Finite Group Databasebeta

← C4×#10622521 #14907095

Subgroups — C4×#10622521 #14907095

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622521C211yesmaximal, characteristic
2C4×#66957C211yesmaximal, characteristic, complemented
3C2×C4×D88C211yesmaximal, characteristic, complemented
4#13070493C212yesmaximal, complemented
5#13070482C212yesmaximal, complemented
6C4×#66864C212yesmaximal, complemented
7C4×D176C212yesmaximal, complemented
8#13070404C211yesmaximal, characteristic, complemented
9#13070333C211yesmaximal, characteristic, complemented
10#13070329C211yesmaximal, characteristic, complemented
11C4×C11×M32C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13C22×D88C2211yescharacteristic
14C4×#4339—21no—
15C2×C4×D44—21no—
16C2×C11×M32C2211yescharacteristic
17C2×C11×M32C2211yescharacteristic
18C2×C4×C8×C11C2211yescharacteristic
19#10622726—21no—
20C2×#66885—21no—
21#10622719C2211yescharacteristic
22C2×#66882C2211yescharacteristic
23#10622521C418yesdirect product factor
24C2×#66864C2212yes—
25C2×D176C2212yes—
26C4×Dic44C2211yescharacteristic, complemented
27C4×Dic44C2211yescharacteristic, complemented
28C4×D88—21no—
29C4×D88—21no—
30C4×D88C2212yes—
31C4×D88C2212yes—
32C4×D88C2211yescharacteristic, complemented
33C4×D88C2211yescharacteristic, complemented
34C4×#4314—21no—
35C4×#4314—21no—
36C11×#346C2212yescomplemented
37C4×C11×C16C2212yescomplemented
38#10622147C2212yes—
39#10622147C2212yes—
40#10622147C2212yescomplemented
41#10622143C2212yescomplemented
42#10622142C2212yescomplemented
43#10622141C2212yescomplemented
44C2×#4339—21no—
45C22×D44—21no—
46C22×C4×D11—41no—
47C22×C8×C11D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C2×C42×C11D411yescharacteristic
50C4×C22⋊D11—41no—
51C4×C22⋊D11—41no—
52C2×(C2×D11)⋊C4—41no—
53#66979—21no—
54C2×C4⋊Dic11—21no—
55C2×Dic44C2311yescharacteristic
56#66957—22no—
57#66957C2×C414yescomplemented
58C2×D88—21no—
59C2×D88—22no—
60C2×D88C2×C414yescomplemented
61C2×D88C2312yes—
62C2×D88C2311yescharacteristic
63C2×#4314—21no—
64C4×D44—22no—
65C4×D44—22no—
66C4×D44—21no—
67C4×D44—21no—
68C4×D44—41no—
69C4×D44—41no—
70#66925—41no—
71C42×D11—41no—
72C4×Dic22—21no—
73C4×Dic22—21no—
74C11×M32—22no—
75C11×M32C2×C414yescomplemented
76C2×C11×C16C2312yes—
77C2×C11×C16C2312yes—
78C4×C8×C11D411yescharacteristic
79C4×C8×C11D411yescharacteristic
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66885—22no—
83#66885—22no—
84#66885—21no—
85#66885—21no—
86#66882—21no—
87#66882C2312yes—
88#66882C2311yescharacteristic
89#66882C2311yescharacteristic
90#66881—21no—
91#66880—21no—
92#66880—21no—
93#66864C2×C418yescomplemented
94D176C2×C418yescomplemented
95C4×#509—111nomaximal, Sylow
96C23×D11—41no—
97C22×C4×C11D811yescharacteristic
98C22×C4×C11D811yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C2×C22⋊D11—41no—
101C22×Dic11—41no—
102#4339—24no—
103#4339—42no—
104C2×D44—24no—
105C2×D44—21no—
106C2×D44—22no—
107C2×D44—41no—
108C2×D44—42no—
109C2×C4×D11—41no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C2×C4×D11—42no—
113C2×C4×D11—42no—
114C2×C4×D11—84no—
115C2×Dic22—21no—
116C2×C8×C11—22no—
117C2×C8×C11C22×C412yes—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11#4112yes—
122C2×C8×C11C2411yescharacteristic
123C42×C11D811yescharacteristic
124C42×C11D811yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C22⋊Dic11—41no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—42no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—22no—
135C4⋊Dic11—41no—
136Dic11⋊C4—41no—
137Dic11⋊C4—41no—
138C4×Dic11—41no—
139C4×Dic11—41no—
140C4×Dic11—41no—
141Dic44—21no—
142Dic44C22×C412yescomplemented
143D88—24no—
144D88—22no—
145D88—21no—
146D88C22×C414yes—
147D88C22×C412yescomplemented
148#4314—24no—
149C11×C16—22no—
150C11×C16C22×C414yescomplemented
151C2×#509—111no—
152C4×#135—111no—
153C2×C4×D8—111no—
154#2177—112no—
155#2175—112no—
156C4×SD32—112no—
157C4×D16—112no—
158#2159—111no—
159#2140—111no—
160#2139—111no—
161C4×M32D1111yescharacteristic, complemented
162C23×C11C2×D811yescharacteristic
163C22×D11—41no—
164C22×D11—42no—
165C22×D11—44no—
166C22×D11—82no—
167C22×D11—82no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11C4×D412yes—
171C2×C4×C11C2×D811yescharacteristic
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11#13512yes—
177C2×C4×C11C22×D411yescharacteristic
178C22⋊D11—44no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—42no—
183C2×Dic11—82no—
184D44—22no—
185D44—24no—
186D44—42no—
187D44—41no—
188D44—44no—
189C4×D11—44no—
190C4×D11—82no—
191C4×D11—84no—
192C4×D11—82no—
193C4×D11—84no—
194Dic22—22no—
195Dic22—41no—
196C8×C11—21no—
197C8×C11—21no—
198C8×C11C4×D412yes—
199C8×C11C23×C411yescharacteristic
200C8×C11C2×#4111yescharacteristic
201C2×#135—111no—
202C22×D8—111no—
203C4×#41—221no—
204C2×C4×D4—221no—
205#509—118no—
206C2×SD32—112no—
207C2×D16—112no—
208C2×M32C2×D1111yescharacteristic
209C2×M32C2×D1111yescharacteristic
210C4×Q16—111no—
211C4×Q16—111no—
212C4×SD16—221no—
213C4×SD16—221no—
214C4×D8—112no—
215C4×D8—112no—
216C4×D8—111no—
217C4×D8—111no—
218C4×D8—221no—
219C4×D8—221no—
220#427—111no—
221C2×#107—111no—
222#416—221no—
223C2×#102—221no—
224C2×C4×C8C2×D1111yescharacteristic
225#367—112no—
226#366—112no—
227#358—112no—
228#357—112no—
229#357—112no—
230#357—112no—
231#346C2×D1112yescomplemented
232C4×C16C2×D1112yescomplemented
233C22×C11—21no—
234C22×C11—21no—
235C22×C11C4×D812yes—
236C22×C11C22×D811yescharacteristic
237C2×D11—44no—
238C2×D11—42no—
239C2×D11—88no—
240C2×D11—82no—
241C2×D11—81no—
242C2×D11—82no—
243C2×D11—81no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11C4×D812yes—
248C4×C11#50912yescomplemented
249C4×C11C2×C4×D411yescharacteristic
250C4×C11C2×#13511yescharacteristic
251Dic11—42no—
252Dic11—82no—
253Dic11—81no—
254Dic11—81no—
255C2×#41—221no—
256C22×D4—221no—
257C23×C4—441no—
258#135—114no—
259#135—222no—
260C2×Q16—111no—
261C2×SD16—221no—
262C2×D8—114no—
263C2×D8—112no—
264C2×D8—111no—
265C2×D8—221no—
266C2×D8—222no—
267C22×C8D4411yescharacteristic
268C22×C8C22×D1111yescharacteristic
269C4×Q8—221no—
270C4×Q8—221no—
271C4×D4—222no—
272C4×D4—222no—
273C4×D4—221no—
274C4×D4—221no—
275C4×D4—441no—
276C4×D4—441no—
277C4×D4—441no—
278C4×D4—441no—
279#117—221no—
280#117—441no—
281C2×C4⋊C4—221no—
282C2×C22⋊C4—441no—
283C2×C42—441no—
284C2×C42D4411yescharacteristic
285SD32—118no—
286D16—118no—
287M32—22no—
288M32C4×D1114yescomplemented
289C2×C16C22×D1112yes—
290C2×C16C22×D1112yes—
291#107—111no—
292#107—111no—
293#107—112no—
294#107—221no—
295#106—221no—
296#103—221no—
297#103—221no—
298#102—222no—
299#102—222no—
300#102—221no—
301#102—221no—
302C4×C8D4411yescharacteristic
303C4×C8D4411yescharacteristic
304C4×C8C22×D1111yescharacteristic
305C4×C8C22×D1111yescharacteristic
306C2×C11—22no—
307C2×C11C2×C4×D811yescharacteristic
308C2×C11C2×#50911yescharacteristic
309C2×C11#341411yescharacteristic
310D11—82no—
311D11—84no—
312C24—441no—
313#41—224no—
314#41—442no—
315C2×Q8—221no—
316C2×D4—224no—
317C2×D4—222no—
318C2×D4—221no—
319C2×D4—441no—
320C2×D4—441no—
321C2×D4—442no—
322C22×C4—441no—
323C22×C4—441no—
324C22×C4—441no—
325C22×C4—442no—
326C22×C4—441no—
327C22×C4—442no—
328C22×C4—884no—
329C22×C4D8811yescharacteristic
330C22×C4D8811yescharacteristic
331C22×C4C2×D4411yescharacteristic
332Q16—112no—
333Q16—221no—
334SD16—224no—
335D8—112no—
336D8—114no—
337D8—224no—
338D8—222no—
339D8—221no—
340C2×C8—22no—
341C2×C8C2×C4×D1112yes—
342C2×C8C2×D4411yescharacteristic
343C2×C8C2×D4411yescharacteristic
344C2×C8C2×D4411yescharacteristic
345C2×C8#433912yes—
346C2×C8C23×D1111yescharacteristic
347C4⋊C4—222no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C4⋊C4—441no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C22⋊C4—441no—
354C22⋊C4—442no—
355C22⋊C4—442no—
356C22⋊C4—441no—
357C22⋊C4—441no—
358C42—441no—
359C42—441no—
360C42—441no—
361C42D8811yescharacteristic
362C42D8811yescharacteristic
363C42C2×D4411yescharacteristic
364C42C2×D4411yescharacteristic
365C16—22no—
366C16C2×C4×D1114yescomplemented
367C11C4×#50911yescharacteristic, complemented, Sylow
368C23—441no—
369C23—442no—
370C23—444no—
371C23—882no—
372C23—882no—
373C23C2×D8811yescharacteristic
374Q8—222no—
375Q8—441no—
376D4—224no—
377D4—222no—
378D4—444no—
379D4—442no—
380D4—441no—
381D4—444no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—441no—
385C2×C4—444no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—442no—
389C2×C4—884no—
390C2×C4—882no—
391C2×C4—882no—
392C2×C4—884no—
393C2×C4—882no—
394C2×C4C4×D4412yes—
395C2×C4C2×D8811yescharacteristic
396C2×C4C2×D8811yescharacteristic
397C2×C4C2×D8811yescharacteristic
398C2×C4C2×D8811yescharacteristic
399C2×C4C2×D8811yescharacteristic
400C2×C4#6695712yes—
401C2×C4C22×D4411yescharacteristic
402C8—21no—
403C8—21no—
404C8C4×D4412yes—
405C8C22×C4×D1111yescharacteristic
406C8C2×#433911yescharacteristic
407C22—21no—
408C22—21no—
409C22—442no—
410C22—444no—
411C22—888no—
412C22—882no—
413C22—881no—
414C22—881no—
415C22—882no—
416C22C4×D8812yes—
417C22C22×D8811yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—442no—
422C4—882no—
423C4—881no—
424C4—881no—
425C4C4×D8812yes—
426C4#1062252112yesdirect product factor
427C4C2×C4×D4411yescharacteristic
428C4C2×#6695711yescharacteristic
429C2—22no—
430C2—884no—
431C2—882no—
432C2C2×C4×D8811yescharacteristic
433C2C2×#1062252111yescharacteristic
434C2#1308175211yescharacteristic
subgroupG/H
centerC2×C4C2×D88
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC4×C11×M32C2
socleC22×C11C22×D8
prime radicalC2×#10622521C2
cosocleC2×C8×C11C24
hypercenterC4×M32D11
hypocenterC11C4×#509
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×M32

Complements

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

NH ≅ G/Ntype
2. C4×#66957C2semidirect
3. C2×C4×D88C2semidirect
4. #13070493C2semidirect
5. #13070482C2semidirect
6. C4×#66864C2semidirect
7. C4×D176C2semidirect
8. #13070404C2semidirect
9. #13070333C2semidirect
10. #13070329C2semidirect
11. C4×C11×M32C2semidirect
23. #10622521C4direct (N × H)
26. C4×Dic44C22semidirect
27. C4×Dic44C22semidirect
32. C4×D88C22semidirect
33. C4×D88C22semidirect
36. C11×#346C22semidirect
37. C4×C11×C16C22semidirect
40. #10622147C22semidirect
41. #10622143C22semidirect
42. #10622142C22semidirect
43. #10622141C22semidirect
57. #66957C2×C4semidirect
60. C2×D88C2×C4semidirect
75. C11×M32C2×C4semidirect
93. #66864C2×C4semidirect
94. D176C2×C4semidirect
142. Dic44C22×C4semidirect
147. D88C22×C4semidirect
150. C11×C16C22×C4semidirect
161. C4×M32D11semidirect
231. #346C2×D11semidirect
232. C4×C16C2×D11semidirect
248. C4×C11#509semidirect
288. M32C4×D11semidirect
366. C16C2×C4×D11semidirect
367. C11C4×#509semidirect
426. C4#10622521direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225212
C4×#669572
C2×C4×D882
#130704932
#130704822
C4×#668642
C4×D1762
#130704042
#130703332
#130703292
C4×C11×M322
C4×#50911