Finite Group Databasebeta

← C2×#13067577 #14725868

Subgroups — C2×#13067577 #14725868

Order 2816.

1232 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623046C211yesmaximal, characteristic
2C2×#10622841C211yesmaximal, characteristic, complemented
3C2×#10622840C211yesmaximal, characteristic
4#13067577C218yesmaximal, direct product factor
5C2×#10622090C211yesmaximal, characteristic, complemented
6C2×#10622089C211yesmaximal, characteristic
7C2×#10622166C211yesmaximal, characteristic, complemented
8C2×C11×#395C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C22×C11×C4⋊C4—21no—
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×#4326—21no—
13C22×#4325—21no—
14C2×#66983C2211yescharacteristic
15C2×#66982—21no—
16C2×C4×C22⋊D11—21no—
17C2×#66977C2211yescharacteristic
18#10623046—22no—
19#10623046—22no—
20#10623046—22no—
21#10623046C2214yes—
22C2×#66951—21no—
23C2×#66949—21no—
24C2×#66947—21no—
25C2×#66942—21no—
26C11×#395—22no—
27C11×#395C2214yescomplemented
28C2×C11×#95—21no—
29C2×C11×#95C2211yescharacteristic
30#10622841—22no—
31#10622841C2214yescomplemented
32#10622840—22no—
33#10622840C2214yes—
34C2×#66899—21no—
35C2×#66899—21no—
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38#10622166C2214yescomplemented
39#10622090C2214yescomplemented
40#10622089C2214yes—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—44no—
47C22×Q8×C11C2312yes—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—21no—
54C22×D44D411yescharacteristic
55C22×C4×D11—21no—
56C22×Dic22D411yescharacteristic
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—44no—
63C2×C11×C4⋊C4D412yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C22⋊Dic11—21no—
66C2×#4326—24no—
67C2×#4326—44no—
68C2×#4325—24no—
69C2×#4325—44no—
70#66983—21no—
71#66983—21no—
72#66983D412yes—
73#66983C2312yes—
74#66982—24no—
75#66982—24no—
76C4×C22⋊D11—24no—
77C4×C22⋊D11—24no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×C4⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11D411yescharacteristic
84#66977—21no—
85#66977—21no—
86#66977D412yes—
87#66977C2312yes—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C22×C11⋊C8—21no—
94C22×C11⋊C8—21no—
95#66951—24no—
96#66951—24no—
97#66949—24no—
98#66949—24no—
99#66947—24no—
100#66947—24no—
101#66942—24no—
102#66942—24no—
103C11×#95—24no—
104C11×#95—21no—
105C11×#95C2312yes—
106#66899—24no—
107#66899—24no—
108C22⋊(C11⋊C8)—21no—
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)C2312yes—
111C22⋊(C11⋊C8)C2312yes—
112C2×#1603—111nomaximal, Sylow
113C24×C11C2×D411yescharacteristic
114C23×D11—21no—
115C2×Q8×C11—24no—
116C2×Q8×C11—24no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—44no—
120C2×Q8×C11—42no—
121C2×Q8×C11—42no—
122C2×Q8×C11—44no—
123C2×Q8×C11—44no—
124C2×Q8×C11—44no—
125C2×Q8×C11—41no—
126C2×Q8×C11—41no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—22no—
153C2×C22⋊D11—22no—
154C2×C22⋊D11—42no—
155C2×C22⋊D11—42no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C2×D44—21no—
160C2×D44—42no—
161C2×D44C2×D412yes—
162C2×C4×D11—24no—
163C2×C4×D11—82no—
164C2×Dic22—21no—
165C2×Dic22—42no—
166C2×Dic22C2×D412yes—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—48no—
172C22⋊Dic11—22no—
173C22⋊Dic11—22no—
174#4326—48no—
175#4325—48no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4—24no—
179(C2×D11)⋊C4—22no—
180(C2×D11)⋊C4—22no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11C2×D412yes—
184C4⋊Dic11C2×D412yes—
185Dic11⋊C4—24no—
186Dic11⋊C4—24no—
187Dic11⋊C4—24no—
188Dic11⋊C4—22no—
189Dic11⋊C4—22no—
190C4×Dic11—24no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—42no—
194C2×C11⋊C8—42no—
195C2×#539—111no—
196C2×#451—111no—
197C2×#448—111no—
198C2×#395D1111yescharacteristic, complemented
199#1603—118no—
200C2×#328—111no—
201C2×#327—111no—
202C2×#324—111no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11#12011yescharacteristic
206C23×C11#12011yescharacteristic
207C23×C11#13512yes—
208C23×C11#13712yes—
209C23×C11C22×D411yescharacteristic
210C22×D11—22no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214Q8×C11—24no—
215Q8×C11—24no—
216Q8×C11—44no—
217Q8×C11—44no—
218Q8×C11—42no—
219Q8×C11—42no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—48no—
234C2×C4×C11—42no—
235C2×C4×C11—44no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—44no—
242C2×C4×C11—42no—
243C2×C4×C11—81no—
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C22⋊D11—42no—
249C22⋊D11—42no—
250C22⋊D11—44no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257D44—42no—
258D44—81no—
259C4×D11—84no—
260Dic22—42no—
261Dic22—81no—
262C11⋊C8—42no—
263C11⋊C8—42no—
264C23×Q8C2×D1111yescharacteristic
265C22×Q16—221no—
266C22×SD16—221no—
267#539—114no—
268#539—222no—
269#539—222no—
270#539—222no—
271C2×#126—221no—
272C2×#125—221no—
273C2×#123—221no—
274C2×#123—221no—
275C2×C22⋊Q8—111no—
276C2×C22⋊Q8—221no—
277C2×#121—111no—
278C2×C4×D4—221no—
279C22×C4⋊C4—21no—
280C22×C4⋊C4C2×D1111yescharacteristic
281#451—114no—
282#451—222no—
283#448—114no—
284#448—222no—
285C2×#103—221no—
286C2×#103—221no—
287C2×C22⋊C8—111no—
288C2×C22⋊C8—111no—
289#395—22no—
290#395C2×D1114yescomplemented
291C2×#95—21no—
292C2×#95C2×D1111yescharacteristic
293#328—114no—
294#327—114no—
295#324—114no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11#45212yes—
303C22×C11#45212yes—
304C22×C11#45612yes—
305C22×C11B(4,𝔽2)12yes—
306C22×C11C2×#12011yescharacteristic
307C22×C11C2×#13511yescharacteristic
308C22×C11C2×#13711yescharacteristic
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—84no—
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—21no—
316C4×C11—21no—
317C4×C11—44no—
318C4×C11—42no—
319C4×C11—44no—
320C4×C11—42no—
321Dic11—42no—
322Dic11—42no—
323Dic11—42no—
324C22×Q8—21no—
325C22×Q8—21no—
326C22×Q8—21no—
327C22×Q8—21no—
328C22×Q8—21no—
329C22×Q8—44no—
330C22×Q8—111no—
331C22×Q8C22×D1112yes—
332C22×D4—111no—
333C22×D4—221no—
334C23×C4—21no—
335C23×C4—21no—
336C23×C4—221no—
337C23×C4C22⋊D1111yescharacteristic
338C23×C4C22⋊D1111yescharacteristic
339C23×C4C22×D1111yescharacteristic
340C2×Q16—224no—
341C2×Q16—444no—
342C2×SD16—224no—
343C2×SD16—444no—
344C22×C8—221no—
345C22×C8—221no—
346#126—224no—
347#126—224no—
348#125—224no—
349#125—224no—
350#123—224no—
351#123—224no—
352#123—224no—
353#123—224no—
354C22⋊Q8—112no—
355C22⋊Q8—112no—
356C22⋊Q8—224no—
357C22⋊Q8—224no—
358C22⋊Q8—221no—
359C22⋊Q8—221no—
360#121—112no—
361#121—112no—
362#121—221no—
363#121—221no—
364C4×D4—224no—
365C4×D4—224no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4C22⋊D1112yes—
379C2×C4⋊C4C22×D1112yes—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C42—221no—
386#103—224no—
387#103—224no—
388C22⋊C8—112no—
389C22⋊C8—112no—
390C22⋊C8—221no—
391C22⋊C8—221no—
392#95—24no—
393#95—21no—
394#95C22×D1112yes—
395C2×C11—21no—
396C2×C11—21no—
397C2×C11—22no—
398C2×C11#160314yescomplemented
399C2×C11C2×#45211yescharacteristic
400C2×C11C2×#45611yescharacteristic
401C2×C11C2×B(4,𝔽2)11yescharacteristic
402D11—82no—
403C24—221no—
404C24C2×C22⋊D1111yescharacteristic
405C2×Q8—24no—
406C2×Q8—24no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—44no—
410C2×Q8—42no—
411C2×Q8—42no—
412C2×Q8—44no—
413C2×Q8—44no—
414C2×Q8—44no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—112no—
418C2×Q8—221no—
419C2×Q8—442no—
420C2×D4—112no—
421C2×D4—222no—
422C2×D4—222no—
423C2×D4—221no—
424C2×D4—442no—
425C2×D4—442no—
426C2×D4—442no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—224no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—882no—
449C22×C4D4×D1111yescharacteristic
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4C2×C22⋊D1112yes—
454C22×C4C2×C22⋊D1112yes—
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C23×D1111yescharacteristic
457Q16—448no—
458SD16—448no—
459C2×C8—222no—
460C2×C8—222no—
461C2×C8—442no—
462C2×C8—442no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—48no—
468C4⋊C4—112no—
469C4⋊C4—112no—
470C4⋊C4—224no—
471C4⋊C4—224no—
472C4⋊C4—224no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—222no—
476C4⋊C4—222no—
477C22⋊C4—224no—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C22⋊C4—222no—
481C22⋊C4—222no—
482C22⋊C4—222no—
483C22⋊C4—222no—
484C42—224no—
485C11C2×#160311yescharacteristic, complemented, Sylow
486C23—22no—
487C23—22no—
488C23—222no—
489C23—442no—
490C23—442no—
491C23—442no—
492C23#6699011yescharacteristic
493C23#6699011yescharacteristic
494C23#6699512yes—
495C23#6700312yes—
496C23C22×C22⋊D1111yescharacteristic
497Q8—24no—
498Q8—24no—
499Q8—42no—
500Q8—42no—
501Q8—44no—
502Q8—44no—
503Q8—442no—
504Q8—881no—
505D4—442no—
506D4—442no—
507D4—442no—
508D4—444no—
509D4—881no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—48no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—81no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—222no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—884no—
541C2×C4#6699011yescharacteristic
542C2×C4#6699011yescharacteristic
543C2×C4C2×D4×D1111yescharacteristic
544C2×C4C2×D4×D1111yescharacteristic
545C8—442no—
546C8—442no—
547C22—24no—
548C22—24no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—442no—
554C22—442no—
555C22—442no—
556C22—884no—
557C22#1062264512yes—
558C22#1062266012yes—
559C22#1062266012yes—
560C22#1062270812yes—
561C22C2×#6699011yescharacteristic
562C22C2×#6699511yescharacteristic
563C22C2×#6700311yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—44no—
569C4—42no—
570C4—44no—
571C4—42no—
572C4—442no—
573C4—442no—
574C4—442no—
575C2—21no—
576C2—21no—
577C2—22no—
578C2—882no—
579C2#1306757714yesdirect product factor
580C2C2×#1062266011yescharacteristic
581C2C2×#1062270811yescharacteristic
582C2C2×#1062264511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#395C2
socleC23×C11#120
prime radicalC2×#66983C22
hypercenterC2×#395D11
hypocenterC11C2×#1603
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
2. C2×#10622841C2semidirect
4. #13067577C2direct (N × H)
5. C2×#10622090C2semidirect
7. C2×#10622166C2semidirect
8. C2×C11×#395C2semidirect
27. C11×#395C22semidirect
31. #10622841C22semidirect
38. #10622166C22semidirect
39. #10622090C22semidirect
198. C2×#395D11semidirect
290. #395C2×D11semidirect
398. C2×C11#1603semidirect
485. C11C2×#1603semidirect
579. C2#13067577direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230462
C2×#106228412
C2×#106228402
#130675772
C2×#106220902
C2×#106220892
C2×#106221662
C2×C11×#3952
C2×#160311