Finite Group Databasebeta

← C2×#13070747 #14908343

Subgroups — C2×#13070747 #14908343

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66864C211yesmaximal, characteristic, complemented
2C2×#10622514C211yesmaximal, characteristic, complemented
3C2×#10622509C211yesmaximal, characteristic, complemented
4C2×#10622510C211yesmaximal, characteristic
5#13070747C218yesmaximal, direct product factor
6C2×#10622134C211yesmaximal, characteristic, complemented
7C2×#10622133C211yesmaximal, characteristic, complemented
8C2×C11×#368C211yesmaximal, characteristic, complemented
9C2×#66962—21no—
10C2×#66961—21no—
11C22×Dic44C2211yescharacteristic
12C22×D88C2211yescharacteristic
13C2×#66954C2211yescharacteristic
14C22×C11×C16C2211yescharacteristic
15C2×C11×#108C2211yescharacteristic
16C2×C11×#108C2211yescharacteristic
17C2×#66888—21no—
18C2×#66887—21no—
19C2×#66876C2211yescharacteristic
20C2×#66864—21no—
21C2×#66864—21no—
22C2×#66864—22no—
23C2×#66864C2214yescomplemented
24#10622514—22no—
25#10622514C2214yescomplemented
26C2×#66862—21no—
27C2×C16×D11—21no—
28#10622510—22no—
29#10622510C2214yes—
30#10622509—22no—
31#10622509C2214yescomplemented
32C11×#368C2214yescomplemented
33#10622134C2214yescomplemented
34#10622133C2214yescomplemented
35C2×#4339D411yescharacteristic
36C22×D44—21no—
37C22×Dic22—21no—
38C2×C11×M16—21no—
39C2×C11×M16—21no—
40C22×C8×C11C2311yescharacteristic
41C2×#4318D411yescharacteristic
42#66962—24no—
43#66962—42no—
44#66961—24no—
45#66961—42no—
46C2×Dic44—21no—
47C2×Dic44—21no—
48C2×Dic44—21no—
49C2×Dic44—21no—
50C2×Dic44—21no—
51C2×Dic44—41no—
52C2×Dic44C2312yes—
53C2×D88—21no—
54C2×D88—21no—
55C2×D88—21no—
56C2×D88—21no—
57C2×D88—21no—
58C2×D88—41no—
59C2×D88C2312yes—
60C2×#4314—41no—
61C2×#4314—41no—
62#66954—21no—
63#66954—21no—
64#66954D412yes—
65#66954C2312yes—
66C2×#4313—21no—
67C2×C8×D11—21no—
68C2×C11×C16D411yescharacteristic
69C2×C11×C16D411yescharacteristic
70C2×C11×C16D412yes—
71C2×C11×C16C2312yes—
72C11×#108—21no—
73C11×#108—21no—
74C11×#108C2312yes—
75C11×#108C2312yes—
76#66888—24no—
77#66887—24no—
78#66876—21no—
79#66876C2312yes—
80C2×C11⋊C16—21no—
81#66864—24no—
82#66864—24no—
83#66862—24no—
84C16×D11—24no—
85C2×#2223—111nomaximal, Sylow
86C23×D11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C2×C22⋊D11—21no—
89C22×Dic11—41no—
90#4339—21no—
91#4339—21no—
92#4339D812yes—
93#4339C2×D412yes—
94C2×D44—22no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44D811yescharacteristic
101C2×C4×D11—21no—
102C2×Dic22—22no—
103C2×Dic22—41no—
104C2×Dic22—41no—
105C2×Dic22—41no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C2×Dic22D811yescharacteristic
109C11×M16—22no—
110C11×M16—22no—
111C11×M16—41no—
112C11×M16—41no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11#4111yescharacteristic
119C2×C8×C11#4111yescharacteristic
120C2×C8×C11C2411yescharacteristic
121#4318—21no—
122#4318C2×D412yes—
123C2×C11⋊C8—21no—
124Dic44—22no—
125Dic44—22no—
126Dic44—44no—
127Dic44—41no—
128Dic44—41no—
129D88—22no—
130D88—22no—
131D88—44no—
132D88—41no—
133D88—41no—
134#4314—44no—
135#4314—44no—
136#4313—22no—
137#4313—22no—
138C8×D11—22no—
139C8×D11—22no—
140C11×C16C2×D412yes—
141C11×C16C2×D412yes—
142C11⋊C16—22no—
143C22×SD32—111no—
144C2×#504—111no—
145C2×#473—111no—
146C2×#472—111no—
147#2223—118no—
148C2×#368D1111yescharacteristic, complemented
149C2×#362—111no—
150C2×#361—111no—
151C23×C11#13511yescharacteristic
152C22×D11—21no—
153C22×D11—42no—
154C22×D11—81no—
155C22×D11—81no—
156C22×D11—162no—
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11#13511yescharacteristic
162C2×C4×C11C22×D411yescharacteristic
163C22⋊D11—22no—
164C22⋊D11—22no—
165C2×Dic11—21no—
166C2×Dic11—42no—
167C2×Dic11—81no—
168C2×Dic11—81no—
169D44—21no—
170D44—42no—
171D44—42no—
172D44—81no—
173D44—81no—
174D44C2×D812yes—
175C4×D11—22no—
176C4×D11—22no—
177Dic22—21no—
178Dic22—42no—
179Dic22—42no—
180Dic22—81no—
181Dic22—81no—
182Dic22C2×D812yes—
183C8×C11—42no—
184C8×C11—42no—
185C8×C11#12111yescharacteristic
186C8×C11#12111yescharacteristic
187C8×C11C22×D411yescharacteristic
188C8×C11C2×#4111yescharacteristic
189C11⋊C8—22no—
190C2×#137—221no—
191C2×AGL(1,ℤ/8)—221no—
192C22×Q16—111no—
193C22×D8—111no—
194C2×#131—111no—
195C2×SD32—114no—
196C2×SD32—221no—
197C2×SD32—221no—
198C2×SD32—222no—
199#504—114no—
200#504—222no—
201C2×M32—111no—
202C2×M32—221no—
203C22×C16—221no—
204C22×C16C2×D1111yescharacteristic
205#473—114no—
206#473—222no—
207#472—114no—
208#472—222no—
209C2×#108C2×D1111yescharacteristic
210C2×#108C2×D1111yescharacteristic
211C2×#101—221no—
212C2×#100—221no—
213#368C2×D1114yescomplemented
214#362—114no—
215#361—114no—
216C22×C11—22no—
217C22×C11#46611yescharacteristic
218C22×C11#46611yescharacteristic
219C22×C11C2×#13511yescharacteristic
220C2×D11—22no—
221C2×D11—42no—
222C2×D11—82no—
223C2×D11—162no—
224C2×D11—162no—
225C2×D11—162no—
226C4×C11#46611yescharacteristic
227C4×C11#46611yescharacteristic
228C4×C11C2×#12111yescharacteristic
229C4×C11C22×D811yescharacteristic
230Dic11—22no—
231Dic11—82no—
232C2×#41—111no—
233C22×Q8—221no—
234C22×D4—221no—
235#137—224no—
236#137—442no—
237AGL(1,ℤ/8)—224no—
238AGL(1,ℤ/8)—442no—
239C2×Q16—112no—
240C2×Q16—221no—
241C2×Q16—221no—
242C2×Q16—221no—
243C2×Q16—221no—
244C2×Q16—221no—
245C2×Q16—441no—
246C2×SD16—441no—
247C2×SD16—441no—
248C2×D8—112no—
249C2×D8—221no—
250C2×D8—221no—
251C2×D8—221no—
252C2×D8—221no—
253C2×D8—221no—
254C2×D8—441no—
255#131—112no—
256#131—112no—
257#131—221no—
258#131—221no—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—111no—
262C2×M16—221no—
263C22×C8—221no—
264C22×C8C22×D1111yescharacteristic
265SD32—224no—
266SD32—224no—
267M32—112no—
268M32—221no—
269M32—224no—
270C2×C16—221no—
271C2×C16—224no—
272C2×C16D4411yescharacteristic
273C2×C16D4411yescharacteristic
274C2×C16D4412yes—
275C2×C16C22×D1112yes—
276#108—21no—
277#108—21no—
278#108C22×D1112yes—
279#108C22×D1112yes—
280#101—224no—
281#100—224no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11#222312yescomplemented
285C2×C11C2×#46611yescharacteristic
286D11—42no—
287D11—162no—
288C24—441no—
289#41—112no—
290#41—112no—
291#41—221no—
292#41—221no—
293C2×Q8—111no—
294C2×Q8—222no—
295C2×Q8—441no—
296C2×Q8—441no—
297C2×Q8—441no—
298C2×Q8—441no—
299C2×Q8—441no—
300C2×D4—111no—
301C2×D4—221no—
302C2×D4—222no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4—441no—
308C22×C4—221no—
309C22×C4—441no—
310C22×C4D4×D1111yescharacteristic
311Q16—222no—
312Q16—222no—
313Q16—444no—
314Q16—441no—
315Q16—441no—
316SD16—444no—
317SD16—444no—
318D8—222no—
319D8—222no—
320D8—444no—
321D8—441no—
322D8—441no—
323M16—22no—
324M16—22no—
325M16—41no—
326M16—41no—
327M16—112no—
328M16—221no—
329M16—222no—
330M16—222no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—221no—
334C2×C8—222no—
335C2×C8—222no—
336C2×C8C2×D4411yescharacteristic
337C2×C8C2×D4411yescharacteristic
338C2×C8D4×D1111yescharacteristic
339C2×C8#434311yescharacteristic
340C2×C8#434311yescharacteristic
341C2×C8C23×D1111yescharacteristic
342C16—222no—
343C16C2×D4412yes—
344C16C2×D4412yes—
345C11C2×#222311yescharacteristic, complemented, Sylow
346C23—221no—
347C23—442no—
348C23—881no—
349C23—881no—
350C23—1762no—
351C23#6697211yescharacteristic
352Q8—112no—
353Q8—221no—
354Q8—442no—
355Q8—442no—
356Q8—881no—
357Q8—881no—
358D4—112no—
359D4—222no—
360D4—222no—
361D4—221no—
362D4—442no—
363D4—442no—
364D4—881no—
365D4—881no—
366C2×C4—221no—
367C2×C4—222no—
368C2×C4—222no—
369C2×C4—442no—
370C2×C4—881no—
371C2×C4—881no—
372C2×C4#6694811yescharacteristic
373C2×C4#6694811yescharacteristic
374C2×C4D8×D1111yescharacteristic
375C2×C4D8×D1111yescharacteristic
376C2×C4#6697211yescharacteristic
377C2×C4C2×D4×D1111yescharacteristic
378C8—42no—
379C8—42no—
380C8—222no—
381C8#6694811yescharacteristic
382C8#6694811yescharacteristic
383C8C22×D4411yescharacteristic
384C8C2×#434311yescharacteristic
385C22—22no—
386C22—222no—
387C22—442no—
388C22—882no—
389C22—1762no—
390C22—1762no—
391C22—1762no—
392C22#1062249611yescharacteristic
393C22#1062249611yescharacteristic
394C22C2×#6697211yescharacteristic
395C4—222no—
396C4—882no—
397C4#1062249611yescharacteristic
398C4#1062249611yescharacteristic
399C4C2×#6694811yescharacteristic
400C4C2×D8×D1111yescharacteristic
401C2—21no—
402C2—21no—
403C2—442no—
404C2—1762no—
405C2#1307074712yesdirect product factor
406C2C2×#1062249611yescharacteristic
subgroupG/H
centerC22#10622496
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#368C2
socleC22×C11#466
prime radicalC2×#10622510C2
hypercenterC2×#368D11
hypocenterC11C2×#2223
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#368

Complements

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

NH ≅ G/Ntype
1. C22×#66864C2semidirect
2. C2×#10622514C2semidirect
3. C2×#10622509C2semidirect
5. #13070747C2direct (N × H)
6. C2×#10622134C2semidirect
7. C2×#10622133C2semidirect
8. C2×C11×#368C2semidirect
23. C2×#66864C22semidirect
25. #10622514C22semidirect
31. #10622509C22semidirect
32. C11×#368C22semidirect
33. #10622134C22semidirect
34. #10622133C22semidirect
148. C2×#368D11semidirect
213. #368C2×D11semidirect
284. C2×C11#2223semidirect
345. C11C2×#2223semidirect
405. C2#13070747direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668642
C2×#106225142
C2×#106225092
C2×#106225102
#130707472
C2×#106221342
C2×#106221332
C2×C11×#3682
C2×#222311