Finite Group Databasebeta

← C2×#13070744 #14908340

Subgroups — C2×#13070744 #14908340

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×#66891C211yesmaximal, characteristic, complemented
2C2×#10622753C211yesmaximal, characteristic, complemented
3C2×#10622756C211yesmaximal, characteristic, complemented
4#13070744C218yesmaximal, direct product factor
5C2×#10622131C211yesmaximal, characteristic, complemented
6C2×#10622134C211yesmaximal, characteristic, complemented
7C2×#10622201C211yesmaximal, characteristic, complemented
8C2×C11×#472C211yesmaximal, characteristic
9C2×C11×AGL(1,ℤ/8)—21no—
10C22×C11×D8C2211yescharacteristic
11C2×C11×#131C2211yescharacteristic
12C2×#67004—21no—
13C22×Dic44C2211yescharacteristic
14C11×#472—22no—
15C11×#472C2214yes—
16C2×C11×#108C2211yescharacteristic
17C2×C11×#100—21no—
18C2×#66891—22no—
19C2×#66891—21no—
20C2×#66891—21no—
21C2×#66891C2214yescomplemented
22#10622756—22no—
23#10622756C2214yescomplemented
24#10622753—22no—
25#10622753C2214yescomplemented
26C2×#66888—21no—
27C2×#66883C2211yescharacteristic
28C2×#66876—21no—
29C2×#66876C2211yescharacteristic
30C22×C11⋊C16—21no—
31C22×C11⋊C16C2211yescharacteristic
32#10622201C2214yescomplemented
33#10622134C2214yescomplemented
34#10622131C2214yescomplemented
35C2×C11×#41D411yescharacteristic
36C22×D4×C11—21no—
37C22×Dic22—21no—
38C11×AGL(1,ℤ/8)—24no—
39C11×AGL(1,ℤ/8)—42no—
40C2×C11×SD16—41no—
41C2×C11×D8—21no—
42C2×C11×D8—21no—
43C2×C11×D8—21no—
44C2×C11×D8—21no—
45C2×C11×D8—21no—
46C2×C11×D8—41no—
47C2×C11×D8C2312yes—
48C11×#131—21no—
49C11×#131—21no—
50C11×#131D412yes—
51C11×#131C2312yes—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16D411yescharacteristic
55C22×C8×C11—21no—
56C22×C8×C11C2311yescharacteristic
57#67004—24no—
58#67004—42no—
59C2×#4326—41no—
60C2×#4324—41no—
61C2×#4318—21no—
62C2×Dic44—21no—
63C2×Dic44—21no—
64C2×Dic44—21no—
65C2×Dic44—21no—
66C2×Dic44—21no—
67C2×Dic44C2312yes—
68C11×#108—21no—
69C11×#108C2312yes—
70C11×#100—24no—
71#66891—24no—
72#66891—24no—
73#66888—24no—
74#66883—21no—
75#66883C2312yes—
76#66876—21no—
77#66876—24no—
78#66876C2312yes—
79C2×C11⋊C16—21no—
80C2×C11⋊C16—24no—
81C2×C11⋊C16D412yes—
82C2×C11⋊C16D411yescharacteristic
83C2×C11⋊C16D411yescharacteristic
84C2×C11⋊C16C2312yes—
85C2×#2223—111nomaximal, Sylow
86C24×C11—41no—
87C11×#41—21no—
88C11×#41—21no—
89C11×#41D812yes—
90C11×#41C2×D412yes—
91C2×Q8×C11D811yescharacteristic
92C2×D4×C11—21no—
93C2×D4×C11—22no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11D811yescharacteristic
100C22×C4×C11—21no—
101C22×C4×C11C2×D411yescharacteristic
102C22×Dic11—41no—
103C2×Dic22—22no—
104C2×Dic22—41no—
105C2×Dic22—41no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C11×SD16—44no—
110C11×D8—22no—
111C11×D8—22no—
112C11×D8—41no—
113C11×D8—41no—
114C11×D8—44no—
115C11×M16—22no—
116C11×M16—22no—
117C11×M16—21no—
118C11×M16—22no—
119C11×M16—41no—
120C11×M16C2×D412yes—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—21no—
124C2×C8×C11—41no—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11#4111yescharacteristic
129C2×C8×C11#4111yescharacteristic
130C2×C8×C11C2411yescharacteristic
131#4326—44no—
132#4324—44no—
133#4318—22no—
134#4318—41no—
135C2×C11⋊C8—41no—
136Dic44—22no—
137Dic44—22no—
138Dic44—41no—
139Dic44—41no—
140C11⋊C16—22no—
141C11⋊C16C2×D412yes—
142C11⋊C16C2×D412yes—
143C22×SD32—111no—
144C2×#504—111no—
145C2×#473—111no—
146C2×#472D1111yescharacteristic
147#2223—118no—
148C2×#368—111no—
149C2×#362—111no—
150C2×#361—111no—
151C23×C11—21no—
152C23×C11—42no—
153C23×C11—81no—
154C23×C11—81no—
155C23×C11—162no—
156C23×C11#13511yescharacteristic
157Q8×C11—21no—
158Q8×C11C2×D812yes—
159D4×C11—22no—
160D4×C11—22no—
161D4×C11—21no—
162D4×C11—42no—
163D4×C11—42no—
164D4×C11—81no—
165D4×C11—81no—
166D4×C11C2×D812yes—
167C2×C4×C11—21no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11#13511yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×Dic11—42no—
177C2×Dic11—81no—
178C2×Dic11—81no—
179Dic22—42no—
180Dic22—42no—
181Dic22—81no—
182Dic22—81no—
183C8×C11—22no—
184C8×C11—42no—
185C8×C11#12111yescharacteristic
186C8×C11#12111yescharacteristic
187C8×C11C22×D411yescharacteristic
188C8×C11C2×#4111yescharacteristic
189C11⋊C8—42no—
190C2×#137—221no—
191C2×AGL(1,ℤ/8)—21no—
192C22×Q16—111no—
193C22×D8C2×D1111yescharacteristic
194C2×#131C2×D1111yescharacteristic
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—111no—
204C22×C16—221no—
205#473—114no—
206#473—222no—
207#472—22no—
208#472C2×D1114yes—
209C2×#108—111no—
210C2×#108C2×D1111yescharacteristic
211C2×#101—221no—
212C2×#100—21no—
213#368—114no—
214#362—114no—
215#361—114no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—42no—
219C22×C11—82no—
220C22×C11—162no—
221C22×C11—162no—
222C22×C11—162no—
223C22×C11#46611yescharacteristic
224C22×C11#46611yescharacteristic
225C22×C11C2×#13511yescharacteristic
226C4×C11—22no—
227C4×C11#46611yescharacteristic
228C4×C11#46611yescharacteristic
229C4×C11C2×#12111yescharacteristic
230C4×C11C22×D811yescharacteristic
231Dic11—82no—
232C2×#41C22⋊D1111yescharacteristic
233C22×Q8—221no—
234C22×D4—21no—
235#137—224no—
236#137—442no—
237AGL(1,ℤ/8)—24no—
238AGL(1,ℤ/8)—42no—
239C2×Q16—112no—
240C2×Q16—221no—
241C2×Q16—221no—
242C2×Q16—221no—
243C2×Q16—221no—
244C2×Q16—221no—
245C2×Q16—441no—
246C2×SD16—41no—
247C2×SD16—441no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—21no—
251C2×D8—21no—
252C2×D8—21no—
253C2×D8—41no—
254C2×D8C22×D1112yes—
255#131—21no—
256#131—21no—
257#131C22⋊D1112yes—
258#131C22×D1112yes—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—221no—
262C2×M16C22⋊D1111yescharacteristic
263C22×C8—21no—
264C22×C8C22×D1111yescharacteristic
265SD32—224no—
266SD32—224no—
267M32—112no—
268M32—224no—
269M32—221no—
270C2×C16—111no—
271C2×C16—111no—
272C2×C16—112no—
273C2×C16—112no—
274C2×C16—224no—
275C2×C16—221no—
276#108—21no—
277#108—112no—
278#108—221no—
279#108C22×D1112yes—
280#101—224no—
281#100—24no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—42no—
285C2×C11—162no—
286C2×C11#222312yescomplemented
287C2×C11C2×#46611yescharacteristic
288C24—41no—
289#41—21no—
290#41—21no—
291#41#432312yes—
292#41C2×C22⋊D1112yes—
293C2×Q8—222no—
294C2×Q8—441no—
295C2×Q8—441no—
296C2×Q8—441no—
297C2×Q8—441no—
298C2×Q8—441no—
299C2×Q8#432311yescharacteristic
300C2×D4—21no—
301C2×D4—22no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4#432311yescharacteristic
308C22×C4—21no—
309C22×C4—441no—
310C22×C4C2×C22⋊D1111yescharacteristic
311Q16—222no—
312Q16—222no—
313Q16—444no—
314Q16—441no—
315Q16—441no—
316SD16—44no—
317SD16—444no—
318D8—22no—
319D8—22no—
320D8—44no—
321D8—41no—
322D8—41no—
323M16—21no—
324M16—22no—
325M16—22no—
326M16—22no—
327M16—41no—
328M16—222no—
329M16—441no—
330M16C2×C22⋊D1112yes—
331C2×C8—21no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—41no—
335C2×C8—441no—
336C2×C8D4×D1111yescharacteristic
337C2×C8D4×D1111yescharacteristic
338C2×C8#434111yescharacteristic
339C2×C8#434111yescharacteristic
340C2×C8C2×C22⋊D1111yescharacteristic
341C2×C8C23×D1111yescharacteristic
342C16—112no—
343C16—112no—
344C16—222no—
345C11C2×#222311yescharacteristic, complemented, Sylow
346C23—21no—
347C23—42no—
348C23—81no—
349C23—81no—
350C23—162no—
351C23#6700311yescharacteristic
352Q8—21no—
353Q8—442no—
354Q8—442no—
355Q8—881no—
356Q8—881no—
357Q8C2×#432312yes—
358D4—22no—
359D4—22no—
360D4—21no—
361D4—42no—
362D4—42no—
363D4—81no—
364D4—81no—
365D4C2×#432312yes—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—442no—
370C2×C4—881no—
371C2×C4—881no—
372C2×C4C2×#432311yescharacteristic
373C2×C4C2×#432311yescharacteristic
374C2×C4#6699211yescharacteristic
375C2×C4#6699211yescharacteristic
376C2×C4#6700311yescharacteristic
377C2×C4C22×C22⋊D1111yescharacteristic
378C8—22no—
379C8—42no—
380C8—442no—
381C8#6699211yescharacteristic
382C8#6699211yescharacteristic
383C8C2×D4×D1111yescharacteristic
384C8C2×#434111yescharacteristic
385C22—22no—
386C22—22no—
387C22—42no—
388C22—82no—
389C22—162no—
390C22—162no—
391C22—162no—
392C22#1062265111yescharacteristic
393C22#1062265111yescharacteristic
394C22C2×#6700311yescharacteristic
395C4—22no—
396C4—882no—
397C4#1062265111yescharacteristic
398C4#1062265111yescharacteristic
399C4C22×#432311yescharacteristic
400C4C2×#6699211yescharacteristic
401C2—21no—
402C2—21no—
403C2—42no—
404C2—162no—
405C2#1307074412yesdirect product factor
406C2C2×#1062265111yescharacteristic
subgroupG/H
centerC22#10622651
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC2×C11×#472C2
socleC22×C11#466
hypercenterC2×#472D11
hypocenterC11C2×#2223
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
1. C22×#66891C2semidirect
2. C2×#10622753C2semidirect
3. C2×#10622756C2semidirect
4. #13070744C2direct (N × H)
5. C2×#10622131C2semidirect
6. C2×#10622134C2semidirect
7. C2×#10622201C2semidirect
21. C2×#66891C22semidirect
23. #10622756C22semidirect
25. #10622753C22semidirect
32. #10622201C22semidirect
33. #10622134C22semidirect
34. #10622131C22semidirect
286. C2×C11#2223semidirect
345. C11C2×#2223semidirect
405. C2#13070744direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668912
C2×#106227532
C2×#106227562
#130707442
C2×#106221312
C2×#106221342
C2×#106222012
C2×C11×#4722
C2×#222311