Finite Group Databasebeta

← C2×#13068061 #14736166

Subgroups — C2×#13068061 #14736166

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622307C211yesmaximal, characteristic
2C2×#10622462C211yesmaximal, characteristic, complemented
3C2×#10622461C211yesmaximal, characteristic
4C2×C8×Dic22C211yesmaximal, characteristic, complemented
5#13068061C218yesmaximal, direct product factor
6C2×#10622120C211yesmaximal, characteristic, complemented
7C2×#10622123C211yesmaximal, characteristic
8C2×C11×#335C211yesmaximal, characteristic, complemented
9C22×Dic44—21no—
10C22×#4314—21no—
11C2×#66927C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C2×C4×Dic22C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C2×#66885—21no—
18C2×#66885—21no—
19C2×#66885—21no—
20C2×#66880—21no—
21C2×Dic11⋊C8—21no—
22C2×C8×Dic11—21no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622462—22no—
25#10622462C2214yescomplemented
26#10622461—22no—
27#10622461C2214yes—
28#10622307—22no—
29#10622307C2214yes—
30C8×Dic22—22no—
31C8×Dic22C2214yescomplemented
32C11×#335C2214yescomplemented
33#10622123C2214yes—
34#10622120C2214yescomplemented
35C22×D44—21no—
36C22×D44—21no—
37C22×D44—21no—
38C22×Dic22—21no—
39C22×Dic22D411yescharacteristic
40C22×C8×C11—21no—
41C22×C8×C11—21no—
42C22×C8×C11D411yescharacteristic
43C22×C8×C11D411yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11D411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50C22×C11⋊C8—21no—
51C2×Dic44—24no—
52C2×Dic44—44no—
53C2×#4314—24no—
54C2×#4314—44no—
55#66927—21no—
56#66927—21no—
57#66927—21no—
58#66927C2312yes—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62#66922C2312yes—
63C4×Dic22—21no—
64C4×Dic22—21no—
65C4×Dic22D412yes—
66C4×Dic22C2312yes—
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×C4⋊C8C2312yes—
71C4×C8×C11D412yes—
72C4×C8×C11C2312yes—
73#66885—24no—
74#66885—24no—
75#66885—24no—
76#66880—24no—
77Dic11⋊C8—24no—
78C8×Dic11—24no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)C2312yes—
81C2×#1682—111nomaximal, Sylow
82C23×D11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—41no—
89C2×D44—22no—
90C2×D44—22no—
91C2×D44—22no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—42no—
96C2×D44—42no—
97C2×D44—42no—
98C2×D44—42no—
99C2×D44—82no—
100C2×Dic22—21no—
101C2×Dic22—22no—
102C2×Dic22—22no—
103C2×Dic22—41no—
104C2×Dic22—42no—
105C2×Dic22—42no—
106C2×Dic22D814yes—
107C2×Dic22C2×D412yes—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—42no—
113C2×C8×C11—42no—
114C2×C8×C11C2×D412yes—
115C2×C8×C11C2×D412yes—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120C4⋊Dic11—21no—
121C4⋊Dic11—22no—
122C4⋊Dic11—22no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125C4⋊Dic11C2×D412yes—
126Dic11⋊C4—22no—
127Dic11⋊C4—22no—
128C4×Dic11—22no—
129C4×Dic11—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132Dic44—48no—
133#4314—48no—
134C2×#486—111no—
135C2×#462—111no—
136C2×#460—111no—
137C2×C8×Q8—111no—
138#1682—118no—
139C2×#335D1111yescharacteristic, complemented
140C2×#332—111no—
141C2×#331—111no—
142C23×C11#12111yescharacteristic
143C22×D11—42no—
144C22×D11—82no—
145C22×D11—82no—
146C22×D11—82no—
147C2×C4×C11—22no—
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11C2×D812yes—
152C2×C4×C11#13512yes—
153C2×C4×C11#13512yes—
154C2×C4×C11#13712yes—
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C2×Dic11—22no—
159C2×Dic11—24no—
160C2×Dic11—22no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—82no—
164D44—42no—
165D44—42no—
166D44—42no—
167D44—42no—
168D44—82no—
169D44—82no—
170D44—82no—
171D44—82no—
172Dic22—22no—
173Dic22—24no—
174Dic22—42no—
175Dic22—42no—
176Dic22—82no—
177Dic22C2×D814yes—
178C8×C11—22no—
179C8×C11—22no—
180C8×C11—42no—
181C8×C11—42no—
182C11⋊C8—42no—
183C22×Q16—221no—
184C22×SD16—221no—
185C2×C4⋊Q8—111no—
186C2×#127—111no—
187C2×C4×Q8—111no—
188#486—114no—
189#486—222no—
190#462—114no—
191#462—222no—
192#460—114no—
193#460—222no—
194C8×Q8—114no—
195C8×Q8—222no—
196C2×C4⋊C8—111no—
197C2×C4⋊C8—221no—
198C2×C4⋊C8C2×D1111yescharacteristic
199C2×C4⋊C8C2×D1111yescharacteristic
200C2×#103—221no—
201C2×#102—221no—
202C2×#102—221no—
203C2×#102—221no—
204C2×C4×C8—221no—
205C2×C4×C8C2×D1111yescharacteristic
206#335C2×D1114yescomplemented
207#332—114no—
208#331—114no—
209C22×C11#46412yes—
210C22×C11#46612yes—
211C22×C11#47112yes—
212C22×C11C2×#12111yescharacteristic
213C2×D11—82no—
214C2×D11—82no—
215C2×D11—82no—
216C2×D11—164no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11#46412yes—
220C4×C11#46612yes—
221C4×C11C22×D811yescharacteristic
222C4×C11C2×#13511yescharacteristic
223C4×C11C2×#13511yescharacteristic
224C4×C11C2×#13711yescharacteristic
225Dic11—24no—
226Dic11—42no—
227Dic11—82no—
228C22×Q8—111no—
229C22×Q8—221no—
230C22×D4—221no—
231C22×D4—221no—
232C22×D4—221no—
233C2×Q16—224no—
234C2×Q16—444no—
235C2×SD16—224no—
236C2×SD16—444no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—221no—
240C22×C8D4411yescharacteristic
241C22×C8D4411yescharacteristic
242C4⋊Q8—112no—
243C4⋊Q8—221no—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
246#127—112no—
247#127—221no—
248#127—221no—
249#127—221no—
250C4×Q8—112no—
251C4×Q8—112no—
252C4×Q8—221no—
253C4×Q8—221no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—221no—
258C2×C42—221no—
259C2×C42C22×D1111yescharacteristic
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—112no—
263C4⋊C8—224no—
264C4⋊C8—221no—
265C4⋊C8C22×D1112yes—
266C4⋊C8C22×D1112yes—
267#103—224no—
268#102—224no—
269#102—224no—
270#102—224no—
271C4×C8—224no—
272C4×C8D4412yes—
273C4×C8C22×D1112yes—
274C2×C11#168214yescomplemented
275C2×C11C2×#46411yescharacteristic
276C2×C11C2×#46611yescharacteristic
277C2×C11C2×#47111yescharacteristic
278D11—162no—
279C24—441no—
280C2×Q8—114no—
281C2×Q8—112no—
282C2×Q8—221no—
283C2×Q8—222no—
284C2×Q8—222no—
285C2×Q8—441no—
286C2×Q8—442no—
287C2×Q8—442no—
288C2×D4—222no—
289C2×D4—222no—
290C2×D4—222no—
291C2×D4—441no—
292C2×D4—441no—
293C2×D4—441no—
294C2×D4—442no—
295C2×D4—442no—
296C2×D4—442no—
297C2×D4—442no—
298C2×D4—882no—
299C22×C4—221no—
300C22×C4—221no—
301C22×C4—441no—
302C22×C4C2×D4411yescharacteristic
303C22×C4D4×D1111yescharacteristic
304C22×C4#434311yescharacteristic
305Q16—448no—
306SD16—448no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—42no—
312C2×C8—42no—
313C2×C8—222no—
314C2×C8—442no—
315C2×C8C2×D4412yes—
316C2×C8C2×D4412yes—
317C4⋊C4—112no—
318C4⋊C4—221no—
319C4⋊C4—222no—
320C4⋊C4—222no—
321C4⋊C4—222no—
322C4⋊C4—222no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C42—222no—
326C42—222no—
327C42C2×D4411yescharacteristic
328C42D4×D1111yescharacteristic
329C42#434311yescharacteristic
330C42C23×D1111yescharacteristic
331C11C2×#168211yescharacteristic, complemented, Sylow
332C23—442no—
333C23—882no—
334C23—882no—
335C23—882no—
336C23#6694811yescharacteristic
337Q8—114no—
338Q8—224no—
339Q8—222no—
340Q8—442no—
341Q8—442no—
342Q8—882no—
343D4—442no—
344D4—442no—
345D4—442no—
346D4—442no—
347D4—882no—
348D4—882no—
349D4—882no—
350D4—882no—
351C2×C4—22no—
352C2×C4—224no—
353C2×C4—222no—
354C2×C4—222no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—882no—
358C2×C4#6694811yescharacteristic
359C2×C4#6694811yescharacteristic
360C2×C4#6694811yescharacteristic
361C2×C4#6695712yes—
362C2×C4#6696212yes—
363C2×C4D8×D1112yes—
364C2×C4#6697212yes—
365C2×C4C22×D4411yescharacteristic
366C2×C4C2×D4×D1111yescharacteristic
367C2×C4C2×#434311yescharacteristic
368C8—22no—
369C8—22no—
370C8—42no—
371C8—42no—
372C8—442no—
373C22—882no—
374C22—882no—
375C22—882no—
376C22—1764no—
377C22#1062245812yes—
378C22#1062249612yes—
379C22#1062251112yes—
380C22C2×#6694811yescharacteristic
381C4—21no—
382C4—21no—
383C4—224no—
384C4—442no—
385C4—882no—
386C4#1062245812yes—
387C4#1062249612yes—
388C4C2×#6695711yescharacteristic
389C4C2×#6696211yescharacteristic
390C4C2×D8×D1111yescharacteristic
391C4C2×#6697211yescharacteristic
392C2—1762no—
393C2#1306806114yesdirect product factor
394C2C2×#1062245811yescharacteristic
395C2C2×#1062249611yescharacteristic
396C2C2×#1062251111yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#335C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenterC2×#335D11
hypocenterC11C2×#1682
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. C2×#10622462C2semidirect
4. C2×C8×Dic22C2semidirect
5. #13068061C2direct (N × H)
6. C2×#10622120C2semidirect
8. C2×C11×#335C2semidirect
25. #10622462C22semidirect
31. C8×Dic22C22semidirect
32. C11×#335C22semidirect
34. #10622120C22semidirect
139. C2×#335D11semidirect
206. #335C2×D11semidirect
274. C2×C11#1682semidirect
331. C11C2×#1682semidirect
393. C2#13068061direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106223072
C2×#106224622
C2×#106224612
C2×C8×Dic222
#130680612
C2×#106221202
C2×#106221232
C2×C11×#3352
C2×#168211