Finite Group Databasebeta

← C2×#13073585 #14924932

Subgroups — C2×#13073585 #14924932

Order 2816.

4174 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic
2C22×#66938C211yesmaximal, characteristic, complemented
3C22×#66938C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
5#13073585C2116yesmaximal, direct product factor
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622572C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622835C211yesmaximal, characteristic, complemented
10C2×#10622259C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622262C211yesmaximal, 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
23C23×D44C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C23×Dic22C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×#66993—28no—
34C2×#66993C2218yes—
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×(C2×D11)⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66938—28no—
51C2×#66938—28no—
52C2×#66938C2218yescomplemented
53C2×#66938C2218yescomplemented
54C11×#386C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57#10622835C2218yescomplemented
58#10622826C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63#10622572C2218yescomplemented
64#10622572C2218yescomplemented
65#10622570C2218yescomplemented
66#10622569C2218yescomplemented
67#10622285C2218yescomplemented
68#10622278C2218yescomplemented
69#10622262C2218yescomplemented
70#10622259C2218yescomplemented
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⋊D11D418yes—
100C22×C22⋊D11C2314yes—
101C22×C22⋊D11C2314yes—
102C22×C22⋊D11C2314yes—
103C22×C22⋊D11C2314yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C22×D44—24no—
111C22×D44—24no—
112C22×D44—42no—
113C22×D44C2314yes—
114C22×C4×D11—24no—
115C22×C4×D11—42no—
116C22×C4×D11—42no—
117C22×C4×D11C2314yes—
118C22×Dic22—24no—
119C22×Dic22—24no—
120C22×Dic22—24no—
121C22×Dic22C2314yes—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4—24no—
124C2×C11×C22⋊C4—42no—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yes—
127C2×C11×C22⋊C4C2314yes—
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11—42no—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136#66993—232no—
137C4×C22⋊D11—232no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—42no—
144C2×(C2×D11)⋊C4—42no—
145C2×(C2×D11)⋊C4C2314yes—
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⋊C4C2314yes—
156C2×Dic11⋊C4C2314yes—
157C2×Dic11⋊C4C2314yes—
158C2×C4×Dic11—24no—
159C2×C4×Dic11—24no—
160C2×C4×Dic11D418yescomplemented
161C2×C4×Dic11C2314yes—
162C2×C4×Dic11C2314yes—
163C2×C4×Dic11C2314yes—
164#66938—232no—
165#66938—232no—
166C11×#95C2314yes—
167C11×#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2544—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×C11—22no—
186C24×C11C2×D414yes—
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×D11—22no—
203C23×D11C2×D414yes—
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—28no—
224C22×C4×C11—44no—
225C22×C4×C11—44no—
226C22×C4×C11—416no—
227C22×C4×C11C2×D414yes—
228C22×C4×C11#4114yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C2×C22⋊D11—232no—
235C2×C22⋊D11—28no—
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—44no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11—416no—
247C2×C22⋊D11—416no—
248C2×C22⋊D11—416no—
249C2×C22⋊D11C2×D4116yes—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
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×Dic11C2×D414yes—
264C22×Dic11C2×D414yes—
265C22×Dic11C2×D414yes—
266C22×Dic11#4114yes—
267C22×Dic11#4114yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C2×D44—28no—
275C2×D44—28no—
276C2×D44—44no—
277C2×D44—416no—
278C2×C4×D11—28no—
279C2×C4×D11—44no—
280C2×C4×D11—44no—
281C2×C4×D11—416no—
282C2×Dic22—28no—
283C2×Dic22—28no—
284C2×Dic22—28no—
285C2×Dic22—416no—
286C11×C22⋊C4—28no—
287C11×C22⋊C4—28no—
288C11×C22⋊C4—44no—
289C22⋊Dic11—28no—
290C22⋊Dic11—28no—
291C22⋊Dic11—28no—
292C22⋊Dic11—44no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—44no—
299(C2×D11)⋊C4—44no—
300Dic11⋊C4—28no—
301Dic11⋊C4—28no—
302Dic11⋊C4—28no—
303C4×Dic11—28no—
304C4×Dic11—28no—
305C4×Dic11C2×D4116yescomplemented
306C22×#127—111no—
307C22×#124—111no—
308C22×#124—111no—
309C22×C4×D4—111no—
310#2544—1116no—
311C2×#394—111no—
312C2×#394—111no—
313C2×#394—111no—
314C2×#394—111no—
315C2×#391—111no—
316C2×#390—111no—
317C2×#386—111no—
318C2×#386—111no—
319C2×#386—111no—
320C2×#386D1111yescharacteristic, complemented
321C2×C4×C4⋊C4—111no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
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—44no—
339C23×C11—44no—
340C23×C11—44no—
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×#4112yes—
353C23×C11C2×#4112yes—
354C23×C11C2×#4112yes—
355C23×C11H(5,𝔽2)12yes—
356C23×C11H(5,𝔽2)12yes—
357C23×C11C2511yescharacteristic
358C22×D11—28no—
359C22×D11—28no—
360C22×D11—28no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
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—44no—
375C22×D11—44no—
376C22×D11—44no—
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—
386D4×C11—416no—
387C2×C4×C11—28no—
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—416no—
403C2×C4×C11—44no—
404C2×C4×C11—44no—
405C2×C4×C11—44no—
406C2×C4×C11C22×D414yes—
407C2×C4×C11C2×#4114yes—
408C22⋊D11—232no—
409C22⋊D11—416no—
410C22⋊D11—416no—
411C22⋊D11—416no—
412C2×Dic11—28no—
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—44no—
428C2×Dic11—44no—
429C2×Dic11—44no—
430C2×Dic11#121116yes—
431C2×Dic11C22×D414yes—
432C2×Dic11C22×D414yes—
433C2×Dic11C22×D414yes—
434C2×Dic11C2×#4114yes—
435C2×Dic11C2×#4114yes—
436D44—416no—
437C4×D11—416no—
438Dic22—416no—
439C23×Q8—111no—
440C23×D4—111no—
441C23×D4—111no—
442C23×D4—111no—
443C23×D4—111no—
444C23×D4—111no—
445C23×D4C2×D1111yescharacteristic
446C24×C4—111no—
447C24×C4C2×D1111yescharacteristic
448C2×#127—118no—
449C2×#127—228no—
450C2×#124—118no—
451C2×#124—118no—
452C2×#124—228no—
453C2×#124—228no—
454C2×C4×D4—118no—
455C2×C4×D4—228no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—111no—
462C22×C22⋊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⋊C4C2×D1111yescharacteristic
471C22×C22⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C42—111no—
474C22×C42—111no—
475C22×C42—111no—
476#394—118no—
477#394—118no—
478#394—118no—
479#394—118no—
480#391—118no—
481#390—118no—
482#386—118no—
483#386—118no—
484#386—118no—
485#386C2×D1118yescomplemented
486C4×C4⋊C4—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95C2×D1111yescharacteristic
492C2×#95C2×D1111yescharacteristic
493C22×C11—24no—
494C22×C11—24no—
495C22×C11—24no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—416no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—88no—
509C22×C11C2×#12114yes—
510C22×C11#53214yes—
511C22×C11#53514yes—
512C22×C11#54614yes—
513C22×C11#54614yes—
514C22×C11#55914yes—
515C22×C11#55914yes—
516C22×C11C23×D411yescharacteristic
517C22×C11C23×D411yescharacteristic
518C22×C11C22×#4111yescharacteristic
519C22×C11C22×#4111yescharacteristic
520C22×C11C22×#4111yescharacteristic
521C22×C11C2×H(5,𝔽2)11yescharacteristic
522C22×C11C2×H(5,𝔽2)11yescharacteristic
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—416no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—88no—
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—42no—
542C4×C11—42no—
543C4×C11—42no—
544Dic11—24no—
545Dic11—24no—
546Dic11—42no—
547Dic11—42no—
548Dic11—42no—
549Dic11C2×#12118yes—
550C25—111no—
551C25—111no—
552C25C22×D1111yescharacteristic
553C25C22×D1111yescharacteristic
554C22×Q8—114no—
555C22×Q8—224no—
556C22×Q8—224no—
557C22×Q8—224no—
558C22×D4—24no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—118no—
562C22×D4—114no—
563C22×D4—114no—
564C22×D4—114no—
565C22×D4—114no—
566C22×D4—114no—
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—224no—
577C22×D4—224no—
578C22×D4—442no—
579C22×D4—442no—
580C22×D4—442no—
581C22×D4C22×D1114yes—
582C23×C4—24no—
583C23×C4—42no—
584C23×C4—42no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—114no—
592C23×C4—224no—
593C23×C4—442no—
594C23×C4—442no—
595C23×C4C22×D1111yescharacteristic
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1114yes—
601#127—2232no—
602#124—2232no—
603#124—2232no—
604C4×D4—2232no—
605C2×C4⋊C4—114no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—224no—
609C2×C4⋊C4—224no—
610C2×C4⋊C4—224no—
611C2×C22⋊C4—24no—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—42no—
614C2×C22⋊C4—114no—
615C2×C22⋊C4—114no—
616C2×C22⋊C4—114no—
617C2×C22⋊C4—114no—
618C2×C22⋊C4—114no—
619C2×C22⋊C4—114no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4—114no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—224no—
626C2×C22⋊C4—224no—
627C2×C22⋊C4—224no—
628C2×C22⋊C4—224no—
629C2×C22⋊C4—224no—
630C2×C22⋊C4—224no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—224no—
633C2×C22⋊C4—442no—
634C2×C22⋊C4—442no—
635C2×C22⋊C4—442no—
636C2×C22⋊C4C22×D1114yes—
637C2×C22⋊C4C22×D1114yes—
638C2×C22⋊C4C22×D1114yes—
639C2×C42—118no—
640C2×C42—114no—
641C2×C42—114no—
642C2×C42—114no—
643C2×C42—224no—
644C2×C42—224no—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95C22×D1114yes—
650#95C22×D1114yes—
651C2×C11—44no—
652C2×C11—82no—
653C2×C11#254418yescomplemented
654C2×C11C22×#12111yescharacteristic
655C2×C11C2×#53211yescharacteristic
656C2×C11C2×#53511yescharacteristic
657C2×C11C2×#54611yescharacteristic
658C2×C11C2×#54611yescharacteristic
659C2×C11C2×#55911yescharacteristic
660C2×C11C2×#55911yescharacteristic
661D11—44no—
662D11—82no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—114no—
677C24—112no—
678C24—112no—
679C24—222no—
680C24—222no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24—222no—
691C24—222no—
692C24D4×D1114yes—
693C24C23×D1112yes—
694C24C23×D1112yes—
695C24C23×D1111yescharacteristic
696C2×Q8—228no—
697C2×Q8—228no—
698C2×Q8—228no—
699C2×Q8—4416no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—44no—
703C2×D4—416no—
704C2×D4—1116no—
705C2×D4—228no—
706C2×D4—228no—
707C2×D4—2232no—
708C2×D4—228no—
709C2×D4—228no—
710C2×D4—228no—
711C2×D4—228no—
712C2×D4—228no—
713C2×D4—228no—
714C2×D4—228no—
715C2×D4—228no—
716C2×D4—228no—
717C2×D4—444no—
718C2×D4—4416no—
719C2×D4—4416no—
720C2×D4—444no—
721C2×D4—444no—
722C2×D4—4416no—
723C2×D4—4416no—
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—22no—
737C22×C4—28no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—416no—
741C22×C4—114no—
742C22×C4—114no—
743C22×C4—114no—
744C22×C4—112no—
745C22×C4—114no—
746C22×C4—114no—
747C22×C4—112no—
748C22×C4—112no—
749C22×C4—112no—
750C22×C4—112no—
751C22×C4—112no—
752C22×C4—222no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—222no—
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—228no—
766C22×C4—444no—
767C22×C4—444no—
768C22×C4—4416no—
769C22×C4#433914yes—
770C22×C4D4×D1114yes—
771C22×C4C23×D1112yes—
772C22×C4C23×D1112yes—
773C22×C4C23×D1112yes—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C4⋊C4—228no—
777C4⋊C4—228no—
778C4⋊C4—228no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—44no—
782C22⋊C4—228no—
783C22⋊C4—228no—
784C22⋊C4—228no—
785C22⋊C4—228no—
786C22⋊C4—228no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—444no—
791C22⋊C4—444no—
792C22⋊C4—444no—
793C42—1116no—
794C42—228no—
795C42—228no—
796C11C2×#254411yescharacteristic, complemented, Sylow
797C23—28no—
798C23—28no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—114no—
825C23—228no—
826C23—228no—
827C23—228no—
828C23—222no—
829C23—222no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—444no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23—444no—
852C23C2×#433912yes—
853C23C2×D4×D1114yes—
854C23C2×D4×D1112yes—
855C23C2×D4×D1112yes—
856C23#6703712yes—
857C23#6703712yes—
858C23#41×D1112yes—
859C23#41×D1112yes—
860C23C24×D1111yescharacteristic
861Q8—4416no—
862D4—416no—
863D4—2232no—
864D4—4416no—
865D4—4416no—
866D4—4416no—
867D4—4416no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—22no—
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—416no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—1116no—
888C2×C4—114no—
889C2×C4—114no—
890C2×C4—114no—
891C2×C4—114no—
892C2×C4—114no—
893C2×C4—228no—
894C2×C4—228no—
895C2×C4—222no—
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—4416no—
909C2×C4—444no—
910C2×C4—444no—
911C2×C4—444no—
912C2×C4C2×#433914yes—
913C2×C4C2×D4×D1114yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—416no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—88no—
930C22—224no—
931C22—224no—
932C22—224no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—4416no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—888no—
946C22#1062302114yes—
947C22#1062307914yes—
948C22#1062309014yes—
949C22#1062312314yes—
950C22D11×#12114yes—
951C22#1062314114yes—
952C22#1062319514yes—
953C22C22×#433911yescharacteristic
954C22C22×D4×D1111yescharacteristic
955C22C22×D4×D1111yescharacteristic
956C22C2×#6703711yescharacteristic
957C22C2×#6703711yescharacteristic
958C22C2×#41×D1111yescharacteristic
959C22C2×#41×D1111yescharacteristic
960C4—24no—
961C4—24no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—118no—
966C4—224no—
967C4—224no—
968C4—442no—
969C4—442no—
970C4—442no—
971C2—44no—
972C2—82no—
973C2—444no—
974C2—882no—
975C2#1307358518yesdirect product factor
976C2C2×D11×#12111yescharacteristic
977C2C2×#1062307911yescharacteristic
978C2C2×#1062312311yescharacteristic
979C2C2×#1062314111yescharacteristic
980C2C2×#1062302111yescharacteristic
981C2C2×#1062309011yescharacteristic
982C2C2×#1062319511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC22×#66993C2
hypercenterC2×#386D11
hypocenterC11C2×#2544
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×#66938C2semidirect
3. C22×#66938C2semidirect
4. C22×C4×C22⋊D11C2semidirect
5. #13073585C2direct (N × H)
6. C2×#10622285C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622835C2semidirect
10. C2×#10622259C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622262C2semidirect
16. C2×C11×#386C2semidirect
36. C2×C4×C22⋊D11C22semidirect
52. C2×#66938C22semidirect
53. C2×#66938C22semidirect
54. C11×#386C22semidirect
57. #10622835C22semidirect
58. #10622826C22semidirect
63. #10622572C22semidirect
64. #10622572C22semidirect
65. #10622570C22semidirect
66. #10622569C22semidirect
67. #10622285C22semidirect
68. #10622278C22semidirect
69. #10622262C22semidirect
70. #10622259C22semidirect
160. C2×C4×Dic11D4semidirect
305. C4×Dic11C2×D4semidirect
320. C2×#386D11semidirect
485. #386C2×D11semidirect
653. C2×C11#2544semidirect
796. C11C2×#2544semidirect
975. C2#13073585direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669932
C22×#669382
C22×C4×C22⋊D112
#130735852
C2×#106222852
C2×#106225722
C2×#106228352
C2×#106222592
C2×#106225702
C2×#106228262
C2×#106222782
C2×#106225692
C2×#106222622
C2×C11×#3862
C2×#254411