Finite Group Databasebeta

← C2×#13070746 #14908342

Subgroups — C2×#13070746 #14908342

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×#10622756C211yesmaximal, characteristic, complemented
3C2×#10622755C211yesmaximal, characteristic
4#13070746C218yesmaximal, direct product factor
5C2×#10622144C211yesmaximal, characteristic, complemented
6C2×#10622155C211yesmaximal, characteristic, complemented
7C2×#10622154C211yesmaximal, characteristic, complemented
8C2×C11×#504C211yesmaximal, characteristic, complemented
9C2×C11×#131C2211yescharacteristic
10C2×#67004—21no—
11C2×#67002—21no—
12C22×Dic44C2211yescharacteristic
13C22×D88C2211yescharacteristic
14C11×#504—22no—
15C11×#504C2214yescomplemented
16C2×C11×M32—21no—
17C2×C11×M32C2211yescharacteristic
18C22×C11×C16—21no—
19C22×C11×C16C2211yescharacteristic
20#10622756—22no—
21#10622756C2214yescomplemented
22#10622755—22no—
23#10622755C2214yes—
24C2×#66888—21no—
25C2×#66887—21no—
26C2×#66883C2211yescharacteristic
27C2×#66883C2211yescharacteristic
28C2×#66864—21no—
29C2×#66864—21no—
30C2×#66864—22no—
31C2×#66864C2214yescomplemented
32#10622155C2214yescomplemented
33#10622154C2214yescomplemented
34#10622144C2214yescomplemented
35C2×C11×#41D411yescharacteristic
36C22×D44—21no—
37C22×Dic22—21no—
38C11×#131—21no—
39C11×#131—21no—
40C11×#131D412yes—
41C11×#131C2312yes—
42C2×C11×M16—21no—
43C2×C11×M16D411yescharacteristic
44C22×C8×C11—21no—
45C22×C8×C11C2311yescharacteristic
46#67004—24no—
47#67004—42no—
48#67002—24no—
49#67002—42no—
50C2×#4326—41no—
51C2×#4325—41no—
52C2×#4324—41no—
53C2×#4323—41no—
54C2×#4318—21no—
55C2×#4318—21no—
56C2×Dic44—21no—
57C2×Dic44—21no—
58C2×Dic44—21no—
59C2×Dic44—21no—
60C2×Dic44—21no—
61C2×Dic44C2312yes—
62C2×D88—21no—
63C2×D88—21no—
64C2×D88—21no—
65C2×D88—21no—
66C2×D88—21no—
67C2×D88C2312yes—
68C11×M32—21no—
69C11×M32—24no—
70C11×M32C2312yes—
71C2×C11×C16—21no—
72C2×C11×C16—24no—
73C2×C11×C16D411yescharacteristic
74C2×C11×C16D411yescharacteristic
75C2×C11×C16D412yes—
76C2×C11×C16C2312yes—
77#66888—24no—
78#66887—24no—
79#66883—21no—
80#66883—21no—
81#66883C2312yes—
82#66883C2312yes—
83#66864—24no—
84#66864—24no—
85C2×#2223—111nomaximal, Sylow
86C23×D11—41no—
87C11×#41—21no—
88C11×#41—21no—
89C11×#41D812yes—
90C11×#41C2×D412yes—
91C2×Q8×C11D811yescharacteristic
92C2×D4×C11—21no—
93C2×D4×C11D811yescharacteristic
94C22×C4×C11—21no—
95C22×C4×C11C2×D411yescharacteristic
96C22×Dic11—41no—
97C2×D44—22no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×Dic22—22no—
104C2×Dic22—41no—
105C2×Dic22—41no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C11×M16—22no—
110C11×M16—22no—
111C11×M16—21no—
112C11×M16C2×D412yes—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—21no—
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11#4111yescharacteristic
120C2×C8×C11#4111yescharacteristic
121C2×C8×C11C2411yescharacteristic
122#4326—44no—
123#4325—44no—
124#4324—44no—
125#4323—44no—
126#4318—22no—
127#4318—22no—
128#4318—41no—
129#4318—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132Dic44—22no—
133Dic44—22no—
134Dic44—41no—
135Dic44—41no—
136D88—22no—
137D88—22no—
138D88—41no—
139D88—41no—
140C11×C16—22no—
141C11×C16C2×D412yes—
142C11×C16C2×D412yes—
143C22×SD32—111no—
144C2×#504D1111yescharacteristic, complemented
145C2×#473—111no—
146C2×#472—111no—
147#2223—118no—
148C2×#368—111no—
149C2×#362—111no—
150C2×#361—111no—
151C23×C11—21no—
152C23×C11#13511yescharacteristic
153C22×D11—42no—
154C22×D11—81no—
155C22×D11—81no—
156C22×D11—162no—
157Q8×C11—21no—
158Q8×C11C2×D812yes—
159D4×C11—22no—
160D4×C11—22no—
161D4×C11—21no—
162D4×C11C2×D812yes—
163C2×C4×C11—21no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11#13511yescharacteristic
171C2×C4×C11C22×D411yescharacteristic
172C2×Dic11—42no—
173C2×Dic11—81no—
174C2×Dic11—81no—
175D44—42no—
176D44—42no—
177D44—81no—
178D44—81no—
179Dic22—42no—
180Dic22—42no—
181Dic22—81no—
182Dic22—81no—
183C8×C11—22no—
184C8×C11#12111yescharacteristic
185C8×C11#12111yescharacteristic
186C8×C11C22×D411yescharacteristic
187C8×C11C2×#4111yescharacteristic
188C11⋊C8—42no—
189C11⋊C8—42no—
190C2×#137—221no—
191C2×AGL(1,ℤ/8)—221no—
192C22×Q16—111no—
193C22×D8—111no—
194C2×#131C2×D1111yescharacteristic
195C2×SD32—114no—
196C2×SD32—221no—
197C2×SD32—221no—
198C2×SD32—222no—
199#504—22no—
200#504C2×D1114yescomplemented
201C2×M32—21no—
202C2×M32C2×D1111yescharacteristic
203C22×C16—21no—
204C22×C16C2×D1111yescharacteristic
205#473—114no—
206#473—222no—
207#472—114no—
208#472—222no—
209C2×#108—111no—
210C2×#108—111no—
211C2×#101—221no—
212C2×#100—221no—
213#368—114no—
214#362—114no—
215#361—114no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—42no—
219C22×C11#46611yescharacteristic
220C22×C11#46611yescharacteristic
221C22×C11C2×#13511yescharacteristic
222C2×D11—82no—
223C2×D11—162no—
224C2×D11—162no—
225C2×D11—162no—
226C4×C11—22no—
227C4×C11#46611yescharacteristic
228C4×C11#46611yescharacteristic
229C4×C11C2×#12111yescharacteristic
230C4×C11C22×D811yescharacteristic
231Dic11—82no—
232C2×#41D4411yescharacteristic
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—21no—
256#131—21no—
257#131D4412yes—
258#131C22×D1112yes—
259C2×M16—21no—
260C2×M16—221no—
261C2×M16—221no—
262C2×M16D4411yescharacteristic
263C22×C8—21no—
264C22×C8C22×D1111yescharacteristic
265SD32—224no—
266SD32—224no—
267M32—21no—
268M32—24no—
269M32C22×D1112yes—
270C2×C16—21no—
271C2×C16—24no—
272C2×C16C22⋊D1111yescharacteristic
273C2×C16C22⋊D1111yescharacteristic
274C2×C16C22⋊D1112yes—
275C2×C16C22×D1112yes—
276#108—112no—
277#108—112no—
278#108—221no—
279#108—221no—
280#101—224no—
281#100—224no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—42no—
285C2×C11#222312yescomplemented
286C2×C11C2×#46611yescharacteristic
287D11—162no—
288C24—441no—
289#41—21no—
290#41—21no—
291#41D8812yes—
292#41C2×D4412yes—
293C2×Q8—222no—
294C2×Q8—441no—
295C2×Q8—441no—
296C2×Q8—441no—
297C2×Q8—441no—
298C2×Q8—441no—
299C2×Q8D8811yescharacteristic
300C2×D4—21no—
301C2×D4—222no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4D8811yescharacteristic
308C22×C4—21no—
309C22×C4—441no—
310C22×C4C2×D4411yescharacteristic
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—21no—
324M16—22no—
325M16—22no—
326M16—222no—
327M16—222no—
328M16—441no—
329M16—441no—
330M16C2×D4412yes—
331C2×C8—21no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—441no—
335C2×C8—441no—
336C2×C8C2×D4411yescharacteristic
337C2×C8#433911yescharacteristic
338C2×C8#433911yescharacteristic
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C2×C22⋊D1111yescharacteristic
341C2×C8C23×D1111yescharacteristic
342C16—22no—
343C16C2×C22⋊D1112yes—
344C16C2×C22⋊D1112yes—
345C11C2×#222311yescharacteristic, complemented, Sylow
346C23—21no—
347C23—442no—
348C23—881no—
349C23—881no—
350C23—1762no—
351C23#6695711yescharacteristic
352Q8—21no—
353Q8—442no—
354Q8—442no—
355Q8—881no—
356Q8—881no—
357Q8C2×D8812yes—
358D4—22no—
359D4—22no—
360D4—21no—
361D4—442no—
362D4—442no—
363D4—881no—
364D4—881no—
365D4C2×D8812yes—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—442no—
370C2×C4—881no—
371C2×C4—881no—
372C2×C4C2×D8811yescharacteristic
373C2×C4C2×D8811yescharacteristic
374C2×C4#6695711yescharacteristic
375C2×C4#6698311yescharacteristic
376C2×C4#6698311yescharacteristic
377C2×C4C22×D4411yescharacteristic
378C8—22no—
379C8—442no—
380C8—442no—
381C8#6698311yescharacteristic
382C8#6698311yescharacteristic
383C8C2×#433911yescharacteristic
384C8C22×C22⋊D1111yescharacteristic
385C22—22no—
386C22—22no—
387C22—42no—
388C22—882no—
389C22—1762no—
390C22—1762no—
391C22—1762no—
392C22#1062272811yescharacteristic
393C22#1062272811yescharacteristic
394C22C2×#6695711yescharacteristic
395C4—22no—
396C4—882no—
397C4#1062272811yescharacteristic
398C4#1062272811yescharacteristic
399C4C22×D8811yescharacteristic
400C4C2×#6698311yescharacteristic
401C2—21no—
402C2—21no—
403C2—42no—
404C2—1762no—
405C2#1307074612yesdirect product factor
406C2C2×#1062272811yescharacteristic
subgroupG/H
centerC22#10622728
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#504C2
socleC22×C11#466
prime radicalC2×#10622755C2
hypercenterC2×#504D11
hypocenterC11C2×#2223
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
1. C22×#66864C2semidirect
2. C2×#10622756C2semidirect
4. #13070746C2direct (N × H)
5. C2×#10622144C2semidirect
6. C2×#10622155C2semidirect
7. C2×#10622154C2semidirect
8. C2×C11×#504C2semidirect
15. C11×#504C22semidirect
21. #10622756C22semidirect
31. C2×#66864C22semidirect
32. #10622155C22semidirect
33. #10622154C22semidirect
34. #10622144C22semidirect
144. C2×#504D11semidirect
200. #504C2×D11semidirect
285. C2×C11#2223semidirect
345. C11C2×#2223semidirect
405. C2#13070746direct (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×#106227562
C2×#106227552
#130707462
C2×#106221442
C2×#106221552
C2×#106221542
C2×C11×#5042
C2×#222311