Finite Group Databasebeta

← C2×#13071933 #14922380

Subgroups — C2×#13071933 #14922380

Order 2816.

7222 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4339C211yesmaximal, characteristic, complemented
2C22×#66935C211yesmaximal, characteristic, complemented
3C22×#66990C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#13071933C2116yesmaximal, direct product factor
6C2×#10622286C211yesmaximal, characteristic, complemented
7C2×#10622560C211yesmaximal, characteristic, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622836C211yesmaximal, characteristic, complemented
10C2×#10622826C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622277C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic, complemented
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic, complemented
24C22×#4339—28no—
25C22×#4339—28no—
26C22×#4339—28no—
27C22×#4339C2218yescomplemented
28C23×D44C2211yescharacteristic
29C23×D44C2211yescharacteristic
30C23×C4×D11C2211yescharacteristic
31C23×C4×D11C2211yescharacteristic
32C23×C4×D11C2211yescharacteristic, complemented
33C23×Dic22C2211yescharacteristic, complemented
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C11×C22⋊C4C2211yescharacteristic, complemented
37C22×C22⋊Dic11C2211yescharacteristic
38C22×C22⋊Dic11C2211yescharacteristic
39C22×C22⋊Dic11C2211yescharacteristic, complemented
40C2×#66990—28no—
41C2×#66990C2218yescomplemented
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×(C2×D11)⋊C4C2211yescharacteristic
47C22×(C2×D11)⋊C4C2211yescharacteristic
48C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
49C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
50C2×#66935—28no—
51C2×#66935C2218yescomplemented
52C2×C22⋊C4×D11—28no—
53C2×C22⋊C4×D11C2218yescomplemented
54C11×#386C2218yescomplemented
55C2×C11×#95C2211yescharacteristic, complemented
56C2×C11×#95C2211yescharacteristic, complemented
57#10622836C2218yescomplemented
58#10622826C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61C2×C11⋊#95C2211yescharacteristic, complemented
62C2×C11⋊#95C2211yescharacteristic, complemented
63C2×C11⋊#95C2211yescharacteristic, complemented
64C2×C11⋊#95C2211yescharacteristic, complemented
65#10622573C2218yescomplemented
66#10622569C2218yescomplemented
67#10622569C2218yescomplemented
68#10622560C2218yescomplemented
69#10622286C2218yescomplemented
70#10622278C2218yescomplemented
71#10622278C2218yescomplemented
72#10622277C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C24×D11—24no—
76C24×D11—24no—
77C24×D11—24no—
78C24×D11—24no—
79C24×D11—24no—
80C24×D11—42no—
81C24×D11—42no—
82C24×D11C2311yescharacteristic
83C24×D11C2311yescharacteristic
84C24×D11C2314yes—
85C24×D11C2311yescharacteristic
86C22×D4×C11—24no—
87C22×D4×C11—24no—
88C22×D4×C11—42no—
89C22×D4×C11C2314yes—
90C23×C4×C11—24no—
91C23×C4×C11—24no—
92C23×C4×C11—24no—
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2314yescomplemented
99C22×C22⋊D11—24no—
100C22×C22⋊D11—24no—
101C22×C22⋊D11—24no—
102C22×C22⋊D11—24no—
103C22×C22⋊D11—24no—
104C22×C22⋊D11—24no—
105C22×C22⋊D11—24no—
106C22×C22⋊D11—24no—
107C22×C22⋊D11—24no—
108C22×C22⋊D11—42no—
109C22×C22⋊D11—42no—
110C22×C22⋊D11D418yescomplemented
111C22×C22⋊D11C2314yes—
112C22×C22⋊D11C2314yes—
113C22×C22⋊D11C2314yes—
114C22×C22⋊D11C2314yescomplemented
115C23×Dic11C2311yescharacteristic
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2311yescharacteristic
118C23×Dic11C2311yescharacteristic
119C23×Dic11C2311yescharacteristic
120C2×#4339—2128no—
121C2×#4339—232no—
122C2×#4339—232no—
123C2×#4339—232no—
124C22×D44—24no—
125C22×D44—24no—
126C22×D44—24no—
127C22×D44—24no—
128C22×D44—42no—
129C22×D44D418yescomplemented
130C22×D44C2314yes—
131C22×D44C2314yes—
132C22×C4×D11—24no—
133C22×C4×D11—24no—
134C22×C4×D11—24no—
135C22×C4×D11—24no—
136C22×C4×D11—24no—
137C22×C4×D11—24no—
138C22×C4×D11—42no—
139C22×C4×D11—42no—
140C22×C4×D11D418yescomplemented
141C22×C4×D11C2314yes—
142C22×C4×D11C2314yes—
143C22×C4×D11C2314yescomplemented
144C22×Dic22—24no—
145C22×Dic22—24no—
146C22×Dic22—24no—
147C22×Dic22C2314yescomplemented
148C2×C11×C22⋊C4—24no—
149C2×C11×C22⋊C4—24no—
150C2×C11×C22⋊C4—42no—
151C2×C11×C22⋊C4C2314yes—
152C2×C11×C22⋊C4C2314yes—
153C2×C11×C22⋊C4C2314yescomplemented
154C2×C22⋊Dic11—24no—
155C2×C22⋊Dic11—24no—
156C2×C22⋊Dic11—42no—
157C2×C22⋊Dic11C2314yes—
158C2×C22⋊Dic11C2314yes—
159C2×C22⋊Dic11C2314yescomplemented
160#66990—232no—
161C2×(C2×D11)⋊C4—24no—
162C2×(C2×D11)⋊C4—24no—
163C2×(C2×D11)⋊C4—24no—
164C2×(C2×D11)⋊C4—24no—
165C2×(C2×D11)⋊C4—24no—
166C2×(C2×D11)⋊C4—24no—
167C2×(C2×D11)⋊C4—42no—
168C2×(C2×D11)⋊C4—42no—
169C2×(C2×D11)⋊C4C2314yes—
170C2×(C2×D11)⋊C4C2314yes—
171C2×(C2×D11)⋊C4C2314yes—
172C2×(C2×D11)⋊C4C2314yes—
173C2×(C2×D11)⋊C4C2314yes—
174C2×(C2×D11)⋊C4C2314yes—
175C2×(C2×D11)⋊C4C2314yescomplemented
176C2×(C2×D11)⋊C4C2314yescomplemented
177#66935—232no—
178C22⋊C4×D11—232no—
179C11×#95C2314yescomplemented
180C11×#95C2314yescomplemented
181C11⋊#95C2314yescomplemented
182C11⋊#95C2314yescomplemented
183C11⋊#95C2314yescomplemented
184C11⋊#95C2314yescomplemented
185C11⋊#95C2314yescomplemented
186C11⋊#95C2314yescomplemented
187C2×#2404—111nomaximal, Sylow
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11—22no—
193C24×C11—22no—
194C24×C11—22no—
195C24×C11—22no—
196C24×C11—22no—
197C24×C11—22no—
198C24×C11—22no—
199C24×C11—22no—
200C24×C11C2×D414yes—
201C24×C11#4114yescomplemented
202C24×C11C2412yes—
203C24×C11C2412yes—
204C24×C11C2411yescharacteristic
205C23×D11—22no—
206C23×D11—22no—
207C23×D11—22no—
208C23×D11—22no—
209C23×D11—232no—
210C23×D11—22no—
211C23×D11—22no—
212C23×D11—22no—
213C23×D11—22no—
214C23×D11—22no—
215C23×D11—22no—
216C23×D11—22no—
217C23×D11—22no—
218C23×D11—28no—
219C23×D11—22no—
220C23×D11—22no—
221C23×D11—22no—
222C23×D11—22no—
223C23×D11—28no—
224C23×D11—28no—
225C23×D11—28no—
226C23×D11—28no—
227C23×D11—44no—
228C23×D11—44no—
229C23×D11—416no—
230C23×D11—416no—
231C23×D11—416no—
232C23×D11—416no—
233C23×D11—416no—
234C23×D11—416no—
235C23×D11C2×D414yes—
236C23×D11C2×D414yes—
237C23×D11C2×D414yes—
238C23×D11C2×D414yes—
239C23×D11#4114yescomplemented
240C23×D11C2412yes—
241C23×D11C2412yes—
242C23×D11C2412yes—
243C2×D4×C11—28no—
244C2×D4×C11—28no—
245C2×D4×C11—44no—
246C2×D4×C11—416no—
247C22×C4×C11—232no—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—22no—
251C22×C4×C11—22no—
252C22×C4×C11—28no—
253C22×C4×C11—28no—
254C22×C4×C11—28no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—22no—
259C22×C4×C11—22no—
260C22×C4×C11—22no—
261C22×C4×C11—22no—
262C22×C4×C11—22no—
263C22×C4×C11—22no—
264C22×C4×C11C2×D414yes—
265C22×C4×C11C2×D414yes—
266C22×C4×C11C2412yes—
267C22×C4×C11C2412yes—
268C22×C4×C11C2412yes—
269C22×C4×C11C2412yes—
270C22×C4×C11C2412yes—
271C2×C22⋊D11—232no—
272C2×C22⋊D11—28no—
273C2×C22⋊D11—28no—
274C2×C22⋊D11—28no—
275C2×C22⋊D11—28no—
276C2×C22⋊D11—232no—
277C2×C22⋊D11—28no—
278C2×C22⋊D11—28no—
279C2×C22⋊D11—28no—
280C2×C22⋊D11—28no—
281C2×C22⋊D11—28no—
282C2×C22⋊D11—44no—
283C2×C22⋊D11—44no—
284C2×C22⋊D11—416no—
285C2×C22⋊D11—416no—
286C2×C22⋊D11C2×D4116yescomplemented
287C22×Dic11—22no—
288C22×Dic11—22no—
289C22×Dic11—22no—
290C22×Dic11—22no—
291C22×Dic11—22no—
292C22×Dic11—22no—
293C22×Dic11—22no—
294C22×Dic11—22no—
295C22×Dic11—22no—
296C22×Dic11—22no—
297C22×Dic11—22no—
298C22×Dic11—22no—
299C22×Dic11—22no—
300C22×Dic11C2×D414yes—
301C22×Dic11C2×D414yes—
302C22×Dic11C2412yes—
303C22×Dic11C2412yes—
304C22×Dic11C2412yes—
305C22×Dic11C2412yes—
306C22×Dic11C2412yes—
307#4339—2256no—
308C2×D44—232no—
309C2×D44—28no—
310C2×D44—28no—
311C2×D44—28no—
312C2×D44—28no—
313C2×D44—44no—
314C2×D44—416no—
315C2×D44C2×D4116yescomplemented
316C2×C4×D11—232no—
317C2×C4×D11—28no—
318C2×C4×D11—232no—
319C2×C4×D11—28no—
320C2×C4×D11—28no—
321C2×C4×D11—28no—
322C2×C4×D11—28no—
323C2×C4×D11—28no—
324C2×C4×D11—44no—
325C2×C4×D11—44no—
326C2×C4×D11—416no—
327C2×C4×D11C2×D4116yescomplemented
328C2×Dic22—232no—
329C2×Dic22—28no—
330C2×Dic22—28no—
331C2×Dic22—28no—
332C11×C22⋊C4—28no—
333C11×C22⋊C4—28no—
334C11×C22⋊C4—44no—
335C22⋊Dic11—28no—
336C22⋊Dic11—28no—
337C22⋊Dic11—44no—
338(C2×D11)⋊C4—28no—
339(C2×D11)⋊C4—28no—
340(C2×D11)⋊C4—28no—
341(C2×D11)⋊C4—28no—
342(C2×D11)⋊C4—28no—
343(C2×D11)⋊C4—28no—
344(C2×D11)⋊C4—44no—
345(C2×D11)⋊C4—44no—
346C23×#41—111no—
347C22×#120—111no—
348C22×#120—111no—
349C23×C22⋊C4—111no—
350#2404—1116no—
351C2×#393—111no—
352C2×#393—111no—
353C2×#392—111no—
354C2×#392—111no—
355C2×#386—111no—
356C2×#386—111no—
357C2×#386—111no—
358C2×#386—111no—
359C2×#386—111no—
360C2×#386D1111yescharacteristic, complemented
361C2×#381—111no—
362C23×C11—28no—
363C23×C11—28no—
364C23×C11—28no—
365C23×C11—28no—
366C23×C11—28no—
367C23×C11—28no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—44no—
381C23×C11—44no—
382C23×C11—44no—
383C23×C11—44no—
384C23×C11—44no—
385C23×C11—44no—
386C23×C11—44no—
387C23×C11—44no—
388C23×C11C22×D414yes—
389C23×C11C22×D412yes—
390C23×C11C22×D412yes—
391C23×C11C22×D412yes—
392C23×C11C2×#4112yes—
393C23×C11C2×#4112yes—
394C23×C11C2×#4114yescomplemented
395C23×C11H(5,𝔽2)12yes—
396C23×C11H(5,𝔽2)12yes—
397C23×C11C2511yescharacteristic
398C22×D11—28no—
399C22×D11—28no—
400C22×D11—28no—
401C22×D11—28no—
402C22×D11—28no—
403C22×D11—28no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—232no—
409C22×D11—28no—
410C22×D11—28no—
411C22×D11—28no—
412C22×D11—28no—
413C22×D11—28no—
414C22×D11—28no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—22no—
425C22×D11—22no—
426C22×D11—22no—
427C22×D11—416no—
428C22×D11—416no—
429C22×D11—416no—
430C22×D11—416no—
431C22×D11—4128no—
432C22×D11—416no—
433C22×D11—44no—
434C22×D11—44no—
435C22×D11—44no—
436C22×D11—44no—
437C22×D11—44no—
438C22×D11—44no—
439C22×D11—44no—
440C22×D11—44no—
441C22×D11—416no—
442C22×D11#120116yes—
443C22×D11C22×D414yes—
444C22×D11C22×D414yes—
445C22×D11C22×D414yes—
446C22×D11C22×D414yes—
447C22×D11C2×#4114yescomplemented
448D4×C11—416no—
449C2×C4×C11—232no—
450C2×C4×C11—28no—
451C2×C4×C11—28no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—44no—
466C2×C4×C11—44no—
467C2×C4×C11—44no—
468C2×C4×C11C22×D414yes—
469C2×C4×C11C22×D414yes—
470C22⋊D11—232no—
471C22⋊D11—232no—
472C22⋊D11—416no—
473C22⋊D11—416no—
474C2×Dic11—28no—
475C2×Dic11—28no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—44no—
490C2×Dic11—44no—
491C2×Dic11—44no—
492C2×Dic11C22×D414yes—
493C2×Dic11C22×D414yes—
494D44—232no—
495D44—416no—
496C4×D11—232no—
497C4×D11—232no—
498C4×D11—416no—
499Dic22—232no—
500C26—111no—
501C22×#41—118no—
502C22×#41—228no—
503C22×#41—228no—
504C22×#41—228no—
505C23×Q8—111no—
506C23×D4—111no—
507C23×D4—111no—
508C23×D4—111no—
509C23×D4—111no—
510C23×D4—111no—
511C23×D4—111no—
512C23×D4C2×D1111yescharacteristic
513C24×C4—111no—
514C24×C4—111no—
515C24×C4—111no—
516C24×C4C2×D1111yescharacteristic, complemented
517C2×#120—118no—
518C2×#120—118no—
519C2×#120—228no—
520C2×#120—228no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4—111no—
529C22×C22⋊C4—111no—
530C22×C22⋊C4—111no—
531C22×C22⋊C4—111no—
532C22×C22⋊C4—118no—
533C22×C22⋊C4—228no—
534C22×C22⋊C4C2×D1111yescharacteristic
535C22×C22⋊C4C2×D1111yescharacteristic
536C22×C22⋊C4C2×D1111yescharacteristic, complemented
537#393—118no—
538#393—118no—
539#392—118no—
540#392—118no—
541#386—118no—
542#386—118no—
543#386—118no—
544#386—118no—
545#386—118no—
546#386C2×D1118yescomplemented
547#381—118no—
548C2×#95—111no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95—111no—
552C2×#95—111no—
553C2×#95—111no—
554C2×#95C2×D1111yescharacteristic, complemented
555C2×#95C2×D1111yescharacteristic, complemented
556C22×C11—24no—
557C22×C11—24no—
558C22×C11—24no—
559C22×C11—24no—
560C22×C11—24no—
561C22×C11—24no—
562C22×C11—416no—
563C22×C11—416no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—42no—
572C22×C11C2×#12014yes—
573C22×C11#52514yes—
574C22×C11#53514yes—
575C22×C11#54614yes—
576C22×C11#54614yes—
577C22×C11#54614yes—
578C22×C11#54614yes—
579C22×C11C23×D411yescharacteristic
580C22×C11C23×D411yescharacteristic
581C22×C11C23×D411yescharacteristic
582C22×C11C22×#4111yescharacteristic
583C22×C11C22×#4111yescharacteristic
584C22×C11C2×H(5,𝔽2)11yescharacteristic
585C22×C11C2×H(5,𝔽2)11yescharacteristic
586C2×D11—232no—
587C2×D11—24no—
588C2×D11—24no—
589C2×D11—24no—
590C2×D11—24no—
591C2×D11—24no—
592C2×D11—24no—
593C2×D11—24no—
594C2×D11—24no—
595C2×D11—24no—
596C2×D11—24no—
597C2×D11—24no—
598C2×D11—24no—
599C2×D11—464no—
600C2×D11—416no—
601C2×D11—416no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C2×D11—42no—
606C2×D11—42no—
607C2×D11—42no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11C2×#12018yes—
611C4×C11—24no—
612C4×C11—24no—
613C4×C11—42no—
614C4×C11—42no—
615C4×C11—42no—
616Dic11—24no—
617Dic11—24no—
618Dic11—42no—
619Dic11—42no—
620Dic11—42no—
621C25—111no—
622C25—111no—
623C25—111no—
624C25—114no—
625C25—224no—
626C25—224no—
627C25—224no—
628C25—224no—
629C25—224no—
630C25—442no—
631C25—442no—
632C25C22×D1111yescharacteristic
633C25C22×D1111yescharacteristic
634C2×#41—2232no—
635C2×#41—2232no—
636C2×#41—2232no—
637C2×#41—22128no—
638C22×Q8—114no—
639C22×Q8—224no—
640C22×Q8—224no—
641C22×Q8—224no—
642C22×D4—24no—
643C22×D4—24no—
644C22×D4—42no—
645C22×D4—118no—
646C22×D4—114no—
647C22×D4—114no—
648C22×D4—114no—
649C22×D4—114no—
650C22×D4—118no—
651C22×D4—114no—
652C22×D4—114no—
653C22×D4—224no—
654C22×D4—224no—
655C22×D4—224no—
656C22×D4—224no—
657C22×D4—224no—
658C22×D4—224no—
659C22×D4—224no—
660C22×D4—224no—
661C22×D4—224no—
662C22×D4—224no—
663C22×D4—224no—
664C22×D4—224no—
665C22×D4—224no—
666C22×D4—442no—
667C22×D4—442no—
668C22×D4—442no—
669C22×D4C22×D1114yes—
670C23×C4—24no—
671C23×C4—24no—
672C23×C4—24no—
673C23×C4—111no—
674C23×C4—111no—
675C23×C4—118no—
676C23×C4—114no—
677C23×C4—111no—
678C23×C4—111no—
679C23×C4—111no—
680C23×C4—114no—
681C23×C4—114no—
682C23×C4—224no—
683C23×C4—224no—
684C23×C4—224no—
685C23×C4—224no—
686C23×C4—224no—
687C23×C4—224no—
688C23×C4—442no—
689C23×C4—442no—
690C23×C4C22×D1111yescharacteristic
691C23×C4C22×D1111yescharacteristic
692C23×C4C22×D1111yescharacteristic
693C23×C4C22×D1111yescharacteristic
694C23×C4C22×D1111yescharacteristic
695C23×C4C22×D1114yescomplemented
696#120—2232no—
697#120—2232no—
698C2×C22⋊C4—24no—
699C2×C22⋊C4—24no—
700C2×C22⋊C4—42no—
701C2×C22⋊C4—114no—
702C2×C22⋊C4—114no—
703C2×C22⋊C4—114no—
704C2×C22⋊C4—114no—
705C2×C22⋊C4—114no—
706C2×C22⋊C4—114no—
707C2×C22⋊C4—114no—
708C2×C22⋊C4—114no—
709C2×C22⋊C4—114no—
710C2×C22⋊C4—114no—
711C2×C22⋊C4—114no—
712C2×C22⋊C4—2232no—
713C2×C22⋊C4—224no—
714C2×C22⋊C4—224no—
715C2×C22⋊C4—224no—
716C2×C22⋊C4—224no—
717C2×C22⋊C4—224no—
718C2×C22⋊C4—224no—
719C2×C22⋊C4—224no—
720C2×C22⋊C4—224no—
721C2×C22⋊C4—442no—
722C2×C22⋊C4—442no—
723C2×C22⋊C4—442no—
724C2×C22⋊C4C22×D1114yes—
725C2×C22⋊C4C22×D1114yes—
726C2×C22⋊C4C22×D1114yescomplemented
727#95—114no—
728#95—114no—
729#95—114no—
730#95—114no—
731#95—114no—
732#95—114no—
733#95C22×D1114yescomplemented
734#95C22×D1114yescomplemented
735C2×C11—44no—
736C2×C11—44no—
737C2×C11#240418yescomplemented
738C2×C11C22×#12011yescharacteristic
739C2×C11C2×#52511yescharacteristic
740C2×C11C2×#53511yescharacteristic
741C2×C11C2×#54611yescharacteristic
742C2×C11C2×#54611yescharacteristic
743C2×C11C2×#54611yescharacteristic
744C2×C11C2×#54611yescharacteristic
745D11—28no—
746D11—44no—
747D11—44no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—22no—
753C24—22no—
754C24—22no—
755C24—22no—
756C24—22no—
757C24—22no—
758C24—22no—
759C24—22no—
760C24—114no—
761C24—114no—
762C24—114no—
763C24—112no—
764C24—114no—
765C24—114no—
766C24—112no—
767C24—112no—
768C24—228no—
769C24—228no—
770C24—228no—
771C24—228no—
772C24—2232no—
773C24—222no—
774C24—222no—
775C24—222no—
776C24—222no—
777C24—222no—
778C24—222no—
779C24—228no—
780C24—222no—
781C24—222no—
782C24—222no—
783C24—222no—
784C24—222no—
785C24—222no—
786C24—222no—
787C24—222no—
788C24—222no—
789C24—222no—
790C24—444no—
791C24—444no—
792C24—4416no—
793C24—4416no—
794C24—4416no—
795C24—4416no—
796C24—4416no—
797C24—4416no—
798C24#433914yescomplemented
799C24D4×D1114yes—
800C24C23×D1112yes—
801C24C23×D1112yes—
802C24C23×D1111yescharacteristic
803#41—22256no—
804C2×Q8—228no—
805C2×Q8—228no—
806C2×Q8—2232no—
807C2×Q8—228no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—44no—
811C2×D4—416no—
812C2×D4—1116no—
813C2×D4—1116no—
814C2×D4—2232no—
815C2×D4—228no—
816C2×D4—228no—
817C2×D4—228no—
818C2×D4—228no—
819C2×D4—228no—
820C2×D4—2232no—
821C2×D4—228no—
822C2×D4—228no—
823C2×D4—228no—
824C2×D4—2232no—
825C2×D4—228no—
826C2×D4—228no—
827C2×D4—228no—
828C2×D4—228no—
829C2×D4—228no—
830C2×D4—444no—
831C2×D4—4416no—
832C2×D4—444no—
833C2×D4—444no—
834C2×D4—4416no—
835C2×D4—4416no—
836C22×C4—232no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—28no—
842C22×C4—28no—
843C22×C4—28no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—114no—
854C22×C4—114no—
855C22×C4—112no—
856C22×C4—112no—
857C22×C4—1116no—
858C22×C4—112no—
859C22×C4—112no—
860C22×C4—112no—
861C22×C4—228no—
862C22×C4—2232no—
863C22×C4—228no—
864C22×C4—228no—
865C22×C4—228no—
866C22×C4—2232no—
867C22×C4—228no—
868C22×C4—222no—
869C22×C4—222no—
870C22×C4—222no—
871C22×C4—222no—
872C22×C4—228no—
873C22×C4—222no—
874C22×C4—222no—
875C22×C4—222no—
876C22×C4—222no—
877C22×C4—222no—
878C22×C4—222no—
879C22×C4—222no—
880C22×C4—222no—
881C22×C4—222no—
882C22×C4—444no—
883C22×C4—444no—
884C22×C4—4416no—
885C22×C4D4×D1114yes—
886C22×C4D4×D1114yes—
887C22×C4C23×D1112yes—
888C22×C4C23×D1112yes—
889C22×C4C23×D1112yes—
890C22×C4C23×D1112yes—
891C22×C4C23×D1112yes—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—44no—
895C22⋊C4—228no—
896C22⋊C4—228no—
897C22⋊C4—228no—
898C22⋊C4—228no—
899C22⋊C4—228no—
900C22⋊C4—228no—
901C22⋊C4—228no—
902C22⋊C4—228no—
903C22⋊C4—444no—
904C22⋊C4—444no—
905C22⋊C4—444no—
906C11C2×#240411yescharacteristic, complemented, Sylow
907C23—28no—
908C23—28no—
909C23—28no—
910C23—28no—
911C23—28no—
912C23—28no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—44no—
926C23—44no—
927C23—44no—
928C23—44no—
929C23—44no—
930C23—44no—
931C23—44no—
932C23—44no—
933C23—1116no—
934C23—114no—
935C23—114no—
936C23—114no—
937C23—114no—
938C23—114no—
939C23—2232no—
940C23—228no—
941C23—228no—
942C23—228no—
943C23—228no—
944C23—228no—
945C23—228no—
946C23—222no—
947C23—222no—
948C23—222no—
949C23—222no—
950C23—228no—
951C23—228no—
952C23—228no—
953C23—228no—
954C23—228no—
955C23—228no—
956C23—222no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—222no—
963C23—222no—
964C23—222no—
965C23—222no—
966C23—222no—
967C23—222no—
968C23—4416no—
969C23—4416no—
970C23—4416no—
971C23—4416no—
972C23—4416no—
973C23—44128no—
974C23—4416no—
975C23—444no—
976C23—444no—
977C23—444no—
978C23—444no—
979C23—444no—
980C23—444no—
981C23—444no—
982C23—444no—
983C23C2×#433912yes—
984C23C2×#433914yescomplemented
985C23C2×D4×D1114yes—
986C23C2×D4×D1112yes—
987C23C2×D4×D1112yes—
988C23C2×D4×D1112yes—
989C23#6703712yes—
990C23#41×D1112yes—
991C23#6704212yes—
992C23C24×D1111yescharacteristic
993Q8—2232no—
994D4—416no—
995D4—2232no—
996D4—2232no—
997D4—2232no—
998D4—4416no—
999D4—4416no—
1000D4—4416no—
1001C2×C4—232no—
1002C2×C4—28no—
1003C2×C4—28no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—44no—
1018C2×C4—44no—
1019C2×C4—44no—
1020C2×C4—114no—
1021C2×C4—114no—
1022C2×C4—2232no—
1023C2×C4—2232no—
1024C2×C4—228no—
1025C2×C4—228no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—4416no—
1040C2×C4—444no—
1041C2×C4—444no—
1042C2×C4—444no—
1043C2×C4C2×D4×D1114yes—
1044C2×C4C2×D4×D1114yes—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—24no—
1050C22—24no—
1051C22—42no—
1052C22—416no—
1053C22—416no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—118no—
1062C22—224no—
1063C22—2232no—
1064C22—224no—
1065C22—224no—
1066C22—224no—
1067C22—224no—
1068C22—224no—
1069C22—224no—
1070C22—224no—
1071C22—224no—
1072C22—224no—
1073C22—224no—
1074C22—224no—
1075C22—4464no—
1076C22—442no—
1077C22—4416no—
1078C22—4416no—
1079C22—442no—
1080C22—442no—
1081C22—442no—
1082C22—442no—
1083C22—442no—
1084C22—442no—
1085C22—442no—
1086C22#1062302114yes—
1087C22#1062307814yes—
1088C22#1062308114yes—
1089C22D11×#12014yes—
1090C22#1062313814yes—
1091C22#1062314314yes—
1092C22#1062318514yes—
1093C22C22×#433911yescharacteristic
1094C22C22×D4×D1111yescharacteristic
1095C22C22×D4×D1111yescharacteristic
1096C22C22×D4×D1111yescharacteristic
1097C22C2×#6703711yescharacteristic
1098C22C2×#41×D1111yescharacteristic
1099C22C2×#6704211yescharacteristic
1100C4—24no—
1101C4—24no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—224no—
1106C4—224no—
1107C4—442no—
1108C4—442no—
1109C4—442no—
1110C2—44no—
1111C2—44no—
1112C2—228no—
1113C2—444no—
1114C2—444no—
1115C2#1307193318yesdirect product factor
1116C2C2×D11×#12011yescharacteristic
1117C2C2×#1062307811yescharacteristic
1118C2C2×#1062313811yescharacteristic
1119C2C2×#1062302111yescharacteristic
1120C2C2×#1062318511yescharacteristic
1121C2C2×#1062308111yescharacteristic
1122C2C2×#1062314311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
hypercenterC2×#386D11
hypocenterC11C2×#2404
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C23×#4339C2semidirect
2. C22×#66935C2semidirect
3. C22×#66990C2semidirect
4. C22×C22⋊C4×D11C2semidirect
5. #13071933C2direct (N × H)
6. C2×#10622286C2semidirect
7. C2×#10622560C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622836C2semidirect
10. C2×#10622826C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622277C2semidirect
16. C2×C11×#386C2semidirect
19. C24×C4×C11C22semidirect
23. C23×C22⋊D11C22semidirect
27. C22×#4339C22semidirect
32. C23×C4×D11C22semidirect
33. C23×Dic22C22semidirect
36. C22×C11×C22⋊C4C22semidirect
39. C22×C22⋊Dic11C22semidirect
41. C2×#66990C22semidirect
48. C22×(C2×D11)⋊C4C22semidirect
49. C22×(C2×D11)⋊C4C22semidirect
51. C2×#66935C22semidirect
53. C2×C22⋊C4×D11C22semidirect
54. C11×#386C22semidirect
55. C2×C11×#95C22semidirect
56. C2×C11×#95C22semidirect
57. #10622836C22semidirect
58. #10622826C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. C2×C11⋊#95C22semidirect
62. C2×C11⋊#95C22semidirect
63. C2×C11⋊#95C22semidirect
64. C2×C11⋊#95C22semidirect
65. #10622573C22semidirect
66. #10622569C22semidirect
67. #10622569C22semidirect
68. #10622560C22semidirect
69. #10622286C22semidirect
70. #10622278C22semidirect
71. #10622278C22semidirect
72. #10622277C22semidirect
98. C23×C4×C11C23semidirect
110. C22×C22⋊D11D4semidirect
114. C22×C22⋊D11C23semidirect
129. C22×D44D4semidirect
140. C22×C4×D11D4semidirect
143. C22×C4×D11C23semidirect
147. C22×Dic22C23semidirect
153. C2×C11×C22⋊C4C23semidirect
159. C2×C22⋊Dic11C23semidirect
175. C2×(C2×D11)⋊C4C23semidirect
176. C2×(C2×D11)⋊C4C23semidirect
179. C11×#95C23semidirect
180. C11×#95C23semidirect
181. C11⋊#95C23semidirect
182. C11⋊#95C23semidirect
183. C11⋊#95C23semidirect
184. C11⋊#95C23semidirect
185. C11⋊#95C23semidirect
186. C11⋊#95C23semidirect
201. C24×C11#41semidirect
239. C23×D11#41semidirect
286. C2×C22⋊D11C2×D4semidirect
315. C2×D44C2×D4semidirect
327. C2×C4×D11C2×D4semidirect
360. C2×#386D11semidirect
394. C23×C11C2×#41semidirect
447. C22×D11C2×#41semidirect
516. C24×C4C2×D11semidirect
536. C22×C22⋊C4C2×D11semidirect
546. #386C2×D11semidirect
554. C2×#95C2×D11semidirect
555. C2×#95C2×D11semidirect
695. C23×C4C22×D11semidirect
726. C2×C22⋊C4C22×D11semidirect
733. #95C22×D11semidirect
734. #95C22×D11semidirect
737. C2×C11#2404semidirect
798. C24#4339semidirect
906. C11C2×#2404semidirect
984. C23C2×#4339semidirect
1115. C2#13071933direct (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×#669352
C22×#669902
C22×C22⋊C4×D112
#130719332
C2×#106222862
C2×#106225602
C2×#106225732
C2×#106228362
C2×#106228262
C2×#106222782
C2×#106225692
C2×#106222772
C2×C11×#3862
C2×#240411