Finite Group Databasebeta

← C2×#13070065 #14782673

Subgroups — C2×#13070065 #14782673

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66872C211yesmaximal, characteristic, complemented
2C2×#10622746C211yesmaximal, characteristic
3C2×#10622579C211yesmaximal, characteristic
4C2×#10622742C211yesmaximal, characteristic
5#13070065C218yesmaximal, direct product factor
6C2×#10622192C211yesmaximal, characteristic, complemented
7C2×#10622196C211yesmaximal, characteristic, complemented
8C2×C11×#343C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16#10622746—22no—
17#10622746C2214yes—
18#10622742—22no—
19#10622742C2214yes—
20C2×#66885—21no—
21C2×(C2×D11)⋊C8—22no—
22C2×#66880—21no—
23C2×#66874—21no—
24#10622579—22no—
25#10622579C2214yes—
26C2×#66873—21no—
27C2×#66872—22no—
28C2×#66872—22no—
29C2×#66872C2214yescomplemented
30C11×#343C2214yescomplemented
31#10622196C2214yescomplemented
32#10622192C2214yescomplemented
33C23×C4×C11—21no—
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11—21no—
36C23×Dic11—21no—
37C2×#4339—21no—
38C2×#4339—21no—
39C2×#4339—22no—
40C2×#4339—22no—
41C2×#4339—22no—
42C2×#4339—22no—
43C2×#4339D412yes—
44C2×#4339C2312yes—
45C22×D44D411yescharacteristic
46C22×C4×D11—21no—
47C22×Dic22D411yescharacteristic
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16C2312yes—
55C2×C11×M16C2312yes—
56C22×C8×C11—21no—
57C22×C8×C11—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2312yes—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2312yes—
70C2×#4318—21no—
71C2×#4318—22no—
72C2×#4318—22no—
73C2×#4318C2312yes—
74C22×C11⋊C8—22no—
75C22×C11⋊C8—22no—
76C22×C11⋊C8—21no—
77C22×C11⋊C8D412yes—
78C22×C11⋊C8D412yes—
79C22×C11⋊C8C2312yes—
80#66885—24no—
81(C2×D11)⋊C8—28no—
82#66880—24no—
83#66874—24no—
84#66873—24no—
85#66872—28no—
86C2×#2079—111nomaximal, Sylow
87C24×C11#4111yescharacteristic
88C23×D11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—82no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×C4×C11#4112yes—
99C22×C4×C11#4112yes—
100C22×C4×C11#4112yes—
101C22×C4×C11#4112yes—
102C22×C4×C11C2411yescharacteristic
103C2×C22⋊D11—22no—
104C2×C22⋊D11—22no—
105C2×C22⋊D11—42no—
106C2×C22⋊D11—42no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11—82no—
112#4339—24no—
113#4339—24no—
114#4339—22no—
115#4339—22no—
116#4339—22no—
117#4339—22no—
118#4339—42no—
119#4339—42no—
120#4339—42no—
121#4339—42no—
122C2×D44—21no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44C2×D412yes—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C2×Dic22—21no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22C2×D412yes—
134C11×M16—22no—
135C11×M16—22no—
136C11×M16—22no—
137C11×M16—22no—
138C11×M16—42no—
139C11×M16—42no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—42no—
143C2×C8×C11—42no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152#4318—22no—
153#4318—22no—
154#4318—42no—
155C2×C11⋊C8—24no—
156C2×C11⋊C8—24no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—42no—
161C2×C11⋊C8C2×D414yes—
162C22×#106—111no—
163C2×#417—111no—
164C2×#417—111no—
165C2×#408—111no—
166#2079—118no—
167C2×#343—111no—
168C2×#343D1111yescharacteristic, complemented
169C2×#341—111no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11#12111yescharacteristic
173C23×C11#12111yescharacteristic
174C23×C11#12612yes—
175C23×C11#12612yes—
176C23×C11C2×#4111yescharacteristic
177C22×D11—22no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—82no—
183C2×C4×C11—82no—
184C2×C4×C11—82no—
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12312yes—
188C2×C4×C11#12312yes—
189C2×C4×C11#12312yes—
190C2×C4×C11#12312yes—
191C2×C4×C11#12312yes—
192C2×C4×C11#12312yes—
193C2×C4×C11#12412yes—
194C2×C4×C11#12412yes—
195C2×C4×C11#12612yes—
196C2×C4×C11#12612yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C22⋊D11—42no—
204C22⋊D11—42no—
205C22⋊D11—44no—
206C2×Dic11—22no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—82no—
210C2×Dic11—82no—
211C2×Dic11—82no—
212D44—22no—
213D44—22no—
214D44—42no—
215C4×D11—42no—
216C4×D11—42no—
217C4×D11—44no—
218Dic22—22no—
219Dic22—22no—
220Dic22—42no—
221C8×C11—42no—
222C8×C11—42no—
223C11⋊C8—24no—
224C11⋊C8—42no—
225C22×#41—111no—
226C22×M16—111no—
227C22×M16C2×D1111yescharacteristic
228C22×M16C2×D1111yescharacteristic
229C23×C8—111no—
230C22×C4⋊C4—111no—
231C22×C4⋊C4C2×D1111yescharacteristic
232C2×#106—114no—
233C2×#106—222no—
234C2×#106—222no—
235#417—114no—
236#417—114no—
237#417—222no—
238#417—222no—
239C2×#103—221no—
240C2×#103—221no—
241C2×#102—221no—
242C2×#102—221no—
243#408—114no—
244#408—222no—
245C2×C22⋊C8—222no—
246#343—114no—
247#343C2×D1114yescomplemented
248#341—114no—
249C22×C11—24no—
250C22×C11—24no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11#39712yes—
256C22×C11#39712yes—
257C22×C11#47112yes—
258C22×C11#47112yes—
259C22×C11C2×#12111yescharacteristic
260C22×C11C2×#12611yescharacteristic
261C22×C11C2×#12611yescharacteristic
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—84no—
266C4×C11—82no—
267C4×C11#39712yes—
268C4×C11#39712yes—
269C4×C11C2×#12311yescharacteristic
270C4×C11C2×#12311yescharacteristic
271C4×C11C2×#12311yescharacteristic
272C4×C11C2×#12411yescharacteristic
273Dic11—42no—
274Dic11—82no—
275C2×#41—112no—
276C2×#41—112no—
277C2×#41—221no—
278C2×#41—221no—
279C2×#41—222no—
280C2×#41—222no—
281C2×#41—222no—
282C2×#41—222no—
283C22×Q8—111no—
284C22×D4—111no—
285C22×D4—221no—
286C23×C4—21no—
287C23×C4—221no—
288C23×C4—221no—
289C23×C4C22×D1111yescharacteristic
290C2×M16—21no—
291C2×M16—21no—
292C2×M16—22no—
293C2×M16—22no—
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—112no—
297C2×M16—221no—
298C2×M16—222no—
299C2×M16—222no—
300C2×M16C22×D1112yes—
301C2×M16C22×D1112yes—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—112no—
305C22×C8—112no—
306C22×C8—112no—
307C22×C8—222no—
308C22×C8—222no—
309C22×C8—221no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4C22×D1112yes—
322#106—228no—
323#103—224no—
324#103—224no—
325#102—224no—
326#102—224no—
327C22⋊C8—228no—
328C2×C11—21no—
329C2×C11—21no—
330C2×C11—22no—
331C2×C11#207914yescomplemented
332C2×C11C2×#39711yescharacteristic
333C2×C11C2×#47111yescharacteristic
334C2×C11C2×#47111yescharacteristic
335D11—82no—
336C24—221no—
337C24#433911yescharacteristic
338#41—224no—
339#41—224no—
340#41—222no—
341#41—222no—
342#41—222no—
343#41—222no—
344#41—442no—
345#41—442no—
346#41—442no—
347#41—442no—
348C2×Q8—112no—
349C2×Q8—221no—
350C2×Q8—222no—
351C2×Q8—222no—
352C2×D4—112no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—221no—
357C2×D4—222no—
358C2×D4—442no—
359C2×D4—442no—
360C22×C4—22no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—82no—
364C22×C4—221no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—442no—
369C22×C4—442no—
370C22×C4—441no—
371C22×C4—441no—
372C22×C4—882no—
373C22×C4#433911yescharacteristic
374C22×C4#433912yes—
375C22×C4#433912yes—
376C22×C4D4×D1111yescharacteristic
377C22×C4D4×D1111yescharacteristic
378C22×C4D4×D1111yescharacteristic
379C22×C4D4×D1111yescharacteristic
380C22×C4#434112yes—
381C22×C4#434312yes—
382C22×C4C23×D1111yescharacteristic
383M16—22no—
384M16—22no—
385M16—22no—
386M16—22no—
387M16—42no—
388M16—42no—
389M16—222no—
390M16—222no—
391M16—442no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—42no—
395C2×C8—42no—
396C2×C8—114no—
397C2×C8—224no—
398C2×C8—224no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—222no—
402C2×C8—442no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—222no—
408C4⋊C4—222no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C11C2×#207911yescharacteristic, complemented, Sylow
412C23—22no—
413C23—22no—
414C23—222no—
415C23—442no—
416C23—442no—
417C23—442no—
418C23#6692912yes—
419C23#6693711yescharacteristic
420C23#6693711yescharacteristic
421C23#6695112yes—
422C23C2×#433911yescharacteristic
423Q8—222no—
424Q8—222no—
425Q8—442no—
426D4—222no—
427D4—222no—
428D4—442no—
429D4—442no—
430D4—444no—
431D4—442no—
432C2×C4—42no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—222no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—444no—
441C2×C4—442no—
442C2×C4—882no—
443C2×C4—882no—
444C2×C4—882no—
445C2×C4#6692912yes—
446C2×C4#6693612yes—
447C2×C4#6693612yes—
448C2×C4#6693711yescharacteristic
449C2×C4#6693711yescharacteristic
450C2×C4#6693812yes—
451C2×C4#6693812yes—
452C2×C4#6694712yes—
453C2×C4#6694712yes—
454C2×C4#6694712yes—
455C2×C4#6694712yes—
456C2×C4#6695112yes—
457C2×C4C2×#433911yescharacteristic
458C2×C4C2×#433911yescharacteristic
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4C2×#434111yescharacteristic
462C2×C4C2×#434311yescharacteristic
463C8—42no—
464C8—42no—
465C8—224no—
466C8—442no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—24no—
472C22—24no—
473C22—442no—
474C22—442no—
475C22—442no—
476C22—884no—
477C22#1062228812yes—
478C22#1062228812yes—
479C22#1062236112yes—
480C22#1062236712yes—
481C22C2×#6692911yescharacteristic
482C22C2×#6693711yescharacteristic
483C22C2×#6695111yescharacteristic
484C4—82no—
485C4—442no—
486C4—882no—
487C4#1062228812yes—
488C4#1062228812yes—
489C4C2×#6693611yescharacteristic
490C4C2×#6693811yescharacteristic
491C4C2×#6694711yescharacteristic
492C4C2×#6694711yescharacteristic
493C2—21no—
494C2—21no—
495C2—22no—
496C2—882no—
497C2#1307006514yesdirect product factor
498C2C2×#1062228811yescharacteristic
499C2C2×#1062236111yescharacteristic
500C2C2×#1062236711yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#343C2
socleC23×C11#121
prime radicalC22×#4339C22
hypercenterC2×#343D11
hypocenterC11C2×#2079
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
1. C22×#66872C2semidirect
5. #13070065C2direct (N × H)
6. C2×#10622192C2semidirect
7. C2×#10622196C2semidirect
8. C2×C11×#343C2semidirect
29. C2×#66872C22semidirect
30. C11×#343C22semidirect
31. #10622196C22semidirect
32. #10622192C22semidirect
168. C2×#343D11semidirect
247. #343C2×D11semidirect
331. C2×C11#2079semidirect
411. C11C2×#2079semidirect
497. C2#13070065direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668722
C2×#106227462
C2×#106225792
C2×#106227422
#130700652
C2×#106221922
C2×#106221962
C2×C11×#3432
C2×#207911