Finite Group Databasebeta

← C4⋊C4×#4326 #14772202

Subgroups — C4⋊C4×#4326 #14772202

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4326C212yesmaximal
2C2×C4×#4326C211yesmaximal, characteristic
3C4⋊C4×Dic22C211yesmaximal, characteristic
4#13069346C212yesmaximal
5#13068870C212yesmaximal
6#13068869C212yesmaximal
7#13068775C211yesmaximal, characteristic
8#13068621C211yesmaximal, characteristic
9#13068618C211yesmaximal, characteristic
10C4⋊C4×C11⋊C8C211yesmaximal, characteristic
11Q8×C11×C4⋊C4C211yesmaximal, characteristic
12C2×C4×Q8×C11C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C22×#4326C2211yescharacteristic
15C2×C4×Dic22C2212yes—
16C2×C4×Dic22C2211yescharacteristic
17C11×#389—22no—
18C11×#389C2212yes—
19C11×#384—21no—
20C11×#384C2211yescharacteristic
21C4×C11×C4⋊C4—21no—
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66899C2212yes—
24C2×#66899C2211yescharacteristic
25C4×#4326—28no—
26C4×#4326C418yescomplemented
27#10622589—21no—
28C4⋊C4×Dic11—21no—
29C2×#66874C2212yes—
30C2×#66874C2211yescharacteristic
31C2×#66871C2212yes—
32C2×#66871C2212yes—
33C2×#66871C2211yescharacteristic
34#10622548C2211yescharacteristic
35#10622541C2212yes—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4×C11⋊C8C2212yes—
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622260—22no—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×Dic22C2311yescharacteristic
45C4×Q8×C11—22no—
46C4×Q8×C11—24no—
47C4×Q8×C11—42no—
48C4×Q8×C11C2×C414yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C42×C11—21no—
59C2×C42×C11—22no—
60C2×C42×C11C2312yes—
61C2×C42×C11C2311yescharacteristic
62C2×#4326C2×C414yes—
63C2×#4326D414yes—
64C2×#4326Q814yes—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11C2312yes—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—22no—
74C22×C11⋊C8C2312yes—
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2311yescharacteristic
77C4×Dic22—22no—
78C4×Dic22—24no—
79C4×Dic22—42no—
80C4×Dic22C2×C414yes—
81C11×#95—22no—
82C11×#95D412yes—
83#66899—24no—
84#66899C2×C414yes—
85C11⋊#95—22no—
86#66874—24no—
87#66874C2×C414yes—
88#66871—24no—
89#66871—42no—
90#66871C2×C414yes—
91C4⋊(C11⋊C8)—22no—
92C4×C11⋊C8—24no—
93C4×C11⋊C8C2×C414yes—
94C4⋊C4×Q16—111nomaximal, Sylow
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11C22×C412yes—
99C2×Q8×C11C2×D412yes—
100C2×Q8×C11C2×Q812yes—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C2×Dic22—21no—
113C2×Dic22—21no—
114C2×Dic22—21no—
115C2×Dic22C22×C412yes—
116C2×Dic22C2×D412yes—
117C2×Dic22C2×Q812yes—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—44no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—81no—
126C11×C4⋊C4—82no—
127C11×C4⋊C4Q1614yescomplemented
128C11×C4⋊C4C22×C412yes—
129C42×C11—24no—
130C42×C11—22no—
131C42×C11—22no—
132C42×C11—44no—
133C42×C11C22×C412yes—
134C42×C11#4112yes—
135#4326C4⋊C4116yesdirect product factor
136C4⋊Dic11—22no—
137C4⋊Dic11—21no—
138C4⋊Dic11—22no—
139C4⋊Dic11—42no—
140C4⋊Dic11—81no—
141C4⋊Dic11C22×C412yes—
142Dic11⋊C4—24no—
143Dic11⋊C4—44no—
144Dic11⋊C4—82no—
145C4×Dic11—24no—
146C4×Dic11—44no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8C22×C412yes—
153C2×C11⋊C8C22×C412yes—
154C2×C11⋊C8C2×D412yes—
155C2×C11⋊C8C2×Q812yes—
156C2×C4×Q16—111no—
157C2×C4×Q16—112no—
158Q8×C4⋊C4—111no—
159Q8×C4⋊C4D1111yescharacteristic
160#1942—112no—
161#1863—112no—
162#1863—112no—
163#1845—111no—
164#1803—111no—
165#1803—111no—
166C8×C4⋊C4—111no—
167C23×C11C22×D411yescharacteristic
168Q8×C11—22no—
169Q8×C11—22no—
170Q8×C11—22no—
171Q8×C11C2×C4⋊C414yes—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11C4×D412yes—
189C2×C4×C11C4×D412yes—
190C2×C4×C11C2×Q1614yes—
191C2×C4×C11C2×Q1612yes—
192C2×C4×C11#13512yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×Q811yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11H(5,𝔽2)11yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208Dic22—22no—
209Dic22—22no—
210Dic22—22no—
211Dic22C2×C4⋊C414yes—
212C11⋊C8—22no—
213C11⋊C8—42no—
214C11⋊C8C2×C4⋊C414yes—
215C22×Q16—111no—
216C2×C4×Q8—111no—
217C2×C4×Q8—112no—
218C2×C4×Q8C2×D1112yes—
219C2×C4×Q8C2×D1111yescharacteristic
220C4×Q16—118no—
221C4×Q16—228no—
222C2×#107—111no—
223C2×#107—112no—
224C2×#107—112no—
225C2×C4⋊C8—111no—
226C2×#103—111no—
227C2×#103—111no—
228C2×#103—112no—
229C2×#103—112no—
230C2×C4×C8—111no—
231C2×C4×C8—112no—
232#389—22no—
233#389—112no—
234#389—222no—
235#389C2×D1112yes—
236#384—21no—
237#384—111no—
238#384—221no—
239#384C2×D1111yescharacteristic
240C4×C4⋊C4—21no—
241C4×C4⋊C4—221no—
242C4×C4⋊C4C2×D1111yescharacteristic
243#340—112no—
244#340—112no—
245#336—112no—
246C22×C11C2×C4×D411yescharacteristic
247C22×C11D4211yescharacteristic
248C22×C11D4×Q811yescharacteristic
249C22×C11C22×Q1611yescharacteristic
250C22×C11C2×#13511yescharacteristic
251C22×C11#57611yescharacteristic
252C22×C11#57811yescharacteristic
253C4×C11—24no—
254C4×C11—22no—
255C4×C11—24no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—82no—
259C4×C11C4×Q1614yescomplemented
260C4×C11C22×C4⋊C411yescharacteristic
261C4×C11#52011yescharacteristic
262C4×C11#54711yescharacteristic
263C4×C11#55411yescharacteristic
264Dic11—24no—
265Dic11—42no—
266Dic11—82no—
267C22×Q8—111no—
268C22×Q8C22×D1111yescharacteristic
269C2×Q16—114no—
270C2×Q16—114no—
271C2×Q16—114no—
272C22×C8—111no—
273C22×C8—111no—
274C22×C8—112no—
275C4×Q8—22no—
276C4×Q8—24no—
277C4×Q8—42no—
278C4×Q8—114no—
279C4×Q8—224no—
280C4×Q8—222no—
281C4×Q8—442no—
282C4×Q8C4×D1114yes—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4C22⋊D1111yescharacteristic
296C2×C4⋊C4C22⋊D1111yescharacteristic
297C2×C4⋊C4C22×D1112yes—
298C2×C4⋊C4C22×D1111yescharacteristic
299C2×C42—21no—
300C2×C42—22no—
301C2×C42—221no—
302C2×C42—222no—
303C2×C42C22×D1112yes—
304C2×C42C22×D1111yescharacteristic
305#107—114no—
306#107—224no—
307#107—442no—
308C4⋊C8—222no—
309#103—114no—
310#103—114no—
311#103—224no—
312#103—224no—
313C4×C8—114no—
314C4×C8—224no—
315#95—22no—
316#95—222no—
317#95C22⋊D1112yes—
318C2×C11D4×C4⋊C411yescharacteristic
319C2×C11C2×C4×Q1611yescharacteristic
320C2×C11#295111yescharacteristic
321C2×C11D4×Q1611yescharacteristic
322C2×C11#328711yescharacteristic
323C2×C11Q8×Q1611yescharacteristic
324C2×C11#338311yescharacteristic
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—112no—
329C2×Q8—112no—
330C2×Q8—112no—
331C2×Q8—221no—
332C2×Q8—221no—
333C2×Q8—221no—
334C2×Q8C2×C4×D1112yes—
335C2×Q8D4×D1112yes—
336C2×Q8Q8×D1112yes—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4—222no—
343C22×C4C2×C22⋊D1112yes—
344C22×C4C2×C22⋊D1111yescharacteristic
345C22×C4C2×C22⋊D1112yes—
346C22×C4C2×C22⋊D1111yescharacteristic
347C22×C4C23×D1111yescharacteristic
348Q16—1116no—
349C2×C8—112no—
350C2×C8—112no—
351C2×C8—112no—
352C2×C8—112no—
353C2×C8—221no—
354C2×C8—221no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—222no—
358C4⋊C4—24no—
359C4⋊C4—22no—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—44no—
364C4⋊C4—42no—
365C4⋊C4—81no—
366C4⋊C4—82no—
367C4⋊C4—112no—
368C4⋊C4—224no—
369C4⋊C4—221no—
370C4⋊C4—222no—
371C4⋊C4—222no—
372C4⋊C4—444no—
373C4⋊C4—442no—
374C4⋊C4—882no—
375C4⋊C4—881no—
376C4⋊C4#432614yesdirect product factor
377C4⋊C4C2×C4×D1112yes—
378C42—24no—
379C42—22no—
380C42—22no—
381C42—44no—
382C42—224no—
383C42—444no—
384C42C2×C4×D1112yes—
385C42#433912yes—
386C11C4⋊C4×Q1611yescharacteristic, complemented, Sylow
387C23C22×C22⋊D1111yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—22no—
391Q8—114no—
392Q8—222no—
393Q8—222no—
394Q8—222no—
395Q8C4⋊C4×D1114yes—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4C4×C22⋊D1112yes—
422C2×C4C4×C22⋊D1112yes—
423C2×C4C2×#432614yes—
424C2×C4C2×#432612yes—
425C2×C4#6700312yes—
426C2×C4C22×C4×D1111yescharacteristic
427C2×C4C2×#433911yescharacteristic
428C2×C4C2×D4×D1111yescharacteristic
429C2×C4#6703711yescharacteristic
430C2×C4C2×Q8×D1111yescharacteristic
431C2×C4#6704011yescharacteristic
432C8—114no—
433C8—222no—
434C8—442no—
435C22C2×C4×C22⋊D1111yescharacteristic
436C22D4×C22⋊D1111yescharacteristic
437C22C22×#432611yescharacteristic
438C22Q8×C22⋊D1111yescharacteristic
439C22C2×#6700311yescharacteristic
440C22#1062336611yescharacteristic
441C22#1062336911yescharacteristic
442C4—24no—
443C4—24no—
444C4—22no—
445C4—42no—
446C4—42no—
447C4—82no—
448C4—224no—
449C4—442no—
450C4—882no—
451C4C4×#432614yescomplemented
452C4C2×C4⋊C4×D1111yescharacteristic
453C4#1062303511yescharacteristic
454C4#1062303811yescharacteristic
455C4#1062304211yescharacteristic
456C2C4⋊C4×C22⋊D1111yescharacteristic
457C2C2×C4×#432611yescharacteristic
458C2#1307748911yescharacteristic
459C2D4×#432611yescharacteristic
460C2#1308037211yescharacteristic
461C2Q8×#432611yescharacteristic
462C2#1308150311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingQ8×C11×C4⋊C4C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterQ8×C4⋊C4D11
hypocenterC11C4⋊C4×Q16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
26. C4×#4326C4semidirect
127. C11×C4⋊C4Q16semidirect
135. #4326C4⋊C4direct (N × H)
259. C4×C11C4×Q16semidirect
376. C4⋊C4#4326direct (N × H)
386. C11C4⋊C4×Q16semidirect
451. C4C4×#4326semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43262
C4⋊C4×Dic222
#130693462
#130688702
#130688692
#130687752
#130686212
#130686182
C4⋊C4×C11⋊C82
Q8×C11×C4⋊C42
C4⋊C4×Q1611