Finite Group Databasebeta

← C2×#13073516 #14924923

Subgroups — C2×#13073516 #14924923

Order 2816.

4390 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5#13073516C2116yesmaximal, direct product factor
6C2×#10622288C211yesmaximal, characteristic, complemented
7C2×#10622565C211yesmaximal, characteristic, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622836C211yesmaximal, characteristic, complemented
10C2×#10622826C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622263C211yesmaximal, characteristic, complemented
14C2×#10622280C211yesmaximal, characteristic, complemented
15C2×#10622555C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C23×D44C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×#66992—28no—
34C2×#66992C2218yescomplemented
35C2×C4×C22⋊D11—28no—
36C2×C4×C22⋊D11C2218yescomplemented
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×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C2×#66937—28no—
49C2×#66937C2218yescomplemented
50C2×(C22⋊D11)⋊C4—28no—
51C2×(C22⋊D11)⋊C4C2218yescomplemented
52C11×#386C2218yescomplemented
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55#10622836C2218yescomplemented
56#10622826C2218yescomplemented
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63#10622573C2218yescomplemented
64#10622569C2218yescomplemented
65#10622565C2218yescomplemented
66#10622555C2218yescomplemented
67#10622288C2218yescomplemented
68#10622280C2218yescomplemented
69#10622278C2218yescomplemented
70#10622263C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—42no—
78C22×D4×C11C2314yes—
79C23×C4×C11—24no—
80C23×C4×C11—42no—
81C23×C4×C11—42no—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2314yes—
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—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—42no—
98C22×C22⋊D11—42no—
99C22×C22⋊D11D418yescomplemented
100C22×C22⋊D11C2314yes—
101C22×C22⋊D11C2314yes—
102C22×C22⋊D11C2314yes—
103C22×C22⋊D11C2314yes—
104C23×Dic11—24no—
105C23×Dic11—24no—
106C23×Dic11—24no—
107C23×Dic11C2314yes—
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C22×D44—24no—
115C22×D44—24no—
116C22×D44—42no—
117C22×D44C2314yes—
118C22×C4×D11—24no—
119C22×C4×D11—24no—
120C22×C4×D11—24no—
121C22×C4×D11—24no—
122C22×C4×D11—42no—
123C22×C4×D11—42no—
124C22×C4×D11C2314yes—
125C22×C4×D11C2314yes—
126C2×C11×C22⋊C4—24no—
127C2×C11×C22⋊C4—24no—
128C2×C11×C22⋊C4—42no—
129C2×C11×C22⋊C4C2314yes—
130C2×C11×C22⋊C4C2314yes—
131C2×C11×C22⋊C4C2314yes—
132C2×C22⋊Dic11—24no—
133C2×C22⋊Dic11—24no—
134C2×C22⋊Dic11—42no—
135C2×C22⋊Dic11C2314yes—
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yes—
138#66992—232no—
139C4×C22⋊D11—232no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—42no—
145C2×(C2×D11)⋊C4—42no—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×Dic11⋊C4—24no—
153C2×Dic11⋊C4—24no—
154C2×Dic11⋊C4—24no—
155C2×Dic11⋊C4—24no—
156C2×Dic11⋊C4C2314yes—
157C2×Dic11⋊C4C2314yes—
158C2×Dic11⋊C4C2314yes—
159C2×Dic11⋊C4C2314yes—
160C2×C4×Dic11D418yescomplemented
161C2×C4×Dic11C2314yes—
162#66937—232no—
163(C22⋊D11)⋊C4—232no—
164C11×#95C2314yes—
165C11×#95C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2535—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11C2×D414yes—
186C24×C11#4114yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
190C23×D11—22no—
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×D11C2×D414yes—
203C23×D11#4114yes—
204C23×D11C2412yes—
205C23×D11C2412yes—
206C2×D4×C11—28no—
207C2×D4×C11—28no—
208C2×D4×C11—44no—
209C2×D4×C11—416no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—28no—
225C22×C4×C11—44no—
226C22×C4×C11—44no—
227C22×C4×C11—416no—
228C22×C4×C11C2×D414yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C2×C22⋊D11—232no—
235C2×C22⋊D11—232no—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—28no—
243C2×C22⋊D11—28no—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—416no—
248C2×C22⋊D11—416no—
249C2×C22⋊D11C2×D4116yescomplemented
250C22×Dic11—28no—
251C22×Dic11—28no—
252C22×Dic11—28no—
253C22×Dic11—22no—
254C22×Dic11—22no—
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×Dic11—416no—
268C22×Dic11C2×D414yes—
269C22×Dic11C2×D414yes—
270C22×Dic11C2×D414yes—
271C22×Dic11#4114yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2412yes—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C2×D44—28no—
279C2×D44—28no—
280C2×D44—44no—
281C2×D44—416no—
282C2×C4×D11—28no—
283C2×C4×D11—28no—
284C2×C4×D11—28no—
285C2×C4×D11—28no—
286C2×C4×D11—44no—
287C2×C4×D11—44no—
288C2×C4×D11—416no—
289C2×C4×D11—416no—
290C11×C22⋊C4—28no—
291C11×C22⋊C4—28no—
292C11×C22⋊C4—44no—
293C22⋊Dic11—28no—
294C22⋊Dic11—28no—
295C22⋊Dic11—44no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4—28no—
300(C2×D11)⋊C4—44no—
301(C2×D11)⋊C4—44no—
302Dic11⋊C4—28no—
303Dic11⋊C4—28no—
304Dic11⋊C4—28no—
305Dic11⋊C4—28no—
306C4×Dic11C2×D4116yescomplemented
307C22×#121—111no—
308C22×#121—111no—
309C22×C4×D4—111no—
310C22×C4×D4—111no—
311#2535—1116no—
312C2×#397—111no—
313C2×#397—111no—
314C2×#392—111no—
315C2×#392—111no—
316C2×#386—111no—
317C2×#386—111no—
318C2×#386—111no—
319C2×#386D1111yescharacteristic, complemented
320C2×#382—111no—
321C2×#380—111no—
322C2×#380—111no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—28no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—28no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—44no—
342C23×C11—44no—
343C23×C11—44no—
344C23×C11—44no—
345C23×C11—44no—
346C23×C11—44no—
347C23×C11—44no—
348C23×C11—44no—
349C23×C11C22×D414yes—
350C23×C11C22×D412yes—
351C23×C11C22×D412yes—
352C23×C11C2×#4114yes—
353C23×C11C2×#4112yes—
354C23×C11C2×#4112yes—
355C23×C11C2×#4112yes—
356C23×C11H(5,𝔽2)12yes—
357C23×C11H(5,𝔽2)12yes—
358C23×C11C2511yescharacteristic
359C22×D11—28no—
360C22×D11—28no—
361C22×D11—28no—
362C22×D11—28no—
363C22×D11—28no—
364C22×D11—28no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—44no—
378C22×D11—44no—
379C22×D11—44no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11—44no—
385C22×D11C22×D414yes—
386C22×D11C2×#4114yes—
387D4×C11—416no—
388C2×C4×C11—28no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—416no—
404C2×C4×C11—44no—
405C2×C4×C11—44no—
406C2×C4×C11—44no—
407C2×C4×C11—44no—
408C2×C4×C11C22×D414yes—
409C22⋊D11—232no—
410C22⋊D11—232no—
411C22⋊D11—416no—
412C22⋊D11—416no—
413C2×Dic11—28no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—44no—
429C2×Dic11—44no—
430C2×Dic11—44no—
431C2×Dic11—44no—
432C2×Dic11—416no—
433C2×Dic11#121116yes—
434C2×Dic11C22×D414yes—
435C2×Dic11C22×D414yes—
436C2×Dic11C22×D414yes—
437C2×Dic11C2×#4114yes—
438D44—416no—
439C4×D11—416no—
440C4×D11—416no—
441C23×D4—111no—
442C23×D4—111no—
443C23×D4—111no—
444C23×D4—111no—
445C23×D4—111no—
446C23×D4C2×D1111yescharacteristic
447C24×C4—111no—
448C24×C4—111no—
449C24×C4—111no—
450C24×C4C2×D1111yescharacteristic
451C2×#121—118no—
452C2×#121—118no—
453C2×#121—228no—
454C2×#121—228no—
455C2×C4×D4—118no—
456C2×C4×D4—118no—
457C2×C4×D4—228no—
458C2×C4×D4—228no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C22⋊C4—111no—
471C22×C22⋊C4—111no—
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C22⋊C4C2×D1111yescharacteristic
474C22×C22⋊C4C2×D1111yescharacteristic
475C22×C42—111no—
476#397—118no—
477#397—118no—
478#392—118no—
479#392—118no—
480#386—118no—
481#386—118no—
482#386—118no—
483#386C2×D1118yescomplemented
484#382—118no—
485#380—118no—
486#380—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C2×#95C2×D1111yescharacteristic
494C2×#95C2×D1111yescharacteristic
495C22×C11—24no—
496C22×C11—24no—
497C22×C11—24no—
498C22×C11—24no—
499C22×C11—24no—
500C22×C11—24no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—416no—
510C22×C11—416no—
511C22×C11C2×#12114yes—
512C22×C11#52514yes—
513C22×C11#53514yes—
514C22×C11#54614yes—
515C22×C11#54614yes—
516C22×C11#55314yes—
517C22×C11#55314yes—
518C22×C11C23×D411yescharacteristic
519C22×C11C23×D411yescharacteristic
520C22×C11C22×#4111yescharacteristic
521C22×C11C22×#4111yescharacteristic
522C22×C11C22×#4111yescharacteristic
523C22×C11C2×H(5,𝔽2)11yescharacteristic
524C22×C11C2×H(5,𝔽2)11yescharacteristic
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—24no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—416no—
540C2×D11—416no—
541C4×C11—24no—
542C4×C11—42no—
543C4×C11—42no—
544C4×C11—42no—
545C4×C11—42no—
546Dic11—24no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550Dic11—42no—
551Dic11C2×#12118yes—
552C25—111no—
553C25—111no—
554C25C22×D1111yescharacteristic
555C25C22×D1111yescharacteristic
556C22×D4—24no—
557C22×D4—24no—
558C22×D4—42no—
559C22×D4—118no—
560C22×D4—114no—
561C22×D4—114no—
562C22×D4—114no—
563C22×D4—114no—
564C22×D4—114no—
565C22×D4—224no—
566C22×D4—224no—
567C22×D4—224no—
568C22×D4—224no—
569C22×D4—224no—
570C22×D4—224no—
571C22×D4—224no—
572C22×D4—224no—
573C22×D4—224no—
574C22×D4—224no—
575C22×D4—224no—
576C22×D4—442no—
577C22×D4—442no—
578C22×D4—442no—
579C22×D4C22×D1114yes—
580C23×C4—24no—
581C23×C4—42no—
582C23×C4—42no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—114no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—114no—
591C23×C4—114no—
592C23×C4—224no—
593C23×C4—224no—
594C23×C4—224no—
595C23×C4—224no—
596C23×C4—224no—
597C23×C4—224no—
598C23×C4—224no—
599C23×C4—442no—
600C23×C4—442no—
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1114yes—
607#121—2232no—
608#121—2232no—
609C4×D4—2232no—
610C4×D4—2232no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—114no—
614C2×C4⋊C4—114no—
615C2×C4⋊C4—224no—
616C2×C4⋊C4—224no—
617C2×C4⋊C4—224no—
618C2×C4⋊C4—224no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—42no—
622C2×C22⋊C4—114no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—114no—
630C2×C22⋊C4—114no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—224no—
633C2×C22⋊C4—224no—
634C2×C22⋊C4—224no—
635C2×C22⋊C4—224no—
636C2×C22⋊C4—224no—
637C2×C22⋊C4—442no—
638C2×C22⋊C4—442no—
639C2×C22⋊C4—442no—
640C2×C22⋊C4C22×D1114yes—
641C2×C22⋊C4C22×D1114yes—
642C2×C22⋊C4C22×D1114yes—
643C2×C42—118no—
644C2×C42—114no—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95—114no—
650#95—114no—
651#95C22×D1114yes—
652#95C22×D1114yes—
653C2×C11—44no—
654C2×C11—44no—
655C2×C11#253518yescomplemented
656C2×C11C22×#12111yescharacteristic
657C2×C11C2×#52511yescharacteristic
658C2×C11C2×#53511yescharacteristic
659C2×C11C2×#54611yescharacteristic
660C2×C11C2×#54611yescharacteristic
661C2×C11C2×#55311yescharacteristic
662C2×C11C2×#55311yescharacteristic
663D11—44no—
664D11—44no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—114no—
678C24—114no—
679C24—112no—
680C24—112no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24—222no—
691C24—222no—
692C24—222no—
693C24#433914yes—
694C24D4×D1114yes—
695C24C23×D1112yes—
696C24C23×D1112yes—
697C24C23×D1111yescharacteristic
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—44no—
701C2×D4—416no—
702C2×D4—1116no—
703C2×D4—228no—
704C2×D4—228no—
705C2×D4—228no—
706C2×D4—228no—
707C2×D4—2232no—
708C2×D4—228no—
709C2×D4—228no—
710C2×D4—2232no—
711C2×D4—228no—
712C2×D4—228no—
713C2×D4—228no—
714C2×D4—228no—
715C2×D4—228no—
716C2×D4—444no—
717C2×D4—4416no—
718C2×D4—444no—
719C2×D4—444no—
720C2×D4—4416no—
721C2×D4—4416no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—28no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—416no—
740C22×C4—114no—
741C22×C4—114no—
742C22×C4—114no—
743C22×C4—112no—
744C22×C4—114no—
745C22×C4—112no—
746C22×C4—112no—
747C22×C4—112no—
748C22×C4—112no—
749C22×C4—112no—
750C22×C4—228no—
751C22×C4—228no—
752C22×C4—228no—
753C22×C4—228no—
754C22×C4—228no—
755C22×C4—228no—
756C22×C4—222no—
757C22×C4—222no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—222no—
768C22×C4—222no—
769C22×C4—222no—
770C22×C4—228no—
771C22×C4—444no—
772C22×C4—444no—
773C22×C4—4416no—
774C22×C4—4416no—
775C22×C4—4416no—
776C22×C4D4×D1114yes—
777C22×C4C23×D1112yes—
778C22×C4C23×D1112yes—
779C22×C4C23×D1112yes—
780C22×C4C23×D1112yes—
781C22×C4C23×D1112yes—
782C4⋊C4—228no—
783C4⋊C4—228no—
784C4⋊C4—228no—
785C4⋊C4—228no—
786C22⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—44no—
789C22⋊C4—228no—
790C22⋊C4—228no—
791C22⋊C4—228no—
792C22⋊C4—228no—
793C22⋊C4—228no—
794C22⋊C4—228no—
795C22⋊C4—444no—
796C22⋊C4—444no—
797C22⋊C4—444no—
798C42—1116no—
799C11C2×#253511yescharacteristic, complemented, Sylow
800C23—28no—
801C23—28no—
802C23—28no—
803C23—28no—
804C23—28no—
805C23—28no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—44no—
825C23—44no—
826C23—114no—
827C23—114no—
828C23—228no—
829C23—228no—
830C23—228no—
831C23—228no—
832C23—228no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—228no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23—444no—
852C23—444no—
853C23—444no—
854C23C2×#433914yes—
855C23C2×#433912yes—
856C23C2×D4×D1114yes—
857C23C2×D4×D1112yes—
858C23C2×D4×D1112yes—
859C23#6703712yes—
860C23#6703712yes—
861C23#41×D1112yes—
862C23#41×D1112yes—
863C23C24×D1111yescharacteristic
864D4—416no—
865D4—2232no—
866D4—2232no—
867D4—4416no—
868D4—4416no—
869D4—4416no—
870C2×C4—28no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—416no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—1116no—
891C2×C4—114no—
892C2×C4—114no—
893C2×C4—114no—
894C2×C4—114no—
895C2×C4—228no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—4416no—
911C2×C4—4416no—
912C2×C4—4416no—
913C2×C4—444no—
914C2×C4—444no—
915C2×C4—444no—
916C2×C4—444no—
917C2×C4C2×D4×D1114yes—
918C22—24no—
919C22—24no—
920C22—24no—
921C22—24no—
922C22—24no—
923C22—24no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—416no—
931C22—416no—
932C22—42no—
933C22—42no—
934C22—224no—
935C22—224no—
936C22—224no—
937C22—224no—
938C22—224no—
939C22—224no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22—4416no—
947C22—4416no—
948C22—442no—
949C22—442no—
950C22#1062302114yes—
951C22#1062307114yes—
952C22#1062307814yes—
953C22#1062312314yes—
954C22D11×#12114yes—
955C22#1062314114yes—
956C22#1062319214yes—
957C22C22×#433911yescharacteristic
958C22C22×D4×D1111yescharacteristic
959C22C22×D4×D1111yescharacteristic
960C22C2×#6703711yescharacteristic
961C22C2×#6703711yescharacteristic
962C22C2×#41×D1111yescharacteristic
963C22C2×#41×D1111yescharacteristic
964C4—24no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—118no—
970C4—224no—
971C4—442no—
972C4—442no—
973C4—442no—
974C4—442no—
975C2—44no—
976C2—44no—
977C2—444no—
978C2—444no—
979C2#1307351618yesdirect product factor
980C2C2×D11×#12111yescharacteristic
981C2C2×#1062307811yescharacteristic
982C2C2×#1062312311yescharacteristic
983C2C2×#1062314111yescharacteristic
984C2C2×#1062302111yescharacteristic
985C2C2×#1062319211yescharacteristic
986C2C2×#1062307111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
hypercenterC2×#386D11
hypocenterC11C2×#2535
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66937C2semidirect
2. C22×#66992C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. #13073516C2direct (N × H)
6. C2×#10622288C2semidirect
7. C2×#10622565C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622836C2semidirect
10. C2×#10622826C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622263C2semidirect
14. C2×#10622280C2semidirect
15. C2×#10622555C2semidirect
16. C2×C11×#386C2semidirect
34. C2×#66992C22semidirect
36. C2×C4×C22⋊D11C22semidirect
49. C2×#66937C22semidirect
51. C2×(C22⋊D11)⋊C4C22semidirect
52. C11×#386C22semidirect
55. #10622836C22semidirect
56. #10622826C22semidirect
63. #10622573C22semidirect
64. #10622569C22semidirect
65. #10622565C22semidirect
66. #10622555C22semidirect
67. #10622288C22semidirect
68. #10622280C22semidirect
69. #10622278C22semidirect
70. #10622263C22semidirect
99. C22×C22⋊D11D4semidirect
160. C2×C4×Dic11D4semidirect
249. C2×C22⋊D11C2×D4semidirect
306. C4×Dic11C2×D4semidirect
319. C2×#386D11semidirect
483. #386C2×D11semidirect
655. C2×C11#2535semidirect
799. C11C2×#2535semidirect
979. C2#13073516direct (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×#669922
C22×C4×C22⋊D112
C22×(C22⋊D11)⋊C42
#130735162
C2×#106222882
C2×#106225652
C2×#106225732
C2×#106228362
C2×#106228262
C2×#106222782
C2×#106225692
C2×#106222632
C2×#106222802
C2×#106225552
C2×C11×#3862
C2×#253511