Finite Group Databasebeta

← C2×#13072225 #14922405

Subgroups — C2×#13072225 #14922405

Order 2816.

6042 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4339C211yesmaximal, characteristic, complemented
2C22×#66947C211yesmaximal, characteristic, complemented
3C22×#66948C211yesmaximal, characteristic, complemented
4C22×#66937C211yesmaximal, characteristic, complemented
5#13072225C2116yesmaximal, direct product factor
6C2×#10622592C211yesmaximal, characteristic, complemented
7C2×#10622572C211yesmaximal, characteristic, complemented
8C2×#10622286C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic, complemented
10C2×#10622826C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×D11×#95C211yesmaximal, characteristic, complemented
16C2×C11×#385C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C22×#4339—28no—
22C22×#4339—28no—
23C22×#4339—28no—
24C22×#4339C2218yescomplemented
25C23×D44C2211yescharacteristic
26C23×D44C2211yescharacteristic
27C23×D44C2211yescharacteristic
28C23×C4×D11C2211yescharacteristic
29C23×C4×D11C2211yescharacteristic
30C23×C4×D11C2211yescharacteristic
31C23×C4×D11C2211yescharacteristic
32C23×Dic22C2211yescharacteristic
33C22×C11×C4⋊C4C2211yescharacteristic
34C22×C11×C4⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C2×#66948—28no—
49C2×#66948C2218yescomplemented
50C2×#66947—28no—
51C2×#66947C2218yescomplemented
52C2×#66937—28no—
53C2×#66937C2218yescomplemented
54C11×#385C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57#10622826C2218yescomplemented
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64#10622602C2218yescomplemented
65#10622592C2218yescomplemented
66#10622573C2218yescomplemented
67#10622572C2218yescomplemented
68#10622569C2218yescomplemented
69#10622286C2218yescomplemented
70#10622278C2218yescomplemented
71#10622278C2218yescomplemented
72D11×#95C2218yescomplemented
73C25×C11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C23×C4×C11—24no—
78C23×C4×C11—24no—
79C23×C4×C11—24no—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2314yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11D418yescomplemented
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C22×C22⋊D11C2314yes—
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C2×#4339—2128no—
105C2×#4339—232no—
106C2×#4339—232no—
107C2×#4339—232no—
108C22×D44—24no—
109C22×D44—24no—
110C22×D44—24no—
111C22×D44—24no—
112C22×D44—24no—
113C22×D44—24no—
114C22×D44—24no—
115C22×D44—42no—
116C22×D44D418yescomplemented
117C22×D44C2314yes—
118C22×D44C2314yes—
119C22×D44C2314yes—
120C22×C4×D11—24no—
121C22×C4×D11—24no—
122C22×C4×D11—24no—
123C22×C4×D11—24no—
124C22×C4×D11—24no—
125C22×C4×D11—24no—
126C22×C4×D11—24no—
127C22×C4×D11—24no—
128C22×C4×D11—24no—
129C22×C4×D11—42no—
130C22×C4×D11—42no—
131C22×C4×D11D418yescomplemented
132C22×C4×D11C2314yes—
133C22×C4×D11C2314yes—
134C22×C4×D11C2314yes—
135C22×C4×D11C2314yes—
136C22×Dic22—24no—
137C22×Dic22—24no—
138C22×Dic22—24no—
139C22×Dic22C2314yes—
140C2×C11×C4⋊C4—24no—
141C2×C11×C4⋊C4—24no—
142C2×C11×C4⋊C4C2314yes—
143C2×C11×C4⋊C4C2314yes—
144C2×C11×C22⋊C4—24no—
145C2×C11×C22⋊C4—24no—
146C2×C11×C22⋊C4C2314yes—
147C2×C11×C22⋊C4C2314yes—
148C2×C22⋊Dic11—42no—
149C2×C22⋊Dic11C2314yes—
150C2×(C2×D11)⋊C4—24no—
151C2×(C2×D11)⋊C4—24no—
152C2×(C2×D11)⋊C4—24no—
153C2×(C2×D11)⋊C4—24no—
154C2×(C2×D11)⋊C4—24no—
155C2×(C2×D11)⋊C4—24no—
156C2×(C2×D11)⋊C4—24no—
157C2×(C2×D11)⋊C4—42no—
158C2×(C2×D11)⋊C4C2314yes—
159C2×(C2×D11)⋊C4C2314yes—
160C2×(C2×D11)⋊C4C2314yes—
161C2×(C2×D11)⋊C4C2314yes—
162C2×(C2×D11)⋊C4C2314yes—
163C2×(C2×D11)⋊C4C2314yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2314yes—
166C2×Dic11⋊C4—24no—
167C2×Dic11⋊C4—24no—
168C2×Dic11⋊C4C2314yes—
169C2×Dic11⋊C4C2314yes—
170#66948—232no—
171#66947—232no—
172#66937—232no—
173C11×#95C2314yes—
174C11×#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180C11⋊#95C2314yes—
181C2×#2430—111nomaximal, Sylow
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11—22no—
187C24×C11—22no—
188C24×C11C2×D414yes—
189C24×C11C2412yes—
190C24×C11C2411yescharacteristic
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—22no—
204C23×D11—22no—
205C23×D11—22no—
206C23×D11—22no—
207C23×D11—22no—
208C23×D11C2×D414yes—
209C23×D11C2×D414yes—
210C23×D11C2×D414yes—
211C23×D11C2×D414yes—
212C23×D11C2412yes—
213C23×D11C2412yes—
214C23×D11C2412yes—
215C22×C4×C11—232no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—28no—
222C22×C4×C11—22no—
223C22×C4×C11—28no—
224C22×C4×C11—28no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11C2×D414yes—
235C22×C4×C11C2×D414yes—
236C22×C4×C11#4114yescomplemented
237C22×C4×C11C2412yes—
238C22×C4×C11C2412yes—
239C22×C4×C11C2412yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2412yes—
243C2×C22⋊D11—232no—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—28no—
246C2×C22⋊D11—28no—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—232no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—416no—
254C2×C22⋊D11C2×D4116yescomplemented
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11C2×D414yes—
268C22×Dic11C2×D414yes—
269C22×Dic11#4114yescomplemented
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2412yes—
275#4339—2256no—
276C2×D44—232no—
277C2×D44—28no—
278C2×D44—28no—
279C2×D44—28no—
280C2×D44—28no—
281C2×D44—28no—
282C2×D44—28no—
283C2×D44—28no—
284C2×D44—44no—
285C2×D44—416no—
286C2×D44—416no—
287C2×D44C2×D4116yescomplemented
288C2×C4×D11—232no—
289C2×C4×D11—28no—
290C2×C4×D11—28no—
291C2×C4×D11—232no—
292C2×C4×D11—28no—
293C2×C4×D11—28no—
294C2×C4×D11—28no—
295C2×C4×D11—28no—
296C2×C4×D11—28no—
297C2×C4×D11—28no—
298C2×C4×D11—28no—
299C2×C4×D11—44no—
300C2×C4×D11—44no—
301C2×C4×D11—416no—
302C2×C4×D11—416no—
303C2×C4×D11C2×D4116yescomplemented
304C2×Dic22—232no—
305C2×Dic22—28no—
306C2×Dic22—28no—
307C2×Dic22—28no—
308C11×C4⋊C4—28no—
309C11×C4⋊C4—28no—
310C11×C22⋊C4—28no—
311C11×C22⋊C4—28no—
312C22⋊Dic11—44no—
313(C2×D11)⋊C4—28no—
314(C2×D11)⋊C4—28no—
315(C2×D11)⋊C4—28no—
316(C2×D11)⋊C4—28no—
317(C2×D11)⋊C4—28no—
318(C2×D11)⋊C4—28no—
319(C2×D11)⋊C4—28no—
320(C2×D11)⋊C4—44no—
321Dic11⋊C4—28no—
322Dic11⋊C4—28no—
323C23×#41—111no—
324C22×#123—111no—
325C22×#121—111no—
326C22×#121—111no—
327#2430—1116no—
328C2×#395—111no—
329C2×#394—111no—
330C2×#393—111no—
331C2×#392—111no—
332C2×#386—111no—
333C2×#386—111no—
334C2×#386—111no—
335C2×#386—111no—
336C2×#385—111no—
337C2×#385D1111yescharacteristic, complemented
338C22×#95—111no—
339C23×C11—28no—
340C23×C11—28no—
341C23×C11—28no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—44no—
349C23×C11—44no—
350C23×C11—44no—
351C23×C11—44no—
352C23×C11C22×D414yes—
353C23×C11C22×D412yes—
354C23×C11C22×D412yes—
355C23×C11C22×D412yes—
356C23×C11C2×#4112yes—
357C23×C11C2×#4112yes—
358C23×C11H(5,𝔽2)12yes—
359C23×C112−1+412yes—
360C23×C11C2511yescharacteristic
361C22×D11—28no—
362C22×D11—28no—
363C22×D11—28no—
364C22×D11—28no—
365C22×D11—28no—
366C22×D11—28no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—28no—
372C22×D11—28no—
373C22×D11—28no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—44no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—44no—
393C22×D11—44no—
394C22×D11—44no—
395C22×D11—44no—
396C22×D11—44no—
397C22×D11—44no—
398C22×D11#120116yes—
399C22×D11C22×D414yes—
400C22×D11C22×D414yes—
401C22×D11C22×D414yes—
402C22×D11C22×D414yes—
403C2×C4×C11—232no—
404C2×C4×C11—28no—
405C2×C4×C11—28no—
406C2×C4×C11—28no—
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—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—44no—
423C2×C4×C11—44no—
424C2×C4×C11—44no—
425C2×C4×C11C22×D414yes—
426C2×C4×C11C22×D414yes—
427C2×C4×C11C2×#4114yescomplemented
428C22⋊D11—232no—
429C22⋊D11—232no—
430C22⋊D11—416no—
431C2×Dic11—28no—
432C2×Dic11—28no—
433C2×Dic11—28no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—44no—
447C2×Dic11—44no—
448C2×Dic11C22×D414yes—
449C2×Dic11C22×D414yes—
450C2×Dic11C2×#4114yescomplemented
451D44—232no—
452D44—416no—
453D44—416no—
454C4×D11—232no—
455C4×D11—232no—
456C4×D11—416no—
457C4×D11—416no—
458Dic22—232no—
459C22×#41—118no—
460C22×#41—228no—
461C22×#41—228no—
462C22×#41—228no—
463C23×Q8—111no—
464C23×D4—111no—
465C23×D4—111no—
466C23×D4—111no—
467C23×D4—111no—
468C23×D4—111no—
469C23×D4—111no—
470C24×C4—111no—
471C24×C4—111no—
472C24×C4—111no—
473C24×C4—111no—
474C24×C4C2×D1111yescharacteristic
475C2×#123—118no—
476C2×#123—228no—
477C2×#121—118no—
478C2×#121—118no—
479C2×#121—228no—
480C2×#121—228no—
481C22×C4⋊C4—111no—
482C22×C4⋊C4—111no—
483C22×C4⋊C4C2×D1111yescharacteristic
484C22×C4⋊C4C2×D1111yescharacteristic
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487C22×C22⋊C4—111no—
488C22×C22⋊C4—111no—
489C22×C22⋊C4—111no—
490C22×C22⋊C4—111no—
491C22×C22⋊C4—111no—
492C22×C22⋊C4—111no—
493C22×C22⋊C4—111no—
494C22×C22⋊C4C2×D1111yescharacteristic
495C22×C22⋊C4C2×D1111yescharacteristic
496#395—118no—
497#394—118no—
498#393—118no—
499#392—118no—
500#386—118no—
501#386—118no—
502#386—118no—
503#386—118no—
504#385—118no—
505#385C2×D1118yescomplemented
506C2×#95—111no—
507C2×#95—111no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
511C2×#95—111no—
512C2×#95—118no—
513C2×#95C2×D1111yescharacteristic
514C2×#95C2×D1111yescharacteristic
515C22×C11—24no—
516C22×C11—24no—
517C22×C11—24no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—416no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11C2×#12014yes—
524C22×C11#53214yes—
525C22×C11#53714yes—
526C22×C11#54614yes—
527C22×C11#54614yes—
528C22×C11#54714yes—
529C22×C11#54714yes—
530C22×C11C23×D411yescharacteristic
531C22×C11C23×D411yescharacteristic
532C22×C11C23×D411yescharacteristic
533C22×C11C22×#4111yescharacteristic
534C22×C11C22×#4111yescharacteristic
535C22×C11C2×H(5,𝔽2)11yescharacteristic
536C22×C11C2×2−1+411yescharacteristic
537C2×D11—24no—
538C2×D11—24no—
539C2×D11—232no—
540C2×D11—24no—
541C2×D11—24no—
542C2×D11—24no—
543C2×D11—24no—
544C2×D11—24no—
545C2×D11—24no—
546C2×D11—24no—
547C2×D11—42no—
548C2×D11—42no—
549C2×D11—416no—
550C2×D11—42no—
551C2×D11—42no—
552C2×D11—42no—
553C2×D11—42no—
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—88no—
560C2×D11C2×#12018yes—
561C4×C11—24no—
562C4×C11—24no—
563C4×C11—24no—
564C4×C11—42no—
565C4×C11—42no—
566C4×C11—42no—
567Dic11—24no—
568Dic11—24no—
569Dic11—24no—
570Dic11—42no—
571Dic11—42no—
572C25—111no—
573C25—111no—
574C25—111no—
575C25C22×D1111yescharacteristic
576C2×#41—2232no—
577C2×#41—2232no—
578C2×#41—2232no—
579C2×#41—22128no—
580C22×Q8—114no—
581C22×Q8—224no—
582C22×Q8—224no—
583C22×Q8—224no—
584C22×D4—118no—
585C22×D4—114no—
586C22×D4—114no—
587C22×D4—114no—
588C22×D4—118no—
589C22×D4—114no—
590C22×D4—114no—
591C22×D4—114no—
592C22×D4—224no—
593C22×D4—224no—
594C22×D4—224no—
595C22×D4—224no—
596C22×D4—224no—
597C22×D4—224no—
598C22×D4—224no—
599C22×D4—224no—
600C22×D4—224no—
601C22×D4—224no—
602C22×D4—224no—
603C22×D4—224no—
604C22×D4—224no—
605C22×D4—224no—
606C22×D4—442no—
607C22×D4—442no—
608C23×C4—24no—
609C23×C4—24no—
610C23×C4—24no—
611C23×C4—111no—
612C23×C4—111no—
613C23×C4—111no—
614C23×C4—118no—
615C23×C4—114no—
616C23×C4—111no—
617C23×C4—111no—
618C23×C4—114no—
619C23×C4—114no—
620C23×C4—114no—
621C23×C4—224no—
622C23×C4—224no—
623C23×C4—224no—
624C23×C4—224no—
625C23×C4—224no—
626C23×C4—224no—
627C23×C4—224no—
628C23×C4—224no—
629C23×C4—224no—
630C23×C4—442no—
631C23×C4—442no—
632C23×C4C22×D1114yes—
633C23×C4C22×D1111yescharacteristic
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C23×C4C22×D1111yescharacteristic
637C23×C4C22×D1111yescharacteristic
638C23×C4C22×D1111yescharacteristic
639#123—2232no—
640#121—2232no—
641#121—2232no—
642C2×C4⋊C4—24no—
643C2×C4⋊C4—24no—
644C2×C4⋊C4—114no—
645C2×C4⋊C4—114no—
646C2×C4⋊C4—224no—
647C2×C4⋊C4—224no—
648C2×C4⋊C4C22×D1114yes—
649C2×C4⋊C4C22×D1114yes—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—114no—
657C2×C22⋊C4—114no—
658C2×C22⋊C4—114no—
659C2×C22⋊C4—114no—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—224no—
662C2×C22⋊C4—224no—
663C2×C22⋊C4—224no—
664C2×C22⋊C4—224no—
665C2×C22⋊C4—224no—
666C2×C22⋊C4—224no—
667C2×C22⋊C4—224no—
668C2×C22⋊C4—442no—
669C2×C22⋊C4—442no—
670C2×C22⋊C4C22×D1114yes—
671C2×C22⋊C4C22×D1114yes—
672#95—114no—
673#95—114no—
674#95—114no—
675#95—114no—
676#95—114no—
677#95—114no—
678#95C22×D1114yes—
679#95C22×D1114yes—
680C2×C11—44no—
681C2×C11#243018yescomplemented
682C2×C11C22×#12011yescharacteristic
683C2×C11C2×#53211yescharacteristic
684C2×C11C2×#53711yescharacteristic
685C2×C11C2×#54611yescharacteristic
686C2×C11C2×#54611yescharacteristic
687C2×C11C2×#54711yescharacteristic
688C2×C11C2×#54711yescharacteristic
689D11—28no—
690D11—44no—
691D11—82no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—114no—
699C24—114no—
700C24—114no—
701C24—112no—
702C24—114no—
703C24—112no—
704C24—112no—
705C24—222no—
706C24—222no—
707C24—222no—
708C24—222no—
709C24—222no—
710C24—222no—
711C24—222no—
712C24—222no—
713C24—222no—
714C24—222no—
715C24—222no—
716C24—222no—
717C24—222no—
718C24—222no—
719C24—222no—
720C24—222no—
721C24—222no—
722C24D4×D1114yes—
723C24C23×D1112yes—
724C24C23×D1111yescharacteristic
725#41—22256no—
726C2×Q8—228no—
727C2×Q8—228no—
728C2×Q8—2232no—
729C2×Q8—228no—
730C2×D4—1116no—
731C2×D4—1116no—
732C2×D4—2232no—
733C2×D4—228no—
734C2×D4—228no—
735C2×D4—228no—
736C2×D4—228no—
737C2×D4—228no—
738C2×D4—228no—
739C2×D4—228no—
740C2×D4—228no—
741C2×D4—2232no—
742C2×D4—228no—
743C2×D4—228no—
744C2×D4—228no—
745C2×D4—2232no—
746C2×D4—228no—
747C2×D4—228no—
748C2×D4—228no—
749C2×D4—444no—
750C2×D4—4416no—
751C2×D4—4416no—
752C2×D4—444no—
753C2×D4—4416no—
754C22×C4—232no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—28no—
761C22×C4—22no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—114no—
774C22×C4—114no—
775C22×C4—114no—
776C22×C4—112no—
777C22×C4—112no—
778C22×C4—112no—
779C22×C4—1116no—
780C22×C4—112no—
781C22×C4—112no—
782C22×C4—228no—
783C22×C4—228no—
784C22×C4—2232no—
785C22×C4—228no—
786C22×C4—228no—
787C22×C4—228no—
788C22×C4—2232no—
789C22×C4—228no—
790C22×C4—228no—
791C22×C4—222no—
792C22×C4—222no—
793C22×C4—222no—
794C22×C4—222no—
795C22×C4—222no—
796C22×C4—222no—
797C22×C4—228no—
798C22×C4—222no—
799C22×C4—222no—
800C22×C4—222no—
801C22×C4—222no—
802C22×C4—222no—
803C22×C4—222no—
804C22×C4—228no—
805C22×C4—444no—
806C22×C4—444no—
807C22×C4—4416no—
808C22×C4—4416no—
809C22×C4#433914yescomplemented
810C22×C4D4×D1114yes—
811C22×C4D4×D1114yes—
812C22×C4C23×D1112yes—
813C22×C4C23×D1112yes—
814C22×C4C23×D1112yes—
815C22×C4C23×D1112yes—
816C22×C4C23×D1112yes—
817C22×C4C23×D1112yes—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—228no—
821C4⋊C4—228no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—228no—
825C22⋊C4—228no—
826C22⋊C4—228no—
827C22⋊C4—228no—
828C22⋊C4—228no—
829C22⋊C4—228no—
830C22⋊C4—228no—
831C22⋊C4—444no—
832C22⋊C4—444no—
833C11C2×#243011yescharacteristic, complemented, Sylow
834C23—28no—
835C23—28no—
836C23—28no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—44no—
844C23—44no—
845C23—44no—
846C23—44no—
847C23—1116no—
848C23—114no—
849C23—114no—
850C23—114no—
851C23—114no—
852C23—228no—
853C23—228no—
854C23—228no—
855C23—228no—
856C23—228no—
857C23—228no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—228no—
863C23—228no—
864C23—228no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—444no—
879C23—444no—
880C23—444no—
881C23—444no—
882C23—444no—
883C23—444no—
884C23—444no—
885C23—444no—
886C23—444no—
887C23—444no—
888C23—444no—
889C23C2×#433912yes—
890C23C2×D4×D1114yes—
891C23C2×D4×D1112yes—
892C23C2×D4×D1112yes—
893C23C2×D4×D1112yes—
894C23#6704012yes—
895C23#41×D1112yes—
896C23#6704212yes—
897C23C24×D1111yescharacteristic
898Q8—2232no—
899D4—2232no—
900D4—2232no—
901D4—2232no—
902D4—4416no—
903D4—4416no—
904D4—4416no—
905C2×C4—232no—
906C2×C4—28no—
907C2×C4—28no—
908C2×C4—28no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—114no—
928C2×C4—114no—
929C2×C4—114no—
930C2×C4—2232no—
931C2×C4—2232no—
932C2×C4—228no—
933C2×C4—228no—
934C2×C4—228no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—222no—
947C2×C4—4416no—
948C2×C4—4416no—
949C2×C4—444no—
950C2×C4—444no—
951C2×C4C2×#433914yescomplemented
952C2×C4C2×D4×D1114yes—
953C2×C4C2×D4×D1114yes—
954C22—24no—
955C22—24no—
956C22—24no—
957C22—42no—
958C22—42no—
959C22—416no—
960C22—42no—
961C22—42no—
962C22—118no—
963C22—224no—
964C22—224no—
965C22—2232no—
966C22—224no—
967C22—224no—
968C22—224no—
969C22—224no—
970C22—224no—
971C22—224no—
972C22—224no—
973C22—442no—
974C22—442no—
975C22—4416no—
976C22—442no—
977C22—442no—
978C22—442no—
979C22—442no—
980C22—442no—
981C22—442no—
982C22—442no—
983C22—442no—
984C22—442no—
985C22—888no—
986C22#1062303814yes—
987C22#1062307914yes—
988C22#1062308114yes—
989C22D11×#12014yes—
990C22#1062316014yes—
991C22#1062316214yes—
992C22#1062318514yes—
993C22C22×#433911yescharacteristic
994C22C22×D4×D1111yescharacteristic
995C22C22×D4×D1111yescharacteristic
996C22C22×D4×D1111yescharacteristic
997C22C2×#6704011yescharacteristic
998C22C2×#41×D1111yescharacteristic
999C22C2×#6704211yescharacteristic
1000C4—24no—
1001C4—24no—
1002C4—24no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—224no—
1007C4—224no—
1008C4—224no—
1009C4—442no—
1010C4—442no—
1011C2—44no—
1012C2—228no—
1013C2—444no—
1014C2—882no—
1015C2#1307222518yesdirect product factor
1016C2C2×D11×#12011yescharacteristic
1017C2C2×#1062307911yescharacteristic
1018C2C2×#1062316011yescharacteristic
1019C2C2×#1062318511yescharacteristic
1020C2C2×#1062308111yescharacteristic
1021C2C2×#1062303811yescharacteristic
1022C2C2×#1062316211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
hypercenterC2×#385D11
hypocenterC11C2×#2430
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C23×#4339C2semidirect
2. C22×#66947C2semidirect
3. C22×#66948C2semidirect
4. C22×#66937C2semidirect
5. #13072225C2direct (N × H)
6. C2×#10622592C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622286C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622826C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622602C2semidirect
15. C2×D11×#95C2semidirect
16. C2×C11×#385C2semidirect
24. C22×#4339C22semidirect
49. C2×#66948C22semidirect
51. C2×#66947C22semidirect
53. C2×#66937C22semidirect
54. C11×#385C22semidirect
57. #10622826C22semidirect
64. #10622602C22semidirect
65. #10622592C22semidirect
66. #10622573C22semidirect
67. #10622572C22semidirect
68. #10622569C22semidirect
69. #10622286C22semidirect
70. #10622278C22semidirect
71. #10622278C22semidirect
72. D11×#95C22semidirect
95. C22×C22⋊D11D4semidirect
116. C22×D44D4semidirect
131. C22×C4×D11D4semidirect
236. C22×C4×C11#41semidirect
254. C2×C22⋊D11C2×D4semidirect
269. C22×Dic11#41semidirect
287. C2×D44C2×D4semidirect
303. C2×C4×D11C2×D4semidirect
337. C2×#385D11semidirect
427. C2×C4×C11C2×#41semidirect
450. C2×Dic11C2×#41semidirect
505. #385C2×D11semidirect
681. C2×C11#2430semidirect
809. C22×C4#4339semidirect
833. C11C2×#2430semidirect
951. C2×C4C2×#4339semidirect
1015. C2#13072225direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43392
C22×#669472
C22×#669482
C22×#669372
#130722252
C2×#106225922
C2×#106225722
C2×#106222862
C2×#106225732
C2×#106228262
C2×#106222782
C2×#106225692
C2×#106226022
C2×D11×#952
C2×C11×#3852
C2×#243011