Finite Group Databasebeta

← C2×#13070687 #14908147

Subgroups — C2×#13070687 #14908147

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622806C211yesmaximal, characteristic
2C2×#10622804C211yesmaximal, characteristic, complemented
3C2×#10622809C211yesmaximal, characteristic, complemented
4#13070687C218yesmaximal, direct product factor
5C2×#10622149C211yesmaximal, characteristic, complemented
6C2×#10622203C211yesmaximal, characteristic, complemented
7C2×#10622154C211yesmaximal, characteristic, complemented
8C2×C11×#510C211yesmaximal, characteristic, complemented
9C2×C11×#135C2211yescharacteristic
10C22×C11×Q16C2211yescharacteristic
11C2×#67001—21no—
12C2×#67000—21no—
13C22×#4325—21no—
14C22×D88C2211yescharacteristic
15C11×#510—22no—
16C11×#510C2214yescomplemented
17C2×C11×Q32—21no—
18C2×C11×SD32—21no—
19C2×C11×M32C2211yescharacteristic
20C2×#66901—21no—
21#10622809—22no—
22#10622809C2214yescomplemented
23#10622806—22no—
24#10622806C2214yes—
25#10622804—22no—
26#10622804C2214yescomplemented
27C2×#66892—21no—
28C2×#66890—21no—
29C2×#66883C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32#10622203C2214yescomplemented
33#10622154C2214yescomplemented
34#10622149C2214yescomplemented
35C2×C11×#41—21no—
36C22×Q8×C11—21no—
37C22×D44—21no—
38C11×#135—21no—
39C11×#135—21no—
40C11×#135D412yes—
41C11×#135C2312yes—
42C2×C11×Q16—21no—
43C2×C11×Q16—21no—
44C2×C11×Q16—21no—
45C2×C11×Q16—21no—
46C2×C11×Q16—21no—
47C2×C11×Q16D411yescharacteristic
48C2×C11×Q16C2312yes—
49C2×C11×SD16—21no—
50C2×C11×D8D411yescharacteristic
51C22×C8×C11C2311yescharacteristic
52#67001—24no—
53#67001—42no—
54#67000—24no—
55#67000—42no—
56C2×#4325—24no—
57C2×#4325—41no—
58C2×#4325—41no—
59C2×#4325—42no—
60C2×(C2×D11)⋊C4—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×Q32—24no—
73C11×SD32—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×#2212—111nomaximal, Sylow
88C23×D11—41no—
89C11×#41—22no—
90C11×#41—22no—
91C11×#41—41no—
92C11×#41—41no—
93C2×Q8×C11—21no—
94C2×Q8×C11—22no—
95C2×Q8×C11—41no—
96C2×Q8×C11—41no—
97C2×Q8×C11—41no—
98C2×Q8×C11—41no—
99C2×Q8×C11—41no—
100C2×D4×C11—21no—
101C2×D4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C22×Dic11—21no—
106C2×D44—22no—
107C2×D44—41no—
108C2×D44—41no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—41no—
112C11×Q16—21no—
113C11×Q16—22no—
114C11×Q16—22no—
115C11×Q16—41no—
116C11×Q16—41no—
117C11×Q16C2×D412yes—
118C11×SD16—22no—
119C11×SD16—22no—
120C11×D8—21no—
121C11×D8C2×D412yes—
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11#4111yescharacteristic
126C2×C8×C11#4111yescharacteristic
127C2×C8×C11C2411yescharacteristic
128#4325—44no—
129#4325—44no—
130(C2×D11)⋊C4—48no—
131C4×Dic11—21no—
132C4×Dic11C2×D412yes—
133#4318—22no—
134#4318—44no—
135#4318—41no—
136C2×C11⋊C8—44no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8D811yescharacteristic
139C2×C11⋊C8D811yescharacteristic
140C2×C11⋊C8D812yes—
141C2×C11⋊C8C2×D412yes—
142D88—22no—
143D88—22no—
144D88—41no—
145D88—41no—
146C11×C16—22no—
147C11⋊C16—22no—
148C2×#510D1111yescharacteristic, complemented
149C2×#509—111no—
150C2×#495—111no—
151C2×#443—111no—
152#2212—118no—
153C2×#364—111no—
154C2×#362—111no—
155C2×#361—111no—
156C23×C11—41no—
157C23×C11AGL(1,ℤ/8)11yescharacteristic
158C22×D11—42no—
159C22×D11—84no—
160C22×D11—81no—
161C22×D11—81no—
162Q8×C11—22no—
163Q8×C11—41no—
164Q8×C11—42no—
165Q8×C11—42no—
166Q8×C11—81no—
167Q8×C11—81no—
168D4×C11—22no—
169D4×C11—42no—
170D4×C11—42no—
171D4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11C2×D811yescharacteristic
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×Dic11—22no—
185C2×Dic11—42no—
186D44—42no—
187D44—42no—
188D44—81no—
189D44—81no—
190C8×C11#12111yescharacteristic
191C8×C11#12111yescharacteristic
192C8×C11C22×D411yescharacteristic
193C8×C11C2×#4111yescharacteristic
194C11⋊C8—42no—
195C11⋊C8C2×D812yes—
196C11⋊C8C2×D812yes—
197C2×#135C2×D1111yescharacteristic
198C22×Q16C2×D1111yescharacteristic
199C22×SD16—221no—
200C22×D8—111no—
201C2×#131—221no—
202C2×#124—221no—
203#510—22no—
204#510C2×D1114yescomplemented
205#509—114no—
206#509—222no—
207C2×Q32—21no—
208C2×SD32—21no—
209C2×SD32—221no—
210C2×D16—221no—
211C2×M32—111no—
212C2×M32C2×D1111yescharacteristic
213#495—114no—
214#495—222no—
215#443—114no—
216#443—222no—
217C2×#108—111no—
218C2×#104—221no—
219C2×C4×C8—111no—
220#364—114no—
221#362—114no—
222#361—114no—
223C22×C11—22no—
224C22×C11—42no—
225C22×C11—82no—
226C22×C11#45911yescharacteristic
227C22×C11#45911yescharacteristic
228C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
229C2×D11—84no—
230C2×D11—82no—
231C2×D11—162no—
232C2×D11—162no—
233C4×C11—42no—
234C4×C11—82no—
235C4×C11#45911yescharacteristic
236C4×C11#45911yescharacteristic
237C4×C11C2×#12111yescharacteristic
238C4×C11C22×D811yescharacteristic
239Dic11—42no—
240C2×#41—21no—
241C22×Q8—21no—
242C22×D4—221no—
243#135—21no—
244#135—21no—
245#135C22⋊D1112yes—
246#135C22×D1112yes—
247C2×Q16—21no—
248C2×Q16—21no—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16—21no—
252C2×Q16C22⋊D1111yescharacteristic
253C2×Q16C22×D1112yes—
254C2×SD16—21no—
255C2×SD16—224no—
256C2×SD16—441no—
257C2×SD16—441no—
258C2×SD16—442no—
259C2×D8—112no—
260C2×D8—221no—
261C2×D8—221no—
262C2×D8—221no—
263C2×D8—221no—
264C2×D8—221no—
265C2×D8C22⋊D1111yescharacteristic
266#131—224no—
267#131—442no—
268C2×M16—221no—
269C2×M16—441no—
270C22×C8—111no—
271C22×C8—441no—
272C22×C8C22×D1111yescharacteristic
273#124—224no—
274#124—442no—
275C2×C22⋊C4—442no—
276C2×C42—111no—
277Q32—24no—
278SD32—24no—
279SD32—224no—
280D16—224no—
281M32—21no—
282M32—112no—
283M32—221no—
284M32C22×D1112yes—
285C2×C16—21no—
286C2×C16—221no—
287#108—112no—
288#108—221no—
289#104—224no—
290C4×C8—112no—
291C4×C8—112no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—82no—
295C2×C11#221212yescomplemented
296C2×C11C2×#45911yescharacteristic
297D11—162no—
298C24—441no—
299#41—22no—
300#41—22no—
301#41—41no—
302#41—41no—
303C2×Q8—21no—
304C2×Q8—22no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×D4—21no—
311C2×D4—41no—
312C2×D4—222no—
313C2×D4—441no—
314C2×D4—441no—
315C2×D4—441no—
316C2×D4—441no—
317C2×D4—441no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—221no—
321C22×C4D4×D1111yescharacteristic
322Q16—21no—
323Q16—22no—
324Q16—22no—
325Q16—41no—
326Q16—41no—
327Q16C2×C22⋊D1112yes—
328SD16—22no—
329SD16—22no—
330SD16—444no—
331SD16—444no—
332D8—21no—
333D8—222no—
334D8—222no—
335D8—441no—
336D8—441no—
337D8C2×C22⋊D1112yes—
338M16—222no—
339M16—444no—
340M16—441no—
341C2×C8—111no—
342C2×C8—111no—
343C2×C8—112no—
344C2×C8—112no—
345C2×C8—444no—
346C2×C8—441no—
347C2×C8D4×D1111yescharacteristic
348C2×C8#434111yescharacteristic
349C2×C8#434111yescharacteristic
350C2×C8C2×C22⋊D1111yescharacteristic
351C2×C8C2×C22⋊D1111yescharacteristic
352C2×C8C23×D1111yescharacteristic
353C22⋊C4—448no—
354C42—112no—
355C42—221no—
356C16—22no—
357C16—222no—
358C11C2×#221211yescharacteristic, complemented, Sylow
359C23—41no—
360C23—442no—
361C23—884no—
362C23—881no—
363C23—881no—
364C23#6696411yescharacteristic
365Q8—22no—
366Q8—41no—
367Q8—42no—
368Q8—42no—
369Q8—81no—
370Q8—81no—
371D4—22no—
372D4—42no—
373D4—42no—
374D4—41no—
375D4—442no—
376D4—442no—
377D4—881no—
378D4—881no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—222no—
386C2×C4—442no—
387C2×C4D8×D1111yescharacteristic
388C2×C4D8×D1111yescharacteristic
389C2×C4#6696411yescharacteristic
390C2×C4#6699211yescharacteristic
391C2×C4#6699211yescharacteristic
392C2×C4C2×D4×D1111yescharacteristic
393C8—112no—
394C8—112no—
395C8—442no—
396C8#6699211yescharacteristic
397C8#6699211yescharacteristic
398C8C2×#434111yescharacteristic
399C8C22×C22⋊D1111yescharacteristic
400C22—22no—
401C22—42no—
402C22—82no—
403C22—884no—
404C22—882no—
405C22—1762no—
406C22—1762no—
407C22#1062276311yescharacteristic
408C22#1062276311yescharacteristic
409C22C2×#6696411yescharacteristic
410C4—42no—
411C4—82no—
412C4—442no—
413C4#1062276311yescharacteristic
414C4#1062276311yescharacteristic
415C4C2×D8×D1111yescharacteristic
416C4C2×#6699211yescharacteristic
417C2—21no—
418C2—21no—
419C2—82no—
420C2—1762no—
421C2#1307068712yesdirect product factor
422C2C2×#1062276311yescharacteristic
subgroupG/H
centerC22#10622763
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#510C2
socleC22×C11#459
prime radicalC2×#10622806C2
hypercenterC2×#510D11
hypocenterC11C2×#2212
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
2. C2×#10622804C2semidirect
3. C2×#10622809C2semidirect
4. #13070687C2direct (N × H)
5. C2×#10622149C2semidirect
6. C2×#10622203C2semidirect
7. C2×#10622154C2semidirect
8. C2×C11×#510C2semidirect
16. C11×#510C22semidirect
22. #10622809C22semidirect
26. #10622804C22semidirect
32. #10622203C22semidirect
33. #10622154C22semidirect
34. #10622149C22semidirect
148. C2×#510D11semidirect
204. #510C2×D11semidirect
295. C2×C11#2212semidirect
358. C11C2×#2212semidirect
421. C2#13070687direct (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×#106228042
C2×#106228092
#130706872
C2×#106221492
C2×#106222032
C2×#106221542
C2×C11×#5102
C2×#221211