Finite Group Databasebeta

← C2×#13082368 #15662203

Subgroups — C2×#13082368 #15662203

Order 2816.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082368C2132yesmaximal, direct product factor
2C2×#10623064C212yesmaximal, complemented
3C2×#10623042C212yesmaximal, complemented
4C2×#10623060C212yesmaximal, complemented
5C2×#10623044C212yesmaximal, complemented
6C2×#10623062C214yesmaximal, complemented
7C2×#10623026C214yesmaximal, complemented
8C2×#10623050C211yesmaximal, characteristic, complemented
9C2×#10623065C212yesmaximal, complemented
10C2×#10623049C212yesmaximal, complemented
11C2×#10623057C211yesmaximal, characteristic, complemented
12C2×#10623001C212yesmaximal, complemented
13C2×#10623010C212yesmaximal, complemented
14C2×#10623322C211yesmaximal, characteristic
15C22×#66977C211yesmaximal, characteristic, complemented
16C2×#10623054C211yesmaximal, characteristic, complemented
17C2×#10623047C211yesmaximal, characteristic, complemented
18C22×C11×#117C211yesmaximal, characteristic, complemented
19C24×C4×C11C2211yescharacteristic
20C22×#4339C2211yescharacteristic
21C23×Dic22C2211yescharacteristic
22C2×C11×#117C2212yes—
23C2×C11×#117C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C2×C11×#117C2212yes—
27C2×C11×#117C2211yescharacteristic
28C2×C11×#117C22116yescomplemented
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2212yes—
32C22×C42×C11C2212yes—
33C2×#67006C2212yes—
34C22×C22⋊Dic11C2212yes—
35#10623322C22116yes—
36C2×#66983C2211yescharacteristic
37C2×#66983C2211yescharacteristic
38C2×#66982C2214yes—
39C2×#66982C2212yes—
40C2×C4×C22⋊D11C2214yes—
41C2×C4×C22⋊D11C2212yes—
42C2×C4×C22⋊D11C2212yes—
43C2×#66979C2214yes—
44C2×#66979C2211yescharacteristic
45C22×C4⋊Dic11C2211yescharacteristic
46C2×#66977C2214yes—
47C2×#66977C2211yescharacteristic
48C2×#66977C2211yescharacteristic
49C2×#66977C2212yes—
50C2×#66977C2212yes—
51C2×#66977C2212yes—
52C2×#66977C2212yes—
53C2×#66977C22116yescomplemented
54C22×Dic11⋊C4C2212yes—
55#10623065C22132yescomplemented
56#10623064C22132yescomplemented
57#10623062C22164yescomplemented
58#10623060C22132yescomplemented
59#10623057C22116yescomplemented
60#10623054C22116yescomplemented
61#10623050C22116yescomplemented
62#10623049C22132yescomplemented
63#10623047C22116yescomplemented
64#10623044C22132yescomplemented
65C2×#66951C2214yescomplemented
66#10623042C22132yescomplemented
67C2×#66950C2212yescomplemented
68C2×#66950C2212yescomplemented
69C2×#66949C2214yescomplemented
70C2×#66945C2212yescomplemented
71C2×C4⋊C4×D11C2212yescomplemented
72C2×#66943C2212yescomplemented
73C2×#66942C2214yescomplemented
74C2×#66942C2214yescomplemented
75C2×#66941C2212yescomplemented
76C2×#66940C2212yescomplemented
77C2×#66940C2212yescomplemented
78#10623026C22164yescomplemented
79C2×#66939C2214yes—
80C2×#66938C2214yes—
81C2×#66936C2214yes—
82C2×(C22⋊D11)⋊C4C2214yes—
83C2×#66932C2214yes—
84C2×#66932C2214yes—
85C2×#66931C2214yes—
86C2×#66930C2214yes—
87#10623010C22132yescomplemented
88C2×#66929C2214yescomplemented
89C2×#66928C2212yescomplemented
90C2×C4×D44C2212yescomplemented
91C2×#66925C2214yescomplemented
92#10623001C22132yescomplemented
93C2×#66923C2214yescomplemented
94C2×#66923C2212yescomplemented
95C2×#66922C2212yescomplemented
96C2×#66922C2212yescomplemented
97C2×C4×Dic22C2214yescomplemented
98C2×C4×Dic22C2212yescomplemented
99C2×C4×Dic22C2212yescomplemented
100C2×C4×Dic22C2212yescomplemented
101C25×C11C2311yescharacteristic
102C23×C4×C11—28no—
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C23×C4×C11C2318yes—
109C23×C4×C11C2312yes—
110C23×C4×C11C2312yes—
111C23×C4×C11C2311yescharacteristic
112C22×C22⋊D11C2312yes—
113C22×C22⋊D11C2312yes—
114C22×C22⋊D11C2312yes—
115C23×Dic11C2312yes—
116C23×Dic11C2312yes—
117C2×#4339—28no—
118C2×#4339C2318yes—
119C22×D44C2311yescharacteristic
120C22×C4×D11C2312yes—
121C22×C4×D11C2314yes—
122C22×Dic22—28no—
123C22×Dic22C2311yescharacteristic
124C22×Dic22C2312yes—
125C22×Dic22C2312yes—
126C22×Dic22C2318yes—
127C22×Dic22C2314yes—
128C11×#117C2318yes—
129C11×#117C23116yes—
130C11×#117C2318yes—
131C11×#117C2318yes—
132C11×#117C23116yes—
133C11×#117C2318yes—
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2318yes—
141C2×C11×C4⋊C4C2318yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C23116yes—
147C2×C42×C11C2312yes—
148C2×C42×C11C2312yes—
149C2×C42×C11C2312yes—
150C2×C42×C11C2312yes—
151C2×C42×C11C23116yes—
152#67006C23116yes—
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2314yes—
156C2×C22⋊Dic11C23116yes—
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2314yes—
159#66983C2318yes—
160#66983C2318yes—
161#66982C23132yes—
162#66982C23116yes—
163C4×C22⋊D11C23132yes—
164C4×C22⋊D11C23116yes—
165C4×C22⋊D11C23116yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C2314yes—
169C2×(C2×D11)⋊C4C2314yes—
170C2×(C2×D11)⋊C4C2312yes—
171#66979C23132yes—
172#66979C2318yes—
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2314yes—
177C2×C4⋊Dic11C2314yes—
178C2×C4⋊Dic11C2314yes—
179C2×C4⋊Dic11C2312yes—
180C2×C4⋊Dic11C2318yes—
181#66977C2318yes—
182#66977C23116yes—
183#66977C23132yes—
184#66977C23116yes—
185#66977C2318yes—
186#66977C23116yes—
187#66977C23116yes—
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2314yes—
190C2×Dic11⋊C4C2314yes—
191C2×Dic11⋊C4C2314yes—
192C2×Dic11⋊C4C2314yes—
193C2×Dic11⋊C4C2314yes—
194C2×Dic11⋊C4C2314yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2314yes—
197C2×Dic11⋊C4C23116yes—
198C2×C4×Dic11C2314yes—
199C2×C4×Dic11C2314yes—
200C2×C4×Dic11C2314yes—
201C2×C4×Dic11C2312yes—
202#66951C23132yescomplemented
203#66950C23116yescomplemented
204#66950C23116yescomplemented
205#66949C23132yescomplemented
206#66945C23116yescomplemented
207C4⋊C4×D11C23116yescomplemented
208#66943C23116yescomplemented
209#66942C23132yescomplemented
210#66942C23132yescomplemented
211#66941C23116yescomplemented
212#66940C23116yescomplemented
213#66940C23116yescomplemented
214#66939C23132yes—
215#66938C23132yes—
216#66936C23132yes—
217(C22⋊D11)⋊C4C23132yes—
218#66932C23132yes—
219#66932C23132yes—
220#66931C23132yes—
221#66930C23132yes—
222#66929C23132yescomplemented
223#66928C23116yescomplemented
224C4×D44C23116yescomplemented
225#66925C23132yescomplemented
226#66923C23132yescomplemented
227#66923C23116yescomplemented
228#66922C23116yescomplemented
229#66922C23116yescomplemented
230C4×Dic22C23116yescomplemented
231C4×Dic22C23116yescomplemented
232C4×Dic22C23132yescomplemented
233C4×Dic22C23116yescomplemented
234C2×#3495—111nomaximal, Sylow
235C24×C11—24no—
236C24×C11—24no—
237C24×C11—42no—
238C24×C11C2411yescharacteristic
239C24×C11C2414yes—
240C24×C11C2411yescharacteristic
241C24×C11C2411yescharacteristic
242C23×D11C2412yes—
243C22×C4×C11—24no—
244C22×C4×C11—28no—
245C22×C4×C11—24no—
246C22×C4×C11—24no—
247C22×C4×C11—24no—
248C22×C4×C11—24no—
249C22×C4×C11—232no—
250C22×C4×C11—44no—
251C22×C4×C11#4118yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2414yes—
257C22×C4×C11C2412yes—
258C22×C4×C11C2412yes—
259C22×C4×C11C2414yes—
260C22×C4×C11C2414yes—
261C22×C4×C11C2414yes—
262C22×C4×C11C2414yes—
263C22×C4×C11C2418yes—
264C22×C4×C11C2418yes—
265C22×C4×C11C2411yescharacteristic
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2414yes—
268C2×C22⋊D11—28no—
269C2×C22⋊D11—28no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11C2418yes—
272C2×C22⋊D11C2418yes—
273C2×C22⋊D11C2418yes—
274C22×Dic11—28no—
275C22×Dic11—44no—
276C22×Dic11C2418yes—
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C22×Dic11C2414yes—
281C22×Dic11C2414yes—
282C22×Dic11C2418yes—
283#4339—232no—
284C2×D44—24no—
285C2×D44C2414yes—
286C2×C4×D11—28no—
287C2×C4×D11—48no—
288C2×C4×D11C2418yes—
289C2×C4×D11C24116yes—
290C2×Dic22—28no—
291C2×Dic22—28no—
292C2×Dic22—232no—
293C2×Dic22—24no—
294C2×Dic22—48no—
295C2×Dic22C2414yes—
296C2×Dic22C2418yes—
297C2×Dic22C2418yes—
298C2×Dic22C24116yes—
299C11×C4⋊C4C2414yes—
300C11×C4⋊C4C2414yes—
301C11×C4⋊C4C2414yes—
302C11×C4⋊C4C2418yes—
303C11×C4⋊C4C2418yes—
304C11×C4⋊C4C2414yes—
305C11×C22⋊C4C2418yes—
306C11×C22⋊C4C2418yes—
307C11×C22⋊C4C2418yes—
308C11×C22⋊C4C2418yes—
309C42×C11C2418yes—
310C42×C11C2418yes—
311C42×C11C2418yes—
312C42×C11C2418yes—
313C22⋊Dic11C2418yes—
314C22⋊Dic11C2418yes—
315C22⋊Dic11C24116yes—
316C22⋊Dic11C2418yes—
317C22⋊Dic11C24116yes—
318(C2×D11)⋊C4C2418yes—
319(C2×D11)⋊C4C24116yes—
320(C2×D11)⋊C4C24116yes—
321(C2×D11)⋊C4C24116yes—
322(C2×D11)⋊C4C2418yes—
323C4⋊Dic11C2414yes—
324C4⋊Dic11C2414yes—
325C4⋊Dic11C2418yes—
326C4⋊Dic11C24116yes—
327C4⋊Dic11C24116yes—
328C4⋊Dic11C24116yes—
329C4⋊Dic11C2418yes—
330Dic11⋊C4C2418yes—
331Dic11⋊C4C24116yes—
332Dic11⋊C4C24116yes—
333Dic11⋊C4C24116yes—
334Dic11⋊C4C24116yes—
335Dic11⋊C4C24116yes—
336Dic11⋊C4C24116yes—
337Dic11⋊C4C2418yes—
338Dic11⋊C4C24116yes—
339C4×Dic11C24116yes—
340C4×Dic11C24116yes—
341C4×Dic11C24116yes—
342C4×Dic11C2418yes—
343#3495—1132no—
344C2×#556—112no—
345C2×#554—112no—
346C2×#552—114no—
347C2×#552—112no—
348C2×#552—112no—
349C2×#551—114no—
350C2×#544—111no—
351C2×#542—112no—
352C2×#541—112no—
353C2×#536—111no—
354C2×#533—112no—
355C2×#529—112no—
356C2×#525—111no—
357C22×C22⋊Q8—111no—
358C2×#520—111no—
359C2×#519—111no—
360C22×#117D1111yescharacteristic, complemented
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—28no—
366C23×C11—22no—
367C23×C11—28no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—44no—
371C23×C11—416no—
372C23×C11C2×#4114yes—
373C23×C112−1+414yes—
374C23×C11C2512yes—
375C23×C11C2512yes—
376C23×C11C2512yes—
377C23×C11C2511yescharacteristic
378C22×D11—24no—
379C22×D11—24no—
380C22×D11—24no—
381C22×D11C2514yes—
382C2×C4×C11—28no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—216no—
386C2×C4×C11—24no—
387C2×C4×C11—24no—
388C2×C4×C11—24no—
389C2×C4×C11—24no—
390C2×C4×C11—28no—
391C2×C4×C11—28no—
392C2×C4×C11—28no—
393C2×C4×C11—28no—
394C2×C4×C11—48no—
395C2×C4×C11C2×#4114yes—
396C2×C4×C11C2×#4114yes—
397C2×C4×C11C2×#41116yes—
398C2×C4×C11C2514yes—
399C2×C4×C11C2514yes—
400C2×C4×C11C2512yes—
401C2×C4×C11C2512yes—
402C2×C4×C11C2514yes—
403C2×C4×C11C2514yes—
404C2×C4×C11C2512yes—
405C2×C4×C11C2512yes—
406C22⋊D11—216no—
407C22⋊D11—216no—
408C22⋊D11—48no—
409C2×Dic11—216no—
410C2×Dic11—28no—
411C2×Dic11—24no—
412C2×Dic11—24no—
413C2×Dic11—24no—
414C2×Dic11—28no—
415C2×Dic11—48no—
416C2×Dic11C2514yes—
417C2×Dic11C2514yes—
418C2×Dic11C2514yes—
419C2×Dic11C2518yes—
420C2×Dic11C2518yes—
421D44—28no—
422C4×D11—216no—
423C4×D11—416no—
424Dic22—216no—
425Dic22—216no—
426Dic22—28no—
427Dic22—416no—
428C22×#41—111no—
429C23×Q8—111no—
430C24×C4C2×D1111yescharacteristic
431#556—1132no—
432#554—1132no—
433#552—1132no—
434#552—1164no—
435#552—1132no—
436#551—1164no—
437#544—1116no—
438#542—1132no—
439#541—1132no—
440#536—1116no—
441#533—1132no—
442C2×C4⋊Q8—112no—
443C2×C4⋊Q8—112no—
444C2×C4⋊Q8—112no—
445#529—1132no—
446C2×#126—114no—
447C2×#126—114no—
448C2×#126—114no—
449C2×#126—114no—
450C2×#125—114no—
451C2×#125—114no—
452C2×#125—112no—
453C2×#125—112no—
454C2×#125—114no—
455C2×#124—114no—
456C2×#124—112no—
457#525—1116no—
458C2×#123—112no—
459C2×#123—114no—
460C2×#123—114no—
461C2×#123—114no—
462C2×C22⋊Q8—112no—
463C2×C22⋊Q8—112no—
464C2×C22⋊Q8—112no—
465C2×C22⋊Q8—112no—
466C2×C22⋊Q8—111no—
467C2×C22⋊Q8—111no—
468C2×C22⋊Q8—114no—
469C2×C22⋊Q8—1116no—
470C2×C22⋊Q8—114no—
471C2×C22⋊Q8—112no—
472C2×C22⋊Q8—112no—
473C2×C22⋊Q8—114no—
474C2×#121—111no—
475C2×#121—111no—
476C2×#120—112no—
477#520—1116no—
478#519—1116no—
479C2×C4×Q8—112no—
480C2×C4×Q8—112no—
481C2×C4×Q8—112no—
482C2×C4×Q8—112no—
483C2×C4×Q8—112no—
484C2×C4×Q8—114no—
485C2×C4×D4—112no—
486C2×C4×D4—112no—
487C2×C4×D4—114no—
488C2×C4×D4—114no—
489C2×C4×D4—112no—
490C2×#117—111no—
491C2×#117—114no—
492C2×#117—112no—
493C2×#117—114no—
494C2×#117—114no—
495C2×#117C2×D1111yescharacteristic
496C2×#117C2×D1111yescharacteristic
497C2×#117C2×D1112yes—
498C2×#117C2×D1111yescharacteristic
499C2×#117C2×D1112yes—
500C2×#117C2×D1111yescharacteristic
501C2×#117C2×D11116yescomplemented
502C22×C4⋊C4—112no—
503C22×C4⋊C4—111no—
504C22×C4⋊C4—112no—
505C22×C4⋊C4C2×D1111yescharacteristic
506C22×C4⋊C4C2×D1111yescharacteristic
507C22×C22⋊C4—112no—
508C22×C22⋊C4C2×D1112yes—
509C22×C42C2×D1112yes—
510C22×C11—22no—
511C22×C11—22no—
512C22×C11—22no—
513C22×C11—22no—
514C22×C11—28no—
515C22×C11—28no—
516C22×C11—22no—
517C22×C11—22no—
518C22×C11—22no—
519C22×C11—416no—
520C22×C11—44no—
521C22×C11C22×#4114yes—
522C22×C11C22×#4112yes—
523C22×C11C2×2−1+414yes—
524C22×C11C2×2−1+412yes—
525C22×C11#58512yes—
526C22×C11C2611yescharacteristic
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—48no—
531C4×C11—22no—
532C4×C11—22no—
533C4×C11—24no—
534C4×C11—24no—
535C4×C11—24no—
536C4×C11—24no—
537C4×C11C22×#4114yes—
538C4×C11C22×#4114yes—
539Dic11—28no—
540Dic11—24no—
541Dic11—24no—
542Dic11—24no—
543Dic11—28no—
544C25C22×D1111yescharacteristic
545C2×#41—118no—
546C2×#41—228no—
547C22×Q8—112no—
548C22×Q8—112no—
549C22×Q8—111no—
550C22×Q8—118no—
551C22×Q8—114no—
552C22×Q8—228no—
553C22×D4—112no—
554C22×D4—112no—
555C22×D4—112no—
556C22×D4—111no—
557C23×C4—28no—
558C23×C4—112no—
559C23×C4—112no—
560C23×C4—112no—
561C23×C4—114no—
562C23×C4C22×D1112yes—
563C23×C4C22×D1111yescharacteristic
564C23×C4C22×D1111yescharacteristic
565C23×C4C22×D1111yescharacteristic
566C23×C4C22×D1111yescharacteristic
567C23×C4C22×D1118yes—
568C23×C4C22×D1111yescharacteristic
569C23×C4C22×D1112yes—
570C23×C4C22×D1111yescharacteristic
571C4⋊Q8—1116no—
572C4⋊Q8—1116no—
573C4⋊Q8—1116no—
574#126—1132no—
575#126—1132no—
576#126—1132no—
577#126—1132no—
578#125—1132no—
579#125—1132no—
580#125—1116no—
581#125—1116no—
582#125—1132no—
583#124—1132no—
584#124—1116no—
585#123—1116no—
586#123—1132no—
587#123—1132no—
588#123—1132no—
589C22⋊Q8—1116no—
590C22⋊Q8—1116no—
591C22⋊Q8—1116no—
592C22⋊Q8—1116no—
593C22⋊Q8—118no—
594C22⋊Q8—118no—
595C22⋊Q8—1132no—
596C22⋊Q8—1116no—
597C22⋊Q8—1116no—
598C22⋊Q8—1132no—
599C22⋊Q8—1132no—
600#121—118no—
601#121—118no—
602#120—1116no—
603C4×Q8—1116no—
604C4×Q8—1116no—
605C4×Q8—1116no—
606C4×Q8—1116no—
607C4×Q8—1116no—
608C4×Q8—1132no—
609C4×D4—1116no—
610C4×D4—1116no—
611C4×D4—1132no—
612C4×D4—1132no—
613C4×D4—1116no—
614#117—118no—
615#117—1132no—
616#117—1116no—
617#117—1132no—
618#117—1132no—
619#117C22×D1118yes—
620#117C22×D1118yes—
621#117C22×D11116yes—
622#117C22×D1118yes—
623#117C22×D11116yes—
624#117C22×D1118yes—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—114no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—114no—
629C2×C4⋊C4—118no—
630C2×C4⋊C4—114no—
631C2×C4⋊C4—1116no—
632C2×C4⋊C4—111no—
633C2×C4⋊C4—111no—
634C2×C4⋊C4—114no—
635C2×C4⋊C4—114no—
636C2×C4⋊C4—114no—
637C2×C4⋊C4—114no—
638C2×C4⋊C4—114no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—114no—
642C2×C4⋊C4—114no—
643C2×C4⋊C4—1116no—
644C2×C4⋊C4C22×D1111yescharacteristic
645C2×C4⋊C4C22×D1111yescharacteristic
646C2×C4⋊C4C22×D1112yes—
647C2×C4⋊C4C22×D1111yescharacteristic
648C2×C4⋊C4C22×D1111yescharacteristic
649C2×C4⋊C4C22×D1112yes—
650C2×C4⋊C4C22×D1118yes—
651C2×C4⋊C4C22×D1118yes—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—1116no—
655C2×C22⋊C4—112no—
656C2×C22⋊C4—112no—
657C2×C22⋊C4—112no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—114no—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—112no—
662C2×C22⋊C4—114no—
663C2×C22⋊C4C22×D1112yes—
664C2×C22⋊C4C22×D1112yes—
665C2×C22⋊C4C22×D1112yes—
666C2×C22⋊C4C22×D1112yes—
667C2×C22⋊C4C22×D11116yes—
668C2×C42—114no—
669C2×C42—114no—
670C2×C42—114no—
671C2×C42—112no—
672C2×C42C22×D1112yes—
673C2×C42C22×D1112yes—
674C2×C42C22×D1112yes—
675C2×C42C22×D1112yes—
676C2×C42C22×D11116yes—
677C2×C11—24no—
678C2×C11—24no—
679C2×C11—42no—
680C2×C11#349514yescomplemented
681C2×C11C23×#4111yescharacteristic
682C2×C11C22×2−1+411yescharacteristic
683C2×C11C2×#58511yescharacteristic
684D11—44no—
685C24—24no—
686C24—24no—
687C24—42no—
688C24—112no—
689C24C23×D1111yescharacteristic
690C24C23×D1114yes—
691C24C23×D1111yescharacteristic
692C24C23×D1111yescharacteristic
693#41—2232no—
694C2×Q8—118no—
695C2×Q8—118no—
696C2×Q8—114no—
697C2×Q8—1116no—
698C2×Q8—228no—
699C2×Q8—228no—
700C2×Q8—2232no—
701C2×Q8—224no—
702C2×Q8—448no—
703C2×D4—118no—
704C2×D4—118no—
705C2×D4—118no—
706C2×D4—114no—
707C2×D4—228no—
708C2×D4—228no—
709C2×D4—224no—
710C2×D4—444no—
711C22×C4—24no—
712C22×C4—28no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—232no—
718C22×C4—44no—
719C22×C4—118no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—114no—
723C22×C4—112no—
724C22×C4—114no—
725C22×C4—118no—
726C22×C4—118no—
727C22×C4—1116no—
728C22×C4—228no—
729C22×C4—228no—
730C22×C4—448no—
731C22×C4—444no—
732C22×C4#433918yes—
733C22×C4C23×D1114yes—
734C22×C4C23×D1118yes—
735C22×C4C23×D1114yes—
736C22×C4C23×D1114yes—
737C22×C4C23×D1114yes—
738C22×C4C23×D1114yes—
739C22×C4C23×D1112yes—
740C22×C4C23×D1112yes—
741C22×C4C23×D1111yescharacteristic
742C22×C4C23×D1112yes—
743C22×C4C23×D1112yes—
744C22×C4C23×D1111yescharacteristic
745C22×C4C23×D1118yes—
746C22×C4C23×D1114yes—
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1111yescharacteristic
749C4⋊C4—118no—
750C4⋊C4—1116no—
751C4⋊C4—118no—
752C4⋊C4—1116no—
753C4⋊C4—1116no—
754C4⋊C4—114no—
755C4⋊C4—114no—
756C4⋊C4—1116no—
757C4⋊C4—1116no—
758C4⋊C4—1116no—
759C4⋊C4—1116no—
760C4⋊C4—1116no—
761C4⋊C4—118no—
762C4⋊C4—118no—
763C4⋊C4—1116no—
764C4⋊C4—1116no—
765C4⋊C4C23×D1114yes—
766C4⋊C4C23×D1114yes—
767C4⋊C4C23×D1118yes—
768C4⋊C4C23×D1114yes—
769C4⋊C4C23×D1114yes—
770C4⋊C4C23×D1118yes—
771C22⋊C4—1116no—
772C22⋊C4—1116no—
773C22⋊C4—118no—
774C22⋊C4—118no—
775C22⋊C4—118no—
776C22⋊C4—118no—
777C22⋊C4—1116no—
778C22⋊C4—1116no—
779C22⋊C4—118no—
780C22⋊C4—1116no—
781C22⋊C4C23×D1118yes—
782C22⋊C4C23×D1118yes—
783C22⋊C4C23×D1118yes—
784C22⋊C4C23×D1118yes—
785C42—1116no—
786C42—1116no—
787C42—1116no—
788C42—118no—
789C42C23×D1118yes—
790C42C23×D1118yes—
791C42C23×D1118yes—
792C42C23×D1118yes—
793C11C2×#349511yescharacteristic, complemented, Sylow
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—28no—
799C23—22no—
800C23—28no—
801C23—22no—
802C23—22no—
803C23—44no—
804C23—416no—
805C23—114no—
806C23—224no—
807C23—224no—
808C23—224no—
809C23C2×#433914yes—
810C23#6704314yes—
811C23C24×D1112yes—
812C23C24×D1112yes—
813C23C24×D1112yes—
814C23C24×D1111yescharacteristic
815Q8—2216no—
816Q8—2216no—
817Q8—228no—
818Q8—4416no—
819D4—2216no—
820D4—2216no—
821D4—228no—
822D4—448no—
823C2×C4—28no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—216no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—48no—
836C2×C4—114no—
837C2×C4—114no—
838C2×C4—118no—
839C2×C4—114no—
840C2×C4—118no—
841C2×C4—224no—
842C2×C4—2216no—
843C2×C4—228no—
844C2×C4—224no—
845C2×C4—228no—
846C2×C4—224no—
847C2×C4—2216no—
848C2×C4—4416no—
849C2×C4—448no—
850C2×C4C2×#433914yes—
851C2×C4C2×#433914yes—
852C2×C4C2×#4339116yes—
853C2×C4C24×D1114yes—
854C2×C4C24×D1114yes—
855C2×C4C24×D1112yes—
856C2×C4C24×D1114yes—
857C2×C4C24×D1114yes—
858C2×C4C24×D1112yes—
859C2×C4C24×D1112yes—
860C2×C4C24×D1112yes—
861C22—28no—
862C22—28no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—416no—
871C22—44no—
872C22—224no—
873C22—224no—
874C22—224no—
875C22—448no—
876C22C22×#433914yes—
877C22C22×#433912yes—
878C22C2×#6704314yes—
879C22C2×#6704312yes—
880C22#1062345312yes—
881C22C25×D1111yescharacteristic
882C4—22no—
883C4—22no—
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—224no—
889C4—228no—
890C4—224no—
891C4—228no—
892C4—224no—
893C4C22×#433914yes—
894C4C22×#433914yes—
895C2—24no—
896C2—24no—
897C2—42no—
898C2—444no—
899C2#1308236814yesdirect product factor
900C2C23×#433911yescharacteristic
901C2C22×#6704311yescharacteristic
902C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×#117C2
socleC23×C11C25
prime radicalC2×#10623322C2
hypercenterC22×#117D11
hypocenterC11C2×#3495
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. #13082368C2direct (N × H)
2. C2×#10623064C2semidirect
3. C2×#10623042C2semidirect
4. C2×#10623060C2semidirect
5. C2×#10623044C2semidirect
6. C2×#10623062C2semidirect
7. C2×#10623026C2semidirect
8. C2×#10623050C2semidirect
9. C2×#10623065C2semidirect
10. C2×#10623049C2semidirect
11. C2×#10623057C2semidirect
12. C2×#10623001C2semidirect
13. C2×#10623010C2semidirect
15. C22×#66977C2semidirect
16. C2×#10623054C2semidirect
17. C2×#10623047C2semidirect
18. C22×C11×#117C2semidirect
28. C2×C11×#117C22semidirect
53. C2×#66977C22semidirect
55. #10623065C22semidirect
56. #10623064C22semidirect
57. #10623062C22semidirect
58. #10623060C22semidirect
59. #10623057C22semidirect
60. #10623054C22semidirect
61. #10623050C22semidirect
62. #10623049C22semidirect
63. #10623047C22semidirect
64. #10623044C22semidirect
65. C2×#66951C22semidirect
66. #10623042C22semidirect
67. C2×#66950C22semidirect
68. C2×#66950C22semidirect
69. C2×#66949C22semidirect
70. C2×#66945C22semidirect
71. C2×C4⋊C4×D11C22semidirect
72. C2×#66943C22semidirect
73. C2×#66942C22semidirect
74. C2×#66942C22semidirect
75. C2×#66941C22semidirect
76. C2×#66940C22semidirect
77. C2×#66940C22semidirect
78. #10623026C22semidirect
87. #10623010C22semidirect
88. C2×#66929C22semidirect
89. C2×#66928C22semidirect
90. C2×C4×D44C22semidirect
91. C2×#66925C22semidirect
92. #10623001C22semidirect
93. C2×#66923C22semidirect
94. C2×#66923C22semidirect
95. C2×#66922C22semidirect
96. C2×#66922C22semidirect
97. C2×C4×Dic22C22semidirect
98. C2×C4×Dic22C22semidirect
99. C2×C4×Dic22C22semidirect
100. C2×C4×Dic22C22semidirect
202. #66951C23semidirect
203. #66950C23semidirect
204. #66950C23semidirect
205. #66949C23semidirect
206. #66945C23semidirect
207. C4⋊C4×D11C23semidirect
208. #66943C23semidirect
209. #66942C23semidirect
210. #66942C23semidirect
211. #66941C23semidirect
212. #66940C23semidirect
213. #66940C23semidirect
222. #66929C23semidirect
223. #66928C23semidirect
224. C4×D44C23semidirect
225. #66925C23semidirect
226. #66923C23semidirect
227. #66923C23semidirect
228. #66922C23semidirect
229. #66922C23semidirect
230. C4×Dic22C23semidirect
231. C4×Dic22C23semidirect
232. C4×Dic22C23semidirect
233. C4×Dic22C23semidirect
360. C22×#117D11semidirect
501. C2×#117C2×D11semidirect
680. C2×C11#3495semidirect
793. C11C2×#3495semidirect
899. C2#13082368direct (N × H)

Maximal subgroups

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

subgroupindex
#130823682
C2×#106230642
C2×#106230422
C2×#106230602
C2×#106230442
C2×#106230622
C2×#106230262
C2×#106230502
C2×#106230652
C2×#106230492
C2×#106230572
C2×#106230012
C2×#106230102
C2×#106233222
C22×#669772
C2×#106230542
C2×#106230472
C22×C11×#1172
C2×#349511