Finite Group Databasebeta

← C2×#13073195 #14922909

Subgroups — C2×#13073195 #14922909

Order 2816.

2726 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66951C211yesmaximal, characteristic, complemented
2C22×#66932C211yesmaximal, characteristic, complemented
3#13073195C2116yesmaximal, direct product factor
4C2×#10622288C211yesmaximal, characteristic, complemented
5C2×#10622565C211yesmaximal, characteristic, complemented
6C2×#10622607C211yesmaximal, characteristic, complemented
7C2×#10622570C211yesmaximal, characteristic
8C2×#10622570C211yesmaximal, characteristic
9C2×#10622570C211yesmaximal, characteristic
10C2×#10622585C211yesmaximal, characteristic, complemented
11C2×#10622564C211yesmaximal, characteristic, complemented
12C2×#10622603C211yesmaximal, characteristic, complemented
13C2×#10622589C211yesmaximal, characteristic, complemented
14C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
15C2×#10622262C211yesmaximal, characteristic, complemented
16C2×C11×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66951—28no—
47C2×#66951C2218yescomplemented
48C2×#66932—28no—
49C2×#66932C2218yescomplemented
50C11×#396C2218yescomplemented
51C2×C11×#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622607C2218yescomplemented
58#10622603C2218yescomplemented
59#10622589C2218yescomplemented
60C4⋊C4×Dic11C2218yescomplemented
61#10622585C2218yescomplemented
62#10622570C2218yes—
63#10622570C2218yes—
64#10622570C2218yes—
65#10622565C2218yescomplemented
66#10622564C2218yescomplemented
67#10622288C2218yescomplemented
68#10622262C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11—24no—
78C22×C22⋊D11—24no—
79C22×C22⋊D11—24no—
80C22×C22⋊D11C2314yes—
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C2×C11×C4⋊C4—24no—
89C2×C11×C4⋊C4—24no—
90C2×C11×C4⋊C4—42no—
91C2×C11×C4⋊C4C2314yes—
92C2×C11×C4⋊C4C2314yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—42no—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C22⋊Dic11—24no—
101C2×C22⋊Dic11—24no—
102C2×C22⋊Dic11—42no—
103C2×C22⋊Dic11C2314yes—
104C2×C22⋊Dic11C2314yes—
105C2×C22⋊Dic11C2314yes—
106C2×(C2×D11)⋊C4—24no—
107C2×(C2×D11)⋊C4—24no—
108C2×(C2×D11)⋊C4—24no—
109C2×(C2×D11)⋊C4—24no—
110C2×(C2×D11)⋊C4—42no—
111C2×(C2×D11)⋊C4—42no—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2314yes—
114C2×(C2×D11)⋊C4C2314yes—
115C2×(C2×D11)⋊C4C2314yes—
116C2×(C2×D11)⋊C4C2314yes—
117C2×(C2×D11)⋊C4C2314yes—
118C2×C4⋊Dic11—42no—
119C2×C4⋊Dic11D418yescomplemented
120C2×C4⋊Dic11C2314yes—
121C2×C4⋊Dic11C2314yes—
122C2×Dic11⋊C4—24no—
123C2×Dic11⋊C4—24no—
124C2×Dic11⋊C4—24no—
125C2×Dic11⋊C4—24no—
126C2×Dic11⋊C4—24no—
127C2×Dic11⋊C4—24no—
128C2×Dic11⋊C4C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×C4×Dic11—24no—
135C2×C4×Dic11—24no—
136C2×C4×Dic11—24no—
137C2×C4×Dic11—24no—
138C2×C4×Dic11—24no—
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2314yes—
143C2×C4×Dic11C2314yes—
144#66951—232no—
145#66932—232no—
146C11×#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C2×#2512—111nomaximal, Sylow
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11—22no—
159C24×C11—22no—
160C24×C11C2412yes—
161C24×C11C2411yescharacteristic
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—22no—
167C23×D11—22no—
168C23×D11—22no—
169C23×D11C2412yes—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11C2×D414yes—
187C22×C4×C11#4114yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C2×C22⋊D11—28no—
195C2×C22⋊D11—28no—
196C2×C22⋊D11—28no—
197C2×C22⋊D11—416no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11C2×D414yes—
215C22×Dic11C2×D414yes—
216C22×Dic11#4114yes—
217C22×Dic11#4114yes—
218C22×Dic11#4114yes—
219C22×Dic11C2412yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222C22×Dic11C2412yes—
223C22×Dic11C2412yes—
224C22×Dic11C2412yes—
225C22×Dic11C2412yes—
226C11×C4⋊C4—28no—
227C11×C4⋊C4—28no—
228C11×C4⋊C4—44no—
229C11×C22⋊C4—28no—
230C11×C22⋊C4—28no—
231C11×C22⋊C4—44no—
232C22⋊Dic11—28no—
233C22⋊Dic11—28no—
234C22⋊Dic11—44no—
235(C2×D11)⋊C4—28no—
236(C2×D11)⋊C4—28no—
237(C2×D11)⋊C4—28no—
238(C2×D11)⋊C4—28no—
239(C2×D11)⋊C4—44no—
240(C2×D11)⋊C4—44no—
241C4⋊Dic11—44no—
242C4⋊Dic11C2×D4116yescomplemented
243Dic11⋊C4—28no—
244Dic11⋊C4—28no—
245Dic11⋊C4—28no—
246Dic11⋊C4—28no—
247Dic11⋊C4—28no—
248Dic11⋊C4—28no—
249C4×Dic11—28no—
250C4×Dic11—28no—
251C4×Dic11—28no—
252C4×Dic11—28no—
253C4×Dic11—28no—
254C22×#126—111no—
255C22×#126—111no—
256#2512—1116no—
257C2×#397—111no—
258C2×#397—111no—
259C2×#396—111no—
260C2×#396D1111yescharacteristic, complemented
261C2×#390—111no—
262C2×#390—111no—
263C2×#390—111no—
264C2×#389—111no—
265C2×#388—111no—
266C2×#388—111no—
267C2×#384—111no—
268C2×C4×C4⋊C4—111no—
269C2×C4×C4⋊C4—111no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—44no—
278C23×C11—44no—
279C23×C11—44no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11—44no—
283C23×C11—44no—
284C23×C11C22×D412yes—
285C23×C11C2×#4112yes—
286C23×C11C2×#4112yes—
287C23×C11C2×#4112yes—
288C23×C11C2×#4112yes—
289C23×C11H(5,𝔽2)12yes—
290C23×C112−1+412yes—
291C23×C11C2511yescharacteristic
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—44no—
300C22×D11—44no—
301C22×D11—44no—
302C22×D11—44no—
303C22×D11—44no—
304C22×D11—44no—
305C22×D11—44no—
306C2×C4×C11—28no—
307C2×C4×C11—28no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—44no—
325C2×C4×C11—44no—
326C2×C4×C11—44no—
327C2×C4×C11—44no—
328C2×C4×C11C22×D414yes—
329C2×C4×C11C2×#4114yes—
330C22⋊D11—416no—
331C2×Dic11—28no—
332C2×Dic11—28no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—44no—
350C2×Dic11—44no—
351C2×Dic11—44no—
352C2×Dic11—44no—
353C2×Dic11#126116yescomplemented
354C2×Dic11C22×D414yes—
355C2×Dic11C22×D414yes—
356C2×Dic11C2×#4114yes—
357C2×Dic11C2×#4114yes—
358C2×Dic11C2×#4114yes—
359C23×D4—111no—
360C2×#126—118no—
361C2×#126—118no—
362C2×#126—228no—
363C2×#126—228no—
364C22×C4⋊C4—111no—
365C22×C4⋊C4—111no—
366C22×C4⋊C4—111no—
367C22×C4⋊C4—111no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—111no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4C2×D1111yescharacteristic
373C22×C4⋊C4C2×D1111yescharacteristic
374C22×C4⋊C4C2×D1111yescharacteristic
375C22×C22⋊C4—111no—
376C22×C22⋊C4—111no—
377C22×C22⋊C4—111no—
378C22×C22⋊C4—111no—
379C22×C22⋊C4—111no—
380C22×C22⋊C4—111no—
381C22×C22⋊C4—111no—
382C22×C22⋊C4—111no—
383C22×C22⋊C4—111no—
384C22×C22⋊C4C2×D1111yescharacteristic
385C22×C22⋊C4C2×D1111yescharacteristic
386C22×C22⋊C4C2×D1111yescharacteristic
387C22×C42—111no—
388C22×C42—111no—
389C22×C42—111no—
390C22×C42—111no—
391C22×C42—111no—
392#397—118no—
393#397—118no—
394#396—118no—
395#396C2×D1118yescomplemented
396#390—118no—
397#390—118no—
398#390—118no—
399#389—118no—
400#388—118no—
401#388—118no—
402#384—118no—
403C4×C4⋊C4—118no—
404C4×C4⋊C4—118no—
405C2×#95—111no—
406C2×#95—111no—
407C2×#95—111no—
408C2×#95—111no—
409C2×#95—111no—
410C2×#95C2×D1111yescharacteristic
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—88no—
419C22×C11C2×#12614yes—
420C22×C11#53214yes—
421C22×C11#54214yes—
422C22×C11#54714yes—
423C22×C11#55014yes—
424C22×C11#55314yes—
425C22×C11#55614yes—
426C22×C11C23×D411yescharacteristic
427C22×C11C22×#4111yescharacteristic
428C22×C11C22×#4111yescharacteristic
429C22×C11C22×#4111yescharacteristic
430C22×C11C22×#4111yescharacteristic
431C22×C11C2×H(5,𝔽2)11yescharacteristic
432C22×C11C2×2−1+411yescharacteristic
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—88no—
441C4×C11—24no—
442C4×C11—24no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11—42no—
447Dic11—24no—
448Dic11—24no—
449Dic11—42no—
450Dic11—42no—
451Dic11—42no—
452Dic11—42no—
453Dic11C2×#12618yescomplemented
454C25—111no—
455C25C22×D1111yescharacteristic
456C22×D4—114no—
457C22×D4—224no—
458C22×D4—224no—
459C22×D4—224no—
460C23×C4—111no—
461C23×C4—111no—
462C23×C4—111no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4C22×D1111yescharacteristic
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470C23×C4C22×D1111yescharacteristic
471C23×C4C22×D1111yescharacteristic
472C23×C4C22×D1111yescharacteristic
473#126—2232no—
474#126—2232no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—118no—
479C2×C4⋊C4—114no—
480C2×C4⋊C4—114no—
481C2×C4⋊C4—114no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4—114no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—114no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—224no—
488C2×C4⋊C4—224no—
489C2×C4⋊C4—224no—
490C2×C4⋊C4—224no—
491C2×C4⋊C4—224no—
492C2×C4⋊C4—224no—
493C2×C4⋊C4—442no—
494C2×C4⋊C4C22×D1114yes—
495C2×C4⋊C4C22×D1114yes—
496C2×C4⋊C4C22×D1114yes—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—114no—
501C2×C22⋊C4—114no—
502C2×C22⋊C4—114no—
503C2×C22⋊C4—114no—
504C2×C22⋊C4—114no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—114no—
507C2×C22⋊C4—114no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—224no—
510C2×C22⋊C4—224no—
511C2×C22⋊C4—224no—
512C2×C22⋊C4—224no—
513C2×C22⋊C4—224no—
514C2×C22⋊C4—224no—
515C2×C22⋊C4—442no—
516C2×C22⋊C4—442no—
517C2×C22⋊C4—442no—
518C2×C22⋊C4C22×D1114yes—
519C2×C22⋊C4C22×D1114yes—
520C2×C22⋊C4C22×D1114yes—
521C2×C42—114no—
522C2×C42—114no—
523C2×C42—114no—
524C2×C42—114no—
525C2×C42—114no—
526C2×C42—224no—
527C2×C42—224no—
528C2×C42—224no—
529C2×C42—224no—
530C2×C42—224no—
531#95—114no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95—114no—
536#95C22×D1114yes—
537C2×C11—82no—
538C2×C11#251218yescomplemented
539C2×C11C22×#12611yescharacteristic
540C2×C11C2×#53211yescharacteristic
541C2×C11C2×#54211yescharacteristic
542C2×C11C2×#54711yescharacteristic
543C2×C11C2×#55011yescharacteristic
544C2×C11C2×#55311yescharacteristic
545C2×C11C2×#55611yescharacteristic
546D11—82no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—112no—
555C24—222no—
556C24—222no—
557C24—222no—
558C24—222no—
559C24—222no—
560C24—222no—
561C24—222no—
562C24C23×D1112yes—
563C24C23×D1111yescharacteristic
564C2×D4—228no—
565C2×D4—228no—
566C2×D4—228no—
567C2×D4—4416no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—114no—
585C22×C4—114no—
586C22×C4—114no—
587C22×C4—112no—
588C22×C4—114no—
589C22×C4—114no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—112no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4D4×D1114yes—
613C22×C4#434114yes—
614C22×C4C23×D1112yes—
615C22×C4C23×D1112yes—
616C22×C4C23×D1112yes—
617C22×C4C23×D1112yes—
618C22×C4C23×D1112yes—
619C22×C4C23×D1112yes—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—1116no—
624C4⋊C4—228no—
625C4⋊C4—228no—
626C4⋊C4—228no—
627C4⋊C4—228no—
628C4⋊C4—228no—
629C4⋊C4—228no—
630C4⋊C4—444no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—44no—
634C22⋊C4—228no—
635C22⋊C4—228no—
636C22⋊C4—228no—
637C22⋊C4—228no—
638C22⋊C4—228no—
639C22⋊C4—228no—
640C22⋊C4—444no—
641C22⋊C4—444no—
642C22⋊C4—444no—
643C42—228no—
644C42—228no—
645C42—228no—
646C42—228no—
647C42—228no—
648C11C2×#251211yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—222no—
664C23—222no—
665C23—222no—
666C23—222no—
667C23—222no—
668C23—222no—
669C23—222no—
670C23—444no—
671C23—444no—
672C23—444no—
673C23—444no—
674C23—444no—
675C23—444no—
676C23—444no—
677C23C2×D4×D1112yes—
678C23C2×#434112yes—
679C23#6703712yes—
680C23#6704012yes—
681C23#41×D1112yes—
682C23#41×D1112yes—
683C23#41×D1112yes—
684C23C24×D1111yescharacteristic
685D4—4416no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—1116no—
709C2×C4—114no—
710C2×C4—114no—
711C2×C4—114no—
712C2×C4—114no—
713C2×C4—114no—
714C2×C4—228no—
715C2×C4—228no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—444no—
733C2×C4—444no—
734C2×C4—444no—
735C2×C4—444no—
736C2×C4C2×D4×D1114yes—
737C2×C4C2×#434114yes—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—88no—
746C22—442no—
747C22—442no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22—442no—
753C22—888no—
754C22#1062312714yes—
755C22#1062313014yes—
756C22#1062313214yes—
757C22#1062316214yes—
758C22#1062317114yes—
759C22#1062317214yes—
760C22D11×#12614yes—
761C22C22×D4×D1111yescharacteristic
762C22C22×#434111yescharacteristic
763C22C2×#6703711yescharacteristic
764C22C2×#6704011yescharacteristic
765C22C2×#41×D1111yescharacteristic
766C22C2×#41×D1111yescharacteristic
767C22C2×#41×D1111yescharacteristic
768C4—24no—
769C4—24no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—118no—
775C4—224no—
776C4—224no—
777C4—442no—
778C4—442no—
779C4—442no—
780C4—442no—
781C2—82no—
782C2—882no—
783C2#1307319518yesdirect product factor
784C2C2×D11×#12611yescharacteristic
785C2C2×#1062312711yescharacteristic
786C2C2×#1062317111yescharacteristic
787C2C2×#1062316211yescharacteristic
788C2C2×#1062313011yescharacteristic
789C2C2×#1062313211yescharacteristic
790C2C2×#1062317211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#396C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#396D11
hypocenterC11C2×#2512
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#66951C2semidirect
2. C22×#66932C2semidirect
3. #13073195C2direct (N × H)
4. C2×#10622288C2semidirect
5. C2×#10622565C2semidirect
6. C2×#10622607C2semidirect
10. C2×#10622585C2semidirect
11. C2×#10622564C2semidirect
12. C2×#10622603C2semidirect
13. C2×#10622589C2semidirect
14. C2×C4⋊C4×Dic11C2semidirect
15. C2×#10622262C2semidirect
16. C2×C11×#396C2semidirect
47. C2×#66951C22semidirect
49. C2×#66932C22semidirect
50. C11×#396C22semidirect
57. #10622607C22semidirect
58. #10622603C22semidirect
59. #10622589C22semidirect
60. C4⋊C4×Dic11C22semidirect
61. #10622585C22semidirect
65. #10622565C22semidirect
66. #10622564C22semidirect
67. #10622288C22semidirect
68. #10622262C22semidirect
119. C2×C4⋊Dic11D4semidirect
242. C4⋊Dic11C2×D4semidirect
260. C2×#396D11semidirect
353. C2×Dic11#126semidirect
395. #396C2×D11semidirect
453. Dic11C2×#126semidirect
538. C2×C11#2512semidirect
648. C11C2×#2512semidirect
783. C2#13073195direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669512
C22×#669322
#130731952
C2×#106222882
C2×#106225652
C2×#106226072
C2×#106225702
C2×#106225852
C2×#106225642
C2×#106226032
C2×#106225892
C2×C4⋊C4×Dic112
C2×#106222622
C2×C11×#3962
C2×#251211