Finite Group Databasebeta

← C2×#13070690 #14908151

Subgroups — C2×#13070690 #14908151

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×#10622806C211yesmaximal, characteristic, complemented
2C2×#10622764C211yesmaximal, characteristic, complemented
3C2×#10622809C211yesmaximal, characteristic, complemented
4#13070690C218yesmaximal, direct product factor
5C2×#10622149C211yesmaximal, characteristic, complemented
6C2×#10622154C211yesmaximal, characteristic, complemented
7C2×#10622201C211yesmaximal, characteristic, complemented
8C2×C11×#509C211yesmaximal, characteristic, complemented
9C2×C11×#135C2211yescharacteristic
10C22×C11×D8C2211yescharacteristic
11C2×#67001—21no—
12C2×#66993—21no—
13C22×#4323—21no—
14C22×D88C2211yescharacteristic
15C11×#509—22no—
16C11×#509C2214yescomplemented
17C2×C11×SD32—21no—
18C2×C11×D16—21no—
19C2×C11×M32C2211yescharacteristic
20C2×#66901—21no—
21#10622809—22no—
22#10622809C2214yescomplemented
23#10622806—22no—
24#10622806C2214yescomplemented
25C2×#66892—21no—
26#10622764—22no—
27#10622764C2214yescomplemented
28C2×#66890—21no—
29C2×#66883C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32#10622201C2214yescomplemented
33#10622154C2214yescomplemented
34#10622149C2214yescomplemented
35C2×C11×#41—21no—
36C22×D4×C11—21no—
37C22×C22⋊D11—42no—
38C22×D44—21no—
39C11×#135—21no—
40C11×#135—21no—
41C11×#135D412yescomplemented
42C11×#135C2312yes—
43C2×C11×Q16D411yescharacteristic, complemented
44C2×C11×SD16—21no—
45C2×C11×D8—21no—
46C2×C11×D8—21no—
47C2×C11×D8—21no—
48C2×C11×D8—21no—
49C2×C11×D8—21no—
50C2×C11×D8D411yescharacteristic, complemented
51C2×C11×D8C2312yes—
52C22×C8×C11C2311yescharacteristic
53#67001—24no—
54#67001—42no—
55#66993—24no—
56#66993—42no—
57C2×#4323—24no—
58C2×#4323—41no—
59C2×#4323—41no—
60C2×#4323—42no—
61C2×C4×Dic11D411yescharacteristic
62C2×#4318—21no—
63C2×#4318—41no—
64C22×C11⋊C8—41no—
65C22×C11⋊C8D411yescharacteristic
66C2×D88—21no—
67C2×D88—21no—
68C2×D88—21no—
69C2×D88—21no—
70C2×D88—21no—
71C2×D88C2312yes—
72C11×SD32—24no—
73C11×D16—24no—
74C11×M32—21no—
75C11×M32C2312yes—
76C2×C11×C16—21no—
77#66901—24no—
78#66892—24no—
79#66890—24no—
80#66883—21no—
81#66883C2312yes—
82C8×Dic11D412yes—
83C8×Dic11C2312yes—
84#66876—21no—
85#66876C2312yes—
86C2×C11⋊C16—21no—
87C2×#2213—111nomaximal, Sylow
88C24×C11—41no—
89C23×D11—41no—
90C11×#41—22no—
91C11×#41—22no—
92C11×#41—41no—
93C11×#41—41no—
94C2×Q8×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C2×C22⋊D11—48no—
106C2×C22⋊D11—88no—
107C22×Dic11—21no—
108C2×D44—22no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—41no—
112C2×D44—41no—
113C2×D44—41no—
114C11×Q16—21no—
115C11×Q16C2×D412yescomplemented
116C11×SD16—22no—
117C11×SD16—22no—
118C11×D8—21no—
119C11×D8—22no—
120C11×D8—22no—
121C11×D8—41no—
122C11×D8—41no—
123C11×D8C2×D412yescomplemented
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11#4111yescharacteristic
128C2×C8×C11#4111yescharacteristic
129C2×C8×C11C2411yescharacteristic
130#4323—44no—
131#4323—44no—
132C4×Dic11—21no—
133C4×Dic11C2×D412yes—
134#4318—22no—
135#4318—44no—
136#4318—41no—
137C2×C11⋊C8—44no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8D811yescharacteristic
140C2×C11⋊C8D811yescharacteristic
141C2×C11⋊C8D812yes—
142C2×C11⋊C8C2×D412yes—
143D88—22no—
144D88—22no—
145D88—41no—
146D88—41no—
147C11×C16—22no—
148C11⋊C16—22no—
149C2×#509—111no—
150C2×#509D1111yescharacteristic, complemented
151C2×#493—111no—
152C2×#443—111no—
153#2213—118no—
154C2×#364—111no—
155C2×#361—111no—
156C2×#361—111no—
157C23×C11—41no—
158C23×C11—42no—
159C23×C11—84no—
160C23×C11—81no—
161C23×C11—81no—
162C23×C11AGL(1,ℤ/8)11yescharacteristic
163C22×D11—42no—
164C22×D11—84no—
165C22×D11—81no—
166C22×D11—81no—
167Q8×C11—22no—
168Q8×C11—41no—
169D4×C11—22no—
170D4×C11—42no—
171D4×C11—42no—
172D4×C11—42no—
173D4×C11—42no—
174D4×C11—41no—
175D4×C11—81no—
176D4×C11—81no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C22⋊D11—816no—
187C2×Dic11—24no—
188C2×Dic11—22no—
189D44—42no—
190D44—42no—
191D44—81no—
192D44—81no—
193C8×C11#12111yescharacteristic
194C8×C11#12111yescharacteristic
195C8×C11C22×D411yescharacteristic
196C8×C11C2×#4111yescharacteristic
197C11⋊C8—42no—
198C11⋊C8C2×D812yes—
199C11⋊C8C2×D812yes—
200C2×#135C2×D1111yescharacteristic
201C22×D8—111no—
202C22×D8—221no—
203C22×D8C2×D1111yescharacteristic
204C2×#131—221no—
205C2×#127—221no—
206#509—22no—
207#509—114no—
208#509—222no—
209#509C2×D1114yescomplemented
210C2×SD32—21no—
211C2×SD32—221no—
212C2×D16—21no—
213C2×D16—221no—
214C2×M32—111no—
215C2×M32C2×D1111yescharacteristic
216#493—114no—
217#493—222no—
218#443—114no—
219#443—222no—
220C2×#108—111no—
221C2×#104—221no—
222C2×C4×C8—111no—
223#364—114no—
224#361—114no—
225#361—114no—
226C22×C11—22no—
227C22×C11—42no—
228C22×C11—84no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11—162no—
232C22×C11—162no—
233C22×C11#45911yescharacteristic
234C22×C11#45911yescharacteristic
235C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
236C2×D11—84no—
237C2×D11—82no—
238C2×D11—162no—
239C2×D11—162no—
240C4×C11—42no—
241C4×C11#45911yescharacteristic
242C4×C11#45911yescharacteristic
243C4×C11C2×#12111yescharacteristic
244C4×C11C22×D811yescharacteristic
245Dic11—24no—
246C2×#41—21no—
247C22×D4—21no—
248C22×D4—221no—
249C22×D4—442no—
250#135—21no—
251#135—21no—
252#135C22⋊D1112yescomplemented
253#135C22×D1112yes—
254C2×Q16C22⋊D1111yescharacteristic, complemented
255C2×SD16—21no—
256C2×D8—21no—
257C2×D8—21no—
258C2×D8—21no—
259C2×D8—21no—
260C2×D8—21no—
261C2×D8—112no—
262C2×D8—224no—
263C2×D8—221no—
264C2×D8—221no—
265C2×D8—221no—
266C2×D8—221no—
267C2×D8—221no—
268C2×D8—441no—
269C2×D8—441no—
270C2×D8—442no—
271C2×D8C22⋊D1111yescharacteristic, complemented
272C2×D8C22×D1112yes—
273#131—224no—
274#131—442no—
275C2×M16—221no—
276C2×M16—441no—
277C22×C8—111no—
278C22×C8—441no—
279C22×C8C22×D1111yescharacteristic
280#127—224no—
281#127—442no—
282C2×C42—111no—
283SD32—24no—
284SD32—224no—
285D16—24no—
286D16—224no—
287M32—21no—
288M32—112no—
289M32—221no—
290M32C22×D1112yes—
291C2×C16—21no—
292C2×C16—221no—
293#108—112no—
294#108—221no—
295#104—224no—
296C4×C8—112no—
297C4×C8—112no—
298C2×C11—21no—
299C2×C11—21no—
300C2×C11—82no—
301C2×C11—162no—
302C2×C11#221312yescomplemented
303C2×C11C2×#45911yescharacteristic
304D11—162no—
305C24—41no—
306C24—441no—
307#41—22no—
308#41—22no—
309#41—41no—
310#41—41no—
311C2×Q8—21no—
312C2×D4—21no—
313C2×D4—22no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—222no—
321C2×D4—448no—
322C2×D4—441no—
323C2×D4—441no—
324C2×D4—441no—
325C2×D4—441no—
326C2×D4—441no—
327C2×D4—888no—
328C22×C4—41no—
329C22×C4—221no—
330C22×C4D4×D1111yescharacteristic
331Q16—21no—
332Q16C2×C22⋊D1112yescomplemented
333SD16—22no—
334SD16—22no—
335D8—21no—
336D8—22no—
337D8—22no—
338D8—41no—
339D8—41no—
340D8—222no—
341D8—222no—
342D8—444no—
343D8—444no—
344D8—441no—
345D8—441no—
346D8C2×C22⋊D1112yescomplemented
347M16—222no—
348M16—444no—
349M16—441no—
350C2×C8—111no—
351C2×C8—111no—
352C2×C8—112no—
353C2×C8—112no—
354C2×C8—444no—
355C2×C8—441no—
356C2×C8D4×D1111yescharacteristic
357C2×C8#434111yescharacteristic
358C2×C8#434111yescharacteristic
359C2×C8C2×C22⋊D1111yescharacteristic
360C2×C8C2×C22⋊D1111yescharacteristic
361C2×C8C23×D1111yescharacteristic
362C42—112no—
363C42—221no—
364C16—22no—
365C16—222no—
366C11C2×#221311yescharacteristic, complemented, Sylow
367C23—41no—
368C23—42no—
369C23—84no—
370C23—81no—
371C23—81no—
372C23—442no—
373C23—884no—
374C23—881no—
375C23—881no—
376C23#6696411yescharacteristic
377Q8—22no—
378Q8—41no—
379D4—22no—
380D4—42no—
381D4—42no—
382D4—41no—
383D4—42no—
384D4—42no—
385D4—81no—
386D4—81no—
387D4—442no—
388D4—442no—
389D4—8816no—
390D4—881no—
391D4—881no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—224no—
396C2×C4—222no—
397C2×C4D8×D1111yescharacteristic
398C2×C4D8×D1111yescharacteristic
399C2×C4#6696411yescharacteristic
400C2×C4#6699211yescharacteristic
401C2×C4#6699211yescharacteristic
402C2×C4C2×D4×D1111yescharacteristic
403C8—112no—
404C8—112no—
405C8—442no—
406C8#6699211yescharacteristic
407C8#6699211yescharacteristic
408C8C2×#434111yescharacteristic
409C8C22×C22⋊D1111yescharacteristic
410C22—22no—
411C22—42no—
412C22—84no—
413C22—82no—
414C22—82no—
415C22—162no—
416C22—162no—
417C22—884no—
418C22—882no—
419C22—1762no—
420C22—1762no—
421C22#1062276311yescharacteristic
422C22#1062276311yescharacteristic
423C22C2×#6696411yescharacteristic
424C4—42no—
425C4—224no—
426C4#1062276311yescharacteristic
427C4#1062276311yescharacteristic
428C4C2×D8×D1111yescharacteristic
429C4C2×#6699211yescharacteristic
430C2—21no—
431C2—21no—
432C2—82no—
433C2—162no—
434C2—1762no—
435C2#1307069012yesdirect product factor
436C2C2×#1062276311yescharacteristic
subgroupG/H
centerC22#10622763
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#509C2
socleC22×C11#459
hypercenterC2×#509D11
hypocenterC11C2×#2213
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×#10622806C2semidirect
2. C2×#10622764C2semidirect
3. C2×#10622809C2semidirect
4. #13070690C2direct (N × H)
5. C2×#10622149C2semidirect
6. C2×#10622154C2semidirect
7. C2×#10622201C2semidirect
8. C2×C11×#509C2semidirect
16. C11×#509C22semidirect
22. #10622809C22semidirect
24. #10622806C22semidirect
27. #10622764C22semidirect
32. #10622201C22semidirect
33. #10622154C22semidirect
34. #10622149C22semidirect
41. C11×#135D4semidirect
43. C2×C11×Q16D4semidirect
50. C2×C11×D8D4semidirect
115. C11×Q16C2×D4semidirect
123. C11×D8C2×D4semidirect
150. C2×#509D11semidirect
209. #509C2×D11semidirect
252. #135C22⋊D11semidirect
254. C2×Q16C22⋊D11semidirect
271. C2×D8C22⋊D11semidirect
302. C2×C11#2213semidirect
332. Q16C2×C22⋊D11semidirect
346. D8C2×C22⋊D11semidirect
366. C11C2×#2213semidirect
435. C2#13070690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228062
C2×#106227642
C2×#106228092
#130706902
C2×#106221492
C2×#106221542
C2×#106222012
C2×C11×#5092
C2×#221311