Finite Group Databasebeta

← C2×#13074507 #14920170

Subgroups — C2×#13074507 #14920170

Order 2816.

3606 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic, complemented
2C22×C4×D44C211yesmaximal, characteristic, complemented
3#13074507C2116yesmaximal, direct product factor
4C2×#10622273C211yesmaximal, characteristic, complemented
5C2×#10622605C211yesmaximal, characteristic, complemented
6C2×#10622604C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622284C211yesmaximal, characteristic, complemented
10C2×#10622573C211yesmaximal, characteristic, complemented
11C2×#10622573C211yesmaximal, characteristic, complemented
12C2×#10622553C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622277C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×C4⋊Dic11C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C2×#66937—28no—
45C2×#66937C2218yescomplemented
46C2×C4×D44—28no—
47C2×C4×D44C2218yescomplemented
48C11×#388C2218yescomplemented
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#10622605C2218yescomplemented
58#10622604C2218yescomplemented
59#10622574C2218yescomplemented
60#10622573C2218yescomplemented
61#10622573C2218yescomplemented
62#10622572C2218yescomplemented
63#10622569C2218yescomplemented
64#10622553C2218yescomplemented
65#10622284C2218yescomplemented
66#10622278C2218yescomplemented
67#10622277C2218yescomplemented
68#10622273C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—24no—
80C22×C22⋊D11—24no—
81C22×C22⋊D11—24no—
82C22×C22⋊D11—42no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11—42no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11—42no—
88C22×C22⋊D11C2314yes—
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C22×D44—24no—
97C22×D44—24no—
98C22×D44—24no—
99C22×D44—24no—
100C22×D44—24no—
101C22×D44—42no—
102C22×D44—42no—
103C22×D44—42no—
104C22×D44—42no—
105C22×D44C2314yes—
106C22×D44C2314yes—
107C22×D44C2314yes—
108C22×C4×D11—24no—
109C22×C4×D11—42no—
110C22×C4×D11—42no—
111C22×C4×D11—42no—
112C22×C4×D11—42no—
113C22×C4×D11D418yescomplemented
114C22×C4×D11C2314yes—
115C22×C4×D11C2314yes—
116C2×C11×C4⋊C4—42no—
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—42no—
121C2×C11×C22⋊C4C2314yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C42×C11—24no—
125C2×C42×C11C2314yes—
126C2×C22⋊Dic11—42no—
127C2×C22⋊Dic11C2314yes—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—42no—
133C2×(C2×D11)⋊C4—42no—
134C2×(C2×D11)⋊C4—42no—
135C2×(C2×D11)⋊C4—42no—
136C2×(C2×D11)⋊C4—42no—
137C2×(C2×D11)⋊C4—42no—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×C4⋊Dic11—24no—
149C2×C4⋊Dic11C2314yes—
150C2×Dic11⋊C4—24no—
151C2×Dic11⋊C4—42no—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154#66937—232no—
155C4×D44—232no—
156C11×#95C2314yes—
157C11×#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2635—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11C2412yes—
173C24×C11C2411yescharacteristic
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11C2×D414yes—
194C23×D11#4114yes—
195C23×D11C2412yes—
196C23×D11C2412yes—
197C23×D11C2412yes—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11C2×D414yes—
215C22×C4×C11#4114yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C2×C22⋊D11—28no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—28no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—416no—
232C2×C22⋊D11—416no—
233C2×C22⋊D11—416no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11C2×D414yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C2×D44—232no—
255C2×D44—28no—
256C2×D44—28no—
257C2×D44—28no—
258C2×D44—28no—
259C2×D44—28no—
260C2×D44—44no—
261C2×D44—44no—
262C2×D44—44no—
263C2×D44—44no—
264C2×D44—416no—
265C2×D44—416no—
266C2×C4×D11—28no—
267C2×C4×D11—416no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C2×C4×D11—416no—
273C2×C4×D11C2×D4116yescomplemented
274C11×C4⋊C4—44no—
275C11×C22⋊C4—28no—
276C11×C22⋊C4—28no—
277C11×C22⋊C4—44no—
278C42×C11—28no—
279C22⋊Dic11—44no—
280(C2×D11)⋊C4—28no—
281(C2×D11)⋊C4—28no—
282(C2×D11)⋊C4—28no—
283(C2×D11)⋊C4—28no—
284(C2×D11)⋊C4—44no—
285(C2×D11)⋊C4—44no—
286(C2×D11)⋊C4—44no—
287(C2×D11)⋊C4—44no—
288(C2×D11)⋊C4—44no—
289(C2×D11)⋊C4—44no—
290C4⋊Dic11—28no—
291Dic11⋊C4—28no—
292Dic11⋊C4—44no—
293C22×#121—111no—
294C22×C4×D4—111no—
295#2635—1116no—
296C2×#400—111no—
297C2×#399—111no—
298C2×#394—111no—
299C2×#394—111no—
300C2×#394—111no—
301C2×#392—111no—
302C2×#392—111no—
303C2×#392—111no—
304C2×#388—111no—
305C2×#388D1111yescharacteristic, complemented
306C2×#386—111no—
307C2×#386—111no—
308C2×#381—111no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11—44no—
319C23×C11—44no—
320C23×C11—44no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11C22×D412yes—
324C23×C11C2×#4112yes—
325C23×C11C2×#4112yes—
326C23×C11H(5,𝔽2)12yes—
327C23×C11H(5,𝔽2)12yes—
328C23×C11H(5,𝔽2)12yes—
329C23×C11H(5,𝔽2)12yes—
330C23×C11C2511yescharacteristic
331C22×D11—28no—
332C22×D11—28no—
333C22×D11—28no—
334C22×D11—28no—
335C22×D11—28no—
336C22×D11—28no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—44no—
357C22×D11—44no—
358C22×D11—44no—
359C22×D11—44no—
360C22×D11—44no—
361C22×D11—44no—
362C22×D11—44no—
363C22×D11—44no—
364C22×D11—44no—
365C22×D11—44no—
366C22×D11—44no—
367C22×D11—44no—
368C22×D11—44no—
369C22×D11—44no—
370C22×D11—44no—
371C22×D11C22×D414yes—
372C22×D11C2×#4114yes—
373C2×C4×C11—28no—
374C2×C4×C11—28no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—44no—
392C2×C4×C11—44no—
393C2×C4×C11—44no—
394C2×C4×C11—44no—
395C2×C4×C11C22×D414yes—
396C2×C4×C11C2×#4114yes—
397C22⋊D11—416no—
398C22⋊D11—416no—
399C22⋊D11—416no—
400C2×Dic11—28no—
401C2×Dic11—22no—
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—44no—
416C2×Dic11—44no—
417C2×Dic11—44no—
418C2×Dic11—44no—
419C2×Dic11C22×D414yes—
420D44—232no—
421D44—416no—
422D44—416no—
423C4×D11—416no—
424C4×D11—416no—
425C23×D4—111no—
426C23×D4—111no—
427C23×D4—111no—
428C23×D4—111no—
429C23×D4—111no—
430C23×D4—111no—
431C24×C4—111no—
432C24×C4—111no—
433C2×#121—118no—
434C2×#121—228no—
435C2×C4×D4—118no—
436C2×C4×D4—228no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4—111no—
440C22×C4⋊C4C2×D1111yescharacteristic
441C22×C22⋊C4—111no—
442C22×C22⋊C4—111no—
443C22×C22⋊C4—111no—
444C22×C22⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4C2×D1111yescharacteristic
453C22×C22⋊C4C2×D1111yescharacteristic
454C22×C22⋊C4C2×D1111yescharacteristic
455C22×C42C2×D1111yescharacteristic
456#400—118no—
457#399—118no—
458#394—118no—
459#394—118no—
460#394—118no—
461#392—118no—
462#392—118no—
463#392—118no—
464#388—118no—
465#388C2×D1118yescomplemented
466#386—118no—
467#386—118no—
468#381—118no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95C2×D1111yescharacteristic
476C2×#95C2×D1111yescharacteristic
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—88no—
485C22×C11#52514yes—
486C22×C11#53414yes—
487C22×C11#53514yes—
488C22×C11#53814yes—
489C22×C11#53814yes—
490C22×C11#54014yes—
491C22×C11#54014yes—
492C22×C11C23×D411yescharacteristic
493C22×C11C22×#4111yescharacteristic
494C22×C11C22×#4111yescharacteristic
495C22×C11C2×H(5,𝔽2)11yescharacteristic
496C22×C11C2×H(5,𝔽2)11yescharacteristic
497C22×C11C2×H(5,𝔽2)11yescharacteristic
498C22×C11C2×H(5,𝔽2)11yescharacteristic
499C2×D11—24no—
500C2×D11—24no—
501C2×D11—24no—
502C2×D11—24no—
503C2×D11—24no—
504C2×D11—24no—
505C2×D11—416no—
506C2×D11—416no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—88no—
523C4×C11—24no—
524C4×C11—24no—
525C4×C11—42no—
526C4×C11—42no—
527C4×C11—42no—
528C4×C11—42no—
529Dic11—24no—
530Dic11—42no—
531Dic11—42no—
532Dic11—42no—
533Dic11—42no—
534C25—111no—
535C25—111no—
536C25—111no—
537C25C22×D1111yescharacteristic
538C22×D4—114no—
539C22×D4—114no—
540C22×D4—114no—
541C22×D4—114no—
542C22×D4—114no—
543C22×D4—114no—
544C22×D4—224no—
545C22×D4—224no—
546C22×D4—224no—
547C22×D4—224no—
548C22×D4—224no—
549C22×D4—224no—
550C22×D4—224no—
551C22×D4—224no—
552C22×D4—442no—
553C22×D4—442no—
554C22×D4—442no—
555C22×D4—442no—
556C22×D4—442no—
557C22×D4—442no—
558C22×D4—442no—
559C22×D4—442no—
560C22×D4—442no—
561C22×D4—442no—
562C23×C4—111no—
563C23×C4—118no—
564C23×C4—114no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—114no—
570C23×C4—224no—
571C23×C4—442no—
572C23×C4—442no—
573C23×C4—442no—
574C23×C4—442no—
575C23×C4C22×D1111yescharacteristic
576C23×C4C22×D1111yescharacteristic
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581#121—2232no—
582C4×D4—2232no—
583C2×C4⋊C4—42no—
584C2×C4⋊C4—114no—
585C2×C4⋊C4—114no—
586C2×C4⋊C4—114no—
587C2×C4⋊C4—224no—
588C2×C4⋊C4—224no—
589C2×C4⋊C4—442no—
590C2×C4⋊C4C22×D1114yes—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—114no—
595C2×C22⋊C4—114no—
596C2×C22⋊C4—114no—
597C2×C22⋊C4—114no—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—114no—
600C2×C22⋊C4—114no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—224no—
606C2×C22⋊C4—224no—
607C2×C22⋊C4—224no—
608C2×C22⋊C4—224no—
609C2×C22⋊C4—442no—
610C2×C22⋊C4—442no—
611C2×C22⋊C4—442no—
612C2×C22⋊C4—442no—
613C2×C22⋊C4—442no—
614C2×C22⋊C4—442no—
615C2×C22⋊C4—442no—
616C2×C22⋊C4C22×D1114yes—
617C2×C22⋊C4C22×D1114yes—
618C2×C22⋊C4C22×D1114yes—
619C2×C42—24no—
620C2×C42C22×D1114yes—
621#95—114no—
622#95—114no—
623#95—114no—
624#95—114no—
625#95—114no—
626#95—114no—
627#95C22×D1114yes—
628#95C22×D1114yes—
629C2×C11—82no—
630C2×C11#263518yescomplemented
631C2×C11C2×#52511yescharacteristic
632C2×C11C2×#53411yescharacteristic
633C2×C11C2×#53511yescharacteristic
634C2×C11C2×#53811yescharacteristic
635C2×C11C2×#53811yescharacteristic
636C2×C11C2×#54011yescharacteristic
637C2×C11C2×#54011yescharacteristic
638D11—44no—
639D11—44no—
640D11—82no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—114no—
649C24—114no—
650C24—112no—
651C24—112no—
652C24—112no—
653C24—222no—
654C24—222no—
655C24—222no—
656C24—222no—
657C24—222no—
658C24—222no—
659C24—222no—
660C24—222no—
661C24—222no—
662C24—222no—
663C24—222no—
664C24—222no—
665C24—222no—
666C24—222no—
667C24—222no—
668C24—222no—
669C24—222no—
670C24—222no—
671C24—222no—
672C24C23×D1112yes—
673C24C23×D1111yescharacteristic
674C2×D4—228no—
675C2×D4—228no—
676C2×D4—2232no—
677C2×D4—228no—
678C2×D4—228no—
679C2×D4—228no—
680C2×D4—228no—
681C2×D4—228no—
682C2×D4—228no—
683C2×D4—444no—
684C2×D4—444no—
685C2×D4—444no—
686C2×D4—444no—
687C2×D4—4416no—
688C2×D4—4416no—
689C2×D4—444no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4—444no—
694C2×D4—444no—
695C2×D4—4416no—
696C2×D4—4416no—
697C2×D4—4416no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—114no—
715C22×C4—112no—
716C22×C4—1116no—
717C22×C4—112no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—112no—
721C22×C4—222no—
722C22×C4—222no—
723C22×C4—222no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—222no—
734C22×C4—222no—
735C22×C4—228no—
736C22×C4—4416no—
737C22×C4—444no—
738C22×C4—444no—
739C22×C4—444no—
740C22×C4—444no—
741C22×C4—4416no—
742C22×C4#433914yes—
743C22×C4D4×D1114yes—
744C22×C4C23×D1112yes—
745C22×C4C23×D1112yes—
746C22×C4C23×D1112yes—
747C22×C4C23×D1112yes—
748C22×C4C23×D1112yes—
749C22×C4C23×D1112yes—
750C4⋊C4—44no—
751C4⋊C4—228no—
752C4⋊C4—228no—
753C4⋊C4—444no—
754C22⋊C4—28no—
755C22⋊C4—28no—
756C22⋊C4—44no—
757C22⋊C4—228no—
758C22⋊C4—228no—
759C22⋊C4—228no—
760C22⋊C4—228no—
761C22⋊C4—444no—
762C22⋊C4—444no—
763C22⋊C4—444no—
764C22⋊C4—444no—
765C22⋊C4—444no—
766C22⋊C4—444no—
767C22⋊C4—444no—
768C42—28no—
769C11C2×#263511yescharacteristic, complemented, Sylow
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—114no—
785C23—114no—
786C23—228no—
787C23—228no—
788C23—228no—
789C23—228no—
790C23—228no—
791C23—222no—
792C23—222no—
793C23—222no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—222no—
801C23—222no—
802C23—222no—
803C23—228no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—444no—
812C23—444no—
813C23—444no—
814C23—444no—
815C23—444no—
816C23—444no—
817C23—444no—
818C23—444no—
819C23—444no—
820C23—444no—
821C23—444no—
822C23—444no—
823C23—444no—
824C23—444no—
825C23—444no—
826C23C2×#433912yes—
827C23C2×D4×D1112yes—
828C23#6703712yes—
829C23#41×D1112yes—
830C23#6704212yes—
831C23#6704212yes—
832C23#6704212yes—
833C23C24×D1111yescharacteristic
834D4—2232no—
835D4—4416no—
836D4—4416no—
837D4—4416no—
838D4—4416no—
839D4—4416no—
840C2×C4—28no—
841C2×C4—28no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—114no—
863C2×C4—228no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—4416no—
879C2×C4—4416no—
880C2×C4—444no—
881C2×C4—444no—
882C2×C4—444no—
883C2×C4—444no—
884C2×C4C2×#433914yes—
885C2×C4C2×D4×D1114yes—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—88no—
894C22—224no—
895C22—224no—
896C22—224no—
897C22—224no—
898C22—224no—
899C22—224no—
900C22—442no—
901C22—442no—
902C22—4416no—
903C22—4416no—
904C22—442no—
905C22—442no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—442no—
911C22—442no—
912C22—442no—
913C22—442no—
914C22—442no—
915C22—442no—
916C22—442no—
917C22—888no—
918C22#1062306614yes—
919C22#1062307814yes—
920C22#1062309314yes—
921C22#1062313814yes—
922C22#1062318414yes—
923C22#1062320914yes—
924C22#1062323514yes—
925C22C22×#433911yescharacteristic
926C22C22×D4×D1111yescharacteristic
927C22C2×#6703711yescharacteristic
928C22C2×#41×D1111yescharacteristic
929C22C2×#6704211yescharacteristic
930C22C2×#6704211yescharacteristic
931C22C2×#6704211yescharacteristic
932C4—24no—
933C4—24no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—42no—
938C4—224no—
939C4—442no—
940C4—442no—
941C4—442no—
942C4—442no—
943C2—82no—
944C2—444no—
945C2—444no—
946C2—882no—
947C2#1307450718yesdirect product factor
948C2C2×#1062307811yescharacteristic
949C2C2×#1062318411yescharacteristic
950C2C2×#1062313811yescharacteristic
951C2C2×#1062320911yescharacteristic
952C2C2×#1062323511yescharacteristic
953C2C2×#1062309311yescharacteristic
954C2C2×#1062306611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
hypercenterC2×#388D11
hypocenterC11C2×#2635
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66937C2semidirect
2. C22×C4×D44C2semidirect
3. #13074507C2direct (N × H)
4. C2×#10622273C2semidirect
5. C2×#10622605C2semidirect
6. C2×#10622604C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622284C2semidirect
10. C2×#10622573C2semidirect
11. C2×#10622573C2semidirect
12. C2×#10622553C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622277C2semidirect
16. C2×C11×#388C2semidirect
45. C2×#66937C22semidirect
47. C2×C4×D44C22semidirect
48. C11×#388C22semidirect
57. #10622605C22semidirect
58. #10622604C22semidirect
59. #10622574C22semidirect
60. #10622573C22semidirect
61. #10622573C22semidirect
62. #10622572C22semidirect
63. #10622569C22semidirect
64. #10622553C22semidirect
65. #10622284C22semidirect
66. #10622278C22semidirect
67. #10622277C22semidirect
68. #10622273C22semidirect
113. C22×C4×D11D4semidirect
273. C2×C4×D11C2×D4semidirect
305. C2×#388D11semidirect
465. #388C2×D11semidirect
630. C2×C11#2635semidirect
769. C11C2×#2635semidirect
947. C2#13074507direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669372
C22×C4×D442
#130745072
C2×#106222732
C2×#106226052
C2×#106226042
C2×#106225742
C2×#106225722
C2×#106222842
C2×#106225732
C2×#106225532
C2×#106222782
C2×#106225692
C2×#106222772
C2×C11×#3882
C2×#263511