Finite Group Databasebeta

← C2×#13083267 #15661286

Subgroups — C2×#13083267 #15661286

Order 2816.

6554 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13083267C2132yesmaximal, direct product factor
2C2×#10623177C212yesmaximal, complemented
3C2×#10623215C212yesmaximal, complemented
4C2×#10623100C211yesmaximal, characteristic, complemented
5C2×#10623115C211yesmaximal, characteristic, complemented
6C2×#10623202C212yesmaximal, complemented
7C2×#10623147C211yesmaximal, characteristic, complemented
8C2×#10623074C211yesmaximal, characteristic, complemented
9C2×#10623149C211yesmaximal, characteristic, complemented
10C2×#10623089C211yesmaximal, characteristic, complemented
11C2×#10623173C212yesmaximal, complemented
12C2×#10623173C211yesmaximal, characteristic, complemented
13C2×#10623170C211yesmaximal, characteristic, complemented
14C2×#10623050C211yesmaximal, characteristic, complemented
15C2×#10623260C211yesmaximal, characteristic, complemented
16C2×#10623213C211yesmaximal, characteristic, complemented
17C2×#10623193C212yesmaximal, complemented
18C2×#10623241C212yesmaximal, complemented
19C2×#10623232C212yesmaximal, complemented
20C2×#10623196C212yesmaximal, complemented
21C2×#10623259C211yesmaximal, characteristic, complemented
22C2×#10623211C211yesmaximal, characteristic, complemented
23C2×#10623059C211yesmaximal, characteristic, complemented
24C2×C11×#542C211yesmaximal, characteristic, complemented
25C11×#542C22116yescomplemented
26C2×C11×C4⋊Q8C2211yescharacteristic
27C2×C11×#126C2212yes—
28C2×C11×#124C2211yescharacteristic
29C2×C11×#124C2212yes—
30C2×C11×#123C2212yes—
31C2×C11×C22⋊Q8C2211yescharacteristic
32C2×C11×C22⋊Q8C2212yes—
33C2×C11×#121C2211yescharacteristic
34C2×C4×Q8×C11C2211yescharacteristic
35C2×C4×D4×C11C2211yescharacteristic
36C2×C11×#117C2211yescharacteristic
37C2×#66999C2211yescharacteristic
38C2×#66999C2211yescharacteristic
39C2×#66999C2212yes—
40C2×#66999C2212yes—
41C2×Q8×Dic11C2211yescharacteristic
42C2×Q8×Dic11C2212yes—
43C2×Q8×Dic11C2211yescharacteristic
44C2×#66997C2212yes—
45C2×#66992C2212yes—
46C2×#66992C2212yes—
47C2×#66991C2211yescharacteristic
48C2×#66991C2211yescharacteristic
49C2×#66989C2212yes—
50C2×D4×Dic11C2211yescharacteristic
51C2×D4×Dic11C2212yes—
52C2×D4×Dic11C2211yescharacteristic
53C2×#66982C2212yes—
54C2×C4×C22⋊D11C2211yescharacteristic
55C2×C4×C22⋊D11C2211yescharacteristic
56C2×C4×C22⋊D11C2212yes—
57C2×#66979C2211yescharacteristic
58C22×C4⋊Dic11C2211yescharacteristic
59C22×C4⋊Dic11C2212yes—
60C2×#66977C2212yes—
61#10623260C22116yescomplemented
62#10623259C22116yescomplemented
63#10623241C22132yescomplemented
64#10623232C22132yescomplemented
65#10623215C22132yescomplemented
66#10623213C22116yescomplemented
67#10623211C22116yescomplemented
68#10623202C22132yescomplemented
69#10623196C22132yescomplemented
70#10623193C22132yescomplemented
71#10623177C22132yescomplemented
72#10623173C22132yescomplemented
73#10623173C22116yescomplemented
74#10623170C22116yescomplemented
75#10623149C22116yescomplemented
76#10623147C22116yescomplemented
77#10623115C22116yescomplemented
78#10623100C22116yescomplemented
79#10623089C22116yescomplemented
80#10623074C22116yescomplemented
81#10623059C22116yescomplemented
82#10623050C22116yescomplemented
83C2×#66951C2211yescharacteristic
84C2×#66951C2212yes—
85C2×#66951C2212yes—
86C2×#66951C2212yes—
87C2×#66950C2212yes—
88C2×#66949C2211yescharacteristic
89C2×#66949C2212yes—
90C2×#66947C2211yescharacteristic
91C2×#66945C2212yes—
92C2×#66945C2211yescharacteristic
93C2×#66945C2211yescharacteristic
94C2×#66945C2211yescharacteristic
95C2×C4⋊C4×D11C2211yescharacteristic
96C2×#66943C2211yescharacteristic
97C2×#66943C2212yes—
98C2×#66943C2211yescharacteristic
99C2×#66943C2212yes—
100C2×#66943C2212yes—
101C2×#66943C2211yescharacteristic
102C2×#66942C2212yes—
103C2×#66942C2211yescharacteristic
104C2×#66942C2212yes—
105C2×#66941C2211yescharacteristic
106C2×#66941C2212yes—
107C2×#66941C2212yes—
108C2×#66940C2212yes—
109C2×#66939C2212yes—
110C2×#66939C2212yes—
111C2×#66939C2212yes—
112C2×#66938C2211yescharacteristic
113C2×#66938C2212yes—
114C2×#66938C2212yes—
115C2×#66937C2211yescharacteristic
116C2×#66937C2212yes—
117C2×#66936C2212yes—
118C2×#66936C2211yescharacteristic
119C2×#66936C2212yes—
120C2×(C22⋊D11)⋊C4C2212yes—
121C2×#66932C2212yes—
122C2×#66932C2211yescharacteristic
123C2×#66932C2212yes—
124C2×#66932C2212yes—
125C2×#66932C2212yes—
126C2×#66932C2212yes—
127C2×#66931C2212yes—
128C2×#66931C2212yes—
129C2×#66931C2212yes—
130C2×#66931C2212yes—
131C2×#66931C2212yes—
132C2×#66930C2212yes—
133C2×#66930C2212yes—
134C2×#66930C2212yes—
135C2×#66928C2212yes—
136C2×C4×D44C2211yescharacteristic
137C2×#66925C2211yescharacteristic
138C2×C42×D11C2211yescharacteristic
139C2×#66923C2211yescharacteristic
140C2×#66923C2211yescharacteristic
141C2×#66923C2212yes—
142C2×#66922C2211yescharacteristic
143C2×#66922C2211yescharacteristic
144C2×C4×Dic22C2211yescharacteristic
145C2×C4×Dic22C2212yes—
146C2×C4×Dic22C2212yes—
147C22×Q8×C11C2311yescharacteristic
148C22×Q8×C11C2312yes—
149C22×D4×C11C2311yescharacteristic
150C22×D4×C11C2312yes—
151C23×C4×C11C2311yescharacteristic
152C23×C4×C11C2312yes—
153C22×C22⋊D11C2312yes—
154C22×C22⋊D11C2311yescharacteristic
155C22×C22⋊D11C2311yescharacteristic
156C22×C22⋊D11C2312yes—
157C23×Dic11C2312yes—
158C23×Dic11C2312yes—
159C23×Dic11C2312yes—
160C22×D44C2311yescharacteristic
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2311yescharacteristic
164C22×C4×D11C2311yescharacteristic
165C22×C4×D11C2312yes—
166C22×Dic22C2312yes—
167C22×Dic22C2311yescharacteristic
168C22×Dic22C2312yes—
169C22×Dic22C2312yes—
170C11×C4⋊Q8C2318yes—
171C11×#126C23116yes—
172C11×#124C23116yes—
173C11×#124C2318yes—
174C11×#123C23116yes—
175C11×C22⋊Q8C2318yes—
176C11×C22⋊Q8C23116yes—
177C11×#121C2318yes—
178C4×Q8×C11C2318yes—
179C4×D4×C11C2318yes—
180C11×#117C2318yes—
181C2×C11×C4⋊C4C2312yes—
182C2×C11×C4⋊C4C2311yescharacteristic
183C2×C11×C4⋊C4C2311yescharacteristic
184C2×C11×C4⋊C4C2312yes—
185C2×C11×C4⋊C4C2312yes—
186C2×C11×C4⋊C4C2311yescharacteristic
187C2×C11×C4⋊C4C2311yescharacteristic
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2312yes—
191C2×C11×C22⋊C4C2311yescharacteristic
192C2×C11×C22⋊C4C2312yes—
193C2×C11×C22⋊C4C2311yescharacteristic
194C2×C11×C22⋊C4C2312yes—
195C2×C42×C11C2312yes—
196C2×C42×C11C2311yescharacteristic
197C2×C42×C11C2311yescharacteristic
198C2×C22⋊Dic11C2312yes—
199C2×C22⋊Dic11C2311yescharacteristic
200C2×C22⋊Dic11C2312yes—
201C2×C22⋊Dic11C2312yes—
202C2×C22⋊Dic11C2312yes—
203C2×C22⋊Dic11C2312yes—
204C2×C22⋊Dic11C2311yescharacteristic
205#66999C23116yes—
206#66999C23116yes—
207#66999C2318yes—
208#66999C2318yes—
209Q8×Dic11C23116yes—
210Q8×Dic11C2318yes—
211Q8×Dic11C2318yes—
212#66997C23116yes—
213#66992C23116yes—
214#66992C23116yes—
215#66991C2318yes—
216#66991C2318yes—
217#66989C23116yes—
218D4×Dic11C2318yes—
219D4×Dic11C2318yes—
220D4×Dic11C23116yes—
221#66982C23116yes—
222C4×C22⋊D11C2318yes—
223C4×C22⋊D11C2318yes—
224C4×C22⋊D11C23116yes—
225C2×(C2×D11)⋊C4C2311yescharacteristic
226C2×(C2×D11)⋊C4C2311yescharacteristic
227C2×(C2×D11)⋊C4C2311yescharacteristic
228C2×(C2×D11)⋊C4C2311yescharacteristic
229C2×(C2×D11)⋊C4C2312yes—
230C2×(C2×D11)⋊C4C2312yes—
231C2×(C2×D11)⋊C4C2312yes—
232C2×(C2×D11)⋊C4C2312yes—
233C2×(C2×D11)⋊C4C2312yes—
234C2×(C2×D11)⋊C4C2311yescharacteristic
235C2×(C2×D11)⋊C4C2311yescharacteristic
236#66979C2318yes—
237C2×C4⋊Dic11C2311yescharacteristic
238C2×C4⋊Dic11C2311yescharacteristic
239C2×C4⋊Dic11C2312yes—
240C2×C4⋊Dic11C2311yescharacteristic
241C2×C4⋊Dic11C2311yescharacteristic
242C2×C4⋊Dic11C2311yescharacteristic
243C2×C4⋊Dic11C2312yes—
244C2×C4⋊Dic11C2312yes—
245C2×C4⋊Dic11C2311yescharacteristic
246C2×C4⋊Dic11C2312yes—
247C2×C4⋊Dic11C2312yes—
248C2×C4⋊Dic11C2312yes—
249C2×C4⋊Dic11C2312yes—
250C2×C4⋊Dic11C2312yes—
251C2×C4⋊Dic11C2318yes—
252C2×C4⋊Dic11C23116yes—
253#66977C23116yes—
254C2×Dic11⋊C4C2311yescharacteristic
255C2×Dic11⋊C4C2311yescharacteristic
256C2×Dic11⋊C4C2312yes—
257C2×Dic11⋊C4C2312yes—
258C2×Dic11⋊C4C2312yes—
259C2×Dic11⋊C4C2312yes—
260C2×Dic11⋊C4C2312yes—
261C2×Dic11⋊C4C2312yes—
262C2×Dic11⋊C4C2312yes—
263C2×Dic11⋊C4C2312yes—
264C2×Dic11⋊C4C2311yescharacteristic
265C2×Dic11⋊C4C2311yescharacteristic
266C2×Dic11⋊C4C2311yescharacteristic
267C2×Dic11⋊C4C2312yes—
268C2×Dic11⋊C4C2312yes—
269C2×Dic11⋊C4C2311yescharacteristic
270C2×Dic11⋊C4C2312yes—
271C2×C4×Dic11C2311yescharacteristic
272C2×C4×Dic11C2311yescharacteristic
273C2×C4×Dic11C2312yes—
274C2×C4×Dic11C2312yes—
275C2×C4×Dic11C2312yes—
276C2×C4×Dic11C2312yes—
277C2×C4×Dic11C2311yescharacteristic
278C2×C4×Dic11C2311yescharacteristic
279C2×C4×Dic11C2312yes—
280C2×C4×Dic11C2312yes—
281#66951C23116yes—
282#66951C2318yes—
283#66951C23116yes—
284#66951C23116yes—
285#66950C23116yes—
286#66949C23116yes—
287#66949C2318yes—
288#66947C2318yes—
289#66945C23116yes—
290#66945C2318yes—
291#66945C2318yes—
292#66945C2318yes—
293C4⋊C4×D11C2318yes—
294#66943C23116yes—
295#66943C2318yes—
296#66943C2318yes—
297#66943C2318yes—
298#66943C23116yes—
299#66943C23116yes—
300#66942C2318yes—
301#66942C23116yes—
302#66942C23116yes—
303#66941C23116yes—
304#66941C2318yes—
305#66941C23116yes—
306#66940C23116yes—
307#66939C23116yes—
308#66939C23116yes—
309#66939C23116yes—
310#66938C23116yes—
311#66938C23116yes—
312#66938C2318yes—
313#66937C23116yes—
314#66937C2318yes—
315#66936C2318yes—
316#66936C23116yes—
317#66936C23116yes—
318(C22⋊D11)⋊C4C23116yes—
319#66932C23116yes—
320#66932C23116yes—
321#66932C23116yes—
322#66932C2318yes—
323#66932C23116yes—
324#66932C23116yes—
325#66931C23116yes—
326#66931C23116yes—
327#66931C23116yes—
328#66931C23116yes—
329#66931C23116yes—
330#66930C23116yes—
331#66930C23116yes—
332#66930C23116yes—
333#66928C23116yes—
334C4×D44C2318yes—
335#66925C2318yes—
336C42×D11C2318yes—
337#66923C23116yes—
338#66923C2318yes—
339#66923C2318yes—
340#66922C2318yes—
341#66922C2318yes—
342C4×Dic22C23116yes—
343C4×Dic22C23116yes—
344C4×Dic22C2318yes—
345C2×#3565—111nomaximal, Sylow
346C24×C11C2411yescharacteristic
347C24×C11C2412yes—
348C23×D11C2411yescharacteristic
349C23×D11C2411yescharacteristic
350C2×Q8×C11—24no—
351C2×Q8×C11—44no—
352C2×Q8×C11C2414yes—
353C2×Q8×C11C2418yes—
354C2×D4×C11—24no—
355C2×D4×C11—44no—
356C2×D4×C11C2414yes—
357C2×D4×C11C2418yes—
358C22×C4×C11—24no—
359C22×C4×C11—44no—
360C22×C4×C11C2412yes—
361C22×C4×C11C2411yescharacteristic
362C22×C4×C11C2412yes—
363C22×C4×C11C2411yescharacteristic
364C22×C4×C11C2412yes—
365C22×C4×C11C2411yescharacteristic
366C22×C4×C11C2411yescharacteristic
367C22×C4×C11C2411yescharacteristic
368C22×C4×C11C2414yes—
369C22×C4×C11C2418yes—
370C22×C4×C11C2411yescharacteristic
371C2×C22⋊D11—42no—
372C2×C22⋊D11—42no—
373C2×C22⋊D11—44no—
374C2×C22⋊D11—44no—
375C2×C22⋊D11C2418yes—
376C2×C22⋊D11C2414yes—
377C2×C22⋊D11C2414yes—
378C2×C22⋊D11C2418yes—
379C22×Dic11—44no—
380C22×Dic11—44no—
381C22×Dic11—44no—
382C22×Dic11C2411yescharacteristic
383C22×Dic11C2411yescharacteristic
384C22×Dic11C2411yescharacteristic
385C22×Dic11C2411yescharacteristic
386C22×Dic11C2411yescharacteristic
387C22×Dic11C2412yes—
388C22×Dic11C2412yes—
389C22×Dic11C2412yes—
390C22×Dic11C2411yescharacteristic
391C22×Dic11C2412yes—
392C22×Dic11C2418yes—
393C22×Dic11C2418yes—
394C22×Dic11C2418yes—
395C2×D44—42no—
396C2×D44C2414yes—
397C2×C4×D11—24no—
398C2×C4×D11—24no—
399C2×C4×D11—42no—
400C2×C4×D11—44no—
401C2×C4×D11—42no—
402C2×C4×D11C2414yes—
403C2×C4×D11C2414yes—
404C2×C4×D11C2414yes—
405C2×C4×D11C2414yes—
406C2×C4×D11C2418yes—
407C2×Dic22—44no—
408C2×Dic22—44no—
409C2×Dic22—42no—
410C2×Dic22—44no—
411C2×Dic22C2418yes—
412C2×Dic22C2414yes—
413C2×Dic22C2418yes—
414C2×Dic22C2418yes—
415C11×C4⋊C4C2418yes—
416C11×C4⋊C4C2414yes—
417C11×C4⋊C4C2414yes—
418C11×C4⋊C4C2418yes—
419C11×C4⋊C4C2418yes—
420C11×C4⋊C4C2414yes—
421C11×C4⋊C4C2414yes—
422C11×C22⋊C4C2418yes—
423C11×C22⋊C4C2418yes—
424C11×C22⋊C4C2418yes—
425C11×C22⋊C4C2414yes—
426C11×C22⋊C4C2418yes—
427C11×C22⋊C4C2414yes—
428C11×C22⋊C4C2418yes—
429C42×C11C2418yes—
430C42×C11C2414yes—
431C42×C11C2414yes—
432C22⋊Dic11C2418yes—
433C22⋊Dic11C2414yes—
434C22⋊Dic11C2418yes—
435C22⋊Dic11C2418yes—
436C22⋊Dic11C2418yes—
437C22⋊Dic11C2418yes—
438C22⋊Dic11C2414yes—
439(C2×D11)⋊C4C2414yes—
440(C2×D11)⋊C4C2414yes—
441(C2×D11)⋊C4C2414yes—
442(C2×D11)⋊C4C2414yes—
443(C2×D11)⋊C4C2418yes—
444(C2×D11)⋊C4C2418yes—
445(C2×D11)⋊C4C2418yes—
446(C2×D11)⋊C4C2418yes—
447(C2×D11)⋊C4C2418yes—
448(C2×D11)⋊C4C2414yes—
449(C2×D11)⋊C4C2414yes—
450C4⋊Dic11C2414yes—
451C4⋊Dic11C2414yes—
452C4⋊Dic11C2418yes—
453C4⋊Dic11C2414yes—
454C4⋊Dic11C2414yes—
455C4⋊Dic11C2414yes—
456C4⋊Dic11C2418yes—
457C4⋊Dic11C2418yes—
458C4⋊Dic11C2414yes—
459C4⋊Dic11C2418yes—
460C4⋊Dic11C2418yes—
461C4⋊Dic11C2418yes—
462C4⋊Dic11C2418yes—
463C4⋊Dic11C2418yes—
464Dic11⋊C4C2414yes—
465Dic11⋊C4C2414yes—
466Dic11⋊C4C2418yes—
467Dic11⋊C4C2418yes—
468Dic11⋊C4C2418yes—
469Dic11⋊C4C2418yes—
470Dic11⋊C4C2418yes—
471Dic11⋊C4C2418yes—
472Dic11⋊C4C2418yes—
473Dic11⋊C4C2418yes—
474Dic11⋊C4C2414yes—
475Dic11⋊C4C2414yes—
476Dic11⋊C4C2414yes—
477Dic11⋊C4C2418yes—
478Dic11⋊C4C2418yes—
479Dic11⋊C4C2414yes—
480Dic11⋊C4C2418yes—
481C4×Dic11C2414yes—
482C4×Dic11C2414yes—
483C4×Dic11C2418yes—
484C4×Dic11C2418yes—
485C4×Dic11C2418yes—
486C4×Dic11C2418yes—
487C4×Dic11C2414yes—
488C4×Dic11C2414yes—
489C4×Dic11C2418yes—
490C4×Dic11C2418yes—
491#3565—1132no—
492C2×#563—112no—
493C2×#562—112no—
494C2×#557—111no—
495C2×#556—112no—
496C2×#556—111no—
497C2×#555—111no—
498C2×#554—111no—
499C2×#553—111no—
500C2×#553—111no—
501C2×#552—111no—
502C2×#552—112no—
503C2×#552—111no—
504C2×#544—111no—
505C2×#544—111no—
506C2×#542—112no—
507C2×#542—111no—
508C2×#542—112no—
509C2×#542D1111yescharacteristic, complemented
510C2×#541—112no—
511C2×#539—112no—
512C2×#533—111no—
513C2×#529—111no—
514C2×#529—111no—
515C23×C11—22no—
516C23×C11—24no—
517C23×C11—22no—
518C23×C11—24no—
519C23×C11—24no—
520C23×C11—22no—
521C23×C11C2512yes—
522C23×C11C2514yes—
523C23×C11C2511yescharacteristic
524C22×D11—22no—
525C22×D11—22no—
526C22×D11—22no—
527C22×D11—22no—
528C22×D11—22no—
529C22×D11—22no—
530C22×D11C2512yes—
531C22×D11C2512yes—
532Q8×C11—28no—
533Q8×C11—48no—
534D4×C11—28no—
535D4×C11—48no—
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—24no—
543C2×C4×C11—22no—
544C2×C4×C11—28no—
545C2×C4×C11—48no—
546C2×C4×C112−1+414yes—
547C2×C4×C11C2514yes—
548C2×C4×C11C2512yes—
549C2×C4×C11C2514yes—
550C2×C4×C11C2512yes—
551C2×C4×C11C2514yes—
552C2×C4×C11C2512yes—
553C2×C4×C11C2512yes—
554C2×C4×C11C2512yes—
555C2×C4×C11C2512yes—
556C22⋊D11—44no—
557C22⋊D11—48no—
558C22⋊D11—48no—
559C22⋊D11—44no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—24no—
564C2×Dic11—22no—
565C2×Dic11—24no—
566C2×Dic11—24no—
567C2×Dic11—24no—
568C2×Dic11—22no—
569C2×Dic11—22no—
570C2×Dic11—48no—
571C2×Dic11—48no—
572C2×Dic11—48no—
573C2×Dic11C2512yes—
574C2×Dic11C2512yes—
575C2×Dic11C2512yes—
576C2×Dic11C2512yes—
577C2×Dic11C2512yes—
578C2×Dic11C2514yes—
579C2×Dic11C2514yes—
580C2×Dic11C2514yes—
581C2×Dic11C2512yes—
582C2×Dic11C2514yes—
583D44—44no—
584C4×D11—28no—
585C4×D11—28no—
586C4×D11—48no—
587C4×D11—44no—
588C4×D11—44no—
589Dic22—44no—
590Dic22—48no—
591Dic22—48no—
592Dic22—48no—
593#563—1132no—
594#562—1132no—
595#557—1116no—
596#556—1132no—
597#556—1116no—
598#555—1116no—
599#554—1116no—
600#553—1116no—
601#553—1116no—
602#552—1116no—
603#552—1132no—
604#552—1116no—
605#544—1116no—
606#544—1116no—
607#542—1132no—
608#542—1116no—
609#542—1132no—
610#542C2×D11116yescomplemented
611#541—1132no—
612#539—1132no—
613#533—1116no—
614C2×C4⋊Q8—112no—
615C2×C4⋊Q8—112no—
616C2×C4⋊Q8—112no—
617C2×C4⋊Q8—111no—
618C2×C4⋊Q8—111no—
619C2×C4⋊Q8—111no—
620C2×C4⋊Q8C2×D1111yescharacteristic
621#529—1116no—
622#529—1116no—
623C2×#126—111no—
624C2×#126—112no—
625C2×#126—112no—
626C2×#126—112no—
627C2×#126—112no—
628C2×#126—111no—
629C2×#126—112no—
630C2×#126—112no—
631C2×#126—112no—
632C2×#126—112no—
633C2×#126C2×D1112yes—
634C2×#125—111no—
635C2×#125—112no—
636C2×#125—112no—
637C2×#125—111no—
638C2×#125—111no—
639C2×#125—112no—
640C2×#125—112no—
641C2×#125—111no—
642C2×#125—112no—
643C2×#125—111no—
644C2×#125—112no—
645C2×#125—111no—
646C2×#124—112no—
647C2×#124—111no—
648C2×#124—112no—
649C2×#124—112no—
650C2×#124—112no—
651C2×#124C2×D1111yescharacteristic
652C2×#124C2×D1112yes—
653C2×#123—112no—
654C2×#123—111no—
655C2×#123—111no—
656C2×#123—112no—
657C2×#123—112no—
658C2×#123—112no—
659C2×#123—112no—
660C2×#123—112no—
661C2×#123C2×D1112yes—
662C2×C22⋊Q8—111no—
663C2×C22⋊Q8—112no—
664C2×C22⋊Q8—111no—
665C2×C22⋊Q8—112no—
666C2×C22⋊Q8—112no—
667C2×C22⋊Q8—111no—
668C2×C22⋊Q8—112no—
669C2×C22⋊Q8—112no—
670C2×C22⋊Q8—112no—
671C2×C22⋊Q8—112no—
672C2×C22⋊Q8—112no—
673C2×C22⋊Q8—112no—
674C2×C22⋊Q8—112no—
675C2×C22⋊Q8C2×D1111yescharacteristic
676C2×C22⋊Q8C2×D1112yes—
677C2×#121—111no—
678C2×#121—111no—
679C2×#121—112no—
680C2×#121—112no—
681C2×#121—111no—
682C2×#121—112no—
683C2×#121C2×D1111yescharacteristic
684C2×C4×Q8—111no—
685C2×C4×Q8—112no—
686C2×C4×Q8—111no—
687C2×C4×Q8—112no—
688C2×C4×Q8—111no—
689C2×C4×Q8—112no—
690C2×C4×Q8—112no—
691C2×C4×Q8C2×D1111yescharacteristic
692C2×C4×D4—111no—
693C2×C4×D4—112no—
694C2×C4×D4—111no—
695C2×C4×D4—111no—
696C2×C4×D4—111no—
697C2×C4×D4—112no—
698C2×C4×D4—112no—
699C2×C4×D4—111no—
700C2×C4×D4C2×D1111yescharacteristic
701C2×#117—111no—
702C2×#117—111no—
703C2×#117—111no—
704C2×#117—112no—
705C2×#117—111no—
706C2×#117—112no—
707C2×#117—112no—
708C2×#117—112no—
709C2×#117—111no—
710C2×#117C2×D1111yescharacteristic
711C22×C4⋊C4—112no—
712C22×C4⋊C4—111no—
713C22×C4⋊C4—111no—
714C22×C42—111no—
715C22×C11—22no—
716C22×C11—24no—
717C22×C11—24no—
718C22×C11—22no—
719C22×C11—22no—
720C22×C11—24no—
721C22×C11—44no—
722C22×C11—48no—
723C22×C11C2×2−1+412yes—
724C22×C11#58512yes—
725C22×C11#58512yes—
726C22×C11C2611yescharacteristic
727C2×D11—22no—
728C2×D11—22no—
729C2×D11—22no—
730C2×D11—22no—
731C2×D11—22no—
732C2×D11—22no—
733C2×D11—44no—
734C2×D11—44no—
735C4×C11—22no—
736C4×C11—24no—
737C4×C11—22no—
738C4×C11—24no—
739C4×C11—24no—
740C4×C11—22no—
741C4×C11—22no—
742C4×C11—22no—
743C4×C11C2×2−1+414yes—
744Dic11—22no—
745Dic11—22no—
746Dic11—22no—
747Dic11—24no—
748Dic11—22no—
749Dic11—24no—
750Dic11—24no—
751Dic11—24no—
752Dic11—22no—
753Dic11—22no—
754C22×Q8—111no—
755C22×Q8—112no—
756C22×Q8—112no—
757C22×Q8—112no—
758C22×Q8C22×D1111yescharacteristic
759C22×Q8C22×D1112yes—
760C22×D4—111no—
761C22×D4—111no—
762C22×D4—112no—
763C22×D4—112no—
764C22×D4—111no—
765C22×D4C22×D1111yescharacteristic
766C22×D4C22×D1112yes—
767C23×C4—112no—
768C23×C4—112no—
769C23×C4—112no—
770C23×C4—111no—
771C23×C4—111no—
772C23×C4—112no—
773C23×C4—111no—
774C23×C4—111no—
775C23×C4C22×D1111yescharacteristic
776C23×C4C22×D1112yes—
777C4⋊Q8—1116no—
778C4⋊Q8—1116no—
779C4⋊Q8—1116no—
780C4⋊Q8—118no—
781C4⋊Q8—118no—
782C4⋊Q8—118no—
783C4⋊Q8C22×D1118yes—
784#126—118no—
785#126—1116no—
786#126—1116no—
787#126—1116no—
788#126—1116no—
789#126—118no—
790#126—1116no—
791#126—1116no—
792#126—1116no—
793#126—1116no—
794#126C22×D11116yes—
795#125—118no—
796#125—118no—
797#125—118no—
798#125—1116no—
799#125—1116no—
800#125—1116no—
801#125—1116no—
802#125—118no—
803#125—1116no—
804#125—118no—
805#125—1116no—
806#125—118no—
807#124—1116no—
808#124—118no—
809#124—1116no—
810#124—1116no—
811#124—1116no—
812#124C22×D1118yes—
813#124C22×D11116yes—
814#123—1116no—
815#123—118no—
816#123—118no—
817#123—1116no—
818#123—1116no—
819#123—1116no—
820#123—1116no—
821#123—1116no—
822#123C22×D11116yes—
823C22⋊Q8—118no—
824C22⋊Q8—1116no—
825C22⋊Q8—118no—
826C22⋊Q8—1116no—
827C22⋊Q8—1116no—
828C22⋊Q8—118no—
829C22⋊Q8—1116no—
830C22⋊Q8—1116no—
831C22⋊Q8—1116no—
832C22⋊Q8—1116no—
833C22⋊Q8—1116no—
834C22⋊Q8—1116no—
835C22⋊Q8—1116no—
836C22⋊Q8C22×D1118yes—
837C22⋊Q8C22×D11116yes—
838#121—118no—
839#121—1116no—
840#121—118no—
841#121—1116no—
842#121—118no—
843#121—1116no—
844#121C22×D1118yes—
845C4×Q8—118no—
846C4×Q8—1116no—
847C4×Q8—118no—
848C4×Q8—1116no—
849C4×Q8—118no—
850C4×Q8—1116no—
851C4×Q8—1116no—
852C4×Q8C22×D1118yes—
853C4×D4—118no—
854C4×D4—1116no—
855C4×D4—118no—
856C4×D4—118no—
857C4×D4—118no—
858C4×D4—1116no—
859C4×D4—1116no—
860C4×D4—118no—
861C4×D4C22×D1118yes—
862#117—118no—
863#117—118no—
864#117—118no—
865#117—1116no—
866#117—118no—
867#117—1116no—
868#117—1116no—
869#117—1116no—
870#117—118no—
871#117C22×D1118yes—
872C2×C4⋊C4—111no—
873C2×C4⋊C4—111no—
874C2×C4⋊C4—111no—
875C2×C4⋊C4—111no—
876C2×C4⋊C4—112no—
877C2×C4⋊C4—112no—
878C2×C4⋊C4—112no—
879C2×C4⋊C4—112no—
880C2×C4⋊C4—112no—
881C2×C4⋊C4—1116no—
882C2×C4⋊C4—118no—
883C2×C4⋊C4—111no—
884C2×C4⋊C4—111no—
885C2×C4⋊C4—112no—
886C2×C4⋊C4—112no—
887C2×C4⋊C4—112no—
888C2×C4⋊C4—111no—
889C2×C4⋊C4—112no—
890C2×C4⋊C4—111no—
891C2×C4⋊C4—112no—
892C2×C4⋊C4—111no—
893C2×C4⋊C4—112no—
894C2×C4⋊C4—112no—
895C2×C4⋊C4—111no—
896C2×C4⋊C4—111no—
897C2×C4⋊C4—111no—
898C2×C4⋊C4—112no—
899C2×C4⋊C4—112no—
900C2×C4⋊C4—112no—
901C2×C4⋊C4—112no—
902C2×C4⋊C4—112no—
903C2×C4⋊C4—112no—
904C2×C4⋊C4—112no—
905C2×C4⋊C4—118no—
906C2×C4⋊C4C22×D1111yescharacteristic
907C2×C4⋊C4C22×D1111yescharacteristic
908C2×C4⋊C4C22×D1112yes—
909C2×C4⋊C4C22×D1111yescharacteristic
910C2×C4⋊C4C22×D1111yescharacteristic
911C2×C4⋊C4C22×D1112yes—
912C2×C4⋊C4C22×D1112yes—
913C2×C22⋊C4—112no—
914C2×C22⋊C4—111no—
915C2×C22⋊C4—112no—
916C2×C22⋊C4—111no—
917C2×C22⋊C4—112no—
918C2×C22⋊C4—112no—
919C2×C22⋊C4—112no—
920C2×C22⋊C4—111no—
921C2×C22⋊C4—112no—
922C2×C22⋊C4—111no—
923C2×C22⋊C4—112no—
924C2×C22⋊C4—112no—
925C2×C22⋊C4—111no—
926C2×C22⋊C4—112no—
927C2×C22⋊C4—111no—
928C2×C22⋊C4—111no—
929C2×C22⋊C4—112no—
930C2×C22⋊C4—111no—
931C2×C22⋊C4C22×D1112yes—
932C2×C22⋊C4C22×D1112yes—
933C2×C22⋊C4C22×D1112yes—
934C2×C22⋊C4C22×D1111yescharacteristic
935C2×C22⋊C4C22×D1111yescharacteristic
936C2×C22⋊C4C22×D1112yes—
937C2×C22⋊C4C22×D1112yes—
938C2×C42—112no—
939C2×C42—112no—
940C2×C42—112no—
941C2×C42—112no—
942C2×C42—111no—
943C2×C42—111no—
944C2×C42—112no—
945C2×C42—112no—
946C2×C42—111no—
947C2×C42—111no—
948C2×C42—118no—
949C2×C42C22×D1111yescharacteristic
950C2×C42C22×D1111yescharacteristic
951C2×C42C22×D1112yes—
952C2×C11—42no—
953C2×C11—44no—
954C2×C11#356514yescomplemented
955C2×C11C22×2−1+411yescharacteristic
956C2×C11C2×#58511yescharacteristic
957C2×C11C2×#58511yescharacteristic
958D11—42no—
959D11—42no—
960C24—111no—
961C24—111no—
962C24C23×D1111yescharacteristic
963C24C23×D1112yes—
964C2×Q8—24no—
965C2×Q8—44no—
966C2×Q8—114no—
967C2×Q8—118no—
968C2×Q8—118no—
969C2×Q8—118no—
970C2×Q8—442no—
971C2×Q8—444no—
972C2×Q8—444no—
973C2×Q8—444no—
974C2×Q8C23×D1114yes—
975C2×Q8C23×D1118yes—
976C2×D4—24no—
977C2×D4—44no—
978C2×D4—114no—
979C2×D4—114no—
980C2×D4—118no—
981C2×D4—118no—
982C2×D4—114no—
983C2×D4—442no—
984C2×D4—444no—
985C2×D4—442no—
986C2×D4—442no—
987C2×D4—444no—
988C2×D4C23×D1114yes—
989C2×D4C23×D1118yes—
990C22×C4—24no—
991C22×C4—44no—
992C22×C4—111no—
993C22×C4—111no—
994C22×C4—111no—
995C22×C4—111no—
996C22×C4—112no—
997C22×C4—112no—
998C22×C4—111no—
999C22×C4—112no—
1000C22×C4—112no—
1001C22×C4—111no—
1002C22×C4—118no—
1003C22×C4—118no—
1004C22×C4—118no—
1005C22×C4—114no—
1006C22×C4—114no—
1007C22×C4—114no—
1008C22×C4—114no—
1009C22×C4—118no—
1010C22×C4—224no—
1011C22×C4—224no—
1012C22×C4—444no—
1013C22×C4—442no—
1014C22×C4—442no—
1015C22×C4—444no—
1016C22×C4—444no—
1017C22×C4—444no—
1018C22×C4C23×D1114yes—
1019C22×C4C23×D1112yes—
1020C22×C4C23×D1112yes—
1021C22×C4C23×D1111yescharacteristic
1022C22×C4C23×D1111yescharacteristic
1023C22×C4C23×D1111yescharacteristic
1024C22×C4C23×D1112yes—
1025C22×C4C23×D1111yescharacteristic
1026C22×C4C23×D1111yescharacteristic
1027C22×C4C23×D1118yes—
1028C22×C4C23×D1111yescharacteristic
1029C4⋊C4—114no—
1030C4⋊C4—114no—
1031C4⋊C4—114no—
1032C4⋊C4—114no—
1033C4⋊C4—118no—
1034C4⋊C4—118no—
1035C4⋊C4—118no—
1036C4⋊C4—118no—
1037C4⋊C4—118no—
1038C4⋊C4—114no—
1039C4⋊C4—114no—
1040C4⋊C4—118no—
1041C4⋊C4—118no—
1042C4⋊C4—118no—
1043C4⋊C4—114no—
1044C4⋊C4—118no—
1045C4⋊C4—114no—
1046C4⋊C4—118no—
1047C4⋊C4—114no—
1048C4⋊C4—118no—
1049C4⋊C4—118no—
1050C4⋊C4—114no—
1051C4⋊C4—114no—
1052C4⋊C4—114no—
1053C4⋊C4—118no—
1054C4⋊C4—118no—
1055C4⋊C4—118no—
1056C4⋊C4—118no—
1057C4⋊C4—118no—
1058C4⋊C4—118no—
1059C4⋊C4—118no—
1060C4⋊C4C23×D1114yes—
1061C4⋊C4C23×D1114yes—
1062C4⋊C4C23×D1118yes—
1063C4⋊C4C23×D1114yes—
1064C4⋊C4C23×D1114yes—
1065C4⋊C4C23×D1118yes—
1066C4⋊C4C23×D1118yes—
1067C22⋊C4—118no—
1068C22⋊C4—114no—
1069C22⋊C4—118no—
1070C22⋊C4—114no—
1071C22⋊C4—118no—
1072C22⋊C4—118no—
1073C22⋊C4—118no—
1074C22⋊C4—114no—
1075C22⋊C4—118no—
1076C22⋊C4—114no—
1077C22⋊C4—118no—
1078C22⋊C4—118no—
1079C22⋊C4—114no—
1080C22⋊C4—118no—
1081C22⋊C4—114no—
1082C22⋊C4—114no—
1083C22⋊C4—118no—
1084C22⋊C4—114no—
1085C22⋊C4C23×D1118yes—
1086C22⋊C4C23×D1118yes—
1087C22⋊C4C23×D1118yes—
1088C22⋊C4C23×D1114yes—
1089C22⋊C4C23×D1114yes—
1090C22⋊C4C23×D1118yes—
1091C22⋊C4C23×D1118yes—
1092C42—114no—
1093C42—114no—
1094C42—114no—
1095C42—118no—
1096C42—118no—
1097C42—118no—
1098C42—118no—
1099C42—114no—
1100C42—118no—
1101C42—118no—
1102C42C23×D1114yes—
1103C42C23×D1114yes—
1104C42C23×D1118yes—
1105C11C2×#356511yescharacteristic, complemented, Sylow
1106C23—22no—
1107C23—24no—
1108C23—24no—
1109C23—22no—
1110C23—22no—
1111C23—24no—
1112C23—112no—
1113C23—112no—
1114C23—222no—
1115C23—222no—
1116C23—222no—
1117C23—222no—
1118C23—222no—
1119C23—222no—
1120C23C24×D1112yes—
1121C23C24×D1114yes—
1122C23C24×D1111yescharacteristic
1123Q8—28no—
1124Q8—48no—
1125Q8—444no—
1126Q8—448no—
1127Q8—448no—
1128Q8—448no—
1129D4—28no—
1130D4—48no—
1131D4—444no—
1132D4—448no—
1133D4—444no—
1134D4—444no—
1135D4—448no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—28no—
1145C2×C4—48no—
1146C2×C4—112no—
1147C2×C4—112no—
1148C2×C4—112no—
1149C2×C4—112no—
1150C2×C4—114no—
1151C2×C4—112no—
1152C2×C4—114no—
1153C2×C4—114no—
1154C2×C4—114no—
1155C2×C4—112no—
1156C2×C4—222no—
1157C2×C4—222no—
1158C2×C4—224no—
1159C2×C4—222no—
1160C2×C4—222no—
1161C2×C4—222no—
1162C2×C4—222no—
1163C2×C4—224no—
1164C2×C4—224no—
1165C2×C4—224no—
1166C2×C4—228no—
1167C2×C4—228no—
1168C2×C4—448no—
1169C2×C4—444no—
1170C2×C4—444no—
1171C2×C4—448no—
1172C2×C4—448no—
1173C2×C4—448no—
1174C2×C4#6704314yes—
1175C2×C4C24×D1114yes—
1176C2×C4C24×D1114yes—
1177C2×C4C24×D1112yes—
1178C2×C4C24×D1112yes—
1179C2×C4C24×D1112yes—
1180C2×C4C24×D1114yes—
1181C2×C4C24×D1112yes—
1182C2×C4C24×D1112yes—
1183C2×C4C24×D1112yes—
1184C22—22no—
1185C22—24no—
1186C22—24no—
1187C22—22no—
1188C22—22no—
1189C22—24no—
1190C22—44no—
1191C22—48no—
1192C22—222no—
1193C22—222no—
1194C22—222no—
1195C22—222no—
1196C22—222no—
1197C22—222no—
1198C22—444no—
1199C22—444no—
1200C22C2×#6704312yes—
1201C22#1062345512yes—
1202C22#1062345712yes—
1203C22C25×D1111yescharacteristic
1204C4—22no—
1205C4—24no—
1206C4—22no—
1207C4—24no—
1208C4—22no—
1209C4—24no—
1210C4—22no—
1211C4—22no—
1212C4—222no—
1213C4—222no—
1214C4—222no—
1215C4—224no—
1216C4—222no—
1217C4—222no—
1218C4—222no—
1219C4—224no—
1220C4—224no—
1221C4—224no—
1222C4C2×#6704314yes—
1223C2—42no—
1224C2—44no—
1225C2—442no—
1226C2—442no—
1227C2#1308326714yesdirect product factor
1228C2C22×#6704311yescharacteristic
1229C2C2×#1062345511yescharacteristic
1230C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#542C2
socleC23×C11C25
hypercenterC2×#542D11
hypocenterC11C2×#3565
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #13083267C2direct (N × H)
2. C2×#10623177C2semidirect
3. C2×#10623215C2semidirect
4. C2×#10623100C2semidirect
5. C2×#10623115C2semidirect
6. C2×#10623202C2semidirect
7. C2×#10623147C2semidirect
8. C2×#10623074C2semidirect
9. C2×#10623149C2semidirect
10. C2×#10623089C2semidirect
11. C2×#10623173C2semidirect
12. C2×#10623173C2semidirect
13. C2×#10623170C2semidirect
14. C2×#10623050C2semidirect
15. C2×#10623260C2semidirect
16. C2×#10623213C2semidirect
17. C2×#10623193C2semidirect
18. C2×#10623241C2semidirect
19. C2×#10623232C2semidirect
20. C2×#10623196C2semidirect
21. C2×#10623259C2semidirect
22. C2×#10623211C2semidirect
23. C2×#10623059C2semidirect
24. C2×C11×#542C2semidirect
25. C11×#542C22semidirect
61. #10623260C22semidirect
62. #10623259C22semidirect
63. #10623241C22semidirect
64. #10623232C22semidirect
65. #10623215C22semidirect
66. #10623213C22semidirect
67. #10623211C22semidirect
68. #10623202C22semidirect
69. #10623196C22semidirect
70. #10623193C22semidirect
71. #10623177C22semidirect
72. #10623173C22semidirect
73. #10623173C22semidirect
74. #10623170C22semidirect
75. #10623149C22semidirect
76. #10623147C22semidirect
77. #10623115C22semidirect
78. #10623100C22semidirect
79. #10623089C22semidirect
80. #10623074C22semidirect
81. #10623059C22semidirect
82. #10623050C22semidirect
509. C2×#542D11semidirect
610. #542C2×D11semidirect
954. C2×C11#3565semidirect
1105. C11C2×#3565semidirect
1227. C2#13083267direct (N × H)

Maximal subgroups

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

subgroupindex
#130832672
C2×#106231772
C2×#106232152
C2×#106231002
C2×#106231152
C2×#106232022
C2×#106231472
C2×#106230742
C2×#106231492
C2×#106230892
C2×#106231732
C2×#106231702
C2×#106230502
C2×#106232602
C2×#106232132
C2×#106231932
C2×#106232412
C2×#106232322
C2×#106231962
C2×#106232592
C2×#106232112
C2×#106230592
C2×C11×#5422
C2×#356511