Finite Group Databasebeta

← #14680669

Subgroups — #14680669

Order 2816.

1766 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×#10622574C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic
3C2×#10622564C211yesmaximal, characteristic, complemented
4C2×#10622282C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
6#13066880C211yesmaximal, characteristic, complemented
7#13066868C211yesmaximal, characteristic, complemented
8#13066862C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066858C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic
12#13066853C211yesmaximal, characteristic, complemented
13#13066852C211yesmaximal, characteristic, complemented
14#13066840C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
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
51C4⋊C4×Dic11—24no—
52#10622574C418yescomplemented
53#10622570—24no—
54#10622564—24no—
55#10622282—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—41no—
67C22×C22⋊D11—41no—
68C22×C22⋊D11—41no—
69C22×C22⋊D11—41no—
70C22×C22⋊D11C2×C414yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4—41no—
87C2×C11×C22⋊C4—41no—
88C2×C11×C22⋊C4—41no—
89C2×C11×C22⋊C4C2×C414yes—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—41no—
95C2×C22⋊Dic11—41no—
96C2×C22⋊Dic11—41no—
97C2×C22⋊Dic11—41no—
98C2×C22⋊Dic11C2×C414yes—
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—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
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)⋊C4—41no—
113C2×(C2×D11)⋊C4—41no—
114C2×(C2×D11)⋊C4—41no—
115C2×(C2×D11)⋊C4C2×C414yes—
116C2×(C2×D11)⋊C4C2×C414yes—
117C2×C4⋊Dic11—22no—
118C2×C4⋊Dic11—22no—
119C2×C4⋊Dic11—22no—
120C2×C4⋊Dic11—41no—
121C2×C4⋊Dic11—41no—
122C2×C4⋊Dic11C2×C414yes—
123C2×Dic11⋊C4—22no—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4—41no—
126C2×Dic11⋊C4—41no—
127C2×Dic11⋊C4—41no—
128C2×Dic11⋊C4—41no—
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×Dic11D414yes—
137C2×C4×Dic11D414yescomplemented
138C11×#95—22no—
139C11×#95—41no—
140C11×#95—41no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95C2×C414yes—
152#14312—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×C11C22×C412yes—
221C22×C4×C11C22×C412yes—
222C22×C4×C11C2×D412yes—
223C22×C4×C11C2×D412yes—
224C22×C4×C11#4112yes—
225C22×C4×C11#4112yes—
226C2×C22⋊D11—28no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—44no—
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×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11C22×C412yes—
274C22×Dic11C22×C412yes—
275C22×Dic11C22×C412yes—
276C22×Dic11C2×D412yes—
277C22×Dic11C2×D412yes—
278C22×Dic11C2×D412yes—
279C22×Dic11C2×D412yes—
280C22×Dic11#4112yes—
281C22×Dic11#4112yes—
282C11×C4⋊C4—28no—
283C11×C22⋊C4—28no—
284C11×C22⋊C4—44no—
285C11×C22⋊C4—44no—
286C22⋊Dic11—44no—
287C22⋊Dic11—44no—
288C22⋊Dic11—44no—
289(C2×D11)⋊C4—28no—
290(C2×D11)⋊C4—44no—
291(C2×D11)⋊C4—44no—
292(C2×D11)⋊C4—44no—
293(C2×D11)⋊C4—44no—
294(C2×D11)⋊C4—44no—
295C4⋊Dic11—28no—
296C4⋊Dic11—44no—
297Dic11⋊C4—44no—
298Dic11⋊C4—44no—
299C4×Dic11—28no—
300C4×Dic11—44no—
301C4×Dic11—44no—
302C2×#394—111no—
303C2×#390—111no—
304C2×#388—111no—
305C2×#388—111no—
306C2×C4×C4⋊C4—111no—
307#1444—111no—
308#1441—111no—
309#1439—111no—
310#1439—111no—
311#1439—111no—
312#1439D1111yescharacteristic, complemented
313#1438—111no—
314#1437—111no—
315#1437—111no—
316#1434—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×C11H(5,𝔽2)11yescharacteristic
360C23×C11H(5,𝔽2)11yescharacteristic
361C23×C11H(5,𝔽2)11yescharacteristic
362C23×C11H(5,𝔽2)11yescharacteristic
363C23×C11H(5,𝔽2)11yescharacteristic
364C23×C11H(5,𝔽2)11yescharacteristic
365C23×C112−1+411yescharacteristic
366C23×C112−1+411yescharacteristic
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×C11C4×D414yes—
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—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
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—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11C4×D414yes—
493C2×Dic11#12114yes—
494C23×D4—111no—
495C22×C4⋊C4—111no—
496C22×C4⋊C4—111no—
497C22×C4⋊C4—111no—
498C22×C4⋊C4—111no—
499C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
508C22×C22⋊C4—111no—
509C22×C22⋊C4C2×D1111yescharacteristic
510C22×C22⋊C4C2×D1111yescharacteristic
511C22×C22⋊C4C2×D1111yescharacteristic
512C22×C42—111no—
513C22×C42—111no—
514C22×C42—111no—
515#394—118no—
516#390—224no—
517#388—224no—
518#388—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×#95—111no—
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×C4×D411yescharacteristic
550C22×C11C2×C4×D411yescharacteristic
551C22×C11C4×#4111yescharacteristic
552C22×C11#51811yescharacteristic
553C22×C11#51811yescharacteristic
554C22×C11#52011yescharacteristic
555C22×C11#52011yescharacteristic
556C22×C11C2×#12111yescharacteristic
557C22×C11#52511yescharacteristic
558C22×C11#52911yescharacteristic
559C22×C11#53211yescharacteristic
560C22×C11#53411yescharacteristic
561C22×C11#53511yescharacteristic
562C22×C11#53511yescharacteristic
563C22×C11#53511yescharacteristic
564C22×C11#53511yescharacteristic
565C22×C11#53611yescharacteristic
566C22×C11#53711yescharacteristic
567C22×C11#53711yescharacteristic
568C22×C11#53811yescharacteristic
569C22×C11#53811yescharacteristic
570C22×C11#53811yescharacteristic
571C22×C11#53811yescharacteristic
572C22×C11#53911yescharacteristic
573C22×C11#53911yescharacteristic
574C22×C11#54011yescharacteristic
575C22×C11#54011yescharacteristic
576C22×C11#54011yescharacteristic
577C22×C11#54011yescharacteristic
578C22×C11#54211yescharacteristic
579C22×C11#54211yescharacteristic
580C22×C11#54211yescharacteristic
581C22×C11#54211yescharacteristic
582C22×C11#54211yescharacteristic
583C22×C11#54211yescharacteristic
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—24no—
600C4×C11—42no—
601C4×C11—42no—
602C4×C11—42no—
603C4×C11—81no—
604C4×C11—81no—
605Dic11—24no—
606Dic11—24no—
607Dic11—42no—
608Dic11—42no—
609Dic11—42no—
610Dic11—81no—
611Dic11—81no—
612C25—111no—
613C25C22×D1111yescharacteristic
614C22×D4—114no—
615C22×D4—222no—
616C22×D4—222no—
617C22×D4—441no—
618C22×D4—441no—
619C22×D4—441no—
620C22×D4—441no—
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—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—114no—
638C2×C4⋊C4—222no—
639C2×C4⋊C4—222no—
640C2×C4⋊C4—222no—
641C2×C4⋊C4—222no—
642C2×C4⋊C4—222no—
643C2×C4⋊C4—441no—
644C2×C4⋊C4—441no—
645C2×C4⋊C4—441no—
646C2×C4⋊C4—441no—
647C2×C4⋊C4—441no—
648C2×C4⋊C4—441no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4—41no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—114no—
658C2×C22⋊C4—114no—
659C2×C22⋊C4—114no—
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—222no—
668C2×C22⋊C4—222no—
669C2×C22⋊C4—222no—
670C2×C22⋊C4—222no—
671C2×C22⋊C4—222no—
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⋊C4—441no—
679C2×C22⋊C4—441no—
680C2×C22⋊C4—441no—
681C2×C22⋊C4—441no—
682C2×C22⋊C4—441no—
683C2×C22⋊C4—441no—
684C2×C22⋊C4C4×D1114yes—
685C2×C42—114no—
686C2×C42—114no—
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—41no—
696#95—41no—
697#95—114no—
698#95—222no—
699#95—222no—
700#95—222no—
701#95—222no—
702#95—222no—
703#95—222no—
704#95—441no—
705#95—441no—
706#95—441no—
707#95—441no—
708C2×C11—82no—
709C2×C11C4×#12111yescharacteristic
710C2×C11#232111yescharacteristic
711C2×C11#232411yescharacteristic
712C2×C11#232411yescharacteristic
713C2×C11#232611yescharacteristic
714C2×C11#233511yescharacteristic
715C2×C11#233511yescharacteristic
716C2×C11#261811yescharacteristic
717C2×C11#261911yescharacteristic
718C2×C11#263211yescharacteristic
719C2×C11#263511yescharacteristic
720C2×C11#265111yescharacteristic
721C2×C11#265111yescharacteristic
722C2×C11#266211yescharacteristic
723C2×C11#266211yescharacteristic
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—444no—
758C2×D4—444no—
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—112no—
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—221no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×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×C4C2×C4×D1112yes—
849C22×C4C2×C4×D1112yes—
850C22×C4D4×D1112yes—
851C22×C4D4×D1112yes—
852C22×C4#434112yes—
853C22×C4#434112yes—
854C4⋊C4—28no—
855C4⋊C4—228no—
856C4⋊C4—444no—
857C4⋊C4—444no—
858C4⋊C4—444no—
859C22⋊C4—28no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—228no—
863C22⋊C4—444no—
864C22⋊C4—444no—
865C22⋊C4—444no—
866C22⋊C4—444no—
867C22⋊C4—444no—
868C22⋊C4—444no—
869C22⋊C4—444no—
870C22⋊C4—444no—
871C42—228no—
872C42—444no—
873C42—444no—
874C11#1431211yescharacteristic, 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
949C23C2×#434111yescharacteristic
950C23#6703711yescharacteristic
951C23#6703711yescharacteristic
952C23#6703711yescharacteristic
953C23#6704011yescharacteristic
954C23#41×D1111yescharacteristic
955C23#41×D1111yescharacteristic
956C23#6704211yescharacteristic
957C23#6704211yescharacteristic
958C23#6704211yescharacteristic
959C23#6704311yescharacteristic
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—114no—
1003C2×C4—114no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
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—441no—
1026C2×C4—441no—
1027C2×C4—441no—
1028C2×C4—441no—
1029C2×C4—441no—
1030C2×C4—441no—
1031C2×C4—441no—
1032C2×C4—441no—
1033C2×C4—441no—
1034C2×C4—441no—
1035C2×C4—441no—
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(C22⋊D11)⋊C414yes—
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—
1082C22C2×(C22⋊D11)⋊C411yescharacteristic
1083C22#1062303511yescharacteristic
1084C22#1062305211yescharacteristic
1085C22C4×#434111yescharacteristic
1086C22C4×D4×D1111yescharacteristic
1087C22#1062307611yescharacteristic
1088C22#1062307711yescharacteristic
1089C22#1062311711yescharacteristic
1090C22#1062312311yescharacteristic
1091C22#1062312411yescharacteristic
1092C22#1062312711yescharacteristic
1093C22D11×#12111yescharacteristic
1094C22#1062313611yescharacteristic
1095C22#1062313811yescharacteristic
1096C22#1062313811yescharacteristic
1097C22#1062313911yescharacteristic
1098C22#1062314811yescharacteristic
1099C22#1062315011yescharacteristic
1100C22#1062315911yescharacteristic
1101C22#1062316011yescharacteristic
1102C22#1062316911yescharacteristic
1103C22#1062317111yescharacteristic
1104C22#1062317411yescharacteristic
1105C22#1062317411yescharacteristic
1106C22#1062318011yescharacteristic
1107C22#1062318811yescharacteristic
1108C22#1062319311yescharacteristic
1109C22#1062319411yescharacteristic
1110C22#1062319411yescharacteristic
1111C22#1062320511yescharacteristic
1112C22#1062321311yescharacteristic
1113C22#1062321311yescharacteristic
1114C22#1062323511yescharacteristic
1115C22#1062323811yescharacteristic
1116C22#1062325011yescharacteristic
1117C4—24no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—81no—
1122C4—81no—
1123C4—224no—
1124C4—224no—
1125C4—442no—
1126C4—442no—
1127C4—442no—
1128C4—881no—
1129C4—881no—
1130C2—82no—
1131C2—882no—
1132C2#1307112611yescharacteristic
1133C2#1307126911yescharacteristic
1134C2#1307130511yescharacteristic
1135C2#1307131211yescharacteristic
1136C2#1307132211yescharacteristic
1137C2#1307139911yescharacteristic
1138C2#1307140111yescharacteristic
1139C2#1307436311yescharacteristic
1140C2#1307436811yescharacteristic
1141C2#1307447511yescharacteristic
1142C2#1307449911yescharacteristic
1143C2#1307464211yescharacteristic
1144C2#1307464411yescharacteristic
1145C2#1307475211yescharacteristic
1146C2#1307475411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14312
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#10622564C2semidirect
4. C2×#10622282C2semidirect
5. C2×C4⋊C4×Dic11C2semidirect
6. #13066880C2semidirect
7. #13066868C2semidirect
8. #13066862C2semidirect
9. #13066859C2semidirect
10. #13066858C2semidirect
12. #13066853C2semidirect
13. #13066852C2semidirect
14. #13066840C2semidirect
15. C11×#1439C2semidirect
52. #10622574C4semidirect
137. C2×C4×Dic11D4semidirect
312. #1439D11semidirect
874. C11#14312semidirect

Maximal subgroups

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

subgroupindex
C2×#106225742
C2×#106225702
C2×#106225642
C2×#106222822
C2×C4⋊C4×Dic112
#130668802
#130668682
#130668622
#130668592
#130668582
#130668552
#130668532
#130668522
#130668402
C11×#14392
#1431211