Finite Group Databasebeta

← C2×#13083113 #15661221

Subgroups — C2×#13083113 #15661221

Order 2816.

6554 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13083113C2132yesmaximal, direct product factor
2C2×#10623182C212yesmaximal, complemented
3C2×#10623203C212yesmaximal, complemented
4C2×#10623244C211yesmaximal, characteristic, complemented
5C2×#10623098C211yesmaximal, characteristic, complemented
6C2×#10623100C211yesmaximal, characteristic, complemented
7C2×#10623202C211yesmaximal, characteristic, complemented
8C2×#10623202C211yesmaximal, characteristic, complemented
9C2×#10623070C211yesmaximal, characteristic, complemented
10C2×#10623074C211yesmaximal, characteristic, complemented
11C2×#10623072C212yesmaximal, complemented
12C2×#10623181C212yesmaximal, complemented
13C2×#10623213C211yesmaximal, characteristic, complemented
14C2×#10623193C212yesmaximal, complemented
15C2×#10623092C211yesmaximal, characteristic, complemented
16C2×#10623200C212yesmaximal, complemented
17C2×#10623114C211yesmaximal, characteristic, complemented
18C2×#10623250C211yesmaximal, characteristic
19C2×#10623196C212yesmaximal, complemented
20C2×#10623095C212yesmaximal, complemented
21C2×#10623109C211yesmaximal, characteristic, complemented
22C2×#10623088C211yesmaximal, characteristic, complemented
23C2×#10623211C211yesmaximal, characteristic, complemented
24C2×C11×#559C211yesmaximal, characteristic, complemented
25C11×#559C22116yescomplemented
26C2×C11×#127C2211yescharacteristic
27C2×C11×#124C2211yescharacteristic
28C2×C11×#124C2211yescharacteristic
29C2×C11×#124C2212yes—
30C2×C11×#123C2212yes—
31C2×C11×#123C2212yes—
32C2×C4×Q8×C11C2211yescharacteristic
33C2×C4×Q8×C11C2211yescharacteristic
34C2×C4×D4×C11C2212yes—
35C2×C4×D4×C11C2211yescharacteristic
36C2×C4×D4×C11C2211yescharacteristic
37C2×#66999C2211yescharacteristic
38C2×#66999C2211yescharacteristic
39C2×Q8×Dic11C2211yescharacteristic
40C2×Q8×Dic11C2211yescharacteristic
41C2×#66997C2211yescharacteristic
42C2×#66997C2211yescharacteristic
43C2×#66997C2212yes—
44C2×#66992C2212yes—
45C2×#66992C2212yes—
46C2×#66991C2211yescharacteristic
47C2×#66991C2211yescharacteristic
48C2×#66989C2211yescharacteristic
49C2×#66989C2211yescharacteristic
50C2×#66989C2212yes—
51C2×#66988C2212yes—
52C2×#66988C2212yes—
53C2×#66988C2212yes—
54C2×#66988C2212yes—
55C2×D4×Dic11C2212yes—
56C2×D4×Dic11C2211yescharacteristic
57C2×D4×Dic11C2211yescharacteristic
58C2×D4×Dic11C2211yescharacteristic
59C2×D4×Dic11C2211yescharacteristic
60C2×#66982C2212yes—
61C2×C4×C22⋊D11C2212yes—
62C2×#66979C2212yes—
63C22×C4⋊Dic11C2212yes—
64C2×#66977C2212yes—
65C2×#66977C2212yes—
66C2×#66977C2212yes—
67C22×Dic11⋊C4C2212yes—
68#10623250C22116yes—
69#10623244C22116yescomplemented
70#10623213C22116yescomplemented
71#10623211C22116yescomplemented
72#10623203C22132yescomplemented
73#10623202C22116yescomplemented
74#10623202C22116yescomplemented
75#10623200C22132yescomplemented
76#10623196C22132yescomplemented
77#10623193C22132yescomplemented
78#10623182C22132yescomplemented
79#10623181C22132yescomplemented
80#10623114C22116yescomplemented
81#10623109C22116yescomplemented
82#10623100C22116yescomplemented
83#10623098C22116yescomplemented
84#10623095C22132yescomplemented
85#10623092C22116yescomplemented
86#10623088C22116yescomplemented
87#10623074C22116yescomplemented
88#10623072C22132yescomplemented
89#10623070C22116yescomplemented
90C2×#66951C2212yes—
91C2×#66950C2211yescharacteristic
92C2×#66950C2211yescharacteristic
93C2×#66949C2211yescharacteristic
94C2×#66949C2211yescharacteristic
95C2×#66943C2212yes—
96C2×#66943C2211yescharacteristic
97C2×#66943C2211yescharacteristic
98C2×#66942C2211yescharacteristic
99C2×#66942C2212yes—
100C2×#66942C2211yescharacteristic
101C2×#66942C2212yes—
102C2×#66942C2212yes—
103C2×#66941C2211yescharacteristic
104C2×#66941C2211yescharacteristic
105C2×#66941C2212yes—
106C2×#66940C2212yes—
107C2×#66939C2212yes—
108C2×#66938C2212yes—
109C2×#66938C2212yes—
110C2×#66936C2212yes—
111C2×#66936C2212yes—
112C2×(C22⋊D11)⋊C4C2212yes—
113C2×#66932C2212yes—
114C2×#66932C2212yes—
115C2×#66932C2212yes—
116C2×#66932C2212yes—
117C2×#66932C2212yes—
118C2×#66932C2212yes—
119C2×#66932C2212yes—
120C2×#66932C2212yes—
121C2×#66931C2212yes—
122C2×#66931C2212yes—
123C2×#66931C2212yes—
124C2×#66931C2212yes—
125C2×#66931C2212yes—
126C2×#66931C2212yes—
127C2×#66931C2212yes—
128C2×#66930C2212yes—
129C2×#66930C2212yes—
130C2×#66930C2212yes—
131C2×#66929C2212yes—
132C2×#66925C2211yescharacteristic
133C2×#66925C2211yescharacteristic
134C2×C42×D11C2211yescharacteristic
135C2×#66923C2212yes—
136C2×#66923C2211yescharacteristic
137C2×#66923C2211yescharacteristic
138C2×#66923C2212yes—
139C2×#66922C2211yescharacteristic
140C2×C4×Dic22C2212yes—
141C2×C4×Dic22C2211yescharacteristic
142C2×C4×Dic22C2211yescharacteristic
143C2×C4×Dic22C2211yescharacteristic
144C2×C4×Dic22C2211yescharacteristic
145C2×C4×Dic22C2211yescharacteristic
146C2×C4×Dic22C2211yescharacteristic
147C22×Q8×C11C2311yescharacteristic
148C22×Q8×C11C2311yescharacteristic
149C22×D4×C11C2311yescharacteristic
150C22×D4×C11C2311yescharacteristic
151C22×D4×C11C2312yes—
152C22×D4×C11C2312yes—
153C23×C4×C11C2312yes—
154C23×C4×C11C2312yes—
155C22×C22⋊D11C2312yes—
156C22×C22⋊D11C2312yes—
157C23×Dic11C2312yes—
158C23×Dic11C2312yes—
159C23×Dic11C2312yes—
160C23×Dic11C2312yes—
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2311yescharacteristic
164C22×Dic22C2311yescharacteristic
165C22×Dic22C2311yescharacteristic
166C22×Dic22C2311yescharacteristic
167C22×Dic22C2312yes—
168C22×Dic22C2311yescharacteristic
169C22×Dic22C2312yes—
170C11×#127C2318yes—
171C11×#124C23116yes—
172C11×#124C2318yes—
173C11×#124C2318yes—
174C11×#123C23116yes—
175C11×#123C23116yes—
176C4×Q8×C11C2318yes—
177C4×Q8×C11C2318yes—
178C4×D4×C11C2318yes—
179C4×D4×C11C23116yes—
180C4×D4×C11C2318yes—
181C2×C11×C4⋊C4C2311yescharacteristic
182C2×C11×C4⋊C4C2311yescharacteristic
183C2×C11×C4⋊C4C2312yes—
184C2×C11×C4⋊C4C2311yescharacteristic
185C2×C11×C4⋊C4C2311yescharacteristic
186C2×C11×C22⋊C4C2312yes—
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2312yes—
191C2×C11×C22⋊C4C2312yes—
192C2×C42×C11C2311yescharacteristic
193C2×C42×C11C2311yescharacteristic
194C2×C42×C11C2311yescharacteristic
195C2×C42×C11C2312yes—
196C2×C22⋊Dic11C2312yes—
197C2×C22⋊Dic11C2312yes—
198C2×C22⋊Dic11C2312yes—
199C2×C22⋊Dic11C2312yes—
200C2×C22⋊Dic11C2312yes—
201C2×C22⋊Dic11C2312yes—
202C2×C22⋊Dic11C2312yes—
203C2×C22⋊Dic11C2312yes—
204C2×C22⋊Dic11C2312yes—
205C2×C22⋊Dic11C2312yes—
206#66999C2318yes—
207#66999C2318yes—
208Q8×Dic11C2318yes—
209Q8×Dic11C2318yes—
210#66997C23116yes—
211#66997C2318yes—
212#66997C2318yes—
213#66992C23116yes—
214#66992C23116yes—
215#66991C2318yes—
216#66991C2318yes—
217#66989C2318yes—
218#66989C2318yes—
219#66989C23116yes—
220#66988C23116yes—
221#66988C23116yes—
222#66988C23116yes—
223#66988C23116yes—
224D4×Dic11C2318yes—
225D4×Dic11C2318yes—
226D4×Dic11C23116yes—
227D4×Dic11C2318yes—
228D4×Dic11C2318yes—
229#66982C23116yes—
230C4×C22⋊D11C23116yes—
231C2×(C2×D11)⋊C4C2311yescharacteristic
232C2×(C2×D11)⋊C4C2311yescharacteristic
233C2×(C2×D11)⋊C4C2311yescharacteristic
234C2×(C2×D11)⋊C4C2311yescharacteristic
235C2×(C2×D11)⋊C4C2312yes—
236C2×(C2×D11)⋊C4C2312yes—
237#66979C23116yes—
238C2×C4⋊Dic11C2311yescharacteristic
239C2×C4⋊Dic11C2311yescharacteristic
240C2×C4⋊Dic11C2311yescharacteristic
241C2×C4⋊Dic11C2311yescharacteristic
242C2×C4⋊Dic11C2312yes—
243C2×C4⋊Dic11C2311yescharacteristic
244C2×C4⋊Dic11C2311yescharacteristic
245C2×C4⋊Dic11C2312yes—
246C2×C4⋊Dic11C2312yes—
247C2×C4⋊Dic11C2312yes—
248C2×C4⋊Dic11C2312yes—
249C2×C4⋊Dic11C2312yes—
250C2×C4⋊Dic11C23116yes—
251#66977C23116yes—
252#66977C23116yes—
253#66977C23116yes—
254C2×Dic11⋊C4C2311yescharacteristic
255C2×Dic11⋊C4C2312yes—
256C2×Dic11⋊C4C2311yescharacteristic
257C2×Dic11⋊C4C2312yes—
258C2×Dic11⋊C4C2311yescharacteristic
259C2×Dic11⋊C4C2311yescharacteristic
260C2×Dic11⋊C4C2311yescharacteristic
261C2×Dic11⋊C4C2312yes—
262C2×Dic11⋊C4C2312yes—
263C2×Dic11⋊C4C2311yescharacteristic
264C2×Dic11⋊C4C2311yescharacteristic
265C2×Dic11⋊C4C2312yes—
266C2×Dic11⋊C4C2312yes—
267C2×Dic11⋊C4C2312yes—
268C2×Dic11⋊C4C2312yes—
269C2×Dic11⋊C4C2312yes—
270C2×Dic11⋊C4C2312yes—
271C2×Dic11⋊C4C2312yes—
272C2×Dic11⋊C4C2311yescharacteristic
273C2×Dic11⋊C4C2311yescharacteristic
274C2×Dic11⋊C4C2311yescharacteristic
275C2×Dic11⋊C4C2312yes—
276C2×Dic11⋊C4C2312yes—
277C2×Dic11⋊C4C23116yes—
278C2×C4×Dic11C2311yescharacteristic
279C2×C4×Dic11C2311yescharacteristic
280C2×C4×Dic11C2311yescharacteristic
281C2×C4×Dic11C2312yes—
282C2×C4×Dic11C2312yes—
283C2×C4×Dic11C2312yes—
284C2×C4×Dic11C2312yes—
285C2×C4×Dic11C2312yes—
286C2×C4×Dic11C2311yescharacteristic
287C2×C4×Dic11C2311yescharacteristic
288#66951C23116yes—
289#66950C2318yes—
290#66950C2318yes—
291#66949C2318yes—
292#66949C2318yes—
293#66943C2318yes—
294#66943C2318yes—
295#66943C23116yes—
296#66942C2318yes—
297#66942C23116yes—
298#66942C23116yes—
299#66942C2318yes—
300#66942C23116yes—
301#66941C2318yes—
302#66941C23116yes—
303#66941C2318yes—
304#66940C23116yes—
305#66939C23116yes—
306#66938C23116yes—
307#66938C23116yes—
308#66936C23116yes—
309#66936C23116yes—
310(C22⋊D11)⋊C4C23116yes—
311#66932C23116yes—
312#66932C23116yes—
313#66932C23116yes—
314#66932C23116yes—
315#66932C23116yes—
316#66932C23116yes—
317#66932C23116yes—
318#66932C23116yes—
319#66931C23116yes—
320#66931C23116yes—
321#66931C23116yes—
322#66931C23116yes—
323#66931C23116yes—
324#66931C23116yes—
325#66931C23116yes—
326#66930C23116yes—
327#66930C23116yes—
328#66930C23116yes—
329#66929C23116yes—
330#66925C2318yes—
331#66925C2318yes—
332C42×D11C2318yes—
333#66923C2318yes—
334#66923C2318yes—
335#66923C23116yes—
336#66923C23116yes—
337#66922C2318yes—
338C4×Dic22C2318yes—
339C4×Dic22C2318yes—
340C4×Dic22C2318yes—
341C4×Dic22C23116yes—
342C4×Dic22C2318yes—
343C4×Dic22C2318yes—
344C4×Dic22C2318yes—
345C2×#3557—111nomaximal, Sylow
346C24×C11C2412yes—
347C24×C11C2412yes—
348C23×D11C2411yescharacteristic
349C2×Q8×C11—24no—
350C2×Q8×C11—42no—
351C2×Q8×C11C2414yes—
352C2×Q8×C11C2414yes—
353C2×D4×C11—24no—
354C2×D4×C11—24no—
355C2×D4×C11—44no—
356C2×D4×C11—44no—
357C2×D4×C11C2414yes—
358C2×D4×C11C2414yes—
359C2×D4×C11C2418yes—
360C2×D4×C11C2418yes—
361C22×C4×C11—44no—
362C22×C4×C11—44no—
363C22×C4×C11C2411yescharacteristic
364C22×C4×C11C2412yes—
365C22×C4×C11C2411yescharacteristic
366C22×C4×C11C2411yescharacteristic
367C22×C4×C11C2411yescharacteristic
368C22×C4×C11C2411yescharacteristic
369C22×C4×C11C2411yescharacteristic
370C22×C4×C11C2412yes—
371C22×C4×C11C2418yes—
372C22×C4×C11C2418yes—
373C22×C4×C11C2411yescharacteristic
374C2×C22⋊D11—44no—
375C2×C22⋊D11—44no—
376C2×C22⋊D11C2418yes—
377C2×C22⋊D11C2418yes—
378C22×Dic11—44no—
379C22×Dic11—44no—
380C22×Dic11—44no—
381C22×Dic11—44no—
382C22×Dic11C2411yescharacteristic
383C22×Dic11C2412yes—
384C22×Dic11C2411yescharacteristic
385C22×Dic11C2411yescharacteristic
386C22×Dic11C2412yes—
387C22×Dic11C2412yes—
388C22×Dic11C2411yescharacteristic
389C22×Dic11C2411yescharacteristic
390C22×Dic11C2411yescharacteristic
391C22×Dic11C2411yescharacteristic
392C22×Dic11C2412yes—
393C22×Dic11C2418yes—
394C22×Dic11C2418yes—
395C22×Dic11C2418yes—
396C22×Dic11C2418yes—
397C2×C4×D11—24no—
398C2×C4×D11—42no—
399C2×C4×D11—42no—
400C2×C4×D11C2414yes—
401C2×C4×D11C2414yes—
402C2×C4×D11C2414yes—
403C2×Dic22—24no—
404C2×Dic22—44no—
405C2×Dic22—42no—
406C2×Dic22—44no—
407C2×Dic22—42no—
408C2×Dic22—42no—
409C2×Dic22C2414yes—
410C2×Dic22C2414yes—
411C2×Dic22C2414yes—
412C2×Dic22C2418yes—
413C2×Dic22C2414yes—
414C2×Dic22C2418yes—
415C11×C4⋊C4C2414yes—
416C11×C4⋊C4C2414yes—
417C11×C4⋊C4C2418yes—
418C11×C4⋊C4C2414yes—
419C11×C4⋊C4C2414yes—
420C11×C22⋊C4C2418yes—
421C11×C22⋊C4C2418yes—
422C11×C22⋊C4C2418yes—
423C11×C22⋊C4C2418yes—
424C11×C22⋊C4C2418yes—
425C11×C22⋊C4C2418yes—
426C42×C11C2414yes—
427C42×C11C2414yes—
428C42×C11C2414yes—
429C42×C11C2418yes—
430C22⋊Dic11C2418yes—
431C22⋊Dic11C2418yes—
432C22⋊Dic11C2418yes—
433C22⋊Dic11C2418yes—
434C22⋊Dic11C2418yes—
435C22⋊Dic11C2418yes—
436C22⋊Dic11C2418yes—
437C22⋊Dic11C2418yes—
438C22⋊Dic11C2418yes—
439C22⋊Dic11C2418yes—
440(C2×D11)⋊C4C2414yes—
441(C2×D11)⋊C4C2414yes—
442(C2×D11)⋊C4C2414yes—
443(C2×D11)⋊C4C2414yes—
444(C2×D11)⋊C4C2418yes—
445(C2×D11)⋊C4C2418yes—
446C4⋊Dic11C2414yes—
447C4⋊Dic11C2414yes—
448C4⋊Dic11C2414yes—
449C4⋊Dic11C2414yes—
450C4⋊Dic11C2418yes—
451C4⋊Dic11C2414yes—
452C4⋊Dic11C2414yes—
453C4⋊Dic11C2418yes—
454C4⋊Dic11C2418yes—
455C4⋊Dic11C2418yes—
456C4⋊Dic11C2418yes—
457C4⋊Dic11C2418yes—
458Dic11⋊C4C2414yes—
459Dic11⋊C4C2418yes—
460Dic11⋊C4C2414yes—
461Dic11⋊C4C2418yes—
462Dic11⋊C4C2414yes—
463Dic11⋊C4C2414yes—
464Dic11⋊C4C2414yes—
465Dic11⋊C4C2418yes—
466Dic11⋊C4C2418yes—
467Dic11⋊C4C2414yes—
468Dic11⋊C4C2414yes—
469Dic11⋊C4C2418yes—
470Dic11⋊C4C2418yes—
471Dic11⋊C4C2418yes—
472Dic11⋊C4C2418yes—
473Dic11⋊C4C2418yes—
474Dic11⋊C4C2418yes—
475Dic11⋊C4C2418yes—
476Dic11⋊C4C2414yes—
477Dic11⋊C4C2414yes—
478Dic11⋊C4C2414yes—
479Dic11⋊C4C2418yes—
480Dic11⋊C4C2418yes—
481C4×Dic11C2414yes—
482C4×Dic11C2414yes—
483C4×Dic11C2414yes—
484C4×Dic11C2418yes—
485C4×Dic11C2418yes—
486C4×Dic11C2418yes—
487C4×Dic11C2418yes—
488C4×Dic11C2418yes—
489C4×Dic11C2414yes—
490C4×Dic11C2414yes—
491#3557—1132no—
492C2×#563—112no—
493C2×#563—112no—
494C2×#559—111no—
495C2×#559D1111yescharacteristic, complemented
496C2×#557—111no—
497C2×#557—111no—
498C2×#556—111no—
499C2×#556—111no—
500C2×#554—111no—
501C2×#554—111no—
502C2×#552—112no—
503C2×#552—112no—
504C2×#542—112no—
505C2×#542—111no—
506C2×#542—112no—
507C2×#542—111no—
508C2×#541—111no—
509C2×#540—111no—
510C2×#539—112no—
511C2×#539—112no—
512C2×#533—111no—
513C2×#529—111no—
514C2×#529—111no—
515C23×C11—24no—
516C23×C11—24no—
517C23×C11—24no—
518C23×C11—24no—
519C23×C11—24no—
520C23×C11—24no—
521C23×C11C2514yes—
522C23×C11C2514yes—
523C23×C11C2511yescharacteristic
524C22×D11—22no—
525C22×D11—22no—
526C22×D11—22no—
527C22×D11C2512yes—
528Q8×C11—28no—
529Q8×C11—44no—
530D4×C11—28no—
531D4×C11—28no—
532D4×C11—48no—
533D4×C11—48no—
534C2×C4×C11—24no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—24no—
538C2×C4×C11—22no—
539C2×C4×C11—22no—
540C2×C4×C11—22no—
541C2×C4×C11—22no—
542C2×C4×C11—48no—
543C2×C4×C11—48no—
544C2×C4×C112−1+414yes—
545C2×C4×C11C2512yes—
546C2×C4×C11C2514yes—
547C2×C4×C11C2512yes—
548C2×C4×C11C2512yes—
549C2×C4×C11C2512yes—
550C2×C4×C11C2512yes—
551C2×C4×C11C2512yes—
552C2×C4×C11C2514yes—
553C2×C4×C11C2512yes—
554C22⋊D11—48no—
555C22⋊D11—48no—
556C2×Dic11—24no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—24no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—24no—
565C2×Dic11—24no—
566C2×Dic11—22no—
567C2×Dic11—48no—
568C2×Dic11—48no—
569C2×Dic11—48no—
570C2×Dic11—48no—
571C2×Dic11C2512yes—
572C2×Dic11C2514yes—
573C2×Dic11C2512yes—
574C2×Dic11C2512yes—
575C2×Dic11C2514yes—
576C2×Dic11C2514yes—
577C2×Dic11C2512yes—
578C2×Dic11C2512yes—
579C2×Dic11C2512yes—
580C2×Dic11C2512yes—
581C2×Dic11C2514yes—
582C4×D11—28no—
583C4×D11—44no—
584C4×D11—44no—
585Dic22—28no—
586Dic22—44no—
587Dic22—48no—
588Dic22—44no—
589Dic22—44no—
590Dic22—48no—
591#563—1132no—
592#563—1132no—
593#559—1116no—
594#559C2×D11116yescomplemented
595#557—1116no—
596#557—1116no—
597#556—1116no—
598#556—1116no—
599#554—1116no—
600#554—1116no—
601#552—1132no—
602#552—1132no—
603#542—1132no—
604#542—1116no—
605#542—1132no—
606#542—1116no—
607#541—1116no—
608#540—1116no—
609#539—1132no—
610#539—1132no—
611#533—1116no—
612C2×C4⋊Q8—111no—
613C2×C4⋊Q8—111no—
614C2×C4⋊Q8—112no—
615C2×C4⋊Q8—111no—
616C2×C4⋊Q8—111no—
617C2×C4⋊Q8—112no—
618C2×C4⋊Q8—111no—
619C2×#127C2×D1111yescharacteristic
620#529—1116no—
621#529—1116no—
622C2×#126—112no—
623C2×#126—112no—
624C2×#126—112no—
625C2×#126—112no—
626C2×#126—112no—
627C2×#126—112no—
628C2×#126—112no—
629C2×#126—112no—
630C2×#126—112no—
631C2×#126—112no—
632C2×#125—111no—
633C2×#125—111no—
634C2×#125—112no—
635C2×#125—112no—
636C2×#125—112no—
637C2×#125—111no—
638C2×#125—112no—
639C2×#125—111no—
640C2×#125—111no—
641C2×#125—112no—
642C2×#125—111no—
643C2×#125—112no—
644C2×#124—111no—
645C2×#124—111no—
646C2×#124—112no—
647C2×#124—112no—
648C2×#124—112no—
649C2×#124C2×D1111yescharacteristic
650C2×#124C2×D1111yescharacteristic
651C2×#124C2×D1112yes—
652C2×#123—112no—
653C2×#123—112no—
654C2×#123—112no—
655C2×#123—112no—
656C2×#123—112no—
657C2×#123—112no—
658C2×#123—112no—
659C2×#123—112no—
660C2×#123C2×D1112yes—
661C2×#123C2×D1112yes—
662C2×C22⋊Q8—111no—
663C2×C22⋊Q8—111no—
664C2×C22⋊Q8—112no—
665C2×C22⋊Q8—112no—
666C2×C22⋊Q8—112no—
667C2×C22⋊Q8—111no—
668C2×C22⋊Q8—111no—
669C2×C22⋊Q8—111no—
670C2×C22⋊Q8—111no—
671C2×C22⋊Q8—112no—
672C2×C22⋊Q8—112no—
673C2×C22⋊Q8—112no—
674C2×C22⋊Q8—112no—
675C2×C22⋊Q8—112no—
676C2×C22⋊Q8—112no—
677C2×C22⋊Q8—112no—
678C2×#121—111no—
679C2×#121—111no—
680C2×#121—112no—
681C2×#121—112no—
682C2×C4×Q8—111no—
683C2×C4×Q8—111no—
684C2×C4×Q8—112no—
685C2×C4×Q8—111no—
686C2×C4×Q8—111no—
687C2×C4×Q8—111no—
688C2×C4×Q8—111no—
689C2×C4×Q8—111no—
690C2×C4×Q8—112no—
691C2×C4×Q8—111no—
692C2×C4×Q8C2×D1111yescharacteristic
693C2×C4×Q8C2×D1111yescharacteristic
694C2×C4×D4—111no—
695C2×C4×D4—112no—
696C2×C4×D4—111no—
697C2×C4×D4—111no—
698C2×C4×D4—111no—
699C2×C4×D4—112no—
700C2×C4×D4—112no—
701C2×C4×D4C2×D1111yescharacteristic
702C2×C4×D4C2×D1112yes—
703C2×C4×D4C2×D1111yescharacteristic
704C2×#117—112no—
705C2×#117—112no—
706C2×#117—112no—
707C2×#117—112no—
708C2×#117—111no—
709C2×#117—111no—
710C22×C4⋊C4—112no—
711C22×C4⋊C4—112no—
712C22×C42—111no—
713C22×C11—24no—
714C22×C11—24no—
715C22×C11—24no—
716C22×C11—24no—
717C22×C11—24no—
718C22×C11—24no—
719C22×C11—48no—
720C22×C11—48no—
721C22×C11C2×2−1+412yes—
722C22×C11#58512yes—
723C22×C11#58512yes—
724C22×C11C2611yescharacteristic
725C2×D11—22no—
726C2×D11—22no—
727C2×D11—22no—
728C2×D11—44no—
729C4×C11—24no—
730C4×C11—22no—
731C4×C11—24no—
732C4×C11—22no—
733C4×C11—22no—
734C4×C11—22no—
735C4×C11—22no—
736C4×C11—22no—
737C4×C11C2×2−1+414yes—
738Dic11—24no—
739Dic11—22no—
740Dic11—22no—
741Dic11—22no—
742Dic11—22no—
743Dic11—22no—
744Dic11—22no—
745Dic11—24no—
746Dic11—24no—
747Dic11—24no—
748Dic11—22no—
749C22×Q8—111no—
750C22×Q8—111no—
751C22×Q8—111no—
752C22×Q8—112no—
753C22×Q8—112no—
754C22×Q8—111no—
755C22×Q8C22×D1111yescharacteristic
756C22×Q8C22×D1111yescharacteristic
757C22×D4—112no—
758C22×D4—112no—
759C22×D4C22×D1111yescharacteristic
760C22×D4C22×D1111yescharacteristic
761C22×D4C22×D1112yes—
762C22×D4C22×D1112yes—
763C23×C4—112no—
764C23×C4—112no—
765C23×C4—112no—
766C23×C4—112no—
767C23×C4—111no—
768C23×C4—111no—
769C23×C4—111no—
770C23×C4C22×D1112yes—
771C23×C4C22×D1112yes—
772C4⋊Q8—118no—
773C4⋊Q8—118no—
774C4⋊Q8—1116no—
775C4⋊Q8—118no—
776C4⋊Q8—118no—
777C4⋊Q8—1116no—
778C4⋊Q8—118no—
779#127C22×D1118yes—
780#126—1116no—
781#126—1116no—
782#126—1116no—
783#126—1116no—
784#126—1116no—
785#126—1116no—
786#126—1116no—
787#126—1116no—
788#126—1116no—
789#126—1116no—
790#125—118no—
791#125—118no—
792#125—118no—
793#125—1116no—
794#125—1116no—
795#125—1116no—
796#125—1116no—
797#125—118no—
798#125—118no—
799#125—1116no—
800#125—118no—
801#125—1116no—
802#124—118no—
803#124—118no—
804#124—1116no—
805#124—1116no—
806#124—1116no—
807#124C22×D1118yes—
808#124C22×D1118yes—
809#124C22×D11116yes—
810#123—1116no—
811#123—1116no—
812#123—1116no—
813#123—1116no—
814#123—1116no—
815#123—1116no—
816#123—1116no—
817#123—1116no—
818#123C22×D11116yes—
819#123C22×D11116yes—
820C22⋊Q8—118no—
821C22⋊Q8—118no—
822C22⋊Q8—1116no—
823C22⋊Q8—1116no—
824C22⋊Q8—1116no—
825C22⋊Q8—118no—
826C22⋊Q8—118no—
827C22⋊Q8—118no—
828C22⋊Q8—118no—
829C22⋊Q8—1116no—
830C22⋊Q8—1116no—
831C22⋊Q8—1116no—
832C22⋊Q8—1116no—
833C22⋊Q8—1116no—
834C22⋊Q8—1116no—
835C22⋊Q8—1116no—
836#121—118no—
837#121—118no—
838#121—1116no—
839#121—1116no—
840C4×Q8—118no—
841C4×Q8—118no—
842C4×Q8—1116no—
843C4×Q8—118no—
844C4×Q8—118no—
845C4×Q8—118no—
846C4×Q8—118no—
847C4×Q8—118no—
848C4×Q8—1116no—
849C4×Q8—118no—
850C4×Q8C22×D1118yes—
851C4×Q8C22×D1118yes—
852C4×D4—118no—
853C4×D4—1116no—
854C4×D4—118no—
855C4×D4—118no—
856C4×D4—118no—
857C4×D4—1116no—
858C4×D4—1116no—
859C4×D4C22×D1118yes—
860C4×D4C22×D11116yes—
861C4×D4C22×D1118yes—
862#117—1116no—
863#117—1116no—
864#117—1116no—
865#117—1116no—
866#117—118no—
867#117—118no—
868C2×C4⋊C4—111no—
869C2×C4⋊C4—111no—
870C2×C4⋊C4—112no—
871C2×C4⋊C4—112no—
872C2×C4⋊C4—112no—
873C2×C4⋊C4—112no—
874C2×C4⋊C4—112no—
875C2×C4⋊C4—112no—
876C2×C4⋊C4—1116no—
877C2×C4⋊C4—1116no—
878C2×C4⋊C4—111no—
879C2×C4⋊C4—111no—
880C2×C4⋊C4—112no—
881C2×C4⋊C4—112no—
882C2×C4⋊C4—111no—
883C2×C4⋊C4—111no—
884C2×C4⋊C4—112no—
885C2×C4⋊C4—112no—
886C2×C4⋊C4—111no—
887C2×C4⋊C4—111no—
888C2×C4⋊C4—111no—
889C2×C4⋊C4—111no—
890C2×C4⋊C4—111no—
891C2×C4⋊C4—111no—
892C2×C4⋊C4—112no—
893C2×C4⋊C4—112no—
894C2×C4⋊C4—111no—
895C2×C4⋊C4—112no—
896C2×C4⋊C4—112no—
897C2×C4⋊C4—111no—
898C2×C4⋊C4—111no—
899C2×C4⋊C4—112no—
900C2×C4⋊C4—112no—
901C2×C4⋊C4—111no—
902C2×C4⋊C4—112no—
903C2×C4⋊C4—112no—
904C2×C4⋊C4—112no—
905C2×C4⋊C4C22×D1111yescharacteristic
906C2×C4⋊C4C22×D1111yescharacteristic
907C2×C4⋊C4C22×D1111yescharacteristic
908C2×C4⋊C4C22×D1111yescharacteristic
909C2×C4⋊C4C22×D1112yes—
910C2×C22⋊C4—112no—
911C2×C22⋊C4—112no—
912C2×C22⋊C4—112no—
913C2×C22⋊C4—112no—
914C2×C22⋊C4—112no—
915C2×C22⋊C4—112no—
916C2×C22⋊C4—112no—
917C2×C22⋊C4—112no—
918C2×C22⋊C4—112no—
919C2×C22⋊C4—112no—
920C2×C22⋊C4—111no—
921C2×C22⋊C4—111no—
922C2×C22⋊C4—111no—
923C2×C22⋊C4—111no—
924C2×C22⋊C4—112no—
925C2×C22⋊C4—112no—
926C2×C22⋊C4C22×D1112yes—
927C2×C22⋊C4C22×D1112yes—
928C2×C22⋊C4C22×D1112yes—
929C2×C22⋊C4C22×D1112yes—
930C2×C22⋊C4C22×D1112yes—
931C2×C22⋊C4C22×D1112yes—
932C2×C42—111no—
933C2×C42—112no—
934C2×C42—112no—
935C2×C42—111no—
936C2×C42—111no—
937C2×C42—112no—
938C2×C42—112no—
939C2×C42—111no—
940C2×C42—112no—
941C2×C42—111no—
942C2×C42—118no—
943C2×C42C22×D1111yescharacteristic
944C2×C42C22×D1111yescharacteristic
945C2×C42C22×D1111yescharacteristic
946C2×C42C22×D1112yes—
947C2×C11—44no—
948C2×C11—44no—
949C2×C11#355714yescomplemented
950C2×C11C22×2−1+411yescharacteristic
951C2×C11C2×#58511yescharacteristic
952C2×C11C2×#58511yescharacteristic
953D11—42no—
954C24—111no—
955C24C23×D1112yes—
956C24C23×D1112yes—
957C2×Q8—24no—
958C2×Q8—42no—
959C2×Q8—114no—
960C2×Q8—114no—
961C2×Q8—114no—
962C2×Q8—118no—
963C2×Q8—118no—
964C2×Q8—114no—
965C2×Q8—224no—
966C2×Q8—442no—
967C2×Q8—444no—
968C2×Q8—442no—
969C2×Q8—444no—
970C2×Q8—442no—
971C2×Q8C23×D1114yes—
972C2×Q8C23×D1114yes—
973C2×D4—24no—
974C2×D4—24no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—118no—
978C2×D4—118no—
979C2×D4—444no—
980C2×D4—444no—
981C2×D4C23×D1114yes—
982C2×D4C23×D1114yes—
983C2×D4C23×D1118yes—
984C2×D4C23×D1118yes—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—111no—
988C22×C4—112no—
989C22×C4—111no—
990C22×C4—111no—
991C22×C4—111no—
992C22×C4—112no—
993C22×C4—112no—
994C22×C4—111no—
995C22×C4—111no—
996C22×C4—112no—
997C22×C4—111no—
998C22×C4—118no—
999C22×C4—118no—
1000C22×C4—118no—
1001C22×C4—118no—
1002C22×C4—114no—
1003C22×C4—114no—
1004C22×C4—114no—
1005C22×C4—224no—
1006C22×C4—442no—
1007C22×C4—442no—
1008C22×C4—444no—
1009C22×C4—444no—
1010C22×C4—444no—
1011C22×C4—444no—
1012C22×C4C23×D1111yescharacteristic
1013C22×C4C23×D1112yes—
1014C22×C4C23×D1111yescharacteristic
1015C22×C4C23×D1111yescharacteristic
1016C22×C4C23×D1111yescharacteristic
1017C22×C4C23×D1111yescharacteristic
1018C22×C4C23×D1111yescharacteristic
1019C22×C4C23×D1112yes—
1020C22×C4C23×D1118yes—
1021C22×C4C23×D1118yes—
1022C22×C4C23×D1111yescharacteristic
1023C4⋊C4—114no—
1024C4⋊C4—114no—
1025C4⋊C4—118no—
1026C4⋊C4—118no—
1027C4⋊C4—118no—
1028C4⋊C4—118no—
1029C4⋊C4—118no—
1030C4⋊C4—118no—
1031C4⋊C4—114no—
1032C4⋊C4—114no—
1033C4⋊C4—118no—
1034C4⋊C4—118no—
1035C4⋊C4—114no—
1036C4⋊C4—114no—
1037C4⋊C4—118no—
1038C4⋊C4—118no—
1039C4⋊C4—114no—
1040C4⋊C4—114no—
1041C4⋊C4—114no—
1042C4⋊C4—114no—
1043C4⋊C4—114no—
1044C4⋊C4—114no—
1045C4⋊C4—118no—
1046C4⋊C4—118no—
1047C4⋊C4—114no—
1048C4⋊C4—118no—
1049C4⋊C4—118no—
1050C4⋊C4—114no—
1051C4⋊C4—114no—
1052C4⋊C4—118no—
1053C4⋊C4—118no—
1054C4⋊C4—114no—
1055C4⋊C4—118no—
1056C4⋊C4—118no—
1057C4⋊C4—118no—
1058C4⋊C4C23×D1114yes—
1059C4⋊C4C23×D1114yes—
1060C4⋊C4C23×D1114yes—
1061C4⋊C4C23×D1114yes—
1062C4⋊C4C23×D1118yes—
1063C22⋊C4—118no—
1064C22⋊C4—118no—
1065C22⋊C4—118no—
1066C22⋊C4—118no—
1067C22⋊C4—118no—
1068C22⋊C4—118no—
1069C22⋊C4—118no—
1070C22⋊C4—118no—
1071C22⋊C4—118no—
1072C22⋊C4—118no—
1073C22⋊C4—114no—
1074C22⋊C4—114no—
1075C22⋊C4—114no—
1076C22⋊C4—114no—
1077C22⋊C4—118no—
1078C22⋊C4—118no—
1079C22⋊C4C23×D1118yes—
1080C22⋊C4C23×D1118yes—
1081C22⋊C4C23×D1118yes—
1082C22⋊C4C23×D1118yes—
1083C22⋊C4C23×D1118yes—
1084C22⋊C4C23×D1118yes—
1085C42—114no—
1086C42—114no—
1087C42—114no—
1088C42—118no—
1089C42—118no—
1090C42—114no—
1091C42—114no—
1092C42—118no—
1093C42—118no—
1094C42—118no—
1095C42C23×D1114yes—
1096C42C23×D1114yes—
1097C42C23×D1114yes—
1098C42C23×D1118yes—
1099C11C2×#355711yescharacteristic, complemented, Sylow
1100C23—24no—
1101C23—24no—
1102C23—24no—
1103C23—24no—
1104C23—24no—
1105C23—24no—
1106C23—112no—
1107C23—222no—
1108C23—222no—
1109C23—222no—
1110C23C24×D1114yes—
1111C23C24×D1114yes—
1112C23C24×D1111yescharacteristic
1113Q8—28no—
1114Q8—44no—
1115Q8—228no—
1116Q8—444no—
1117Q8—448no—
1118Q8—444no—
1119Q8—444no—
1120Q8—448no—
1121D4—28no—
1122D4—28no—
1123D4—48no—
1124D4—48no—
1125D4—448no—
1126D4—448no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—48no—
1136C2×C4—48no—
1137C2×C4—112no—
1138C2×C4—114no—
1139C2×C4—112no—
1140C2×C4—112no—
1141C2×C4—112no—
1142C2×C4—114no—
1143C2×C4—114no—
1144C2×C4—112no—
1145C2×C4—112no—
1146C2×C4—112no—
1147C2×C4—114no—
1148C2×C4—222no—
1149C2×C4—224no—
1150C2×C4—222no—
1151C2×C4—222no—
1152C2×C4—222no—
1153C2×C4—224no—
1154C2×C4—224no—
1155C2×C4—222no—
1156C2×C4—224no—
1157C2×C4—222no—
1158C2×C4—222no—
1159C2×C4—228no—
1160C2×C4—444no—
1161C2×C4—444no—
1162C2×C4—448no—
1163C2×C4—448no—
1164C2×C4—448no—
1165C2×C4—448no—
1166C2×C4#6704314yes—
1167C2×C4C24×D1112yes—
1168C2×C4C24×D1114yes—
1169C2×C4C24×D1112yes—
1170C2×C4C24×D1112yes—
1171C2×C4C24×D1112yes—
1172C2×C4C24×D1112yes—
1173C2×C4C24×D1112yes—
1174C2×C4C24×D1114yes—
1175C2×C4C24×D1112yes—
1176C22—24no—
1177C22—24no—
1178C22—24no—
1179C22—24no—
1180C22—24no—
1181C22—24no—
1182C22—48no—
1183C22—48no—
1184C22—222no—
1185C22—222no—
1186C22—222no—
1187C22—444no—
1188C22C2×#6704312yes—
1189C22#1062345312yes—
1190C22#1062345512yes—
1191C22C25×D1111yescharacteristic
1192C4—24no—
1193C4—22no—
1194C4—24no—
1195C4—22no—
1196C4—22no—
1197C4—22no—
1198C4—22no—
1199C4—22no—
1200C4—222no—
1201C4—224no—
1202C4—222no—
1203C4—224no—
1204C4—222no—
1205C4—222no—
1206C4—222no—
1207C4—222no—
1208C4—222no—
1209C4—224no—
1210C4—224no—
1211C4C2×#6704314yes—
1212C2—44no—
1213C2—44no—
1214C2—442no—
1215C2#1308311314yesdirect product factor
1216C2C22×#6704311yescharacteristic
1217C2C2×#1062345511yescharacteristic
1218C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#559C2
socleC23×C11C25
prime radicalC2×#10623250C2
hypercenterC2×#559D11
hypocenterC11C2×#3557
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. #13083113C2direct (N × H)
2. C2×#10623182C2semidirect
3. C2×#10623203C2semidirect
4. C2×#10623244C2semidirect
5. C2×#10623098C2semidirect
6. C2×#10623100C2semidirect
7. C2×#10623202C2semidirect
8. C2×#10623202C2semidirect
9. C2×#10623070C2semidirect
10. C2×#10623074C2semidirect
11. C2×#10623072C2semidirect
12. C2×#10623181C2semidirect
13. C2×#10623213C2semidirect
14. C2×#10623193C2semidirect
15. C2×#10623092C2semidirect
16. C2×#10623200C2semidirect
17. C2×#10623114C2semidirect
19. C2×#10623196C2semidirect
20. C2×#10623095C2semidirect
21. C2×#10623109C2semidirect
22. C2×#10623088C2semidirect
23. C2×#10623211C2semidirect
24. C2×C11×#559C2semidirect
25. C11×#559C22semidirect
69. #10623244C22semidirect
70. #10623213C22semidirect
71. #10623211C22semidirect
72. #10623203C22semidirect
73. #10623202C22semidirect
74. #10623202C22semidirect
75. #10623200C22semidirect
76. #10623196C22semidirect
77. #10623193C22semidirect
78. #10623182C22semidirect
79. #10623181C22semidirect
80. #10623114C22semidirect
81. #10623109C22semidirect
82. #10623100C22semidirect
83. #10623098C22semidirect
84. #10623095C22semidirect
85. #10623092C22semidirect
86. #10623088C22semidirect
87. #10623074C22semidirect
88. #10623072C22semidirect
89. #10623070C22semidirect
495. C2×#559D11semidirect
594. #559C2×D11semidirect
949. C2×C11#3557semidirect
1099. C11C2×#3557semidirect
1215. C2#13083113direct (N × H)

Maximal subgroups

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

subgroupindex
#130831132
C2×#106231822
C2×#106232032
C2×#106232442
C2×#106230982
C2×#106231002
C2×#106232022
C2×#106230702
C2×#106230742
C2×#106230722
C2×#106231812
C2×#106232132
C2×#106231932
C2×#106230922
C2×#106232002
C2×#106231142
C2×#106232502
C2×#106231962
C2×#106230952
C2×#106231092
C2×#106230882
C2×#106232112
C2×C11×#5592
C2×#355711