Finite Group Databasebeta

← #14682268

Subgroups — #14682268

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic
2C2×#10622266C211yesmaximal, characteristic, complemented
3C2×#10622267C211yesmaximal, characteristic, complemented
4#13066887C211yesmaximal, characteristic, complemented
5#13066882C211yesmaximal, characteristic, complemented
6#13066882C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic
8#13066860C211yesmaximal, characteristic
9#13066852C211yesmaximal, characteristic
10#13066852C211yesmaximal, characteristic
11Dic11⋊#95C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1446C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×#66999—24no—
19C2×#66999—24no—
20C2×#66999C418yescomplemented
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×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622267—24no—
55#10622266—24no—
56C24×D11C2311yescharacteristic
57C22×Q8×C11—22no—
58C22×Q8×C11—22no—
59C22×Q8×C11—41no—
60C22×Q8×C11—41no—
61C22×Q8×C11—41no—
62C22×Q8×C11—41no—
63C22×Q8×C11C2×C414yes—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—41no—
81C22×C4×D11—41no—
82C22×C4×D11—41no—
83C22×C4×D11—41no—
84C22×C4×D11C2×C414yes—
85#66999—232no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
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)⋊C4C2×C414yes—
102C2×(C2×D11)⋊C4C2×C414yes—
103C2×(C2×D11)⋊C4Q814yescomplemented
104C2×C4⋊Dic11C2×C414yes—
105C2×C4⋊Dic11D414yes—
106C2×C4⋊Dic11D414yes—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—41no—
116C2×Dic11⋊C4—41no—
117C2×Dic11⋊C4C2×C414yes—
118C2×Dic11⋊C4C2×C414yes—
119C2×C4×Dic11—22no—
120C2×C4×Dic11—22no—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—41no—
124C2×C4×Dic11—41no—
125C11×#95—22no—
126C11×#95—22no—
127C11×#95—41no—
128C11×#95—41no—
129C11×#95—41no—
130C11×#95—41no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145#14448—111nomaximal, Sylow
146C24×C11C2411yescharacteristic
147C23×D11—21no—
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×D11C22×C412yes—
160C23×D11C2×Q812yes—
161C23×D11#4112yes—
162C2×Q8×C11—28no—
163C2×Q8×C11—44no—
164C2×Q8×C11—44no—
165C2×Q8×C11—44no—
166C2×Q8×C11—44no—
167C2×Q8×C11—44no—
168C2×Q8×C11—44no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
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×C11C22×C412yes—
212C22×C4×C11C22×C412yes—
213C22×C4×C11C22×C412yes—
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2×Q812yes—
217C22×C4×C11#4112yes—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
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×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C22×C412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×D412yes—
264C22×Dic11C2×D412yes—
265C22×Dic11C2×Q812yes—
266C22×Dic11#4112yes—
267C2×C4×D11—28no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11—44no—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—44no—
277(C2×D11)⋊C4—44no—
278(C2×D11)⋊C4—44no—
279(C2×D11)⋊C4—44no—
280C4⋊Dic11C22⋊C4116yescomplemented
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4—44no—
284Dic11⋊C4—44no—
285C4×Dic11—44no—
286C4×Dic11—44no—
287C22×C22⋊Q8—111no—
288C2×#387—111no—
289C2×#387—111no—
290#1446—111no—
291#1446D1111yescharacteristic, complemented
292#1445—111no—
293#1445—111no—
294#1439—111no—
295#1439—111no—
296#1437—111no—
297#1437—111no—
298C4⋊#95—111no—
299C4⋊#95—111no—
300C22⋊#95—111no—
301C22⋊#95—111no—
302C23×C11C23×C411yescharacteristic
303C23×C11C22×D411yescharacteristic
304C23×C11C22×D411yescharacteristic
305C23×C11C22×Q811yescharacteristic
306C23×C11C2×#4111yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11C2×#4111yescharacteristic
309C23×C11H(5,𝔽2)11yescharacteristic
310C23×C11H(5,𝔽2)11yescharacteristic
311C23×C11H(5,𝔽2)11yescharacteristic
312C23×C11H(5,𝔽2)11yescharacteristic
313C23×C11H(5,𝔽2)11yescharacteristic
314C23×C112−1+411yescharacteristic
315C23×C112−1+411yescharacteristic
316C23×C112−1+411yescharacteristic
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
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—41no—
336C22×D11—41no—
337C22×D11—41no—
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×D11C4×Q814yes—
352Q8×C11—416no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11C2×C22⋊C414yes—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11C2×C22⋊C414yes—
450C2×Dic11C2×C22⋊C414yes—
451C4×D11—416no—
452C23×Q8C2×D1111yescharacteristic
453C24×C4—111no—
454C2×C22⋊Q8—118no—
455C2×C22⋊Q8—224no—
456C2×C22⋊Q8—224no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
461C22×C4⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C42—111no—
469C22×C42—111no—
470#387—224no—
471#387—224no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95C2×D1111yescharacteristic
487C2×#95C2×D1111yescharacteristic
488C2×#95C2×D1111yescharacteristic
489C2×#95C2×D1111yescharacteristic
490C2×#95C2×D1111yescharacteristic
491C2×#95C2×D1111yescharacteristic
492C22×C11C22×C22⋊C411yescharacteristic
493C22×C11C2×C4×Q811yescharacteristic
494C22×C11C4×#4111yescharacteristic
495C22×C11#51811yescharacteristic
496C22×C11#51811yescharacteristic
497C22×C11#51911yescharacteristic
498C22×C11#52011yescharacteristic
499C22×C11#53511yescharacteristic
500C22×C11#53511yescharacteristic
501C22×C11#53511yescharacteristic
502C22×C11#53511yescharacteristic
503C22×C11#53811yescharacteristic
504C22×C11#53911yescharacteristic
505C22×C11#53911yescharacteristic
506C22×C11#53911yescharacteristic
507C22×C11#54211yescharacteristic
508C22×C11#54211yescharacteristic
509C22×C11#54311yescharacteristic
510C22×C11#54411yescharacteristic
511C22×C11#54611yescharacteristic
512C22×C11#54611yescharacteristic
513C22×C11#54711yescharacteristic
514C22×C11#54711yescharacteristic
515C22×C11#54811yescharacteristic
516C22×C11#54811yescharacteristic
517C22×C11D4×Q811yescharacteristic
518C22×C11D4×Q811yescharacteristic
519C22×C11#55111yescharacteristic
520C22×C11#55111yescharacteristic
521C22×C11#55411yescharacteristic
522C22×C11#55411yescharacteristic
523C22×C11#56211yescharacteristic
524C22×C11#56211yescharacteristic
525C22×C11#56311yescharacteristic
526C22×C11#56311yescharacteristic
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C4×C11—24no—
543C4×C11—42no—
544C4×C11—42no—
545C4×C11—42no—
546C4×C11—42no—
547C4×C11—81no—
548C4×C11—81no—
549Dic11—24no—
550Dic11—24no—
551Dic11—42no—
552Dic11—42no—
553Dic11—42no—
554Dic11—81no—
555Dic11—81no—
556C25—111no—
557C22×Q8—22no—
558C22×Q8—22no—
559C22×Q8—41no—
560C22×Q8—41no—
561C22×Q8—41no—
562C22×Q8—41no—
563C22×Q8C4×D1114yes—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—114no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—222no—
573C23×C4—222no—
574C23×C4—441no—
575C23×C4—441no—
576C23×C4—441no—
577C23×C4—441no—
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582C23×C4C22×D1111yescharacteristic
583C23×C4C22×D1111yescharacteristic
584C23×C4C22×D1111yescharacteristic
585C22⋊Q8—2232no—
586C2×C4⋊C4—114no—
587C2×C4⋊C4—114no—
588C2×C4⋊C4—114no—
589C2×C4⋊C4—114no—
590C2×C4⋊C4—114no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—222no—
596C2×C4⋊C4—222no—
597C2×C4⋊C4—222no—
598C2×C4⋊C4—222no—
599C2×C4⋊C4—441no—
600C2×C4⋊C4—441no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—222no—
605C2×C22⋊C4—222no—
606C2×C22⋊C4—222no—
607C2×C22⋊C4—222no—
608C2×C22⋊C4—222no—
609C2×C22⋊C4—222no—
610C2×C22⋊C4—222no—
611C2×C22⋊C4—222no—
612C2×C22⋊C4—222no—
613C2×C22⋊C4—441no—
614C2×C22⋊C4—441no—
615C2×C22⋊C4—441no—
616C2×C22⋊C4—441no—
617C2×C22⋊C4—441no—
618C2×C22⋊C4—441no—
619C2×C42—222no—
620C2×C42—222no—
621C2×C42—222no—
622C2×C42—222no—
623C2×C42—441no—
624C2×C42—441no—
625#95—22no—
626#95—22no—
627#95—41no—
628#95—41no—
629#95—41no—
630#95—41no—
631#95—222no—
632#95—222no—
633#95—222no—
634#95—222no—
635#95—222no—
636#95—222no—
637#95—441no—
638#95—441no—
639#95—441no—
640#95—441no—
641#95—441no—
642#95—441no—
643#95—441no—
644#95—441no—
645C2×C11#230911yescharacteristic
646C2×C11#232911yescharacteristic
647C2×C11#233211yescharacteristic
648C2×C11#233911yescharacteristic
649C2×C11Q8×C22⋊C411yescharacteristic
650C2×C11#236811yescharacteristic
651C2×C11#237811yescharacteristic
652C2×C11#269211yescharacteristic
653C2×C11#269211yescharacteristic
654C2×C11#269611yescharacteristic
655C2×C11#269611yescharacteristic
656C2×C11#272011yescharacteristic
657C2×C11#272011yescharacteristic
658C2×C11#272311yescharacteristic
659C2×C11#272311yescharacteristic
660D11—44no—
661C24—112no—
662C24—112no—
663C24—112no—
664C24—221no—
665C24—221no—
666C24—221no—
667C24—221no—
668C24—221no—
669C24—221no—
670C24—221no—
671C24—221no—
672C24—221no—
673C24—221no—
674C24—221no—
675C24—221no—
676C24C23×D1111yescharacteristic
677C2×Q8—28no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—44no—
682C2×Q8—44no—
683C2×Q8—44no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—112no—
733C22×C4—112no—
734C22×C4—112no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—228no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—444no—
777C22×C4—444no—
778C22×C4—444no—
779C22×C4—444no—
780C22×C4—444no—
781C22×C4—444no—
782C22×C4C2×C4×D1112yes—
783C22×C4C2×C4×D1112yes—
784C22×C4C2×C4×D1112yes—
785C22×C4D4×D1112yes—
786C22×C4D4×D1112yes—
787C22×C4Q8×D1112yes—
788C22×C4#434312yes—
789C4⋊C4—1116no—
790C4⋊C4—228no—
791C4⋊C4—228no—
792C4⋊C4—444no—
793C4⋊C4—444no—
794C22⋊C4—228no—
795C22⋊C4—228no—
796C22⋊C4—444no—
797C22⋊C4—444no—
798C22⋊C4—444no—
799C22⋊C4—444no—
800C42—444no—
801C42—444no—
802C11#1444811yescharacteristic, complemented, Sylow
803C23—114no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—222no—
816C23—222no—
817C23—222no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—441no—
823C23—441no—
824C23—441no—
825C23—441no—
826C23—441no—
827C23—441no—
828C23—441no—
829C23—441no—
830C23—441no—
831C23—441no—
832C23—441no—
833C23—441no—
834C23—441no—
835C23—441no—
836C23—441no—
837C23—441no—
838C23C22×C4×D1111yescharacteristic
839C23C2×D4×D1111yescharacteristic
840C23C2×D4×D1111yescharacteristic
841C23#6703711yescharacteristic
842C23#6703711yescharacteristic
843C23#6703711yescharacteristic
844C23#6703711yescharacteristic
845C23C2×Q8×D1111yescharacteristic
846C23C2×#434311yescharacteristic
847C23#6704011yescharacteristic
848C23#6704011yescharacteristic
849C23#41×D1111yescharacteristic
850C23#41×D1111yescharacteristic
851C23#6704211yescharacteristic
852C23#6704311yescharacteristic
853Q8—416no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—114no—
903C2×C4—114no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—4416no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4—441no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—441no—
952C2×C4C22⋊C4×D1114yes—
953C22—224no—
954C22—224no—
955C22—224no—
956C22—442no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22—442no—
961C22—442no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—442no—
966C22—442no—
967C22—442no—
968C22C2×C22⋊C4×D1111yescharacteristic
969C22#1062301711yescharacteristic
970C22#1062301711yescharacteristic
971C22C4×Q8×D1111yescharacteristic
972C22#1062310311yescharacteristic
973C22C4×#434311yescharacteristic
974C22#1062310511yescharacteristic
975C22#1062312311yescharacteristic
976C22#1062312311yescharacteristic
977C22#1062312311yescharacteristic
978C22#1062312311yescharacteristic
979C22#1062316111yescharacteristic
980C22#1062316211yescharacteristic
981C22#1062316311yescharacteristic
982C22#1062316411yescharacteristic
983C22#1062316511yescharacteristic
984C22#1062316711yescharacteristic
985C22#1062316811yescharacteristic
986C22#1062316911yescharacteristic
987C22#1062316911yescharacteristic
988C22#1062317611yescharacteristic
989C22#1062317711yescharacteristic
990C22#1062317811yescharacteristic
991C22#1062320011yescharacteristic
992C22#1062320711yescharacteristic
993C22#1062320811yescharacteristic
994C22#1062320911yescharacteristic
995C22#1062321011yescharacteristic
996C22#1062321511yescharacteristic
997C22#1062325711yescharacteristic
998C22#1062325811yescharacteristic
999C22#1062326011yescharacteristic
1000C22#1062326111yescharacteristic
1001C22#1062326411yescharacteristic
1002C22#1062326611yescharacteristic
1003C4—24no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—81no—
1009C4—81no—
1010C4—224no—
1011C4—224no—
1012C4—442no—
1013C4—442no—
1014C4—442no—
1015C4—881no—
1016C4—881no—
1017C2—444no—
1018C2#1307119711yescharacteristic
1019C2#1307134811yescharacteristic
1020C2#1307137111yescharacteristic
1021C2#1307144511yescharacteristic
1022C2#1307145011yescharacteristic
1023C2#1307169511yescharacteristic
1024C2#1307177711yescharacteristic
1025C2#1307511711yescharacteristic
1026C2#1307511911yescharacteristic
1027C2#1307517111yescharacteristic
1028C2#1307517311yescharacteristic
1029C2#1307550111yescharacteristic
1030C2#1307550311yescharacteristic
1031C2#1307554011yescharacteristic
1032C2#1307554211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1446C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1446D11
hypocenterC11#14448
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
2. C2×#10622266C2semidirect
3. C2×#10622267C2semidirect
4. #13066887C2semidirect
5. #13066882C2semidirect
6. #13066882C2semidirect
11. Dic11⋊#95C2semidirect
12. Dic11⋊#95C2semidirect
15. C11×#1446C2semidirect
20. C2×#66999C4semidirect
103. C2×(C2×D11)⋊C4Q8semidirect
280. C4⋊Dic11C22⋊C4semidirect
291. #1446D11semidirect
802. C11#14448semidirect

Maximal subgroups

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

subgroupindex
C22×#669992
C2×#106222662
C2×#106222672
#130668872
#130668822
#130668602
#130668522
Dic11⋊#952
(C2×D11)⋊#952
C11×#14462
#1444811