Finite Group Databasebeta

← C2×#13074355 #14920108

Subgroups — C2×#13074355 #14920108

Order 2816.

5222 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic, complemented
2C22×#66935C211yesmaximal, characteristic, complemented
3C22×#66990C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#13074355C2116yesmaximal, direct product factor
6C2×#10622288C211yesmaximal, characteristic, complemented
7C2×#10622565C211yesmaximal, characteristic, complemented
8C2×#10622604C211yesmaximal, characteristic, complemented
9C2×#10622574C211yesmaximal, characteristic, complemented
10C2×#10622574C211yesmaximal, characteristic, complemented
11C2×#10622573C211yesmaximal, characteristic, complemented
12C2×#10622836C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622600C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic, complemented
23C23×D44C2211yescharacteristic
24C23×D44C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic, complemented
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic, complemented
31C22×C11×C22⋊C4C2211yescharacteristic, complemented
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic, complemented
35C2×#66990—28no—
36C2×#66990C2218yescomplemented
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
46C22×C4⋊Dic11C2211yescharacteristic, complemented
47C22×Dic11⋊C4C2211yescharacteristic, complemented
48C2×#66937—28no—
49C2×#66937C2218yescomplemented
50C2×#66935—28no—
51C2×#66935C2218yescomplemented
52C2×C22⋊C4×D11—28no—
53C2×C22⋊C4×D11C2218yescomplemented
54C11×#394C2218yescomplemented
55C2×C11×#95C2211yescharacteristic, complemented
56#10622836C2218yescomplemented
57C2×C11⋊#95C2211yescharacteristic, complemented
58C2×C11⋊#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61C2×C11⋊#95C2211yescharacteristic, complemented
62#10622604C2218yescomplemented
63#10622600C2218yescomplemented
64#10622574C2218yescomplemented
65#10622574C2218yescomplemented
66#10622573C2218yescomplemented
67#10622569C2218yescomplemented
68#10622565C2218yescomplemented
69#10622288C2218yescomplemented
70#10622278C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—42no—
76C24×D11—42no—
77C24×D11—42no—
78C24×D11—42no—
79C24×D11D418yescomplemented
80C24×D11C2311yescharacteristic
81C24×D11C2311yescharacteristic
82C24×D11C2311yescharacteristic
83C24×D11C2314yes—
84C22×D4×C11—24no—
85C22×D4×C11—42no—
86C22×D4×C11—42no—
87C22×D4×C11C2314yes—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—42no—
100C22×C22⋊D11—42no—
101C22×C22⋊D11—42no—
102C22×C22⋊D11—42no—
103C22×C22⋊D11—42no—
104C22×C22⋊D11—42no—
105C22×C22⋊D11C2314yes—
106C22×C22⋊D11C2314yes—
107C22×C22⋊D11C2314yes—
108C22×C22⋊D11C2314yescomplemented
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C22×D44—24no—
115C22×D44—24no—
116C22×D44—24no—
117C22×D44—24no—
118C22×D44—42no—
119C22×D44—42no—
120C22×D44C2314yes—
121C22×D44C2314yes—
122C22×C4×D11—24no—
123C22×C4×D11—42no—
124C22×C4×D11—42no—
125C22×C4×D11—42no—
126C22×C4×D11—42no—
127C22×C4×D11D418yescomplemented
128C22×C4×D11C2314yes—
129C22×C4×D11C2314yes—
130C2×C11×C4⋊C4—42no—
131C2×C11×C4⋊C4C2314yescomplemented
132C2×C11×C22⋊C4—24no—
133C2×C11×C22⋊C4—24no—
134C2×C11×C22⋊C4—24no—
135C2×C11×C22⋊C4—42no—
136C2×C11×C22⋊C4C2314yes—
137C2×C11×C22⋊C4C2314yes—
138C2×C11×C22⋊C4C2314yescomplemented
139C2×C11×C22⋊C4C2314yescomplemented
140C2×C22⋊Dic11—24no—
141C2×C22⋊Dic11—24no—
142C2×C22⋊Dic11—42no—
143C2×C22⋊Dic11C2314yes—
144C2×C22⋊Dic11C2314yes—
145C2×C22⋊Dic11C2314yescomplemented
146#66990—232no—
147C2×(C2×D11)⋊C4—24no—
148C2×(C2×D11)⋊C4—24no—
149C2×(C2×D11)⋊C4—24no—
150C2×(C2×D11)⋊C4—24no—
151C2×(C2×D11)⋊C4—24no—
152C2×(C2×D11)⋊C4—24no—
153C2×(C2×D11)⋊C4—24no—
154C2×(C2×D11)⋊C4—42no—
155C2×(C2×D11)⋊C4—42no—
156C2×(C2×D11)⋊C4C2314yes—
157C2×(C2×D11)⋊C4C2314yes—
158C2×(C2×D11)⋊C4C2314yes—
159C2×(C2×D11)⋊C4C2314yes—
160C2×(C2×D11)⋊C4C2314yes—
161C2×(C2×D11)⋊C4C2314yes—
162C2×(C2×D11)⋊C4C2314yescomplemented
163C2×(C2×D11)⋊C4C2314yescomplemented
164C2×(C2×D11)⋊C4C2314yescomplemented
165C2×C4⋊Dic11—42no—
166C2×C4⋊Dic11C2314yescomplemented
167C2×Dic11⋊C4—24no—
168C2×Dic11⋊C4C2314yescomplemented
169#66937—232no—
170#66935—232no—
171C22⋊C4×D11—232no—
172C11×#95C2314yescomplemented
173C11⋊#95C2314yescomplemented
174C11⋊#95C2314yescomplemented
175C11⋊#95C2314yescomplemented
176C11⋊#95C2314yescomplemented
177C11⋊#95C2314yescomplemented
178C2×#2617—111nomaximal, Sylow
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11—22no—
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11C2×D414yes—
193C24×C11C2412yes—
194C24×C11C2412yes—
195C24×C11C2411yescharacteristic
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—232no—
207C23×D11—28no—
208C23×D11—28no—
209C23×D11—22no—
210C23×D11—22no—
211C23×D11—22no—
212C23×D11—22no—
213C23×D11—22no—
214C23×D11—22no—
215C23×D11—22no—
216C23×D11—416no—
217C23×D11—416no—
218C23×D11—44no—
219C23×D11—44no—
220C23×D11—44no—
221C23×D11—44no—
222C23×D11—416no—
223C23×D11—416no—
224C23×D11—416no—
225C23×D11—416no—
226C23×D11C2×D414yes—
227C23×D11C2×D414yes—
228C23×D11C2×D414yes—
229C23×D11C2×D4116yescomplemented
230C23×D11#4114yes—
231C23×D11C2412yes—
232C23×D11C2412yes—
233C23×D11C2412yes—
234C2×D4×C11—28no—
235C2×D4×C11—44no—
236C2×D4×C11—44no—
237C2×D4×C11—416no—
238C22×C4×C11—22no—
239C22×C4×C11—22no—
240C22×C4×C11—22no—
241C22×C4×C11—22no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—22no—
251C22×C4×C11—22no—
252C22×C4×C11C2×D414yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2412yes—
257C22×C4×C11C2412yes—
258C2×C22⋊D11—28no—
259C2×C22⋊D11—28no—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—28no—
263C2×C22⋊D11—28no—
264C2×C22⋊D11—44no—
265C2×C22⋊D11—44no—
266C2×C22⋊D11—44no—
267C2×C22⋊D11—44no—
268C2×C22⋊D11—44no—
269C2×C22⋊D11—44no—
270C2×C22⋊D11—416no—
271C2×C22⋊D11—416no—
272C2×C22⋊D11—416no—
273C2×C22⋊D11—416no—
274C22×Dic11—22no—
275C22×Dic11—22no—
276C22×Dic11—22no—
277C22×Dic11—22no—
278C22×Dic11—22no—
279C22×Dic11—22no—
280C22×Dic11—22no—
281C22×Dic11—22no—
282C22×Dic11—22no—
283C22×Dic11—22no—
284C22×Dic11—22no—
285C22×Dic11—22no—
286C22×Dic11—22no—
287C22×Dic11—22no—
288C22×Dic11C2×D414yes—
289C22×Dic11C2412yes—
290C22×Dic11C2412yes—
291C22×Dic11C2412yes—
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C2×D44—28no—
295C2×D44—28no—
296C2×D44—28no—
297C2×D44—28no—
298C2×D44—44no—
299C2×D44—44no—
300C2×D44—416no—
301C2×D44—416no—
302C2×C4×D11—28no—
303C2×C4×D11—416no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—416no—
309C2×C4×D11C2×D4116yescomplemented
310C11×C4⋊C4—44no—
311C11×C22⋊C4—28no—
312C11×C22⋊C4—28no—
313C11×C22⋊C4—28no—
314C11×C22⋊C4—44no—
315C22⋊Dic11—28no—
316C22⋊Dic11—28no—
317C22⋊Dic11—44no—
318(C2×D11)⋊C4—28no—
319(C2×D11)⋊C4—28no—
320(C2×D11)⋊C4—28no—
321(C2×D11)⋊C4—28no—
322(C2×D11)⋊C4—28no—
323(C2×D11)⋊C4—28no—
324(C2×D11)⋊C4—28no—
325(C2×D11)⋊C4—44no—
326(C2×D11)⋊C4—44no—
327C4⋊Dic11—44no—
328Dic11⋊C4—28no—
329C22×#121—111no—
330C22×#120—111no—
331C22×#120—111no—
332C23×C22⋊C4—111no—
333#2617—1116no—
334C2×#397—111no—
335C2×#397—111no—
336C2×#394—111no—
337C2×#394—111no—
338C2×#394—111no—
339C2×#394D1111yescharacteristic, complemented
340C2×#392—111no—
341C2×#392—111no—
342C2×#386—111no—
343C2×#386—111no—
344C2×#380—111no—
345C23×C11—28no—
346C23×C11—28no—
347C23×C11—28no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—44no—
362C23×C11—44no—
363C23×C11—44no—
364C23×C11—44no—
365C23×C11—44no—
366C23×C11—44no—
367C23×C11—44no—
368C23×C11—44no—
369C23×C11—44no—
370C23×C11—44no—
371C23×C11—44no—
372C23×C11C22×D414yes—
373C23×C11C22×D412yes—
374C23×C11C22×D412yes—
375C23×C11C2×#4112yes—
376C23×C11H(5,𝔽2)12yes—
377C23×C11H(5,𝔽2)12yes—
378C23×C11H(5,𝔽2)12yes—
379C23×C11H(5,𝔽2)12yes—
380C23×C11C2511yescharacteristic
381C22×D11—28no—
382C22×D11—28no—
383C22×D11—28no—
384C22×D11—28no—
385C22×D11—28no—
386C22×D11—28no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—28no—
392C22×D11—28no—
393C22×D11—28no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—232no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—416no—
409C22×D11—416no—
410C22×D11—4128no—
411C22×D11—416no—
412C22×D11—416no—
413C22×D11—416no—
414C22×D11—416no—
415C22×D11—44no—
416C22×D11—44no—
417C22×D11—44no—
418C22×D11—44no—
419C22×D11—44no—
420C22×D11—44no—
421C22×D11—44no—
422C22×D11—44no—
423C22×D11—44no—
424C22×D11—44no—
425C22×D11—44no—
426C22×D11#121116yes—
427C22×D11C22×D414yes—
428C22×D11C22×D414yes—
429C22×D11C22×D414yes—
430C22×D11C2×#4114yes—
431D4×C11—416no—
432C2×C4×C11—28no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—44no—
448C2×C4×C11—44no—
449C2×C4×C11—44no—
450C2×C4×C11—44no—
451C2×C4×C11C22×D414yes—
452C22⋊D11—416no—
453C22⋊D11—416no—
454C22⋊D11—416no—
455C22⋊D11—416no—
456C2×Dic11—28no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—44no—
472C2×Dic11—44no—
473C2×Dic11—44no—
474C2×Dic11—44no—
475C2×Dic11C22×D414yes—
476D44—416no—
477D44—416no—
478C4×D11—416no—
479C4×D11—416no—
480C26—111no—
481C23×D4—111no—
482C23×D4—111no—
483C23×D4—111no—
484C23×D4—111no—
485C23×D4—111no—
486C23×D4—111no—
487C23×D4C2×D1111yescharacteristic
488C24×C4—111no—
489C24×C4—111no—
490C2×#121—118no—
491C2×#121—228no—
492C2×#120—118no—
493C2×#120—118no—
494C2×#120—228no—
495C2×#120—228no—
496C22×C4⋊C4—111no—
497C22×C4⋊C4—111no—
498C22×C4⋊C4C2×D1111yescharacteristic, complemented
499C22×C22⋊C4—111no—
500C22×C22⋊C4—111no—
501C22×C22⋊C4—111no—
502C22×C22⋊C4—111no—
503C22×C22⋊C4—111no—
504C22×C22⋊C4—111no—
505C22×C22⋊C4—111no—
506C22×C22⋊C4—111no—
507C22×C22⋊C4—111no—
508C22×C22⋊C4—111no—
509C22×C22⋊C4—111no—
510C22×C22⋊C4—111no—
511C22×C22⋊C4—118no—
512C22×C22⋊C4—228no—
513C22×C22⋊C4C2×D1111yescharacteristic
514C22×C22⋊C4C2×D1111yescharacteristic
515C22×C22⋊C4C2×D1111yescharacteristic, complemented
516C22×C22⋊C4C2×D1111yescharacteristic, complemented
517#397—118no—
518#397—118no—
519#394—118no—
520#394—118no—
521#394—118no—
522#394C2×D1118yescomplemented
523#392—118no—
524#392—118no—
525#386—118no—
526#386—118no—
527#380—118no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95—111no—
533C2×#95C2×D1111yescharacteristic, complemented
534C22×C11—24no—
535C22×C11—24no—
536C22×C11—24no—
537C22×C11—416no—
538C22×C11—42no—
539C22×C11—42no—
540C22×C11—42no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—88no—
550C22×C11C2×#12114yes—
551C22×C11#53414yes—
552C22×C11#53414yes—
553C22×C11#53414yes—
554C22×C11#53514yes—
555C22×C11#53814yes—
556C22×C11#53814yes—
557C22×C11C23×D411yescharacteristic
558C22×C11C23×D411yescharacteristic
559C22×C11C22×#4111yescharacteristic
560C22×C11C2×H(5,𝔽2)11yescharacteristic
561C22×C11C2×H(5,𝔽2)11yescharacteristic
562C22×C11C2×H(5,𝔽2)11yescharacteristic
563C22×C11C2×H(5,𝔽2)11yescharacteristic
564C2×D11—232no—
565C2×D11—24no—
566C2×D11—24no—
567C2×D11—24no—
568C2×D11—24no—
569C2×D11—24no—
570C2×D11—24no—
571C2×D11—24no—
572C2×D11—24no—
573C2×D11—24no—
574C2×D11—464no—
575C2×D11—416no—
576C2×D11—42no—
577C2×D11—42no—
578C2×D11—42no—
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—42no—
584C2×D11—42no—
585C2×D11—42no—
586C2×D11—42no—
587C2×D11—88no—
588C2×D11C2×#12118yes—
589C4×C11—24no—
590C4×C11—42no—
591C4×C11—42no—
592C4×C11—42no—
593C4×C11—42no—
594Dic11—24no—
595Dic11—42no—
596Dic11—42no—
597Dic11—42no—
598Dic11—42no—
599C25—111no—
600C25—111no—
601C25—118no—
602C25—114no—
603C25—111no—
604C25—224no—
605C25—224no—
606C25—442no—
607C25—442no—
608C25—442no—
609C25—442no—
610C25C22×D1111yescharacteristic
611C25C22×D1111yescharacteristic
612C22×D4—24no—
613C22×D4—42no—
614C22×D4—42no—
615C22×D4—114no—
616C22×D4—114no—
617C22×D4—114no—
618C22×D4—114no—
619C22×D4—114no—
620C22×D4—114no—
621C22×D4—224no—
622C22×D4—224no—
623C22×D4—224no—
624C22×D4—224no—
625C22×D4—224no—
626C22×D4—224no—
627C22×D4—224no—
628C22×D4—224no—
629C22×D4—224no—
630C22×D4—224no—
631C22×D4—442no—
632C22×D4—442no—
633C22×D4—442no—
634C22×D4—442no—
635C22×D4—442no—
636C22×D4—442no—
637C22×D4—442no—
638C22×D4—442no—
639C22×D4C22×D1114yes—
640C23×C4—111no—
641C23×C4—118no—
642C23×C4—114no—
643C23×C4—111no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—111no—
647C23×C4—114no—
648C23×C4—224no—
649C23×C4—442no—
650C23×C4—442no—
651C23×C4—442no—
652C23×C4—442no—
653C23×C4C22×D1111yescharacteristic
654C23×C4C22×D1111yescharacteristic
655C23×C4C22×D1111yescharacteristic
656C23×C4C22×D1111yescharacteristic
657C23×C4C22×D1111yescharacteristic
658#121—2232no—
659#120—2232no—
660#120—2232no—
661C2×C4⋊C4—42no—
662C2×C4⋊C4—114no—
663C2×C4⋊C4—114no—
664C2×C4⋊C4—224no—
665C2×C4⋊C4—442no—
666C2×C4⋊C4C22×D1114yescomplemented
667C2×C22⋊C4—24no—
668C2×C22⋊C4—24no—
669C2×C22⋊C4—24no—
670C2×C22⋊C4—42no—
671C2×C22⋊C4—114no—
672C2×C22⋊C4—114no—
673C2×C22⋊C4—114no—
674C2×C22⋊C4—114no—
675C2×C22⋊C4—114no—
676C2×C22⋊C4—114no—
677C2×C22⋊C4—114no—
678C2×C22⋊C4—114no—
679C2×C22⋊C4—114no—
680C2×C22⋊C4—114no—
681C2×C22⋊C4—114no—
682C2×C22⋊C4—114no—
683C2×C22⋊C4—2232no—
684C2×C22⋊C4—224no—
685C2×C22⋊C4—224no—
686C2×C22⋊C4—224no—
687C2×C22⋊C4—224no—
688C2×C22⋊C4—224no—
689C2×C22⋊C4—224no—
690C2×C22⋊C4—224no—
691C2×C22⋊C4—224no—
692C2×C22⋊C4—224no—
693C2×C22⋊C4—442no—
694C2×C22⋊C4—442no—
695C2×C22⋊C4—442no—
696C2×C22⋊C4C22×D1114yes—
697C2×C22⋊C4C22×D1114yes—
698C2×C22⋊C4C22×D1114yescomplemented
699C2×C22⋊C4C22×D1114yescomplemented
700#95—114no—
701#95—114no—
702#95—114no—
703#95—114no—
704#95—114no—
705#95C22×D1114yescomplemented
706C2×C11—44no—
707C2×C11—82no—
708C2×C11#261718yescomplemented
709C2×C11C22×#12111yescharacteristic
710C2×C11C2×#53411yescharacteristic
711C2×C11C2×#53411yescharacteristic
712C2×C11C2×#53411yescharacteristic
713C2×C11C2×#53511yescharacteristic
714C2×C11C2×#53811yescharacteristic
715C2×C11C2×#53811yescharacteristic
716D11—28no—
717D11—44no—
718D11—82no—
719C24—22no—
720C24—22no—
721C24—22no—
722C24—22no—
723C24—22no—
724C24—22no—
725C24—22no—
726C24—22no—
727C24—22no—
728C24—22no—
729C24—22no—
730C24—22no—
731C24—22no—
732C24—114no—
733C24—114no—
734C24—114no—
735C24—112no—
736C24—114no—
737C24—112no—
738C24—1116no—
739C24—112no—
740C24—228no—
741C24—2232no—
742C24—228no—
743C24—222no—
744C24—222no—
745C24—222no—
746C24—222no—
747C24—222no—
748C24—222no—
749C24—222no—
750C24—222no—
751C24—222no—
752C24—222no—
753C24—222no—
754C24—222no—
755C24—222no—
756C24—222no—
757C24—222no—
758C24—222no—
759C24—222no—
760C24—4416no—
761C24—4416no—
762C24—444no—
763C24—444no—
764C24—444no—
765C24—444no—
766C24—4416no—
767C24—4416no—
768C24—4416no—
769C24—4416no—
770C24D4×D1114yes—
771C24C23×D1112yes—
772C24C23×D1112yes—
773C24C23×D1111yescharacteristic
774C2×D4—28no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—416no—
778C2×D4—228no—
779C2×D4—228no—
780C2×D4—228no—
781C2×D4—228no—
782C2×D4—228no—
783C2×D4—228no—
784C2×D4—228no—
785C2×D4—228no—
786C2×D4—228no—
787C2×D4—228no—
788C2×D4—444no—
789C2×D4—444no—
790C2×D4—4416no—
791C2×D4—4416no—
792C2×D4—444no—
793C2×D4—444no—
794C2×D4—444no—
795C2×D4—444no—
796C2×D4—444no—
797C2×D4—444no—
798C2×D4—4416no—
799C2×D4—4416no—
800C2×D4—4416no—
801C2×D4—4416no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—114no—
817C22×C4—112no—
818C22×C4—1116no—
819C22×C4—112no—
820C22×C4—112no—
821C22×C4—112no—
822C22×C4—112no—
823C22×C4—228no—
824C22×C4—222no—
825C22×C4—222no—
826C22×C4—222no—
827C22×C4—222no—
828C22×C4—222no—
829C22×C4—222no—
830C22×C4—222no—
831C22×C4—222no—
832C22×C4—222no—
833C22×C4—222no—
834C22×C4—222no—
835C22×C4—222no—
836C22×C4—222no—
837C22×C4—222no—
838C22×C4—4416no—
839C22×C4—444no—
840C22×C4—444no—
841C22×C4—444no—
842C22×C4—444no—
843C22×C4—4416no—
844C22×C4D4×D1114yes—
845C22×C4C23×D1112yes—
846C22×C4C23×D1112yes—
847C22×C4C23×D1112yes—
848C22×C4C23×D1112yes—
849C22×C4C23×D1112yes—
850C4⋊C4—44no—
851C4⋊C4—228no—
852C4⋊C4—444no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—44no—
857C22⋊C4—228no—
858C22⋊C4—228no—
859C22⋊C4—228no—
860C22⋊C4—228no—
861C22⋊C4—228no—
862C22⋊C4—228no—
863C22⋊C4—228no—
864C22⋊C4—228no—
865C22⋊C4—228no—
866C22⋊C4—444no—
867C22⋊C4—444no—
868C22⋊C4—444no—
869C11C2×#261711yescharacteristic, complemented, Sylow
870C23—28no—
871C23—28no—
872C23—28no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—44no—
887C23—44no—
888C23—44no—
889C23—44no—
890C23—44no—
891C23—44no—
892C23—44no—
893C23—44no—
894C23—44no—
895C23—44no—
896C23—44no—
897C23—1116no—
898C23—114no—
899C23—114no—
900C23—114no—
901C23—114no—
902C23—2232no—
903C23—228no—
904C23—228no—
905C23—228no—
906C23—228no—
907C23—228no—
908C23—222no—
909C23—222no—
910C23—222no—
911C23—222no—
912C23—228no—
913C23—228no—
914C23—228no—
915C23—228no—
916C23—222no—
917C23—222no—
918C23—222no—
919C23—222no—
920C23—222no—
921C23—222no—
922C23—222no—
923C23—222no—
924C23—222no—
925C23—222no—
926C23—222no—
927C23—222no—
928C23—222no—
929C23—4416no—
930C23—4416no—
931C23—4416no—
932C23—4416no—
933C23—4416no—
934C23—4416no—
935C23—44128no—
936C23—444no—
937C23—444no—
938C23—444no—
939C23—444no—
940C23—444no—
941C23—444no—
942C23—444no—
943C23—444no—
944C23—444no—
945C23—444no—
946C23—444no—
947C23C2×D4×D1114yes—
948C23C2×D4×D1112yes—
949C23C2×D4×D1112yes—
950C23#6703712yes—
951C23#6703712yes—
952C23#41×D1112yes—
953C23#6704212yes—
954C23#6704212yes—
955C23C24×D1111yescharacteristic
956D4—416no—
957D4—4416no—
958D4—4416no—
959D4—4416no—
960D4—4416no—
961D4—4416no—
962D4—4416no—
963C2×C4—28no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—44no—
979C2×C4—44no—
980C2×C4—44no—
981C2×C4—44no—
982C2×C4—114no—
983C2×C4—228no—
984C2×C4—222no—
985C2×C4—222no—
986C2×C4—222no—
987C2×C4—222no—
988C2×C4—222no—
989C2×C4—222no—
990C2×C4—222no—
991C2×C4—222no—
992C2×C4—222no—
993C2×C4—222no—
994C2×C4—222no—
995C2×C4—222no—
996C2×C4—222no—
997C2×C4—222no—
998C2×C4—4416no—
999C2×C4—4416no—
1000C2×C4—444no—
1001C2×C4—444no—
1002C2×C4—444no—
1003C2×C4—444no—
1004C2×C4C2×D4×D1114yes—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—416no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—88no—
1021C22—118no—
1022C22—224no—
1023C22—224no—
1024C22—224no—
1025C22—224no—
1026C22—224no—
1027C22—224no—
1028C22—2232no—
1029C22—224no—
1030C22—224no—
1031C22—224no—
1032C22—4464no—
1033C22—442no—
1034C22—442no—
1035C22—442no—
1036C22—442no—
1037C22—4416no—
1038C22—442no—
1039C22—442no—
1040C22—442no—
1041C22—442no—
1042C22—442no—
1043C22—442no—
1044C22—442no—
1045C22—888no—
1046C22#1062312014yes—
1047C22D11×#12114yes—
1048C22#1062313614yes—
1049C22#1062313814yes—
1050C22#1062318414yes—
1051C22#1062318814yes—
1052C22#1062320914yes—
1053C22C22×D4×D1111yescharacteristic
1054C22C22×D4×D1111yescharacteristic
1055C22C2×#6703711yescharacteristic
1056C22C2×#6703711yescharacteristic
1057C22C2×#41×D1111yescharacteristic
1058C22C2×#6704211yescharacteristic
1059C22C2×#6704211yescharacteristic
1060C4—24no—
1061C4—42no—
1062C4—42no—
1063C4—42no—
1064C4—42no—
1065C4—224no—
1066C4—442no—
1067C4—442no—
1068C4—442no—
1069C4—442no—
1070C2—44no—
1071C2—82no—
1072C2—228no—
1073C2—444no—
1074C2—882no—
1075C2#1307435518yesdirect product factor
1076C2C2×D11×#12111yescharacteristic
1077C2C2×#1062313611yescharacteristic
1078C2C2×#1062312011yescharacteristic
1079C2C2×#1062318411yescharacteristic
1080C2C2×#1062313811yescharacteristic
1081C2C2×#1062320911yescharacteristic
1082C2C2×#1062318811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2617
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66937C2semidirect
2. C22×#66935C2semidirect
3. C22×#66990C2semidirect
4. C22×C22⋊C4×D11C2semidirect
5. #13074355C2direct (N × H)
6. C2×#10622288C2semidirect
7. C2×#10622565C2semidirect
8. C2×#10622604C2semidirect
9. C2×#10622574C2semidirect
10. C2×#10622574C2semidirect
11. C2×#10622573C2semidirect
12. C2×#10622836C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622600C2semidirect
16. C2×C11×#394C2semidirect
22. C23×C22⋊D11C22semidirect
27. C22×C11×C4⋊C4C22semidirect
30. C22×C11×C22⋊C4C22semidirect
31. C22×C11×C22⋊C4C22semidirect
34. C22×C22⋊Dic11C22semidirect
36. C2×#66990C22semidirect
43. C22×(C2×D11)⋊C4C22semidirect
44. C22×(C2×D11)⋊C4C22semidirect
45. C22×(C2×D11)⋊C4C22semidirect
46. C22×C4⋊Dic11C22semidirect
47. C22×Dic11⋊C4C22semidirect
49. C2×#66937C22semidirect
51. C2×#66935C22semidirect
53. C2×C22⋊C4×D11C22semidirect
54. C11×#394C22semidirect
55. C2×C11×#95C22semidirect
56. #10622836C22semidirect
57. C2×C11⋊#95C22semidirect
58. C2×C11⋊#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. C2×C11⋊#95C22semidirect
62. #10622604C22semidirect
63. #10622600C22semidirect
64. #10622574C22semidirect
65. #10622574C22semidirect
66. #10622573C22semidirect
67. #10622569C22semidirect
68. #10622565C22semidirect
69. #10622288C22semidirect
70. #10622278C22semidirect
79. C24×D11D4semidirect
108. C22×C22⋊D11C23semidirect
127. C22×C4×D11D4semidirect
131. C2×C11×C4⋊C4C23semidirect
138. C2×C11×C22⋊C4C23semidirect
139. C2×C11×C22⋊C4C23semidirect
145. C2×C22⋊Dic11C23semidirect
162. C2×(C2×D11)⋊C4C23semidirect
163. C2×(C2×D11)⋊C4C23semidirect
164. C2×(C2×D11)⋊C4C23semidirect
166. C2×C4⋊Dic11C23semidirect
168. C2×Dic11⋊C4C23semidirect
172. C11×#95C23semidirect
173. C11⋊#95C23semidirect
174. C11⋊#95C23semidirect
175. C11⋊#95C23semidirect
176. C11⋊#95C23semidirect
177. C11⋊#95C23semidirect
229. C23×D11C2×D4semidirect
309. C2×C4×D11C2×D4semidirect
339. C2×#394D11semidirect
498. C22×C4⋊C4C2×D11semidirect
515. C22×C22⋊C4C2×D11semidirect
516. C22×C22⋊C4C2×D11semidirect
522. #394C2×D11semidirect
533. C2×#95C2×D11semidirect
666. C2×C4⋊C4C22×D11semidirect
698. C2×C22⋊C4C22×D11semidirect
699. C2×C22⋊C4C22×D11semidirect
705. #95C22×D11semidirect
708. C2×C11#2617semidirect
869. C11C2×#2617semidirect
1075. C2#13074355direct (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×#669352
C22×#669902
C22×C22⋊C4×D112
#130743552
C2×#106222882
C2×#106225652
C2×#106226042
C2×#106225742
C2×#106225732
C2×#106228362
C2×#106222782
C2×#106225692
C2×#106226002
C2×C11×#3942
C2×#261711