Finite Group Databasebeta

← C2×#13082829 #15660980

Subgroups — C2×#13082829 #15660980

Order 2816.

7302 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082829C2132yesmaximal, direct product factor
2C2×#10623182C212yesmaximal, complemented
3C2×#10623198C212yesmaximal, complemented
4C2×#10623042C212yesmaximal, complemented
5C2×#10623181C212yesmaximal, complemented
6C2×#10623026C212yesmaximal, complemented
7C2×#10623026C212yesmaximal, complemented
8C2×#10623186C212yesmaximal, complemented
9C2×#10623337C212yesmaximal, complemented
10C2×#10623031C211yesmaximal, characteristic, complemented
11C2×#10623014C211yesmaximal, characteristic, complemented
12C2×#10623193C212yesmaximal, complemented
13C2×#10623046C211yesmaximal, characteristic, complemented
14C2×#10623196C212yesmaximal, complemented
15C2×#10623191C212yesmaximal, complemented
16C2×#10623025C211yesmaximal, characteristic, complemented
17C2×#10623179C212yesmaximal, complemented
18C2×#10623322C211yesmaximal, characteristic, complemented
19C22×#66977C211yesmaximal, characteristic, complemented
20C22×C11×#123C211yesmaximal, characteristic, complemented
21C23×D4×C11C2211yescharacteristic
22C24×C4×C11C2211yescharacteristic
23C22×#4341C2212yes—
24C22×#4339C2211yescharacteristic, complemented
25C23×Dic22C2211yescharacteristic, complemented
26C2×C11×#123C2212yes—
27C2×C11×#123C2212yes—
28C2×C11×#123C2212yes—
29C2×C11×#123C2212yes—
30C2×C11×#123C22116yescomplemented
31C22×C11×C4⋊C4C2211yescharacteristic
32C22×C11×C4⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C2×#67006C2212yes—
37C2×#67006C2212yes—
38C22×C22⋊Dic11C2212yes—
39C22×C22⋊Dic11C2212yes—
40#10623337C22132yescomplemented
41C2×#66992C2212yes—
42C2×#66992C2212yes—
43C2×#66991C2212yes—
44C2×#66989C2212yes—
45C2×#66988C2212yes—
46C2×#66988C2212yes—
47C2×D4×Dic11C2212yes—
48#10623322C22116yescomplemented
49C2×#66983C2211yescharacteristic
50C2×#66983C2211yescharacteristic, complemented
51C2×#66982C2212yes—
52C2×#66982C2212yescomplemented
53C2×C4×C22⋊D11C2212yes—
54C2×C4×C22⋊D11C2212yes—
55C2×C4×C22⋊D11C2212yes—
56C2×C4×C22⋊D11C2212yescomplemented
57C2×#66979C2212yes—
58C2×#66979C2211yescharacteristic, complemented
59C22×C4⋊Dic11C2211yescharacteristic, complemented
60C2×#66977C2212yes—
61C2×#66977C2212yes—
62C2×#66977C2211yescharacteristic
63C2×#66977C2212yes—
64C2×#66977C2211yescharacteristic
65C2×#66977C2211yescharacteristic
66C2×#66977C2211yescharacteristic, complemented
67C2×#66977C2211yescharacteristic, complemented
68C2×#66977C2212yescomplemented
69C2×#66977C2211yescharacteristic, complemented
70C2×#66977C22116yescomplemented
71C22×Dic11⋊C4C2212yescomplemented
72#10623198C22132yescomplemented
73#10623196C22132yescomplemented
74#10623193C22132yescomplemented
75#10623191C22132yescomplemented
76#10623186C22132yescomplemented
77#10623182C22132yescomplemented
78#10623181C22132yescomplemented
79#10623179C22132yescomplemented
80#10623046C22116yescomplemented
81C2×#66951C2212yescomplemented
82#10623042C22132yescomplemented
83C2×#66950C2212yescomplemented
84C2×#66949C2212yescomplemented
85C2×#66949C2212yescomplemented
86C2×#66949C2212yescomplemented
87C2×#66947C2212yescomplemented
88C2×C4⋊C4×D11C2212yescomplemented
89#10623031C22116yescomplemented
90C2×#66943C2212yescomplemented
91C2×#66943C2212yescomplemented
92C2×#66942C2212yescomplemented
93C2×#66942C2212yescomplemented
94C2×#66942C2212yescomplemented
95C2×#66941C2212yescomplemented
96C2×#66941C2212yescomplemented
97C2×#66941C2212yescomplemented
98C2×#66940C2212yescomplemented
99#10623026C22132yescomplemented
100#10623026C22132yescomplemented
101#10623025C22116yescomplemented
102C2×#66939C2212yescomplemented
103C2×#66939C2212yescomplemented
104C2×#66938C2212yescomplemented
105C2×#66938C2212yescomplemented
106C2×#66938C2212yescomplemented
107C2×#66937C2212yescomplemented
108C2×#66936C2212yescomplemented
109C2×#66936C2212yescomplemented
110C2×#66936C2212yescomplemented
111C2×(C22⋊D11)⋊C4C2212yescomplemented
112C2×(C22⋊D11)⋊C4C2212yescomplemented
113#10623014C22116yescomplemented
114C2×#66932C2212yescomplemented
115C2×#66932C2212yescomplemented
116C2×#66932C2212yescomplemented
117C2×#66932C2212yescomplemented
118C2×#66932C2212yescomplemented
119C2×#66931C2212yescomplemented
120C2×#66931C2212yescomplemented
121C2×#66931C2212yescomplemented
122C2×#66931C2212yescomplemented
123C2×#66931C2212yescomplemented
124C2×#66931C2212yescomplemented
125C2×#66930C2212yescomplemented
126C2×#66930C2212yescomplemented
127C25×C11C2311yescharacteristic
128C25×C11C2311yescharacteristic
129C22×D4×C11—44no—
130C22×D4×C11C2312yes—
131C22×D4×C11C2312yes—
132C22×D4×C11C2318yes—
133C23×C4×C11—44no—
134C23×C4×C11C2311yescharacteristic
135C23×C4×C11C2311yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C23×C4×C11C2311yescharacteristic
139C23×C4×C11C2311yescharacteristic
140C23×C4×C11C2311yescharacteristic
141C23×C4×C11C2311yescharacteristic
142C23×C4×C11C2311yescharacteristic
143C23×C4×C11C2318yes—
144C22×C22⋊D11C2312yes—
145C22×C22⋊D11C2312yes—
146C22×C22⋊D11C2312yes—
147C22×C22⋊D11C2312yes—
148C22×C22⋊D11C2312yes—
149C23×Dic11C2312yes—
150C23×Dic11C2312yes—
151C23×Dic11C2312yes—
152C23×Dic11C2312yes—
153C2×#4341—48no—
154C2×#4341C23116yes—
155C2×#4339—44no—
156C2×#4339C2318yescomplemented
157C22×D44C2311yescharacteristic
158C22×C4×D11C2312yes—
159C22×C4×D11C2312yes—
160C22×C4×D11C2312yes—
161C22×Dic22—44no—
162C22×Dic22C2312yes—
163C22×Dic22C2311yescharacteristic
164C22×Dic22C2311yescharacteristic
165C22×Dic22C2312yes—
166C22×Dic22C2311yescharacteristic
167C22×Dic22C2312yes—
168C22×Dic22C2318yescomplemented
169C11×#123C23116yes—
170C11×#123C23116yes—
171C11×#123C23116yes—
172C11×#123C23116yes—
173C2×C11×C4⋊C4C2312yes—
174C2×C11×C4⋊C4C2312yes—
175C2×C11×C4⋊C4C2312yes—
176C2×C11×C4⋊C4C2312yes—
177C2×C11×C4⋊C4C2318yes—
178C2×C11×C4⋊C4C2318yes—
179C2×C11×C22⋊C4C2312yes—
180C2×C11×C22⋊C4C2312yes—
181C2×C11×C22⋊C4C2312yes—
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C2312yes—
185C2×C11×C22⋊C4C2318yes—
186C2×C11×C22⋊C4C2318yes—
187C2×C11×C22⋊C4C2318yes—
188#67006C23116yes—
189#67006C23116yes—
190C2×C22⋊Dic11C2312yes—
191C2×C22⋊Dic11C2312yes—
192C2×C22⋊Dic11C2312yes—
193C2×C22⋊Dic11C2312yes—
194C2×C22⋊Dic11C2312yes—
195C2×C22⋊Dic11C2312yes—
196C2×C22⋊Dic11C2312yes—
197C2×C22⋊Dic11C2312yes—
198C2×C22⋊Dic11C23116yes—
199C2×C22⋊Dic11C23116yes—
200C2×C22⋊Dic11C2312yes—
201C2×C22⋊Dic11C2312yes—
202C2×C22⋊Dic11C2312yes—
203#66992C23116yes—
204#66992C23116yes—
205#66991C23116yes—
206#66989C23116yes—
207#66988C23116yes—
208#66988C23116yes—
209D4×Dic11C23116yes—
210#66983C2318yes—
211#66983C2318yescomplemented
212#66982C23116yes—
213#66982C23116yescomplemented
214C4×C22⋊D11C23116yes—
215C4×C22⋊D11C23116yes—
216C4×C22⋊D11C23116yes—
217C4×C22⋊D11C23116yescomplemented
218C2×(C2×D11)⋊C4C2312yes—
219C2×(C2×D11)⋊C4C2312yes—
220C2×(C2×D11)⋊C4C2312yes—
221C2×(C2×D11)⋊C4C2312yes—
222C2×(C2×D11)⋊C4C2312yes—
223C2×(C2×D11)⋊C4C2312yes—
224#66979C23116yes—
225#66979C2318yescomplemented
226C2×C4⋊Dic11C2312yes—
227C2×C4⋊Dic11C2311yescharacteristic
228C2×C4⋊Dic11C2311yescharacteristic
229C2×C4⋊Dic11C2312yes—
230C2×C4⋊Dic11C2312yes—
231C2×C4⋊Dic11C2311yescharacteristic
232C2×C4⋊Dic11C2312yes—
233C2×C4⋊Dic11C2311yescharacteristic
234C2×C4⋊Dic11C2312yes—
235C2×C4⋊Dic11C2318yescomplemented
236#66977C23116yes—
237#66977C2318yes—
238#66977C2318yes—
239#66977C2318yes—
240#66977C23116yes—
241#66977C23116yes—
242#66977C23116yescomplemented
243#66977C2318yescomplemented
244#66977C2318yescomplemented
245#66977C2318yescomplemented
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⋊C4C2312yes—
255C2×Dic11⋊C4C2312yes—
256C2×Dic11⋊C4C2312yes—
257C2×Dic11⋊C4C2312yes—
258C2×Dic11⋊C4C2312yes—
259C2×Dic11⋊C4C2312yes—
260C2×Dic11⋊C4C23116yescomplemented
261C2×C4×Dic11C2312yes—
262C2×C4×Dic11C2312yes—
263C2×C4×Dic11C2312yes—
264C2×C4×Dic11C2312yes—
265C2×C4×Dic11C2312yes—
266#66951C23116yescomplemented
267#66950C23116yescomplemented
268#66949C23116yescomplemented
269#66949C23116yescomplemented
270#66949C23116yescomplemented
271#66947C23116yescomplemented
272C4⋊C4×D11C23116yescomplemented
273#66943C23116yescomplemented
274#66943C23116yescomplemented
275#66942C23116yescomplemented
276#66942C23116yescomplemented
277#66942C23116yescomplemented
278#66941C23116yescomplemented
279#66941C23116yescomplemented
280#66941C23116yescomplemented
281#66940C23116yescomplemented
282#66939C23116yescomplemented
283#66939C23116yescomplemented
284#66938C23116yescomplemented
285#66938C23116yescomplemented
286#66938C23116yescomplemented
287#66937C23116yescomplemented
288#66936C23116yescomplemented
289#66936C23116yescomplemented
290#66936C23116yescomplemented
291(C22⋊D11)⋊C4C23116yescomplemented
292(C22⋊D11)⋊C4C23116yescomplemented
293#66932C23116yescomplemented
294#66932C23116yescomplemented
295#66932C23116yescomplemented
296#66932C23116yescomplemented
297#66932C23116yescomplemented
298#66931C23116yescomplemented
299#66931C23116yescomplemented
300#66931C23116yescomplemented
301#66931C23116yescomplemented
302#66931C23116yescomplemented
303#66931C23116yescomplemented
304#66930C23116yescomplemented
305#66930C23116yescomplemented
306C2×#3535—111nomaximal, Sylow
307C24×C11—24no—
308C24×C11—24no—
309C24×C11—24no—
310C24×C11—42no—
311C24×C11—42no—
312C24×C11—42no—
313C24×C11C2411yescharacteristic
314C24×C11C2412yes—
315C24×C11C2414yes—
316C24×C11C2411yescharacteristic
317C24×C11C2411yescharacteristic
318C24×C11C2414yes—
319C23×D11C2412yes—
320C2×D4×C11—28no—
321C2×D4×C11—44no—
322C2×D4×C11—416no—
323C2×D4×C11C2418yes—
324C2×D4×C11C2418yes—
325C22×C4×C11—24no—
326C22×C4×C11—24no—
327C22×C4×C11—24no—
328C22×C4×C11—42no—
329C22×C4×C11—42no—
330C22×C4×C11—42no—
331C22×C4×C11—42no—
332C22×C4×C11—416no—
333C22×C4×C11—42no—
334C22×C4×C11—42no—
335C22×C4×C11C2411yescharacteristic
336C22×C4×C11C2412yes—
337C22×C4×C11C2412yes—
338C22×C4×C11C2412yes—
339C22×C4×C11C2411yescharacteristic
340C22×C4×C11C2411yescharacteristic
341C22×C4×C11C2411yescharacteristic
342C22×C4×C11C2414yes—
343C22×C4×C11C2414yes—
344C22×C4×C11C2414yes—
345C22×C4×C11C2414yes—
346C22×C4×C11C2414yes—
347C22×C4×C11C2414yes—
348C22×C4×C11C2414yes—
349C22×C4×C11C2414yes—
350C22×C4×C11C2414yes—
351C2×C22⋊D11—28no—
352C2×C22⋊D11—28no—
353C2×C22⋊D11—44no—
354C2×C22⋊D11—44no—
355C2×C22⋊D11—44no—
356C2×C22⋊D11C2418yes—
357C2×C22⋊D11C2418yes—
358C2×C22⋊D11C2418yes—
359C2×C22⋊D11C2418yes—
360C2×C22⋊D11C2418yes—
361C22×Dic11—28no—
362C22×Dic11—44no—
363C22×Dic11—44no—
364C22×Dic11—44no—
365C22×Dic11C2418yes—
366C22×Dic11C2412yes—
367C22×Dic11C2412yes—
368C22×Dic11C2412yes—
369C22×Dic11C2412yes—
370C22×Dic11C2412yes—
371C22×Dic11C2412yes—
372C22×Dic11C2412yes—
373C22×Dic11C2418yes—
374C22×Dic11C2418yes—
375C22×Dic11C2418yes—
376#4341—432no—
377#4339—416no—
378C2×D44—42no—
379C2×D44C2414yes—
380C2×C4×D11—44no—
381C2×C4×D11—44no—
382C2×C4×D11—44no—
383C2×C4×D11C2418yes—
384C2×C4×D11C2418yes—
385C2×C4×D11C2418yes—
386C2×Dic22—42no—
387C2×Dic22—44no—
388C2×Dic22—42no—
389C2×Dic22—416no—
390C2×Dic22—44no—
391C2×Dic22—42no—
392C2×Dic22—44no—
393C2×Dic22C2418yes—
394C2×Dic22C2414yes—
395C2×Dic22C2414yes—
396C2×Dic22C2418yes—
397C2×Dic22C2414yes—
398C2×Dic22C2418yes—
399C11×C4⋊C4C2418yes—
400C11×C4⋊C4C2418yes—
401C11×C4⋊C4C2418yes—
402C11×C4⋊C4C2418yes—
403C11×C22⋊C4C2418yes—
404C11×C22⋊C4C2418yes—
405C11×C22⋊C4C2418yes—
406C11×C22⋊C4C2418yes—
407C11×C22⋊C4C2418yes—
408C11×C22⋊C4C2418yes—
409C22⋊Dic11C2418yes—
410C22⋊Dic11C2418yes—
411C22⋊Dic11C2418yes—
412C22⋊Dic11C2418yes—
413C22⋊Dic11C2418yes—
414C22⋊Dic11C2418yes—
415C22⋊Dic11C2418yes—
416C22⋊Dic11C2418yes—
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—
426C4⋊Dic11C2418yes—
427C4⋊Dic11C2414yes—
428C4⋊Dic11C2414yes—
429C4⋊Dic11C2418yes—
430C4⋊Dic11C2418yes—
431C4⋊Dic11C2414yes—
432C4⋊Dic11C2418yes—
433C4⋊Dic11C2414yes—
434C4⋊Dic11C2418yes—
435Dic11⋊C4C2418yes—
436Dic11⋊C4C2418yes—
437Dic11⋊C4C2418yes—
438Dic11⋊C4C2418yes—
439Dic11⋊C4C2418yes—
440Dic11⋊C4C2418yes—
441Dic11⋊C4C2418yes—
442Dic11⋊C4C2418yes—
443Dic11⋊C4C2418yes—
444Dic11⋊C4C2418yes—
445Dic11⋊C4C2418yes—
446Dic11⋊C4C2418yes—
447Dic11⋊C4C2418yes—
448Dic11⋊C4C2418yes—
449C4×Dic11C2418yes—
450C4×Dic11C2418yes—
451C4×Dic11C2418yes—
452C4×Dic11C2418yes—
453C4×Dic11C2418yes—
454#3535—1132no—
455C2×#563—112no—
456C2×#562—112no—
457C2×#554—112no—
458C2×#552—112no—
459C2×#551—112no—
460C2×#551—112no—
461C2×#547—112no—
462C2×#546—112no—
463C2×#544—111no—
464C2×#543—111no—
465C2×#542—112no—
466C2×#539—112no—
467C2×#539—112no—
468C2×#539—111no—
469C2×#538—111no—
470C2×#536—112no—
471C2×#525—111no—
472C22×#123D1111yescharacteristic, complemented
473C22×C22⋊Q8—111no—
474C23×C11—22no—
475C23×C11—22no—
476C23×C11—22no—
477C23×C11—22no—
478C23×C11—24no—
479C23×C11—28no—
480C23×C11—22no—
481C23×C11—28no—
482C23×C11—22no—
483C23×C11—24no—
484C23×C11—24no—
485C23×C11—22no—
486C23×C11—28no—
487C23×C11—44no—
488C23×C11—44no—
489C23×C11—44no—
490C23×C11—416no—
491C23×C11—88no—
492C23×C11H(5,𝔽2)14yes—
493C23×C112−1+414yes—
494C23×C11C2512yes—
495C23×C11C2514yes—
496C23×C11C2512yes—
497C23×C11C2512yes—
498C23×C11C2511yescharacteristic
499C22×D11—24no—
500C22×D11—24no—
501C22×D11—24no—
502C22×D11C2514yes—
503D4×C11—216no—
504D4×C11—48no—
505C2×C4×C11—28no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—24no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—28no—
512C2×C4×C11—28no—
513C2×C4×C11—24no—
514C2×C4×C11—24no—
515C2×C4×C11—44no—
516C2×C4×C11—44no—
517C2×C4×C11—44no—
518C2×C4×C11—44no—
519C2×C4×C11—44no—
520C2×C4×C11—44no—
521C2×C4×C11C2512yes—
522C2×C4×C11C2514yes—
523C2×C4×C11C2514yes—
524C2×C4×C11C2514yes—
525C2×C4×C11C2512yes—
526C2×C4×C11C2512yes—
527C2×C4×C11C2512yes—
528C22⋊D11—216no—
529C22⋊D11—216no—
530C22⋊D11—48no—
531C22⋊D11—48no—
532C22⋊D11—48no—
533C2×Dic11—24no—
534C2×Dic11—24no—
535C2×Dic11—24no—
536C2×Dic11—216no—
537C2×Dic11—24no—
538C2×Dic11—24no—
539C2×Dic11—24no—
540C2×Dic11—24no—
541C2×Dic11—48no—
542C2×Dic11—48no—
543C2×Dic11—48no—
544C2×Dic11C2514yes—
545C2×Dic11C2514yes—
546C2×Dic11C2514yes—
547C2×Dic11C2514yes—
548C2×Dic11C2514yes—
549C2×Dic11C2514yes—
550C2×Dic11C2514yes—
551D44—44no—
552C4×D11—48no—
553C4×D11—48no—
554C4×D11—48no—
555Dic22—44no—
556Dic22—48no—
557Dic22—44no—
558Dic22—48no—
559Dic22—44no—
560Dic22—48no—
561C22×#41—112no—
562C22×#41—111no—
563C23×Q8—111no—
564C23×D4C2×D1111yescharacteristic
565C24×C4C2×D1111yescharacteristic
566#563—1132no—
567#562—1132no—
568#554—1132no—
569#552—1132no—
570#551—1132no—
571#551—1132no—
572#547—1132no—
573#546—1132no—
574#544—1116no—
575#543—1116no—
576#542—1132no—
577#539—1132no—
578#539—1132no—
579#539—1116no—
580#538—1116no—
581#536—1132no—
582C2×C4⋊Q8—112no—
583C2×C4⋊Q8—112no—
584C2×C4⋊Q8—112no—
585C2×#126—112no—
586C2×#126—112no—
587C2×#126—112no—
588C2×#126—112no—
589C2×#126—112no—
590C2×#126—112no—
591C2×#125—112no—
592C2×#125—112no—
593C2×#125—112no—
594C2×#125—112no—
595C2×#125—112no—
596C2×#124—112no—
597C2×#124—112no—
598C2×#124—112no—
599C2×#124—112no—
600#525—1116no—
601C2×#123—112no—
602C2×#123—112no—
603C2×#123—112no—
604C2×#123—112no—
605C2×#123—112no—
606C2×#123—112no—
607C2×#123—112no—
608C2×#123—112no—
609C2×#123—112no—
610C2×#123—112no—
611C2×#123C2×D1112yes—
612C2×#123C2×D1112yes—
613C2×#123C2×D1112yes—
614C2×#123C2×D1112yes—
615C2×#123C2×D11116yescomplemented
616C2×C22⋊Q8—111no—
617C2×C22⋊Q8—111no—
618C2×C22⋊Q8—112no—
619C2×C22⋊Q8—111no—
620C2×C22⋊Q8—112no—
621C2×C22⋊Q8—112no—
622C2×C22⋊Q8—111no—
623C2×C22⋊Q8—111no—
624C2×C22⋊Q8—112no—
625C2×C22⋊Q8—1116no—
626C2×C22⋊Q8—111no—
627C2×C22⋊Q8—112no—
628C2×C22⋊Q8—112no—
629C2×C22⋊Q8—112no—
630C2×C22⋊Q8—112no—
631C2×C22⋊Q8—112no—
632C2×C22⋊Q8—112no—
633C2×C22⋊Q8—112no—
634C2×C22⋊Q8—112no—
635C2×C22⋊Q8—112no—
636C2×C22⋊Q8—112no—
637C2×#121—112no—
638C2×#121—112no—
639C2×#121—112no—
640C2×#121—111no—
641C2×#121—111no—
642C2×#121—112no—
643C2×#120—112no—
644C2×#120—112no—
645C2×C4×Q8—112no—
646C2×C4×D4—112no—
647C2×C4×D4—112no—
648C2×C4×D4—112no—
649C2×C4×D4—112no—
650C2×C4×D4—112no—
651C2×C4×D4—112no—
652C2×C4×D4—112no—
653C2×#117—112no—
654C2×#117—111no—
655C2×#117—112no—
656C2×#117—112no—
657C22×C4⋊C4—112no—
658C22×C4⋊C4—111no—
659C22×C4⋊C4—112no—
660C22×C4⋊C4C2×D1111yescharacteristic
661C22×C4⋊C4C2×D1111yescharacteristic
662C22×C22⋊C4—112no—
663C22×C22⋊C4—112no—
664C22×C22⋊C4C2×D1111yescharacteristic
665C22×C22⋊C4C2×D1111yescharacteristic
666C22×C22⋊C4C2×D1111yescharacteristic
667C22×C11—22no—
668C22×C11—22no—
669C22×C11—22no—
670C22×C11—22no—
671C22×C11—28no—
672C22×C11—28no—
673C22×C11—22no—
674C22×C11—24no—
675C22×C11—22no—
676C22×C11—24no—
677C22×C11—24no—
678C22×C11—22no—
679C22×C11—416no—
680C22×C11—44no—
681C22×C11—48no—
682C22×C11—88no—
683C22×C11C2×H(5,𝔽2)14yes—
684C22×C11C2×H(5,𝔽2)12yes—
685C22×C11C2×2−1+414yes—
686C22×C11C2×2−1+412yes—
687C22×C11#58512yes—
688C22×C11C2611yescharacteristic
689C2×D11—24no—
690C2×D11—24no—
691C2×D11—24no—
692C2×D11—48no—
693C4×C11—22no—
694C4×C11—22no—
695C4×C11—22no—
696C4×C11—22no—
697C4×C11—24no—
698C4×C11—24no—
699C4×C11—24no—
700Dic11—24no—
701Dic11—24no—
702Dic11—24no—
703Dic11—24no—
704Dic11—24no—
705Dic11—24no—
706Dic11—24no—
707C25C22×D1111yescharacteristic
708C25C22×D1111yescharacteristic
709C2×#41—1116no—
710C2×#41—118no—
711C2×#41—444no—
712C2×#41—448no—
713C22×Q8—112no—
714C22×Q8—111no—
715C22×Q8—112no—
716C22×Q8—111no—
717C22×Q8—111no—
718C22×Q8—112no—
719C22×Q8—118no—
720C22×Q8—444no—
721C22×D4—44no—
722C22×D4—112no—
723C22×D4—112no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—111no—
728C22×D4C22×D1112yes—
729C22×D4C22×D1112yes—
730C22×D4C22×D1118yes—
731C23×C4—44no—
732C23×C4—112no—
733C23×C4—112no—
734C23×C4—112no—
735C23×C4—112no—
736C23×C4—112no—
737C23×C4—112no—
738C23×C4—112no—
739C23×C4C22×D1111yescharacteristic
740C23×C4C22×D1111yescharacteristic
741C23×C4C22×D1111yescharacteristic
742C23×C4C22×D1111yescharacteristic
743C23×C4C22×D1111yescharacteristic
744C23×C4C22×D1111yescharacteristic
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1111yescharacteristic
748C23×C4C22×D1118yes—
749C4⋊Q8—1116no—
750C4⋊Q8—1116no—
751C4⋊Q8—1116no—
752#126—1116no—
753#126—1116no—
754#126—1116no—
755#126—1116no—
756#126—1116no—
757#126—1116no—
758#125—1116no—
759#125—1116no—
760#125—1116no—
761#125—1116no—
762#125—1116no—
763#124—1116no—
764#124—1116no—
765#124—1116no—
766#124—1116no—
767#123—1116no—
768#123—1116no—
769#123—1116no—
770#123—1116no—
771#123—1116no—
772#123—1116no—
773#123—1116no—
774#123—1116no—
775#123—1116no—
776#123—1116no—
777#123C22×D11116yes—
778#123C22×D11116yes—
779#123C22×D11116yes—
780#123C22×D11116yes—
781C22⋊Q8—118no—
782C22⋊Q8—118no—
783C22⋊Q8—118no—
784C22⋊Q8—118no—
785C22⋊Q8—1116no—
786C22⋊Q8—1116no—
787C22⋊Q8—118no—
788C22⋊Q8—118no—
789C22⋊Q8—1116no—
790C22⋊Q8—1116no—
791C22⋊Q8—1116no—
792C22⋊Q8—1116no—
793C22⋊Q8—1116no—
794C22⋊Q8—1116no—
795C22⋊Q8—1116no—
796C22⋊Q8—1116no—
797C22⋊Q8—1116no—
798C22⋊Q8—1116no—
799C22⋊Q8—1116no—
800C22⋊Q8—1116no—
801#121—1116no—
802#121—1116no—
803#121—1116no—
804#121—118no—
805#121—118no—
806#121—1116no—
807#120—1116no—
808#120—1116no—
809C4×Q8—1116no—
810C4×D4—1116no—
811C4×D4—1116no—
812C4×D4—1116no—
813C4×D4—1116no—
814C4×D4—1116no—
815C4×D4—1116no—
816C4×D4—1116no—
817#117—118no—
818#117—1116no—
819#117—1116no—
820#117—1116no—
821C2×C4⋊C4—112no—
822C2×C4⋊C4—112no—
823C2×C4⋊C4—112no—
824C2×C4⋊C4—112no—
825C2×C4⋊C4—112no—
826C2×C4⋊C4—111no—
827C2×C4⋊C4—112no—
828C2×C4⋊C4—112no—
829C2×C4⋊C4—111no—
830C2×C4⋊C4—118no—
831C2×C4⋊C4—1116no—
832C2×C4⋊C4—111no—
833C2×C4⋊C4—111no—
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—112no—
841C2×C4⋊C4—112no—
842C2×C4⋊C4—112no—
843C2×C4⋊C4—112no—
844C2×C4⋊C4—112no—
845C2×C4⋊C4—112no—
846C2×C4⋊C4—1116no—
847C2×C4⋊C4C22×D1112yes—
848C2×C4⋊C4C22×D1112yes—
849C2×C4⋊C4C22×D1112yes—
850C2×C4⋊C4C22×D1112yes—
851C2×C4⋊C4C22×D1118yes—
852C2×C4⋊C4C22×D1118yes—
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—1116no—
861C2×C22⋊C4—1116no—
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⋊C4—112no—
869C2×C22⋊C4—112no—
870C2×C22⋊C4—112no—
871C2×C22⋊C4—112no—
872C2×C22⋊C4C22×D1112yes—
873C2×C22⋊C4C22×D1112yes—
874C2×C22⋊C4C22×D1112yes—
875C2×C22⋊C4C22×D1112yes—
876C2×C22⋊C4C22×D1112yes—
877C2×C22⋊C4C22×D1112yes—
878C2×C22⋊C4C22×D1118yes—
879C2×C22⋊C4C22×D1118yes—
880C2×C22⋊C4C22×D1118yes—
881C2×C42—112no—
882C2×C42—112no—
883C2×C42—112no—
884C2×C42—112no—
885C2×C42—112no—
886C2×C11—24no—
887C2×C11—24no—
888C2×C11—42no—
889C2×C11—44no—
890C2×C11#353514yescomplemented
891C2×C11C22×H(5,𝔽2)11yescharacteristic
892C2×C11C22×2−1+411yescharacteristic
893C2×C11C2×#58511yescharacteristic
894D11—44no—
895C24—24no—
896C24—24no—
897C24—24no—
898C24—42no—
899C24—42no—
900C24—42no—
901C24—112no—
902C24C23×D1111yescharacteristic
903C24C23×D1112yes—
904C24C23×D1114yes—
905C24C23×D1111yescharacteristic
906C24C23×D1111yescharacteristic
907C24C23×D1114yes—
908#41—4416no—
909#41—4432no—
910C2×Q8—118no—
911C2×Q8—114no—
912C2×Q8—118no—
913C2×Q8—114no—
914C2×Q8—114no—
915C2×Q8—118no—
916C2×Q8—442no—
917C2×Q8—444no—
918C2×Q8—442no—
919C2×Q8—4416no—
920C2×Q8—442no—
921C2×Q8—444no—
922C2×Q8—444no—
923C2×D4—28no—
924C2×D4—44no—
925C2×D4—416no—
926C2×D4—118no—
927C2×D4—118no—
928C2×D4—118no—
929C2×D4—118no—
930C2×D4—118no—
931C2×D4—114no—
932C2×D4—228no—
933C2×D4—228no—
934C2×D4—442no—
935C2×D4—444no—
936C2×D4—444no—
937C2×D4—444no—
938C2×D4C23×D1118yes—
939C2×D4C23×D1118yes—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—416no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—118no—
951C22×C4—112no—
952C22×C4—112no—
953C22×C4—112no—
954C22×C4—112no—
955C22×C4—112no—
956C22×C4—112no—
957C22×C4—112no—
958C22×C4—118no—
959C22×C4—118no—
960C22×C4—118no—
961C22×C4—118no—
962C22×C4—118no—
963C22×C4—118no—
964C22×C4—228no—
965C22×C4—444no—
966C22×C4—444no—
967C22×C4—444no—
968C22×C4—444no—
969C22×C4—444no—
970C22×C4—444no—
971C22×C4C23×D1114yes—
972C22×C4C23×D1114yes—
973C22×C4C23×D1114yes—
974C22×C4C23×D1112yes—
975C22×C4C23×D1111yescharacteristic
976C22×C4C23×D1112yes—
977C22×C4C23×D1112yes—
978C22×C4C23×D1111yescharacteristic
979C22×C4C23×D1111yescharacteristic
980C22×C4C23×D1111yescharacteristic
981C22×C4C23×D1114yes—
982C22×C4C23×D1114yes—
983C22×C4C23×D1114yes—
984C22×C4C23×D1114yes—
985C22×C4C23×D1114yes—
986C22×C4C23×D1114yes—
987C4⋊C4—118no—
988C4⋊C4—118no—
989C4⋊C4—118no—
990C4⋊C4—118no—
991C4⋊C4—118no—
992C4⋊C4—114no—
993C4⋊C4—118no—
994C4⋊C4—118no—
995C4⋊C4—114no—
996C4⋊C4—114no—
997C4⋊C4—114no—
998C4⋊C4—118no—
999C4⋊C4—118no—
1000C4⋊C4—118no—
1001C4⋊C4—118no—
1002C4⋊C4—118no—
1003C4⋊C4—118no—
1004C4⋊C4—118no—
1005C4⋊C4—118no—
1006C4⋊C4—118no—
1007C4⋊C4—118no—
1008C4⋊C4—118no—
1009C4⋊C4—118no—
1010C4⋊C4C23×D1118yes—
1011C4⋊C4C23×D1118yes—
1012C4⋊C4C23×D1118yes—
1013C4⋊C4C23×D1118yes—
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⋊C4—118no—
1027C22⋊C4—118no—
1028C22⋊C4—118no—
1029C22⋊C4—118no—
1030C22⋊C4—118no—
1031C22⋊C4C23×D1118yes—
1032C22⋊C4C23×D1118yes—
1033C22⋊C4C23×D1118yes—
1034C22⋊C4C23×D1118yes—
1035C22⋊C4C23×D1118yes—
1036C22⋊C4C23×D1118yes—
1037C42—118no—
1038C42—118no—
1039C42—118no—
1040C42—118no—
1041C42—118no—
1042C11C2×#353511yescharacteristic, complemented, Sylow
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—28no—
1048C23—22no—
1049C23—24no—
1050C23—28no—
1051C23—22no—
1052C23—24no—
1053C23—24no—
1054C23—22no—
1055C23—28no—
1056C23—44no—
1057C23—44no—
1058C23—44no—
1059C23—416no—
1060C23—88no—
1061C23—114no—
1062C23—224no—
1063C23—224no—
1064C23—224no—
1065C23#6703714yes—
1066C23#6704314yes—
1067C23C24×D1112yes—
1068C23C24×D1114yes—
1069C23C24×D1112yes—
1070C23C24×D1112yes—
1071C23C24×D1111yescharacteristic
1072Q8—444no—
1073Q8—448no—
1074Q8—444no—
1075Q8—444no—
1076Q8—448no—
1077Q8—448no—
1078D4—216no—
1079D4—48no—
1080D4—2216no—
1081D4—2216no—
1082D4—444no—
1083D4—448no—
1084D4—448no—
1085D4—448no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—28no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—28no—
1092C2×C4—24no—
1093C2×C4—28no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—44no—
1097C2×C4—44no—
1098C2×C4—44no—
1099C2×C4—44no—
1100C2×C4—44no—
1101C2×C4—44no—
1102C2×C4—114no—
1103C2×C4—114no—
1104C2×C4—114no—
1105C2×C4—114no—
1106C2×C4—114no—
1107C2×C4—114no—
1108C2×C4—114no—
1109C2×C4—224no—
1110C2×C4—224no—
1111C2×C4—2216no—
1112C2×C4—224no—
1113C2×C4—224no—
1114C2×C4—224no—
1115C2×C4—224no—
1116C2×C4—224no—
1117C2×C4—448no—
1118C2×C4—448no—
1119C2×C4—448no—
1120C2×C4—448no—
1121C2×C4—448no—
1122C2×C4—448no—
1123C2×C4C24×D1114yes—
1124C2×C4C24×D1112yes—
1125C2×C4C24×D1114yes—
1126C2×C4C24×D1114yes—
1127C2×C4C24×D1112yes—
1128C2×C4C24×D1112yes—
1129C2×C4C24×D1112yes—
1130C22—22no—
1131C22—22no—
1132C22—22no—
1133C22—22no—
1134C22—28no—
1135C22—28no—
1136C22—22no—
1137C22—24no—
1138C22—22no—
1139C22—24no—
1140C22—24no—
1141C22—22no—
1142C22—416no—
1143C22—44no—
1144C22—48no—
1145C22—88no—
1146C22—224no—
1147C22—224no—
1148C22—224no—
1149C22—448no—
1150C22C2×#6703714yes—
1151C22C2×#6703712yes—
1152C22C2×#6704314yes—
1153C22C2×#6704312yes—
1154C22#1062345312yes—
1155C22C25×D1111yescharacteristic
1156C4—22no—
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—24no—
1161C4—24no—
1162C4—24no—
1163C4—224no—
1164C4—224no—
1165C4—224no—
1166C4—224no—
1167C4—224no—
1168C4—224no—
1169C4—224no—
1170C2—24no—
1171C2—24no—
1172C2—42no—
1173C2—44no—
1174C2—444no—
1175C2#1308282914yesdirect product factor
1176C2C22×#6703711yescharacteristic
1177C2C22×#6704311yescharacteristic
1178C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×#123C2
socleC23×C11C25
hypercenterC22×#123D11
hypocenterC11C2×#3535
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. #13082829C2direct (N × H)
2. C2×#10623182C2semidirect
3. C2×#10623198C2semidirect
4. C2×#10623042C2semidirect
5. C2×#10623181C2semidirect
6. C2×#10623026C2semidirect
7. C2×#10623026C2semidirect
8. C2×#10623186C2semidirect
9. C2×#10623337C2semidirect
10. C2×#10623031C2semidirect
11. C2×#10623014C2semidirect
12. C2×#10623193C2semidirect
13. C2×#10623046C2semidirect
14. C2×#10623196C2semidirect
15. C2×#10623191C2semidirect
16. C2×#10623025C2semidirect
17. C2×#10623179C2semidirect
18. C2×#10623322C2semidirect
19. C22×#66977C2semidirect
20. C22×C11×#123C2semidirect
24. C22×#4339C22semidirect
25. C23×Dic22C22semidirect
30. C2×C11×#123C22semidirect
40. #10623337C22semidirect
48. #10623322C22semidirect
50. C2×#66983C22semidirect
52. C2×#66982C22semidirect
56. C2×C4×C22⋊D11C22semidirect
58. C2×#66979C22semidirect
59. C22×C4⋊Dic11C22semidirect
66. C2×#66977C22semidirect
67. C2×#66977C22semidirect
68. C2×#66977C22semidirect
69. C2×#66977C22semidirect
70. C2×#66977C22semidirect
71. C22×Dic11⋊C4C22semidirect
72. #10623198C22semidirect
73. #10623196C22semidirect
74. #10623193C22semidirect
75. #10623191C22semidirect
76. #10623186C22semidirect
77. #10623182C22semidirect
78. #10623181C22semidirect
79. #10623179C22semidirect
80. #10623046C22semidirect
81. C2×#66951C22semidirect
82. #10623042C22semidirect
83. C2×#66950C22semidirect
84. C2×#66949C22semidirect
85. C2×#66949C22semidirect
86. C2×#66949C22semidirect
87. C2×#66947C22semidirect
88. C2×C4⋊C4×D11C22semidirect
89. #10623031C22semidirect
90. C2×#66943C22semidirect
91. C2×#66943C22semidirect
92. C2×#66942C22semidirect
93. C2×#66942C22semidirect
94. C2×#66942C22semidirect
95. C2×#66941C22semidirect
96. C2×#66941C22semidirect
97. C2×#66941C22semidirect
98. C2×#66940C22semidirect
99. #10623026C22semidirect
100. #10623026C22semidirect
101. #10623025C22semidirect
102. C2×#66939C22semidirect
103. C2×#66939C22semidirect
104. C2×#66938C22semidirect
105. C2×#66938C22semidirect
106. C2×#66938C22semidirect
107. C2×#66937C22semidirect
108. C2×#66936C22semidirect
109. C2×#66936C22semidirect
110. C2×#66936C22semidirect
111. C2×(C22⋊D11)⋊C4C22semidirect
112. C2×(C22⋊D11)⋊C4C22semidirect
113. #10623014C22semidirect
114. C2×#66932C22semidirect
115. C2×#66932C22semidirect
116. C2×#66932C22semidirect
117. C2×#66932C22semidirect
118. C2×#66932C22semidirect
119. C2×#66931C22semidirect
120. C2×#66931C22semidirect
121. C2×#66931C22semidirect
122. C2×#66931C22semidirect
123. C2×#66931C22semidirect
124. C2×#66931C22semidirect
125. C2×#66930C22semidirect
126. C2×#66930C22semidirect
156. C2×#4339C23semidirect
168. C22×Dic22C23semidirect
211. #66983C23semidirect
213. #66982C23semidirect
217. C4×C22⋊D11C23semidirect
225. #66979C23semidirect
235. C2×C4⋊Dic11C23semidirect
242. #66977C23semidirect
243. #66977C23semidirect
244. #66977C23semidirect
245. #66977C23semidirect
260. C2×Dic11⋊C4C23semidirect
266. #66951C23semidirect
267. #66950C23semidirect
268. #66949C23semidirect
269. #66949C23semidirect
270. #66949C23semidirect
271. #66947C23semidirect
272. C4⋊C4×D11C23semidirect
273. #66943C23semidirect
274. #66943C23semidirect
275. #66942C23semidirect
276. #66942C23semidirect
277. #66942C23semidirect
278. #66941C23semidirect
279. #66941C23semidirect
280. #66941C23semidirect
281. #66940C23semidirect
282. #66939C23semidirect
283. #66939C23semidirect
284. #66938C23semidirect
285. #66938C23semidirect
286. #66938C23semidirect
287. #66937C23semidirect
288. #66936C23semidirect
289. #66936C23semidirect
290. #66936C23semidirect
291. (C22⋊D11)⋊C4C23semidirect
292. (C22⋊D11)⋊C4C23semidirect
293. #66932C23semidirect
294. #66932C23semidirect
295. #66932C23semidirect
296. #66932C23semidirect
297. #66932C23semidirect
298. #66931C23semidirect
299. #66931C23semidirect
300. #66931C23semidirect
301. #66931C23semidirect
302. #66931C23semidirect
303. #66931C23semidirect
304. #66930C23semidirect
305. #66930C23semidirect
472. C22×#123D11semidirect
615. C2×#123C2×D11semidirect
890. C2×C11#3535semidirect
1042. C11C2×#3535semidirect
1175. C2#13082829direct (N × H)

Maximal subgroups

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

subgroupindex
#130828292
C2×#106231822
C2×#106231982
C2×#106230422
C2×#106231812
C2×#106230262
C2×#106231862
C2×#106233372
C2×#106230312
C2×#106230142
C2×#106231932
C2×#106230462
C2×#106231962
C2×#106231912
C2×#106230252
C2×#106231792
C2×#106233222
C22×#669772
C22×C11×#1232
C2×#353511