Finite Group Databasebeta

← C4×C11×#578 #14637366

Subgroups — C4×C11×#578 #14637366

Order 2816.

2658 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#578C211yesmaximal, characteristic
2C4×C11×2−1+4C212yesmaximal, complemented
3C11×#2951C213yesmaximal, complemented
4C11×#2950C213yesmaximal, complemented
5C11×#2947C216yesmaximal, complemented
6C4×C11×#137C216yesmaximal, complemented
7C4×C11×#135C213yesmaximal, complemented
8C2×C4×C11×Q16C213yesmaximal, complemented
9C11×#2913C211yesmaximal, characteristic, complemented
10C11×#2898C212yesmaximal, complemented
11C4×C11×#131C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2212yes—
13C11×#578C4116yesdirect product factor
14C2×C11×#137C2216yes—
15C2×C11×#135C2213yes—
16C22×C11×Q16C2213yes—
17C2×C11×#131C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic
19C11×#520—26no—
20C11×#520C2216yes—
21C11×#520C2212yes—
22C11×#519—22no—
23C11×#519C2216yes—
24C4×C11×#41—26no—
25C4×C11×#41C2216yes—
26C4×C11×#41C2211yescharacteristic
27C2×C4×Q8×C11—22no—
28C2×C4×Q8×C11C2216yes—
29C11×#441C22112yes—
30C11×#440C22112yes—
31C4×C11×Q16C2213yes—
32C4×C11×Q16C2216yes—
33C4×C11×Q16C2216yes—
34C4×C11×Q16C2216yes—
35C4×C11×Q16C2213yes—
36C4×C11×SD16C2216yes—
37C4×C11×SD16C2216yes—
38C4×C11×D8C2211yescharacteristic
39C4×C11×D8C2213yes—
40C11×#428C2216yes—
41C11×#427C2213yes—
42C2×C11×#107C2213yes—
43C11×#419C2216yes—
44C11×#417C2216yes—
45C11×#416C2216yes—
46C2×C11×#103C2216yes—
47C11×#405C2213yes—
48C11×#405C2213yes—
49C4×C11×M16C2213yes—
50C2×C4×C8×C11C2213yes—
51C11×2−1+4—28no—
52C11×2−1+4C2×C4116yescomplemented
53C2×C11×#41—26no—
54C2×C11×#41C2316yes—
55C2×C11×#41C2311yescharacteristic
56C22×Q8×C11—22no—
57C22×Q8×C11C2316yes—
58C11×#137C2×C4148yescomplemented
59C11×#135C2×C4124yescomplemented
60C2×C11×Q16C2×C4124yescomplemented
61C2×C11×Q16C2313yes—
62C2×C11×Q16C2316yes—
63C2×C11×SD16C2316yes—
64C2×C11×D8C2311yescharacteristic
65C11×#131—24no—
66C11×#131C2×C418yescomplemented
67C2×C11×M16C2313yes—
68C2×C11×M16C2313yes—
69C22×C8×C11C2313yes—
70C22×C8×C11C2313yes—
71C4×Q8×C11—22no—
72C4×Q8×C11—26no—
73C4×Q8×C11—26no—
74C4×Q8×C11—26no—
75C4×Q8×C11—26no—
76C4×Q8×C11D411yescharacteristic
77C4×Q8×C11D411yescharacteristic
78C4×Q8×C11C2316yes—
79C4×Q8×C11C23112yes—
80C4×Q8×C11C2316yes—
81C4×D4×C11—26no—
82C4×D4×C11—26no—
83C4×D4×C11—26no—
84C4×D4×C11—212no—
85C4×D4×C11D413yes—
86C4×D4×C11D413yes—
87C4×D4×C11C2312yes—
88C4×D4×C11C2316yes—
89C11×#117—26no—
90C11×#117—212no—
91C11×#117—26no—
92C11×#117C2316yes—
93C11×#117C2313yes—
94C2×C11×C4⋊C4—26no—
95C2×C11×C4⋊C4—26no—
96C2×C11×C4⋊C4C2316yes—
97C2×C42×C11—26no—
98C2×C42×C11—26no—
99C2×C42×C11C2313yes—
100C11×#107C2313yes—
101C11×#107C2316yes—
102C11×#107C2311yescharacteristic
103C11×#106C2316yes—
104C11×#103C2316yes—
105C11×#103C23112yes—
106C11×#103C2316yes—
107C11×#102C2312yes—
108C11×#102C2316yes—
109C11×#97C2316yes—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2313yes—
112C4×C8×C11C2313yes—
113C4×C8×C11C2313yes—
114C4×#578C1111yesmaximal, characteristic, direct product factor, Sylow
115C11×#41—248no—
116C11×#41—212no—
117C11×#41C22×C4124yes—
118C11×#41C22×C414yes—
119C11×#41#4114yes—
120C2×Q8×C11—216no—
121C2×Q8×C11—26no—
122C2×Q8×C11—212no—
123C2×Q8×C11C22×C4124yes—
124C2×Q8×C11C2×D411yescharacteristic
125C2×Q8×C11C2416yes—
126C2×D4×C11—26no—
127C2×D4×C11C2×D413yes—
128C2×D4×C11C2412yes—
129C22×C4×C11—26no—
130C22×C4×C11—26no—
131C22×C4×C11—26no—
132C22×C4×C11—22no—
133C22×C4×C11—26no—
134C22×C4×C11C2×D413yes—
135C22×C4×C11C2×D413yes—
136C22×C4×C11C2413yes—
137C11×Q16C22×C4112yes—
138C11×Q16C22×C4124yes—
139C11×SD16C22×C4124yes—
140C11×D8C22×C414yes—
141C11×M16—26no—
142C11×M16C22×C4112yes—
143C2×C8×C11—26no—
144C2×C8×C11C22×C4112yes—
145C2×C8×C11C2411yescharacteristic
146C2×C8×C11C2413yes—
147C2×C8×C11C2411yescharacteristic
148C2×C8×C11C2413yes—
149C11×C4⋊C4—212no—
150C11×C4⋊C4—26no—
151C11×C4⋊C4—26no—
152C11×C4⋊C4—26no—
153C11×C4⋊C4C2×D413yes—
154C11×C4⋊C4C2×D413yes—
155C11×C4⋊C4C2412yes—
156C11×C4⋊C4C2416yes—
157C11×C22⋊C4—26no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—26no—
160C11×C22⋊C4C2×D416yes—
161C42×C11—26no—
162C42×C11—212no—
163C42×C11—26no—
164C42×C11—26no—
165C42×C11C2×D413yes—
166C42×C11C2×D413yes—
167C42×C11C2413yes—
168C42×C11C2411yescharacteristic
169C2×#578C2×C1111yescharacteristic
170C4×2−1+4C2×C1112yescomplemented
171#2951C2×C1113yescomplemented
172#2950C2×C1113yescomplemented
173#2947C2×C1116yescomplemented
174C4×#137C2×C1116yescomplemented
175C4×#135C2×C1113yescomplemented
176C2×C4×Q16C2×C1113yescomplemented
177#2913C2×C1111yescharacteristic, complemented
178#2898C2×C1112yescomplemented
179C4×#131C2×C1111yescharacteristic, complemented
180C23×C11—22no—
181C23×C11C22×D413yes—
182Q8×C11—224no—
183Q8×C11—26no—
184Q8×C11C4×D414yes—
185Q8×C11C23×C4112yes—
186D4×C11—224no—
187D4×C11—22no—
188D4×C11C4×D4112yes—
189D4×C11C23×C414yes—
190C2×C4×C11—224no—
191C2×C4×C11—26no—
192C2×C4×C11—224no—
193C2×C4×C11—26no—
194C2×C4×C11—22no—
195C2×C4×C11—26no—
196C2×C4×C11—43no—
197C2×C4×C11—44no—
198C2×C4×C11—86no—
199C2×C4×C11—86no—
200C2×C4×C11C23×C416yes—
201C2×C4×C11C22×D413yes—
202C2×C4×C11C22×D413yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D413yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4116yes—
207C2×C4×C11C2511yescharacteristic
208C8×C11—21no—
209C8×C11—23no—
210C8×C11C23×C412yes—
211C8×C11C23×C416yes—
212C2×2−1+4C22×C1112yes—
213#578C4×C11116yesdirect product factor
214C2×#137C22×C1116yes—
215C2×#135C22×C1113yes—
216C22×Q16C22×C1113yes—
217C2×#131C22×C1111yescharacteristic
218C2×#131C22×C1111yescharacteristic
219#520—26no—
220#520C22×C1116yes—
221#520C22×C1112yes—
222#519—22no—
223#519C22×C1116yes—
224C4×#41—26no—
225C4×#41C22×C1116yes—
226C4×#41C22×C1111yescharacteristic
227C2×C4×Q8—22no—
228C2×C4×Q8C22×C1116yes—
229#441C22×C11112yes—
230#440C22×C11112yes—
231C4×Q16C22×C1113yes—
232C4×Q16C22×C1116yes—
233C4×Q16C22×C1116yes—
234C4×Q16C22×C1116yes—
235C4×Q16C22×C1113yes—
236C4×SD16C22×C1116yes—
237C4×SD16C22×C1116yes—
238C4×D8C22×C1111yescharacteristic
239C4×D8C22×C1113yes—
240#428C22×C1116yes—
241#427C22×C1113yes—
242C2×#107C22×C1113yes—
243#419C22×C1116yes—
244#417C22×C1116yes—
245#416C22×C1116yes—
246C2×#103C22×C1116yes—
247#405C22×C1113yes—
248#405C22×C1113yes—
249C4×M16C22×C1113yes—
250C2×C4×C8C22×C1113yes—
251C22×C11—23no—
252C22×C11—23no—
253C22×C11—24no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11C2×C4×D416yes—
257C22×C11C23×D411yescharacteristic
258C4×C11—21no—
259C4×C11—23no—
260C4×C11—212no—
261C4×C11—23no—
262C4×C11—46no—
263C4×C11—42no—
264C4×C11C2×C4×D416yes—
265C4×C11#57812yesdirect product factor
266C4×C11C24×C411yescharacteristic
267C4×C11C22×#4111yescharacteristic
2682−1+4—28no—
2692−1+4C2×C4×C11116yescomplemented
270C2×#41—26no—
271C2×#41C23×C1116yes—
272C2×#41C23×C1111yescharacteristic
273C22×Q8—22no—
274C22×Q8C23×C1116yes—
275#137C2×C4×C11148yescomplemented
276#135C2×C4×C11124yescomplemented
277C2×Q16C2×C4×C11124yescomplemented
278C2×Q16C23×C1113yes—
279C2×Q16C23×C1116yes—
280C2×SD16C23×C1116yes—
281C2×D8C23×C1111yescharacteristic
282#131—24no—
283#131C2×C4×C1118yescomplemented
284C2×M16C23×C1113yes—
285C2×M16C23×C1113yes—
286C22×C8C23×C1113yes—
287C22×C8C23×C1113yes—
288C4×Q8—22no—
289C4×Q8—26no—
290C4×Q8—26no—
291C4×Q8—26no—
292C4×Q8—26no—
293C4×Q8D4×C1111yescharacteristic
294C4×Q8D4×C1111yescharacteristic
295C4×Q8C23×C1116yes—
296C4×Q8C23×C11112yes—
297C4×Q8C23×C1116yes—
298C4×D4—26no—
299C4×D4—26no—
300C4×D4—26no—
301C4×D4—212no—
302C4×D4D4×C1113yes—
303C4×D4D4×C1113yes—
304C4×D4C23×C1112yes—
305C4×D4C23×C1116yes—
306#117—26no—
307#117—212no—
308#117—26no—
309#117C23×C1116yes—
310#117C23×C1113yes—
311C2×C4⋊C4—26no—
312C2×C4⋊C4—26no—
313C2×C4⋊C4C23×C1116yes—
314C2×C42—26no—
315C2×C42—26no—
316C2×C42C23×C1113yes—
317#107C23×C1113yes—
318#107C23×C1116yes—
319#107C23×C1111yescharacteristic
320#106C23×C1116yes—
321#103C23×C1116yes—
322#103C23×C11112yes—
323#103C23×C1116yes—
324#102C23×C1112yes—
325#102C23×C1116yes—
326#97C23×C1116yes—
327C4×C8C23×C1111yescharacteristic
328C4×C8C23×C1113yes—
329C4×C8C23×C1113yes—
330C4×C8C23×C1113yes—
331C2×C11—26no—
332C2×C11—44no—
333C2×C11C22×C4×D411yescharacteristic
334C2×C11C2×#57811yescharacteristic
335C2×C11#358411yescharacteristic
336#41—248no—
337#41—212no—
338#41C22×C4×C11124yes—
339#41C22×C4×C1114yes—
340#41C11×#4114yes—
341C2×Q8—216no—
342C2×Q8—26no—
343C2×Q8—212no—
344C2×Q8C22×C4×C11124yes—
345C2×Q8C2×D4×C1111yescharacteristic
346C2×Q8C24×C1116yes—
347C2×D4—26no—
348C2×D4C2×D4×C1113yes—
349C2×D4C24×C1112yes—
350C22×C4—26no—
351C22×C4—26no—
352C22×C4—26no—
353C22×C4—22no—
354C22×C4—26no—
355C22×C4C2×D4×C1113yes—
356C22×C4C2×D4×C1113yes—
357C22×C4C24×C1113yes—
358Q16C22×C4×C11112yes—
359Q16C22×C4×C11124yes—
360SD16C22×C4×C11124yes—
361D8C22×C4×C1114yes—
362M16—26no—
363M16C22×C4×C11112yes—
364C2×C8—26no—
365C2×C8C22×C4×C11112yes—
366C2×C8C24×C1111yescharacteristic
367C2×C8C24×C1113yes—
368C2×C8C24×C1111yescharacteristic
369C2×C8C24×C1113yes—
370C4⋊C4—212no—
371C4⋊C4—26no—
372C4⋊C4—26no—
373C4⋊C4—26no—
374C4⋊C4C2×D4×C1113yes—
375C4⋊C4C2×D4×C1113yes—
376C4⋊C4C24×C1112yes—
377C4⋊C4C24×C1116yes—
378C22⋊C4—26no—
379C22⋊C4—22no—
380C22⋊C4—26no—
381C22⋊C4C2×D4×C1116yes—
382C42—26no—
383C42—26no—
384C42—212no—
385C42—26no—
386C42C2×D4×C1113yes—
387C42C2×D4×C1113yes—
388C42C24×C1111yescharacteristic
389C42C24×C1113yes—
390C11C4×#57811yescharacteristic, direct product factor, Sylow
391C23—22no—
392C23C22×D4×C1113yes—
393Q8—224no—
394Q8—26no—
395Q8C4×D4×C1114yes—
396Q8C23×C4×C11112yes—
397D4—224no—
398D4—22no—
399D4C4×D4×C11112yes—
400D4C23×C4×C1114yes—
401C2×C4—224no—
402C2×C4—26no—
403C2×C4—224no—
404C2×C4—26no—
405C2×C4—22no—
406C2×C4—26no—
407C2×C4—43no—
408C2×C4—44no—
409C2×C4—86no—
410C2×C4—86no—
411C2×C4C23×C4×C1116yes—
412C2×C4C22×D4×C1113yes—
413C2×C4C22×D4×C1113yes—
414C2×C4C22×D4×C1111yescharacteristic
415C2×C4C22×D4×C1113yes—
416C2×C4C22×D4×C1111yescharacteristic
417C2×C4C2×C11×#4116yes—
418C2×C4C25×C1111yescharacteristic
419C8—21no—
420C8—23no—
421C8C23×C4×C1112yes—
422C8C23×C4×C1116yes—
423C22—23no—
424C22—23no—
425C22—24no—
426C22—42no—
427C22—42no—
428C22C2×C4×D4×C1116yes—
429C22C23×D4×C1111yescharacteristic
430C4—212no—
431C4—23no—
432C4—21no—
433C4—23no—
434C4—42no—
435C4—46no—
436C4C2×C4×D4×C1116yes—
437C4C11×#57812yesdirect product factor
438C4C24×C4×C1111yescharacteristic
439C4C22×C11×#4111yescharacteristic
440C2—26no—
441C2—44no—
442C2C22×C4×D4×C1111yescharacteristic
443C2C2×C11×#57811yescharacteristic
444C2C11×#358411yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC4C24×C4×C11
Frattini, cosocleC2×C4C25×C11
socleC22×C11C23×D4
prime radicalC2×C11×#578C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×2−1+4C2semidirect
3. C11×#2951C2semidirect
4. C11×#2950C2semidirect
5. C11×#2947C2semidirect
6. C4×C11×#137C2semidirect
7. C4×C11×#135C2semidirect
8. C2×C4×C11×Q16C2semidirect
9. C11×#2913C2semidirect
10. C11×#2898C2semidirect
11. C4×C11×#131C2semidirect
13. C11×#578C4direct (N × H)
52. C11×2−1+4C2×C4semidirect
58. C11×#137C2×C4semidirect
59. C11×#135C2×C4semidirect
60. C2×C11×Q16C2×C4semidirect
66. C11×#131C2×C4semidirect
114. C4×#578C11direct (N × H)
170. C4×2−1+4C2×C11semidirect
171. #2951C2×C11semidirect
172. #2950C2×C11semidirect
173. #2947C2×C11semidirect
174. C4×#137C2×C11semidirect
175. C4×#135C2×C11semidirect
176. C2×C4×Q16C2×C11semidirect
177. #2913C2×C11semidirect
178. #2898C2×C11semidirect
179. C4×#131C2×C11semidirect
213. #578C4×C11direct (N × H)
265. C4×C11#578direct (N × H)
269. 2−1+4C2×C4×C11semidirect
275. #137C2×C4×C11semidirect
276. #135C2×C4×C11semidirect
277. C2×Q16C2×C4×C11semidirect
283. #131C2×C4×C11semidirect
390. C11C4×#578direct (N × H)
437. C4C11×#578direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5782
C4×C11×2−1+42
C11×#29512
C11×#29502
C11×#29472
C4×C11×#1372
C4×C11×#1352
C2×C4×C11×Q162
C11×#29132
C11×#28982
C4×C11×#1312
C4×#57811