Finite Group Databasebeta

← C2×#13082494 #15662208

Subgroups — C2×#13082494 #15662208

Order 2816.

7022 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082494C2132yesmaximal, direct product factor
2C2×#10623216C212yesmaximal, complemented
3C2×#10623216C211yesmaximal, characteristic, complemented
4C2×#10623100C211yesmaximal, characteristic, complemented
5C2×#10623172C211yesmaximal, characteristic, complemented
6C2×#10623064C211yesmaximal, characteristic, complemented
7C2×#10623233C212yesmaximal, complemented
8C2×#10623173C211yesmaximal, characteristic, complemented
9C2×#10623072C211yesmaximal, characteristic, complemented
10C2×#10623181C212yesmaximal, complemented
11C2×#10623044C211yesmaximal, characteristic, complemented
12C2×#10623062C212yesmaximal, complemented
13C2×#10623227C212yesmaximal, complemented
14C2×#10623232C212yesmaximal, complemented
15C2×#10623179C212yesmaximal
16C2×#10623219C211yesmaximal, characteristic, complemented
17C2×#10623109C211yesmaximal, characteristic, complemented
18C2×#10623048C211yesmaximal, characteristic, complemented
19C2×#10623153C211yesmaximal, characteristic, complemented
20C2×#10623153C211yesmaximal, characteristic, complemented
21C22×#66941C211yesmaximal, characteristic, complemented
22C2×#10623047C212yesmaximal, complemented
23C2×C4×#4341C211yesmaximal, characteristic
24C2×C11×#552C211yesmaximal, characteristic, complemented
25C22×#4341C2211yescharacteristic
26C23×Dic22C2212yes—
27C11×#552C22116yescomplemented
28C2×C11×#126C2212yes—
29C2×C11×#125C2211yescharacteristic
30C2×C11×#125C2212yes—
31C2×C11×#123C2212yes—
32C2×C11×C22⋊Q8C2211yescharacteristic
33C2×C11×C22⋊Q8C2211yescharacteristic
34C2×C4×Q8×C11C2211yescharacteristic
35C2×C4×D4×C11C2211yescharacteristic
36C2×C11×#117C2212yes—
37C2×C11×#117C2211yescharacteristic
38C22×C11×C4⋊C4C2211yescharacteristic
39C2×#66999C2211yescharacteristic
40C2×Q8×Dic11C2211yescharacteristic
41C2×Q8×Dic11C2211yescharacteristic
42C2×#66997C2211yescharacteristic
43C2×#66988C2212yes—
44C2×D4×Dic11C2211yescharacteristic
45C2×#66982C2212yes—
46C2×C4×C22⋊D11C2211yescharacteristic
47C2×C4×C22⋊D11C2211yescharacteristic
48C2×#66979C2212yes—
49C2×#66979C2211yescharacteristic
50C22×C4⋊Dic11C2211yescharacteristic
51C2×#66977C2211yescharacteristic
52C2×#66977C2211yescharacteristic
53C22×Dic11⋊C4C2212yes—
54C22×C4×Dic11C2211yescharacteristic
55C22×C4×Dic11C2211yescharacteristic
56#10623233C22132yescomplemented
57#10623232C22132yescomplemented
58#10623227C22132yescomplemented
59#10623219C22116yescomplemented
60#10623216C22132yescomplemented
61#10623216C22116yescomplemented
62#10623181C22132yescomplemented
63#10623179C22132yes—
64#10623173C22116yescomplemented
65#10623172C22116yescomplemented
66#10623153C22116yescomplemented
67#10623153C22116yescomplemented
68#10623109C22116yescomplemented
69#10623100C22116yescomplemented
70#10623072C22116yescomplemented
71C4×#4341C22116yes—
72#10623064C22116yescomplemented
73#10623062C22132yescomplemented
74#10623048C22116yescomplemented
75#10623047C22132yescomplemented
76#10623044C22116yescomplemented
77C2×#66951C2212yes—
78C2×#66951C2212yes—
79C2×#66951C2212yes—
80C2×#66950C2211yescharacteristic
81C2×#66949C2212yes—
82C2×#66949C2212yes—
83C2×#66949C2212yes—
84C2×#66945C2211yescharacteristic
85C2×#66945C2211yescharacteristic
86C2×#66945C2211yescharacteristic
87C2×#66943C2211yescharacteristic
88C2×#66943C2212yes—
89C2×#66943C2211yescharacteristic
90C2×#66943C2212yes—
91C2×#66942C2212yes—
92C2×#66942C2212yes—
93C2×#66942C2212yes—
94C2×#66942C2212yes—
95C2×#66942C2212yes—
96C2×#66942C2212yes—
97C2×#66942C2212yes—
98C2×#66941C2211yescharacteristic
99C2×#66941C2211yescharacteristic
100C2×#66941C2212yes—
101C2×#66941C2211yescharacteristic
102C2×#66941C2211yescharacteristic
103C2×#66941C2212yes—
104C2×#66941C2211yescharacteristic
105C2×#66941C2212yes—
106C2×#66941C2212yes—
107C2×#66941C22116yescomplemented
108C2×#66940C2211yescharacteristic
109C2×#66940C2212yes—
110C2×#66940C2212yes—
111C2×#66940C2211yescharacteristic
112C2×#66940C2212yes—
113C2×#66940C2212yes—
114C2×#66940C2212yes—
115C2×#66940C2212yes—
116C2×#66940C2211yescharacteristic
117C2×#66939C2212yes—
118C2×#66938C2212yes—
119C2×#66938C2212yes—
120C2×(C22⋊D11)⋊C4C2211yescharacteristic
121C2×(C22⋊D11)⋊C4C2211yescharacteristic
122C2×#66932C2212yes—
123C2×#66932C2212yes—
124C2×#66932C2212yes—
125C2×#66931C2212yes—
126C2×#66931C2212yes—
127C2×#66931C2212yes—
128C2×#66931C2212yes—
129C2×#66930C2212yes—
130C2×#66930C2212yes—
131C2×#66930C2212yes—
132C2×#66930C2212yes—
133C2×#66930C2211yescharacteristic
134C2×#66930C2211yescharacteristic
135C2×#66929C2212yes—
136C2×#66925C2212yes—
137C2×C42×D11C2211yescharacteristic
138C2×#66923C2212yes—
139C2×#66923C2211yescharacteristic
140C2×C4×Dic22C2212yes—
141C2×C4×Dic22C2211yescharacteristic
142C2×C4×Dic22C2212yes—
143C2×C4×Dic22C2212yes—
144C2×C4×Dic22C2212yes—
145C2×C4×Dic22C2212yes—
146C2×C4×Dic22C2211yescharacteristic
147C22×Q8×C11C2311yescharacteristic
148C22×D4×C11C2311yescharacteristic
149C23×C4×C11C2311yescharacteristic
150C23×C4×C11C2311yescharacteristic
151C23×C4×C11C2312yes—
152C22×C22⋊D11C2311yescharacteristic
153C22×C22⋊D11C2311yescharacteristic
154C23×Dic11C2311yescharacteristic
155C23×Dic11C2312yes—
156C23×Dic11C2311yescharacteristic
157C23×Dic11C2311yescharacteristic
158C23×Dic11C2311yescharacteristic
159C2×#4341—28no—
160C2×#4341C2318yes—
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2311yescharacteristic
164C22×Dic22—216no—
165C22×Dic22C2312yes—
166C22×Dic22C2312yes—
167C22×Dic22C2312yes—
168C22×Dic22C2311yescharacteristic
169C22×Dic22C2311yescharacteristic
170C22×Dic22C2312yes—
171C22×Dic22C2312yes—
172C22×Dic22C23116yes—
173C11×#126C23116yes—
174C11×#125C2318yes—
175C11×#125C23116yes—
176C11×#123C23116yes—
177C11×C22⋊Q8C2318yes—
178C11×C22⋊Q8C2318yes—
179C4×Q8×C11C2318yes—
180C4×D4×C11C2318yes—
181C11×#117C23116yes—
182C11×#117C2318yes—
183C2×C11×C4⋊C4C2312yes—
184C2×C11×C4⋊C4C2312yes—
185C2×C11×C4⋊C4C2311yescharacteristic
186C2×C11×C4⋊C4C2312yes—
187C2×C11×C4⋊C4C2311yescharacteristic
188C2×C11×C4⋊C4C2311yescharacteristic
189C2×C11×C4⋊C4C2312yes—
190C2×C11×C4⋊C4C2312yes—
191C2×C11×C4⋊C4C2311yescharacteristic
192C2×C11×C4⋊C4C2312yes—
193C2×C11×C4⋊C4C2318yes—
194C2×C11×C22⋊C4C2311yescharacteristic
195C2×C11×C22⋊C4C2312yes—
196C2×C11×C22⋊C4C2312yes—
197C2×C11×C22⋊C4C2311yescharacteristic
198C2×C11×C22⋊C4C2312yes—
199C2×C42×C11C2312yes—
200C2×C42×C11C2311yescharacteristic
201C2×C42×C11C2312yes—
202C2×C22⋊Dic11C2311yescharacteristic
203C2×C22⋊Dic11C2312yes—
204C2×C22⋊Dic11C2312yes—
205C2×C22⋊Dic11C2311yescharacteristic
206C2×C22⋊Dic11C2312yes—
207#66999C2318yes—
208Q8×Dic11C2318yes—
209Q8×Dic11C2318yes—
210#66997C2318yes—
211#66988C23116yes—
212D4×Dic11C2318yes—
213#66982C23116yes—
214C4×C22⋊D11C2318yes—
215C4×C22⋊D11C2318yes—
216C2×(C2×D11)⋊C4C2312yes—
217C2×(C2×D11)⋊C4C2312yes—
218C2×(C2×D11)⋊C4C2311yescharacteristic
219C2×(C2×D11)⋊C4C2312yes—
220C2×(C2×D11)⋊C4C2311yescharacteristic
221C2×(C2×D11)⋊C4C2312yes—
222#66979C23116yes—
223#66979C2318yes—
224C2×C4⋊Dic11C2312yes—
225C2×C4⋊Dic11C2312yes—
226C2×C4⋊Dic11C2312yes—
227C2×C4⋊Dic11C2311yescharacteristic
228C2×C4⋊Dic11C2311yescharacteristic
229C2×C4⋊Dic11C2312yes—
230C2×C4⋊Dic11C2312yes—
231C2×C4⋊Dic11C2311yescharacteristic
232C2×C4⋊Dic11C2311yescharacteristic
233C2×C4⋊Dic11C2312yes—
234C2×C4⋊Dic11C2318yes—
235#66977C2318yes—
236#66977C2318yes—
237C2×Dic11⋊C4C2311yescharacteristic
238C2×Dic11⋊C4C2311yescharacteristic
239C2×Dic11⋊C4C2312yes—
240C2×Dic11⋊C4C2311yescharacteristic
241C2×Dic11⋊C4C2312yes—
242C2×Dic11⋊C4C2312yes—
243C2×Dic11⋊C4C2312yes—
244C2×Dic11⋊C4C2312yes—
245C2×Dic11⋊C4C2312yes—
246C2×Dic11⋊C4C2312yes—
247C2×Dic11⋊C4C2312yes—
248C2×Dic11⋊C4C2312yes—
249C2×Dic11⋊C4C2312yes—
250C2×Dic11⋊C4C2312yes—
251C2×Dic11⋊C4C2312yes—
252C2×Dic11⋊C4C2312yes—
253C2×Dic11⋊C4C2312yes—
254C2×Dic11⋊C4C2311yescharacteristic
255C2×Dic11⋊C4C2312yes—
256C2×Dic11⋊C4C2312yes—
257C2×Dic11⋊C4C2312yes—
258C2×Dic11⋊C4C23116yes—
259C2×C4×Dic11C2311yescharacteristic
260C2×C4×Dic11C2312yes—
261C2×C4×Dic11C2311yescharacteristic
262C2×C4×Dic11C2312yes—
263C2×C4×Dic11C2311yescharacteristic
264C2×C4×Dic11C2312yes—
265C2×C4×Dic11C2312yes—
266C2×C4×Dic11C2312yes—
267C2×C4×Dic11C2312yes—
268C2×C4×Dic11C2311yescharacteristic
269C2×C4×Dic11C2311yescharacteristic
270C2×C4×Dic11C2311yescharacteristic
271C2×C4×Dic11C2311yescharacteristic
272C2×C4×Dic11C2312yes—
273C2×C4×Dic11C2311yescharacteristic
274C2×C4×Dic11C2312yes—
275C2×C4×Dic11C2311yescharacteristic
276C2×C4×Dic11C2318yes—
277C2×C4×Dic11C2318yes—
278#66951C23116yes—
279#66951C23116yes—
280#66951C23116yes—
281#66950C2318yes—
282#66949C23116yes—
283#66949C23116yes—
284#66949C23116yes—
285#66945C2318yes—
286#66945C2318yes—
287#66945C2318yes—
288#66943C23116yes—
289#66943C2318yes—
290#66943C2318yes—
291#66943C23116yes—
292#66942C23116yes—
293#66942C23116yes—
294#66942C23116yes—
295#66942C23116yes—
296#66942C23116yes—
297#66942C23116yes—
298#66942C23116yes—
299#66941C23116yes—
300#66941C23116yes—
301#66941C2318yes—
302#66941C2318yes—
303#66941C2318yes—
304#66941C2318yes—
305#66941C2318yes—
306#66941C23116yes—
307#66941C23116yes—
308#66940C23116yes—
309#66940C23116yes—
310#66940C23116yes—
311#66940C2318yes—
312#66940C23116yes—
313#66940C23116yes—
314#66940C2318yes—
315#66940C2318yes—
316#66940C23116yes—
317#66939C23116yes—
318#66938C23116yes—
319#66938C23116yes—
320(C22⋊D11)⋊C4C2318yes—
321(C22⋊D11)⋊C4C2318yes—
322#66932C23116yes—
323#66932C23116yes—
324#66932C23116yes—
325#66931C23116yes—
326#66931C23116yes—
327#66931C23116yes—
328#66931C23116yes—
329#66930C2318yes—
330#66930C23116yes—
331#66930C2318yes—
332#66930C23116yes—
333#66930C23116yes—
334#66930C23116yes—
335#66929C23116yes—
336#66925C23116yes—
337C42×D11C2318yes—
338#66923C23116yes—
339#66923C2318yes—
340C4×Dic22C23116yes—
341C4×Dic22C23116yes—
342C4×Dic22C23116yes—
343C4×Dic22C23116yes—
344C4×Dic22C23116yes—
345C4×Dic22C2318yes—
346C4×Dic22C2318yes—
347C2×#3509—111nomaximal, Sylow
348C24×C11C2411yescharacteristic
349C24×C11C2411yescharacteristic
350C23×D11C2411yescharacteristic
351C2×Q8×C11—24no—
352C2×Q8×C11C2414yes—
353C2×D4×C11—24no—
354C2×D4×C11C2414yes—
355C22×C4×C11—28no—
356C22×C4×C11—24no—
357C22×C4×C11—24no—
358C22×C4×C11C2411yescharacteristic
359C22×C4×C11C2411yescharacteristic
360C22×C4×C11C2412yes—
361C22×C4×C11C2411yescharacteristic
362C22×C4×C11C2412yes—
363C22×C4×C11C2412yes—
364C22×C4×C11C2414yes—
365C22×C4×C11C2414yes—
366C22×C4×C11C2411yescharacteristic
367C22×C4×C11C2412yes—
368C22×C4×C11C2418yes—
369C22×C4×C11C2411yescharacteristic
370C2×C22⋊D11—24no—
371C2×C22⋊D11—24no—
372C2×C22⋊D11C2414yes—
373C2×C22⋊D11C2414yes—
374C22×Dic11—24no—
375C22×Dic11—24no—
376C22×Dic11—24no—
377C22×Dic11—28no—
378C22×Dic11#4118yes—
379C22×Dic11C2414yes—
380C22×Dic11C2418yes—
381C22×Dic11C2414yes—
382C22×Dic11C2414yes—
383C22×Dic11C2411yescharacteristic
384C22×Dic11C2411yescharacteristic
385C22×Dic11C2412yes—
386C22×Dic11C2412yes—
387C22×Dic11C2411yescharacteristic
388C22×Dic11C2411yescharacteristic
389C22×Dic11C2412yes—
390C22×Dic11C2412yes—
391C22×Dic11C2414yes—
392C22×Dic11C2411yescharacteristic
393C22×Dic11C2411yescharacteristic
394C22×Dic11C2411yescharacteristic
395#4341—232no—
396C2×C4×D11—24no—
397C2×C4×D11—24no—
398C2×C4×D11—24no—
399C2×C4×D11C2414yes—
400C2×C4×D11C2414yes—
401C2×C4×D11C2414yes—
402C2×Dic22—28no—
403C2×Dic22—28no—
404C2×Dic22—28no—
405C2×Dic22—28no—
406C2×Dic22—264no—
407C2×Dic22—24no—
408C2×Dic22—28no—
409C2×Dic22—24no—
410C2×Dic22C2418yes—
411C2×Dic22C2418yes—
412C2×Dic22C2418yes—
413C2×Dic22C2414yes—
414C2×Dic22C2414yes—
415C2×Dic22C2418yes—
416C2×Dic22C2418yes—
417C11×C4⋊C4C2418yes—
418C11×C4⋊C4C2418yes—
419C11×C4⋊C4C2414yes—
420C11×C4⋊C4C2418yes—
421C11×C4⋊C4C2414yes—
422C11×C4⋊C4C2414yes—
423C11×C4⋊C4C2418yes—
424C11×C4⋊C4C2418yes—
425C11×C4⋊C4C2414yes—
426C11×C4⋊C4C2418yes—
427C11×C22⋊C4C2414yes—
428C11×C22⋊C4C2418yes—
429C11×C22⋊C4C2418yes—
430C11×C22⋊C4C2414yes—
431C11×C22⋊C4C2418yes—
432C42×C11C2418yes—
433C42×C11C2414yes—
434C42×C11C2418yes—
435C22⋊Dic11C2414yes—
436C22⋊Dic11C2418yes—
437C22⋊Dic11C2418yes—
438C22⋊Dic11C2414yes—
439C22⋊Dic11C2418yes—
440(C2×D11)⋊C4C2418yes—
441(C2×D11)⋊C4C2418yes—
442(C2×D11)⋊C4C2414yes—
443(C2×D11)⋊C4C2418yes—
444(C2×D11)⋊C4C2414yes—
445(C2×D11)⋊C4C2418yes—
446C4⋊Dic11C2418yes—
447C4⋊Dic11C2418yes—
448C4⋊Dic11C2418yes—
449C4⋊Dic11C2414yes—
450C4⋊Dic11C2414yes—
451C4⋊Dic11C2418yes—
452C4⋊Dic11C2418yes—
453C4⋊Dic11C2414yes—
454C4⋊Dic11C2414yes—
455C4⋊Dic11C2418yes—
456Dic11⋊C4C2414yes—
457Dic11⋊C4C2414yes—
458Dic11⋊C4C2418yes—
459Dic11⋊C4C2414yes—
460Dic11⋊C4C2418yes—
461Dic11⋊C4C2418yes—
462Dic11⋊C4C2418yes—
463Dic11⋊C4C2418yes—
464Dic11⋊C4C2418yes—
465Dic11⋊C4C2418yes—
466Dic11⋊C4C2418yes—
467Dic11⋊C4C2418yes—
468Dic11⋊C4C2418yes—
469Dic11⋊C4C2418yes—
470Dic11⋊C4C2418yes—
471Dic11⋊C4C2418yes—
472Dic11⋊C4C2418yes—
473Dic11⋊C4C2414yes—
474Dic11⋊C4C2418yes—
475Dic11⋊C4C2418yes—
476Dic11⋊C4C2418yes—
477C4×Dic11C2414yes—
478C4×Dic11C2418yes—
479C4×Dic11C2414yes—
480C4×Dic11C2418yes—
481C4×Dic11C2414yes—
482C4×Dic11C2418yes—
483C4×Dic11C2418yes—
484C4×Dic11C2418yes—
485C4×Dic11C2418yes—
486C4×Dic11C2414yes—
487C4×Dic11C2414yes—
488C4×Dic11C2414yes—
489C4×Dic11C2414yes—
490C4×Dic11C2418yes—
491C4×Dic11C2414yes—
492C4×Dic11C2418yes—
493C4×Dic11C2414yes—
494#3509—1132no—
495C2×#557—112no—
496C2×#557—111no—
497C2×#557—111no—
498C2×#556—112no—
499C2×#556—111no—
500C2×#556—111no—
501C2×#552—112no—
502C2×#552—111no—
503C2×#552—111no—
504C2×#552—112no—
505C2×#552—111no—
506C2×#552D1111yescharacteristic, complemented
507C2×#541—112no—
508C2×#541—112no—
509C2×#536—112no—
510C2×#533—111no—
511C2×#533—111no—
512C2×#533—111no—
513C2×#533—111no—
514C2×#533—111no—
515C22×C4⋊Q8—111no—
516C2×#519—112no—
517C2×C4×#41—111no—
518C23×C11—22no—
519C23×C11—22no—
520C23×C11—22no—
521C23×C11—22no—
522C23×C11—22no—
523C23×C11C2×#4114yes—
524C23×C11C2512yes—
525C23×C11C2512yes—
526C23×C11C2511yescharacteristic
527C22×D11—22no—
528C22×D11—22no—
529C22×D11—22no—
530C22×D11C2512yes—
531Q8×C11—28no—
532D4×C11—28no—
533C2×C4×C11—216no—
534C2×C4×C11—24no—
535C2×C4×C11—24no—
536C2×C4×C11—22no—
537C2×C4×C11—24no—
538C2×C4×C11—22no—
539C2×C4×C11—22no—
540C2×C4×C11—22no—
541C2×C4×C11—24no—
542C2×C4×C11—28no—
543C2×C4×C11—28no—
544C2×C4×C112−1+414yes—
545C2×C4×C11C2512yes—
546C2×C4×C11C2512yes—
547C2×C4×C11C2514yes—
548C2×C4×C11C2512yes—
549C2×C4×C11C2514yes—
550C2×C4×C11C2514yes—
551C2×C4×C11C2512yes—
552C2×C4×C11C2514yes—
553C2×C4×C11C2512yes—
554C22⋊D11—28no—
555C22⋊D11—28no—
556C2×Dic11—216no—
557C2×Dic11—24no—
558C2×Dic11—24no—
559C2×Dic11—22no—
560C2×Dic11—24no—
561C2×Dic11—24no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—22no—
565C2×Dic11—28no—
566C2×Dic11—28no—
567C2×Dic11—28no—
568C2×Dic11C2×#4114yes—
569C2×Dic11C2×#4114yes—
570C2×Dic11C2×#41116yes—
571C2×Dic112−1+414yes—
572C2×Dic11C2512yes—
573C2×Dic11C2512yes—
574C2×Dic11C2514yes—
575C2×Dic11C2514yes—
576C2×Dic11C2512yes—
577C2×Dic11C2512yes—
578C2×Dic11C2514yes—
579C2×Dic11C2514yes—
580C2×Dic11C2512yes—
581C2×Dic11C2512yes—
582C2×Dic11C2512yes—
583C4×D11—28no—
584C4×D11—28no—
585C4×D11—28no—
586Dic22—28no—
587Dic22—216no—
588Dic22—216no—
589Dic22—216no—
590Dic22—216no—
591Dic22—28no—
592Dic22—216no—
593C22×#41—111no—
594C23×Q8—112no—
595#557—1132no—
596#557—1116no—
597#557—1116no—
598#556—1132no—
599#556—1116no—
600#556—1116no—
601#552—1132no—
602#552—1116no—
603#552—1116no—
604#552—1132no—
605#552—1116no—
606#552C2×D11116yescomplemented
607#541—1132no—
608#541—1132no—
609#536—1132no—
610#533—1116no—
611#533—1116no—
612#533—1116no—
613#533—1116no—
614#533—1116no—
615C2×C4⋊Q8—111no—
616C2×C4⋊Q8—111no—
617C2×C4⋊Q8—111no—
618C2×C4⋊Q8—112no—
619C2×C4⋊Q8—112no—
620C2×C4⋊Q8—111no—
621C2×C4⋊Q8—111no—
622C2×C4⋊Q8—111no—
623C2×C4⋊Q8—112no—
624C2×C4⋊Q8—112no—
625C2×C4⋊Q8—1116no—
626C2×#126—112no—
627C2×#126—112no—
628C2×#126—112no—
629C2×#126—112no—
630C2×#126—112no—
631C2×#126—112no—
632C2×#126—112no—
633C2×#126C2×D1112yes—
634C2×#125—112no—
635C2×#125—112no—
636C2×#125—112no—
637C2×#125—112no—
638C2×#125—112no—
639C2×#125—112no—
640C2×#125—112no—
641C2×#125—111no—
642C2×#125—111no—
643C2×#125—112no—
644C2×#125—112no—
645C2×#125—111no—
646C2×#125—112no—
647C2×#125C2×D1111yescharacteristic
648C2×#125C2×D1112yes—
649C2×#124—112no—
650C2×#124—112no—
651C2×#123—112no—
652C2×#123—112no—
653C2×#123—112no—
654C2×#123C2×D1112yes—
655C2×C22⋊Q8—111no—
656C2×C22⋊Q8—111no—
657C2×C22⋊Q8—111no—
658C2×C22⋊Q8—112no—
659C2×C22⋊Q8—112no—
660C2×C22⋊Q8—112no—
661C2×C22⋊Q8—111no—
662C2×C22⋊Q8—112no—
663C2×C22⋊Q8—112no—
664C2×C22⋊Q8—112no—
665C2×C22⋊Q8—112no—
666C2×C22⋊Q8C2×D1111yescharacteristic
667C2×C22⋊Q8C2×D1111yescharacteristic
668#519—1132no—
669C4×#41—1116no—
670C2×C4×Q8—111no—
671C2×C4×Q8—111no—
672C2×C4×Q8—111no—
673C2×C4×Q8—112no—
674C2×C4×Q8—112no—
675C2×C4×Q8—112no—
676C2×C4×Q8—112no—
677C2×C4×Q8—112no—
678C2×C4×Q8—111no—
679C2×C4×Q8—112no—
680C2×C4×Q8—111no—
681C2×C4×Q8—111no—
682C2×C4×Q8—112no—
683C2×C4×Q8—112no—
684C2×C4×Q8—112no—
685C2×C4×Q8—112no—
686C2×C4×Q8—111no—
687C2×C4×Q8—112no—
688C2×C4×Q8C2×D1111yescharacteristic
689C2×C4×D4—111no—
690C2×C4×D4—111no—
691C2×C4×D4—111no—
692C2×C4×D4—111no—
693C2×C4×D4—111no—
694C2×C4×D4C2×D1111yescharacteristic
695C2×#117—112no—
696C2×#117—111no—
697C2×#117—111no—
698C2×#117—111no—
699C2×#117—111no—
700C2×#117—111no—
701C2×#117—111no—
702C2×#117—112no—
703C2×#117—112no—
704C2×#117—112no—
705C2×#117—112no—
706C2×#117—112no—
707C2×#117C2×D1112yes—
708C2×#117C2×D1111yescharacteristic
709C22×C4⋊C4—112no—
710C22×C4⋊C4—111no—
711C22×C4⋊C4C2×D1111yescharacteristic
712C22×C42—111no—
713C22×C42—111no—
714C22×C42—111no—
715C22×C11—22no—
716C22×C11—22no—
717C22×C11—28no—
718C22×C11—22no—
719C22×C11—22no—
720C22×C11—22no—
721C22×C11—44no—
722C22×C11C22×#4114yes—
723C22×C11C22×#4112yes—
724C22×C11C2×2−1+412yes—
725C22×C11C2×2−1+412yes—
726C22×C11C2611yescharacteristic
727C2×D11—22no—
728C2×D11—22no—
729C2×D11—22no—
730C2×D11—44no—
731C4×C11—24no—
732C4×C11—24no—
733C4×C11—22no—
734C4×C11—22no—
735C4×C11—22no—
736C4×C11—24no—
737C4×C11—24no—
738C4×C11—22no—
739C4×C11C2×2−1+414yes—
740Dic11—24no—
741Dic11—24no—
742Dic11—22no—
743Dic11—24no—
744Dic11—24no—
745Dic11—22no—
746Dic11—22no—
747Dic11—22no—
748Dic11C22×#4114yes—
749Dic11C22×#4114yes—
750Dic11C2×2−1+414yes—
751C2×#41—118no—
752C2×#41—228no—
753C22×Q8—112no—
754C22×Q8—111no—
755C22×Q8—112no—
756C22×Q8—112no—
757C22×Q8—112no—
758C22×Q8—112no—
759C22×Q8—111no—
760C22×Q8—1116no—
761C22×Q8—2216no—
762C22×Q8C22×D1111yescharacteristic
763C22×D4—111no—
764C22×D4—111no—
765C22×D4C22×D1111yescharacteristic
766C23×C4—111no—
767C23×C4—112no—
768C23×C4—111no—
769C23×C4—111no—
770C23×C4—111no—
771C23×C4—111no—
772C23×C4—111no—
773C23×C4—111no—
774C23×C4C22×D1112yes—
775C23×C4C22×D1111yescharacteristic
776C23×C4C22×D1111yescharacteristic
777C4⋊Q8—118no—
778C4⋊Q8—118no—
779C4⋊Q8—118no—
780C4⋊Q8—1116no—
781C4⋊Q8—1116no—
782C4⋊Q8—118no—
783C4⋊Q8—118no—
784C4⋊Q8—118no—
785C4⋊Q8—1116no—
786C4⋊Q8—1116no—
787#126—1116no—
788#126—1116no—
789#126—1116no—
790#126—1116no—
791#126—1116no—
792#126—1116no—
793#126—1116no—
794#126C22×D11116yes—
795#125—1116no—
796#125—1116no—
797#125—1116no—
798#125—118no—
799#125—118no—
800#125—1116no—
801#125—1116no—
802#125—1116no—
803#125—1116no—
804#125—1116no—
805#125—1116no—
806#125—118no—
807#125—1116no—
808#125C22×D1118yes—
809#125C22×D11116yes—
810#124—1116no—
811#124—1116no—
812#123—1116no—
813#123—1116no—
814#123—1116no—
815#123C22×D11116yes—
816C22⋊Q8—118no—
817C22⋊Q8—118no—
818C22⋊Q8—118no—
819C22⋊Q8—1116no—
820C22⋊Q8—1116no—
821C22⋊Q8—1116no—
822C22⋊Q8—118no—
823C22⋊Q8—1116no—
824C22⋊Q8—1116no—
825C22⋊Q8—1116no—
826C22⋊Q8—1116no—
827C22⋊Q8C22×D1118yes—
828C22⋊Q8C22×D1118yes—
829C4×Q8—118no—
830C4×Q8—118no—
831C4×Q8—118no—
832C4×Q8—1116no—
833C4×Q8—1116no—
834C4×Q8—1116no—
835C4×Q8—1116no—
836C4×Q8—1116no—
837C4×Q8—118no—
838C4×Q8—1116no—
839C4×Q8—118no—
840C4×Q8—118no—
841C4×Q8—1116no—
842C4×Q8—1116no—
843C4×Q8—1116no—
844C4×Q8—1116no—
845C4×Q8—1116no—
846C4×Q8—118no—
847C4×Q8C22×D1118yes—
848C4×D4—118no—
849C4×D4—118no—
850C4×D4—118no—
851C4×D4—118no—
852C4×D4—118no—
853C4×D4C22×D1118yes—
854#117—1116no—
855#117—118no—
856#117—118no—
857#117—118no—
858#117—118no—
859#117—118no—
860#117—118no—
861#117—1116no—
862#117—1116no—
863#117—1116no—
864#117—1116no—
865#117—1116no—
866#117C22×D11116yes—
867#117C22×D1118yes—
868C2×C4⋊C4—112no—
869C2×C4⋊C4—112no—
870C2×C4⋊C4—111no—
871C2×C4⋊C4—111no—
872C2×C4⋊C4—112no—
873C2×C4⋊C4—112no—
874C2×C4⋊C4—112no—
875C2×C4⋊C4—1116no—
876C2×C4⋊C4—118no—
877C2×C4⋊C4—112no—
878C2×C4⋊C4—111no—
879C2×C4⋊C4—111no—
880C2×C4⋊C4—111no—
881C2×C4⋊C4—111no—
882C2×C4⋊C4—111no—
883C2×C4⋊C4—111no—
884C2×C4⋊C4—112no—
885C2×C4⋊C4—112no—
886C2×C4⋊C4—112no—
887C2×C4⋊C4—112no—
888C2×C4⋊C4—112no—
889C2×C4⋊C4—112no—
890C2×C4⋊C4—112no—
891C2×C4⋊C4—112no—
892C2×C4⋊C4—112no—
893C2×C4⋊C4—112no—
894C2×C4⋊C4—112no—
895C2×C4⋊C4—112no—
896C2×C4⋊C4—112no—
897C2×C4⋊C4—112no—
898C2×C4⋊C4—112no—
899C2×C4⋊C4—112no—
900C2×C4⋊C4—112no—
901C2×C4⋊C4C22×D1111yescharacteristic
902C2×C4⋊C4C22×D1111yescharacteristic
903C2×C4⋊C4C22×D1112yes—
904C2×C4⋊C4C22×D1118yes—
905C2×C4⋊C4C22×D1111yescharacteristic
906C2×C4⋊C4C22×D1111yescharacteristic
907C2×C4⋊C4C22×D1112yes—
908C2×C4⋊C4C22×D1112yes—
909C2×C4⋊C4C22×D1112yes—
910C2×C4⋊C4C22×D1112yes—
911C2×C4⋊C4C22×D1112yes—
912C2×C22⋊C4—111no—
913C2×C22⋊C4—112no—
914C2×C22⋊C4—111no—
915C2×C22⋊C4—112no—
916C2×C22⋊C4—112no—
917C2×C22⋊C4—111no—
918C2×C22⋊C4—111no—
919C2×C22⋊C4—112no—
920C2×C22⋊C4—112no—
921C2×C22⋊C4—112no—
922C2×C22⋊C4—112no—
923C2×C22⋊C4C22×D1111yescharacteristic
924C2×C22⋊C4C22×D1112yes—
925C2×C22⋊C4C22×D1111yescharacteristic
926C2×C22⋊C4C22×D1112yes—
927C2×C22⋊C4C22×D1112yes—
928C2×C42—111no—
929C2×C42—111no—
930C2×C42—112no—
931C2×C42—112no—
932C2×C42—112no—
933C2×C42—112no—
934C2×C42—112no—
935C2×C42—112no—
936C2×C42—111no—
937C2×C42—112no—
938C2×C42—112no—
939C2×C42—111no—
940C2×C42—111no—
941C2×C42—111no—
942C2×C42—111no—
943C2×C42—111no—
944C2×C42—118no—
945C2×C42—118no—
946C2×C42—111no—
947C2×C42—118no—
948C2×C42C22×D1112yes—
949C2×C42C22×D1112yes—
950C2×C42C22×D1111yescharacteristic
951C2×C11—24no—
952C2×C11—42no—
953C2×C11#350914yescomplemented
954C2×C11C23×#4111yescharacteristic
955C2×C11C22×2−1+411yescharacteristic
956C2×C11C22×2−1+411yescharacteristic
957D11—42no—
958C24—111no—
959C24C23×D1111yescharacteristic
960C24C23×D1111yescharacteristic
961#41—2232no—
962C2×Q8—24no—
963C2×Q8—118no—
964C2×Q8—114no—
965C2×Q8—118no—
966C2×Q8—118no—
967C2×Q8—118no—
968C2×Q8—118no—
969C2×Q8—114no—
970C2×Q8—228no—
971C2×Q8—228no—
972C2×Q8—228no—
973C2×Q8—228no—
974C2×Q8—2264no—
975C2×Q8—224no—
976C2×Q8—228no—
977C2×Q8—224no—
978C2×Q8C23×D1114yes—
979C2×D4—24no—
980C2×D4—114no—
981C2×D4—114no—
982C2×D4—224no—
983C2×D4—224no—
984C2×D4C23×D1114yes—
985C22×C4—28no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—118no—
989C22×C4—114no—
990C22×C4—111no—
991C22×C4—111no—
992C22×C4—111no—
993C22×C4—114no—
994C22×C4—114no—
995C22×C4—114no—
996C22×C4—118no—
997C22×C4—111no—
998C22×C4—111no—
999C22×C4—112no—
1000C22×C4—112no—
1001C22×C4—111no—
1002C22×C4—112no—
1003C22×C4—112no—
1004C22×C4—111no—
1005C22×C4—114no—
1006C22×C4—114no—
1007C22×C4—114no—
1008C22×C4—224no—
1009C22×C4—224no—
1010C22×C4—224no—
1011C22×C4—224no—
1012C22×C4—224no—
1013C22×C4—228no—
1014C22×C4—224no—
1015C22×C4C23×D1114yes—
1016C22×C4C23×D1114yes—
1017C22×C4C23×D1118yes—
1018C22×C4C23×D1111yescharacteristic
1019C22×C4C23×D1111yescharacteristic
1020C22×C4C23×D1112yes—
1021C22×C4C23×D1112yes—
1022C22×C4C23×D1111yescharacteristic
1023C22×C4C23×D1112yes—
1024C22×C4C23×D1111yescharacteristic
1025C22×C4C23×D1112yes—
1026C22×C4C23×D1111yescharacteristic
1027C4⋊C4—118no—
1028C4⋊C4—118no—
1029C4⋊C4—114no—
1030C4⋊C4—114no—
1031C4⋊C4—118no—
1032C4⋊C4—118no—
1033C4⋊C4—118no—
1034C4⋊C4—118no—
1035C4⋊C4—114no—
1036C4⋊C4—114no—
1037C4⋊C4—114no—
1038C4⋊C4—114no—
1039C4⋊C4—114no—
1040C4⋊C4—114no—
1041C4⋊C4—118no—
1042C4⋊C4—118no—
1043C4⋊C4—118no—
1044C4⋊C4—118no—
1045C4⋊C4—118no—
1046C4⋊C4—118no—
1047C4⋊C4—118no—
1048C4⋊C4—118no—
1049C4⋊C4—118no—
1050C4⋊C4—118no—
1051C4⋊C4—118no—
1052C4⋊C4—118no—
1053C4⋊C4—118no—
1054C4⋊C4—118no—
1055C4⋊C4—118no—
1056C4⋊C4—118no—
1057C4⋊C4—118no—
1058C4⋊C4C23×D1114yes—
1059C4⋊C4C23×D1114yes—
1060C4⋊C4C23×D1118yes—
1061C4⋊C4C23×D1114yes—
1062C4⋊C4C23×D1114yes—
1063C4⋊C4C23×D1118yes—
1064C4⋊C4C23×D1118yes—
1065C4⋊C4C23×D1118yes—
1066C4⋊C4C23×D1118yes—
1067C4⋊C4C23×D1118yes—
1068C22⋊C4—114no—
1069C22⋊C4—118no—
1070C22⋊C4—114no—
1071C22⋊C4—118no—
1072C22⋊C4—118no—
1073C22⋊C4—114no—
1074C22⋊C4—114no—
1075C22⋊C4—118no—
1076C22⋊C4—118no—
1077C22⋊C4—118no—
1078C22⋊C4—118no—
1079C22⋊C4C23×D1114yes—
1080C22⋊C4C23×D1118yes—
1081C22⋊C4C23×D1114yes—
1082C22⋊C4C23×D1118yes—
1083C22⋊C4C23×D1118yes—
1084C42—114no—
1085C42—114no—
1086C42—114no—
1087C42—114no—
1088C42—114no—
1089C42—114no—
1090C42—114no—
1091C42—114no—
1092C42—114no—
1093C42—118no—
1094C42—118no—
1095C42—118no—
1096C42—118no—
1097C42—118no—
1098C42—118no—
1099C42—118no—
1100C42—118no—
1101C42C23×D1114yes—
1102C42C23×D1118yes—
1103C42C23×D1118yes—
1104C11C2×#350911yescharacteristic, complemented, Sylow
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—112no—
1111C23—222no—
1112C23—222no—
1113C23—222no—
1114C23#41×D1114yes—
1115C23C24×D1112yes—
1116C23C24×D1112yes—
1117C23C24×D1111yescharacteristic
1118Q8—28no—
1119Q8—2216no—
1120Q8—2216no—
1121Q8—2216no—
1122Q8—2216no—
1123Q8—228no—
1124Q8—2216no—
1125Q8—228no—
1126D4—28no—
1127D4—228no—
1128D4—228no—
1129C2×C4—216no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—28no—
1139C2×C4—28no—
1140C2×C4—114no—
1141C2×C4—114no—
1142C2×C4—1116no—
1143C2×C4—114no—
1144C2×C4—112no—
1145C2×C4—112no—
1146C2×C4—112no—
1147C2×C4—112no—
1148C2×C4—112no—
1149C2×C4—114no—
1150C2×C4—114no—
1151C2×C4—112no—
1152C2×C4—114no—
1153C2×C4—114no—
1154C2×C4—112no—
1155C2×C4—228no—
1156C2×C4—228no—
1157C2×C4—228no—
1158C2×C4—228no—
1159C2×C4—228no—
1160C2×C4—222no—
1161C2×C4—2216no—
1162C2×C4—224no—
1163C2×C4—224no—
1164C2×C4—222no—
1165C2×C4—224no—
1166C2×C4—222no—
1167C2×C4—222no—
1168C2×C4—224no—
1169C2×C4—228no—
1170C2×C4#6704314yes—
1171C2×C4C24×D1112yes—
1172C2×C4C24×D1112yes—
1173C2×C4C24×D1114yes—
1174C2×C4C24×D1114yes—
1175C2×C4C24×D1112yes—
1176C2×C4C24×D1114yes—
1177C2×C4C24×D1112yes—
1178C2×C4C24×D1114yes—
1179C2×C4C24×D1112yes—
1180C22—22no—
1181C22—22no—
1182C22—28no—
1183C22—22no—
1184C22—22no—
1185C22—22no—
1186C22—44no—
1187C22—222no—
1188C22—222no—
1189C22—222no—
1190C22—444no—
1191C22C2×#41×D1114yes—
1192C22C2×#41×D1112yes—
1193C22C2×#6704312yes—
1194C22D11×2−1+412yes—
1195C22C25×D1111yescharacteristic
1196C4—24no—
1197C4—24no—
1198C4—22no—
1199C4—22no—
1200C4—24no—
1201C4—22no—
1202C4—22no—
1203C4—24no—
1204C4—114no—
1205C4—114no—
1206C4—114no—
1207C4—222no—
1208C4—224no—
1209C4—224no—
1210C4—222no—
1211C4—222no—
1212C4—224no—
1213C4—222no—
1214C4—224no—
1215C4C2×#6704314yes—
1216C2—24no—
1217C2—42no—
1218C2—442no—
1219C2#1308249414yesdirect product factor
1220C2C22×#41×D1111yescharacteristic
1221C2C2×D11×2−1+411yescharacteristic
1222C2C22×#6704311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#552C2
socleC23×C11C25
prime radicalC22×#4341C22
hypercenterC2×#552D11
hypocenterC11C2×#3509
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. #13082494C2direct (N × H)
2. C2×#10623216C2semidirect
3. C2×#10623216C2semidirect
4. C2×#10623100C2semidirect
5. C2×#10623172C2semidirect
6. C2×#10623064C2semidirect
7. C2×#10623233C2semidirect
8. C2×#10623173C2semidirect
9. C2×#10623072C2semidirect
10. C2×#10623181C2semidirect
11. C2×#10623044C2semidirect
12. C2×#10623062C2semidirect
13. C2×#10623227C2semidirect
14. C2×#10623232C2semidirect
16. C2×#10623219C2semidirect
17. C2×#10623109C2semidirect
18. C2×#10623048C2semidirect
19. C2×#10623153C2semidirect
20. C2×#10623153C2semidirect
21. C22×#66941C2semidirect
22. C2×#10623047C2semidirect
24. C2×C11×#552C2semidirect
27. C11×#552C22semidirect
56. #10623233C22semidirect
57. #10623232C22semidirect
58. #10623227C22semidirect
59. #10623219C22semidirect
60. #10623216C22semidirect
61. #10623216C22semidirect
62. #10623181C22semidirect
64. #10623173C22semidirect
65. #10623172C22semidirect
66. #10623153C22semidirect
67. #10623153C22semidirect
68. #10623109C22semidirect
69. #10623100C22semidirect
70. #10623072C22semidirect
72. #10623064C22semidirect
73. #10623062C22semidirect
74. #10623048C22semidirect
75. #10623047C22semidirect
76. #10623044C22semidirect
107. C2×#66941C22semidirect
506. C2×#552D11semidirect
606. #552C2×D11semidirect
953. C2×C11#3509semidirect
1104. C11C2×#3509semidirect
1219. C2#13082494direct (N × H)

Maximal subgroups

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

subgroupindex
#130824942
C2×#106232162
C2×#106231002
C2×#106231722
C2×#106230642
C2×#106232332
C2×#106231732
C2×#106230722
C2×#106231812
C2×#106230442
C2×#106230622
C2×#106232272
C2×#106232322
C2×#106231792
C2×#106232192
C2×#106231092
C2×#106230482
C2×#106231532
C22×#669412
C2×#106230472
C2×C4×#43412
C2×C11×#5522
C2×#350911