Finite Group Databasebeta

← C2×#13077600 #15618235

Subgroups — C2×#13077600 #15618235

Order 2816.

1970 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623111C211yesmaximal, characteristic
2#13077600C2116yesmaximal, direct product factor
3C2×#10622637C211yesmaximal, characteristic, complemented
4C2×#10622301C211yesmaximal, characteristic, complemented
5C2×#10622451C211yesmaximal, characteristic, complemented
6C2×#10622319C211yesmaximal, characteristic, complemented
7C2×#10622319C211yesmaximal, characteristic, complemented
8C2×#10622449C211yesmaximal, characteristic, complemented
9C2×#10622449C211yesmaximal, characteristic, complemented
10C2×#10622453C211yesmaximal, characteristic, complemented
11C2×#10622453C211yesmaximal, characteristic, complemented
12C2×#10622448C211yesmaximal, characteristic, complemented
13C2×#10622321C211yesmaximal, characteristic, complemented
14C2×#10622302C211yesmaximal, characteristic, complemented
15C2×#10622320C211yesmaximal, characteristic, complemented
16C2×C11×#446C211yesmaximal, characteristic, complemented
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#67000C411yescharacteristic
19C2×#66999C411yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C22×#4313C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24C22×C8×D11C2211yescharacteristic
25C22×C8×D11C2211yescharacteristic
26#10623111C418yes—
27#10623111C2218yes—
28C2×#66951C411yescharacteristic
29C2×#66951C411yescharacteristic
30C2×#66948C411yescharacteristic
31C2×#66947C411yescharacteristic
32C2×#66947C411yescharacteristic
33C2×#66943C411yescharacteristic
34C2×C4×D44C2211yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×C4×D44C2211yescharacteristic
37C2×#66925C2211yescharacteristic
38C2×#66925C2211yescharacteristic
39C2×C42×D11C2211yescharacteristic
40C11×#446C2218yescomplemented
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×C4⋊C8C2211yescharacteristic
43C2×C11×C4⋊C8C2211yescharacteristic
44C2×C11×#97C2211yescharacteristic
45C2×C11×#97C2211yescharacteristic
46C2×C4×C8×C11C2211yescharacteristic
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×(C2×D11)⋊C8C2211yescharacteristic
49C2×(C2×D11)⋊C8C2211yescharacteristic
50C2×(C2×D11)⋊C8C2211yescharacteristic
51C2×(C2×D11)⋊C8C2211yescharacteristic
52C2×(C2×D11)⋊C8C2211yescharacteristic
53C2×#66879C2211yescharacteristic
54C2×#66879C2211yescharacteristic
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#10622453C2218yescomplemented
65#10622453C2218yescomplemented
66#10622451C2218yescomplemented
67#10622449C2218yescomplemented
68#10622449C2218yescomplemented
69#10622448C2218yescomplemented
70#10622321C2218yescomplemented
71#10622320C2218yescomplemented
72#10622319C2218yescomplemented
73#10622319C2218yescomplemented
74#10622302C2218yescomplemented
75#10622301C2218yescomplemented
76C22×Q8×C11C2×C411yescharacteristic
77C22×D44C2×C411yescharacteristic
78C22×D44C2×C411yescharacteristic
79C22×D44C2×C411yescharacteristic
80C22×C4×D11C2×C411yescharacteristic
81C22×C4×D11C2×C411yescharacteristic
82C22×C4×D11C2311yescharacteristic
83C22×C4×D11C2311yescharacteristic
84C22×C4×D11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C4×Q8×C11C2×C414yes—
90C4×Q8×C11C2314yes—
91C2×C11×C4⋊C4C2×C411yescharacteristic
92C2×C11×C4⋊C4C2×C411yescharacteristic
93C2×C11×C4⋊C4C2×C411yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97#67000C2×C418yes—
98#66999C2×C418yes—
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×(C2×D11)⋊C4C2×C411yescharacteristic
102C2×(C2×D11)⋊C4C2×C411yescharacteristic
103C2×(C2×D11)⋊C4C2×C411yescharacteristic
104C2×(C2×D11)⋊C4C2×C411yescharacteristic
105C2×(C2×D11)⋊C4C2×C411yescharacteristic
106C2×(C2×D11)⋊C4C2×C411yescharacteristic
107C2×(C2×D11)⋊C4C2×C411yescharacteristic
108C2×(C2×D11)⋊C4C2×C411yescharacteristic
109C2×C4⋊Dic11C2×C411yescharacteristic
110C2×C4⋊Dic11C2×C411yescharacteristic
111C2×C4⋊Dic11C2×C411yescharacteristic
112C2×Dic11⋊C4C2×C411yescharacteristic
113C2×Dic11⋊C4C2×C411yescharacteristic
114C2×Dic11⋊C4C2×C411yescharacteristic
115C2×Dic11⋊C4C2×C411yescharacteristic
116C2×C4×Dic11C2×C411yescharacteristic
117C2×C4×Dic11C2×C411yescharacteristic
118C2×C4×Dic11C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C2×#4313—24no—
124C2×#4313—24no—
125C2×#4313—24no—
126C2×#4313—24no—
127C2×#4313C2314yes—
128C2×#4313C2314yes—
129C2×#4313C2314yes—
130C2×#4313C2314yes—
131C2×C8×D11—24no—
132C2×C8×D11—24no—
133C2×C8×D11C2314yes—
134C2×C8×D11C2314yes—
135#66951C2×C418yes—
136#66951C2×C418yes—
137#66948C2×C418yes—
138#66947C2×C418yes—
139#66947C2×C418yes—
140#66943C2×C418yes—
141C4×D44C2×C414yes—
142C4×D44C2×C414yes—
143C4×D44C2×C414yes—
144C4×D44C2314yes—
145C4×D44C2314yes—
146C4×D44C2314yes—
147#66925C2×C414yes—
148#66925C2×C414yes—
149#66925C2314yes—
150#66925C2314yes—
151C42×D11C2×C414yes—
152C42×D11C2314yes—
153C11×C4⋊C8C2314yes—
154C11×C4⋊C8C2314yes—
155C11×C4⋊C8C2314yes—
156C11×#97C2314yes—
157C11×#97C2314yes—
158C4×C8×C11C2314yes—
159(C2×D11)⋊C8C2314yes—
160(C2×D11)⋊C8C2314yes—
161(C2×D11)⋊C8C2314yes—
162(C2×D11)⋊C8C2314yes—
163(C2×D11)⋊C8C2314yes—
164(C2×D11)⋊C8C2314yes—
165#66879C2314yes—
166#66879C2314yes—
167C8×Dic11C2314yes—
168C8×Dic11C2314yes—
169C4⋊(C11⋊C8)C2314yes—
170C4⋊(C11⋊C8)C2314yes—
171C4⋊(C11⋊C8)C2314yes—
172#66867C2314yes—
173#66867C2314yes—
174C4×C11⋊C8C2314yes—
175C2×#2967—111nomaximal, Sylow
176C23×D11C22×C411yescharacteristic
177C23×D11C22×C411yescharacteristic
178C23×D11C22×C411yescharacteristic
179C2×Q8×C11—42no—
180C2×Q8×C11C22×C414yes—
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C22×C411yescharacteristic
185C22×C4×C11C22×C411yescharacteristic
186C22×C4×C11C22×C411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C22×Dic11C22×C411yescharacteristic
189C22×Dic11C22×C411yescharacteristic
190C22×Dic11C22×C411yescharacteristic
191C22×Dic11C22×C411yescharacteristic
192C22×Dic11C22×C411yescharacteristic
193C2×D44—42no—
194C2×D44—42no—
195C2×D44—42no—
196C2×D44C22×C414yes—
197C2×D44C22×C414yes—
198C2×D44C22×C414yes—
199C2×C4×D11—22no—
200C2×C4×D11—22no—
201C2×C4×D11—22no—
202C2×C4×D11—22no—
203C2×C4×D11—22no—
204C2×C4×D11—22no—
205C2×C4×D11—42no—
206C2×C4×D11—42no—
207C2×C4×D11C22×C412yes—
208C2×C4×D11C22×C412yes—
209C2×C4×D11C22×C412yes—
210C2×C4×D11C22×C414yes—
211C2×C4×D11C22×C414yes—
212C2×C4×D11C2412yes—
213C2×C4×D11C2412yes—
214C2×C4×D11C2412yes—
215C2×C8×C11—22no—
216C2×C8×C11—22no—
217C2×C8×C11—22no—
218C2×C8×C11#4114yes—
219C2×C8×C11C2412yes—
220C2×C8×C11C2412yes—
221C2×C8×C11C2412yes—
222C2×C8×C11C2412yes—
223C11×C4⋊C4C22×C414yes—
224C11×C4⋊C4C22×C414yes—
225C11×C4⋊C4C22×C414yes—
226C42×C11C22×C412yes—
227C42×C11C22×C412yes—
228C42×C11C22×C412yes—
229C42×C11C2412yes—
230C42×C11C2412yes—
231C42×C11C2412yes—
232(C2×D11)⋊C4C22×C414yes—
233(C2×D11)⋊C4C22×C414yes—
234(C2×D11)⋊C4C22×C414yes—
235(C2×D11)⋊C4C22×C414yes—
236(C2×D11)⋊C4C22×C414yes—
237(C2×D11)⋊C4C22×C414yes—
238(C2×D11)⋊C4C22×C414yes—
239(C2×D11)⋊C4C22×C414yes—
240(C2×D11)⋊C4C22×C414yes—
241(C2×D11)⋊C4C22×C414yes—
242C4⋊Dic11C22×C414yes—
243C4⋊Dic11C22×C414yes—
244C4⋊Dic11C22×C414yes—
245Dic11⋊C4C22×C414yes—
246Dic11⋊C4C22×C414yes—
247Dic11⋊C4C22×C414yes—
248Dic11⋊C4C22×C414yes—
249C4×Dic11C22×C412yes—
250C4×Dic11C22×C414yes—
251C4×Dic11C22×C414yes—
252C4×Dic11C2412yes—
253C2×C11⋊C8—22no—
254C2×C11⋊C8—22no—
255C2×C11⋊C8—22no—
256C2×C11⋊C8#4114yes—
257C2×C11⋊C8C2412yes—
258C2×C11⋊C8C2412yes—
259C2×C11⋊C8C2412yes—
260C2×C11⋊C8C2412yes—
261#4313—28no—
262#4313—28no—
263#4313—28no—
264#4313—28no—
265C8×D11—28no—
266C8×D11—28no—
267C2×#529—111no—
268#2967—1116no—
269C2×#446—111no—
270C2×#446D1111yescharacteristic, complemented
271C2×#436—111no—
272C2×#436—111no—
273C2×#435—111no—
274C2×#435—111no—
275C2×#435—111no—
276C2×#435—111no—
277C2×#433—111no—
278C2×#433—111no—
279C2×#432—111no—
280C2×#405—111no—
281C2×#405—111no—
282C2×C4×M16—111no—
283C23×C11C23×C411yescharacteristic
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11C23×C412yes—
294C22×D11C23×C412yes—
295C22×D11C23×C412yes—
296Q8×C11—44no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11C23×C412yes—
304C2×C4×C11C23×C412yes—
305C2×C4×C11C23×C412yes—
306C2×C4×C11C23×C412yes—
307C2×C4×C11C23×C412yes—
308C2×C4×C11C23×C412yes—
309C2×C4×C11C23×C411yescharacteristic
310C2×C4×C11C2×#4112yes—
311C2×C4×C11C2×#4112yes—
312C2×C4×C11C2511yescharacteristic
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11C23×C412yes—
319C2×Dic11C23×C412yes—
320C2×Dic11C23×C412yes—
321C2×Dic11C23×C412yes—
322C2×Dic11C23×C412yes—
323D44—44no—
324D44—44no—
325D44—44no—
326C4×D11—24no—
327C4×D11—24no—
328C4×D11—24no—
329C4×D11—22no—
330C4×D11—22no—
331C4×D11—22no—
332C4×D11—22no—
333C4×D11—22no—
334C4×D11—22no—
335C4×D11—44no—
336C4×D11—44no—
337C8×C11—22no—
338C8×C11—22no—
339C8×C11—22no—
340C8×C11C2×#4114yes—
341C11⋊C8—22no—
342C11⋊C8—22no—
343C11⋊C8—22no—
344C11⋊C8C2×#4114yes—
345C22×M16—111no—
346C22×M16—111no—
347C22×M16—111no—
348C22×M16—111no—
349C23×C8—111no—
350C23×C8—111no—
351#529—118no—
352#529—118no—
353C2×#126—111no—
354C2×#126—111no—
355C2×#125—111no—
356C2×#124—111no—
357C2×#123—111no—
358C2×#123—111no—
359C2×C22⋊Q8—111no—
360C2×#121—111no—
361C2×C4×Q8C2×D1111yescharacteristic
362C2×C4×D4—111no—
363C2×C4×D4—111no—
364C2×C4×D4—111no—
365C2×#117—111no—
366C2×#117—111no—
367C22×C42—111no—
368#446—118no—
369#446C2×D1118yescomplemented
370#436—118no—
371#436—118no—
372#435—118no—
373#435—118no—
374#435—118no—
375#435—118no—
376#433—118no—
377#433—118no—
378#432—118no—
379C2×C4⋊C8—111no—
380C2×C4⋊C8—111no—
381C2×C4⋊C8—111no—
382C2×C4⋊C8C2×D1111yescharacteristic
383C2×C4⋊C8C2×D1111yescharacteristic
384C2×C4⋊C8C2×D1111yescharacteristic
385C2×C22⋊C8—111no—
386C2×C22⋊C8—111no—
387C2×C22⋊C8—111no—
388C2×C22⋊C8—111no—
389C2×C22⋊C8—111no—
390C2×C22⋊C8—111no—
391#405—118no—
392#405—118no—
393C4×M16—118no—
394C2×#97—111no—
395C2×#97—111no—
396C2×#97—111no—
397C2×#97—111no—
398C2×#97C2×D1111yescharacteristic
399C2×#97C2×D1111yescharacteristic
400C2×C4×C8—111no—
401C2×C4×C8—111no—
402C2×C4×C8—111no—
403C2×C4×C8C2×D1111yescharacteristic
404C22×C11C4×#4112yes—
405C22×C11#56812yes—
406C22×C11#56812yes—
407C22×C11C24×C411yescharacteristic
408C2×D11—22no—
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—22no—
414C2×D11—22no—
415C2×D11—22no—
416C2×D11—22no—
417C2×D11—44no—
418C2×D11—44no—
419C2×D11—44no—
420C4×C11—22no—
421C4×C11—22no—
422C4×C11—22no—
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—22no—
426C4×C11C4×#4112yes—
427C4×C11C22×#4111yescharacteristic
428C4×C11C22×#4111yescharacteristic
429Dic11—22no—
430Dic11—22no—
431Dic11—22no—
432Dic11—22no—
433Dic11—22no—
434C22×Q8C4×D1111yescharacteristic
435C22×D4—111no—
436C22×D4—111no—
437C22×D4—111no—
438C23×C4—111no—
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—111no—
442C23×C4—111no—
443C2×M16—114no—
444C2×M16—114no—
445C2×M16—114no—
446C2×M16—114no—
447C2×M16—224no—
448C2×M16—224no—
449C2×M16—224no—
450C2×M16—224no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—111no—
454C22×C8—111no—
455C22×C8—114no—
456C22×C8—114no—
457C22×C8—224no—
458C22×C8—224no—
459C22×C8C22×D1111yescharacteristic
460C22×C8C22×D1111yescharacteristic
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463#126—118no—
464#126—118no—
465#125—118no—
466#124—118no—
467#123—118no—
468#123—118no—
469C22⋊Q8—118no—
470#121—118no—
471C4×Q8C4×D1114yes—
472C4×Q8C22×D1114yes—
473C4×D4—114no—
474C4×D4—114no—
475C4×D4—114no—
476C4×D4—114no—
477C4×D4—114no—
478C4×D4—114no—
479#117—114no—
480#117—114no—
481#117—114no—
482#117—114no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—111no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4C4×D1111yescharacteristic
491C2×C4⋊C4C4×D1111yescharacteristic
492C2×C4⋊C4C4×D1111yescharacteristic
493C2×C22⋊C4—111no—
494C2×C22⋊C4—111no—
495C2×C22⋊C4—111no—
496C2×C22⋊C4—111no—
497C2×C22⋊C4—111no—
498C2×C22⋊C4—111no—
499C2×C22⋊C4—111no—
500C2×C22⋊C4—111no—
501C2×C22⋊C4—111no—
502C2×C22⋊C4—111no—
503C2×C42—111no—
504C2×C42—111no—
505C2×C42—111no—
506C2×C42—114no—
507C2×C42—114no—
508C2×C42C22×D1111yescharacteristic
509C2×C42C22×D1111yescharacteristic
510C2×C42C22×D1111yescharacteristic
511C4⋊C8—114no—
512C4⋊C8—114no—
513C4⋊C8—114no—
514C4⋊C8C22×D1114yes—
515C4⋊C8C22×D1114yes—
516C4⋊C8C22×D1114yes—
517C22⋊C8—114no—
518C22⋊C8—114no—
519C22⋊C8—114no—
520C22⋊C8—114no—
521C22⋊C8—114no—
522C22⋊C8—114no—
523#97—114no—
524#97—114no—
525#97—114no—
526#97—114no—
527#97C22×D1114yes—
528#97C22×D1114yes—
529C4×C8—114no—
530C4×C8—114no—
531C4×C8—114no—
532C4×C8C22×D1114yes—
533C2×C11#296714yescomplemented
534C2×C11C2×C4×#4111yescharacteristic
535C2×C11C2×#56811yescharacteristic
536C2×C11C2×#56811yescharacteristic
537D11—42no—
538D11—42no—
539D11—42no—
540C24—111no—
541C24—111no—
542C24—111no—
543C2×Q8—42no—
544C2×Q8C2×C4×D1114yes—
545C2×D4—114no—
546C2×D4—114no—
547C2×D4—114no—
548C2×D4—442no—
549C2×D4—442no—
550C2×D4—442no—
551C22×C4—111no—
552C22×C4—111no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—112no—
560C22×C4—112no—
561C22×C4—112no—
562C22×C4—114no—
563C22×C4—114no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—442no—
571C22×C4—442no—
572C22×C4C2×C4×D1111yescharacteristic
573C22×C4C2×C4×D1111yescharacteristic
574C22×C4C2×C4×D1111yescharacteristic
575C22×C4C2×C4×D1111yescharacteristic
576C22×C4C2×C4×D1111yescharacteristic
577C22×C4C2×C4×D1111yescharacteristic
578C22×C4C23×D1111yescharacteristic
579M16—228no—
580M16—228no—
581M16—228no—
582M16—228no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—114no—
587C2×C8—112no—
588C2×C8—112no—
589C2×C8—112no—
590C2×C8—112no—
591C2×C8—228no—
592C2×C8—222no—
593C2×C8—222no—
594C2×C8—222no—
595C2×C8—228no—
596C2×C8#434314yes—
597C2×C8C23×D1112yes—
598C2×C8C23×D1112yes—
599C2×C8C23×D1112yes—
600C2×C8C23×D1112yes—
601C4⋊C4—114no—
602C4⋊C4—114no—
603C4⋊C4—114no—
604C4⋊C4—114no—
605C4⋊C4—114no—
606C4⋊C4—114no—
607C4⋊C4—114no—
608C4⋊C4C2×C4×D1114yes—
609C4⋊C4C2×C4×D1114yes—
610C4⋊C4C2×C4×D1114yes—
611C22⋊C4—114no—
612C22⋊C4—114no—
613C22⋊C4—114no—
614C22⋊C4—114no—
615C22⋊C4—114no—
616C22⋊C4—114no—
617C22⋊C4—114no—
618C22⋊C4—114no—
619C22⋊C4—114no—
620C22⋊C4—114no—
621C42—112no—
622C42—114no—
623C42—114no—
624C42—112no—
625C42C2×C4×D1112yes—
626C42C2×C4×D1112yes—
627C42C2×C4×D1112yes—
628C42C23×D1112yes—
629C42C23×D1112yes—
630C42C23×D1112yes—
631C11C2×#296711yescharacteristic, complemented, Sylow
632C23—112no—
633C23—112no—
634C23—112no—
635C23—222no—
636C23—222no—
637C23—222no—
638C23—222no—
639C23—222no—
640C23—222no—
641C23—222no—
642C23—222no—
643C23—222no—
644C23C22×C4×D1111yescharacteristic
645Q8—44no—
646D4—444no—
647D4—444no—
648D4—444no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—112no—
656C2×C4—112no—
657C2×C4—112no—
658C2×C4—112no—
659C2×C4—112no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—222no—
664C2×C4—222no—
665C2×C4—224no—
666C2×C4—224no—
667C2×C4—224no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—444no—
675C2×C4—444no—
676C2×C4C22×C4×D1112yes—
677C2×C4C22×C4×D1112yes—
678C2×C4C22×C4×D1112yes—
679C2×C4C22×C4×D1112yes—
680C2×C4C22×C4×D1112yes—
681C2×C4C22×C4×D1112yes—
682C2×C4C22×C4×D1111yescharacteristic
683C2×C4C2×#434312yes—
684C2×C4#41×D1112yes—
685C2×C4C24×D1111yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—114no—
690C8—222no—
691C8—222no—
692C8—222no—
693C8C2×#434314yes—
694C22—222no—
695C22—222no—
696C22—222no—
697C22—222no—
698C22—222no—
699C22—222no—
700C22—222no—
701C22—222no—
702C22—222no—
703C22—444no—
704C22—444no—
705C22—444no—
706C22C4×#434312yes—
707C22#1062327612yes—
708C22#1062328112yes—
709C22C23×C4×D1111yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—222no—
717C4—222no—
718C4—222no—
719C4—222no—
720C4—222no—
721C4C4×#434312yes—
722C4C22×#434311yescharacteristic
723C4C2×#41×D1111yescharacteristic
724C2—442no—
725C2—442no—
726C2—442no—
727C2#1307760014yesdirect product factor
728C2C2×C4×#434311yescharacteristic
729C2C2×#1062328111yescharacteristic
730C2C2×#1062327611yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#446C2
socleC23×C11C23×C4
prime radicalC2×#66948C4
cosocleC2×C4×C11C25
hypercenterC2×#446D11
hypocenterC11C2×#2967
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #13077600C2direct (N × H)
3. C2×#10622637C2semidirect
4. C2×#10622301C2semidirect
5. C2×#10622451C2semidirect
6. C2×#10622319C2semidirect
7. C2×#10622319C2semidirect
8. C2×#10622449C2semidirect
9. C2×#10622449C2semidirect
10. C2×#10622453C2semidirect
11. C2×#10622453C2semidirect
12. C2×#10622448C2semidirect
13. C2×#10622321C2semidirect
14. C2×#10622302C2semidirect
15. C2×#10622320C2semidirect
16. C2×C11×#446C2semidirect
40. C11×#446C22semidirect
57. #10622637C22semidirect
64. #10622453C22semidirect
65. #10622453C22semidirect
66. #10622451C22semidirect
67. #10622449C22semidirect
68. #10622449C22semidirect
69. #10622448C22semidirect
70. #10622321C22semidirect
71. #10622320C22semidirect
72. #10622319C22semidirect
73. #10622319C22semidirect
74. #10622302C22semidirect
75. #10622301C22semidirect
270. C2×#446D11semidirect
369. #446C2×D11semidirect
533. C2×C11#2967semidirect
631. C11C2×#2967semidirect
727. C2#13077600direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231112
#130776002
C2×#106226372
C2×#106223012
C2×#106224512
C2×#106223192
C2×#106224492
C2×#106224532
C2×#106224482
C2×#106223212
C2×#106223022
C2×#106223202
C2×C11×#4462
C2×#296711