Finite Group Databasebeta

← #13137590

Subgroups — #13137590

Order 1728.

452 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C3×#63457C211yesmaximal, characteristic, complemented
2#11721004C211yesmaximal, characteristic, complemented
3C2×#88417C211yesmaximal, characteristic, complemented
4C2×D9×C3⋊C8C211yesmaximal, characteristic, complemented
5#11720528C211yesmaximal, characteristic, complemented
6C9×#807C211yesmaximal, characteristic, complemented
7#11720266C211yesmaximal, characteristic, complemented
8#10590576—31nomaximal
9#10588563—31nomaximal
10C2×C4⋊(C3⋊D9)C2211yescharacteristic
11C2×C3×D36—21no—
12C2×C3×D36C2211yescharacteristic
13C2×C3×C4×D9C2211yescharacteristic
14C2×#6192—21no—
15C3×C9×C4⋊C4C2211yescharacteristic
16C2×C3⋊(C9⋊C8)C2211yescharacteristic
17C3×(C2×D9)⋊C4—21no—
18C9×C4⋊Dic3C2211yescharacteristic
19C2×C9×C3⋊C8C2211yescharacteristic
20#88445—21no—
21#88417—22no—
22D9×C3⋊C8—22no—
23C3×#895—31no—
24#63909—31no—
25C2×#3714—31no—
26C2×D3×C3⋊C8—31no—
27#63636—31no—
28C3×#807D311yescharacteristic
29#63562—31no—
30C2×D72—31no—
31C2×C8×D9—31no—
32#63457—31no—
33#63457D311yescharacteristic, complemented
34C9×#107—31no—
35#63369—31no—
36#63369—31no—
37#63369—61no—
38C22×C3⋊D9—21no—
39C22×C3×D9—21no—
40C22×C3×D9D411yescharacteristic
41C2×C3×C4×C9—21no—
42C2×C3×C4×C9C2311yescharacteristic
43C4⋊(C3⋊D9)—21no—
44C4⋊(C3⋊D9)—21no—
45C2×C9×Dic3—21no—
46C2×C3×Dic9D411yescharacteristic
47C3×D36—21no—
48C3×D36—21no—
49C3×D36—42no—
50C3×C4×D9—21no—
51C3×C4×D9—21no—
52#6192—42no—
53C3⋊(C9⋊C8)—21no—
54C9×C3⋊C8D412yescomplemented
55#5038—91no—
56#4883—91no—
57C2×C4⋊(C3⋊D3)—31no—
58C2×C3×D12—31no—
59C2×C3×D12—61no—
60C2×C3×C4×D3—31no—
61C2×#626—61no—
62C32×C4⋊C4C2×D311yescharacteristic
63C2×C3⋊(C3⋊C8)—31no—
64C3×(C2×D3)⋊C4—61no—
65C3×C4⋊Dic3C2×D311yescharacteristic
66C2×C3×C3⋊C8C2×D311yescharacteristic
67#3722—61no—
68#3714—62no—
69D3×C3⋊C8—62no—
70C2×D36—21no—
71C2×D36—31no—
72C2×D36—61no—
73C2×D36—61no—
74C2×D36C2×D311yescharacteristic
75C2×C4×D9C2×D311yescharacteristic
76C2×C8×C9—31no—
77C9×C4⋊C4—21no—
78C9×C4⋊C4—31no—
79C9×C4⋊C4C2×D311yescharacteristic
80(C2×D9)⋊C4—21no—
81(C2×D9)⋊C4—61no—
82C2×C9⋊C8—31no—
83C2×C9⋊C8—61no—
84D72—62no—
85C8×D9—62no—
86C22×C3×C9C2×D411yescharacteristic
87C2×C3⋊D9—41no—
88C2×C3⋊D9—41no—
89C2×C3⋊D9—41no—
90C2×C3×D9—21no—
91C2×C3×D9—21no—
92C2×C3×D9—41no—
93C2×C3×D9—41no—
94C2×C3×D9—41no—
95C2×C3×D9D812yescomplemented
96C3×C4×C9—41no—
97C3×C4×C9C2×D411yescharacteristic
98C3×C4×C9#4111yescharacteristic
99C9×Dic3—41no—
100C3×Dic9—21no—
101C3×#121—91no—
102C2×#213—91no—
103#930—91no—
104C22×C3⋊C8—91no—
105C2×D24—91no—
106C2×D3×C8—91no—
107#895—31no—
108#895—91no—
109C3×#107—31no—
110#832—91no—
111#809—91no—
112#809—91no—
113#809—91no—
114#809—181no—
115#807D911yescharacteristic, complemented
116C22×C3⋊D3—61no—
117C22×C3×D3—31no—
118C22×C3×D3—61no—
119C2×C32×C4—21no—
120C2×C32×C4C22×D311yescharacteristic
121C4⋊(C3⋊D3)—61no—
122C4⋊(C3⋊D3)—61no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—31no—
125C3×D12—61no—
126C3×D12—61no—
127C3×D12—122no—
128C3×C4×D3—61no—
129C3×C4×D3—61no—
130#626—122no—
131C22×D9—21no—
132C22×D9—61no—
133C22×D9—121no—
134C22×D9#6711yescharacteristic
135C3⋊(C3⋊C8)—61no—
136C3×C3⋊C8D1212yes—
137C2×C4×C9—21no—
138C2×C4×C9—21no—
139C2×C4×C9—41no—
140C2×C4×C9—61no—
141C2×C4×C9C22×D311yescharacteristic
142C2×Dic9#6711yescharacteristic
143D36—21no—
144D36—21no—
145D36—42no—
146D36—62no—
147D36—61no—
148D36—61no—
149D36—121no—
150D36—122no—
151C4×D9—21no—
152C4×D9—21no—
153C8×C9—32no—
154C9⋊C8—61no—
155C9⋊C8—121no—
156#466—271noSylow
157C2×C3×C9#12111yescharacteristic
158C2×C3×C9C2×D811yescharacteristic
159C2×C3×C9#13511yescharacteristic
160C3⋊D9—81no—
161C3×D9—22no—
162C3×D9—81no—
163C2×C3×D4—91no—
164C2×C3×D4—181no—
165C22×C3×C4—91no—
166C2×#67—181no—
167C2×D12—31no—
168C2×D12—61no—
169C2×D12—91no—
170C2×D12—91no—
171C2×D12—181no—
172C2×D12—181no—
173C2×C4×D3—31no—
174C2×C3×C8—31no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4C2×D911yescharacteristic
178C3×C4⋊C4D3211yescharacteristic
179C3×C22⋊C4—181no—
180#213—182no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—181no—
183(C2×D3)⋊C4—181no—
184C4⋊Dic3C2×D911yescharacteristic
185C2×C3⋊C8—91no—
186C2×C3⋊C8—91no—
187C2×C3⋊C8—181no—
188C2×C3⋊C8—182no—
189C2×C3⋊C8C2×D911yescharacteristic
190D24—182no—
191D3×C8—182no—
192C22×C32D3×D411yescharacteristic
193C2×C3⋊D3—121no—
194C2×C3⋊D3—121no—
195C2×C3⋊D3—121no—
196C2×C3×D3—32no—
197C2×C3×D3—61no—
198C2×C3×D3—61no—
199C2×C3×D3—121no—
200C2×C3×D3—121no—
201C2×C3×D3—121no—
202C32×C4—41no—
203C32×C4C2×D1211yescharacteristic
204C32×C4#23911yescharacteristic
205C3×Dic3—41no—
206C3×Dic3—61no—
207C22×C9—21no—
208C22×C9C2×#6711yescharacteristic
209C2×D9—21no—
210C2×D9—21no—
211C2×D9—41no—
212C2×D9—41no—
213C2×D9—41no—
214C2×D9—122no—
215C2×D9—121no—
216C2×D9—121no—
217C2×D9—121no—
218C2×D9—241no—
219C2×D9—241no—
220C2×D9#21312yescomplemented
221C4×C9—21no—
222C4×C9—21no—
223C4×C9—41no—
224C4×C9—81no—
225C4×C9—121no—
226C4×C9D3×D411yescharacteristic
227C4×C9#23711yescharacteristic
228Dic9—21no—
229C2×D8—271no—
230C22×C8—271no—
231#121—91no—
232#121—271no—
233#107—31no—
234#102—271no—
235#102—271no—
236C3×C9#46611yescharacteristic, complemented, Sylow
237C23×C3—91no—
238C23×C3—181no—
239C22×D3—31no—
240C22×D3—61no—
241C22×D3—181no—
242C22×D3—181no—
243C22×D3—361no—
244C3×D4—181no—
245C3×D4—181no—
246C3×D4—362no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—41no—
251C2×C3×C4—61no—
252C2×C3×C4—91no—
253C2×C3×C4—181no—
254C2×C3×C4—181no—
255C2×C3×C4C22×D911yescharacteristic
256C2×C3×C4C2×D3211yescharacteristic
257#67—362no—
258C2×Dic3—21no—
259C2×Dic3—31no—
260D12—61no—
261D12—61no—
262D12—122no—
263D12—182no—
264D12—181no—
265D12—181no—
266D12—181no—
267D12—181no—
268D12—361no—
269D12—362no—
270C4×D3—61no—
271C4×D3—61no—
272C3×C8—32no—
273C3⋊C8—181no—
274C3⋊C8—181no—
275C3⋊C8—361no—
276C3⋊C8D3612yescomplemented
277C2×C32#89511yescharacteristic
278C2×C32D3×D811yescharacteristic
279C2×C32#91911yescharacteristic
280C3⋊D3—241no—
281C3×D3—62no—
282C3×D3—241no—
283C2×C9—21no—
284C2×C9—21no—
285C2×C9—21no—
286C2×C9C2×#21311yescharacteristic
287C2×C9#93911yescharacteristic
288C2×C9#95011yescharacteristic
289D9—22no—
290D9—81no—
291D9—242no—
292D9—241no—
293C2×D4—91no—
294C2×D4—181no—
295C2×D4—271no—
296C2×D4—541no—
297C22×C4—91no—
298D8—542no—
299C2×C8—31no—
300C2×C8—271no—
301C2×C8—542no—
302C4⋊C4—31no—
303C4⋊C4D3×D911yescharacteristic
304C22⋊C4—181no—
305C22⋊C4—541no—
306C22×C3—21no—
307C22×C3—92no—
308C22×C3—181no—
309C22×C3—181no—
310C22×C3—361no—
311C22×C3—361no—
312C22×C3—361no—
313C22×C3D4×D911yescharacteristic
314C22×C3D3×#6711yescharacteristic
315C2×D3—32no—
316C2×D3—61no—
317C2×D3—61no—
318C2×D3—121no—
319C2×D3—121no—
320C2×D3—121no—
321C2×D3—362no—
322C2×D3—361no—
323C2×D3—361no—
324C2×D3—361no—
325C2×D3—361no—
326C2×D3—361no—
327C2×D3—361no—
328C2×D3—721no—
329C2×D3—721no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—41no—
333C3×C4—41no—
334C3×C4—81no—
335C3×C4—121no—
336C3×C4—181no—
337C3×C4C2×D3611yescharacteristic
338C3×C4#370111yescharacteristic
339C3×C4#379611yescharacteristic
340C3×C4D3×D1211yescharacteristic
341Dic3—41no—
342Dic3—61no—
343C32#488311yescharacteristic
344C9—21no—
345C9#503811yescharacteristic, complemented
346C23—91no—
347C23—181no—
348C23—541no—
349D4—181no—
350D4—181no—
351D4—362no—
352D4—541no—
353D4—541no—
354D4—1082no—
355C2×C4—21no—
356C2×C4—61no—
357C2×C4—91no—
358C2×C4—181no—
359C2×C4—181no—
360C2×C4C2×D3×D911yescharacteristic
361C8—32no—
362C8—541no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—182no—
367C2×C3—721no—
368C2×C3#6345711yescharacteristic
369C2×C3D8×D911yescharacteristic
370C2×C3#6348111yescharacteristic
371C2×C3#6388611yescharacteristic
372C2×C3D3×#21311yescharacteristic
373C2×C3#6394911yescharacteristic
374D3—62no—
375D3—241no—
376D3—722no—
377D3—721no—
378D3—721no—
379C22—92no—
380C22—181no—
381C22—181no—
382C22—361no—
383C22—361no—
384C22—361no—
385C22—1081no—
386C22—1081no—
387C22—1081no—
388C22D9×#6711yescharacteristic
389C4—41no—
390C4—121no—
391C4—181no—
392C4#8863411yescharacteristic
393C4D3×D3611yescharacteristic
394C3—21no—
395C3#1058856311yescharacteristic, complemented
396C3#1059057611yescharacteristic
397C2—182no—
398C2—721no—
399C2—2161no—
400C2#1172098311yescharacteristic
401C2D9×#21311yescharacteristic
402C2#1172122311yescharacteristic
subgroupG/H
centerC22D9×#67
commutator, cosocleC2×C3×C4×C9C23
FrattiniC2×C3×C4C2×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32D3×D4
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#466
LCSG ▷ C2×C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#63457C2semidirect
2. #11721004C2semidirect
3. C2×#88417C2semidirect
4. C2×D9×C3⋊C8C2semidirect
5. #11720528C2semidirect
6. C9×#807C2semidirect
7. #11720266C2semidirect
33. #63457D3semidirect
54. C9×C3⋊C8D4semidirect
95. C2×C3×D9D8semidirect
115. #807D9semidirect
220. C2×D9#213semidirect
236. C3×C9#466semidirect
276. C3⋊C8D36semidirect
345. C9#5038semidirect
395. C3#10588563semidirect

Maximal subgroups

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

subgroupindex
C3×#634572
#117210042
C2×#884172
C2×D9×C3⋊C82
#117205282
C9×#8072
#117202662
#105905763
#105885633