Finite Group Databasebeta

← C2×#13070691 #14908152

Subgroups — C2×#13070691 #14908152

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622521C211yesmaximal, characteristic, complemented
2C2×#10622760C211yesmaximal, characteristic, complemented
3C2×#10622764C211yesmaximal, characteristic, complemented
4C2×#10622508C211yesmaximal, characteristic, complemented
5#13070691C218yesmaximal, direct product factor
6C2×#10622149C211yesmaximal, characteristic, complemented
7C2×#10622133C211yesmaximal, characteristic, complemented
8C2×C11×#361C211yesmaximal, characteristic, complemented
9C22×C11×D8C2211yescharacteristic
10C2×#66993—21no—
11C22×#4323—21no—
12C2×#66960—21no—
13C2×#66957C2211yescharacteristic
14C22×D88C2211yescharacteristic
15C2×C11×M32C2211yescharacteristic
16C2×C11×#108C2211yescharacteristic
17#10622764—22no—
18#10622764C2214yescomplemented
19C2×#66891—21no—
20#10622760—22no—
21#10622760C2214yescomplemented
22C2×#66890—21no—
23C2×#66889—21no—
24C2×C8×Dic11C2211yescharacteristic
25C2×#66876C2211yescharacteristic
26#10622521—22no—
27#10622521C2214yescomplemented
28C2×#66864—21no—
29C2×D176—21no—
30#10622508—22no—
31#10622508C2214yescomplemented
32C11×#361C2214yescomplemented
33#10622149C2214yescomplemented
34#10622133C2214yescomplemented
35C22×D4×C11—21no—
36C22×C22⋊D11—42no—
37C2×#4339—21no—
38C22×D44—21no—
39C2×C11×D8—21no—
40C2×C11×D8—21no—
41C2×C11×D8—21no—
42C2×C11×D8—21no—
43C2×C11×D8—21no—
44C2×C11×D8C2312yes—
45C2×C11×M16—21no—
46C22×C8×C11C2311yescharacteristic
47#66993—24no—
48#66993—42no—
49C2×#4323—24no—
50C2×#4323—41no—
51C2×#4323—41no—
52C2×#4323—42no—
53C2×C4×Dic11D411yescharacteristic
54C22×C11⋊C8D411yescharacteristic
55#66960—24no—
56#66960—42no—
57C2×Dic44D411yescharacteristic, complemented
58#66957—21no—
59#66957—21no—
60#66957D412yescomplemented
61#66957C2312yes—
62C2×D88—21no—
63C2×D88—21no—
64C2×D88—21no—
65C2×D88—21no—
66C2×D88—21no—
67C2×D88D411yescharacteristic, complemented
68C2×D88C2312yes—
69C2×#4314—21no—
70C2×#4313—41no—
71C2×C8×D11—41no—
72C11×M32—21no—
73C11×M32C2312yes—
74C2×C11×C16—21no—
75C11×#108—21no—
76C11×#108C2312yes—
77#66891—24no—
78#66890—24no—
79#66889—24no—
80C8×Dic11D412yes—
81C8×Dic11C2312yes—
82#66876—21no—
83#66876C2312yes—
84C2×C11⋊C16—21no—
85#66864—24no—
86D176—24no—
87C2×#2213—111nomaximal, Sylow
88C24×C11—41no—
89C23×D11—41no—
90C2×D4×C11—22no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C2×C22⋊D11—48no—
98C2×C22⋊D11—41no—
99C2×C22⋊D11—88no—
100C22×Dic11—21no—
101#4339—22no—
102#4339—22no—
103#4339—41no—
104#4339—41no—
105C2×D44—21no—
106C2×D44—22no—
107C2×D44—41no—
108C2×D44—41no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—41no—
112C2×C4×D11—41no—
113C2×Dic22—21no—
114C11×D8—22no—
115C11×D8—22no—
116C11×D8—41no—
117C11×D8—41no—
118C11×M16—22no—
119C11×M16—41no—
120C2×C8×C11—41no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11#4111yescharacteristic
125C2×C8×C11#4111yescharacteristic
126C2×C8×C11C2411yescharacteristic
127#4323—44no—
128#4323—44no—
129C4×Dic11—21no—
130C4×Dic11C2×D412yes—
131C2×C11⋊C8D811yescharacteristic
132C2×C11⋊C8D811yescharacteristic
133C2×C11⋊C8D812yes—
134C2×C11⋊C8C2×D412yes—
135Dic44—21no—
136Dic44C2×D412yescomplemented
137D88—21no—
138D88—22no—
139D88—22no—
140D88—41no—
141D88—41no—
142D88C2×D412yescomplemented
143#4314—22no—
144#4314—22no—
145#4313—44no—
146C8×D11—44no—
147C11×C16—22no—
148C11⋊C16—22no—
149C2×#509—111no—
150C2×#509—111no—
151C2×#493—111no—
152C2×#443—111no—
153#2213—118no—
154C2×#364—111no—
155C2×#361—111no—
156C2×#361D1111yescharacteristic, complemented
157C23×C11—42no—
158C23×C11—84no—
159C23×C11—81no—
160C23×C11—81no—
161C23×C11AGL(1,ℤ/8)11yescharacteristic
162C22×D11—41no—
163C22×D11—42no—
164C22×D11—84no—
165C22×D11—81no—
166C22×D11—81no—
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—81no—
170D4×C11—81no—
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C22⋊D11—42no—
178C22⋊D11—42no—
179C22⋊D11—816no—
180C2×Dic11—24no—
181C2×Dic11—22no—
182C2×Dic11—41no—
183D44—22no—
184D44—42no—
185D44—42no—
186D44—41no—
187D44—81no—
188D44—81no—
189C4×D11—42no—
190C4×D11—42no—
191Dic22—22no—
192Dic22—41no—
193C8×C11—42no—
194C8×C11#12111yescharacteristic
195C8×C11#12111yescharacteristic
196C8×C11C22×D411yescharacteristic
197C8×C11C2×#4111yescharacteristic
198C11⋊C8C2×D812yes—
199C11⋊C8C2×D812yes—
200C2×#135—111no—
201C22×D8—111no—
202C22×D8—221no—
203C22×D8C2×D1111yescharacteristic
204C2×#131—221no—
205C2×#127—221no—
206#509—114no—
207#509—114no—
208#509—222no—
209#509—222no—
210C2×SD32—221no—
211C2×SD32—221no—
212C2×D16—221no—
213C2×D16—221no—
214C2×M32—111no—
215C2×M32C2×D1111yescharacteristic
216#493—114no—
217#493—222no—
218#443—114no—
219#443—222no—
220C2×#108C2×D1111yescharacteristic
221C2×#104—221no—
222C2×C4×C8—111no—
223#364—114no—
224#361—114no—
225#361C2×D1114yescomplemented
226C22×C11—22no—
227C22×C11—84no—
228C22×C11—82no—
229C22×C11—162no—
230C22×C11—162no—
231C22×C11#45911yescharacteristic
232C22×C11#45911yescharacteristic
233C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
234C2×D11—42no—
235C2×D11—82no—
236C2×D11—84no—
237C2×D11—82no—
238C2×D11—162no—
239C2×D11—162no—
240C4×C11#45911yescharacteristic
241C4×C11#45911yescharacteristic
242C4×C11C2×#12111yescharacteristic
243C4×C11C22×D811yescharacteristic
244Dic11—24no—
245Dic11—42no—
246C2×#41—221no—
247C22×D4—21no—
248C22×D4—221no—
249C22×D4—442no—
250#135—112no—
251#135—112no—
252#135—221no—
253#135—221no—
254C2×Q16—111no—
255C2×SD16—221no—
256C2×D8—21no—
257C2×D8—21no—
258C2×D8—21no—
259C2×D8—21no—
260C2×D8—21no—
261C2×D8—111no—
262C2×D8—112no—
263C2×D8—224no—
264C2×D8—221no—
265C2×D8—221no—
266C2×D8—221no—
267C2×D8—221no—
268C2×D8—221no—
269C2×D8—441no—
270C2×D8—441no—
271C2×D8—442no—
272C2×D8C22×D1112yes—
273#131—224no—
274#131—442no—
275C2×M16—21no—
276C2×M16—441no—
277C22×C8—111no—
278C22×C8—441no—
279C22×C8C22×D1111yescharacteristic
280#127—224no—
281#127—442no—
282C2×C42—111no—
283SD32—224no—
284SD32—224no—
285D16—224no—
286D16—224no—
287M32—21no—
288M32—112no—
289M32—221no—
290M32C22×D1112yes—
291C2×C16—21no—
292C2×C16—221no—
293#108—21no—
294#108C22×D1112yes—
295#104—224no—
296C4×C8—112no—
297C4×C8—112no—
298C2×C11—21no—
299C2×C11—21no—
300C2×C11—162no—
301C2×C11#221312yescomplemented
302C2×C11C2×#45911yescharacteristic
303D11—82no—
304D11—162no—
305C24—41no—
306C24—441no—
307#41—222no—
308#41—222no—
309#41—441no—
310#41—441no—
311C2×Q8—221no—
312C2×D4—22no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—221no—
319C2×D4—222no—
320C2×D4—448no—
321C2×D4—441no—
322C2×D4—441no—
323C2×D4—441no—
324C2×D4—441no—
325C2×D4—441no—
326C2×D4—441no—
327C2×D4—888no—
328C22×C4—221no—
329C22×C4—441no—
330C22×C4D4×D1111yescharacteristic
331Q16—112no—
332Q16—221no—
333SD16—222no—
334SD16—222no—
335D8—22no—
336D8—22no—
337D8—41no—
338D8—41no—
339D8—112no—
340D8—221no—
341D8—222no—
342D8—222no—
343D8—444no—
344D8—444no—
345D8—441no—
346D8—441no—
347M16—22no—
348M16—41no—
349M16—444no—
350C2×C8—41no—
351C2×C8—111no—
352C2×C8—111no—
353C2×C8—112no—
354C2×C8—112no—
355C2×C8—444no—
356C2×C8#433911yescharacteristic
357C2×C8#433911yescharacteristic
358C2×C8D4×D1111yescharacteristic
359C2×C8D4×D1111yescharacteristic
360C2×C8D4×D1111yescharacteristic
361C2×C8C23×D1111yescharacteristic
362C42—112no—
363C42—221no—
364C16—22no—
365C16—222no—
366C11C2×#221311yescharacteristic, complemented, Sylow
367C23—42no—
368C23—84no—
369C23—81no—
370C23—81no—
371C23—441no—
372C23—442no—
373C23—884no—
374C23—881no—
375C23—881no—
376C23#6696711yescharacteristic
377Q8—222no—
378Q8—441no—
379D4—42no—
380D4—42no—
381D4—81no—
382D4—81no—
383D4—222no—
384D4—442no—
385D4—442no—
386D4—442no—
387D4—442no—
388D4—441no—
389D4—8816no—
390D4—881no—
391D4—881no—
392C2×C4—224no—
393C2×C4—222no—
394C2×C4—441no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4#6693711yescharacteristic
398C2×C4#6693711yescharacteristic
399C2×C4D8×D1111yescharacteristic
400C2×C4D8×D1111yescharacteristic
401C2×C4#6696711yescharacteristic
402C2×C4C2×D4×D1111yescharacteristic
403C8—42no—
404C8—112no—
405C8—112no—
406C8#6693711yescharacteristic
407C8#6693711yescharacteristic
408C8C2×#433911yescharacteristic
409C8C2×D4×D1111yescharacteristic
410C22—22no—
411C22—84no—
412C22—82no—
413C22—162no—
414C22—162no—
415C22—442no—
416C22—884no—
417C22—882no—
418C22—882no—
419C22—1762no—
420C22—1762no—
421C22#1062239911yescharacteristic
422C22#1062239911yescharacteristic
423C22C2×#6696711yescharacteristic
424C4—224no—
425C4—442no—
426C4#1062239911yescharacteristic
427C4#1062239911yescharacteristic
428C4C2×#6693711yescharacteristic
429C4C2×D8×D1111yescharacteristic
430C2—21no—
431C2—21no—
432C2—162no—
433C2—882no—
434C2—1762no—
435C2#1307069112yesdirect product factor
436C2C2×#1062239911yescharacteristic
subgroupG/H
centerC22#10622399
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#361C2
socleC22×C11#459
hypercenterC2×#361D11
hypocenterC11C2×#2213
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
1. C2×#10622521C2semidirect
2. C2×#10622760C2semidirect
3. C2×#10622764C2semidirect
4. C2×#10622508C2semidirect
5. #13070691C2direct (N × H)
6. C2×#10622149C2semidirect
7. C2×#10622133C2semidirect
8. C2×C11×#361C2semidirect
18. #10622764C22semidirect
21. #10622760C22semidirect
27. #10622521C22semidirect
31. #10622508C22semidirect
32. C11×#361C22semidirect
33. #10622149C22semidirect
34. #10622133C22semidirect
57. C2×Dic44D4semidirect
60. #66957D4semidirect
67. C2×D88D4semidirect
136. Dic44C2×D4semidirect
142. D88C2×D4semidirect
156. C2×#361D11semidirect
225. #361C2×D11semidirect
301. C2×C11#2213semidirect
366. C11C2×#2213semidirect
435. C2#13070691direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225212
C2×#106227602
C2×#106227642
C2×#106225082
#130706912
C2×#106221492
C2×#106221332
C2×C11×#3612
C2×#221311