Finite Group Databasebeta

← C2×#13082755 #15660665

Subgroups — C2×#13082755 #15660665

Order 2816.

7418 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082755C2132yesmaximal, direct product factor
2C2×#10623230C211yesmaximal, characteristic, complemented
3C2×#10623243C212yesmaximal, complemented
4C2×#10623231C211yesmaximal, characteristic, complemented
5C2×#10623198C212yesmaximal, complemented
6C2×#10623178C212yesmaximal, complemented
7C2×#10623215C211yesmaximal, characteristic, complemented
8C2×#10623214C211yesmaximal, characteristic, complemented
9C2×#10623242C212yesmaximal, complemented
10C2×#10623197C212yesmaximal, complemented
11C2×#10623151C212yesmaximal, complemented
12C2×#10623008C211yesmaximal, characteristic, complemented
13C2×#10623079C212yesmaximal, complemented
14C2×#10623111C212yesmaximal, complemented
15C2×#10623010C211yesmaximal, characteristic, complemented
16C2×#10623059C212yesmaximal, complemented
17C2×#10623055C212yesmaximal, complemented
18C2×#10623078C212yesmaximal, complemented
19C2×#10623078C212yesmaximal, complemented
20C2×C11×#529C211yesmaximal, characteristic, complemented
21C22×#4339C2211yescharacteristic
22C22×#4339C2212yes—
23C22×#4339C2211yescharacteristic, complemented
24C23×C4×D11C2212yescomplemented
25C11×#529C22116yescomplemented
26C2×C11×#126C2212yescomplemented
27C2×C11×#125C2211yescharacteristic, complemented
28C2×C11×#124C2211yescharacteristic
29C2×C11×#123C2212yescomplemented
30C2×C11×C22⋊Q8C2211yescharacteristic, complemented
31C2×C11×#121C2211yescharacteristic
32C2×C4×Q8×C11C2211yescharacteristic, complemented
33C2×C4×D4×C11C2211yescharacteristic
34C2×C4×D4×C11C2212yescomplemented
35C2×C11×#117C2212yescomplemented
36C22×C42×C11C2211yescharacteristic, complemented
37C2×#67000C2212yes—
38C2×#66999C2212yescomplemented
39C2×#66993C2212yes—
40C2×#66992C2212yes—
41C2×#66992C2212yes—
42C2×#66991C2212yescomplemented
43C2×#66990C2212yes—
44C2×#66990C2212yescomplemented
45C2×#66983C2211yescharacteristic
46C2×#66983C2212yescomplemented
47C2×#66983C2212yescomplemented
48C2×#66982C2212yescomplemented
49C2×C4×C22⋊D11C2212yes—
50C2×C4×C22⋊D11C2212yescomplemented
51C2×C4×C22⋊D11C2212yescomplemented
52C2×#66977C2211yescharacteristic, complemented
53#10623243C22132yescomplemented
54#10623242C22132yescomplemented
55#10623231C22116yescomplemented
56#10623230C22116yescomplemented
57#10623215C22116yescomplemented
58#10623214C22116yescomplemented
59#10623198C22132yescomplemented
60#10623197C22132yescomplemented
61#10623178C22132yescomplemented
62#10623151C22132yescomplemented
63#10623111C22132yescomplemented
64#10623079C22132yescomplemented
65#10623078C22132yescomplemented
66#10623078C22132yescomplemented
67#10623059C22132yescomplemented
68#10623055C22132yescomplemented
69C2×#66951C2212yescomplemented
70C2×#66951C2212yescomplemented
71C2×#66951C2212yescomplemented
72C2×#66950C2212yescomplemented
73C2×#66950C2212yescomplemented
74C2×#66949C2212yescomplemented
75C2×#66949C2212yescomplemented
76C2×#66949C2212yescomplemented
77C2×#66948C2212yes—
78C2×#66948C2212yes—
79C2×#66948C2212yes—
80C2×#66948C2212yescomplemented
81C2×#66947C2212yes—
82C2×#66947C2212yescomplemented
83C2×#66947C2212yescomplemented
84C2×#66947C2212yescomplemented
85C2×#66947C2212yescomplemented
86C2×#66943C2212yescomplemented
87C2×#66942C2212yescomplemented
88C2×#66941C2212yescomplemented
89C2×#66939C2212yes—
90C2×#66939C2212yescomplemented
91C2×#66938C2212yes—
92C2×#66938C2212yes—
93C2×#66938C2212yescomplemented
94C2×#66937C2212yes—
95C2×#66937C2212yes—
96C2×#66937C2212yes—
97C2×#66937C2212yescomplemented
98C2×#66937C2212yescomplemented
99C2×#66936C2212yes—
100C2×#66936C2212yescomplemented
101C2×#66936C2212yescomplemented
102C2×#66935C2212yes—
103C2×#66935C2212yes—
104C2×#66935C2212yescomplemented
105C2×#66935C2212yescomplemented
106C2×#66932C2212yescomplemented
107C2×#66931C2212yescomplemented
108C2×#66931C2212yescomplemented
109#10623010C22116yescomplemented
110C2×#66929C2212yescomplemented
111#10623008C22116yescomplemented
112C2×#66928C2211yescharacteristic
113C2×#66928C2211yescharacteristic
114C2×#66928C2211yescharacteristic, complemented
115C2×#66927C2211yescharacteristic
116C2×C4×D44C2212yes—
117C2×C4×D44C2211yescharacteristic
118C2×C4×D44C2212yescomplemented
119C2×C4×D44C2212yescomplemented
120C2×C4×D44C2212yescomplemented
121C2×#66925C2212yescomplemented
122C2×#66925C2212yescomplemented
123C2×C42×D11C2212yescomplemented
124C2×#66923C2211yescharacteristic, complemented
125C2×#66922C2211yescharacteristic, complemented
126C2×C4×Dic22C2211yescharacteristic, complemented
127C24×D11C2312yes—
128C22×Q8×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C23×C4×C11C2312yes—
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2311yescharacteristic
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2312yes—
142C23×Dic11C2312yes—
143C2×#4339—44no—
144C2×#4339—48no—
145C2×#4339—44no—
146C2×#4339C2318yes—
147C2×#4339C23116yes—
148C2×#4339C2318yescomplemented
149C22×D44C2311yescharacteristic
150C22×D44C2312yes—
151C22×D44C2312yes—
152C22×D44C2312yes—
153C22×D44C2312yes—
154C22×D44C2311yescharacteristic
155C22×D44C2311yescharacteristic
156C22×D44C2312yes—
157C22×C4×D11—48no—
158C22×C4×D11C2312yes—
159C22×C4×D11C2312yes—
160C22×C4×D11C2312yes—
161C22×C4×D11C2312yes—
162C22×C4×D11C2312yes—
163C22×C4×D11C2312yes—
164C22×C4×D11C2312yes—
165C22×C4×D11C23116yescomplemented
166C22×Dic22C2311yescharacteristic
167C22×Dic22C2311yescharacteristic
168C22×Dic22C2311yescharacteristic
169C22×Dic22C2312yes—
170C11×#126C23116yescomplemented
171C11×#125C2318yescomplemented
172C11×#124C2318yes—
173C11×#123C23116yescomplemented
174C11×C22⋊Q8C2318yescomplemented
175C11×#121C2318yes—
176C4×Q8×C11C2318yescomplemented
177C4×D4×C11C2318yes—
178C4×D4×C11C23116yescomplemented
179C11×#117C23116yescomplemented
180C2×C11×C4⋊C4C2312yes—
181C2×C11×C4⋊C4C2312yes—
182C2×C11×C4⋊C4C2312yes—
183C2×C11×C4⋊C4C2311yescharacteristic
184C2×C11×C4⋊C4C2311yescharacteristic
185C2×C11×C4⋊C4C2312yes—
186C2×C11×C22⋊C4C2312yes—
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2312yes—
191C2×C42×C11C2311yescharacteristic
192C2×C42×C11C2311yescharacteristic
193C2×C42×C11C2311yescharacteristic
194C2×C42×C11C2312yes—
195C2×C42×C11C2311yescharacteristic
196C2×C42×C11C2318yescomplemented
197C2×C22⋊Dic11C2312yes—
198C2×C22⋊Dic11C2312yes—
199C2×C22⋊Dic11C2312yes—
200#67000C23116yes—
201#66999C23116yescomplemented
202#66993C23116yes—
203#66992C23116yes—
204#66992C23116yes—
205#66991C23116yescomplemented
206#66990C23116yes—
207#66990C23116yescomplemented
208#66983C2318yes—
209#66983C23116yescomplemented
210#66983C23116yescomplemented
211#66982C23116yescomplemented
212C4×C22⋊D11C23116yes—
213C4×C22⋊D11C23116yescomplemented
214C4×C22⋊D11C23116yescomplemented
215C2×(C2×D11)⋊C4C2312yes—
216C2×(C2×D11)⋊C4C2312yes—
217C2×(C2×D11)⋊C4C2312yes—
218C2×(C2×D11)⋊C4C2312yes—
219C2×(C2×D11)⋊C4C2312yes—
220C2×(C2×D11)⋊C4C2312yes—
221C2×(C2×D11)⋊C4C2312yes—
222C2×(C2×D11)⋊C4C2312yes—
223C2×(C2×D11)⋊C4C2312yes—
224C2×(C2×D11)⋊C4C2312yes—
225C2×(C2×D11)⋊C4C2312yes—
226C2×(C2×D11)⋊C4C2312yes—
227C2×(C2×D11)⋊C4C2312yes—
228C2×(C2×D11)⋊C4C2312yes—
229C2×(C2×D11)⋊C4C2312yes—
230C2×(C2×D11)⋊C4C2312yes—
231C2×C4⋊Dic11C2311yescharacteristic
232C2×C4⋊Dic11C2312yes—
233C2×C4⋊Dic11C2312yes—
234C2×C4⋊Dic11C2311yescharacteristic
235C2×C4⋊Dic11C2312yes—
236C2×C4⋊Dic11C2312yes—
237#66977C2318yescomplemented
238C2×Dic11⋊C4C2312yes—
239C2×Dic11⋊C4C2312yes—
240C2×Dic11⋊C4C2312yes—
241C2×Dic11⋊C4C2312yes—
242C2×Dic11⋊C4C2312yes—
243C2×Dic11⋊C4C2312yes—
244C2×Dic11⋊C4C2312yes—
245C2×Dic11⋊C4C2312yes—
246C2×C4×Dic11C2312yes—
247C2×C4×Dic11C2312yes—
248C2×C4×Dic11C2312yes—
249#66951C23116yescomplemented
250#66951C23116yescomplemented
251#66951C23116yescomplemented
252#66950C23116yescomplemented
253#66950C23116yescomplemented
254#66949C23116yescomplemented
255#66949C23116yescomplemented
256#66949C23116yescomplemented
257#66948C23116yes—
258#66948C23116yes—
259#66948C23116yes—
260#66948C23116yescomplemented
261#66947C23116yes—
262#66947C23116yescomplemented
263#66947C23116yescomplemented
264#66947C23116yescomplemented
265#66947C23116yescomplemented
266#66943C23116yescomplemented
267#66942C23116yescomplemented
268#66941C23116yescomplemented
269#66939C23116yes—
270#66939C23116yescomplemented
271#66938C23116yes—
272#66938C23116yes—
273#66938C23116yescomplemented
274#66937C23116yes—
275#66937C23116yes—
276#66937C23116yes—
277#66937C23116yescomplemented
278#66937C23116yescomplemented
279#66936C23116yes—
280#66936C23116yescomplemented
281#66936C23116yescomplemented
282#66935C23116yes—
283#66935C23116yes—
284#66935C23116yescomplemented
285#66935C23116yescomplemented
286#66932C23116yescomplemented
287#66931C23116yescomplemented
288#66931C23116yescomplemented
289#66929C23116yescomplemented
290#66928C2318yes—
291#66928C2318yes—
292#66928C2318yescomplemented
293#66927C2318yes—
294C4×D44C2318yes—
295C4×D44C23116yes—
296C4×D44C23116yescomplemented
297C4×D44C23116yescomplemented
298C4×D44C23116yescomplemented
299#66925C23116yescomplemented
300#66925C23116yescomplemented
301C42×D11C23116yescomplemented
302#66923C2318yescomplemented
303#66922C2318yescomplemented
304C4×Dic22C2318yescomplemented
305C2×#3529—111nomaximal, Sylow
306C24×C11C2412yes—
307C24×C11C2411yescharacteristic
308C23×D11—44no—
309C23×D11—44no—
310C23×D11—44no—
311C23×D11C2412yes—
312C23×D11C2412yes—
313C23×D11C2412yes—
314C23×D11C2418yes—
315C2×Q8×C11—42no—
316C2×Q8×C11C2414yes—
317C2×D4×C11—44no—
318C2×D4×C11—42no—
319C2×D4×C11C2414yes—
320C2×D4×C11C2418yes—
321C22×C4×C11—28no—
322C22×C4×C11—24no—
323C22×C4×C11—42no—
324C22×C4×C11—42no—
325C22×C4×C11C2412yes—
326C22×C4×C11C2412yes—
327C22×C4×C11C2411yescharacteristic
328C22×C4×C11C2411yescharacteristic
329C22×C4×C11C2411yescharacteristic
330C22×C4×C11C2411yescharacteristic
331C22×C4×C11C2412yes—
332C22×C4×C11C2411yescharacteristic
333C22×C4×C11C2418yes—
334C22×C4×C11C2414yes—
335C22×C4×C11C2414yes—
336C22×C4×C11C2414yes—
337C22×C4×C11C2411yescharacteristic
338C2×C22⋊D11—44no—
339C2×C22⋊D11—44no—
340C2×C22⋊D11—44no—
341C2×C22⋊D11—44no—
342C2×C22⋊D11—44no—
343C2×C22⋊D11—44no—
344C2×C22⋊D11—44no—
345C2×C22⋊D11C2418yes—
346C2×C22⋊D11C2418yes—
347C2×C22⋊D11C2418yes—
348C2×C22⋊D11C2418yes—
349C2×C22⋊D11C2418yes—
350C2×C22⋊D11C2418yes—
351C2×C22⋊D11C2418yes—
352C22×Dic11—44no—
353C22×Dic11C2412yes—
354C22×Dic11C2412yes—
355C22×Dic11C2412yes—
356C22×Dic11C2412yes—
357C22×Dic11C2412yes—
358C22×Dic11C2418yes—
359#4339—432no—
360#4339—416no—
361#4339—416no—
362C2×D44—42no—
363C2×D44—44no—
364C2×D44—44no—
365C2×D44—44no—
366C2×D44—44no—
367C2×D44—42no—
368C2×D44—42no—
369C2×D44—44no—
370C2×D44C2414yes—
371C2×D44C2418yes—
372C2×D44C2418yes—
373C2×D44C2418yes—
374C2×D44C2418yes—
375C2×D44C2414yes—
376C2×D44C2414yes—
377C2×D44C2418yes—
378C2×C4×D11—28no—
379C2×C4×D11—28no—
380C2×C4×D11—28no—
381C2×C4×D11—44no—
382C2×C4×D11—44no—
383C2×C4×D11—44no—
384C2×C4×D11—44no—
385C2×C4×D11—432no—
386C2×C4×D11C2418yes—
387C2×C4×D11C2418yes—
388C2×C4×D11C2418yes—
389C2×C4×D11C2418yes—
390C2×C4×D11C2418yes—
391C2×C4×D11C2418yes—
392C2×C4×D11C2418yes—
393C2×Dic22—42no—
394C2×Dic22—42no—
395C2×Dic22—42no—
396C2×Dic22—44no—
397C2×Dic22C2414yes—
398C2×Dic22C2414yes—
399C2×Dic22C2414yes—
400C2×Dic22C2418yes—
401C11×C4⋊C4C2418yes—
402C11×C4⋊C4C2418yes—
403C11×C4⋊C4C2418yes—
404C11×C4⋊C4C2414yes—
405C11×C4⋊C4C2414yes—
406C11×C4⋊C4C2418yes—
407C11×C22⋊C4C2418yes—
408C11×C22⋊C4C2418yes—
409C11×C22⋊C4C2418yes—
410C11×C22⋊C4C2418yes—
411C11×C22⋊C4C2418yes—
412C42×C11C2414yes—
413C42×C11C2414yes—
414C42×C11C2414yes—
415C42×C11C2418yes—
416C42×C11C2414yes—
417C22⋊Dic11C2418yes—
418C22⋊Dic11C2418yes—
419C22⋊Dic11C2418yes—
420(C2×D11)⋊C4C2418yes—
421(C2×D11)⋊C4C2418yes—
422(C2×D11)⋊C4C2418yes—
423(C2×D11)⋊C4C2418yes—
424(C2×D11)⋊C4C2418yes—
425(C2×D11)⋊C4C2418yes—
426(C2×D11)⋊C4C2418yes—
427(C2×D11)⋊C4C2418yes—
428(C2×D11)⋊C4C2418yes—
429(C2×D11)⋊C4C2418yes—
430(C2×D11)⋊C4C2418yes—
431(C2×D11)⋊C4C2418yes—
432(C2×D11)⋊C4C2418yes—
433(C2×D11)⋊C4C2418yes—
434(C2×D11)⋊C4C2418yes—
435(C2×D11)⋊C4C2418yes—
436C4⋊Dic11C2414yes—
437C4⋊Dic11C2418yes—
438C4⋊Dic11C2418yes—
439C4⋊Dic11C2414yes—
440C4⋊Dic11C2418yes—
441C4⋊Dic11C2418yes—
442Dic11⋊C4C2418yes—
443Dic11⋊C4C2418yes—
444Dic11⋊C4C2418yes—
445Dic11⋊C4C2418yes—
446Dic11⋊C4C2418yes—
447Dic11⋊C4C2418yes—
448Dic11⋊C4C2418yes—
449Dic11⋊C4C2418yes—
450C4×Dic11C2418yes—
451C4×Dic11C2418yes—
452C4×Dic11C2418yes—
453#3529—1132no—
454C2×#563—112no—
455C2×#563—111no—
456C2×#562—111no—
457C2×#562—111no—
458C2×#562—112no—
459C2×#562—112no—
460C2×H(3,𝔽4)—111no—
461C2×#560—112no—
462C2×#560—112no—
463C2×#560—112no—
464C2×#532—111no—
465C2×#532—112no—
466C2×#529—111no—
467C2×#529—112no—
468C2×#529—112no—
469C2×#529D1111yescharacteristic, complemented
470C2×#525—112no—
471C2×#525—112no—
472C2×#525—112no—
473C23×C11—24no—
474C23×C11—22no—
475C23×C11—22no—
476C23×C11—24no—
477C23×C11—24no—
478C23×C11—22no—
479C23×C11C2514yes—
480C23×C11C2512yes—
481C23×C11C2511yescharacteristic
482C22×D11—24no—
483C22×D11—24no—
484C22×D11—24no—
485C22×D11—24no—
486C22×D11—24no—
487C22×D11—24no—
488C22×D11—24no—
489C22×D11—24no—
490C22×D11—24no—
491C22×D11—48no—
492C22×D11—48no—
493C22×D11—48no—
494C22×D11—432no—
495C22×D11C2514yes—
496C22×D11C2514yes—
497C22×D11C2514yes—
498Q8×C11—44no—
499D4×C11—44no—
500D4×C11—48no—
501C2×C4×C11—22no—
502C2×C4×C11—24no—
503C2×C4×C11—22no—
504C2×C4×C11—24no—
505C2×C4×C11—24no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—216no—
510C2×C4×C11—28no—
511C2×C4×C11—44no—
512C2×C4×C11—44no—
513C2×C4×C11H(5,𝔽2)14yes—
514C2×C4×C11C2514yes—
515C2×C4×C11C2514yes—
516C2×C4×C11C2512yes—
517C2×C4×C11C2512yes—
518C2×C4×C11C2512yes—
519C2×C4×C11C2512yes—
520C2×C4×C11C2514yes—
521C2×C4×C11C2512yes—
522C2×C4×C11C2512yes—
523C22⋊D11—48no—
524C22⋊D11—48no—
525C22⋊D11—48no—
526C22⋊D11—48no—
527C22⋊D11—48no—
528C22⋊D11—48no—
529C22⋊D11—48no—
530C2×Dic11—24no—
531C2×Dic11—24no—
532C2×Dic11—24no—
533C2×Dic11—24no—
534C2×Dic11—24no—
535C2×Dic11—48no—
536C2×Dic11C2514yes—
537C2×Dic11C2514yes—
538C2×Dic11C2514yes—
539C2×Dic11C2514yes—
540C2×Dic11C2514yes—
541D44—44no—
542D44—48no—
543D44—48no—
544D44—48no—
545D44—48no—
546D44—44no—
547D44—44no—
548D44—48no—
549C4×D11—216no—
550C4×D11—216no—
551C4×D11—216no—
552C4×D11—48no—
553C4×D11—48no—
554C4×D11—48no—
555C4×D11—48no—
556Dic22—44no—
557Dic22—44no—
558Dic22—48no—
559Dic22—44no—
560C22×#41—111no—
561C22×#41—112no—
562C22×#41—111no—
563C24×C4—112no—
564#563—1132no—
565#563—1116no—
566#562—1116no—
567#562—1116no—
568#562—1132no—
569#562—1132no—
570H(3,𝔽4)—1116no—
571#560—1132no—
572#560—1132no—
573#560—1132no—
574#532—1132no—
575#532—1116no—
576C2×C4⋊Q8—112no—
577C2×C4⋊Q8—111no—
578C2×#127—112no—
579C2×#127—111no—
580#529—1132no—
581#529—1132no—
582#529—1116no—
583#529C2×D11116yescomplemented
584C2×#126—112no—
585C2×#126—112no—
586C2×#126—112no—
587C2×#126—112no—
588C2×#126—112no—
589C2×#126C2×D1112yescomplemented
590C2×#125—112no—
591C2×#125—112no—
592C2×#125—111no—
593C2×#125C2×D1111yescharacteristic, complemented
594C2×#124—112no—
595C2×#124—112no—
596C2×#124—112no—
597C2×#124—112no—
598C2×#124—111no—
599C2×#124—111no—
600C2×#124—111no—
601C2×#124C2×D1111yescharacteristic
602#525—1132no—
603#525—1132no—
604#525—1132no—
605C2×#123—112no—
606C2×#123—112no—
607C2×#123—112no—
608C2×#123—112no—
609C2×#123—112no—
610C2×#123—112no—
611C2×#123—112no—
612C2×#123—112no—
613C2×#123—112no—
614C2×#123—112no—
615C2×#123—112no—
616C2×#123C2×D1112yescomplemented
617C2×C22⋊Q8—112no—
618C2×C22⋊Q8—111no—
619C2×C22⋊Q8—112no—
620C2×C22⋊Q8—112no—
621C2×C22⋊Q8—112no—
622C2×C22⋊Q8—112no—
623C2×C22⋊Q8—112no—
624C2×C22⋊Q8—112no—
625C2×C22⋊Q8—112no—
626C2×C22⋊Q8C2×D1111yescharacteristic, complemented
627C2×#121—112no—
628C2×#121—112no—
629C2×#121—112no—
630C2×#121—111no—
631C2×#121—112no—
632C2×#121—112no—
633C2×#121—112no—
634C2×#121—112no—
635C2×#121—112no—
636C2×#121—112no—
637C2×#121—112no—
638C2×#121—112no—
639C2×#121—112no—
640C2×#121—112no—
641C2×#121—112no—
642C2×#121C2×D1111yescharacteristic
643C2×#120—112no—
644C2×#120—112no—
645C2×#120—112no—
646C2×#120—112no—
647C2×#120—112no—
648C2×#120—112no—
649C2×C4×Q8—111no—
650C2×C4×Q8C2×D1111yescharacteristic, complemented
651C2×C4×D4—112no—
652C2×C4×D4—112no—
653C2×C4×D4—112no—
654C2×C4×D4—112no—
655C2×C4×D4—111no—
656C2×C4×D4—112no—
657C2×C4×D4—112no—
658C2×C4×D4—112no—
659C2×C4×D4C2×D1111yescharacteristic
660C2×C4×D4C2×D1112yescomplemented
661C2×#117—112no—
662C2×#117—112no—
663C2×#117C2×D1112yescomplemented
664C22×C42—112no—
665C22×C42C2×D1111yescharacteristic, complemented
666C22×C11—24no—
667C22×C11—22no—
668C22×C11—22no—
669C22×C11—22no—
670C22×C11—24no—
671C22×C11—24no—
672C22×C11—48no—
673C22×C11—44no—
674C22×C11C2×H(5,𝔽2)12yes—
675C22×C11#58512yes—
676C22×C11#58512yes—
677C22×C11C2611yescharacteristic
678C2×D11—24no—
679C2×D11—24no—
680C2×D11—24no—
681C2×D11—24no—
682C2×D11—24no—
683C2×D11—24no—
684C2×D11—24no—
685C2×D11—24no—
686C2×D11—24no—
687C2×D11—432no—
688C2×D11—48no—
689C2×D11—48no—
690C2×D11—48no—
691C4×C11—22no—
692C4×C11—24no—
693C4×C11—22no—
694C4×C11—22no—
695C4×C11—22no—
696C4×C11—22no—
697C4×C11—24no—
698C4×C11—24no—
699C4×C11C2×H(5,𝔽2)14yes—
700Dic11—24no—
701Dic11—24no—
702Dic11—24no—
703Dic11—24no—
704Dic11—24no—
705C25—112no—
706C2×#41—1116no—
707C2×#41—118no—
708C2×#41—118no—
709C2×#41—448no—
710C2×#41—444no—
711C2×#41—444no—
712C22×Q8—111no—
713C22×Q8—112no—
714C22×Q8—111no—
715C22×Q8—111no—
716C22×Q8C22×D1111yescharacteristic
717C22×D4—112no—
718C22×D4—112no—
719C22×D4—112no—
720C22×D4—112no—
721C22×D4—112no—
722C22×D4—112no—
723C22×D4—112no—
724C22×D4—112no—
725C22×D4—111no—
726C22×D4—112no—
727C22×D4—112no—
728C22×D4—112no—
729C22×D4—111no—
730C22×D4—112no—
731C22×D4—111no—
732C22×D4C22×D1111yescharacteristic
733C22×D4C22×D1112yes—
734C23×C4—112no—
735C23×C4—112no—
736C23×C4—112no—
737C23×C4—112no—
738C23×C4—112no—
739C23×C4—112no—
740C23×C4—112no—
741C23×C4—112no—
742C23×C4—1116no—
743C23×C4—448no—
744C23×C4C22×D1112yes—
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1111yescharacteristic
748C4⋊Q8—1116no—
749C4⋊Q8—118no—
750#127—1116no—
751#127—118no—
752#126—1116no—
753#126—1116no—
754#126—1116no—
755#126—1116no—
756#126—1116no—
757#126C22×D11116yescomplemented
758#125—1116no—
759#125—1116no—
760#125—118no—
761#125C22×D1118yescomplemented
762#124—1116no—
763#124—1116no—
764#124—1116no—
765#124—1116no—
766#124—118no—
767#124—118no—
768#124—118no—
769#124C22×D1118yes—
770#123—1116no—
771#123—1116no—
772#123—1116no—
773#123—1116no—
774#123—1116no—
775#123—1116no—
776#123—1116no—
777#123—1116no—
778#123—1116no—
779#123—1116no—
780#123—1116no—
781#123C22×D11116yescomplemented
782C22⋊Q8—1116no—
783C22⋊Q8—118no—
784C22⋊Q8—1116no—
785C22⋊Q8—1116no—
786C22⋊Q8—1116no—
787C22⋊Q8—1116no—
788C22⋊Q8—1116no—
789C22⋊Q8—1116no—
790C22⋊Q8—1116no—
791C22⋊Q8C22×D1118yescomplemented
792#121—1116no—
793#121—1116no—
794#121—1116no—
795#121—118no—
796#121—1116no—
797#121—1116no—
798#121—1116no—
799#121—1116no—
800#121—1116no—
801#121—1116no—
802#121—1116no—
803#121—1116no—
804#121—1116no—
805#121—1116no—
806#121—1116no—
807#121C22×D1118yes—
808#120—1116no—
809#120—1116no—
810#120—1116no—
811#120—1116no—
812#120—1116no—
813#120—1116no—
814C4×Q8—118no—
815C4×Q8C22×D1118yescomplemented
816C4×D4—1116no—
817C4×D4—1116no—
818C4×D4—1116no—
819C4×D4—1116no—
820C4×D4—118no—
821C4×D4—1116no—
822C4×D4—1116no—
823C4×D4—1116no—
824C4×D4C22×D1118yes—
825C4×D4C22×D11116yescomplemented
826#117—1116no—
827#117—1116no—
828#117C22×D11116yescomplemented
829C2×C4⋊C4—112no—
830C2×C4⋊C4—112no—
831C2×C4⋊C4—112no—
832C2×C4⋊C4—112no—
833C2×C4⋊C4—112no—
834C2×C4⋊C4—112no—
835C2×C4⋊C4—112no—
836C2×C4⋊C4—112no—
837C2×C4⋊C4—112no—
838C2×C4⋊C4—112no—
839C2×C4⋊C4—112no—
840C2×C4⋊C4—111no—
841C2×C4⋊C4—112no—
842C2×C4⋊C4—111no—
843C2×C4⋊C4C22×D1112yes—
844C2×C4⋊C4C22×D1112yes—
845C2×C4⋊C4C22×D1111yescharacteristic
846C2×C4⋊C4C22×D1112yes—
847C2×C4⋊C4C22×D1112yes—
848C2×C4⋊C4C22×D1111yescharacteristic
849C2×C22⋊C4—112no—
850C2×C22⋊C4—112no—
851C2×C22⋊C4—112no—
852C2×C22⋊C4—112no—
853C2×C22⋊C4—112no—
854C2×C22⋊C4—112no—
855C2×C22⋊C4—112no—
856C2×C22⋊C4—112no—
857C2×C22⋊C4—112no—
858C2×C22⋊C4—112no—
859C2×C22⋊C4—112no—
860C2×C22⋊C4—112no—
861C2×C22⋊C4—112no—
862C2×C22⋊C4—112no—
863C2×C22⋊C4—112no—
864C2×C22⋊C4—112no—
865C2×C22⋊C4—112no—
866C2×C22⋊C4—112no—
867C2×C22⋊C4—112no—
868C2×C22⋊C4C22×D1112yes—
869C2×C22⋊C4C22×D1112yes—
870C2×C22⋊C4C22×D1112yes—
871C2×C22⋊C4C22×D1112yes—
872C2×C22⋊C4C22×D1112yes—
873C2×C42—112no—
874C2×C42—112no—
875C2×C42—112no—
876C2×C42—1116no—
877C2×C42C22×D1111yescharacteristic
878C2×C42C22×D1111yescharacteristic
879C2×C42C22×D1111yescharacteristic
880C2×C42C22×D1112yes—
881C2×C42C22×D1111yescharacteristic
882C2×C42C22×D1118yescomplemented
883C2×C11—44no—
884C2×C11—42no—
885C2×C11#352914yescomplemented
886C2×C11C22×H(5,𝔽2)11yescharacteristic
887C2×C11C2×#58511yescharacteristic
888C2×C11C2×#58511yescharacteristic
889D11—44no—
890D11—44no—
891D11—44no—
892C24—112no—
893C24—112no—
894C24—112no—
895C24—118no—
896C24—444no—
897C24—444no—
898C24—444no—
899C24C23×D1112yes—
900C24C23×D1111yescharacteristic
901#41—4432no—
902#41—4416no—
903#41—4416no—
904C2×Q8—42no—
905C2×Q8—114no—
906C2×Q8—118no—
907C2×Q8—114no—
908C2×Q8—114no—
909C2×Q8—444no—
910C2×Q8—442no—
911C2×Q8—442no—
912C2×Q8—442no—
913C2×Q8C23×D1114yes—
914C2×D4—42no—
915C2×D4—44no—
916C2×D4—118no—
917C2×D4—118no—
918C2×D4—118no—
919C2×D4—118no—
920C2×D4—118no—
921C2×D4—118no—
922C2×D4—118no—
923C2×D4—118no—
924C2×D4—114no—
925C2×D4—118no—
926C2×D4—118no—
927C2×D4—118no—
928C2×D4—114no—
929C2×D4—118no—
930C2×D4—114no—
931C2×D4—444no—
932C2×D4—442no—
933C2×D4—442no—
934C2×D4—444no—
935C2×D4—444no—
936C2×D4—442no—
937C2×D4—444no—
938C2×D4—444no—
939C2×D4—444no—
940C2×D4—444no—
941C2×D4—444no—
942C2×D4—444no—
943C2×D4—444no—
944C2×D4—444no—
945C2×D4—444no—
946C2×D4C23×D1114yes—
947C2×D4C23×D1118yes—
948C22×C4—28no—
949C22×C4—24no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—112no—
953C22×C4—112no—
954C22×C4—112no—
955C22×C4—112no—
956C22×C4—112no—
957C22×C4—118no—
958C22×C4—118no—
959C22×C4—118no—
960C22×C4—118no—
961C22×C4—118no—
962C22×C4—118no—
963C22×C4—118no—
964C22×C4—118no—
965C22×C4—228no—
966C22×C4—228no—
967C22×C4—228no—
968C22×C4—4432no—
969C22×C4—444no—
970C22×C4—444no—
971C22×C4—444no—
972C22×C4—444no—
973C22×C4—444no—
974C22×C4C23×D1112yes—
975C22×C4C23×D1112yes—
976C22×C4C23×D1111yescharacteristic
977C22×C4C23×D1111yescharacteristic
978C22×C4C23×D1111yescharacteristic
979C22×C4C23×D1111yescharacteristic
980C22×C4C23×D1111yescharacteristic
981C22×C4C23×D1114yes—
982C22×C4C23×D1112yes—
983C22×C4C23×D1118yes—
984C22×C4C23×D1114yes—
985C22×C4C23×D1114yes—
986C22×C4C23×D1111yescharacteristic
987C4⋊C4—118no—
988C4⋊C4—118no—
989C4⋊C4—118no—
990C4⋊C4—118no—
991C4⋊C4—118no—
992C4⋊C4—118no—
993C4⋊C4—118no—
994C4⋊C4—118no—
995C4⋊C4—118no—
996C4⋊C4—118no—
997C4⋊C4—118no—
998C4⋊C4—114no—
999C4⋊C4—118no—
1000C4⋊C4—114no—
1001C4⋊C4C23×D1118yes—
1002C4⋊C4C23×D1118yes—
1003C4⋊C4C23×D1114yes—
1004C4⋊C4C23×D1118yes—
1005C4⋊C4C23×D1118yes—
1006C4⋊C4C23×D1114yes—
1007C22⋊C4—118no—
1008C22⋊C4—118no—
1009C22⋊C4—118no—
1010C22⋊C4—118no—
1011C22⋊C4—118no—
1012C22⋊C4—118no—
1013C22⋊C4—118no—
1014C22⋊C4—118no—
1015C22⋊C4—118no—
1016C22⋊C4—118no—
1017C22⋊C4—118no—
1018C22⋊C4—118no—
1019C22⋊C4—118no—
1020C22⋊C4—118no—
1021C22⋊C4—118no—
1022C22⋊C4—118no—
1023C22⋊C4—118no—
1024C22⋊C4—118no—
1025C22⋊C4—118no—
1026C22⋊C4C23×D1118yes—
1027C22⋊C4C23×D1118yes—
1028C22⋊C4C23×D1118yes—
1029C22⋊C4C23×D1118yes—
1030C22⋊C4C23×D1118yes—
1031C42—118no—
1032C42—118no—
1033C42—118no—
1034C42C23×D1118yes—
1035C42C23×D1114yes—
1036C42C23×D1114yes—
1037C42C23×D1114yes—
1038C42C23×D1114yes—
1039C11C2×#352911yescharacteristic, complemented, Sylow
1040C23—24no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—24no—
1045C23—24no—
1046C23—114no—
1047C23—114no—
1048C23—114no—
1049C23—224no—
1050C23—224no—
1051C23—224no—
1052C23—224no—
1053C23—224no—
1054C23—224no—
1055C23—224no—
1056C23—224no—
1057C23—224no—
1058C23—448no—
1059C23—448no—
1060C23—448no—
1061C23—4432no—
1062C23C24×D1114yes—
1063C23C24×D1112yes—
1064C23C24×D1111yescharacteristic
1065Q8—44no—
1066Q8—448no—
1067Q8—444no—
1068Q8—444no—
1069Q8—444no—
1070D4—44no—
1071D4—48no—
1072D4—448no—
1073D4—444no—
1074D4—444no—
1075D4—448no—
1076D4—448no—
1077D4—444no—
1078D4—448no—
1079D4—448no—
1080D4—448no—
1081D4—448no—
1082D4—448no—
1083D4—448no—
1084D4—448no—
1085D4—448no—
1086D4—448no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—216no—
1096C2×C4—28no—
1097C2×C4—44no—
1098C2×C4—44no—
1099C2×C4—114no—
1100C2×C4—114no—
1101C2×C4—114no—
1102C2×C4—114no—
1103C2×C4—114no—
1104C2×C4—224no—
1105C2×C4—224no—
1106C2×C4—224no—
1107C2×C4—224no—
1108C2×C4—224no—
1109C2×C4—2216no—
1110C2×C4—2216no—
1111C2×C4—2216no—
1112C2×C4—448no—
1113C2×C4—448no—
1114C2×C4—448no—
1115C2×C4—448no—
1116C2×C4—448no—
1117C2×C4#6704214yes—
1118C2×C4C24×D1114yes—
1119C2×C4C24×D1114yes—
1120C2×C4C24×D1112yes—
1121C2×C4C24×D1112yes—
1122C2×C4C24×D1112yes—
1123C2×C4C24×D1112yes—
1124C2×C4C24×D1112yes—
1125C2×C4C24×D1114yes—
1126C2×C4C24×D1112yes—
1127C22—24no—
1128C22—22no—
1129C22—22no—
1130C22—22no—
1131C22—24no—
1132C22—24no—
1133C22—48no—
1134C22—44no—
1135C22—224no—
1136C22—224no—
1137C22—224no—
1138C22—224no—
1139C22—224no—
1140C22—224no—
1141C22—224no—
1142C22—224no—
1143C22—224no—
1144C22—4432no—
1145C22—448no—
1146C22—448no—
1147C22—448no—
1148C22C2×#6704212yes—
1149C22#1062345312yes—
1150C22#1062345312yes—
1151C22C25×D1111yescharacteristic
1152C4—24no—
1153C4—22no—
1154C4—22no—
1155C4—22no—
1156C4—22no—
1157C4—22no—
1158C4—24no—
1159C4—24no—
1160C4—224no—
1161C4—224no—
1162C4—224no—
1163C4—224no—
1164C4—224no—
1165C4C2×#6704214yes—
1166C2—44no—
1167C2—42no—
1168C2—444no—
1169C2—444no—
1170C2—444no—
1171C2#1308275514yesdirect product factor
1172C2C22×#6704211yescharacteristic
1173C2C2×#1062345311yescharacteristic
1174C2C2×#1062345311yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#529C2
socleC23×C11C25
hypercenterC2×#529D11
hypocenterC11C2×#3529
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #13082755C2direct (N × H)
2. C2×#10623230C2semidirect
3. C2×#10623243C2semidirect
4. C2×#10623231C2semidirect
5. C2×#10623198C2semidirect
6. C2×#10623178C2semidirect
7. C2×#10623215C2semidirect
8. C2×#10623214C2semidirect
9. C2×#10623242C2semidirect
10. C2×#10623197C2semidirect
11. C2×#10623151C2semidirect
12. C2×#10623008C2semidirect
13. C2×#10623079C2semidirect
14. C2×#10623111C2semidirect
15. C2×#10623010C2semidirect
16. C2×#10623059C2semidirect
17. C2×#10623055C2semidirect
18. C2×#10623078C2semidirect
19. C2×#10623078C2semidirect
20. C2×C11×#529C2semidirect
23. C22×#4339C22semidirect
24. C23×C4×D11C22semidirect
25. C11×#529C22semidirect
26. C2×C11×#126C22semidirect
27. C2×C11×#125C22semidirect
29. C2×C11×#123C22semidirect
30. C2×C11×C22⋊Q8C22semidirect
32. C2×C4×Q8×C11C22semidirect
34. C2×C4×D4×C11C22semidirect
35. C2×C11×#117C22semidirect
36. C22×C42×C11C22semidirect
38. C2×#66999C22semidirect
42. C2×#66991C22semidirect
44. C2×#66990C22semidirect
46. C2×#66983C22semidirect
47. C2×#66983C22semidirect
48. C2×#66982C22semidirect
50. C2×C4×C22⋊D11C22semidirect
51. C2×C4×C22⋊D11C22semidirect
52. C2×#66977C22semidirect
53. #10623243C22semidirect
54. #10623242C22semidirect
55. #10623231C22semidirect
56. #10623230C22semidirect
57. #10623215C22semidirect
58. #10623214C22semidirect
59. #10623198C22semidirect
60. #10623197C22semidirect
61. #10623178C22semidirect
62. #10623151C22semidirect
63. #10623111C22semidirect
64. #10623079C22semidirect
65. #10623078C22semidirect
66. #10623078C22semidirect
67. #10623059C22semidirect
68. #10623055C22semidirect
69. C2×#66951C22semidirect
70. C2×#66951C22semidirect
71. C2×#66951C22semidirect
72. C2×#66950C22semidirect
73. C2×#66950C22semidirect
74. C2×#66949C22semidirect
75. C2×#66949C22semidirect
76. C2×#66949C22semidirect
80. C2×#66948C22semidirect
82. C2×#66947C22semidirect
83. C2×#66947C22semidirect
84. C2×#66947C22semidirect
85. C2×#66947C22semidirect
86. C2×#66943C22semidirect
87. C2×#66942C22semidirect
88. C2×#66941C22semidirect
90. C2×#66939C22semidirect
93. C2×#66938C22semidirect
97. C2×#66937C22semidirect
98. C2×#66937C22semidirect
100. C2×#66936C22semidirect
101. C2×#66936C22semidirect
104. C2×#66935C22semidirect
105. C2×#66935C22semidirect
106. C2×#66932C22semidirect
107. C2×#66931C22semidirect
108. C2×#66931C22semidirect
109. #10623010C22semidirect
110. C2×#66929C22semidirect
111. #10623008C22semidirect
114. C2×#66928C22semidirect
118. C2×C4×D44C22semidirect
119. C2×C4×D44C22semidirect
120. C2×C4×D44C22semidirect
121. C2×#66925C22semidirect
122. C2×#66925C22semidirect
123. C2×C42×D11C22semidirect
124. C2×#66923C22semidirect
125. C2×#66922C22semidirect
126. C2×C4×Dic22C22semidirect
148. C2×#4339C23semidirect
165. C22×C4×D11C23semidirect
170. C11×#126C23semidirect
171. C11×#125C23semidirect
173. C11×#123C23semidirect
174. C11×C22⋊Q8C23semidirect
176. C4×Q8×C11C23semidirect
178. C4×D4×C11C23semidirect
179. C11×#117C23semidirect
196. C2×C42×C11C23semidirect
201. #66999C23semidirect
205. #66991C23semidirect
207. #66990C23semidirect
209. #66983C23semidirect
210. #66983C23semidirect
211. #66982C23semidirect
213. C4×C22⋊D11C23semidirect
214. C4×C22⋊D11C23semidirect
237. #66977C23semidirect
249. #66951C23semidirect
250. #66951C23semidirect
251. #66951C23semidirect
252. #66950C23semidirect
253. #66950C23semidirect
254. #66949C23semidirect
255. #66949C23semidirect
256. #66949C23semidirect
260. #66948C23semidirect
262. #66947C23semidirect
263. #66947C23semidirect
264. #66947C23semidirect
265. #66947C23semidirect
266. #66943C23semidirect
267. #66942C23semidirect
268. #66941C23semidirect
270. #66939C23semidirect
273. #66938C23semidirect
277. #66937C23semidirect
278. #66937C23semidirect
280. #66936C23semidirect
281. #66936C23semidirect
284. #66935C23semidirect
285. #66935C23semidirect
286. #66932C23semidirect
287. #66931C23semidirect
288. #66931C23semidirect
289. #66929C23semidirect
292. #66928C23semidirect
296. C4×D44C23semidirect
297. C4×D44C23semidirect
298. C4×D44C23semidirect
299. #66925C23semidirect
300. #66925C23semidirect
301. C42×D11C23semidirect
302. #66923C23semidirect
303. #66922C23semidirect
304. C4×Dic22C23semidirect
469. C2×#529D11semidirect
583. #529C2×D11semidirect
589. C2×#126C2×D11semidirect
593. C2×#125C2×D11semidirect
616. C2×#123C2×D11semidirect
626. C2×C22⋊Q8C2×D11semidirect
650. C2×C4×Q8C2×D11semidirect
660. C2×C4×D4C2×D11semidirect
663. C2×#117C2×D11semidirect
665. C22×C42C2×D11semidirect
757. #126C22×D11semidirect
761. #125C22×D11semidirect
781. #123C22×D11semidirect
791. C22⋊Q8C22×D11semidirect
815. C4×Q8C22×D11semidirect
825. C4×D4C22×D11semidirect
828. #117C22×D11semidirect
882. C2×C42C22×D11semidirect
885. C2×C11#3529semidirect
1039. C11C2×#3529semidirect
1171. C2#13082755direct (N × H)

Maximal subgroups

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

subgroupindex
#130827552
C2×#106232302
C2×#106232432
C2×#106232312
C2×#106231982
C2×#106231782
C2×#106232152
C2×#106232142
C2×#106232422
C2×#106231972
C2×#106231512
C2×#106230082
C2×#106230792
C2×#106231112
C2×#106230102
C2×#106230592
C2×#106230552
C2×#106230782
C2×C11×#5292
C2×#352911