Finite Group Databasebeta

← C2×#13073798 #14923995

Subgroups — C2×#13073798 #14923995

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2#13073798C2116yesmaximal, direct product factor
3C2×#10622595C211yesmaximal, characteristic, complemented
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622842C211yesmaximal, characteristic, complemented
6C2×#10622844C211yesmaximal, characteristic, complemented
7C2×#10622591C212yesmaximal, complemented
8C2×#10622571C212yesmaximal
9C2×#10622602C212yesmaximal, complemented
10C2×#10622555C212yesmaximal, complemented
11C22×C11⋊#95C211yesmaximal, characteristic, complemented
12C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C24×Dic11C2212yes—
17C23×C4×D11C2211yescharacteristic
18C2×C11×C22⋊Q8—28no—
19C2×C11×C22⋊Q8C2218yescomplemented
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24C2×C4×C22⋊D11—28no—
25C2×C4×C22⋊D11C2218yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33#10622844C2218yescomplemented
34#10622842C2218yescomplemented
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2218yescomplemented
43#10622605C2218yescomplemented
44#10622602C22116yescomplemented
45#10622595C2218yescomplemented
46#10622591C22116yescomplemented
47#10622571C22116yes—
48#10622555C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C22×Q8×C11—24no—
52C22×Q8×C11—44no—
53C22×Q8×C11C2314yes—
54C23×C4×C11—44no—
55C23×C4×C11D418yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2314yes—
61C22×C22⋊D11—24no—
62C22×C22⋊D11—24no—
63C22×C22⋊D11Q818yescomplemented
64C22×C22⋊D11C2314yes—
65C23×Dic11—28no—
66C23×Dic11—28no—
67C23×Dic11—44no—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2312yes—
71C23×Dic11C2318yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2312yes—
74C22×C4×D11—24no—
75C22×C4×D11—44no—
76C22×C4×D11C2314yes—
77C11×C22⋊Q8—232no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—28no—
80C2×C11×C4⋊C4C2318yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C22⋊C4—28no—
83C2×C11×C22⋊C4C2318yes—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11C2314yes—
86C4×C22⋊D11—232no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—28no—
95C2×Dic11⋊C4—44no—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2318yes—
98C2×Dic11⋊C4C2318yes—
99C2×C4×Dic11—24no—
100C2×C4×Dic11C2314yes—
101C11⋊#95C2318yes—
102C11⋊#95C2318yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C2×#2564—111nomaximal, Sylow
109C24×C11—24no—
110C24×C11—24no—
111C24×C11C2×D414yes—
112C24×C11C2×Q814yes—
113C24×C11#4114yes—
114C24×C11C2412yes—
115C24×C11C2411yescharacteristic
116C23×D11—22no—
117C23×D11—24no—
118C23×D11—22no—
119C23×D11—24no—
120C23×D11C2×Q814yes—
121C23×D11C2412yes—
122C2×Q8×C11—28no—
123C2×Q8×C11—48no—
124C2×Q8×C11—416no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—416no—
134C22×C4×C11—48no—
135C22×C4×C11C2×D414yes—
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2×D4116yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C2×C22⋊D11—232no—
143C2×C22⋊D11—28no—
144C2×C22⋊D11—28no—
145C2×C22⋊D11C2×Q8116yescomplemented
146C22×Dic11—216no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—24no—
153C22×Dic11—216no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—48no—
160C22×Dic11—432no—
161C22×Dic11C2×Q814yes—
162C22×Dic11#4118yes—
163C22×Dic11C2414yes—
164C22×Dic11C2412yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167C22×Dic11C2414yes—
168C2×C4×D11—28no—
169C2×C4×D11—48no—
170C2×C4×D11—416no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—216no—
173C11×C22⋊C4—216no—
174C22⋊Dic11—28no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—48no—
178Dic11⋊C4—216no—
179Dic11⋊C4—28no—
180Dic11⋊C4—48no—
181C4×Dic11—28no—
182C22×C22⋊Q8D1111yescharacteristic, complemented
183C22×C4×D4—111no—
184#2564—1116no—
185C2×#400—111no—
186C2×#399—111no—
187C2×#395—111no—
188C2×#393—111no—
189C2×#387—112no—
190C2×#386—112no—
191C2×#385—112no—
192C2×#380—112no—
193C22×#95—111no—
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—216no—
197C23×C11—216no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11C22⋊Q8116yes—
201C23×C11C22×D414yes—
202C23×C11C22×D412yes—
203C23×C11C22×Q814yes—
204C23×C11C22×Q812yes—
205C23×C11C2×#4114yes—
206C23×C11C2×#4112yes—
207C23×C11C2×#4114yes—
208C23×C11H(5,𝔽2)14yes—
209C23×C11C2511yescharacteristic
210C22×D11—28no—
211C22×D11—216no—
212C22×D11—22no—
213C22×D11—24no—
214C22×D11—22no—
215C22×D11—24no—
216C22×D11—44no—
217C22×D11—44no—
218C22×D11—48no—
219C22×D11C22×Q814yes—
220Q8×C11—416no—
221C2×C4×C11—28no—
222C2×C4×C11—28no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—416no—
232C2×C4×C11—48no—
233C2×C4×C11—48no—
234C2×C4×C11C22×D414yes—
235C2×C4×C11C22×D414yes—
236C22⋊D11—232no—
237C2×Dic11—28no—
238C2×Dic11—216no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—432no—
251C2×Dic11—44no—
252C2×Dic11—44no—
253C2×Dic11—48no—
254C2×Dic11C22×Q814yes—
255C2×Dic11C2×#4118yes—
256C4×D11—416no—
257C23×Q8C2×D1111yescharacteristic
258C23×D4—111no—
259C24×C4—112no—
260C24×C4—111no—
261C24×C4C2×D1111yescharacteristic
262C2×C22⋊Q8—28no—
263C2×C22⋊Q8C2×D1118yescomplemented
264C2×C4×D4—118no—
265C2×C4×D4—228no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—112no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4C2×D1111yescharacteristic
270C22×C4⋊C4C2×D1112yes—
271C22×C22⋊C4—111no—
272C22×C22⋊C4—111no—
273C22×C22⋊C4—112no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4C2×D1112yes—
276C22×C42—111no—
277#400—118no—
278#399—118no—
279#395—118no—
280#393—118no—
281#387—1116no—
282#386—1116no—
283#385—1116no—
284#380—1116no—
285C2×#95—118no—
286C2×#95—111no—
287C2×#95—112no—
288C2×#95—111no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—112no—
293C22×C11—232no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—28no—
297C22×C11—28no—
298C22×C11C2×C22⋊Q818yes—
299C22×C11C2×C22⋊Q814yes—
300C22×C11#53214yes—
301C22×C11#53414yes—
302C22×C11#55118yes—
303C22×C11#55418yes—
304C22×C11C23×D411yescharacteristic
305C22×C11C23×Q811yescharacteristic
306C22×C11C22×#4111yescharacteristic
307C22×C11C22×#4112yes—
308C22×C11C2×H(5,𝔽2)12yes—
309C2×D11—24no—
310C2×D11—28no—
311C2×D11—416no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—44no—
315C4×C11—24no—
316C4×C11—24no—
317C4×C11—44no—
318C4×C11—44no—
319Dic11—24no—
320Dic11—28no—
321Dic11—42no—
322Dic11—42no—
323Dic11—44no—
324C25—111no—
325C25C22×D1111yescharacteristic
326C22×Q8—24no—
327C22×Q8—44no—
328C22×Q8C22×D1114yes—
329C22×D4—118no—
330C22×D4—114no—
331C22×D4—224no—
332C22×D4—224no—
333C23×C4—44no—
334C23×C4—112no—
335C23×C4—111no—
336C23×C4—111no—
337C23×C4—111no—
338C23×C4—112no—
339C23×C4—118no—
340C23×C4—114no—
341C23×C4—228no—
342C23×C4—228no—
343C23×C4—224no—
344C23×C4—444no—
345C23×C4—444no—
346C23×C4C22⋊D1118yes—
347C23×C4C22×D1112yes—
348C23×C4C22×D1112yes—
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1114yes—
352C22⋊Q8—232no—
353C4×D4—2232no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—114no—
357C2×C4⋊C4—118no—
358C2×C4⋊C4—118no—
359C2×C4⋊C4—228no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—444no—
362C2×C4⋊C4C22×D1118yes—
363C2×C4⋊C4C22×D1114yes—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—114no—
366C2×C22⋊C4—114no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—118no—
369C2×C22⋊C4—228no—
370C2×C22⋊C4—224no—
371C2×C22⋊C4—224no—
372C2×C22⋊C4—444no—
373C2×C22⋊C4C22×D1118yes—
374C2×C42—114no—
375C2×C42—224no—
376#95—118no—
377#95—114no—
378#95—114no—
379#95—118no—
380#95—118no—
381#95—118no—
382#95—118no—
383C2×C11—28no—
384C2×C11#256418yescomplemented
385C2×C11C22×C22⋊Q811yescharacteristic
386C2×C11C2×#53211yescharacteristic
387C2×C11C2×#53411yescharacteristic
388C2×C11C2×#55112yes—
389C2×C11C2×#55412yes—
390D11—44no—
391C24—24no—
392C24—24no—
393C24—114no—
394C24—112no—
395C24—224no—
396C24—222no—
397C24—224no—
398C24—222no—
399C24Q8×D1114yes—
400C24#434314yes—
401C24C2×C22⋊D1114yes—
402C24C23×D1112yes—
403C24C23×D1111yescharacteristic
404C2×Q8—28no—
405C2×Q8—48no—
406C2×Q8—416no—
407C2×D4—1116no—
408C2×D4—2232no—
409C2×D4—228no—
410C2×D4—228no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—48no—
420C22×C4—416no—
421C22×C4—114no—
422C22×C4—118no—
423C22×C4—112no—
424C22×C4—114no—
425C22×C4—114no—
426C22×C4—112no—
427C22×C4—112no—
428C22×C4—2216no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—2216no—
436C22×C4—224no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—228no—
442C22×C4—448no—
443C22×C4—4416no—
444C22×C4—448no—
445C22×C4—4432no—
446C22×C4C2×C22⋊D1114yes—
447C22×C4C2×C22⋊D1114yes—
448C22×C4C2×C22⋊D11116yes—
449C22×C4C23×D1114yes—
450C22×C4C23×D1114yes—
451C22×C4C23×D1112yes—
452C22×C4C23×D1112yes—
453C4⋊C4—28no—
454C4⋊C4—216no—
455C4⋊C4—2216no—
456C4⋊C4—228no—
457C4⋊C4—448no—
458C22⋊C4—216no—
459C22⋊C4—2216no—
460C22⋊C4—228no—
461C22⋊C4—228no—
462C22⋊C4—448no—
463C42—228no—
464C11C2×#256411yescharacteristic, complemented, Sylow
465C23—28no—
466C23—28no—
467C23—216no—
468C23—216no—
469C23—24no—
470C23—24no—
471C23—114no—
472C23—228no—
473C23—2216no—
474C23—224no—
475C23—222no—
476C23—224no—
477C23—222no—
478C23—444no—
479C23—444no—
480C23—448no—
481C23#66999116yes—
482C23#6703714yes—
483C23C2×Q8×D1114yes—
484C23C2×Q8×D1112yes—
485C23C2×#434314yes—
486C23C2×#434312yes—
487C23#41×D1114yes—
488C23C22×C22⋊D1114yes—
489C23C22×C22⋊D1112yes—
490C23C24×D1111yescharacteristic
491Q8—416no—
492D4—2232no—
493C2×C4—28no—
494C2×C4—28no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—416no—
504C2×C4—48no—
505C2×C4—48no—
506C2×C4—114no—
507C2×C4—118no—
508C2×C4—228no—
509C2×C4—2216no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—4416no—
522C2×C4—4432no—
523C2×C4—444no—
524C2×C4—444no—
525C2×C4—448no—
526C2×C4C22×C22⋊D1114yes—
527C2×C4C22×C22⋊D1114yes—
528C22—28no—
529C22—28no—
530C22—24no—
531C22—24no—
532C22—232no—
533C22—228no—
534C22—224no—
535C22—444no—
536C22—442no—
537C22—442no—
538C22—4416no—
539C22#1062316718yes—
540C22#1062316818yes—
541C22#1062333514yes—
542C22C2×#6699918yes—
543C22C2×#6699914yes—
544C22#1062336314yes—
545C22C2×#6703712yes—
546C22C22×Q8×D1111yescharacteristic
547C22C22×#434311yescharacteristic
548C22C2×#41×D1112yes—
549C22C23×C22⋊D1111yescharacteristic
550C4—24no—
551C4—24no—
552C4—44no—
553C4—44no—
554C4—228no—
555C4—224no—
556C4—444no—
557C4—442no—
558C4—442no—
559C2—28no—
560C2—444no—
561C2#1307379818yesdirect product factor
562C2C22×#6699911yescharacteristic
563C2C2×#1062336311yescharacteristic
564C2C2×#1062333511yescharacteristic
565C2C2×#1062316812yes—
566C2C2×#1062316712yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2564
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13073798C2direct (N × H)
3. C2×#10622595C2semidirect
4. C2×#10622605C2semidirect
5. C2×#10622842C2semidirect
6. C2×#10622844C2semidirect
7. C2×#10622591C2semidirect
9. C2×#10622602C2semidirect
10. C2×#10622555C2semidirect
11. C22×C11⋊#95C2semidirect
12. C22×C11×C22⋊Q8C2semidirect
19. C2×C11×C22⋊Q8C22semidirect
33. #10622844C22semidirect
34. #10622842C22semidirect
42. C2×C11⋊#95C22semidirect
43. #10622605C22semidirect
44. #10622602C22semidirect
45. #10622595C22semidirect
46. #10622591C22semidirect
48. #10622555C22semidirect
63. C22×C22⋊D11Q8semidirect
145. C2×C22⋊D11C2×Q8semidirect
182. C22×C22⋊Q8D11semidirect
263. C2×C22⋊Q8C2×D11semidirect
384. C2×C11#2564semidirect
464. C11C2×#2564semidirect
561. C2#13073798direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
#130737982
C2×#106225952
C2×#106226052
C2×#106228422
C2×#106228442
C2×#106225912
C2×#106225712
C2×#106226022
C2×#106225552
C22×C11⋊#952
C22×C11×C22⋊Q82
C2×#256411