Finite Group Databasebeta

← C2×#14516793 #72276216

Subgroups — C2×#14516793 #72276216

Order 3888.

775 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 775 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#92299C211yesmaximal, characteristic, complemented
2C22×C9×AGL(1,ℤ/9)C211yesmaximal, characteristic, complemented
3C2×3−1+2×Dic9C211yesmaximal, characteristic, complemented
4#14516793C214yesmaximal, direct product factor
5C2×#6192⋊C3—31nomaximal
6C2×C3×#6195—31nomaximal
7C2×#10619530C311yesmaximal, characteristic, complemented
8C22×C9×3−1+2C2211yescharacteristic
9C2×#92299—22no—
10C2×#92299C2212yescomplemented
11C2×C9×AGL(1,ℤ/9)—22no—
12C2×C9×AGL(1,ℤ/9)C2212yescomplemented
133−1+2×Dic9C2212yescomplemented
14C22×C3⋊AGL(1,ℤ/9)—31no—
15C22×C3×C3⋊D9—31no—
16C22×C3×AGL(1,ℤ/9)D311yescharacteristic
17C22×C3×D3×C9—31no—
18C2×Dic3×3−1+2—31no—
19C2×C32×Dic9D311yescharacteristic
20#6192⋊C3—34no—
21C3×#6195—34no—
22C22×C9⋊D9C2×C311yescharacteristic, complemented
23C22×D9⋊C9—21no—
24C22×#4169—61no—
25C22×C9×D9C2×C311yescharacteristic, complemented
26C2×C9×Dic9—21no—
27C2×C9×Dic9C2×C311yescharacteristic, complemented
28#10619530C2×C314yescomplemented
29C2×C9×3−1+2D412yescomplemented
30C2×C9×3−1+2C2311yescharacteristic
31#92299—22no—
32C9×AGL(1,ℤ/9)—22no—
33C2×C3×#626—91no—
34C2×C3×#611—91no—
35C2×C4⋊AGL(1,ℤ/9)—91no—
36C2×#6195—31no—
37C2×#6192—31no—
38C22×C3×3−1+2C2×D311yescharacteristic
39C22×C32×C9C2×D311yescharacteristic
40C2×C3⋊AGL(1,ℤ/9)—32no—
41C2×C3⋊AGL(1,ℤ/9)—62no—
42C2×C3×C3⋊D9—32no—
43C2×C3×C3⋊D9—62no—
44C2×C3×AGL(1,ℤ/9)—22no—
45C2×C3×AGL(1,ℤ/9)C2×D312yes—
46C2×C3×D3×C9—32no—
47C2×C3×D3×C9—62no—
48Dic3×3−1+2—32no—
49C32×Dic9C2×D312yes—
50C22×C9⋊C9—21no—
51C22×C9⋊C9—41no—
52C22×C32⋊C9—21no—
53C22×C92—21no—
54C22×C92C22×C311yescharacteristic
55C2×C9⋊D9—22no—
56C2×C9⋊D9C22×C312yescomplemented
57C2×D9⋊C9—24no—
58C2×D9⋊C9—22no—
59C2×#4169—62no—
60C2×#4169—64no—
61C2×C9×D9—22no—
62C2×C9×D9C22×C312yescomplemented
63C9×Dic9—22no—
64C9×Dic9C22×C312yescomplemented
65C9×3−1+2C2×D411yescharacteristic, complemented, Sylow
66C22×C3×C3⋊D3—91no—
67C22×C32×D3—31no—
68C2×C32×Dic3—31no—
69C3×#626—94no—
70C23×C3×C9—91no—
71C22×C3⋊D9—31no—
72C22×C3⋊D9—31no—
73C22×C3⋊D9—61no—
74C22×AGL(1,ℤ/9)—21no—
75C22×AGL(1,ℤ/9)—91no—
76C22×AGL(1,ℤ/9)—181no—
77C22×AGL(1,ℤ/9)D911yescharacteristic, complemented
78C22×D3×C9—31no—
79C22×D3×C9—61no—
80C22×C3×D9—91no—
81C22×C3×D9—181no—
82C22×C3×D9C3×D311yescharacteristic
83C2×C4×3−1+2—91no—
84C3×#611—94no—
85C2×C9×Dic3—31no—
86C2×C9×Dic3—61no—
87C2×C3×Dic9—31no—
88C2×C3×Dic9C3×D311yescharacteristic
89C4⋊AGL(1,ℤ/9)—94no—
90#6195—34no—
91#6192—34no—
92C2×C3×3−1+2#6712yes—
93C2×C3×3−1+2C22×D311yescharacteristic
94C2×C32×C9D1212yes—
95C2×C32×C9C22×D311yescharacteristic
96C3⋊AGL(1,ℤ/9)—62no—
97C3×C3⋊D9—62no—
98C3×AGL(1,ℤ/9)—22no—
99C3×D3×C9—62no—
100C2×C9⋊C9—22no—
101C2×C9⋊C9—21no—
102C2×C9⋊C9—42no—
103C2×C9⋊C9—41no—
104C2×C32⋊C9—22no—
105C2×C32⋊C9—21no—
106C2×C92—22no—
107C2×C92—21no—
108C2×C92C3×D412yescomplemented
109C2×C92C23×C311yescharacteristic
110C9⋊D9—22no—
111D9⋊C9—24no—
112#4169—64no—
113C9×D9—22no—
114C2×C3×#67—271no—
115C2×C3×D12—271no—
116C2×#626—91no—
117C2×#611—91no—
118C2×D36—91no—
119C22×C33D3211yescharacteristic
120C2×C3×C3⋊D3—92no—
121C2×C3×C3⋊D3—182no—
122C2×C32×D3—32no—
123C2×C32×D3—62no—
124C32×Dic3—32no—
125C22×3−1+2—21no—
126C22×3−1+2—21no—
127C22×3−1+2—41no—
128C22×3−1+2C2×D911yescharacteristic
129C22×C3×C9—21no—
130C22×C3×C9—21no—
131C22×C3×C9—21no—
132C22×C3×C9—31no—
133C22×C3×C9—41no—
134C22×C3×C9—61no—
135C22×C3×C9—92no—
136C22×C3×C9—182no—
137C22×C3×C9C2×C3×D311yescharacteristic
138C22×C3×C9C2×C3×D311yescharacteristic
139C2×C3⋊D9—32no—
140C2×C3⋊D9—32no—
141C2×C3⋊D9—62no—
142C2×C3⋊D9—64no—
143C2×C3⋊D9—62no—
144C2×C3⋊D9—62no—
145C2×AGL(1,ℤ/9)—24no—
146C2×AGL(1,ℤ/9)—22no—
147C2×AGL(1,ℤ/9)—22no—
148C2×AGL(1,ℤ/9)—92no—
149C2×AGL(1,ℤ/9)—182no—
150C2×AGL(1,ℤ/9)—184no—
151C2×AGL(1,ℤ/9)—182no—
152C2×AGL(1,ℤ/9)C2×D912yescomplemented
153C2×D3×C9—32no—
154C2×D3×C9—62no—
155C2×D3×C9—64no—
156C2×D3×C9—62no—
157C2×C3×D9—22no—
158C2×C3×D9—92no—
159C2×C3×D9—182no—
160C2×C3×D9—182no—
161C2×C3×D9—184no—
162C2×C3×D9C2×C3×D312yes—
163C4×3−1+2—92no—
164C9×Dic3—32no—
165C9×Dic3—62no—
166C3×Dic9—32no—
167C3×Dic9C2×C3×D312yes—
168C3×3−1+2C2×#6711yescharacteristic
169C32×C9C2×D1211yescharacteristic
170C9⋊C9—21no—
171C9⋊C9—41no—
172C32⋊C9—21no—
173C92—21no—
174C92C2×C3×D411yescharacteristic, complemented
175C23×C32—91no—
176C22×C3⋊D3—91no—
177C22×C3×D3—31no—
178C22×C3×D3—31no—
179C22×C3×D3—61no—
180C22×C3×D3—271no—
181C22×C3×D3—271no—
182C22×C3×D3—541no—
183C2×C32×C4—91no—
184C3×#67—274no—
185C2×C3×Dic3—31no—
186C2×C3×Dic3—91no—
187C3×D12—274no—
188#626—94no—
189C23×C9—91no—
190C23×C9—181no—
191C22×D9—91no—
192C22×D9—91no—
193C22×D9—181no—
194C22×D9—181no—
195C22×D9—541no—
196C22×D9C3×D911yescharacteristic, complemented
197C2×C4×C9—91no—
198C2×C4×C9—181no—
199#611—94no—
200C2×Dic9AGL(1,ℤ/9)11yescharacteristic, complemented
201D36—94no—
202C2×C33#62612yes—
203C2×C33C2×D3211yescharacteristic
204C3×C3⋊D3—182no—
205C32×D3—62no—
206C2×3−1+2—22no—
207C2×3−1+2—21no—
208C2×3−1+2—22no—
209C2×3−1+2—21no—
210C2×3−1+2—42no—
211C2×3−1+2—41no—
212C2×3−1+2#61112yescomplemented
213C2×3−1+2C22×D911yescharacteristic
214C2×C3×C9—22no—
215C2×C3×C9—21no—
216C2×C3×C9—22no—
217C2×C3×C9—22no—
218C2×C3×C9—21no—
219C2×C3×C9—21no—
220C2×C3×C9—32no—
221C2×C3×C9—31no—
222C2×C3×C9—42no—
223C2×C3×C9—41no—
224C2×C3×C9—62no—
225C2×C3×C9—61no—
226C2×C3×C9—182no—
227C2×C3×C9C3×D1212yes—
228C2×C3×C9C3×#6712yes—
229C2×C3×C9C22×C3×D311yescharacteristic
230C2×C3×C9C22×C3×D311yescharacteristic
231C3⋊D9—62no—
232C3⋊D9—62no—
233C3⋊D9—64no—
234AGL(1,ℤ/9)—24no—
235AGL(1,ℤ/9)—22no—
236AGL(1,ℤ/9)—184no—
237AGL(1,ℤ/9)—182no—
238D3×C9—64no—
239D3×C9—62no—
240C3×D9—22no—
241C3×D9—182no—
242C3×D9—184no—
243C2×C3×D4—811no—
244C2×#67—271no—
245C2×D12—271no—
246C22×C32—21no—
247C22×C32—31no—
248C22×C32—61no—
249C22×C32—92no—
250C22×C32—182no—
251C22×C32D3×D911yescharacteristic
252C22×C32C3×D3211yescharacteristic
253C2×C3⋊D3—92no—
254C2×C3⋊D3—182no—
255C2×C3×D3—32no—
256C2×C3×D3—32no—
257C2×C3×D3—62no—
258C2×C3×D3—64no—
259C2×C3×D3—62no—
260C2×C3×D3—62no—
261C2×C3×D3—272no—
262C2×C3×D3—272no—
263C2×C3×D3—542no—
264C2×C3×D3—542no—
265C2×C3×D3—544no—
266C2×C3×D3—542no—
267C32×C4—92no—
268C3×Dic3—32no—
269C3×Dic3—92no—
270C22×C9—21no—
271C22×C9—21no—
272C22×C9—21no—
273C22×C9—41no—
274C22×C9—61no—
275C22×C9—61no—
276C22×C9—92no—
277C22×C9—121no—
278C22×C9—182no—
279C22×C9—184no—
280C22×C9—182no—
281C22×C9C2×C3×D911yescharacteristic
282C22×C9C2×AGL(1,ℤ/9)11yescharacteristic
283C2×D9—22no—
284C2×D9—92no—
285C2×D9—92no—
286C2×D9—182no—
287C2×D9—182no—
288C2×D9—184no—
289C2×D9—184no—
290C2×D9—182no—
291C2×D9—182no—
292C2×D9—542no—
293C2×D9—544no—
294C2×D9C2×C3×D912yescomplemented
295C4×C9—92no—
296C4×C9—182no—
297Dic9C2×AGL(1,ℤ/9)12yescomplemented
298C33C2×#62611yescharacteristic
2993−1+2—21no—
3003−1+2—21no—
3013−1+2—41no—
3023−1+2C2×#61111yescharacteristic, complemented
303C3×C9—21no—
304C3×C9—21no—
305C3×C9—21no—
306C3×C9—31no—
307C3×C9—41no—
308C3×C9—61no—
309C3×C9C2×C3×D1211yescharacteristic
310C3×C9C2×C3×#6711yescharacteristic
311C23×C3—91no—
312C23×C3—91no—
313C23×C3—181no—
314C23×C3—811no—
315C22×D3—31no—
316C22×D3—271no—
317C22×D3—271no—
318C22×D3—541no—
319C3×D4—814no—
320C2×C3×C4—91no—
321C2×C3×C4—271no—
322#67—274no—
323C2×Dic3—31no—
324D12—274no—
325C2×C32—21no—
326C2×C32—22no—
327C2×C32—31no—
328C2×C32—32no—
329C2×C32—62no—
330C2×C32—61no—
331C2×C32—182no—
332C2×C32#619512yes—
333C2×C32C2×D3×D911yescharacteristic
334C2×C32C3×#62612yes—
335C2×C32C2×C3×D3211yescharacteristic
336C3⋊D3—182no—
337C3×D3—64no—
338C3×D3—62no—
339C3×D3—62no—
340C3×D3—542no—
341C3×D3—544no—
342C3×D3—542no—
343C2×C9—21no—
344C2×C9—21no—
345C2×C9—21no—
346C2×C9—22no—
347C2×C9—22no—
348C2×C9—22no—
349C2×C9—41no—
350C2×C9—42no—
351C2×C9—61no—
352C2×C9—62no—
353C2×C9—61no—
354C2×C9—62no—
355C2×C9—121no—
356C2×C9—122no—
357C2×C9—184no—
358C2×C9—182no—
359C2×C9C4⋊AGL(1,ℤ/9)12yescomplemented
360C2×C9C3×#61112yescomplemented
361C2×C9C22×C3×D911yescharacteristic
362C2×C9C22×AGL(1,ℤ/9)11yescharacteristic
363D9—22no—
364D9—184no—
365D9—184no—
366D9—182no—
367D9—182no—
368D9—544no—
369C2×D4—811noSylow
370C22×C3—21no—
371C22×C3—31no—
372C22×C3—61no—
373C22×C3—92no—
374C22×C3—92no—
375C22×C3—182no—
376C22×C3—182no—
377C22×C3—184no—
378C22×C3—182no—
379C22×C3—812no—
380C22×C3—1622no—
381C22×C3C3×D3×D911yescharacteristic
382C22×C3D3×AGL(1,ℤ/9)11yescharacteristic
383C2×D3—32no—
384C2×D3—62no—
385C2×D3—272no—
386C2×D3—272no—
387C2×D3—542no—
388C2×D3—544no—
389C2×D3—542no—
390C2×D3—542no—
391C3×C4—92no—
392C3×C4—272no—
393Dic3—32no—
394C32—21no—
395C32—31no—
396C32—61no—
397C32C2×#619511yescharacteristic
398C32C2×C3×#62611yescharacteristic
399C9—21no—
400C9—21no—
401C9—21no—
402C9—41no—
403C9—61no—
404C9—61no—
405C9—121no—
406C9C2×C4⋊AGL(1,ℤ/9)11yescharacteristic, complemented
407C9C2×C3×#61111yescharacteristic, complemented
408C23—91no—
409C23—811no—
410D4—814no—
411C2×C4—91no—
412C2×C3—21no—
413C2×C3—22no—
414C2×C3—31no—
415C2×C3—32no—
416C2×C3—61no—
417C2×C3—62no—
418C2×C3—182no—
419C2×C3—184no—
420C2×C3—182no—
421C2×C3—1622no—
422C2×C3C3×#619512yes—
423C2×C3#6192⋊C312yes—
424C2×C3C2×C3×D3×D911yescharacteristic
425C2×C3C2×D3×AGL(1,ℤ/9)11yescharacteristic
426D3—62no—
427D3—544no—
428D3—542no—
429D3—542no—
430C22—92no—
431C22—182no—
432C22—812no—
433C22—1622no—
434C22D9×AGL(1,ℤ/9)11yescharacteristic
435C4—92no—
436C3—21no—
437C3—31no—
438C3—61no—
439C3C2×C3×#619511yescharacteristic
440C3C2×#6192⋊C311yescharacteristic
441C2—182no—
442C2—1622no—
443C2#1451679312yesdirect product factor
444C2C2×D9×AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
center, hypercenterC22D9×AGL(1,ℤ/9)
commutator, cosocleC2×C92C23×C3
FrattiniC2×C32C2×C3×D32
FittingC22×C9×3−1+2C22
socleC22×C32C3×D32
hypocenterC92C2×C3×D4
LCSG ▷ C2×C92 ▷ C92
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#92299C2semidirect
2. C22×C9×AGL(1,ℤ/9)C2semidirect
3. C2×3−1+2×Dic9C2semidirect
4. #14516793C2direct (N × H)
7. C2×#10619530C3semidirect
10. C2×#92299C22semidirect
12. C2×C9×AGL(1,ℤ/9)C22semidirect
13. 3−1+2×Dic9C22semidirect
22. C22×C9⋊D9C2×C3semidirect
25. C22×C9×D9C2×C3semidirect
27. C2×C9×Dic9C2×C3semidirect
28. #10619530C2×C3semidirect
29. C2×C9×3−1+2D4semidirect
56. C2×C9⋊D9C22×C3semidirect
62. C2×C9×D9C22×C3semidirect
64. C9×Dic9C22×C3semidirect
65. C9×3−1+2C2×D4semidirect
77. C22×AGL(1,ℤ/9)D9semidirect
108. C2×C92C3×D4semidirect
152. C2×AGL(1,ℤ/9)C2×D9semidirect
174. C92C2×C3×D4semidirect
196. C22×D9C3×D9semidirect
200. C2×Dic9AGL(1,ℤ/9)semidirect
212. C2×3−1+2#611semidirect
294. C2×D9C2×C3×D9semidirect
297. Dic9C2×AGL(1,ℤ/9)semidirect
302. 3−1+2C2×#611semidirect
359. C2×C9C4⋊AGL(1,ℤ/9)semidirect
360. C2×C9C3×#611semidirect
406. C9C2×C4⋊AGL(1,ℤ/9)semidirect
407. C9C2×C3×#611semidirect
443. C2#14516793direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#922992
C22×C9×AGL(1,ℤ/9)2
C2×3−1+2×Dic92
#145167932
C2×#6192⋊C33
C2×C3×#61953
C2×#106195303