yescharacteristic
1149C22#1062312911yescharacteristic
1150C22#1062313011yescharacteristic
1151C22D11×#12111yescharacteristic
1152C22D11×#12111yescharacteristic
1153C22#1062313811yescharacteristic
1154C22#1062317911yescharacteristic
1155C22D11×#12311yescharacteristic
1156C22#1062318511yescharacteristic
1157C22#1062320011yescharacteristic
1158C22#1062320811yescharacteristic
1159C22#1062321211yescharacteristic
1160C22#1062323311yescharacteristic
1161C22#1062324111yescharacteristic
1162C22#1062324911yescharacteristic
1163C4—24no—
1164C4—24no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—81no—
1169C4—118no—
1170C4—224no—
1171C4—442no—
1172C4—442no—
1173C4—442no—
1174C4—442no—
1175C4—881no—
1176C2—82no—
1177C2—882no—
1178C2D11×#38611yescharacteristic
1179C2C4×#6693811yescharacteristic
1180C2#1307132511yescharacteristic
1181C2#1307145511yescharacteristic
1182C2#1307145611yescharacteristic
1183C2#1307168811yescharacteristic
1184C2#1307169011yescharacteristic
1185C2#1307217911yescharacteristic
1186C2#1307218111yescharacteristic
1187C2#1307223311yescharacteristic
1188C2#1307227211yescharacteristic
1189C2#1307241111yescharacteristic
1190C2#1307241311yescharacteristic
1191C2#1307359411yescharacteristic
1192C2#1307361711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1437D11
hypocenterC11#14026
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
3. C2×#10622259C2semidirect
6. #13066862C2semidirect
7. #13066861C2semidirect
8. #13066860C2semidirect
9. #13066859C2semidirect
10. #13066854C2semidirect
11. #13066853C2semidirect
12. #13066852C2semidirect
13. Dic11⋊#95C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1437C2semidirect
41. C2×#66938C4semidirect
302. C2×Dic22C22⋊C4semidirect
336. #1437D11semidirect
465. C2×C4×C11#124semidirect
919. C11#14026semidirect
1097. C2×C4#66938semidirect

Maximal subgroups

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

subgroupindex
C22×#669382
C22×C4×Dic222
C2×#106222592
C2×#106225702
#130668622
#130668612
#130668602
#130668592
#130668542
#130668532
#130668522
Dic11⋊#952
#95×Dic112
C11×#14372
#1402611