Finite Group Databasebeta

← C2×#13071985 #14921186

Subgroups — C2×#13071985 #14921186

Order 2816.

8730 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D4×D11C211yesmaximal, characteristic, complemented
2C22×#66948C211yesmaximal, characteristic, complemented
3C22×#66937C211yesmaximal, characteristic, complemented
4C22×#66935C211yesmaximal, characteristic, complemented
5C22×#66935C211yesmaximal, characteristic, complemented
6C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
7#13071985C2116yesmaximal, direct product factor
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic, complemented
10C2×#10622836C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C25×D11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic, complemented
23C23×C22⋊D11C2211yescharacteristic, complemented
24C22×D4×D11—28no—
25C22×D4×D11—28no—
26C22×D4×D11—28no—
27C22×D4×D11C2218yescomplemented
28C23×D44C2211yescharacteristic
29C23×D44C2211yescharacteristic
30C23×D44C2211yescharacteristic, complemented
31C23×D44C2211yescharacteristic, complemented
32C23×C4×D11C2211yescharacteristic
33C23×C4×D11C2211yescharacteristic, complemented
34C23×C4×D11C2211yescharacteristic, complemented
35C22×C11×C4⋊C4C2211yescharacteristic, complemented
36C22×C11×C22⋊C4C2211yescharacteristic, complemented
37C22×C11×C22⋊C4C2211yescharacteristic, complemented
38C22×C11×C22⋊C4C2211yescharacteristic, complemented
39C22×C11×C22⋊C4C2211yescharacteristic, complemented
40C22×C22⋊Dic11C2211yescharacteristic, complemented
41C22×C22⋊Dic11C2211yescharacteristic, complemented
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
46C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
47C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
48C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
49C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
50C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
51C22×Dic11⋊C4C2211yescharacteristic, complemented
52C2×#66948—28no—
53C2×#66948C2218yescomplemented
54C2×#66937—28no—
55C2×#66937C2218yescomplemented
56C2×#66935—28no—
57C2×#66935—28no—
58C2×#66935C2218yescomplemented
59C2×#66935C2218yescomplemented
60C2×C22⋊C4×D11—28no—
61C2×C22⋊C4×D11C2218yescomplemented
62C11×#394C2218yescomplemented
63C2×C11×#95C2211yescharacteristic, complemented
64#10622836C2218yescomplemented
65C2×C11⋊#95C2211yescharacteristic, complemented
66C2×C11⋊#95C2211yescharacteristic, complemented
67C2×C11⋊#95C2211yescharacteristic, complemented
68#10622602C2218yescomplemented
69#10622573C2218yescomplemented
70#10622572C2218yescomplemented
71#10622569C2218yescomplemented
72#10622568C2218yescomplemented
73#10622278C2218yescomplemented
74#10622278C2218yescomplemented
75C25×C11C2311yescharacteristic
76C25×C11C2311yescharacteristic
77C24×D11—24no—
78C24×D11—24no—
79C24×D11—24no—
80C24×D11—24no—
81C24×D11—24no—
82C24×D11—24no—
83C24×D11—24no—
84C24×D11—24no—
85C24×D11—24no—
86C24×D11—42no—
87C24×D11—42no—
88C24×D11—42no—
89C24×D11—42no—
90C24×D11D418yescomplemented
91C24×D11C2311yescharacteristic
92C24×D11C2311yescharacteristic
93C24×D11C2314yes—
94C24×D11C2314yes—
95C24×D11C2311yescharacteristic
96C24×D11C2311yescharacteristic
97C22×D4×C11—24no—
98C22×D4×C11—24no—
99C22×D4×C11—24no—
100C22×D4×C11C2314yes—
101C23×C4×C11C2311yescharacteristic
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C22×C22⋊D11—24no—
107C22×C22⋊D11—24no—
108C22×C22⋊D11—24no—
109C22×C22⋊D11—24no—
110C22×C22⋊D11—24no—
111C22×C22⋊D11—24no—
112C22×C22⋊D11—24no—
113C22×C22⋊D11—24no—
114C22×C22⋊D11—42no—
115C22×C22⋊D11—42no—
116C22×C22⋊D11—42no—
117C22×C22⋊D11D418yescomplemented
118C22×C22⋊D11C2314yes—
119C22×C22⋊D11C2314yes—
120C22×C22⋊D11C2314yescomplemented
121C22×C22⋊D11C2314yescomplemented
122C23×Dic11C2311yescharacteristic
123C23×Dic11C2311yescharacteristic
124C23×Dic11C2311yescharacteristic
125C23×Dic11C2311yescharacteristic
126C2×D4×D11—2128no—
127C2×D4×D11—232no—
128C2×D4×D11—232no—
129C2×D4×D11—232no—
130C22×D44—24no—
131C22×D44—24no—
132C22×D44—24no—
133C22×D44—24no—
134C22×D44—24no—
135C22×D44—24no—
136C22×D44—24no—
137C22×D44—24no—
138C22×D44—24no—
139C22×D44—24no—
140C22×D44—42no—
141C22×D44D418yescomplemented
142C22×D44C2314yes—
143C22×D44C2314yes—
144C22×D44C2314yescomplemented
145C22×D44C2314yescomplemented
146C22×C4×D11—24no—
147C22×C4×D11—24no—
148C22×C4×D11—24no—
149C22×C4×D11—24no—
150C22×C4×D11—24no—
151C22×C4×D11—24no—
152C22×C4×D11—24no—
153C22×C4×D11—42no—
154C22×C4×D11—42no—
155C22×C4×D11C2314yes—
156C22×C4×D11C2314yescomplemented
157C22×C4×D11C2314yescomplemented
158C2×C11×C4⋊C4—24no—
159C2×C11×C4⋊C4C2314yescomplemented
160C2×C11×C22⋊C4—24no—
161C2×C11×C22⋊C4—24no—
162C2×C11×C22⋊C4—24no—
163C2×C11×C22⋊C4—24no—
164C2×C11×C22⋊C4C2314yescomplemented
165C2×C11×C22⋊C4C2314yescomplemented
166C2×C11×C22⋊C4C2314yescomplemented
167C2×C11×C22⋊C4C2314yescomplemented
168C2×C22⋊Dic11—24no—
169C2×C22⋊Dic11—42no—
170C2×C22⋊Dic11C2314yescomplemented
171C2×C22⋊Dic11C2314yescomplemented
172C2×(C2×D11)⋊C4—24no—
173C2×(C2×D11)⋊C4—24no—
174C2×(C2×D11)⋊C4—24no—
175C2×(C2×D11)⋊C4—24no—
176C2×(C2×D11)⋊C4—24no—
177C2×(C2×D11)⋊C4—24no—
178C2×(C2×D11)⋊C4—24no—
179C2×(C2×D11)⋊C4—42no—
180C2×(C2×D11)⋊C4D418yescomplemented
181C2×(C2×D11)⋊C4C2314yes—
182C2×(C2×D11)⋊C4C2314yes—
183C2×(C2×D11)⋊C4C2314yes—
184C2×(C2×D11)⋊C4C2314yescomplemented
185C2×(C2×D11)⋊C4C2314yescomplemented
186C2×(C2×D11)⋊C4C2314yescomplemented
187C2×(C2×D11)⋊C4C2314yescomplemented
188C2×(C2×D11)⋊C4C2314yescomplemented
189C2×(C2×D11)⋊C4C2314yescomplemented
190C2×Dic11⋊C4—24no—
191C2×Dic11⋊C4C2314yescomplemented
192#66948—232no—
193#66937—232no—
194#66935—232no—
195#66935—232no—
196C22⋊C4×D11—232no—
197C11×#95C2314yescomplemented
198C11⋊#95C2314yescomplemented
199C11⋊#95C2314yescomplemented
200C11⋊#95C2314yescomplemented
201C2×#2410—111nomaximal, Sylow
202C24×C11—22no—
203C24×C11—22no—
204C24×C11—22no—
205C24×C11—22no—
206C24×C11—22no—
207C24×C11—22no—
208C24×C11—22no—
209C24×C11—22no—
210C24×C11—22no—
211C24×C11—22no—
212C24×C11—22no—
213C24×C11—22no—
214C24×C11C2×D414yes—
215C24×C11C2×D414yes—
216C24×C11C2412yes—
217C24×C11C2412yes—
218C24×C11C2411yescharacteristic
219C23×D11—22no—
220C23×D11—22no—
221C23×D11—22no—
222C23×D11—22no—
223C23×D11—22no—
224C23×D11—22no—
225C23×D11—22no—
226C23×D11—22no—
227C23×D11—232no—
228C23×D11—22no—
229C23×D11—22no—
230C23×D11—22no—
231C23×D11—28no—
232C23×D11—22no—
233C23×D11—22no—
234C23×D11—22no—
235C23×D11—232no—
236C23×D11—232no—
237C23×D11—28no—
238C23×D11—28no—
239C23×D11—28no—
240C23×D11—28no—
241C23×D11—28no—
242C23×D11—28no—
243C23×D11—22no—
244C23×D11—22no—
245C23×D11—22no—
246C23×D11—22no—
247C23×D11—22no—
248C23×D11—22no—
249C23×D11—22no—
250C23×D11—28no—
251C23×D11—28no—
252C23×D11—416no—
253C23×D11—44no—
254C23×D11—44no—
255C23×D11—44no—
256C23×D11—44no—
257C23×D11—416no—
258C23×D11—416no—
259C23×D11—416no—
260C23×D11—416no—
261C23×D11—416no—
262C23×D11—416no—
263C23×D11—416no—
264C23×D11—416no—
265C23×D11—416no—
266C23×D11—416no—
267C23×D11C2×D414yes—
268C23×D11C2×D414yes—
269C23×D11C2×D414yes—
270C23×D11C2×D414yes—
271C23×D11C2×D414yes—
272C23×D11C2×D414yes—
273C23×D11C2×D4116yescomplemented
274C23×D11#4114yes—
275C23×D11C2412yes—
276C23×D11C2412yes—
277C23×D11C2412yes—
278C23×D11C2412yes—
279C2×D4×C11—232no—
280C2×D4×C11—28no—
281C2×D4×C11—28no—
282C2×D4×C11—28no—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11—22no—
291C22×C4×C11—22no—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11—22no—
295C22×C4×C11—22no—
296C22×C4×C11C2×D414yes—
297C22×C4×C11C2×D414yescomplemented
298C22×C4×C11C2412yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2412yes—
303C2×C22⋊D11—232no—
304C2×C22⋊D11—28no—
305C2×C22⋊D11—28no—
306C2×C22⋊D11—28no—
307C2×C22⋊D11—28no—
308C2×C22⋊D11—28no—
309C2×C22⋊D11—232no—
310C2×C22⋊D11—28no—
311C2×C22⋊D11—28no—
312C2×C22⋊D11—28no—
313C2×C22⋊D11—44no—
314C2×C22⋊D11—44no—
315C2×C22⋊D11—44no—
316C2×C22⋊D11—416no—
317C2×C22⋊D11—416no—
318C2×C22⋊D11C2×D4116yescomplemented
319C22×Dic11—22no—
320C22×Dic11—22no—
321C22×Dic11—22no—
322C22×Dic11—22no—
323C22×Dic11—22no—
324C22×Dic11—22no—
325C22×Dic11—22no—
326C22×Dic11—22no—
327C22×Dic11—22no—
328C22×Dic11—22no—
329C22×Dic11C2×D414yes—
330C22×Dic11C2×D414yescomplemented
331C22×Dic11C2412yes—
332C22×Dic11C2412yes—
333C22×Dic11C2412yes—
334C22×Dic11C2412yes—
335D4×D11—2256no—
336C2×D44—232no—
337C2×D44—28no—
338C2×D44—28no—
339C2×D44—28no—
340C2×D44—28no—
341C2×D44—28no—
342C2×D44—28no—
343C2×D44—28no—
344C2×D44—28no—
345C2×D44—28no—
346C2×D44—28no—
347C2×D44—44no—
348C2×D44—416no—
349C2×D44—416no—
350C2×D44—416no—
351C2×D44C2×D4116yescomplemented
352C2×C4×D11—232no—
353C2×C4×D11—28no—
354C2×C4×D11—28no—
355C2×C4×D11—28no—
356C2×C4×D11—28no—
357C2×C4×D11—28no—
358C2×C4×D11—28no—
359C2×C4×D11—28no—
360C2×C4×D11—44no—
361C2×C4×D11—44no—
362C2×C4×D11—416no—
363C2×C4×D11—416no—
364C11×C4⋊C4—28no—
365C11×C22⋊C4—28no—
366C11×C22⋊C4—28no—
367C11×C22⋊C4—28no—
368C11×C22⋊C4—28no—
369C22⋊Dic11—28no—
370C22⋊Dic11—44no—
371(C2×D11)⋊C4—28no—
372(C2×D11)⋊C4—28no—
373(C2×D11)⋊C4—28no—
374(C2×D11)⋊C4—28no—
375(C2×D11)⋊C4—28no—
376(C2×D11)⋊C4—28no—
377(C2×D11)⋊C4—28no—
378(C2×D11)⋊C4—44no—
379(C2×D11)⋊C4C2×D4116yescomplemented
380Dic11⋊C4—28no—
381C24×D4—111no—
382C22×#121—111no—
383C22×#121—111no—
384C22×#120—111no—
385C22×#120—111no—
386C23×C22⋊C4—111no—
387#2410—1116no—
388C2×#394—111no—
389C2×#394D1111yescharacteristic, complemented
390C2×#392—111no—
391C2×#392—111no—
392C2×#386—111no—
393C2×#386—111no—
394C2×#386—111no—
395C2×#385—111no—
396C2×#379—111no—
397C23×C11—28no—
398C23×C11—28no—
399C23×C11—28no—
400C23×C11—28no—
401C23×C11—28no—
402C23×C11—28no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—22no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—44no—
416C23×C11—44no—
417C23×C11—44no—
418C23×C11—44no—
419C23×C11—44no—
420C23×C11—44no—
421C23×C11—44no—
422C23×C11—44no—
423C23×C11C22×D414yes—
424C23×C11C22×D414yes—
425C23×C11C22×D412yes—
426C23×C11C22×D412yes—
427C23×C11C22×D412yes—
428C23×C11C22×D412yes—
429C23×C11C2×#4112yes—
430C23×C11H(5,𝔽2)12yes—
431C23×C11H(5,𝔽2)12yes—
432C23×C11C2511yescharacteristic
433C22×D11—28no—
434C22×D11—28no—
435C22×D11—28no—
436C22×D11—28no—
437C22×D11—28no—
438C22×D11—28no—
439C22×D11—28no—
440C22×D11—28no—
441C22×D11—28no—
442C22×D11—28no—
443C22×D11—28no—
444C22×D11—28no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—22no—
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—232no—
454C22×D11—28no—
455C22×D11—28no—
456C22×D11—28no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—232no—
464C22×D11—232no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—416no—
473C22×D11—4128no—
474C22×D11—416no—
475C22×D11—416no—
476C22×D11—416no—
477C22×D11—416no—
478C22×D11—416no—
479C22×D11—416no—
480C22×D11—416no—
481C22×D11—416no—
482C22×D11—4128no—
483C22×D11—416no—
484C22×D11—44no—
485C22×D11—44no—
486C22×D11—44no—
487C22×D11—44no—
488C22×D11—416no—
489C22×D11—44no—
490C22×D11—44no—
491C22×D11—44no—
492C22×D11—44no—
493C22×D11—44no—
494C22×D11—44no—
495C22×D11—44no—
496C22×D11#120116yescomplemented
497C22×D11#121116yescomplemented
498C22×D11C22×D414yes—
499C22×D11C22×D414yes—
500C22×D11C22×D414yes—
501C22×D11C22×D414yes—
502C22×D11C22×D414yes—
503C22×D11C22×D414yes—
504C22×D11C2×#4114yes—
505D4×C11—232no—
506C2×C4×C11—28no—
507C2×C4×C11—28no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—44no—
522C2×C4×C11—44no—
523C2×C4×C11—44no—
524C2×C4×C11C22×D414yes—
525C2×C4×C11C22×D414yescomplemented
526C22⋊D11—232no—
527C22⋊D11—232no—
528C22⋊D11—416no—
529C22⋊D11—416no—
530C2×Dic11—28no—
531C2×Dic11—28no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—44no—
543C2×Dic11—44no—
544C2×Dic11C22×D414yes—
545C2×Dic11C22×D414yescomplemented
546D44—232no—
547D44—416no—
548D44—416no—
549D44—416no—
550C4×D11—232no—
551C4×D11—416no—
552C4×D11—416no—
553C26—111no—
554C26—111no—
555C23×D4—111no—
556C23×D4—111no—
557C23×D4—111no—
558C23×D4—111no—
559C23×D4—118no—
560C23×D4—111no—
561C23×D4—111no—
562C23×D4—111no—
563C23×D4—111no—
564C23×D4—228no—
565C23×D4—228no—
566C23×D4—228no—
567C23×D4C2×D1111yescharacteristic
568C24×C4—111no—
569C24×C4—111no—
570C24×C4—111no—
571C2×#121—118no—
572C2×#121—118no—
573C2×#121—228no—
574C2×#121—228no—
575C2×#120—118no—
576C2×#120—118no—
577C2×#120—228no—
578C2×#120—228no—
579C22×C4⋊C4—111no—
580C22×C4⋊C4C2×D1111yescharacteristic, complemented
581C22×C22⋊C4—111no—
582C22×C22⋊C4—111no—
583C22×C22⋊C4—111no—
584C22×C22⋊C4—111no—
585C22×C22⋊C4—111no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—111no—
588C22×C22⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4—118no—
593C22×C22⋊C4—228no—
594C22×C22⋊C4C2×D1111yescharacteristic, complemented
595C22×C22⋊C4C2×D1111yescharacteristic, complemented
596C22×C22⋊C4C2×D1111yescharacteristic, complemented
597C22×C22⋊C4C2×D1111yescharacteristic, complemented
598#394—118no—
599#394C2×D1118yescomplemented
600#392—118no—
601#392—118no—
602#386—118no—
603#386—118no—
604#386—118no—
605#385—118no—
606#379—118no—
607C2×#95—111no—
608C2×#95—111no—
609C2×#95—111no—
610C2×#95C2×D1111yescharacteristic, complemented
611C22×C11—24no—
612C22×C11—24no—
613C22×C11—24no—
614C22×C11—24no—
615C22×C11—24no—
616C22×C11—24no—
617C22×C11—42no—
618C22×C11—416no—
619C22×C11—416no—
620C22×C11—42no—
621C22×C11—42no—
622C22×C11—42no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11—42no—
627C22×C11C2×#12014yes—
628C22×C11C2×#12114yes—
629C22×C11#53414yes—
630C22×C11D4214yes—
631C22×C11D4214yes—
632C22×C11#54614yes—
633C22×C11#54614yes—
634C22×C11C23×D411yescharacteristic
635C22×C11C23×D411yescharacteristic
636C22×C11C23×D411yescharacteristic
637C22×C11C23×D411yescharacteristic
638C22×C11C22×#4111yescharacteristic
639C22×C11C2×H(5,𝔽2)11yescharacteristic
640C22×C11C2×H(5,𝔽2)11yescharacteristic
641C2×D11—24no—
642C2×D11—24no—
643C2×D11—232no—
644C2×D11—232no—
645C2×D11—24no—
646C2×D11—24no—
647C2×D11—24no—
648C2×D11—24no—
649C2×D11—24no—
650C2×D11—24no—
651C2×D11—24no—
652C2×D11—24no—
653C2×D11—24no—
654C2×D11—24no—
655C2×D11—24no—
656C2×D11—24no—
657C2×D11—24no—
658C2×D11—464no—
659C2×D11—464no—
660C2×D11—42no—
661C2×D11—416no—
662C2×D11—42no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—42no—
668C2×D11—42no—
669C2×D11—42no—
670C2×D11—42no—
671C2×D11—42no—
672C2×D11—88no—
673C2×D11C2×#12018yescomplemented
674C2×D11C2×#12118yescomplemented
675C4×C11—24no—
676C4×C11—24no—
677C4×C11—42no—
678C4×C11—42no—
679C4×C11—42no—
680Dic11—24no—
681Dic11—24no—
682Dic11—42no—
683Dic11—42no—
684C25—111no—
685C25—111no—
686C25—111no—
687C25—118no—
688C25—114no—
689C25—111no—
690C25—114no—
691C25—224no—
692C25—224no—
693C25—224no—
694C25—224no—
695C25—224no—
696C25—224no—
697C25—224no—
698C25—224no—
699C25—224no—
700C25—442no—
701C25—442no—
702C25—442no—
703C25—442no—
704C25C22×D1111yescharacteristic
705C25C22×D1111yescharacteristic
706C22×D4—24no—
707C22×D4—24no—
708C22×D4—24no—
709C22×D4—118no—
710C22×D4—114no—
711C22×D4—114no—
712C22×D4—114no—
713C22×D4—114no—
714C22×D4—118no—
715C22×D4—114no—
716C22×D4—114no—
717C22×D4—114no—
718C22×D4—114no—
719C22×D4—224no—
720C22×D4—224no—
721C22×D4—224no—
722C22×D4—224no—
723C22×D4—224no—
724C22×D4—224no—
725C22×D4—224no—
726C22×D4—224no—
727C22×D4—224no—
728C22×D4—224no—
729C22×D4—224no—
730C22×D4—2232no—
731C22×D4—2232no—
732C22×D4—2232no—
733C22×D4—22128no—
734C22×D4—224no—
735C22×D4—224no—
736C22×D4—224no—
737C22×D4—224no—
738C22×D4—224no—
739C22×D4—224no—
740C22×D4—224no—
741C22×D4—442no—
742C22×D4—442no—
743C22×D4—442no—
744C22×D4—442no—
745C22×D4C22×D1114yes—
746C23×C4—111no—
747C23×C4—111no—
748C23×C4—111no—
749C23×C4—111no—
750C23×C4—114no—
751C23×C4—114no—
752C23×C4—114no—
753C23×C4—224no—
754C23×C4—224no—
755C23×C4—224no—
756C23×C4—224no—
757C23×C4—224no—
758C23×C4—224no—
759C23×C4—224no—
760C23×C4—442no—
761C23×C4—442no—
762C23×C4C22×D1111yescharacteristic
763C23×C4C22×D1111yescharacteristic
764C23×C4C22×D1111yescharacteristic
765C23×C4C22×D1111yescharacteristic
766C23×C4C22×D1111yescharacteristic
767#121—2232no—
768#121—2232no—
769#120—2232no—
770#120—2232no—
771C2×C4⋊C4—24no—
772C2×C4⋊C4—114no—
773C2×C4⋊C4—224no—
774C2×C4⋊C4C22×D1114yescomplemented
775C2×C22⋊C4—24no—
776C2×C22⋊C4—24no—
777C2×C22⋊C4—24no—
778C2×C22⋊C4—24no—
779C2×C22⋊C4—118no—
780C2×C22⋊C4—114no—
781C2×C22⋊C4—114no—
782C2×C22⋊C4—114no—
783C2×C22⋊C4—114no—
784C2×C22⋊C4—114no—
785C2×C22⋊C4—114no—
786C2×C22⋊C4—114no—
787C2×C22⋊C4—114no—
788C2×C22⋊C4—114no—
789C2×C22⋊C4—114no—
790C2×C22⋊C4—114no—
791C2×C22⋊C4—2232no—
792C2×C22⋊C4—224no—
793C2×C22⋊C4—224no—
794C2×C22⋊C4—224no—
795C2×C22⋊C4—224no—
796C2×C22⋊C4—224no—
797C2×C22⋊C4—224no—
798C2×C22⋊C4—224no—
799C2×C22⋊C4—224no—
800C2×C22⋊C4—442no—
801C2×C22⋊C4—442no—
802C2×C22⋊C4C22×D1114yescomplemented
803C2×C22⋊C4C22×D1114yescomplemented
804C2×C22⋊C4C22×D1114yescomplemented
805C2×C22⋊C4C22×D1114yescomplemented
806#95—114no—
807#95—114no—
808#95—114no—
809#95C22×D1114yescomplemented
810C2×C11—44no—
811C2×C11—44no—
812C2×C11#241018yescomplemented
813C2×C11C22×#12011yescharacteristic
814C2×C11C22×#12111yescharacteristic
815C2×C11C2×#53411yescharacteristic
816C2×C11C2×D4211yescharacteristic
817C2×C11C2×D4211yescharacteristic
818C2×C11C2×#54611yescharacteristic
819C2×C11C2×#54611yescharacteristic
820D11—28no—
821D11—28no—
822D11—44no—
823D11—82no—
824C24—22no—
825C24—22no—
826C24—22no—
827C24—22no—
828C24—22no—
829C24—22no—
830C24—22no—
831C24—22no—
832C24—22no—
833C24—22no—
834C24—22no—
835C24—22no—
836C24—114no—
837C24—114no—
838C24—114no—
839C24—114no—
840C24—114no—
841C24—114no—
842C24—112no—
843C24—112no—
844C24—114no—
845C24—112no—
846C24—1116no—
847C24—112no—
848C24—228no—
849C24—2232no—
850C24—228no—
851C24—228no—
852C24—228no—
853C24—228no—
854C24—2232no—
855C24—228no—
856C24—228no—
857C24—228no—
858C24—2232no—
859C24—222no—
860C24—222no—
861C24—222no—
862C24—222no—
863C24—222no—
864C24—222no—
865C24—222no—
866C24—222no—
867C24—222no—
868C24—228no—
869C24—222no—
870C24—222no—
871C24—222no—
872C24—222no—
873C24—222no—
874C24—222no—
875C24—222no—
876C24—222no—
877C24—222no—
878C24—222no—
879C24—222no—
880C24—222no—
881C24—4416no—
882C24—444no—
883C24—444no—
884C24—444no—
885C24—444no—
886C24—4416no—
887C24—4416no—
888C24—4416no—
889C24—4416no—
890C24—4416no—
891C24—4416no—
892C24—4416no—
893C24—4416no—
894C24—4416no—
895C24—4416no—
896C24D4×D1114yes—
897C24D4×D1114yes—
898C24C23×D1112yes—
899C24C23×D1112yes—
900C24C23×D1111yescharacteristic
901C2×D4—232no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—1116no—
906C2×D4—1116no—
907C2×D4—2232no—
908C2×D4—228no—
909C2×D4—228no—
910C2×D4—228no—
911C2×D4—228no—
912C2×D4—228no—
913C2×D4—228no—
914C2×D4—228no—
915C2×D4—228no—
916C2×D4—228no—
917C2×D4—228no—
918C2×D4—228no—
919C2×D4—22256no—
920C2×D4—2232no—
921C2×D4—228no—
922C2×D4—228no—
923C2×D4—228no—
924C2×D4—2232no—
925C2×D4—228no—
926C2×D4—228no—
927C2×D4—228no—
928C2×D4—228no—
929C2×D4—444no—
930C2×D4—4416no—
931C2×D4—4416no—
932C2×D4—4416no—
933C2×D4—444no—
934C2×D4—444no—
935C2×D4—444no—
936C2×D4—4416no—
937C2×D4—4416no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—114no—
952C22×C4—114no—
953C22×C4—112no—
954C22×C4—112no—
955C22×C4—112no—
956C22×C4—112no—
957C22×C4—228no—
958C22×C4—228no—
959C22×C4—228no—
960C22×C4—2232no—
961C22×C4—228no—
962C22×C4—228no—
963C22×C4—222no—
964C22×C4—222no—
965C22×C4—222no—
966C22×C4—222no—
967C22×C4—228no—
968C22×C4—222no—
969C22×C4—222no—
970C22×C4—222no—
971C22×C4—222no—
972C22×C4—222no—
973C22×C4—222no—
974C22×C4—228no—
975C22×C4—444no—
976C22×C4—444no—
977C22×C4—4416no—
978C22×C4—4416no—
979C22×C4D4×D1114yes—
980C22×C4D4×D1114yescomplemented
981C22×C4C23×D1112yes—
982C22×C4C23×D1112yes—
983C22×C4C23×D1112yes—
984C22×C4C23×D1112yes—
985C22×C4C23×D1112yes—
986C4⋊C4—28no—
987C4⋊C4—228no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—28no—
991C22⋊C4—28no—
992C22⋊C4—1116no—
993C22⋊C4—228no—
994C22⋊C4—228no—
995C22⋊C4—228no—
996C22⋊C4—228no—
997C22⋊C4—228no—
998C22⋊C4—228no—
999C22⋊C4—228no—
1000C22⋊C4—228no—
1001C22⋊C4—444no—
1002C22⋊C4—444no—
1003C11C2×#241011yescharacteristic, complemented, Sylow
1004C23—28no—
1005C23—28no—
1006C23—28no—
1007C23—28no—
1008C23—28no—
1009C23—28no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—44no—
1023C23—44no—
1024C23—44no—
1025C23—44no—
1026C23—44no—
1027C23—44no—
1028C23—44no—
1029C23—44no—
1030C23—1116no—
1031C23—1116no—
1032C23—114no—
1033C23—114no—
1034C23—114no—
1035C23—114no—
1036C23—114no—
1037C23—114no—
1038C23—114no—
1039C23—2232no—
1040C23—2232no—
1041C23—2232no—
1042C23—228no—
1043C23—228no—
1044C23—228no—
1045C23—228no—
1046C23—228no—
1047C23—228no—
1048C23—228no—
1049C23—228no—
1050C23—228no—
1051C23—228no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—228no—
1061C23—228no—
1062C23—228no—
1063C23—228no—
1064C23—222no—
1065C23—222no—
1066C23—222no—
1067C23—222no—
1068C23—222no—
1069C23—222no—
1070C23—228no—
1071C23—222no—
1072C23—222no—
1073C23—222no—
1074C23—222no—
1075C23—222no—
1076C23—222no—
1077C23—222no—
1078C23—4416no—
1079C23—4416no—
1080C23—4416no—
1081C23—4416no—
1082C23—44128no—
1083C23—4416no—
1084C23—4416no—
1085C23—4416no—
1086C23—4416no—
1087C23—4416no—
1088C23—4416no—
1089C23—4416no—
1090C23—44128no—
1091C23—444no—
1092C23—444no—
1093C23—444no—
1094C23—444no—
1095C23—444no—
1096C23—444no—
1097C23—444no—
1098C23—444no—
1099C23—444no—
1100C23—444no—
1101C23—444no—
1102C23C2×D4×D1114yes—
1103C23C2×D4×D1114yes—
1104C23C2×D4×D1112yes—
1105C23C2×D4×D1112yes—
1106C23C2×D4×D1112yes—
1107C23C2×D4×D1112yes—
1108C23#41×D1112yes—
1109C23#6704212yes—
1110C23#6704212yes—
1111C23C24×D1111yescharacteristic
1112D4—232no—
1113D4—2232no—
1114D4—2232no—
1115D4—2232no—
1116D4—4416no—
1117D4—4416no—
1118D4—4416no—
1119D4—4416no—
1120D4—4416no—
1121C2×C4—28no—
1122C2×C4—28no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—44no—
1137C2×C4—44no—
1138C2×C4—44no—
1139C2×C4—114no—
1140C2×C4—114no—
1141C2×C4—2232no—
1142C2×C4—228no—
1143C2×C4—228no—
1144C2×C4—222no—
1145C2×C4—222no—
1146C2×C4—222no—
1147C2×C4—222no—
1148C2×C4—222no—
1149C2×C4—222no—
1150C2×C4—222no—
1151C2×C4—222no—
1152C2×C4—222no—
1153C2×C4—222no—
1154C2×C4—4416no—
1155C2×C4—4416no—
1156C2×C4—444no—
1157C2×C4—444no—
1158C2×C4C2×D4×D1114yes—
1159C2×C4C2×D4×D1114yescomplemented
1160C22—24no—
1161C22—24no—
1162C22—24no—
1163C22—24no—
1164C22—24no—
1165C22—24no—
1166C22—42no—
1167C22—416no—
1168C22—416no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—42no—
1174C22—42no—
1175C22—42no—
1176C22—118no—
1177C22—118no—
1178C22—224no—
1179C22—224no—
1180C22—2232no—
1181C22—2232no—
1182C22—224no—
1183C22—224no—
1184C22—224no—
1185C22—224no—
1186C22—224no—
1187C22—224no—
1188C22—224no—
1189C22—224no—
1190C22—224no—
1191C22—224no—
1192C22—224no—
1193C22—224no—
1194C22—224no—
1195C22—4464no—
1196C22—4464no—
1197C22—442no—
1198C22—4416no—
1199C22—442no—
1200C22—442no—
1201C22—442no—
1202C22—442no—
1203C22—442no—
1204C22—442no—
1205C22—442no—
1206C22—442no—
1207C22—442no—
1208C22—442no—
1209C22—888no—
1210C22D11×#12014yes—
1211C22D11×#12114yes—
1212C22#1062314014yes—
1213C22#1062314014yes—
1214C22#1062318414yes—
1215C22#1062318514yes—
1216C22#1062320714yes—
1217C22C22×D4×D1111yescharacteristic
1218C22C22×D4×D1111yescharacteristic
1219C22C22×D4×D1111yescharacteristic
1220C22C22×D4×D1111yescharacteristic
1221C22C2×#41×D1111yescharacteristic
1222C22C2×#6704211yescharacteristic
1223C22C2×#6704211yescharacteristic
1224C4—24no—
1225C4—24no—
1226C4—42no—
1227C4—42no—
1228C4—42no—
1229C4—224no—
1230C4—224no—
1231C4—442no—
1232C4—442no—
1233C2—44no—
1234C2—44no—
1235C2—228no—
1236C2—228no—
1237C2—444no—
1238C2—882no—
1239C2#1307198518yesdirect product factor
1240C2C2×D11×#12011yescharacteristic
1241C2C2×D11×#12111yescharacteristic
1242C2C2×#1062318411yescharacteristic
1243C2C2×#1062314011yescharacteristic
1244C2C2×#1062314011yescharacteristic
1245C2C2×#1062318511yescharacteristic
1246C2C2×#1062320711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2410
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C23×D4×D11C2semidirect
2. C22×#66948C2semidirect
3. C22×#66937C2semidirect
4. C22×#66935C2semidirect
5. C22×#66935C2semidirect
6. C22×C22⋊C4×D11C2semidirect
7. #13071985C2direct (N × H)
8. C2×#10622572C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622568C2semidirect
16. C2×C11×#394C2semidirect
22. C23×C22⋊D11C22semidirect
23. C23×C22⋊D11C22semidirect
27. C22×D4×D11C22semidirect
30. C23×D44C22semidirect
31. C23×D44C22semidirect
33. C23×C4×D11C22semidirect
34. C23×C4×D11C22semidirect
35. C22×C11×C4⋊C4C22semidirect
36. C22×C11×C22⋊C4C22semidirect
37. C22×C11×C22⋊C4C22semidirect
38. C22×C11×C22⋊C4C22semidirect
39. C22×C11×C22⋊C4C22semidirect
40. C22×C22⋊Dic11C22semidirect
41. C22×C22⋊Dic11C22semidirect
45. C22×(C2×D11)⋊C4C22semidirect
46. C22×(C2×D11)⋊C4C22semidirect
47. C22×(C2×D11)⋊C4C22semidirect
48. C22×(C2×D11)⋊C4C22semidirect
49. C22×(C2×D11)⋊C4C22semidirect
50. C22×(C2×D11)⋊C4C22semidirect
51. C22×Dic11⋊C4C22semidirect
53. C2×#66948C22semidirect
55. C2×#66937C22semidirect
58. C2×#66935C22semidirect
59. C2×#66935C22semidirect
61. C2×C22⋊C4×D11C22semidirect
62. C11×#394C22semidirect
63. C2×C11×#95C22semidirect
64. #10622836C22semidirect
65. C2×C11⋊#95C22semidirect
66. C2×C11⋊#95C22semidirect
67. C2×C11⋊#95C22semidirect
68. #10622602C22semidirect
69. #10622573C22semidirect
70. #10622572C22semidirect
71. #10622569C22semidirect
72. #10622568C22semidirect
73. #10622278C22semidirect
74. #10622278C22semidirect
90. C24×D11D4semidirect
117. C22×C22⋊D11D4semidirect
120. C22×C22⋊D11C23semidirect
121. C22×C22⋊D11C23semidirect
141. C22×D44D4semidirect
144. C22×D44C23semidirect
145. C22×D44C23semidirect
156. C22×C4×D11C23semidirect
157. C22×C4×D11C23semidirect
159. C2×C11×C4⋊C4C23semidirect
164. C2×C11×C22⋊C4C23semidirect
165. C2×C11×C22⋊C4C23semidirect
166. C2×C11×C22⋊C4C23semidirect
167. C2×C11×C22⋊C4C23semidirect
170. C2×C22⋊Dic11C23semidirect
171. C2×C22⋊Dic11C23semidirect
180. C2×(C2×D11)⋊C4D4semidirect
184. C2×(C2×D11)⋊C4C23semidirect
185. C2×(C2×D11)⋊C4C23semidirect
186. C2×(C2×D11)⋊C4C23semidirect
187. C2×(C2×D11)⋊C4C23semidirect
188. C2×(C2×D11)⋊C4C23semidirect
189. C2×(C2×D11)⋊C4C23semidirect
191. C2×Dic11⋊C4C23semidirect
197. C11×#95C23semidirect
198. C11⋊#95C23semidirect
199. C11⋊#95C23semidirect
200. C11⋊#95C23semidirect
273. C23×D11C2×D4semidirect
297. C22×C4×C11C2×D4semidirect
318. C2×C22⋊D11C2×D4semidirect
330. C22×Dic11C2×D4semidirect
351. C2×D44C2×D4semidirect
379. (C2×D11)⋊C4C2×D4semidirect
389. C2×#394D11semidirect
496. C22×D11#120semidirect
497. C22×D11#121semidirect
525. C2×C4×C11C22×D4semidirect
545. C2×Dic11C22×D4semidirect
580. C22×C4⋊C4C2×D11semidirect
594. C22×C22⋊C4C2×D11semidirect
595. C22×C22⋊C4C2×D11semidirect
596. C22×C22⋊C4C2×D11semidirect
597. C22×C22⋊C4C2×D11semidirect
599. #394C2×D11semidirect
610. C2×#95C2×D11semidirect
673. C2×D11C2×#120semidirect
674. C2×D11C2×#121semidirect
774. C2×C4⋊C4C22×D11semidirect
802. C2×C22⋊C4C22×D11semidirect
803. C2×C22⋊C4C22×D11semidirect
804. C2×C22⋊C4C22×D11semidirect
805. C2×C22⋊C4C22×D11semidirect
809. #95C22×D11semidirect
812. C2×C11#2410semidirect
980. C22×C4D4×D11semidirect
1003. C11C2×#2410semidirect
1159. C2×C4C2×D4×D11semidirect
1239. C2#13071985direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4×D112
C22×#669482
C22×#669372
C22×#669352
C22×C22⋊C4×D112
#130719852
C2×#106225722
C2×#106225732
C2×#106228362
C2×#106222782
C2×#106225692
C2×#106226022
C2×#106225682
C2×C11×#3942
C2×#241011