Finite Group Databasebeta

← C2×#13070749 #14908345

Subgroups — C2×#13070749 #14908345

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×#66892C211yesmaximal, characteristic, complemented
2C2×#10622520C211yesmaximal, characteristic, complemented
3C2×#10622805C211yesmaximal, characteristic, complemented
4C2×#10622510C211yesmaximal, characteristic
5#13070749C218yesmaximal, direct product factor
6C2×#10622131C211yesmaximal, characteristic, complemented
7C2×#10622154C211yesmaximal, characteristic, complemented
8C2×C11×#362C211yesmaximal, characteristic, complemented
9C22×C11×Q16C2211yescharacteristic
10C2×#66995—21no—
11C2×#66961—21no—
12C22×D88C2211yescharacteristic
13C2×#66954C2211yescharacteristic
14C2×C11×M32C2211yescharacteristic
15C2×C11×#108C2211yescharacteristic
16C2×#66900—21no—
17#10622805—22no—
18#10622805C2214yescomplemented
19C2×#66892—21no—
20C2×#66892—21no—
21C2×#66892—22no—
22C2×#66892C2214yescomplemented
23C2×#66887—21no—
24C2×#66883C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26#10622520—22no—
27#10622520C2214yescomplemented
28C2×#66862—21no—
29C2×C16×D11—21no—
30#10622510—22no—
31#10622510C2214yes—
32C11×#362C2214yescomplemented
33#10622154C2214yescomplemented
34#10622131C2214yescomplemented
35C22×Q8×C11—21no—
36C2×#4339D411yescharacteristic
37C22×D44—21no—
38C2×C11×Q16—21no—
39C2×C11×Q16—21no—
40C2×C11×Q16—21no—
41C2×C11×Q16—21no—
42C2×C11×Q16—21no—
43C2×C11×Q16C2312yes—
44C2×C11×M16—21no—
45C22×C8×C11C2311yescharacteristic
46C2×#4326—41no—
47#66995—24no—
48#66995—42no—
49C2×#4325—41no—
50C2×#4318—21no—
51C2×#4318D411yescharacteristic
52#66961—24no—
53#66961—42no—
54C2×D88—21no—
55C2×D88—21no—
56C2×D88—21no—
57C2×D88—21no—
58C2×D88—21no—
59C2×D88—41no—
60C2×D88C2312yes—
61C2×#4314—41no—
62#66954—21no—
63#66954—21no—
64#66954D412yes—
65#66954C2312yes—
66C2×#4313—21no—
67C2×C8×D11—21no—
68C11×M32—21no—
69C11×M32C2312yes—
70C2×C11×C16—21no—
71C11×#108—21no—
72C11×#108C2312yes—
73#66900—24no—
74#66892—24no—
75#66892—24no—
76#66887—24no—
77#66883—21no—
78#66883C2312yes—
79C2×C11⋊C16D411yescharacteristic
80C2×C11⋊C16D411yescharacteristic
81C2×C11⋊C16D412yes—
82C2×C11⋊C16C2312yes—
83#66862—24no—
84C16×D11—24no—
85C2×#2223—111nomaximal, Sylow
86C23×D11—41no—
87C2×Q8×C11—22no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11—41no—
92C2×Q8×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C2×C22⋊D11—21no—
96#4339—21no—
97#4339—21no—
98#4339D812yes—
99#4339C2×D412yes—
100C2×D44—22no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44D811yescharacteristic
107C2×C4×D11—21no—
108C2×Dic22D811yescharacteristic
109C11×Q16—22no—
110C11×Q16—22no—
111C11×Q16—41no—
112C11×Q16—41no—
113C11×M16—22no—
114C11×M16—41no—
115C2×C8×C11—41no—
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#4318—21no—
125#4318—22no—
126#4318—41no—
127#4318C2×D412yes—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—41no—
130D88—22no—
131D88—22no—
132D88—44no—
133D88—41no—
134D88—41no—
135#4314—44no—
136#4313—22no—
137#4313—22no—
138C8×D11—22no—
139C8×D11—22no—
140C11×C16—22no—
141C11⋊C16C2×D412yes—
142C11⋊C16C2×D412yes—
143C22×SD32—111no—
144C2×#504—111no—
145C2×#473—111no—
146C2×#472—111no—
147#2223—118no—
148C2×#368—111no—
149C2×#362D1111yescharacteristic, complemented
150C2×#361—111no—
151C23×C11#13511yescharacteristic
152C22×D11—21no—
153C22×D11—42no—
154C22×D11—81no—
155C22×D11—81no—
156C22×D11—162no—
157Q8×C11—42no—
158Q8×C11—42no—
159Q8×C11—81no—
160Q8×C11—81no—
161C2×C4×C11—42no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11#13511yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C22⋊D11—22no—
171C22⋊D11—22no—
172C2×Dic11—21no—
173D44—21no—
174D44—42no—
175D44—42no—
176D44—81no—
177D44—81no—
178D44C2×D812yes—
179C4×D11—22no—
180C4×D11—22no—
181Dic22—21no—
182Dic22C2×D812yes—
183C8×C11—42no—
184C8×C11#12111yescharacteristic
185C8×C11#12111yescharacteristic
186C8×C11C22×D411yescharacteristic
187C8×C11C2×#4111yescharacteristic
188C11⋊C8—22no—
189C11⋊C8—42no—
190C2×#137—221no—
191C2×AGL(1,ℤ/8)—221no—
192C22×Q16C2×D1111yescharacteristic
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—221no—
202C2×M32C2×D1111yescharacteristic
203C22×C16—111no—
204C22×C16—221no—
205#473—114no—
206#473—222no—
207#472—114no—
208#472—222no—
209C2×#108—111no—
210C2×#108C2×D1111yescharacteristic
211C2×#101—221no—
212C2×#100—221no—
213#368—114no—
214#362C2×D1114yescomplemented
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—82no—
227C4×C11#46611yescharacteristic
228C4×C11#46611yescharacteristic
229C4×C11C2×#12111yescharacteristic
230C4×C11C22×D811yescharacteristic
231Dic11—22no—
232C2×#41—111no—
233C22×Q8—21no—
234C22×D4—221no—
235#137—224no—
236#137—442no—
237AGL(1,ℤ/8)—224no—
238AGL(1,ℤ/8)—442no—
239C2×Q16—21no—
240C2×Q16—21no—
241C2×Q16—21no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—441no—
245C2×Q16C22×D1112yes—
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—111no—
261C2×M16—221no—
262C2×M16—221no—
263C22×C8—221no—
264C22×C8C22×D1111yescharacteristic
265SD32—224no—
266SD32—224no—
267M32—21no—
268M32—224no—
269M32C22×D1112yes—
270C2×C16—21no—
271C2×C16—111no—
272C2×C16—111no—
273C2×C16—112no—
274C2×C16—112no—
275C2×C16—224no—
276#108—21no—
277#108—112no—
278#108—221no—
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—22no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—111no—
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—41no—
309C22×C4—221no—
310C22×C4D4×D1111yescharacteristic
311Q16—22no—
312Q16—22no—
313Q16—41no—
314Q16—41no—
315Q16—444no—
316SD16—444no—
317SD16—444no—
318D8—222no—
319D8—222no—
320D8—444no—
321D8—441no—
322D8—441no—
323M16—22no—
324M16—41no—
325M16—112no—
326M16—221no—
327M16—222no—
328M16—222no—
329M16—222no—
330M16—441no—
331C2×C8—41no—
332C2×C8—221no—
333C2×C8—222no—
334C2×C8—222no—
335C2×C8—441no—
336C2×C8#433911yescharacteristic
337C2×C8#433911yescharacteristic
338C2×C8D4×D1111yescharacteristic
339C2×C8D4×D1111yescharacteristic
340C2×C8D4×D1111yescharacteristic
341C2×C8C23×D1111yescharacteristic
342C16—22no—
343C16—112no—
344C16—112no—
345C11C2×#222311yescharacteristic, complemented, Sylow
346C23—221no—
347C23—442no—
348C23—881no—
349C23—881no—
350C23—1762no—
351C23#6696911yescharacteristic
352Q8—42no—
353Q8—42no—
354Q8—81no—
355Q8—81no—
356Q8—112no—
357Q8—221no—
358D4—112no—
359D4—222no—
360D4—222no—
361D4—221no—
362D4—442no—
363D4—442no—
364D4—881no—
365D4—881no—
366C2×C4—42no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—221no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4#6693711yescharacteristic
373C2×C4#6693711yescharacteristic
374C2×C4D8×D1111yescharacteristic
375C2×C4D8×D1111yescharacteristic
376C2×C4#6696911yescharacteristic
377C2×C4C2×D4×D1111yescharacteristic
378C8—42no—
379C8—222no—
380C8—442no—
381C8#6693711yescharacteristic
382C8#6693711yescharacteristic
383C8C2×#433911yescharacteristic
384C8C2×D4×D1111yescharacteristic
385C22—22no—
386C22—222no—
387C22—442no—
388C22—882no—
389C22—1762no—
390C22—1762no—
391C22—1762no—
392C22#1062238811yescharacteristic
393C22#1062238811yescharacteristic
394C22C2×#6696911yescharacteristic
395C4—82no—
396C4—222no—
397C4#1062238811yescharacteristic
398C4#1062238811yescharacteristic
399C4C2×#6693711yescharacteristic
400C4C2×D8×D1111yescharacteristic
401C2—21no—
402C2—21no—
403C2—442no—
404C2—1762no—
405C2#1307074912yesdirect product factor
406C2C2×#1062238811yescharacteristic
subgroupG/H
centerC22#10622388
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#362C2
socleC22×C11#466
prime radicalC2×#10622510C2
hypercenterC2×#362D11
hypocenterC11C2×#2223
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
1. C22×#66892C2semidirect
2. C2×#10622520C2semidirect
3. C2×#10622805C2semidirect
5. #13070749C2direct (N × H)
6. C2×#10622131C2semidirect
7. C2×#10622154C2semidirect
8. C2×C11×#362C2semidirect
18. #10622805C22semidirect
22. C2×#66892C22semidirect
27. #10622520C22semidirect
32. C11×#362C22semidirect
33. #10622154C22semidirect
34. #10622131C22semidirect
149. C2×#362D11semidirect
214. #362C2×D11semidirect
284. C2×C11#2223semidirect
345. C11C2×#2223semidirect
405. C2#13070749direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668922
C2×#106225202
C2×#106228052
C2×#106225102
#130707492
C2×#106221312
C2×#106221542
C2×C11×#3622
C2×#222311