Finite Group Databasebeta

← C2×#13082325 #15661714

Subgroups — C2×#13082325 #15661714

Order 2816.

7910 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082325C2132yesmaximal, direct product factor
2C2×#10623042C214yesmaximal, complemented
3C2×#10623045C214yesmaximal, complemented
4C2×#10623044C214yesmaximal, complemented
5C2×#10623038C214yesmaximal, complemented
6C2×#10623031C211yesmaximal, characteristic, complemented
7C2×#10623046C214yesmaximal, complemented
8C2×#10623041C211yesmaximal, characteristic, complemented
9C2×#10623322C212yesmaximal, complemented
10C2×#10623322C214yesmaximal, complemented
11C2×#10623035C212yesmaximal, complemented
12C23×C11×C4⋊C4C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2212yes—
15C22×#4339C2212yes—
16C22×#4339C2214yes—
17C22×C11×C4⋊C4C2214yes—
18C22×C11×C4⋊C4C2214yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C22116yescomplemented
23C2×#67006C2214yes—
24#10623322C22164yescomplemented
25#10623322C22132yescomplemented
26C2×#66983C2212yes—
27C2×#66983C2214yes—
28C2×#66983C2214yes—
29C2×#66983C2212yes—
30C2×#66982C2218yes—
31C2×#66982C2214yes—
32C2×C4×C22⋊D11C2214yes—
33C2×C4×C22⋊D11C2214yes—
34C2×C4×C22⋊D11C2218yes—
35C2×C4×C22⋊D11C2218yes—
36C2×#66979C2214yes—
37C2×#66979C2212yes—
38C2×#66977C2212yes—
39C2×#66977C2214yes—
40C2×#66977C2212yes—
41C2×#66977C2214yes—
42#10623046C22164yescomplemented
43#10623045C22164yescomplemented
44#10623044C22164yescomplemented
45C2×#66951C2218yescomplemented
46#10623042C22164yescomplemented
47#10623041C22116yescomplemented
48C2×#66950C2214yescomplemented
49C2×#66949C2218yescomplemented
50#10623038C22164yescomplemented
51C2×#66948C2214yescomplemented
52C2×#66947C2218yescomplemented
53#10623035C22132yescomplemented
54C2×#66946C2214yescomplemented
55C2×#66945C2214yescomplemented
56C2×C4⋊C4×D11C2214yescomplemented
57#10623031C22116yescomplemented
58C2×#66943C2214yescomplemented
59C2×#66942C2218yescomplemented
60C2×#66941C2214yescomplemented
61C2×#66940C2214yescomplemented
62C25×C11C2311yescharacteristic
63C23×C4×C11—28no—
64C23×C4×C11—48no—
65C23×C4×C11C2312yes—
66C23×C4×C11C2312yes—
67C23×C4×C11C2314yes—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2318yes—
70C23×C4×C11C2312yes—
71C23×C4×C11C2314yes—
72C23×C4×C11C2312yes—
73C23×C4×C11C23116yes—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11C2314yes—
76C22×C22⋊D11C2314yes—
77C22×C22⋊D11C2314yes—
78C2×#4339—216no—
79C2×#4339—416no—
80C2×#4339C23116yes—
81C2×#4339C23132yes—
82C22×D44C2312yes—
83C22×D44C2314yes—
84C22×C4×D11C2314yes—
85C22×C4×D11C2318yes—
86C22×Dic22C2312yes—
87C22×Dic22C2314yes—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C4⋊C4C2318yes—
91C2×C11×C4⋊C4C2318yes—
92C2×C11×C4⋊C4C2318yes—
93C2×C11×C4⋊C4C23132yes—
94C2×C11×C4⋊C4C23132yes—
95C2×C11×C4⋊C4C23116yes—
96#67006C23132yes—
97C2×C22⋊Dic11C2314yes—
98C2×C22⋊Dic11C2314yes—
99C2×C22⋊Dic11C2314yes—
100#66983C23116yes—
101#66983C23132yes—
102#66983C23116yes—
103#66983C23132yes—
104#66982C23164yes—
105#66982C23132yes—
106C4×C22⋊D11C23164yes—
107C4×C22⋊D11C23132yes—
108C4×C22⋊D11C23132yes—
109C4×C22⋊D11C23164yes—
110C2×(C2×D11)⋊C4C2318yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2318yes—
114#66979C23116yes—
115#66979C23132yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2314yes—
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2314yes—
120#66977C23132yes—
121#66977C23132yes—
122#66977C23116yes—
123#66977C23116yes—
124C2×Dic11⋊C4C2318yes—
125C2×Dic11⋊C4C2318yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2314yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2318yes—
130#66951C23164yescomplemented
131#66950C23132yescomplemented
132#66949C23164yescomplemented
133#66948C23132yescomplemented
134#66947C23164yescomplemented
135#66946C23132yescomplemented
136#66945C23132yescomplemented
137C4⋊C4×D11C23132yescomplemented
138#66943C23132yescomplemented
139#66942C23164yescomplemented
140#66941C23132yescomplemented
141#66940C23132yescomplemented
142C2×#3492—111nomaximal, Sylow
143C24×C11—24no—
144C24×C11—24no—
145C24×C11—24no—
146C24×C11C2414yes—
147C24×C11C2411yescharacteristic
148C24×C11C2411yescharacteristic
149C24×C11C2411yescharacteristic
150C23×D11C2414yes—
151C22×C4×C11—24no—
152C22×C4×C11—216no—
153C22×C4×C11—28no—
154C22×C4×C11—28no—
155C22×C4×C11—232no—
156C22×C4×C11—44no—
157C22×C4×C11—48no—
158C22×C4×C11—44no—
159C22×C4×C11—432no—
160C22×C4×C11#4118yescomplemented
161C22×C4×C11C2414yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2414yes—
164C22×C4×C11C2418yes—
165C22×C4×C11C2418yes—
166C22×C4×C11C24116yes—
167C22×C4×C11C2414yes—
168C22×C4×C11C2418yes—
169C22×C4×C11C24116yes—
170C22×C4×C11C2418yes—
171C22×C4×C11C2412yes—
172C22×C4×C11C2414yes—
173C2×C22⋊D11—216no—
174C2×C22⋊D11—216no—
175C2×C22⋊D11—216no—
176C2×C22⋊D11C24116yes—
177C2×C22⋊D11C24116yes—
178C2×C22⋊D11C24116yes—
179C22×Dic11C2414yes—
180C22×Dic11C2414yes—
181C22×Dic11C2414yes—
182#4339—264no—
183#4339—464no—
184C2×D44—28no—
185C2×D44—48no—
186C2×D44C2418yes—
187C2×D44C24116yes—
188C2×C4×D11—216no—
189C2×C4×D11—416no—
190C2×C4×D11C24116yes—
191C2×C4×D11C24132yes—
192C2×Dic22—28no—
193C2×Dic22—48no—
194C2×Dic22C2418yes—
195C2×Dic22C24116yes—
196C11×C4⋊C4C24116yes—
197C11×C4⋊C4C24116yes—
198C11×C4⋊C4C24132yes—
199C22⋊Dic11C24116yes—
200C22⋊Dic11C24116yes—
201C22⋊Dic11C24116yes—
202(C2×D11)⋊C4C24132yes—
203(C2×D11)⋊C4C24116yes—
204(C2×D11)⋊C4C24116yes—
205(C2×D11)⋊C4C24132yes—
206C4⋊Dic11C2418yes—
207C4⋊Dic11C24116yes—
208C4⋊Dic11C2418yes—
209C4⋊Dic11C24116yes—
210Dic11⋊C4C24132yes—
211Dic11⋊C4C24132yes—
212Dic11⋊C4C24116yes—
213Dic11⋊C4C24116yes—
214C4×Dic11C24116yes—
215C4×Dic11C24132yes—
216#3492—1132no—
217C2×#554—114no—
218C2×#553—114no—
219C2×#552—114no—
220C2×#547—114no—
221C2×#544—111no—
222C2×#539—114no—
223C2×#537—111no—
224C2×#525—112no—
225C2×#525—114no—
226C2×#520—112no—
227C23×C4⋊C4D1111yescharacteristic, complemented
228C23×C11—232no—
229C23×C11—28no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—28no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—28no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11C2×#4114yes—
239C23×C11H(5,𝔽2)14yes—
240C23×C112−1+414yes—
241C23×C11C2512yes—
242C23×C11C2512yes—
243C23×C11C2512yes—
244C23×C11C2511yescharacteristic
245C22×D11—28no—
246C22×D11—28no—
247C22×D11—28no—
248C22×D11C2518yes—
249C2×C4×C11—28no—
250C2×C4×C11—24no—
251C2×C4×C11—28no—
252C2×C4×C11—28no—
253C2×C4×C11—232no—
254C2×C4×C11—216no—
255C2×C4×C11—216no—
256C2×C4×C11—48no—
257C2×C4×C11—416no—
258C2×C4×C11—48no—
259C2×C4×C11C2×#4118yes—
260C2×C4×C11C2×#41116yescomplemented
261C2×C4×C11C2518yes—
262C2×C4×C11C2514yes—
263C2×C4×C11C2518yes—
264C2×C4×C11C2514yes—
265C22⋊D11—232no—
266C22⋊D11—232no—
267C22⋊D11—232no—
268C2×Dic11—28no—
269C2×Dic11—28no—
270C2×Dic11—28no—
271C2×Dic11C2518yes—
272C2×Dic11C2518yes—
273C2×Dic11C2518yes—
274D44—216no—
275D44—416no—
276C4×D11—232no—
277C4×D11—432no—
278Dic22—216no—
279Dic22—416no—
280C22×#41—112no—
281C22×#41—114no—
282C24×C4C2×D1111yescharacteristic
283C24×C4C2×D1112yes—
284#554—1164no—
285#553—1164no—
286#552—1164no—
287#547—1164no—
288#544—1116no—
289#539—1164no—
290#537—1116no—
291C2×C4⋊Q8—114no—
292C2×#126—118no—
293C2×#125—118no—
294C2×#125—114no—
295#525—1132no—
296#525—1164no—
297C2×#123—114no—
298C2×#123—118no—
299C2×#123—118no—
300C2×C22⋊Q8—114no—
301C2×C22⋊Q8—112no—
302C2×C22⋊Q8—112no—
303C2×C22⋊Q8—114no—
304C2×C22⋊Q8—118no—
305C2×C22⋊Q8—114no—
306C2×#121—114no—
307C2×#121—112no—
308C2×#121—114no—
309C2×#121—112no—
310C2×#121—114no—
311C2×#120—114no—
312#520—1132no—
313C2×C4×Q8—114no—
314C2×C4×D4—118no—
315C2×C4×D4—114no—
316C2×C4×D4—118no—
317C2×C4×D4—114no—
318C2×C4×D4—114no—
319C2×#117—112no—
320C2×#117—114no—
321C2×#117—114no—
322C22×C4⋊C4—114no—
323C22×C4⋊C4C2×D1111yescharacteristic
324C22×C4⋊C4C2×D1111yescharacteristic
325C22×C4⋊C4C2×D1112yes—
326C22×C4⋊C4C2×D1114yes—
327C22×C4⋊C4C2×D1114yes—
328C22×C4⋊C4C2×D11116yescomplemented
329C22×C11—232no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—28no—
337C22×C11—28no—
338C22×C11—28no—
339C22×C11C22×#4114yes—
340C22×C11C22×#4112yes—
341C22×C11C2×H(5,𝔽2)14yes—
342C22×C11C2×H(5,𝔽2)12yes—
343C22×C11C2×2−1+414yes—
344C22×C11C2×2−1+412yes—
345C22×C11C2611yescharacteristic
346C2×D11—28no—
347C2×D11—28no—
348C2×D11—28no—
349C2×D11—416no—
350C4×C11—24no—
351C4×C11—28no—
352C4×C11—28no—
353C4×C11C22×#4118yes—
354Dic11—28no—
355Dic11—28no—
356Dic11—28no—
357C25C22×D1111yescharacteristic
358C2×#41—1116no—
359C2×#41—1132no—
360C2×#41—2216no—
361C2×#41—4416no—
362C22×Q8—112no—
363C22×Q8—114no—
364C22×D4—114no—
365C22×D4—114no—
366C22×D4—114no—
367C22×D4—112no—
368C22×D4—114no—
369C23×C4—28no—
370C23×C4—48no—
371C23×C4—114no—
372C23×C4—118no—
373C23×C4C22×D1114yes—
374C23×C4C22×D1112yes—
375C23×C4C22×D1112yes—
376C23×C4C22×D1111yescharacteristic
377C23×C4C22×D1118yes—
378C23×C4C22×D1112yes—
379C23×C4C22×D1114yes—
380C23×C4C22×D1112yes—
381C23×C4C22×D11116yes—
382C23×C4C22×D1111yescharacteristic
383C4⋊Q8—1132no—
384#126—1164no—
385#125—1164no—
386#125—1132no—
387#123—1132no—
388#123—1164no—
389#123—1164no—
390C22⋊Q8—1132no—
391C22⋊Q8—1116no—
392C22⋊Q8—1116no—
393C22⋊Q8—1132no—
394C22⋊Q8—1132no—
395C22⋊Q8—1164no—
396#121—1132no—
397#121—1116no—
398#121—1132no—
399#121—1116no—
400#121—1132no—
401#120—1132no—
402C4×Q8—1132no—
403C4×D4—1164no—
404C4×D4—1132no—
405C4×D4—1164no—
406C4×D4—1132no—
407C4×D4—1132no—
408#117—1116no—
409#117—1132no—
410#117—1132no—
411C2×C4⋊C4—112no—
412C2×C4⋊C4—118no—
413C2×C4⋊C4—112no—
414C2×C4⋊C4—114no—
415C2×C4⋊C4—114no—
416C2×C4⋊C4—114no—
417C2×C4⋊C4—118no—
418C2×C4⋊C4—114no—
419C2×C4⋊C4—1132no—
420C2×C4⋊C4C22×D1114yes—
421C2×C4⋊C4C22×D1114yes—
422C2×C4⋊C4C22×D1118yes—
423C2×C4⋊C4C22×D1118yes—
424C2×C4⋊C4C22×D1118yes—
425C2×C4⋊C4C22×D11116yes—
426C2×C4⋊C4C22×D11132yes—
427C2×C4⋊C4C22×D11132yes—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—114no—
430C2×C22⋊C4—114no—
431C2×C22⋊C4—118no—
432C2×C22⋊C4—118no—
433C2×C22⋊C4—114no—
434C2×C22⋊C4—114no—
435C2×C42—118no—
436C2×C42—114no—
437C2×C11—24no—
438C2×C11—24no—
439C2×C11—24no—
440C2×C11#349214yescomplemented
441C2×C11C23×#4111yescharacteristic
442C2×C11C22×H(5,𝔽2)11yescharacteristic
443C2×C11C22×2−1+411yescharacteristic
444D11—48no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—114no—
449C24C23×D1114yes—
450C24C23×D1111yescharacteristic
451C24C23×D1111yescharacteristic
452C24C23×D1111yescharacteristic
453#41—2264no—
454#41—4464no—
455C2×Q8—118no—
456C2×Q8—1116no—
457C2×Q8—228no—
458C2×Q8—448no—
459C2×D4—1116no—
460C2×D4—1116no—
461C2×D4—1116no—
462C2×D4—118no—
463C2×D4—1116no—
464C2×D4—2216no—
465C2×D4—2216no—
466C2×D4—2216no—
467C2×D4—228no—
468C2×D4—448no—
469C22×C4—24no—
470C22×C4—216no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—232no—
474C22×C4—44no—
475C22×C4—48no—
476C22×C4—44no—
477C22×C4—432no—
478C22×C4—114no—
479C22×C4—114no—
480C22×C4—114no—
481C22×C4—1116no—
482C22×C4—1132no—
483C22×C4—2216no—
484C22×C4—4416no—
485C22×C4#433918yescomplemented
486C22×C4C23×D11116yes—
487C22×C4C23×D1118yes—
488C22×C4C23×D1118yes—
489C22×C4C23×D1114yes—
490C22×C4C23×D1114yes—
491C22×C4C23×D1112yes—
492C22×C4C23×D1114yes—
493C22×C4C23×D1118yes—
494C22×C4C23×D11116yes—
495C22×C4C23×D1118yes—
496C22×C4C23×D1112yes—
497C22×C4C23×D1114yes—
498C4⋊C4—118no—
499C4⋊C4—1132no—
500C4⋊C4—118no—
501C4⋊C4—1116no—
502C4⋊C4—1116no—
503C4⋊C4—1116no—
504C4⋊C4—1132no—
505C4⋊C4—1116no—
506C4⋊C4C23×D11116yes—
507C4⋊C4C23×D11116yes—
508C4⋊C4C23×D11132yes—
509C22⋊C4—1116no—
510C22⋊C4—1116no—
511C22⋊C4—1116no—
512C22⋊C4—1132no—
513C22⋊C4—1132no—
514C22⋊C4—1116no—
515C22⋊C4—1116no—
516C42—1132no—
517C42—1116no—
518C11C2×#349211yescharacteristic, complemented, Sylow
519C23—232no—
520C23—28no—
521C23—22no—
522C23—22no—
523C23—28no—
524C23—22no—
525C23—22no—
526C23—28no—
527C23—22no—
528C23—22no—
529C23—118no—
530C23—228no—
531C23—228no—
532C23—228no—
533C23C2×#433914yes—
534C23#6703714yes—
535C23#6704014yes—
536C23C24×D1112yes—
537C23C24×D1112yes—
538C23C24×D1112yes—
539C23C24×D1111yescharacteristic
540Q8—2216no—
541Q8—4416no—
542D4—2232no—
543D4—2232no—
544D4—2232no—
545D4—2216no—
546D4—4416no—
547C2×C4—28no—
548C2×C4—24no—
549C2×C4—28no—
550C2×C4—28no—
551C2×C4—232no—
552C2×C4—216no—
553C2×C4—216no—
554C2×C4—48no—
555C2×C4—416no—
556C2×C4—48no—
557C2×C4—118no—
558C2×C4—118no—
559C2×C4—118no—
560C2×C4—228no—
561C2×C4—228no—
562C2×C4—228no—
563C2×C4—2232no—
564C2×C4—4432no—
565C2×C4C2×#433918yes—
566C2×C4C2×#4339116yescomplemented
567C2×C4C24×D1118yes—
568C2×C4C24×D1114yes—
569C2×C4C24×D1118yes—
570C2×C4C24×D1114yes—
571C22—232no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—28no—
579C22—28no—
580C22—28no—
581C22—228no—
582C22—228no—
583C22—228no—
584C22—4416no—
585C22C22×#433914yes—
586C22C22×#433912yes—
587C22C2×#6703714yes—
588C22C2×#6703712yes—
589C22C2×#6704014yes—
590C22C2×#6704012yes—
591C22C25×D1111yescharacteristic
592C4—24no—
593C4—28no—
594C4—28no—
595C4—228no—
596C4—228no—
597C4—228no—
598C4C22×#433918yes—
599C2—24no—
600C2—24no—
601C2—24no—
602C2—448no—
603C2#1308232514yesdirect product factor
604C2C23×#433911yescharacteristic
605C2C22×#6703711yescharacteristic
606C2C22×#6704011yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC23×C11×C4⋊C4C2
socleC23×C11C25
hypercenterC23×C4⋊C4D11
hypocenterC11C2×#3492
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #13082325C2direct (N × H)
2. C2×#10623042C2semidirect
3. C2×#10623045C2semidirect
4. C2×#10623044C2semidirect
5. C2×#10623038C2semidirect
6. C2×#10623031C2semidirect
7. C2×#10623046C2semidirect
8. C2×#10623041C2semidirect
9. C2×#10623322C2semidirect
10. C2×#10623322C2semidirect
11. C2×#10623035C2semidirect
12. C23×C11×C4⋊C4C2semidirect
22. C22×C11×C4⋊C4C22semidirect
24. #10623322C22semidirect
25. #10623322C22semidirect
42. #10623046C22semidirect
43. #10623045C22semidirect
44. #10623044C22semidirect
45. C2×#66951C22semidirect
46. #10623042C22semidirect
47. #10623041C22semidirect
48. C2×#66950C22semidirect
49. C2×#66949C22semidirect
50. #10623038C22semidirect
51. C2×#66948C22semidirect
52. C2×#66947C22semidirect
53. #10623035C22semidirect
54. C2×#66946C22semidirect
55. C2×#66945C22semidirect
56. C2×C4⋊C4×D11C22semidirect
57. #10623031C22semidirect
58. C2×#66943C22semidirect
59. C2×#66942C22semidirect
60. C2×#66941C22semidirect
61. C2×#66940C22semidirect
130. #66951C23semidirect
131. #66950C23semidirect
132. #66949C23semidirect
133. #66948C23semidirect
134. #66947C23semidirect
135. #66946C23semidirect
136. #66945C23semidirect
137. C4⋊C4×D11C23semidirect
138. #66943C23semidirect
139. #66942C23semidirect
140. #66941C23semidirect
141. #66940C23semidirect
160. C22×C4×C11#41semidirect
227. C23×C4⋊C4D11semidirect
260. C2×C4×C11C2×#41semidirect
328. C22×C4⋊C4C2×D11semidirect
440. C2×C11#3492semidirect
485. C22×C4#4339semidirect
518. C11C2×#3492semidirect
566. C2×C4C2×#4339semidirect
603. C2#13082325direct (N × H)

Maximal subgroups

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

subgroupindex
#130823252
C2×#106230422
C2×#106230452
C2×#106230442
C2×#106230382
C2×#106230312
C2×#106230462
C2×#106230412
C2×#106233222
C2×#106230352
C23×C11×C4⋊C42
C2×#349211