Finite Group Databasebeta

← C2×#13072623 #14921617

Subgroups — C2×#13072623 #14921617

Order 2816.

4218 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×#66936C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3C22×#66991C211yesmaximal, characteristic, complemented
4C22×#66946C211yesmaximal, characteristic, complemented
5#13072623C2116yesmaximal, direct product factor
6C2×#10622597C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622564C211yesmaximal, characteristic, complemented
11C2×#10622283C211yesmaximal, characteristic, complemented
12C2×#10622571C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622281C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C2×#66992—28no—
35C2×#66992C2218yescomplemented
36C2×#66991—28no—
37C2×#66991C2218yescomplemented
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×C4⋊Dic11C2211yescharacteristic
45C22×C4⋊Dic11C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66946—28no—
51C2×#66946C2218yescomplemented
52C2×#66936—28no—
53C2×#66936C2218yescomplemented
54C11×#394C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622597C2218yescomplemented
62#10622573C2218yescomplemented
63#10622573C2218yescomplemented
64#10622571C2218yescomplemented
65#10622570C2218yescomplemented
66#10622569C2218yescomplemented
67#10622564C2218yescomplemented
68C22⋊C4×Dic11C2218yescomplemented
69#10622283C2218yescomplemented
70#10622281C2218yescomplemented
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×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11—42no—
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C23×Dic11—24no—
101C23×Dic11—24no—
102C23×Dic11—42no—
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2314yes—
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C22×D44—24no—
111C22×D44—24no—
112C22×D44—24no—
113C22×D44C2314yes—
114C22×C4×D11—24no—
115C22×C4×D11—24no—
116C22×C4×D11—24no—
117C22×C4×D11—24no—
118C22×C4×D11—42no—
119C22×C4×D11—42no—
120C22×C4×D11C2314yes—
121C22×C4×D11C2314yes—
122C2×C11×C4⋊C4—24no—
123C2×C11×C4⋊C4C2314yes—
124C2×C11×C22⋊C4—24no—
125C2×C11×C22⋊C4—24no—
126C2×C11×C22⋊C4—24no—
127C2×C11×C22⋊C4—42no—
128C2×C11×C22⋊C4C2314yes—
129C2×C11×C22⋊C4C2314yes—
130C2×C11×C22⋊C4C2314yes—
131C2×C11×C22⋊C4C2314yes—
132C2×C22⋊Dic11—24no—
133C2×C22⋊Dic11—24no—
134C2×C22⋊Dic11D418yescomplemented
135C2×C22⋊Dic11C2314yes—
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yes—
138#66992—232no—
139#66991—232no—
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)⋊C4D418yescomplemented
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×C4⋊Dic11—24no—
153C2×C4⋊Dic11—24no—
154C2×C4⋊Dic11C2314yes—
155C2×C4⋊Dic11C2314yes—
156C2×Dic11⋊C4—24no—
157C2×Dic11⋊C4—24no—
158C2×Dic11⋊C4C2314yes—
159C2×Dic11⋊C4C2314yes—
160C2×C4×Dic11—24no—
161C2×C4×Dic11—42no—
162C2×C4×Dic11C2314yes—
163C2×C4×Dic11C2314yes—
164#66946—232no—
165#66936—232no—
166C11×#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2464—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×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×C11C2×D414yes—
224C22×C4×C11#4114yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C2×C22⋊D11—28no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—44no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—416no—
243C2×C22⋊D11—416no—
244C2×C22⋊D11—416no—
245C2×C22⋊D11—416no—
246C22×Dic11—28no—
247C22×Dic11—28no—
248C22×Dic11—22no—
249C22×Dic11—22no—
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—44no—
263C22×Dic11—416no—
264C22×Dic11C2×D414yes—
265C22×Dic11C2×D414yes—
266C22×Dic11C2×D414yes—
267C22×Dic11#4114yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C2×D44—232no—
275C2×D44—28no—
276C2×D44—28no—
277C2×D44—28no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—28no—
281C2×C4×D11—28no—
282C2×C4×D11—44no—
283C2×C4×D11—44no—
284C2×C4×D11—416no—
285C2×C4×D11—416no—
286C11×C4⋊C4—28no—
287C11×C22⋊C4—28no—
288C11×C22⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—44no—
291C22⋊Dic11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11C2×D4116yescomplemented
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—44no—
298(C2×D11)⋊C4—44no—
299(C2×D11)⋊C4C2×D4116yescomplemented
300C4⋊Dic11—28no—
301C4⋊Dic11—28no—
302Dic11⋊C4—28no—
303Dic11⋊C4—28no—
304C4×Dic11—28no—
305C4×Dic11—44no—
306C22×#123—111no—
307C22×#121—111no—
308C22×#121—111no—
309C22×C4×D4—111no—
310#2464—1116no—
311C2×#398—111no—
312C2×#394D1111yescharacteristic, complemented
313C2×#392—111no—
314C2×#392—111no—
315C2×#390—111no—
316C2×#388—111no—
317C2×#388—111no—
318C2×#386—111no—
319C2×#386—111no—
320C2×#385—111no—
321C2×C4×C22⋊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—28no—
362C22×D11—28no—
363C22×D11—28no—
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—22no—
375C22×D11—22no—
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×D11C22×D414yes—
385C22×D11C2×#4114yes—
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—44no—
403C2×C4×C11—44no—
404C2×C4×C11—44no—
405C2×C4×C11C22×D414yes—
406C2×C4×C11C2×#4114yes—
407C22⋊D11—416no—
408C22⋊D11—416no—
409C22⋊D11—416no—
410C22⋊D11—416no—
411C2×Dic11—28no—
412C2×Dic11—28no—
413C2×Dic11—28no—
414C2×Dic11—28no—
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—22no—
429C2×Dic11—416no—
430C2×Dic11—44no—
431C2×Dic11—44no—
432C2×Dic11C22×D414yes—
433C2×Dic11C22×D414yes—
434C2×Dic11C22×D414yes—
435C2×Dic11C2×#4114yes—
436D44—232no—
437C4×D11—416no—
438C4×D11—416no—
439C23×D4—111no—
440C23×D4—111no—
441C23×D4—111no—
442C23×D4—111no—
443C23×D4—111no—
444C23×D4C2×D1111yescharacteristic
445C24×C4—111no—
446C24×C4—111no—
447C24×C4—111no—
448C2×#123—118no—
449C2×#123—228no—
450C2×#121—118no—
451C2×#121—118no—
452C2×#121—228no—
453C2×#121—228no—
454C2×C4×D4—118no—
455C2×C4×D4—228no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4C2×D1111yescharacteristic
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×C22⋊C4C2×D1111yescharacteristic
474C22×C42—111no—
475C22×C42—111no—
476#398—118no—
477#394C2×D1118yescomplemented
478#392—118no—
479#392—118no—
480#390—118no—
481#388—118no—
482#388—118no—
483#386—118no—
484#386—118no—
485#385—118no—
486C4×C22⋊C4—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
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×C11#52514yes—
510C22×C11#53214yes—
511C22×C11#54014yes—
512C22×C11D4214yes—
513C22×C11#54614yes—
514C22×C11#54614yes—
515C22×C11#55314yes—
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—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—416no—
538C2×D11—416no—
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—42no—
542C4×C11—42no—
543C4×C11—42no—
544Dic11—24no—
545Dic11—24no—
546Dic11—24no—
547Dic11—24no—
548Dic11—42no—
549Dic11—42no—
550C25—111no—
551C25—111no—
552C25C22×D1111yescharacteristic
553C25C22×D1111yescharacteristic
554C22×D4—24no—
555C22×D4—24no—
556C22×D4—42no—
557C22×D4—114no—
558C22×D4—114no—
559C22×D4—114no—
560C22×D4—114no—
561C22×D4—114no—
562C22×D4—224no—
563C22×D4—224no—
564C22×D4—224no—
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—442no—
574C22×D4—442no—
575C22×D4—442no—
576C22×D4—442no—
577C22×D4C22×D1114yes—
578C23×C4—111no—
579C23×C4—111no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—114no—
585C23×C4—114no—
586C23×C4—114no—
587C23×C4—224no—
588C23×C4—224no—
589C23×C4—224no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—224no—
593C23×C4—442no—
594C23×C4—442no—
595C23×C4—442no—
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601#123—2232no—
602#121—2232no—
603#121—2232no—
604C4×D4—2232no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—114no—
610C2×C4⋊C4—224no—
611C2×C4⋊C4—224no—
612C2×C4⋊C4—224no—
613C2×C4⋊C4—224no—
614C2×C4⋊C4C22×D1114yes—
615C2×C22⋊C4—24no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—42no—
619C2×C22⋊C4—118no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—118no—
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—224no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—224no—
633C2×C22⋊C4—224no—
634C2×C22⋊C4—224no—
635C2×C22⋊C4—442no—
636C2×C22⋊C4—442no—
637C2×C22⋊C4C22×D1114yes—
638C2×C22⋊C4C22×D1114yes—
639C2×C22⋊C4C22×D1114yes—
640C2×C22⋊C4C22×D1114yes—
641C2×C42—114no—
642C2×C42—114no—
643C2×C42—224no—
644C2×C42—442no—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95—114no—
650#95C22×D1114yes—
651C2×C11—44no—
652C2×C11—82no—
653C2×C11#246418yescomplemented
654C2×C11C2×#52511yescharacteristic
655C2×C11C2×#53211yescharacteristic
656C2×C11C2×#54011yescharacteristic
657C2×C11C2×D4211yescharacteristic
658C2×C11C2×#54611yescharacteristic
659C2×C11C2×#54611yescharacteristic
660C2×C11C2×#55311yescharacteristic
661D11—44no—
662D11—44no—
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—114no—
678C24—112no—
679C24—112no—
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×D4—28no—
697C2×D4—28no—
698C2×D4—44no—
699C2×D4—416no—
700C2×D4—228no—
701C2×D4—228no—
702C2×D4—2232no—
703C2×D4—228no—
704C2×D4—228no—
705C2×D4—228no—
706C2×D4—228no—
707C2×D4—228no—
708C2×D4—228no—
709C2×D4—228no—
710C2×D4—228no—
711C2×D4—228no—
712C2×D4—444no—
713C2×D4—444no—
714C2×D4—444no—
715C2×D4—444no—
716C2×D4—4416no—
717C2×D4—4416no—
718C2×D4—4416no—
719C2×D4—4416no—
720C22×C4—22no—
721C22×C4—22no—
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—114no—
734C22×C4—114no—
735C22×C4—114no—
736C22×C4—114no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—228no—
744C22×C4—228no—
745C22×C4—228no—
746C22×C4—228no—
747C22×C4—228no—
748C22×C4—222no—
749C22×C4—222no—
750C22×C4—222no—
751C22×C4—222no—
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—228no—
763C22×C4—444no—
764C22×C4—444no—
765C22×C4—4416no—
766C22×C4—4416no—
767C22×C4—444no—
768C22×C4—4416no—
769C22×C4D4×D1114yes—
770C22×C4#434114yes—
771C22×C4C23×D1112yes—
772C22×C4C23×D1112yes—
773C22×C4C23×D1112yes—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C4⋊C4—28no—
777C4⋊C4—228no—
778C4⋊C4—228no—
779C4⋊C4—228no—
780C4⋊C4—228no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—44no—
785C22⋊C4—1116no—
786C22⋊C4—1116no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—228no—
791C22⋊C4—228no—
792C22⋊C4—444no—
793C22⋊C4—444no—
794C42—228no—
795C42—444no—
796C11C2×#246411yescharacteristic, 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—114no—
826C23—228no—
827C23—228no—
828C23—228no—
829C23—228no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—228no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—228no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23—444no—
852C23C2×D4×D1114yes—
853C23C2×D4×D1112yes—
854C23C2×D4×D1112yes—
855C23C2×#434112yes—
856C23#6703712yes—
857C23#41×D1112yes—
858C23#41×D1112yes—
859C23#6704212yes—
860C23C24×D1111yescharacteristic
861D4—416no—
862D4—2232no—
863D4—4416no—
864D4—4416no—
865D4—4416no—
866D4—4416no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—22no—
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—44no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—114no—
886C2×C4—114no—
887C2×C4—114no—
888C2×C4—114no—
889C2×C4—228no—
890C2×C4—228no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—228no—
900C2×C4—228no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—4416no—
908C2×C4—4416no—
909C2×C4—4416no—
910C2×C4—444no—
911C2×C4—444no—
912C2×C4C2×D4×D1114yes—
913C2×C4C2×#434114yes—
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—224no—
934C22—224no—
935C22—224no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—4416no—
945C22—4416no—
946C22#1062312114yes—
947C22#1062312714yes—
948C22#1062313714yes—
949C22#1062315014yes—
950C22#1062318514yes—
951C22#1062319214yes—
952C22#1062320714yes—
953C22C22×D4×D1111yescharacteristic
954C22C22×D4×D1111yescharacteristic
955C22C22×#434111yescharacteristic
956C22C2×#6703711yescharacteristic
957C22C2×#41×D1111yescharacteristic
958C22C2×#41×D1111yescharacteristic
959C22C2×#6704211yescharacteristic
960C4—24no—
961C4—24no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—224no—
966C4—224no—
967C4—224no—
968C4—224no—
969C4—442no—
970C4—442no—
971C2—44no—
972C2—82no—
973C2—444no—
974C2—444no—
975C2#1307262318yesdirect product factor
976C2C2×#1062313711yescharacteristic
977C2C2×#1062312711yescharacteristic
978C2C2×#1062315011yescharacteristic
979C2C2×#1062312111yescharacteristic
980C2C2×#1062318511yescharacteristic
981C2C2×#1062320711yescharacteristic
982C2C2×#1062319211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2464
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
2. C22×#66992C2semidirect
3. C22×#66991C2semidirect
4. C22×#66946C2semidirect
5. #13072623C2direct (N × H)
6. C2×#10622597C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622564C2semidirect
11. C2×#10622283C2semidirect
12. C2×#10622571C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622281C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C2×C11×#394C2semidirect
35. C2×#66992C22semidirect
37. C2×#66991C22semidirect
51. C2×#66946C22semidirect
53. C2×#66936C22semidirect
54. C11×#394C22semidirect
61. #10622597C22semidirect
62. #10622573C22semidirect
63. #10622573C22semidirect
64. #10622571C22semidirect
65. #10622570C22semidirect
66. #10622569C22semidirect
67. #10622564C22semidirect
68. C22⋊C4×Dic11C22semidirect
69. #10622283C22semidirect
70. #10622281C22semidirect
134. C2×C22⋊Dic11D4semidirect
145. C2×(C2×D11)⋊C4D4semidirect
293. C22⋊Dic11C2×D4semidirect
299. (C2×D11)⋊C4C2×D4semidirect
312. C2×#394D11semidirect
477. #394C2×D11semidirect
653. C2×C11#2464semidirect
796. C11C2×#2464semidirect
975. C2#13072623direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669362
C22×#669922
C22×#669912
C22×#669462
#130726232
C2×#106225972
C2×#106225732
C2×#106225702
C2×#106225642
C2×#106222832
C2×#106225712
C2×#106225692
C2×#106222812
C2×C22⋊C4×Dic112
C2×C11×#3942
C2×#246411