Finite Group Databasebeta

← C2×#13078012 #15620500

Subgroups — C2×#13078012 #15620500

Order 2816.

5318 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67037C211yesmaximal, characteristic, complemented
2C2×#10623335C212yesmaximal, complemented
3#13078012C2116yesmaximal, direct product factor
4C2×#10622666C214yesmaximal, complemented
5C2×#10622645C214yesmaximal, complemented
6C22×#66898C211yesmaximal, characteristic, complemented
7C22×#66870C212yesmaximal, complemented
8C2×C11×#534C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic, complemented
11C23×C22⋊D11—21no—
12C23×C22⋊D11C2212yes—
13C2×#67037—22no—
14C2×#67037—24no—
15C2×#67037—24no—
16C2×#67037—28no—
17C2×#67037C2214yes—
18C2×#67037C2218yescomplemented
19C22×#4341—22no—
20C22×D4×D11—22no—
21C22×#4339—21no—
22C11×#534—24no—
23C11×#534C2218yescomplemented
24C2×C11×#123—21no—
25C2×C11×#123C2212yescomplemented
26C2×C11×#121—22no—
27C2×C11×#120—21no—
28C2×C11×#120C2212yescomplemented
29C22×C11×C22⋊C4C2211yescharacteristic, complemented
30C2×#67006C2214yescomplemented
31C22×C22⋊Dic11C2212yescomplemented
32#10623335—28no—
33#10623335C22116yescomplemented
34C2×#66992—24no—
35C2×#66990—22no—
36C2×#66988—22no—
37C2×#66982C2214yescomplemented
38C2×#66898C2214yescomplemented
39C2×#66898C2218yescomplemented
40#10622666C22132yescomplemented
41#10622645C22132yescomplemented
42C2×#66870C2218yescomplemented
43C2×#66870C22116yescomplemented
44C25×C11D411yescharacteristic, complemented
45C25×C11C2311yescharacteristic
46C25×C11C2311yescharacteristic, complemented
47C24×D11—21no—
48C24×D11D412yescomplemented
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—24no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—24no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11D412yescomplemented
60C22×D4×C11D414yescomplemented
61C22×D4×C11C2312yes—
62C22×D4×C11C2314yes—
63C22×D4×C11C2314yescomplemented
64C23×C4×C11—21no—
65C23×C4×C11D411yescharacteristic, complemented
66C23×C4×C11C2311yescharacteristic, complemented
67C22×C22⋊D11—22no—
68C22×C22⋊D11—24no—
69C22×C22⋊D11—28no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—24no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—24no—
76C22×C22⋊D11—24no—
77C22×C22⋊D11—28no—
78C22×C22⋊D11—24no—
79C22×C22⋊D11D414yescomplemented
80C22×C22⋊D11D418yescomplemented
81C22×C22⋊D11C2314yes—
82C22×C22⋊D11C2318yes—
83C23×Dic11—21no—
84C23×Dic11—22no—
85C23×Dic11D412yescomplemented
86#67037—216no—
87#67037—232no—
88#67037—28no—
89#67037—216no—
90#67037—216no—
91#67037—232no—
92#67037C23116yes—
93C2×#4341—28no—
94C2×#4341—216no—
95C2×#4341—28no—
96C2×#4341—216no—
97C2×D4×D11—28no—
98C2×D4×D11—216no—
99C2×D4×D11—28no—
100C2×D4×D11—216no—
101C2×#4339—24no—
102C2×#4339—28no—
103C2×#4339—24no—
104C2×#4339—28no—
105C22×D44—21no—
106C22×C4×D11—22no—
107C22×Dic22—21no—
108C11×#123—24no—
109C11×#123—28no—
110C11×#123C2318yescomplemented
111C11×#121—216no—
112C11×#120—28no—
113C11×#120—24no—
114C11×#120C2318yescomplemented
115C2×C11×C4⋊C4—22no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4C2312yescomplemented
121C2×C11×C22⋊C4C2314yescomplemented
122#67006—28no—
123#67006C23116yescomplemented
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11C2314yescomplemented
128C2×C22⋊Dic11C2318yescomplemented
129#66992—232no—
130#66990—216no—
131#66988—216no—
132#66982—28no—
133#66982C23116yescomplemented
134C2×(C2×D11)⋊C4—24no—
135C2×Dic11⋊C4—24no—
136#66898C23116yescomplemented
137#66870C23132yescomplemented
138C2×#3026—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—22no—
142C24×C11—22no—
143C24×C11—21no—
144C24×C11—22no—
145C24×C11—21no—
146C24×C11—82no—
147C24×C11—82no—
148C24×C11—82no—
149C24×C11C2×D412yes—
150C24×C11C2×D412yes—
151C24×C11C2×D412yes—
152C24×C11C2×D411yescharacteristic
153C24×C11C2×D411yescharacteristic
154C24×C11C2×D414yes—
155C24×C11C2×D412yes—
156C24×C11C2×D414yescomplemented
157C24×C11C2411yescharacteristic
158C24×C11C2412yes—
159C24×C11C2412yescomplemented
160C23×D11—22no—
161C23×D11—24no—
162C23×D11—28no—
163C23×D11—22no—
164C23×D11—24no—
165C23×D11—84no—
166C23×D11—84no—
167C23×D11C2×D414yes—
168C23×D11C2×D418yescomplemented
169C2×D4×C11—24no—
170C2×D4×C11—28no—
171C2×D4×C11—24no—
172C2×D4×C11—28no—
173C2×D4×C11—24no—
174C2×D4×C11—28no—
175C2×D4×C11—24no—
176C2×D4×C11—28no—
177C2×D4×C11—28no—
178C2×D4×C11—28no—
179C2×D4×C11—24no—
180C2×D4×C11—24no—
181C2×D4×C11—28no—
182C2×D4×C11—41no—
183C2×D4×C11—42no—
184C2×D4×C11—41no—
185C2×D4×C11—44no—
186C2×D4×C11—42no—
187C2×D4×C11—44no—
188C2×D4×C11—42no—
189C2×D4×C11—84no—
190C2×D4×C11C2×D414yes—
191C2×D4×C11C2×D418yescomplemented
192C2×D4×C11C2414yes—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—24no—
202C22×C4×C11—82no—
203C22×C4×C11C2×D412yes—
204C22×C4×C11C2×D414yescomplemented
205C22×C4×C11C2412yescomplemented
206C2×C22⋊D11—28no—
207C2×C22⋊D11—216no—
208C2×C22⋊D11—216no—
209C2×C22⋊D11—232no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—28no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—28no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—28no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—28no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—28no—
225C2×C22⋊D11—216no—
226C2×C22⋊D11—216no—
227C2×C22⋊D11—88no—
228C2×C22⋊D11C2×D418yes—
229C2×C22⋊D11C2×D4116yescomplemented
230C2×C22⋊D11C2418yes—
231C22×Dic11—24no—
232C22×Dic11—28no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—24no—
236C22×Dic11—24no—
237C22×Dic11—28no—
238C22×Dic11—84no—
239C22×Dic11C2×D414yes—
240C22×Dic11C2×D418yescomplemented
241#4341—232no—
242#4341—264no—
243#4341—232no—
244D4×D11—232no—
245D4×D11—264no—
246D4×D11—232no—
247#4339—216no—
248#4339—232no—
249#4339—216no—
250C2×D44—24no—
251C2×D44—28no—
252C2×C4×D11—28no—
253C2×C4×D11—216no—
254C2×Dic22—24no—
255C2×Dic22—28no—
256C11×C4⋊C4—28no—
257C11×C22⋊C4—22no—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—28no—
260C11×C22⋊C4—28no—
261C11×C22⋊C4C2414yescomplemented
262C22⋊Dic11—216no—
263C22⋊Dic11—24no—
264C22⋊Dic11—28no—
265C22⋊Dic11C2418yescomplemented
266(C2×D11)⋊C4—216no—
267Dic11⋊C4—216no—
268C22×H(5,𝔽2)—111no—
269C2×#534—112no—
270C2×#534D1111yescharacteristic, complemented
271#3026—1116no—
272C2×#458—114no—
273C2×B(4,𝔽2)—114no—
274C22×#99—111no—
275C22×#99—112no—
276C23×C11—22no—
277C23×C11—24no—
278C23×C11—22no—
279C23×C11—24no—
280C23×C11—24no—
281C23×C11—22no—
282C23×C11—44no—
283C23×C11—42no—
284C23×C11—44no—
285C23×C11—42no—
286C23×C11—42no—
287C23×C11—44no—
288C23×C11—44no—
289C23×C11—48no—
290C23×C11—44no—
291C23×C11—41no—
292C23×C11—42no—
293C23×C11—41no—
294C23×C11—82no—
295C23×C11—84no—
296C23×C11—82no—
297C23×C11—82no—
298C23×C11—82no—
299C23×C11—84no—
300C23×C11—84no—
301C23×C11—82no—
302C23×C11—84no—
303C23×C11#12011yescharacteristic
304C23×C11#12012yes—
305C23×C11#12011yescharacteristic
306C23×C11#12014yes—
307C23×C11#12012yes—
308C23×C11#12012yes—
309C23×C11#12014yes—
310C23×C11C22×D412yes—
311C23×C11C22×D414yes—
312C23×C11C22×D412yes—
313C23×C11C22×D414yes—
314C23×C11C22×D411yescharacteristic
315C23×C11C22×D414yes—
316C23×C11C22×D411yescharacteristic
317C23×C11C22×D412yes—
318C23×C11C22×D412yes—
319C23×C11C2511yescharacteristic
320C22×D11—24no—
321C22×D11—28no—
322C22×D11—216no—
323C22×D11—24no—
324C22×D11—28no—
325C22×D11—48no—
326C22×D11—48no—
327C22×D11—88no—
328C22×D11—84no—
329C22×D11—88no—
330C22×D11—816no—
331C22×D11—88no—
332C22×D11C22×D418yes—
333D4×C11—28no—
334D4×C11—216no—
335D4×C11—28no—
336D4×C11—44no—
337D4×C11—44no—
338D4×C11—48no—
339D4×C11—88no—
340C2×C4×C11—22no—
341C2×C4×C11—24no—
342C2×C4×C11—22no—
343C2×C4×C11—24no—
344C2×C4×C11—24no—
345C2×C4×C11—24no—
346C2×C4×C11—22no—
347C2×C4×C11—44no—
348C2×C4×C11—41no—
349C2×C4×C11—42no—
350C2×C4×C11—41no—
351C2×C4×C11—84no—
352C2×C4×C11C22×D414yes—
353C22⋊D11—232no—
354C22⋊D11—28no—
355C22⋊D11—216no—
356C22⋊D11—28no—
357C22⋊D11—216no—
358C22⋊D11—28no—
359C22⋊D11—28no—
360C22⋊D11—816no—
361C2×Dic11—216no—
362C2×Dic11—24no—
363C2×Dic11—28no—
364C2×Dic11—24no—
365C2×Dic11—28no—
366C2×Dic11—28no—
367C2×Dic11—48no—
368C2×Dic11—88no—
369C2×Dic11C22×D418yes—
370D44—216no—
371C4×D11—232no—
372Dic22—216no—
373C2×H(5,𝔽2)—114no—
374C2×H(5,𝔽2)—118no—
375C2×H(5,𝔽2)—224no—
376C2×H(5,𝔽2)—228no—
377C2×H(5,𝔽2)—222no—
378C2×H(5,𝔽2)—224no—
379C22×#41—222no—
380C22×#41—221no—
381C23×D4—112no—
382C23×D4—222no—
383C23×D4—221no—
384C23×D4C2×D1111yescharacteristic
385C23×D4C2×D1111yescharacteristic, complemented
386#534—24no—
387#534—1116no—
388#534—228no—
389#534C2×D1118yescomplemented
390C2×#123—21no—
391C2×#123—114no—
392C2×#123—222no—
393C2×#123C2×D1112yescomplemented
394C2×#121—22no—
395C2×#121—224no—
396C2×#120—21no—
397C2×#120—114no—
398C2×#120—222no—
399C2×#120C2×D1112yescomplemented
400C22×C22⋊C4—112no—
401C22×C22⋊C4C2×D1111yescharacteristic, complemented
402#458—1132no—
403B(4,𝔽2)—1132no—
404C2×#99—114no—
405C2×#99—118no—
406C2×#99—118no—
407C2×#99—1116no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—24no—
411C22×C11—24no—
412C22×C11—22no—
413C22×C11—24no—
414C22×C11—42no—
415C22×C11—44no—
416C22×C11—44no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—44no—
423C22×C11—42no—
424C22×C11—44no—
425C22×C11—44no—
426C22×C11—48no—
427C22×C11—44no—
428C22×C11—48no—
429C22×C11—44no—
430C22×C11—42no—
431C22×C11—82no—
432C22×C11—84no—
433C22×C11—84no—
434C22×C11—82no—
435C22×C11—82no—
436C22×C11C2×#12011yescharacteristic
437C22×C11C2×#12012yes—
438C22×C11C2×#12012yes—
439C22×C11C2×#12012yes—
440C22×C11C2×#12014yes—
441C22×C11C2×#12011yescharacteristic
442C22×C11C23×D412yes—
443C22×C11C23×D411yescharacteristic
444C2×D11—28no—
445C2×D11—416no—
446C2×D11—48no—
447C2×D11—48no—
448C2×D11—84no—
449C2×D11—88no—
450C2×D11—816no—
451C4×C11—24no—
452C4×C11—44no—
453C4×C11—42no—
454Dic11—28no—
455Dic11—48no—
456C25—112no—
457C25—221no—
458C25C22⋊D1111yescharacteristic, complemented
459C25C22×D1111yescharacteristic
460C25C22×D1111yescharacteristic, complemented
461H(5,𝔽2)—1116no—
462H(5,𝔽2)—2216no—
463H(5,𝔽2)—2232no—
464H(5,𝔽2)—2216no—
465H(5,𝔽2)—2232no—
466H(5,𝔽2)—228no—
467H(5,𝔽2)—2216no—
468C2×#41—228no—
469C2×#41—224no—
470C2×#41—228no—
471C2×#41—2216no—
472C2×#41—2216no—
473C2×#41—228no—
474C2×#41—224no—
475C2×#41—228no—
476C22×Q8—221no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—24no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—24no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—22no—
486C22×D4—22no—
487C22×D4—114no—
488C22×D4—118no—
489C22×D4—114no—
490C22×D4—118no—
491C22×D4—221no—
492C22×D4—228no—
493C22×D4—2216no—
494C22×D4—2216no—
495C22×D4—228no—
496C22×D4—222no—
497C22×D4—228no—
498C22×D4—224no—
499C22×D4—222no—
500C22×D4—222no—
501C22×D4—224no—
502C22×D4—222no—
503C22×D4—222no—
504C22×D4—224no—
505C22×D4—224no—
506C22×D4—228no—
507C22×D4—224no—
508C22×D4C22⋊D1112yescomplemented
509C22×D4C22⋊D1114yescomplemented
510C22×D4C22×D1112yes—
511C22×D4C22×D1114yes—
512C22×D4C22×D1114yescomplemented
513C23×C4—21no—
514C23×C4—112no—
515C23×C4—222no—
516C23×C4—221no—
517C23×C4—222no—
518C23×C4C22⋊D1111yescharacteristic, complemented
519C23×C4C22×D1111yescharacteristic, complemented
520#123—24no—
521#123—28no—
522#123—1116no—
523#123—228no—
524#123—2216no—
525#123C22×D1118yescomplemented
526#121—216no—
527#121—2232no—
528#120—28no—
529#120—24no—
530#120—1116no—
531#120—2216no—
532#120—228no—
533#120C22×D1118yescomplemented
534C2×C4⋊C4—22no—
535C2×C4⋊C4—224no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—118no—
542C2×C22⋊C4—224no—
543C2×C22⋊C4—224no—
544C2×C22⋊C4—222no—
545C2×C22⋊C4—224no—
546C2×C22⋊C4C22×D1112yescomplemented
547C2×C22⋊C4C22×D1114yescomplemented
548#99—1116no—
549#99—1132no—
550C2×C11—22no—
551C2×C11—21no—
552C2×C11—22no—
553C2×C11—22no—
554C2×C11—24no—
555C2×C11—21no—
556C2×C11—22no—
557C2×C11—44no—
558C2×C11—82no—
559C2×C11#302612yescomplemented
560C2×C11C22×#12011yescharacteristic
561D11—48no—
562C24—21no—
563C24—22no—
564C24—21no—
565C24—22no—
566C24—21no—
567C24—22no—
568C24—21no—
569C24—82no—
570C24—82no—
571C24—82no—
572C24—114no—
573C24—118no—
574C24—228no—
575C24—224no—
576C24—222no—
577C24—224no—
578C24—222no—
579C24—884no—
580C24—884no—
581C24D4×D1112yes—
582C24D4×D1112yes—
583C24D4×D1114yes—
584C24C2×C22⋊D1112yes—
585C24C2×C22⋊D1111yescharacteristic
586C24C2×C22⋊D1111yescharacteristic
587C24C2×C22⋊D1112yes—
588C24C2×C22⋊D1114yescomplemented
589C24C23×D1111yescharacteristic
590C24C23×D1112yes—
591C24C23×D1112yescomplemented
592#41—2216no—
593#41—2232no—
594#41—2232no—
595#41—2232no—
596#41—2264no—
597#41—2216no—
598C2×Q8—228no—
599C2×Q8—224no—
600C2×D4—28no—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—28no—
604C2×D4—28no—
605C2×D4—24no—
606C2×D4—24no—
607C2×D4—28no—
608C2×D4—28no—
609C2×D4—28no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—28no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—42no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—42no—
620C2×D4—84no—
621C2×D4—118no—
622C2×D4—1116no—
623C2×D4—118no—
624C2×D4—228no—
625C2×D4—224no—
626C2×D4—2232no—
627C2×D4—2232no—
628C2×D4—2264no—
629C2×D4—2216no—
630C2×D4—228no—
631C2×D4—2216no—
632C2×D4—2232no—
633C2×D4—228no—
634C2×D4—228no—
635C2×D4—224no—
636C2×D4—224no—
637C2×D4—228no—
638C2×D4—228no—
639C2×D4—228no—
640C2×D4—228no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—228no—
644C2×D4—228no—
645C2×D4—224no—
646C2×D4—224no—
647C2×D4—228no—
648C2×D4—2216no—
649C2×D4—2216no—
650C2×D4—888no—
651C2×D4C2×C22⋊D1114yes—
652C2×D4C2×C22⋊D1118yescomplemented
653C2×D4C23×D1114yes—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—24no—
663C22×C4—82no—
664C22×C4—114no—
665C22×C4—118no—
666C22×C4—2216no—
667C22×C4—228no—
668C22×C4—228no—
669C22×C4—224no—
670C22×C4—222no—
671C22×C4—224no—
672C22×C4—222no—
673C22×C4—224no—
674C22×C4—228no—
675C22×C4—884no—
676C22×C4C2×C22⋊D1112yes—
677C22×C4C2×C22⋊D1114yescomplemented
678C22×C4C23×D1112yescomplemented
679C4⋊C4—28no—
680C4⋊C4—2216no—
681C22⋊C4—22no—
682C22⋊C4—24no—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—118no—
686C22⋊C4—2216no—
687C22⋊C4—2216no—
688C22⋊C4—224no—
689C22⋊C4—228no—
690C22⋊C4C23×D1114yescomplemented
691C11C2×#302611yescharacteristic, complemented, Sylow
692C23—24no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—24no—
697C23—22no—
698C23—42no—
699C23—44no—
700C23—42no—
701C23—42no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—48no—
707C23—41no—
708C23—42no—
709C23—41no—
710C23—82no—
711C23—84no—
712C23—82no—
713C23—82no—
714C23—82no—
715C23—84no—
716C23—84no—
717C23—84no—
718C23—82no—
719C23—118no—
720C23—2216no—
721C23—228no—
722C23—224no—
723C23—224no—
724C23—228no—
725C23—448no—
726C23—448no—
727C23—884no—
728C23—888no—
729C23—888no—
730C23—8816no—
731C23—888no—
732C23#6699011yescharacteristic
733C23#6699011yescharacteristic
734C23#6699012yes—
735C23#6699012yes—
736C23#6699014yes—
737C23#6699012yes—
738C23#6699014yes—
739C23C2×D4×D1112yes—
740C23C2×D4×D1112yes—
741C23C2×D4×D1114yes—
742C23C2×D4×D1114yes—
743C23C22×C22⋊D1111yescharacteristic
744C23C22×C22⋊D1114yes—
745C23C22×C22⋊D1111yescharacteristic
746C23C22×C22⋊D1112yes—
747C23C22×C22⋊D1112yes—
748C23C24×D1111yescharacteristic
749Q8—2216no—
750D4—28no—
751D4—216no—
752D4—28no—
753D4—44no—
754D4—44no—
755D4—48no—
756D4—88no—
757D4—2216no—
758D4—2232no—
759D4—228no—
760D4—2216no—
761D4—228no—
762D4—2216no—
763D4—228no—
764D4—228no—
765D4—8816no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—44no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—84no—
778C2×C4—118no—
779C2×C4—2232no—
780C2×C4—2216no—
781C2×C4—228no—
782C2×C4—224no—
783C2×C4—228no—
784C2×C4—224no—
785C2×C4—228no—
786C2×C4—448no—
787C2×C4—888no—
788C2×C4C22×C22⋊D1114yes—
789C22—22no—
790C22—24no—
791C22—22no—
792C22—22no—
793C22—24no—
794C22—24no—
795C22—42no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—41no—
801C22—41no—
802C22—44no—
803C22—44no—
804C22—42no—
805C22—44no—
806C22—44no—
807C22—48no—
808C22—44no—
809C22—48no—
810C22—44no—
811C22—42no—
812C22—82no—
813C22—84no—
814C22—82no—
815C22—84no—
816C22—82no—
817C22—228no—
818C22—448no—
819C22—4416no—
820C22—448no—
821C22—884no—
822C22—888no—
823C22—8816no—
824C22C2×#6699011yescharacteristic
825C22C2×#6699012yes—
826C22C2×#6699012yes—
827C22C2×#6699012yes—
828C22C2×#6699014yes—
829C22C2×#6699011yescharacteristic
830C22C22×D4×D1112yes—
831C22C23×C22⋊D1111yescharacteristic
832C4—24no—
833C4—44no—
834C4—42no—
835C4—228no—
836C4—448no—
837C2—21no—
838C2—22no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—22no—
843C2—24no—
844C2—44no—
845C2—82no—
846C2—448no—
847C2#1307801212yesdirect product factor
848C2C22×#6699011yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#534C2
socleC22×C11C2×#120
hypercenterC2×#534D11
hypocenterC11C2×#3026
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C22×#67037C2semidirect
2. C2×#10623335C2semidirect
3. #13078012C2direct (N × H)
4. C2×#10622666C2semidirect
5. C2×#10622645C2semidirect
6. C22×#66898C2semidirect
7. C22×#66870C2semidirect
8. C2×C11×#534C2semidirect
10. C23×D4×C11C22semidirect
18. C2×#67037C22semidirect
23. C11×#534C22semidirect
25. C2×C11×#123C22semidirect
28. C2×C11×#120C22semidirect
29. C22×C11×C22⋊C4C22semidirect
30. C2×#67006C22semidirect
31. C22×C22⋊Dic11C22semidirect
33. #10623335C22semidirect
37. C2×#66982C22semidirect
38. C2×#66898C22semidirect
39. C2×#66898C22semidirect
40. #10622666C22semidirect
41. #10622645C22semidirect
42. C2×#66870C22semidirect
43. C2×#66870C22semidirect
44. C25×C11D4semidirect
46. C25×C11C23semidirect
48. C24×D11D4semidirect
59. C22×D4×C11D4semidirect
60. C22×D4×C11D4semidirect
63. C22×D4×C11C23semidirect
65. C23×C4×C11D4semidirect
66. C23×C4×C11C23semidirect
79. C22×C22⋊D11D4semidirect
80. C22×C22⋊D11D4semidirect
85. C23×Dic11D4semidirect
110. C11×#123C23semidirect
114. C11×#120C23semidirect
120. C2×C11×C22⋊C4C23semidirect
121. C2×C11×C22⋊C4C23semidirect
123. #67006C23semidirect
127. C2×C22⋊Dic11C23semidirect
128. C2×C22⋊Dic11C23semidirect
133. #66982C23semidirect
136. #66898C23semidirect
137. #66870C23semidirect
156. C24×C11C2×D4semidirect
159. C24×C11C24semidirect
168. C23×D11C2×D4semidirect
191. C2×D4×C11C2×D4semidirect
204. C22×C4×C11C2×D4semidirect
205. C22×C4×C11C24semidirect
229. C2×C22⋊D11C2×D4semidirect
240. C22×Dic11C2×D4semidirect
261. C11×C22⋊C4C24semidirect
265. C22⋊Dic11C24semidirect
270. C2×#534D11semidirect
385. C23×D4C2×D11semidirect
389. #534C2×D11semidirect
393. C2×#123C2×D11semidirect
399. C2×#120C2×D11semidirect
401. C22×C22⋊C4C2×D11semidirect
458. C25C22⋊D11semidirect
460. C25C22×D11semidirect
508. C22×D4C22⋊D11semidirect
509. C22×D4C22⋊D11semidirect
512. C22×D4C22×D11semidirect
518. C23×C4C22⋊D11semidirect
519. C23×C4C22×D11semidirect
525. #123C22×D11semidirect
533. #120C22×D11semidirect
546. C2×C22⋊C4C22×D11semidirect
547. C2×C22⋊C4C22×D11semidirect
559. C2×C11#3026semidirect
588. C24C2×C22⋊D11semidirect
591. C24C23×D11semidirect
652. C2×D4C2×C22⋊D11semidirect
677. C22×C4C2×C22⋊D11semidirect
678. C22×C4C23×D11semidirect
690. C22⋊C4C23×D11semidirect
691. C11C2×#3026semidirect
847. C2#13078012direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670372
C2×#106233352
#130780122
C2×#106226662
C2×#106226452
C22×#668982
C22×#668702
C2×C11×#5342
C2×#302611