Finite Group Databasebeta

← C4⋊C4×#611 #11805414

Subgroups — C4⋊C4×#611 #11805414

Order 1152.

1164 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C9×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C4×#611C212yesmaximal
3C2×C4×#611C211yesmaximal, characteristic
4C2×C4⋊C4×D9C211yesmaximal, characteristic, complemented
5#10588892C211yesmaximal, characteristic, complemented
6#10588890C212yesmaximal, complemented
7#10588669C212yesmaximal, complemented
8#10588667C211yesmaximal, characteristic, complemented
9#10588656C212yesmaximal, complemented
10#10588655C211yesmaximal, characteristic, complemented
11C4⋊C4×Dic9C211yesmaximal, characteristic, complemented
12C4⋊C4×#67—31nomaximal
13C23×C4×C9C2212yes—
14C23×C4×C9C2211yescharacteristic
15C22×#611C2211yescharacteristic
16C22×C4×D9C2212yes—
17C22×C4×D9C2211yescharacteristic
18C2×C9×C4⋊C4—24no—
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C9×C4⋊C4C2212yes—
21C2×C9×C4⋊C4C2211yescharacteristic
22C2×#3676C2212yes—
23C2×#3676C2211yescharacteristic
24C4×#611—28no—
25C4×#611C418yescomplemented
26C2×(C2×D9)⋊C4C2212yes—
27C2×(C2×D9)⋊C4C2211yescharacteristic
28C2×C4⋊Dic9C2211yescharacteristic
29C2×C4⋊Dic9C2211yescharacteristic
30C2×Dic9⋊C4C2212yes—
31C2×Dic9⋊C4C2212yes—
32C2×Dic9⋊C4C2212yes—
33C2×Dic9⋊C4C2211yescharacteristic
34C2×C4×Dic9C2212yes—
35C2×C4×Dic9C2211yescharacteristic
36C4⋊C4×D9—24no—
37C9⋊#95C2212yes—
38C9⋊#95C2212yes—
39C9⋊#95C2212yes—
40C22×C3×C4⋊C4D311yescharacteristic
41C2×C4×#67—31no—
42C2×C4×#67—32no—
43C2×D3×C4⋊C4—31no—
44#5212—31no—
45#5210—32no—
46#4989—32no—
47#4987—31no—
48#4976—32no—
49#4975—31no—
50Dic3×C4⋊C4—31no—
51C24×C9C2311yescharacteristic
52C23×D9C2311yescharacteristic
53C22×C4×C9—22no—
54C22×C4×C9—22no—
55C22×C4×C9—24no—
56C22×C4×C9—24no—
57C22×C4×C9—42no—
58C22×C4×C9C2×C414yescomplemented
59C22×C4×C9C2312yes—
60C22×C4×C9C2311yescharacteristic
61C22×C4×C9C2312yes—
62C22×C4×C9C2311yescharacteristic
63C2×#611C2×C414yes—
64C2×#611D414yes—
65C2×#611Q814yes—
66C22×Dic9C2312yes—
67C22×Dic9C2312yes—
68C22×Dic9C2311yescharacteristic
69C22×Dic9C2311yescharacteristic
70C22×Dic9C2311yescharacteristic
71C2×C4×D9—22no—
72C2×C4×D9—22no—
73C2×C4×D9—24no—
74C2×C4×D9—24no—
75C2×C4×D9—42no—
76C2×C4×D9C2×C414yescomplemented
77C9×C4⋊C4—24no—
78C9×C4⋊C4—22no—
79C9×C4⋊C4D414yescomplemented
80#3676—24no—
81#3676C2×C414yescomplemented
82(C2×D9)⋊C4—24no—
83(C2×D9)⋊C4C2×C414yescomplemented
84C4⋊Dic9—22no—
85C4⋊Dic9—22no—
86Dic9⋊C4—24no—
87Dic9⋊C4—24no—
88Dic9⋊C4—42no—
89Dic9⋊C4C2×C414yescomplemented
90C4×Dic9—24no—
91C4×Dic9C2×C414yescomplemented
92D4×C4⋊C4—91noSylow
93C23×C3×C4C2×D312yes—
94C23×C3×C4C2×D311yescharacteristic
95C22×#67—31no—
96C22×C4×D3—31no—
97C22×C4×D3—32no—
98C2×C3×C4⋊C4—24no—
99C2×C3×C4⋊C4C2×D311yescharacteristic
100C2×C3×C4⋊C4C2×D312yes—
101C2×C3×C4⋊C4C2×D311yescharacteristic
102C2×#217—31no—
103C2×#217—32no—
104C4×#67—38no—
105C4×#67—68no—
106C2×(C2×D3)⋊C4—31no—
107C2×(C2×D3)⋊C4—32no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—31no—
110C2×Dic3⋊C4—31no—
111C2×Dic3⋊C4—32no—
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4—32no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—32no—
116D3×C4⋊C4—64no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C23×C9—21no—
121C23×C9—21no—
122C23×C9—21no—
123C23×C9—21no—
124C23×C9C22×C412yes—
125C23×C9C2×D412yes—
126C23×C9C2×Q812yes—
127C23×C9C2411yescharacteristic
128C22×D9—21no—
129C22×D9—21no—
130C22×D9—21no—
131C22×D9—21no—
132C22×D9C22×C412yes—
133C22×D9C2×D412yes—
134C22×D9C2×Q812yes—
135C2×C4×C9—22no—
136C2×C4×C9—21no—
137C2×C4×C9—21no—
138C2×C4×C9—22no—
139C2×C4×C9—28no—
140C2×C4×C9—22no—
141C2×C4×C9—22no—
142C2×C4×C9—22no—
143C2×C4×C9—48no—
144C2×C4×C9C22×C412yes—
145C2×C4×C9C22×C412yes—
146C2×C4×C9C2×D414yes—
147C2×C4×C9C2×D412yes—
148C2×C4×C9#4112yes—
149#611C4⋊C4116yesdirect product factor
150C2×Dic9—21no—
151C2×Dic9—21no—
152C2×Dic9—21no—
153C2×Dic9—21no—
154C2×Dic9—22no—
155C2×Dic9—22no—
156C2×Dic9—22no—
157C2×Dic9—22no—
158C2×Dic9—22no—
159C2×Dic9—22no—
160C2×Dic9C22×C412yes—
161C2×Dic9C22×C412yes—
162C2×Dic9C22×C412yes—
163C2×Dic9C2×D412yes—
164C2×Dic9C2×Q812yes—
165C4×D9—28no—
166C4×D9—48no—
167C2×C4×D4—91no—
168C2×C4×D4—92no—
169C22×C4⋊C4—91no—
170C22×C4⋊C4D911yescharacteristic, complemented
171#389—92no—
172#385—92no—
173#385—92no—
174#384—91no—
175#380—91no—
176#380—91no—
177C4×C4⋊C4—91no—
178C24×C3C22×D311yescharacteristic
179C23×D3—31no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—24no—
183C22×C3×C4—24no—
184C22×C3×C4—42no—
185C22×C3×C4C4×D314yes—
186C22×C3×C4C22×D312yes—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D312yes—
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—34no—
191C2×#67—34no—
192C2×#67—34no—
193C22×Dic3—31no—
194C22×Dic3—31no—
195C22×Dic3—31no—
196C22×Dic3—32no—
197C22×Dic3—32no—
198C2×C4×D3—34no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×C4×D3—64no—
202C2×C4×D3—64no—
203C2×C4×D3—122no—
204C3×C4⋊C4—24no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4#6714yes—
207#217—34no—
208#217—64no—
209(C2×D3)⋊C4—34no—
210(C2×D3)⋊C4—64no—
211C4⋊Dic3—62no—
212C4⋊Dic3—62no—
213Dic3⋊C4—34no—
214Dic3⋊C4—64no—
215Dic3⋊C4—64no—
216Dic3⋊C4—122no—
217C4×Dic3—34no—
218C4×Dic3—64no—
219C22×C9—22no—
220C22×C9—22no—
221C22×C9—22no—
222C22×C9—22no—
223C22×C9—22no—
224C22×C9—22no—
225C22×C9C2×C4⋊C414yescomplemented
226C22×C9C23×C411yescharacteristic
227C22×C9C22×D411yescharacteristic
228C22×C9C22×D411yescharacteristic
229C22×C9C22×Q811yescharacteristic
230C22×C9C2×#4111yescharacteristic
231C22×C9H(5,𝔽2)11yescharacteristic
232C22×C92−1+411yescharacteristic
233C2×D9—22no—
234C2×D9—22no—
235C2×D9—22no—
236C2×D9—22no—
237C2×D9—22no—
238C2×D9—22no—
239C2×D9C2×C4⋊C414yescomplemented
240C4×C9—22no—
241C4×C9—24no—
242C4×C9—42no—
243C4×C9C4×D414yescomplemented
244Dic9—22no—
245Dic9—22no—
246Dic9—42no—
247Dic9—42no—
248Dic9C2×C4⋊C414yescomplemented
249C22×D4—91no—
250C23×C4—91no—
251C23×C4—92no—
252C23×C4C2×D912yes—
253C23×C4C2×D911yescharacteristic
254C4×D4—98no—
255C4×D4—188no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—91no—
259C2×C4⋊C4—92no—
260C2×C4⋊C4—92no—
261C2×C4⋊C4—91no—
262C2×C4⋊C4—92no—
263C2×C4⋊C4—184no—
264C2×C4⋊C4C2×D911yescharacteristic
265C2×C4⋊C4C2×D912yes—
266C2×C4⋊C4C2×D911yescharacteristic
267C2×C22⋊C4—91no—
268C2×C22⋊C4—91no—
269C2×C22⋊C4—92no—
270C2×C22⋊C4—92no—
271C2×C42—91no—
272C2×C42—92no—
273#95—92no—
274#95—92no—
275#95—92no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3—21no—
279C23×C3—21no—
280C23×C3C2×C4×D312yes—
281C23×C3D3×D412yes—
282C23×C3D3×Q812yes—
283C23×C3C23×D311yescharacteristic
284C22×D3—32no—
285C22×D3—32no—
286C22×D3—32no—
287C22×D3—61no—
288C22×D3—61no—
289C22×D3—61no—
290C22×D3—61no—
291C2×C3×C4—21no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—28no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—48no—
300C2×C3×C4C2×C4×D312yes—
301C2×C3×C4C2×C4×D312yes—
302C2×C3×C4#23512yes—
303C2×C3×C4C2×#6714yes—
304C2×C3×C4C2×#6712yes—
305#67—316no—
306C2×Dic3—32no—
307C2×Dic3—32no—
308C2×Dic3—32no—
309C2×Dic3—32no—
310C2×Dic3—32no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C4×D3—68no—
322C4×D3—128no—
323C2×C9—24no—
324C2×C9C22×C4⋊C411yescharacteristic
325C2×C9C2×C4×D411yescharacteristic
326C2×C9#52011yescharacteristic
327C2×C9D4211yescharacteristic
328C2×C9#54711yescharacteristic
329C2×C9D4×Q811yescharacteristic
330C2×C9#55411yescharacteristic
331D9—24no—
332C24—91no—
333C24C22×D911yescharacteristic
334C2×D4—94no—
335C2×D4—94no—
336C2×D4—94no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—42no—
342C22×C4—91no—
343C22×C4—91no—
344C22×C4—91no—
345C22×C4—94no—
346C22×C4—92no—
347C22×C4—92no—
348C22×C4—184no—
349C22×C4—182no—
350C22×C4—182no—
351C22×C4—184no—
352C22×C4—362no—
353C22×C4C4×D914yescomplemented
354C22×C4C22×D912yes—
355C22×C4C22×D911yescharacteristic
356C22×C4C22×D912yes—
357C22×C4C22×D911yescharacteristic
358C4⋊C4—24no—
359C4⋊C4—22no—
360C4⋊C4—94no—
361C4⋊C4—184no—
362C4⋊C4—182no—
363C4⋊C4—184no—
364C4⋊C4—182no—
365C4⋊C4—362no—
366C4⋊C4#61114yesdirect product factor
367C22⋊C4—94no—
368C22⋊C4—94no—
369C22⋊C4—184no—
370C22⋊C4—184no—
371C42—94no—
372C42—184no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3D3×C4⋊C414yes—
380C22×C3C22×C4×D311yescharacteristic
381C22×C3C2×#23511yescharacteristic
382C22×C3C2×D3×D411yescharacteristic
383C22×C3#100411yescharacteristic
384C22×C3C2×D3×Q811yescharacteristic
385C22×C3#100711yescharacteristic
386C22×C3C22×#6711yescharacteristic
387C2×D3—34no—
388C2×D3—62no—
389C2×D3—62no—
390C2×D3—62no—
391C2×D3—62no—
392C2×D3—62no—
393C2×D3—62no—
394C3×C4—22no—
395C3×C4—24no—
396C3×C4—42no—
397C3×C4C4×#6714yes—
398Dic3—34no—
399Dic3—62no—
400Dic3—62no—
401Dic3—122no—
402Dic3—122no—
403C9D4×C4⋊C411yescharacteristic, complemented, Sylow
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—92no—
409C23—92no—
410C23—92no—
411C23—181no—
412C23—181no—
413C23—181no—
414C23—181no—
415C23C2×C4×D912yes—
416C23D4×D912yes—
417C23Q8×D912yes—
418C23C23×D911yescharacteristic
419D4—916no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—28no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—48no—
429C2×C4—92no—
430C2×C4—92no—
431C2×C4—92no—
432C2×C4—92no—
433C2×C4—92no—
434C2×C4—181no—
435C2×C4—181no—
436C2×C4—181no—
437C2×C4—181no—
438C2×C4—188no—
439C2×C4—182no—
440C2×C4—182no—
441C2×C4—182no—
442C2×C4—182no—
443C2×C4—182no—
444C2×C4—182no—
445C2×C4—368no—
446C2×C4C2×C4×D912yes—
447C2×C4C2×C4×D912yes—
448C2×C4#369712yes—
449C2×C4C2×#61114yes—
450C2×C4C2×#61112yes—
451C2×C3—24no—
452C2×C3C2×D3×C4⋊C411yescharacteristic
453C2×C3#550411yescharacteristic
454C2×C3#550711yescharacteristic
455C2×C3#551111yescharacteristic
456C2×C3C2×C4×#6711yescharacteristic
457C2×C3D4×#6711yescharacteristic
458C2×C3Q8×#6711yescharacteristic
459D3—64no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—94no—
467C22—182no—
468C22—182no—
469C22—182no—
470C22—182no—
471C22—182no—
472C22—182no—
473C22C4⋊C4×D914yescomplemented
474C22C22×C4×D911yescharacteristic
475C22C2×#369711yescharacteristic
476C22C2×D4×D911yescharacteristic
477C22#6371011yescharacteristic
478C22C2×Q8×D911yescharacteristic
479C22#6371311yescharacteristic
480C22C22×#61111yescharacteristic
481C4—22no—
482C4—24no—
483C4—42no—
484C4—94no—
485C4—182no—
486C4—182no—
487C4—362no—
488C4—362no—
489C4C4×#61114yescomplemented
490C3C4⋊C4×#6711yescharacteristic
491C2—24no—
492C2—184no—
493C2C2×C4⋊C4×D911yescharacteristic
494C2#1058960611yescharacteristic
495C2#1058960911yescharacteristic
496C2#1058961311yescharacteristic
497C2C2×C4×#61111yescharacteristic
498C2D4×#61111yescharacteristic
499C2Q8×#61111yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC22×C9×C4⋊C4C2
prime radicalC22×#611C22
cosocleC23×C9C24
hypercenterC22×C4⋊C4D9
hypocenterC9D4×C4⋊C4
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C9×C4⋊C4C2semidirect
4. C2×C4⋊C4×D9C2semidirect
5. #10588892C2semidirect
6. #10588890C2semidirect
7. #10588669C2semidirect
8. #10588667C2semidirect
9. #10588656C2semidirect
10. #10588655C2semidirect
11. C4⋊C4×Dic9C2semidirect
25. C4×#611C4semidirect
58. C22×C4×C9C2×C4semidirect
76. C2×C4×D9C2×C4semidirect
79. C9×C4⋊C4D4semidirect
81. #3676C2×C4semidirect
83. (C2×D9)⋊C4C2×C4semidirect
89. Dic9⋊C4C2×C4semidirect
91. C4×Dic9C2×C4semidirect
149. #611C4⋊C4direct (N × H)
170. C22×C4⋊C4D9semidirect
225. C22×C9C2×C4⋊C4semidirect
239. C2×D9C2×C4⋊C4semidirect
243. C4×C9C4×D4semidirect
248. Dic9C2×C4⋊C4semidirect
353. C22×C4C4×D9semidirect
366. C4⋊C4#611direct (N × H)
403. C9D4×C4⋊C4semidirect
473. C22C4⋊C4×D9semidirect
489. C4C4×#611semidirect

Maximal subgroups

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

subgroupindex
C22×C9×C4⋊C42
C2×C4×#6112
C2×C4⋊C4×D92
#105888922
#105888902
#105886692
#105886672
#105886562
#105886552
C4⋊C4×Dic92
C4⋊C4×#673