Finite Group Databasebeta

← C2×#13077561 #15618151

Subgroups — C2×#13077561 #15618151

Order 2816.

1938 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2#13077561C2116yesmaximal, direct product factor
3C2×#10622637C211yesmaximal, characteristic, complemented
4C2×#10622441C211yesmaximal, characteristic, complemented
5C2×#10622441C211yesmaximal, characteristic, complemented
6C2×#10622314C211yesmaximal, characteristic, complemented
7C2×#10622314C211yesmaximal, characteristic, complemented
8C2×C8×Dic22C211yesmaximal, characteristic, complemented
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×#10622452C211yesmaximal, characteristic
11C2×#10622452C211yesmaximal, characteristic
12C2×D11×C4⋊C8C211yesmaximal, characteristic
13C2×#10622321C211yesmaximal, characteristic
14C2×#10622302C211yesmaximal, characteristic
15C2×#10622320C211yesmaximal, characteristic
16C2×C11×#446C211yesmaximal, characteristic, complemented
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#66999C411yescharacteristic
19C2×#66997C411yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C22×C8×D11C2211yescharacteristic
24#10623109C418yes—
25#10623109C2218yes—
26C2×#66950C411yescharacteristic
27C2×#66949C411yescharacteristic
28C2×#66949C411yescharacteristic
29C2×#66942C411yescharacteristic
30C2×#66942C411yescharacteristic
31C2×#66941C411yescharacteristic
32C2×#66925C2211yescharacteristic
33C2×#66925C2211yescharacteristic
34C2×C42×D11C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C2×C4×Dic22C2211yescharacteristic
38C11×#446C2218yescomplemented
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#97C2211yescharacteristic
43C2×C11×#97C2211yescharacteristic
44C2×C4×C8×C11C2211yescharacteristic
45C2×#66879C2211yescharacteristic
46C2×#66879C2211yescharacteristic
47C2×Dic11⋊C8C2211yescharacteristic
48C2×Dic11⋊C8C2211yescharacteristic
49C2×Dic11⋊C8C2211yescharacteristic
50C2×Dic11⋊C8C2211yescharacteristic
51C2×Dic11⋊C8C2211yescharacteristic
52C2×Dic11⋊C8C2211yescharacteristic
53C2×C8×Dic11C2211yescharacteristic
54C2×C8×Dic11C2211yescharacteristic
55C2×C8×Dic11C2211yescharacteristic
56C2×C8×Dic11C2211yescharacteristic
57#10622637C2218yescomplemented
58C2×C4⋊(C11⋊C8)C2211yescharacteristic
59C2×C4⋊(C11⋊C8)C2211yescharacteristic
60C2×C4⋊(C11⋊C8)C2211yescharacteristic
61C2×#66867C2211yescharacteristic
62C2×#66867C2211yescharacteristic
63C2×C4×C11⋊C8C2211yescharacteristic
64#10622452C2218yes—
65#10622452C2218yes—
66D11×C4⋊C8C2218yes—
67#10622443C2218yescomplemented
68#10622441C2218yescomplemented
69#10622441C2218yescomplemented
70#10622321C2218yes—
71#10622320C2218yes—
72#10622314C2218yescomplemented
73#10622314C2218yescomplemented
74#10622302C2218yes—
75C8×Dic22C2218yescomplemented
76C22×Q8×C11C2×C411yescharacteristic
77C22×C4×D11C2×C411yescharacteristic
78C22×C4×D11C2×C411yescharacteristic
79C22×C4×D11C2311yescharacteristic
80C22×Dic22C2×C411yescharacteristic
81C22×Dic22C2×C411yescharacteristic
82C22×Dic22C2×C411yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C4×Q8×C11C2×C414yes—
88C4×Q8×C11C2314yes—
89C2×C11×C4⋊C4C2×C411yescharacteristic
90C2×C11×C4⋊C4C2×C411yescharacteristic
91C2×C11×C4⋊C4C2×C411yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95#66999C2×C418yes—
96#66997C2×C418yes—
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×C4⋊Dic11C2×C411yescharacteristic
102C2×C4⋊Dic11C2×C411yescharacteristic
103C2×C4⋊Dic11C2×C411yescharacteristic
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×Dic11⋊C4C2×C411yescharacteristic
106C2×Dic11⋊C4C2×C411yescharacteristic
107C2×Dic11⋊C4C2×C411yescharacteristic
108C2×Dic11⋊C4C2×C411yescharacteristic
109C2×Dic11⋊C4C2×C411yescharacteristic
110C2×Dic11⋊C4C2×C411yescharacteristic
111C2×Dic11⋊C4C2×C411yescharacteristic
112C2×Dic11⋊C4C2×C411yescharacteristic
113C2×Dic11⋊C4C2×C411yescharacteristic
114C2×C4×Dic11C2×C411yescharacteristic
115C2×C4×Dic11C2×C411yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C2×C4×Dic11C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C2×#4313—24no—
124C2×#4313Q818yescomplemented
125C2×#4313C2314yes—
126C2×#4313C2314yes—
127C2×C8×D11—24no—
128C2×C8×D11—24no—
129C2×C8×D11C2314yes—
130C2×C8×D11C2314yes—
131#66950C2×C418yes—
132#66949C2×C418yes—
133#66949C2×C418yes—
134#66942C2×C418yes—
135#66942C2×C418yes—
136#66941C2×C418yes—
137#66925C2×C414yes—
138#66925C2×C414yes—
139#66925C2314yes—
140#66925C2314yes—
141C42×D11C2×C414yes—
142C42×D11C2314yes—
143C4×Dic22C2×C414yes—
144C4×Dic22C2×C414yes—
145C4×Dic22C2×C414yes—
146C4×Dic22C2314yes—
147C4×Dic22C2314yes—
148C4×Dic22C2314yes—
149C11×C4⋊C8C2314yes—
150C11×C4⋊C8C2314yes—
151C11×C4⋊C8C2314yes—
152C11×#97C2314yes—
153C11×#97C2314yes—
154C4×C8×C11C2314yes—
155#66879C2314yes—
156#66879C2314yes—
157Dic11⋊C8C2314yes—
158Dic11⋊C8C2314yes—
159Dic11⋊C8C2314yes—
160Dic11⋊C8C2314yes—
161Dic11⋊C8C2314yes—
162Dic11⋊C8C2314yes—
163C8×Dic11C2314yes—
164C8×Dic11C2314yes—
165C8×Dic11C2314yes—
166C8×Dic11C2314yes—
167C4⋊(C11⋊C8)C2314yes—
168C4⋊(C11⋊C8)C2314yes—
169C4⋊(C11⋊C8)C2314yes—
170#66867C2314yes—
171#66867C2314yes—
172C4×C11⋊C8C2314yes—
173C2×#2962—111nomaximal, Sylow
174C23×D11C22×C411yescharacteristic
175C2×Q8×C11—42no—
176C2×Q8×C11C22×C414yes—
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C22×C411yescharacteristic
180C22×C4×C11C22×C411yescharacteristic
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C22×Dic11C22×C411yescharacteristic
185C22×Dic11C22×C411yescharacteristic
186C22×Dic11C22×C411yescharacteristic
187C22×Dic11C22×C411yescharacteristic
188C22×Dic11C22×C411yescharacteristic
189C22×Dic11C22×C411yescharacteristic
190C22×Dic11C22×C411yescharacteristic
191C2×C4×D11—24no—
192C2×C4×D11—42no—
193C2×C4×D11C22×C414yes—
194C2×C4×D11C22×C414yes—
195C2×C4×D11C22×C412yes—
196C2×C4×D11C2×Q814yes—
197C2×C4×D11#4114yes—
198C2×C4×D11C2412yes—
199C2×Dic22—24no—
200C2×Dic22—24no—
201C2×Dic22—42no—
202C2×Dic22C22×C414yes—
203C2×Dic22C22×C414yes—
204C2×Dic22C22×C414yes—
205C2×C8×C11—22no—
206C2×C8×C11—22no—
207C2×C8×C11—22no—
208C2×C8×C11C2×Q814yes—
209C2×C8×C11C2412yes—
210C2×C8×C11C2412yes—
211C2×C8×C11C2412yes—
212C2×C8×C11C2412yes—
213C11×C4⋊C4C22×C414yes—
214C11×C4⋊C4C22×C414yes—
215C11×C4⋊C4C22×C414yes—
216C42×C11C22×C412yes—
217C42×C11C22×C412yes—
218C42×C11C22×C412yes—
219C42×C11C2412yes—
220C42×C11C2412yes—
221C42×C11C2412yes—
222(C2×D11)⋊C4C22×C414yes—
223(C2×D11)⋊C4C22×C414yes—
224(C2×D11)⋊C4C22×C414yes—
225(C2×D11)⋊C4C22×C414yes—
226C4⋊Dic11C22×C414yes—
227C4⋊Dic11C22×C414yes—
228C4⋊Dic11C22×C414yes—
229Dic11⋊C4C22×C414yes—
230Dic11⋊C4C22×C414yes—
231Dic11⋊C4C22×C414yes—
232Dic11⋊C4C22×C414yes—
233Dic11⋊C4C22×C414yes—
234Dic11⋊C4C22×C414yes—
235Dic11⋊C4C22×C414yes—
236Dic11⋊C4C22×C414yes—
237Dic11⋊C4C22×C414yes—
238Dic11⋊C4C22×C414yes—
239C4×Dic11C22×C412yes—
240C4×Dic11C22×C412yes—
241C4×Dic11C22×C412yes—
242C4×Dic11C22×C414yes—
243C4×Dic11C22×C414yes—
244C4×Dic11C2412yes—
245C4×Dic11C2412yes—
246C4×Dic11C2412yes—
247C2×C11⋊C8—22no—
248C2×C11⋊C8—22no—
249C2×C11⋊C8—22no—
250C2×C11⋊C8C2×Q814yes—
251C2×C11⋊C8C2412yes—
252C2×C11⋊C8C2412yes—
253C2×C11⋊C8C2412yes—
254C2×C11⋊C8C2412yes—
255#4313—28no—
256#4313C2×Q8116yescomplemented
257C8×D11—28no—
258C8×D11—28no—
259C2×#533—111no—
260#2962—1116no—
261C2×#446—111no—
262C2×#446—111no—
263C2×#446—111no—
264C2×#446—111no—
265C2×#446—111no—
266C2×#446D1111yescharacteristic, complemented
267C2×C8×Q8—111no—
268C2×C8×Q8—111no—
269C2×#424—111no—
270C2×#424—111no—
271C22×C4⋊C8—111no—
272C2×#405—111no—
273C2×#405—111no—
274C2×C4×M16—111no—
275C23×C11C23×C411yescharacteristic
276C22×D11—22no—
277C22×D11—22no—
278C22×D11C4×Q814yes—
279C22×D11C23×C412yes—
280Q8×C11—44no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11C23×C412yes—
288C2×C4×C11C23×C412yes—
289C2×C4×C11C23×C412yes—
290C2×C4×C11C23×C412yes—
291C2×C4×C11C23×C412yes—
292C2×C4×C11C23×C412yes—
293C2×C4×C11C23×C411yescharacteristic
294C2×C4×C11C22×Q812yes—
295C2×C4×C11C2×#4112yes—
296C2×C4×C11C2511yescharacteristic
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11C4×Q814yes—
303C2×Dic11#13114yes—
304C2×Dic11C23×C412yes—
305C2×Dic11C23×C412yes—
306C2×Dic11C23×C412yes—
307C2×Dic11C23×C412yes—
308C2×Dic11C23×C412yes—
309C2×Dic11C23×C412yes—
310C2×Dic11C23×C412yes—
311C4×D11—28no—
312C4×D11—44no—
313C4×D11C4×Q818yes—
314C4×D11C22×Q814yes—
315C4×D11C2×#4114yes—
316Dic22—28no—
317Dic22—28no—
318Dic22—44no—
319C8×C11—22no—
320C8×C11—22no—
321C8×C11—22no—
322C8×C11C22×Q814yes—
323C11⋊C8—22no—
324C11⋊C8—22no—
325C11⋊C8—22no—
326C11⋊C8C22×Q814yes—
327C22×M16—111no—
328C22×M16—111no—
329C23×C8—111no—
330C23×C8—111no—
331#533—118no—
332#533—118no—
333C2×C4⋊Q8—111no—
334C2×C4⋊Q8—111no—
335C2×#125—111no—
336C2×#125—111no—
337C2×C22⋊Q8—111no—
338C2×C22⋊Q8—111no—
339C2×C22⋊Q8—111no—
340C2×C22⋊Q8—111no—
341C2×C4×Q8—111no—
342C2×C4×Q8—111no—
343C2×C4×Q8—111no—
344C2×C4×Q8C2×D1111yescharacteristic
345C2×#117—111no—
346C2×#117—111no—
347C22×C42—111no—
348#446—118no—
349#446—118no—
350#446—118no—
351#446—118no—
352#446—118no—
353#446C2×D1118yescomplemented
354C8×Q8—118no—
355C8×Q8—118no—
356#424—118no—
357#424—118no—
358C2×C4⋊C8—111no—
359C2×C4⋊C8—111no—
360C2×C4⋊C8—111no—
361C2×C4⋊C8—111no—
362C2×C4⋊C8—111no—
363C2×C4⋊C8—111no—
364C2×C4⋊C8—111no—
365C2×C4⋊C8—111no—
366C2×C4⋊C8—111no—
367C2×C4⋊C8—118no—
368C2×C4⋊C8C2×D1111yescharacteristic
369C2×C4⋊C8C2×D1111yescharacteristic
370C2×C4⋊C8C2×D1111yescharacteristic
371#405—118no—
372#405—118no—
373C4×M16—118no—
374C2×#97—111no—
375C2×#97—111no—
376C2×#97—111no—
377C2×#97—111no—
378C2×#97C2×D1111yescharacteristic
379C2×#97C2×D1111yescharacteristic
380C2×C4×C8—111no—
381C2×C4×C8—111no—
382C2×C4×C8—111no—
383C2×C4×C8—111no—
384C2×C4×C8—111no—
385C2×C4×C8C2×D1111yescharacteristic
386C22×C11C2×C4×Q812yes—
387C22×C11C2×#13112yes—
388C22×C11#56812yes—
389C22×C11C24×C411yescharacteristic
390C2×D11—28no—
391C2×D11—22no—
392C2×D11—22no—
393C2×D11C2×C4×Q814yes—
394C4×C11—22no—
395C4×C11—22no—
396C4×C11—22no—
397C4×C11—22no—
398C4×C11—22no—
399C4×C11—22no—
400C4×C11C2×C4×Q812yes—
401C4×C11C23×Q811yescharacteristic
402C4×C11C22×#4111yescharacteristic
403Dic11—22no—
404Dic11—22no—
405Dic11—22no—
406Dic11—22no—
407Dic11—22no—
408Dic11C2×C4×Q814yes—
409Dic11C2×#13114yes—
410C22×Q8—111no—
411C22×Q8—111no—
412C22×Q8—111no—
413C22×Q8C4×D1111yescharacteristic
414C23×C4—111no—
415C23×C4—111no—
416C23×C4—111no—
417C2×M16—118no—
418C2×M16—114no—
419C2×M16—114no—
420C2×M16—224no—
421C22×C8—111no—
422C22×C8—111no—
423C22×C8—111no—
424C22×C8—111no—
425C22×C8—114no—
426C22×C8—114no—
427C22×C8—224no—
428C22×C8—224no—
429C22×C8C22×D1111yescharacteristic
430C22×C8C22×D1111yescharacteristic
431C22×C8C22×D1111yescharacteristic
432C22×C8C22×D1111yescharacteristic
433C4⋊Q8—118no—
434C4⋊Q8—118no—
435#125—118no—
436#125—118no—
437C22⋊Q8—118no—
438C22⋊Q8—118no—
439C22⋊Q8—118no—
440C22⋊Q8—118no—
441C4×Q8—114no—
442C4×Q8—114no—
443C4×Q8—114no—
444C4×Q8—114no—
445C4×Q8—114no—
446C4×Q8—114no—
447C4×Q8C4×D1114yes—
448C4×Q8C22×D1114yes—
449#117—114no—
450#117—114no—
451#117—114no—
452#117—114no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4—111no—
455C2×C4⋊C4—111no—
456C2×C4⋊C4—111no—
457C2×C4⋊C4—111no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—111no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—111no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4C4×D1111yescharacteristic
467C2×C4⋊C4C4×D1111yescharacteristic
468C2×C4⋊C4C4×D1111yescharacteristic
469C2×C22⋊C4—111no—
470C2×C22⋊C4—111no—
471C2×C22⋊C4—111no—
472C2×C22⋊C4—111no—
473C2×C42—111no—
474C2×C42—111no—
475C2×C42—111no—
476C2×C42—111no—
477C2×C42—111no—
478C2×C42—114no—
479C2×C42—114no—
480C2×C42C22×D1111yescharacteristic
481C2×C42C22×D1111yescharacteristic
482C2×C42C22×D1111yescharacteristic
483C4⋊C8—114no—
484C4⋊C8—114no—
485C4⋊C8—114no—
486C4⋊C8—114no—
487C4⋊C8—114no—
488C4⋊C8—114no—
489C4⋊C8—114no—
490C4⋊C8—114no—
491C4⋊C8—114no—
492C4⋊C8C22×D1114yes—
493C4⋊C8C22×D1114yes—
494C4⋊C8C22×D1114yes—
495#97—114no—
496#97—114no—
497#97—114no—
498#97—114no—
499#97C22×D1114yes—
500#97C22×D1114yes—
501C4×C8—114no—
502C4×C8—114no—
503C4×C8—114no—
504C4×C8—114no—
505C4×C8—114no—
506C4×C8C22×D1114yes—
507C2×C11#296214yescomplemented
508C2×C11C22×C4×Q811yescharacteristic
509C2×C11C22×#13111yescharacteristic
510C2×C11C2×#56811yescharacteristic
511D11—24no—
512C24—111no—
513C2×Q8—42no—
514C2×Q8—114no—
515C2×Q8—114no—
516C2×Q8—114no—
517C2×Q8—224no—
518C2×Q8—224no—
519C2×Q8—442no—
520C2×Q8C2×C4×D1114yes—
521C22×C4—111no—
522C22×C4—111no—
523C22×C4—112no—
524C22×C4—114no—
525C22×C4—114no—
526C22×C4—112no—
527C22×C4—111no—
528C22×C4—111no—
529C22×C4—111no—
530C22×C4—111no—
531C22×C4—111no—
532C22×C4—114no—
533C22×C4—114no—
534C22×C4—224no—
535C22×C4—442no—
536C22×C4C2×C4×D1111yescharacteristic
537C22×C4C2×C4×D1111yescharacteristic
538C22×C4C2×C4×D1111yescharacteristic
539C22×C4C2×C4×D1111yescharacteristic
540C22×C4C2×C4×D1111yescharacteristic
541C22×C4C2×C4×D1111yescharacteristic
542C22×C4C23×D1111yescharacteristic
543M16—1116no—
544M16—228no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—114no—
549C2×C8—112no—
550C2×C8—112no—
551C2×C8—112no—
552C2×C8—112no—
553C2×C8—228no—
554C2×C8—228no—
555C2×C8—222no—
556C2×C8—222no—
557C2×C8—222no—
558C2×C8Q8×D1114yes—
559C2×C8C23×D1112yes—
560C2×C8C23×D1112yes—
561C2×C8C23×D1112yes—
562C2×C8C23×D1112yes—
563C4⋊C4—114no—
564C4⋊C4—114no—
565C4⋊C4—114no—
566C4⋊C4—114no—
567C4⋊C4—114no—
568C4⋊C4—114no—
569C4⋊C4—114no—
570C4⋊C4—114no—
571C4⋊C4—114no—
572C4⋊C4—114no—
573C4⋊C4—114no—
574C4⋊C4—114no—
575C4⋊C4—114no—
576C4⋊C4C2×C4×D1114yes—
577C4⋊C4C2×C4×D1114yes—
578C4⋊C4C2×C4×D1114yes—
579C22⋊C4—114no—
580C22⋊C4—114no—
581C22⋊C4—114no—
582C22⋊C4—114no—
583C42—112no—
584C42—114no—
585C42—114no—
586C42—112no—
587C42—112no—
588C42—112no—
589C42—112no—
590C42—112no—
591C42C2×C4×D1112yes—
592C42C2×C4×D1112yes—
593C42C2×C4×D1112yes—
594C42C23×D1112yes—
595C42C23×D1112yes—
596C42C23×D1112yes—
597C11C2×#296211yescharacteristic, complemented, Sylow
598C23—114no—
599C23—112no—
600C23—222no—
601C23—222no—
602C23C22×C4×D1111yescharacteristic
603Q8—44no—
604Q8—228no—
605Q8—228no—
606Q8—444no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—114no—
614C2×C4—114no—
615C2×C4—112no—
616C2×C4—112no—
617C2×C4—118no—
618C2×C4—114no—
619C2×C4—114no—
620C2×C4—112no—
621C2×C4—112no—
622C2×C4—112no—
623C2×C4—112no—
624C2×C4—112no—
625C2×C4—228no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—444no—
632C2×C4C22×C4×D1112yes—
633C2×C4C22×C4×D1112yes—
634C2×C4C22×C4×D1112yes—
635C2×C4C22×C4×D1112yes—
636C2×C4C22×C4×D1112yes—
637C2×C4C22×C4×D1112yes—
638C2×C4C22×C4×D1111yescharacteristic
639C2×C4C2×Q8×D1112yes—
640C2×C4#41×D1112yes—
641C2×C4C24×D1111yescharacteristic
642C8—22no—
643C8—22no—
644C8—22no—
645C8—114no—
646C8—222no—
647C8—222no—
648C8—222no—
649C8C2×Q8×D1114yes—
650C22—114no—
651C22—228no—
652C22—222no—
653C22—222no—
654C22C4×Q8×D1112yes—
655C22#1062327612yes—
656C22D11×#13112yes—
657C22C23×C4×D1111yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—114no—
665C4—114no—
666C4—222no—
667C4—222no—
668C4—222no—
669C4—222no—
670C4—222no—
671C4C4×Q8×D1112yes—
672C4C22×Q8×D1111yescharacteristic
673C4C2×#41×D1111yescharacteristic
674C2—224no—
675C2#1307756114yesdirect product factor
676C2C2×C4×Q8×D1111yescharacteristic
677C2C2×D11×#13111yescharacteristic
678C2C2×#1062327611yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#446C2
socleC23×C11C23×C4
prime radicalC23×D11C22×C4
cosocleC2×C4×C11C25
hypercenterC2×#446D11
hypocenterC11C2×#2962
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #13077561C2direct (N × H)
3. C2×#10622637C2semidirect
4. C2×#10622441C2semidirect
5. C2×#10622441C2semidirect
6. C2×#10622314C2semidirect
7. C2×#10622314C2semidirect
8. C2×C8×Dic22C2semidirect
9. C2×#10622443C2semidirect
16. C2×C11×#446C2semidirect
38. C11×#446C22semidirect
57. #10622637C22semidirect
67. #10622443C22semidirect
68. #10622441C22semidirect
69. #10622441C22semidirect
72. #10622314C22semidirect
73. #10622314C22semidirect
75. C8×Dic22C22semidirect
124. C2×#4313Q8semidirect
256. #4313C2×Q8semidirect
266. C2×#446D11semidirect
353. #446C2×D11semidirect
507. C2×C11#2962semidirect
597. C11C2×#2962semidirect
675. C2#13077561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231092
#130775612
C2×#106226372
C2×#106224412
C2×#106223142
C2×C8×Dic222
C2×#106224432
C2×#106224522
C2×D11×C4⋊C82
C2×#106223212
C2×#106223022
C2×#106223202
C2×C11×#4462
C2×#296211