Finite Group Databasebeta

← C2×#13077626 #15618264

Subgroups — C2×#13077626 #15618264

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2#13077626C2116yesmaximal, direct product factor
3C2×#10622441C211yesmaximal, characteristic, complemented
4C2×#10622314C211yesmaximal, characteristic, complemented
5C2×#10622341C211yesmaximal, characteristic, complemented
6C2×#10622624C211yesmaximal, characteristic, complemented
7C2×#10622740C211yesmaximal, characteristic, complemented
8C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
9C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
10C2×#10622448C211yesmaximal, characteristic, complemented
11C2×#10622332C211yesmaximal, characteristic, complemented
12C2×#10622332C211yesmaximal, characteristic, complemented
13C2×M16×Dic11C211yesmaximal, characteristic, complemented
14C22×#66879C211yesmaximal, characteristic, complemented
15C2×D11×#97C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×#4341C411yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×D4×Dic11C411yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C2×C4×C22⋊D11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C23×C11⋊C8C2211yescharacteristic
28C22×C8×D11C2211yescharacteristic
29C22×C8×D11C2211yescharacteristic
30C4×#4341C418yes—
31C4×#4341C2218yes—
32C2×#66945C411yescharacteristic
33C2×#66940C411yescharacteristic
34C2×(C22⋊D11)⋊C4C411yescharacteristic
35C2×(C22⋊D11)⋊C4C411yescharacteristic
36C2×#66930C411yescharacteristic
37C2×#66930C411yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C2×C4×Dic22C2211yescharacteristic
40C11×#435C2218yescomplemented
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×C22⋊C8C2211yescharacteristic
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×#97C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×C22⋊(C11⋊C8)C2211yescharacteristic
47#10622740C2218yescomplemented
48M16×Dic11C2218yescomplemented
49C8×C22⋊D11C2218yescomplemented
50C2×(C2×D11)⋊C8C2211yescharacteristic
51C2×(C2×D11)⋊C8C2211yescharacteristic
52C2×#66879C2211yescharacteristic
53C2×#66879C2211yescharacteristic
54C2×#66879C2211yescharacteristic
55C2×#66879C2211yescharacteristic
56C2×#66879C2211yescharacteristic
57C2×#66879C2211yescharacteristic
58C2×#66879C2218yescomplemented
59C2×Dic11⋊C8C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×Dic11⋊C8C2211yescharacteristic
62C2×Dic11⋊C8C2211yescharacteristic
63C2×C8×Dic11C2211yescharacteristic
64C2×C8×Dic11C2211yescharacteristic
65#10622624C2218yescomplemented
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67C2×#66867C2211yescharacteristic
68#10622448C2218yescomplemented
69#10622441C2218yescomplemented
70#10622341C2218yescomplemented
71(C22⋊D11)⋊C8C2218yescomplemented
72#10622332C2218yescomplemented
73#10622332C2218yescomplemented
74D11×#97C2218yescomplemented
75#10622314C2218yescomplemented
76C22×D4×C11C2×C411yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11C2×C411yescharacteristic
80C22×C22⋊D11C2×C411yescharacteristic
81C23×Dic11C2×C411yescharacteristic
82C23×Dic11C2×C411yescharacteristic
83C23×Dic11C2×C411yescharacteristic
84C23×Dic11C2×C411yescharacteristic
85C2×#4341—28no—
86C2×#4341C2×C418yes—
87C22×C4×D11C2×C411yescharacteristic
88C22×C4×D11C2×C411yescharacteristic
89C22×C4×D11C2311yescharacteristic
90C22×Dic22C2×C411yescharacteristic
91C2×C11×M16—24no—
92C2×C11×M16C2314yes—
93C22×C8×C11—24no—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2314yes—
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C4×D4×C11C2×C414yes—
100C4×D4×C11C2314yes—
101C2×C11×C4⋊C4C2×C411yescharacteristic
102C2×C11×C22⋊C4C2×C411yescharacteristic
103C2×C11×C22⋊C4C2×C411yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11C2×C411yescharacteristic
106C2×C22⋊Dic11C2×C411yescharacteristic
107D4×Dic11C2×C418yes—
108C4×C22⋊D11C2×C414yes—
109C4×C22⋊D11C2×C414yes—
110C4×C22⋊D11C2314yes—
111C4×C22⋊D11C2314yes—
112C2×(C2×D11)⋊C4C2×C411yescharacteristic
113C2×(C2×D11)⋊C4C2×C411yescharacteristic
114C2×C4⋊Dic11C2×C411yescharacteristic
115C2×Dic11⋊C4C2×C411yescharacteristic
116C2×Dic11⋊C4C2×C411yescharacteristic
117C2×Dic11⋊C4C2×C411yescharacteristic
118C2×Dic11⋊C4C2×C411yescharacteristic
119C2×C4×Dic11C2×C411yescharacteristic
120C2×C4×Dic11C2×C411yescharacteristic
121C2×C4×Dic11C2×C411yescharacteristic
122C2×C4×Dic11C2×C411yescharacteristic
123C2×C4×Dic11C2×C411yescharacteristic
124C2×C4×Dic11C2×C411yescharacteristic
125C2×C4×Dic11C2×C414yes—
126C2×C4×Dic11C2×C414yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2311yescharacteristic
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2314yes—
132C2×#4318—24no—
133C2×#4318C2314yes—
134C22×C11⋊C8—24no—
135C22×C11⋊C8C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2314yes—
139C22×C11⋊C8C2311yescharacteristic
140C2×C8×D11—24no—
141C2×C8×D11—24no—
142C2×C8×D11C2314yes—
143C2×C8×D11C2314yes—
144#66945C2×C418yes—
145#66940C2×C418yes—
146(C22⋊D11)⋊C4C2×C418yes—
147(C22⋊D11)⋊C4C2×C418yes—
148#66930C2×C418yes—
149#66930C2×C418yes—
150C42×D11C2×C414yes—
151C42×D11C2314yes—
152C4×Dic22C2×C414yes—
153C4×Dic22C2314yes—
154C11×C4⋊C8C2314yes—
155C11×C22⋊C8C2314yes—
156C11×C22⋊C8C2314yes—
157C11×#97C2314yes—
158C22⋊(C11⋊C8)C2314yes—
159C22⋊(C11⋊C8)C2314yes—
160(C2×D11)⋊C8C2314yes—
161(C2×D11)⋊C8C2314yes—
162#66879C2314yes—
163#66879C2314yes—
164#66879C2314yes—
165#66879C2314yes—
166#66879C2314yes—
167#66879C2314yes—
168Dic11⋊C8C2314yes—
169Dic11⋊C8C2314yes—
170Dic11⋊C8C2314yes—
171Dic11⋊C8C2314yes—
172C8×Dic11C2314yes—
173C8×Dic11C2314yes—
174C4⋊(C11⋊C8)C2314yes—
175#66867C2314yes—
176C2×#2970—111nomaximal, Sylow
177C24×C11C22×C411yescharacteristic
178C24×C11C22×C411yescharacteristic
179C23×D11C22×C411yescharacteristic
180C2×D4×C11—24no—
181C2×D4×C11C22×C414yes—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11C22×C411yescharacteristic
187C22×C4×C11C22×C411yescharacteristic
188C22×C4×C11C22×C412yes—
189C22×C4×C11C22×C412yes—
190C22×C4×C11C22×C411yescharacteristic
191C22×C4×C11C22×C411yescharacteristic
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2411yescharacteristic
195C2×C22⋊D11—24no—
196C2×C22⋊D11M1618yescomplemented
197C2×C22⋊D11C22×C414yes—
198C2×C22⋊D11C22×C414yes—
199C22×Dic11—24no—
200C22×Dic11—24no—
201C22×Dic11—42no—
202C22×Dic11—42no—
203C22×Dic11C22×C414yes—
204C22×Dic11C22×C414yes—
205C22×Dic11C22×C411yescharacteristic
206C22×Dic11C22×C411yescharacteristic
207C22×Dic11C22×C411yescharacteristic
208C22×Dic11C22×C411yescharacteristic
209C22×Dic11C22×C411yescharacteristic
210C22×Dic11C22×C411yescharacteristic
211C22×Dic11C22×C414yes—
212C22×Dic11C22×C414yes—
213C22×Dic11C22×C411yescharacteristic
214#4341—232no—
215C2×C4×D11—24no—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—42no—
219C2×C4×D11C22×C412yes—
220C2×C4×D11C22×C414yes—
221C2×C4×D11C22×C414yes—
222C2×C4×D11C2412yes—
223C2×Dic22—24no—
224C2×Dic22C22×C414yes—
225C11×M16—28no—
226C2×C8×C11—28no—
227C2×C8×C11—22no—
228C2×C8×C11—22no—
229C2×C8×C11—22no—
230C2×C8×C11#4114yescomplemented
231C2×C8×C11C2412yes—
232C2×C8×C11C2412yes—
233C2×C8×C11C2412yes—
234C2×C8×C11C2412yes—
235C11×C4⋊C4C22×C414yes—
236C11×C22⋊C4C22×C414yes—
237C11×C22⋊C4C22×C414yes—
238C42×C11C22×C412yes—
239C42×C11C2412yes—
240C22⋊Dic11C22×C414yes—
241C22⋊Dic11C22×C414yes—
242(C2×D11)⋊C4C22×C414yes—
243(C2×D11)⋊C4C22×C414yes—
244C4⋊Dic11C22×C414yes—
245Dic11⋊C4C22×C414yes—
246Dic11⋊C4C22×C414yes—
247Dic11⋊C4C22×C414yes—
248Dic11⋊C4C22×C414yes—
249C4×Dic11C22×C412yes—
250C4×Dic11C22×C412yes—
251C4×Dic11C22×C412yes—
252C4×Dic11C22×C414yes—
253C4×Dic11C22×C414yes—
254C4×Dic11C22×C414yes—
255C4×Dic11C22×C414yes—
256C4×Dic11C22×C414yes—
257C4×Dic11C22×C414yes—
258C4×Dic11C2412yes—
259C4×Dic11C2412yes—
260C4×Dic11C2412yes—
261#4318—28no—
262C2×C11⋊C8—28no—
263C2×C11⋊C8—22no—
264C2×C11⋊C8—22no—
265C2×C11⋊C8—22no—
266C2×C11⋊C8#4114yescomplemented
267C2×C11⋊C8C2412yes—
268C2×C11⋊C8C2412yes—
269C2×C11⋊C8C2412yes—
270C2×C11⋊C8C2412yes—
271C8×D11—28no—
272C8×D11—28no—
273C2×C4×#41—111no—
274#2970—1116no—
275C2×#446—111no—
276C2×#446—111no—
277C2×#435—111no—
278C2×#435—111no—
279C2×#435—111no—
280C2×#435D1111yescharacteristic, complemented
281C2×C8×D4—111no—
282C2×C8×D4—111no—
283C2×#432—111no—
284C2×#432—111no—
285C2×#432—111no—
286C2×C4×M16—111no—
287C22×#97—111no—
288C22×#97—111no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11C2×M1614yes—
295C23×C11C23×C412yes—
296C23×C11C23×C412yes—
297C23×C11C23×C411yescharacteristic
298C22×D11—22no—
299C22×D11—22no—
300C22×D11C2×M1614yes—
301C22×D11C23×C412yes—
302D4×C11—28no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11C23×C412yes—
314C2×C4×C11C23×C412yes—
315C2×C4×C11C23×C412yes—
316C2×C4×C11C23×C412yes—
317C2×C4×C11C23×C411yescharacteristic
318C2×C4×C11C2×#4112yes—
319C2×C4×C11C2×#4112yes—
320C2×C4×C11C2511yescharacteristic
321C22⋊D11—28no—
322C22⋊D11C2×M16116yescomplemented
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—28no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—28no—
331C2×Dic11—44no—
332C2×Dic11—44no—
333C2×Dic11C2×M1614yes—
334C2×Dic11C23×C412yes—
335C2×Dic11C23×C412yes—
336C2×Dic11C23×C412yes—
337C2×Dic11C23×C412yes—
338C2×Dic11C23×C412yes—
339C2×Dic11C23×C412yes—
340C2×Dic11C23×C412yes—
341C4×D11—28no—
342C4×D11—24no—
343C4×D11—22no—
344C4×D11—22no—
345C4×D11—44no—
346Dic22—28no—
347C8×C11—22no—
348C8×C11—22no—
349C8×C11—22no—
350C8×C11C2×#4114yescomplemented
351C11⋊C8—22no—
352C11⋊C8—22no—
353C11⋊C8—22no—
354C11⋊C8C2×#4114yescomplemented
355C22×#41—111no—
356C22×M16—111no—
357C22×M16C2×D1111yescharacteristic
358C23×C8—111no—
359C23×C8—111no—
360C23×C8—111no—
361C23×C8C2×D1111yescharacteristic
362C4×#41—118no—
363C4×#41—118no—
364C2×C4×Q8—111no—
365C2×C4×Q8—111no—
366C2×C4×D4—111no—
367C2×C4×D4—111no—
368C2×C4×D4—111no—
369C2×C4×D4—111no—
370C2×C4×D4—111no—
371C2×C4×D4C2×D1111yescharacteristic
372C2×#117—111no—
373C2×#117—111no—
374C2×#117—111no—
375C22×C42—111no—
376C22×C42—111no—
377C22×C42—111no—
378#446—118no—
379#446—118no—
380#435—118no—
381#435—118no—
382#435—118no—
383#435C2×D1118yescomplemented
384C8×D4—118no—
385C8×D4—118no—
386#432—118no—
387#432—118no—
388#432—118no—
389C2×C4⋊C8—111no—
390C2×C4⋊C8—111no—
391C2×C4⋊C8—111no—
392C2×C4⋊C8—111no—
393C2×C4⋊C8—111no—
394C2×C4⋊C8C2×D1111yescharacteristic
395C2×C22⋊C8—111no—
396C2×C22⋊C8—111no—
397C2×C22⋊C8—111no—
398C2×C22⋊C8—111no—
399C2×C22⋊C8C2×D1111yescharacteristic
400C2×C22⋊C8C2×D1111yescharacteristic
401C4×M16—118no—
402C2×#97—111no—
403C2×#97—111no—
404C2×#97—111no—
405C2×#97—111no—
406C2×#97—111no—
407C2×#97—118no—
408C2×#97—111no—
409C2×#97—111no—
410C2×#97—118no—
411C2×#97C2×D1111yescharacteristic
412C2×C4×C8—111no—
413C2×C4×C8—111no—
414C22×C11—22no—
415C22×C11—28no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—44no—
421C22×C11C4×#4112yes—
422C22×C11C22×M1614yes—
423C22×C11C22×M1612yes—
424C22×C11#56812yes—
425C22×C11C24×C411yescharacteristic
426C2×D11—22no—
427C2×D11—28no—
428C2×D11—22no—
429C2×D11C22×M1614yes—
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—22no—
434C4×C11C4×#4112yes—
435C4×C11C22×#4111yescharacteristic
436C4×C11C22×#4111yescharacteristic
437Dic11—22no—
438Dic11—22no—
439Dic11—22no—
440Dic11—22no—
441Dic11—22no—
442Dic11—22no—
443Dic11C22×M1614yes—
444C2×#41—118no—
445C2×#41—228no—
446C22×Q8—111no—
447C22×D4—111no—
448C22×D4—111no—
449C22×D4C4×D1111yescharacteristic
450C23×C4—111no—
451C23×C4—111no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C2×M16—24no—
460C2×M16—114no—
461C2×M16—224no—
462C2×M16C22×D1114yes—
463C22×C8—24no—
464C22×C8—111no—
465C22×C8—114no—
466C22×C8—111no—
467C22×C8—111no—
468C22×C8—111no—
469C22×C8—114no—
470C22×C8—114no—
471C22×C8—224no—
472C22×C8—224no—
473C22×C8—224no—
474C22×C8C22×D1114yes—
475C22×C8C22×D1111yescharacteristic
476C22×C8C22×D1111yescharacteristic
477C22×C8C22×D1111yescharacteristic
478C22×C8C22×D1111yescharacteristic
479C4×Q8—118no—
480C4×Q8—114no—
481C4×Q8—114no—
482C4×D4—118no—
483C4×D4—114no—
484C4×D4—114no—
485C4×D4—114no—
486C4×D4—114no—
487C4×D4—118no—
488C4×D4—118no—
489C4×D4C4×D1114yes—
490C4×D4C22×D1114yes—
491#117—118no—
492#117—118no—
493#117—118no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4C4×D1111yescharacteristic
500C2×C22⋊C4—111no—
501C2×C22⋊C4—111no—
502C2×C22⋊C4—111no—
503C2×C22⋊C4—111no—
504C2×C22⋊C4C4×D1111yescharacteristic
505C2×C22⋊C4C4×D1111yescharacteristic
506C2×C42—111no—
507C2×C42—111no—
508C2×C42—111no—
509C2×C42—111no—
510C2×C42—111no—
511C2×C42—111no—
512C2×C42—114no—
513C2×C42—114no—
514C2×C42—114no—
515C2×C42—114no—
516C2×C42—111no—
517C2×C42—111no—
518C2×C42—111no—
519C2×C42—114no—
520C2×C42—114no—
521C2×C42C22×D1111yescharacteristic
522C4⋊C8—114no—
523C4⋊C8—114no—
524C4⋊C8—114no—
525C4⋊C8—114no—
526C4⋊C8—114no—
527C4⋊C8C22×D1114yes—
528C22⋊C8—114no—
529C22⋊C8—114no—
530C22⋊C8—114no—
531C22⋊C8—114no—
532C22⋊C8C22×D1114yes—
533C22⋊C8C22×D1114yes—
534#97—114no—
535#97—114no—
536#97—114no—
537#97—114no—
538#97—114no—
539#97—114no—
540#97—114no—
541#97C22×D1114yes—
542C4×C8—114no—
543C4×C8—114no—
544C2×C11—24no—
545C2×C11—42no—
546C2×C11#297014yescomplemented
547C2×C11C2×C4×#4111yescharacteristic
548C2×C11C23×M1611yescharacteristic
549C2×C11C2×#56811yescharacteristic
550D11—24no—
551C24—111no—
552C24C2×C4×D1111yescharacteristic
553C24C2×C4×D1111yescharacteristic
554#41—2232no—
555C2×Q8—114no—
556C2×Q8—224no—
557C2×D4—24no—
558C2×D4—118no—
559C2×D4—114no—
560C2×D4—114no—
561C2×D4—224no—
562C2×D4C2×C4×D1114yes—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—111no—
568C22×C4—111no—
569C22×C4—111no—
570C22×C4—111no—
571C22×C4—111no—
572C22×C4—111no—
573C22×C4—111no—
574C22×C4—114no—
575C22×C4—114no—
576C22×C4—114no—
577C22×C4—114no—
578C22×C4—114no—
579C22×C4—112no—
580C22×C4—112no—
581C22×C4—114no—
582C22×C4—224no—
583C22×C4—224no—
584C22×C4—224no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—442no—
588C22×C4—442no—
589C22×C4—442no—
590C22×C4C2×C4×D1111yescharacteristic
591C22×C4C2×C4×D1111yescharacteristic
592C22×C4C2×C4×D1112yes—
593C22×C4C2×C4×D1112yes—
594C22×C4C2×C4×D1111yescharacteristic
595C22×C4C2×C4×D1111yescharacteristic
596C22×C4C23×D1112yes—
597C22×C4C23×D1112yes—
598C22×C4C23×D1111yescharacteristic
599M16—28no—
600M16—228no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—28no—
605C2×C8—114no—
606C2×C8—112no—
607C2×C8—112no—
608C2×C8—112no—
609C2×C8—112no—
610C2×C8—228no—
611C2×C8—228no—
612C2×C8—222no—
613C2×C8—222no—
614C2×C8—222no—
615C2×C8—228no—
616C2×C8#434114yescomplemented
617C2×C8C23×D1112yes—
618C2×C8C23×D1112yes—
619C2×C8C23×D1112yes—
620C2×C8C23×D1112yes—
621C4⋊C4—114no—
622C4⋊C4—114no—
623C4⋊C4—114no—
624C4⋊C4—114no—
625C4⋊C4—114no—
626C4⋊C4C2×C4×D1114yes—
627C22⋊C4—114no—
628C22⋊C4—114no—
629C22⋊C4—114no—
630C22⋊C4—114no—
631C22⋊C4C2×C4×D1114yes—
632C22⋊C4C2×C4×D1114yes—
633C42—112no—
634C42—114no—
635C42—114no—
636C42—114no—
637C42—114no—
638C42—112no—
639C42—114no—
640C42—114no—
641C42—112no—
642C42—112no—
643C42—112no—
644C42—112no—
645C42C2×C4×D1112yes—
646C42C23×D1112yes—
647C11C2×#297011yescharacteristic, complemented, Sylow
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—114no—
654C23—112no—
655C23—222no—
656C23—222no—
657C23M16×D1114yes—
658C23C22×C4×D1112yes—
659C23C22×C4×D1112yes—
660C23C22×C4×D1111yescharacteristic
661Q8—228no—
662D4—28no—
663D4—1116no—
664D4—228no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—114no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—112no—
679C2×C4—112no—
680C2×C4—112no—
681C2×C4—112no—
682C2×C4—112no—
683C2×C4—228no—
684C2×C4—228no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—228no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—224no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—444no—
696C2×C4—444no—
697C2×C4—444no—
698C2×C4C22×C4×D1112yes—
699C2×C4C22×C4×D1112yes—
700C2×C4C22×C4×D1112yes—
701C2×C4C22×C4×D1112yes—
702C2×C4C22×C4×D1111yescharacteristic
703C2×C4C2×#434112yes—
704C2×C4#41×D1112yes—
705C2×C4C24×D1111yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—114no—
710C8—222no—
711C8—222no—
712C8—222no—
713C8C2×#434114yescomplemented
714C22—28no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—44no—
721C22—114no—
722C22—228no—
723C22—222no—
724C22—222no—
725C22C4×#434112yes—
726C22C2×M16×D1114yes—
727C22C2×M16×D1112yes—
728C22#1062328112yes—
729C22C23×C4×D1111yescharacteristic
730C4—22no—
731C4—22no—
732C4—22no—
733C4—22no—
734C4—114no—
735C4—222no—
736C4—222no—
737C4—222no—
738C4—222no—
739C4—222no—
740C4—222no—
741C4C4×#434112yes—
742C4C22×#434111yescharacteristic
743C4C2×#41×D1111yescharacteristic
744C2—24no—
745C2—42no—
746C2—224no—
747C2#1307762614yesdirect product factor
748C2C2×C4×#434111yescharacteristic
749C2C22×M16×D1111yescharacteristic
750C2C2×#1062328111yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C23×C4
prime radicalC22×#4341C4
cosocleC2×C4×C11C25
hypercenterC2×#435D11
hypocenterC11C2×#2970
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #13077626C2direct (N × H)
3. C2×#10622441C2semidirect
4. C2×#10622314C2semidirect
5. C2×#10622341C2semidirect
6. C2×#10622624C2semidirect
7. C2×#10622740C2semidirect
8. C2×C8×C22⋊D11C2semidirect
9. C2×(C22⋊D11)⋊C8C2semidirect
10. C2×#10622448C2semidirect
11. C2×#10622332C2semidirect
12. C2×#10622332C2semidirect
13. C2×M16×Dic11C2semidirect
14. C22×#66879C2semidirect
15. C2×D11×#97C2semidirect
16. C2×C11×#435C2semidirect
40. C11×#435C22semidirect
47. #10622740C22semidirect
48. M16×Dic11C22semidirect
49. C8×C22⋊D11C22semidirect
58. C2×#66879C22semidirect
65. #10622624C22semidirect
68. #10622448C22semidirect
69. #10622441C22semidirect
70. #10622341C22semidirect
71. (C22⋊D11)⋊C8C22semidirect
72. #10622332C22semidirect
73. #10622332C22semidirect
74. D11×#97C22semidirect
75. #10622314C22semidirect
196. C2×C22⋊D11M16semidirect
230. C2×C8×C11#41semidirect
266. C2×C11⋊C8#41semidirect
280. C2×#435D11semidirect
322. C22⋊D11C2×M16semidirect
350. C8×C11C2×#41semidirect
354. C11⋊C8C2×#41semidirect
383. #435C2×D11semidirect
546. C2×C11#2970semidirect
616. C2×C8#4341semidirect
647. C11C2×#2970semidirect
713. C8C2×#4341semidirect
747. C2#13077626direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#43412
#130776262
C2×#106224412
C2×#106223142
C2×#106223412
C2×#106226242
C2×#106227402
C2×C8×C22⋊D112
C2×(C22⋊D11)⋊C82
C2×#106224482
C2×#106223322
C2×M16×Dic112
C22×#668792
C2×D11×#972
C2×C11×#4352
C2×#297011