Finite Group Databasebeta

← C2×#13077272 #15617525

Subgroups — C2×#13077272 #15617525

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#117C211yesmaximal, characteristic
2#13077272C2116yesmaximal, direct product factor
3C2×#10622613C211yesmaximal, characteristic, complemented
4C2×#10622333C211yesmaximal, characteristic, complemented
5C2×#10622333C211yesmaximal, characteristic, complemented
6C2×#10622448C211yesmaximal, characteristic, complemented
7C2×#10622318C211yesmaximal, characteristic, complemented
8C2×#10622446C211yesmaximal, characteristic, complemented
9C2×#10622298C211yesmaximal, characteristic, complemented
10C2×#10622452C211yesmaximal, characteristic, complemented
11C2×#10622452C211yesmaximal, characteristic, complemented
12C2×#10622339C211yesmaximal, characteristic
13C2×D11×C22⋊C8C211yesmaximal, characteristic
14C2×#10622321C211yesmaximal, characteristic, complemented
15C2×#10622302C211yesmaximal, characteristic, complemented
16C2×C11×#433C211yesmaximal, characteristic, complemented
17C23×C4×D11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C22×C8×D11C2211yescharacteristic
24D11×#117C418yes—
25D11×#117C2218yes—
26C2×#66945C411yescharacteristic
27C2×#66945C411yescharacteristic
28C2×C4⋊C4×D11C411yescharacteristic
29C2×C4⋊C4×D11C411yescharacteristic
30C2×C22⋊C4×D11C411yescharacteristic
31C2×C22⋊C4×D11C411yescharacteristic
32C2×#66930C411yescharacteristic
33C2×#66930C411yescharacteristic
34C2×#66925C2211yescharacteristic
35C2×#66925C2211yescharacteristic
36C2×C42×D11C2211yescharacteristic
37C2×C42×D11C2211yescharacteristic
38C11×#433C2218yescomplemented
39C2×C11×C4⋊C8C2211yescharacteristic, complemented
40C2×C11×C4⋊C8C2211yescharacteristic, complemented
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C11×C22⋊C8C2211yescharacteristic
43C2×C11×#97C2211yescharacteristic, complemented
44C2×C4×C8×C11C2211yescharacteristic, complemented
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×C22⋊(C11⋊C8)C2211yescharacteristic
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×(C2×D11)⋊C8C2211yescharacteristic
49C2×(C2×D11)⋊C8C2211yescharacteristic
50C2×(C2×D11)⋊C8C2211yescharacteristic
51C2×#66879C2211yescharacteristic, complemented
52C2×#66879C2211yescharacteristic, complemented
53C2×Dic11⋊C8C2211yescharacteristic, complemented
54C2×Dic11⋊C8C2211yescharacteristic, complemented
55C2×Dic11⋊C8C2211yescharacteristic, complemented
56C2×Dic11⋊C8C2211yescharacteristic, complemented
57C2×C8×Dic11C2211yescharacteristic, complemented
58C2×C8×Dic11C2211yescharacteristic, complemented
59#10622613C2218yescomplemented
60C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
61C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
62C2×#66867C2211yescharacteristic, complemented
63C2×C4×C11⋊C8C2211yescharacteristic, complemented
64#10622452C2218yescomplemented
65#10622452C2218yescomplemented
66#10622448C2218yescomplemented
67#10622446C2218yescomplemented
68#10622339C2218yes—
69D11×C22⋊C8C2218yes—
70#10622333C2218yescomplemented
71#10622333C2218yescomplemented
72#10622321C2218yescomplemented
73#10622318C2218yescomplemented
74#10622302C2218yescomplemented
75#10622298C2218yescomplemented
76C24×D11C2×C411yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×Dic11C2×C411yescharacteristic
79C22×C4×D11—24no—
80C22×C4×D11—24no—
81C22×C4×D11C2×C411yescharacteristic
82C22×C4×D11C2×C411yescharacteristic
83C22×C4×D11C2×C411yescharacteristic
84C22×C4×D11C2×C411yescharacteristic
85C22×C4×D11C2×C414yes—
86C22×C4×D11C2×C411yescharacteristic
87C22×C4×D11C2×C411yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2314yes—
90C22×C4×D11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C11×#117C2×C414yes—
96C11×#117C2314yes—
97C2×C11×C4⋊C4C2×C411yescharacteristic
98C2×C11×C4⋊C4C2×C411yescharacteristic
99C2×C11×C22⋊C4C2×C411yescharacteristic
100C2×C11×C22⋊C4C2×C411yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11C2×C411yescharacteristic
104C2×C22⋊Dic11C2×C411yescharacteristic
105C2×(C2×D11)⋊C4C2×C411yescharacteristic
106C2×(C2×D11)⋊C4C2×C411yescharacteristic
107C2×(C2×D11)⋊C4C2×C411yescharacteristic
108C2×(C2×D11)⋊C4C2×C411yescharacteristic
109#66979C2×C414yes—
110#66979C2314yes—
111C2×C4⋊Dic11C2×C411yescharacteristic
112C2×C4⋊Dic11C2×C411yescharacteristic
113C2×Dic11⋊C4C2×C411yescharacteristic
114C2×Dic11⋊C4C2×C411yescharacteristic
115C2×Dic11⋊C4C2×C411yescharacteristic
116C2×Dic11⋊C4C2×C411yescharacteristic
117C2×C4×Dic11C2×C411yescharacteristic
118C2×C4×Dic11C2×C411yescharacteristic
119C2×C4×Dic11C2×C411yescharacteristic
120C2×C4×Dic11C2×C411yescharacteristic
121C2×C4×Dic11C2311yescharacteristic
122C2×C4×Dic11C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C2×#4313—24no—
128C2×#4313—24no—
129C2×#4313C2314yes—
130C2×#4313C2314yes—
131C2×C8×D11—24no—
132C2×C8×D11—24no—
133C2×C8×D11C2314yes—
134C2×C8×D11C2314yes—
135#66945C2×C418yes—
136#66945C2×C418yes—
137C4⋊C4×D11C2×C418yes—
138C4⋊C4×D11C2×C418yes—
139C22⋊C4×D11C2×C418yes—
140C22⋊C4×D11C2×C418yes—
141#66930C2×C418yes—
142#66930C2×C418yes—
143#66925C2×C414yes—
144#66925C2×C414yes—
145#66925C2314yes—
146#66925C2314yes—
147C42×D11C2×C414yes—
148C42×D11C2×C414yes—
149C42×D11C2314yes—
150C42×D11C2314yes—
151C11×C4⋊C8C2314yescomplemented
152C11×C4⋊C8C2314yescomplemented
153C11×C22⋊C8C2314yes—
154C11×C22⋊C8C2314yes—
155C11×#97C2314yescomplemented
156C4×C8×C11C2314yescomplemented
157C22⋊(C11⋊C8)C2314yes—
158C22⋊(C11⋊C8)C2314yes—
159(C2×D11)⋊C8C2314yes—
160(C2×D11)⋊C8C2314yes—
161(C2×D11)⋊C8C2314yes—
162(C2×D11)⋊C8C2314yes—
163#66879C2314yescomplemented
164#66879C2314yescomplemented
165Dic11⋊C8C2314yescomplemented
166Dic11⋊C8C2314yescomplemented
167Dic11⋊C8C2314yescomplemented
168Dic11⋊C8C2314yescomplemented
169C8×Dic11C2314yescomplemented
170C8×Dic11C2314yescomplemented
171C4⋊(C11⋊C8)C2314yescomplemented
172C4⋊(C11⋊C8)C2314yescomplemented
173#66867C2314yescomplemented
174C4×C11⋊C8C2314yescomplemented
175C2×#2924—111nomaximal, Sylow
176C24×C11C22×C411yescharacteristic
177C23×D11—24no—
178C23×D11—24no—
179C23×D11—42no—
180C23×D11C22×C414yes—
181C23×D11C22×C411yescharacteristic
182C23×D11C22×C411yescharacteristic
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11C22×C411yescharacteristic
186C22×C4×C11C22×C411yescharacteristic
187C22×C4×C11C22×C411yescharacteristic
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C22×C411yescharacteristic
190C22×C4×C11C22×C412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2411yescharacteristic
193C22×Dic11—24no—
194C22×Dic11C22×C414yes—
195C22×Dic11C22×C411yescharacteristic
196C22×Dic11C22×C411yescharacteristic
197C22×Dic11C22×C411yescharacteristic
198C22×Dic11C22×C411yescharacteristic
199C22×Dic11C22×C411yescharacteristic
200C22×Dic11C22×C411yescharacteristic
201C2×C4×D11—24no—
202C2×C4×D11—216no—
203C2×C4×D11—28no—
204C2×C4×D11—28no—
205C2×C4×D11—24no—
206C2×C4×D11—24no—
207C2×C4×D11—24no—
208C2×C4×D11—22no—
209C2×C4×D11—22no—
210C2×C4×D11—42no—
211C2×C4×D11—42no—
212C2×C4×D11C22×C412yes—
213C2×C4×D11C22×C414yes—
214C2×C4×D11C22×C414yes—
215C2×C4×D11C22×C414yes—
216C2×C4×D11C22×C414yes—
217C2×C4×D11C22×C414yes—
218C2×C4×D11C22×C414yes—
219C2×C4×D11C22×C412yes—
220C2×C4×D11#4114yes—
221C2×C4×D11#4114yes—
222C2×C4×D11C2412yes—
223C2×C4×D11C2412yes—
224C2×C8×C11—22no—
225C2×C8×C11—22no—
226C2×C8×C11—22no—
227C2×C8×C11—22no—
228C2×C8×C11C2412yes—
229C2×C8×C11C2412yes—
230C2×C8×C11C2412yes—
231C2×C8×C11C2412yes—
232C11×C4⋊C4C22×C414yes—
233C11×C4⋊C4C22×C414yes—
234C11×C22⋊C4C22×C414yes—
235C11×C22⋊C4C22×C414yes—
236C42×C11C22×C412yes—
237C42×C11C22×C412yes—
238C42×C11C2412yes—
239C42×C11C2412yes—
240C22⋊Dic11C22×C414yes—
241C22⋊Dic11C22×C414yes—
242(C2×D11)⋊C4C22×C414yes—
243(C2×D11)⋊C4C22×C414yes—
244(C2×D11)⋊C4C22×C414yes—
245(C2×D11)⋊C4C22×C414yes—
246C4⋊Dic11C22×C414yes—
247C4⋊Dic11C22×C414yes—
248Dic11⋊C4C22×C414yes—
249Dic11⋊C4C22×C414yes—
250Dic11⋊C4C22×C414yes—
251Dic11⋊C4C22×C414yes—
252C4×Dic11C22×C412yes—
253C4×Dic11C22×C412yes—
254C4×Dic11C22×C414yes—
255C4×Dic11C22×C414yes—
256C4×Dic11C22×C414yes—
257C4×Dic11C22×C414yes—
258C4×Dic11C2412yes—
259C4×Dic11C2412yes—
260C2×C11⋊C8—22no—
261C2×C11⋊C8—22no—
262C2×C11⋊C8—22no—
263C2×C11⋊C8—22no—
264C2×C11⋊C8C2412yes—
265C2×C11⋊C8C2412yes—
266C2×C11⋊C8C2412yes—
267C2×C11⋊C8C2412yes—
268#4313—28no—
269#4313—28no—
270C8×D11—28no—
271C8×D11—28no—
272C22×#117—111no—
273#2924—1116no—
274C2×#433—111no—
275C2×#433—111no—
276C2×#433—111no—
277C2×#433D1111yescharacteristic, complemented
278C2×#432—111no—
279C2×#432—111no—
280C2×#431—111no—
281C2×#431—111no—
282C2×#424—111no—
283C2×#424—111no—
284C2×#407—111no—
285C22×C22⋊C8—111no—
286C2×#405—111no—
287C2×#405—111no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11C23×C412yes—
292C23×C11C23×C411yescharacteristic
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—28no—
298C22×D11—28no—
299C22×D11—44no—
300C22×D11—416no—
301C22×D11#11714yes—
302C22×D11#13114yes—
303C22×D11C23×C412yes—
304C22×D11C23×C412yes—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—24no—
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×C412yes—
318C2×C4×C11C23×C411yescharacteristic
319C2×C4×C11C2×#4112yes—
320C2×C4×C11C2×#4112yes—
321C2×C4×C11C2511yescharacteristic
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—28no—
328C2×Dic11#11714yes—
329C2×Dic11C23×C412yes—
330C2×Dic11C23×C412yes—
331C2×Dic11C23×C412yes—
332C2×Dic11C23×C412yes—
333C2×Dic11C23×C412yes—
334C2×Dic11C23×C412yes—
335C4×D11—28no—
336C4×D11—28no—
337C4×D11—28no—
338C4×D11—24no—
339C4×D11—22no—
340C4×D11—22no—
341C4×D11—28no—
342C4×D11—44no—
343C4×D11—44no—
344C4×D11#11718yes—
345C4×D11C2×#4114yes—
346C4×D11C2×#4114yes—
347C8×C11—22no—
348C8×C11—22no—
349C8×C11—22no—
350C8×C11—22no—
351C11⋊C8—22no—
352C11⋊C8—22no—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C24×C4—111no—
356C22×M16—111no—
357C22×M16—111no—
358C23×C8—111no—
359C23×C8—111no—
360C2×#117—111no—
361C2×#117—118no—
362C2×#117—118no—
363C2×#117—111no—
364C2×#117—111no—
365C2×#117—111no—
366C2×#117—111no—
367C2×#117—111no—
368C2×#117—111no—
369C2×#117C2×D1111yescharacteristic
370C22×C4⋊C4—111no—
371C22×C4⋊C4—111no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—111no—
374C22×C42—111no—
375C22×C42—111no—
376#433—118no—
377#433—118no—
378#433—118no—
379#433C2×D1118yescomplemented
380#432—118no—
381#432—118no—
382#431—118no—
383#431—118no—
384#424—118no—
385#424—118no—
386C2×C4⋊C8—111no—
387C2×C4⋊C8—111no—
388C2×C4⋊C8—111no—
389C2×C4⋊C8—111no—
390C2×C4⋊C8—111no—
391C2×C4⋊C8—111no—
392C2×C4⋊C8C2×D1111yescharacteristic, complemented
393C2×C4⋊C8C2×D1111yescharacteristic, complemented
394#407—118no—
395C2×C22⋊C8—111no—
396C2×C22⋊C8—111no—
397C2×C22⋊C8—111no—
398C2×C22⋊C8—111no—
399C2×C22⋊C8—111no—
400C2×C22⋊C8—111no—
401C2×C22⋊C8—118no—
402C2×C22⋊C8C2×D1111yescharacteristic
403C2×C22⋊C8C2×D1111yescharacteristic
404#405—118no—
405#405—118no—
406C2×#97—111no—
407C2×#97—111no—
408C2×#97—111no—
409C2×#97C2×D1111yescharacteristic, complemented
410C2×C4×C8—111no—
411C2×C4×C8—111no—
412C2×C4×C8—111no—
413C2×C4×C8C2×D1111yescharacteristic, complemented
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—44no—
418C22×C11C2×#11712yes—
419C22×C11C2×#13112yes—
420C22×C11#56812yes—
421C22×C11C24×C411yescharacteristic
422C2×D11—22no—
423C2×D11—28no—
424C2×D11—28no—
425C2×D11—22no—
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—416no—
429C2×D11C2×#11714yes—
430C2×D11C2×#13114yes—
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—22no—
434C4×C11—22no—
435C4×C11—22no—
436C4×C11C2×#11712yes—
437C4×C11C22×#4111yescharacteristic
438C4×C11C22×#4111yescharacteristic
439Dic11—22no—
440Dic11—22no—
441Dic11—22no—
442Dic11—22no—
443Dic11—22no—
444Dic11C2×#11714yes—
445C25—111no—
446C23×C4—111no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—114no—
452C23×C4—111no—
453C23×C4—114no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—224no—
458C23×C4—224no—
459C23×C4C22×D1111yescharacteristic
460C2×M16—114no—
461C2×M16—114no—
462C2×M16—224no—
463C2×M16—224no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8—111no—
467C22×C8—111no—
468C22×C8—114no—
469C22×C8—114no—
470C22×C8—224no—
471C22×C8—224no—
472C22×C8C22×D1111yescharacteristic
473C22×C8C22×D1111yescharacteristic
474C22×C8C22×D1111yescharacteristic
475C22×C8C22×D1111yescharacteristic
476#117—114no—
477#117—114no—
478#117—118no—
479#117—118no—
480#117—118no—
481#117—118no—
482#117—114no—
483#117—114no—
484#117—114no—
485#117—114no—
486#117C4×D1114yes—
487#117C22×D1114yes—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—118no—
495C2×C4⋊C4—118no—
496C2×C4⋊C4C4×D1111yescharacteristic
497C2×C4⋊C4C4×D1111yescharacteristic
498C2×C22⋊C4—111no—
499C2×C22⋊C4—111no—
500C2×C22⋊C4—111no—
501C2×C22⋊C4—111no—
502C2×C22⋊C4—111no—
503C2×C22⋊C4—111no—
504C2×C22⋊C4—118no—
505C2×C22⋊C4—118no—
506C2×C22⋊C4C4×D1111yescharacteristic
507C2×C22⋊C4C4×D1111yescharacteristic
508C2×C42—111no—
509C2×C42—111no—
510C2×C42—111no—
511C2×C42—111no—
512C2×C42—111no—
513C2×C42—111no—
514C2×C42—114no—
515C2×C42—114no—
516C2×C42—114no—
517C2×C42—114no—
518C2×C42C22×D1111yescharacteristic
519C2×C42C22×D1111yescharacteristic
520C4⋊C8—114no—
521C4⋊C8—114no—
522C4⋊C8—114no—
523C4⋊C8—114no—
524C4⋊C8—114no—
525C4⋊C8—114no—
526C4⋊C8C22×D1114yescomplemented
527C4⋊C8C22×D1114yescomplemented
528C22⋊C8—114no—
529C22⋊C8—114no—
530C22⋊C8—114no—
531C22⋊C8—114no—
532C22⋊C8—114no—
533C22⋊C8—114no—
534C22⋊C8C22×D1114yes—
535C22⋊C8C22×D1114yes—
536#97—114no—
537#97—114no—
538#97—114no—
539#97C22×D1114yescomplemented
540C4×C8—114no—
541C4×C8—114no—
542C4×C8—114no—
543C4×C8C22×D1114yescomplemented
544C2×C11—42no—
545C2×C11#292414yescomplemented
546C2×C11C22×#11711yescharacteristic
547C2×C11C22×#13111yescharacteristic
548C2×C11C2×#56811yescharacteristic
549D11—24no—
550D11—24no—
551C24—111no—
552C24—111no—
553C24—114no—
554C24—224no—
555C24—224no—
556C24—442no—
557C24C2×C4×D1111yescharacteristic
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—111no—
561C22×C4—112no—
562C22×C4—114no—
563C22×C4—114no—
564C22×C4—112no—
565C22×C4—111no—
566C22×C4—111no—
567C22×C4—111no—
568C22×C4—111no—
569C22×C4—111no—
570C22×C4—114no—
571C22×C4—112no—
572C22×C4—114no—
573C22×C4—114no—
574C22×C4—114no—
575C22×C4—114no—
576C22×C4—112no—
577C22×C4—114no—
578C22×C4—114no—
579C22×C4—224no—
580C22×C4—2216no—
581C22×C4—228no—
582C22×C4—228no—
583C22×C4—224no—
584C22×C4—224no—
585C22×C4—224no—
586C22×C4—224no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—442no—
590C22×C4—442no—
591C22×C4C2×C4×D1111yescharacteristic
592C22×C4C2×C4×D1111yescharacteristic
593C22×C4C2×C4×D1111yescharacteristic
594C22×C4C2×C4×D1111yescharacteristic
595C22×C4C2×C4×D1111yescharacteristic
596C22×C4C2×C4×D1112yes—
597C22×C4C23×D1112yes—
598C22×C4C23×D1111yescharacteristic
599M16—228no—
600M16—228no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—112no—
606C2×C8—112no—
607C2×C8—112no—
608C2×C8—112no—
609C2×C8—228no—
610C2×C8—228no—
611C2×C8—222no—
612C2×C8—222no—
613C2×C8—222no—
614C2×C8—222no—
615C2×C8C23×D1112yes—
616C2×C8C23×D1112yes—
617C2×C8C23×D1112yes—
618C2×C8C23×D1112yes—
619C4⋊C4—114no—
620C4⋊C4—114no—
621C4⋊C4—114no—
622C4⋊C4—114no—
623C4⋊C4—114no—
624C4⋊C4—114no—
625C4⋊C4C2×C4×D1114yes—
626C4⋊C4C2×C4×D1114yes—
627C22⋊C4—114no—
628C22⋊C4—114no—
629C22⋊C4—114no—
630C22⋊C4—114no—
631C22⋊C4—114no—
632C22⋊C4—114no—
633C22⋊C4C2×C4×D1114yes—
634C22⋊C4C2×C4×D1114yes—
635C42—114no—
636C42—114no—
637C42—114no—
638C42—114no—
639C42—112no—
640C42—112no—
641C42—112no—
642C42—112no—
643C42C2×C4×D1112yes—
644C42C2×C4×D1112yes—
645C42C23×D1112yes—
646C42C23×D1112yes—
647C11C2×#292411yescharacteristic, complemented, Sylow
648C23—22no—
649C23—22no—
650C23—22no—
651C23—114no—
652C23—114no—
653C23—112no—
654C23—112no—
655C23—228no—
656C23—228no—
657C23—222no—
658C23—222no—
659C23—222no—
660C23—222no—
661C23—444no—
662C23—4416no—
663C23C22×C4×D1112yes—
664C23C22×C4×D1111yescharacteristic
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—114no—
674C2×C4—112no—
675C2×C4—118no—
676C2×C4—114no—
677C2×C4—114no—
678C2×C4—112no—
679C2×C4—112no—
680C2×C4—112no—
681C2×C4—112no—
682C2×C4—112no—
683C2×C4—228no—
684C2×C4—228no—
685C2×C4—228no—
686C2×C4—228no—
687C2×C4—228no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—224no—
694C2×C4—222no—
695C2×C4—222no—
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×D1112yes—
703C2×C4C22×C4×D1111yescharacteristic
704C2×C4#41×D1112yes—
705C2×C4#41×D1112yes—
706C2×C4C24×D1111yescharacteristic
707C8—22no—
708C8—22no—
709C8—22no—
710C8—22no—
711C8—222no—
712C8—222no—
713C8—222no—
714C8—222no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—44no—
719C22—114no—
720C22—114no—
721C22—228no—
722C22—228no—
723C22—222no—
724C22—222no—
725C22—222no—
726C22—222no—
727C22—4416no—
728C22D11×#11712yes—
729C22D11×#13112yes—
730C22#1062328112yes—
731C22C23×C4×D1111yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—22no—
736C4—22no—
737C4—114no—
738C4—222no—
739C4—222no—
740C4—222no—
741C4—222no—
742C4—222no—
743C4D11×#11712yes—
744C4C2×#41×D1111yescharacteristic
745C4C2×#41×D1111yescharacteristic
746C2—42no—
747C2—224no—
748C2—224no—
749C2#1307727214yesdirect product factor
750C2C2×D11×#11711yescharacteristic
751C2C2×D11×#13111yescharacteristic
752C2C2×#1062328111yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#433C2
socleC23×C11C23×C4
prime radicalC24×D11C2×C4
cosocleC2×C4×C11C25
hypercenterC2×#433D11
hypocenterC11C2×#2924
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #13077272C2direct (N × H)
3. C2×#10622613C2semidirect
4. C2×#10622333C2semidirect
5. C2×#10622333C2semidirect
6. C2×#10622448C2semidirect
7. C2×#10622318C2semidirect
8. C2×#10622446C2semidirect
9. C2×#10622298C2semidirect
10. C2×#10622452C2semidirect
11. C2×#10622452C2semidirect
14. C2×#10622321C2semidirect
15. C2×#10622302C2semidirect
16. C2×C11×#433C2semidirect
38. C11×#433C22semidirect
39. C2×C11×C4⋊C8C22semidirect
40. C2×C11×C4⋊C8C22semidirect
43. C2×C11×#97C22semidirect
44. C2×C4×C8×C11C22semidirect
51. C2×#66879C22semidirect
52. C2×#66879C22semidirect
53. C2×Dic11⋊C8C22semidirect
54. C2×Dic11⋊C8C22semidirect
55. C2×Dic11⋊C8C22semidirect
56. C2×Dic11⋊C8C22semidirect
57. C2×C8×Dic11C22semidirect
58. C2×C8×Dic11C22semidirect
59. #10622613C22semidirect
60. C2×C4⋊(C11⋊C8)C22semidirect
61. C2×C4⋊(C11⋊C8)C22semidirect
62. C2×#66867C22semidirect
63. C2×C4×C11⋊C8C22semidirect
64. #10622452C22semidirect
65. #10622452C22semidirect
66. #10622448C22semidirect
67. #10622446C22semidirect
70. #10622333C22semidirect
71. #10622333C22semidirect
72. #10622321C22semidirect
73. #10622318C22semidirect
74. #10622302C22semidirect
75. #10622298C22semidirect
151. C11×C4⋊C8C23semidirect
152. C11×C4⋊C8C23semidirect
155. C11×#97C23semidirect
156. C4×C8×C11C23semidirect
163. #66879C23semidirect
164. #66879C23semidirect
165. Dic11⋊C8C23semidirect
166. Dic11⋊C8C23semidirect
167. Dic11⋊C8C23semidirect
168. Dic11⋊C8C23semidirect
169. C8×Dic11C23semidirect
170. C8×Dic11C23semidirect
171. C4⋊(C11⋊C8)C23semidirect
172. C4⋊(C11⋊C8)C23semidirect
173. #66867C23semidirect
174. C4×C11⋊C8C23semidirect
277. C2×#433D11semidirect
379. #433C2×D11semidirect
392. C2×C4⋊C8C2×D11semidirect
393. C2×C4⋊C8C2×D11semidirect
409. C2×#97C2×D11semidirect
413. C2×C4×C8C2×D11semidirect
526. C4⋊C8C22×D11semidirect
527. C4⋊C8C22×D11semidirect
539. #97C22×D11semidirect
543. C4×C8C22×D11semidirect
545. C2×C11#2924semidirect
647. C11C2×#2924semidirect
749. C2#13077272direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D11×#1172
#130772722
C2×#106226132
C2×#106223332
C2×#106224482
C2×#106223182
C2×#106224462
C2×#106222982
C2×#106224522
C2×#106223392
C2×D11×C22⋊C82
C2×#106223212
C2×#106223022
C2×C11×#4332
C2×#292411