Finite Group Databasebeta

← C2×#13068179 #14736340

Subgroups — C2×#13068179 #14736340

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic
3C2×#10622625C211yesmaximal, characteristic, complemented
4#13068179C218yesmaximal, direct product factor
5C2×#10622118C211yesmaximal, characteristic, complemented
6C2×#10622185C211yesmaximal, characteristic, complemented
7C2×#10622123C211yesmaximal, characteristic, complemented
8C2×C11×#461C211yesmaximal, characteristic, complemented
9C22×C11×SD16—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C22×#4323—21no—
13C22×#4318—21no—
14C2×#66927C2211yescharacteristic
15C11×#461—22no—
16C11×#461C2214yescomplemented
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#103—21no—
19C2×C22⋊(C11⋊C8)—21no—
20#10622701—22no—
21#10622701C2214yescomplemented
22#10622628—22no—
23#10622628C2214yes—
24#10622625—22no—
25#10622625C2214yescomplemented
26C2×#66873—21no—
27C2×#66873—21no—
28C2×#66873—21no—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622185C2214yescomplemented
33#10622123C2214yescomplemented
34#10622118C2214yescomplemented
35C22×Q8×C11—21no—
36C22×D4×C11D411yescharacteristic
37C23×C4×C11—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—21no—
41C2×C11×SD16—24no—
42C2×C11×SD16—44no—
43C22×C8×C11—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8C2312yes—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11D412yes—
51C4×D4×C11C2312yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C42×C11C2311yescharacteristic
57C2×#4323—24no—
58C2×#4323—44no—
59C2×#4318—24no—
60C2×#4318—44no—
61C22×C11⋊C8—21no—
62C22×C11⋊C8—21no—
63C22×C11⋊C8D411yescharacteristic
64C22×C11⋊C8D411yescharacteristic
65#66927—21no—
66#66927—21no—
67#66927—21no—
68#66927C2312yes—
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2312yes—
71C11×#103—24no—
72C22⋊(C11⋊C8)—24no—
73#66873—24no—
74#66873—24no—
75#66873—24no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)C2312yes—
79C4⋊(C11⋊C8)C2312yes—
80C4×C11⋊C8D412yes—
81C4×C11⋊C8C2312yes—
82C2×#1701—111nomaximal, Sylow
83C24×C11—21no—
84C23×D11—41no—
85C2×Q8×C11—22no—
86C2×Q8×C11—41no—
87C2×Q8×C11—42no—
88C2×Q8×C11—42no—
89C2×D4×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11C2×D412yes—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C2×D44—22no—
103C2×D44—22no—
104C2×D44—22no—
105C2×D44—41no—
106C2×D44—41no—
107C2×D44—41no—
108C2×D44—42no—
109C2×D44—42no—
110C2×D44—42no—
111C2×D44—42no—
112C2×D44—82no—
113C11×SD16—48no—
114C2×C8×C11—22no—
115C2×C8×C11—42no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4C2×D412yes—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—22no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11C2411yescharacteristic
128#4323—48no—
129#4318—48no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—42no—
135C2×C11⋊C8—42no—
136C2×C11⋊C8C2×D412yes—
137C2×C11⋊C8C2×D412yes—
138C2×#486—111no—
139C2×#461D1111yescharacteristic, complemented
140C2×#459—111no—
141C2×#436—111no—
142#1701—118no—
143C2×#334—111no—
144C2×#332—111no—
145C2×#331—111no—
146C23×C11—22no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11#12111yescharacteristic
151C22×D11—42no—
152C22×D11—82no—
153C22×D11—82no—
154C22×D11—82no—
155Q8×C11—42no—
156Q8×C11—42no—
157Q8×C11—82no—
158D4×C11—22no—
159D4×C11—22no—
160D4×C11—42no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—44no—
167C2×C4×C11—42no—
168C2×C4×C11—82no—
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#13512yes—
173C2×C4×C11AGL(1,ℤ/8)12yes—
174C2×C4×C11AGL(1,ℤ/8)12yes—
175C2×C4×C11AGL(1,ℤ/8)12yes—
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179D44—42no—
180D44—42no—
181D44—42no—
182D44—42no—
183D44—82no—
184D44—82no—
185D44—82no—
186D44—82no—
187C8×C11—42no—
188C11⋊C8—22no—
189C11⋊C8—22no—
190C11⋊C8—42no—
191C11⋊C8—42no—
192C22×SD16—21no—
193C22×D8—221no—
194C22×M16—221no—
195C2×C4⋊Q8C2×D1111yescharacteristic
196C2×#127—111no—
197C2×C4×D4C2×D1111yescharacteristic
198#486—114no—
199#486—222no—
200#461—22no—
201#461C2×D1114yescomplemented
202#459—114no—
203#459—222no—
204#436—114no—
205#436—222no—
206C2×C4⋊C8—111no—
207C2×C4⋊C8—111no—
208C2×C4⋊C8C2×D1111yescharacteristic
209C2×#103—21no—
210C2×#102—221no—
211C2×#102—221no—
212C2×#102—221no—
213C2×C22⋊C8—221no—
214C2×C4×C8—111no—
215#334—114no—
216#332—114no—
217#331—114no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—84no—
222C22×C11#46312yes—
223C22×C11#46912yes—
224C22×C11#47112yes—
225C22×C11C2×#12111yescharacteristic
226C2×D11—82no—
227C2×D11—82no—
228C2×D11—82no—
229C2×D11—164no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11—82no—
234C4×C11#46312yes—
235C4×C11#46912yes—
236C4×C11C2×#13511yescharacteristic
237C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
238C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
239C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
240C22×Q8—21no—
241C22×D4—221no—
242C22×D4—221no—
243C22×D4—221no—
244C22×D4C22⋊D1111yescharacteristic
245C23×C4—21no—
246C2×SD16—24no—
247C2×SD16—44no—
248C2×D8—224no—
249C2×D8—444no—
250C2×M16—224no—
251C2×M16—444no—
252C22×C8—21no—
253C22×C8—111no—
254C22×C8—111no—
255C22×C8—221no—
256C22×C8—221no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8C22×D1112yes—
261#127—112no—
262#127—221no—
263#127—221no—
264#127—221no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4C22⋊D1112yes—
268C4×D4C22×D1112yes—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C22⋊D1111yescharacteristic
272C2×C22⋊C4—21no—
273C2×C42C22×D1111yescharacteristic
274C4⋊C8—21no—
275C4⋊C8—112no—
276C4⋊C8—112no—
277C4⋊C8—221no—
278C4⋊C8—221no—
279C4⋊C8C22×D1112yes—
280#103—24no—
281#102—224no—
282#102—224no—
283#102—224no—
284C22⋊C8—224no—
285C4×C8—112no—
286C4×C8—112no—
287C2×C11—82no—
288C2×C11#170114yescomplemented
289C2×C11C2×#46311yescharacteristic
290C2×C11C2×#46911yescharacteristic
291C2×C11C2×#47111yescharacteristic
292D11—162no—
293C24—21no—
294C24—441no—
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—42no—
298C2×Q8—42no—
299C2×D4—22no—
300C2×D4—21no—
301C2×D4—22no—
302C2×D4—222no—
303C2×D4—222no—
304C2×D4—222no—
305C2×D4—442no—
306C2×D4—442no—
307C2×D4—442no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—442no—
312C2×D4—882no—
313C2×D4C2×C22⋊D1112yes—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—41no—
320C22×C4D4×D1111yescharacteristic
321C22×C4#434111yescharacteristic
322C22×C4C2×C22⋊D1111yescharacteristic
323SD16—48no—
324D8—448no—
325M16—448no—
326C2×C8—22no—
327C2×C8—42no—
328C2×C8—112no—
329C2×C8—112no—
330C2×C8—222no—
331C2×C8—222no—
332C2×C8—222no—
333C2×C8—222no—
334C2×C8—442no—
335C2×C8—442no—
336C4⋊C4—21no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4C2×C22⋊D1112yes—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C42D4×D1111yescharacteristic
345C42#434111yescharacteristic
346C42C2×C22⋊D1111yescharacteristic
347C42C23×D1111yescharacteristic
348C11C2×#170111yescharacteristic, complemented, Sylow
349C23—22no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—442no—
354C23—882no—
355C23—882no—
356C23—882no—
357C23#6699211yescharacteristic
358Q8—42no—
359Q8—42no—
360Q8—82no—
361D4—22no—
362D4—22no—
363D4—42no—
364D4—442no—
365D4—442no—
366D4—442no—
367D4—442no—
368D4—882no—
369D4—882no—
370D4—882no—
371D4—882no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—42no—
375C2×C4—44no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—82no—
380C2×C4#6696712yes—
381C2×C4#6696912yes—
382C2×C4#6698512yes—
383C2×C4#6699211yescharacteristic
384C2×C4#6699211yescharacteristic
385C2×C4#6699211yescharacteristic
386C2×C4#6700212yes—
387C2×C4C2×D4×D1111yescharacteristic
388C2×C4C2×#434111yescharacteristic
389C2×C4C22×C22⋊D1111yescharacteristic
390C8—42no—
391C8—222no—
392C8—222no—
393C8—442no—
394C8—442no—
395C22—42no—
396C22—42no—
397C22—42no—
398C22—84no—
399C22—882no—
400C22—882no—
401C22—882no—
402C22—1764no—
403C22#1062265212yes—
404C22#1062277812yes—
405C22#1062281612yes—
406C22C2×#6699211yescharacteristic
407C4—21no—
408C4—21no—
409C4—42no—
410C4—82no—
411C4#1062265212yes—
412C4#1062277812yes—
413C4C2×#6696711yescharacteristic
414C4C2×#6696911yescharacteristic
415C4C2×#6698511yescharacteristic
416C4C2×#6700211yescharacteristic
417C2—82no—
418C2—1762no—
419C2#1306817914yesdirect product factor
420C2C2×#1062277811yescharacteristic
421C2C2×#1062265211yescharacteristic
422C2C2×#1062281611yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#461C2
socleC23×C11#121
prime radicalC2×#10622628C2
hypercenterC2×#461D11
hypocenterC11C2×#1701
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10622701C2semidirect
3. C2×#10622625C2semidirect
4. #13068179C2direct (N × H)
5. C2×#10622118C2semidirect
6. C2×#10622185C2semidirect
7. C2×#10622123C2semidirect
8. C2×C11×#461C2semidirect
16. C11×#461C22semidirect
21. #10622701C22semidirect
25. #10622625C22semidirect
32. #10622185C22semidirect
33. #10622123C22semidirect
34. #10622118C22semidirect
139. C2×#461D11semidirect
201. #461C2×D11semidirect
288. C2×C11#1701semidirect
348. C11C2×#1701semidirect
419. C2#13068179direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106226282
C2×#106226252
#130681792
C2×#106221182
C2×#106221852
C2×#106221232
C2×C11×#4612
C2×#170111