Finite Group Databasebeta

← D3×#4497 #11796766

Subgroups — D3×#4497 #11796766

Order 1152.

476 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
1D3×#904C211yesmaximal, characteristic
2C3×D3×#108C211yesmaximal, characteristic, complemented
3C2×D3×C3⋊C16C211yesmaximal, characteristic, complemented
4#10589363C211yesmaximal, characteristic, complemented
5C3×#4497C211yesmaximal, characteristic, complemented
6#10589122C211yesmaximal, characteristic, complemented
7#10589120C211yesmaximal, characteristic, complemented
8C2×#4497—31nomaximal
9D3×#359—31nomaximal
10D3×#235—21no—
11#64113C2211yescharacteristic
12C3×D3×M16—21no—
13C3×#904C2211yescharacteristic
14C2×C3×D3×C8C2211yescharacteristic
15#63829—21no—
16#63808C411yescharacteristic
17#63807C411yescharacteristic
18#63806—21no—
19D3×Dic12C411yescharacteristic
20D3×D24C411yescharacteristic
21D3×#204—21no—
22C32×#108C2211yescharacteristic, complemented
23C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
24C3×#822—21no—
25C3×#819C2211yescharacteristic, complemented
26C2×C3×C3⋊C16C2211yescharacteristic, complemented
27D3×C3⋊C16—21no—
28D3×C3⋊C16—21no—
29D3×#135—31no—
30C2×#904—31no—
31C2×C3×#108—31no—
32C22×C3⋊C16—31no—
33C2×D3×C16—31no—
34D3×#108D311yescharacteristic, complemented
35C3×#359—31no—
36#4567—31no—
37#4510—31no—
38#4497—31no—
39#4497—31no—
40#4497—31no—
41#4497—31no—
42#4497—61no—
43#4497D311yescharacteristic, direct product factor
44#3828—21no—
45C3×#235—21no—
46C2×C3×C4×D3D411yescharacteristic
47D3×#67—41no—
48#3804—41no—
49D3×D12—21no—
50C4×D32—41no—
51#3799—21no—
52#3798—41no—
53#3795—21no—
54D3×Dic6—21no—
55C32×M16—21no—
56C2×C32×C8C2311yescharacteristic
57#3746C2×C411yescharacteristic
58#3745C2×C411yescharacteristic
59#3744—21no—
60C3×#208—21no—
61C2×C3×C3⋊C8D411yescharacteristic
62C3×Dic12C2×C411yescharacteristic
63C3×D24C2×C411yescharacteristic
64C3×#204—21no—
65C3×ΓL(1,𝔽25)—41no—
66C3×D3×C8—41no—
67C3×D3×C8C2×C411yescharacteristic
68C3×D3×C8C2×C411yescharacteristic
69C3×D3×C8D411yescharacteristic
70C3×D3×C8D411yescharacteristic
71#3719—21no—
72#3717—21no—
73#3716—21no—
74#3714—21no—
75C3⋊(C3⋊C16)—21no—
76C3×C3⋊C16—21no—
77C2×#359—91noSylow
78D3×#41—61no—
79C2×#235—61no—
80C3×#135—31no—
81C2×C3×M16—61no—
82C22×C3×C8—31no—
83#950—61no—
84#919—31no—
85D3×Q16—31no—
86#916—61no—
87D3×SD16—61no—
88#912—31no—
89D3×D8—31no—
90D3×M16—21no—
91C2×Dic12—31no—
92#904—31no—
93#904—31no—
94#904—31no—
95#904—31no—
96#904—61no—
97#904—61no—
98#904—61no—
99#904C2×D311yescharacteristic
100C2×D24—31no—
101C2×#204—61no—
102C2×D3×C8C2×D311yescharacteristic
103C2×C3×C16—31no—
104C3×#108—21no—
105C3×#108—31no—
106C3×#108—61no—
107C3×#108C2×D311yescharacteristic, complemented
108C3×#108C2×D311yescharacteristic, complemented
109#822—21no—
110#819C2×D311yescharacteristic, complemented
111C2×C3⋊C16—31no—
112C2×C3⋊C16—31no—
113C2×C3⋊C16—61no—
114C2×C3⋊C16—61no—
115C2×C3⋊C16—61no—
116C2×C3⋊C16C2×D311yescharacteristic, complemented
117D3×C16—61no—
118D3×C16—61no—
119C22×C3×D3SD1611yescharacteristic
120C2×D32—41no—
121C2×C32×C4C2×D411yescharacteristic
122#638—41no—
123C4⋊(C3⋊D3)—21no—
124C4×C3⋊D3—41no—
125#634—21no—
126C3×#67—41no—
127C2×C3×Dic3SD1611yescharacteristic
128C3×D12—21no—
129C3×C4×D3—41no—
130C3×C4×D3C22⋊C411yescharacteristic
131C3×C4×D3C22⋊C411yescharacteristic
132C3×C4×D3D811yescharacteristic
133C3×C4×D3D811yescharacteristic
134C3×Dic6—21no—
135#627—41no—
136#626—41no—
137#626—41no—
138#625—41no—
139#624—41no—
140D3×Dic3—41no—
141D3×Dic3—41no—
142C32×C8—41no—
143C32×C8C22×C411yescharacteristic
144C32×C8C2×D411yescharacteristic
145C3×C3⋊C8—41no—
146C3×C3⋊C8C22⋊C411yescharacteristic
147C3×C3⋊C8C22⋊C411yescharacteristic
148C2×#135—91no—
149C22×C16—91no—
150C2×#108—31no—
151#359—31no—
152#359—91no—
153#359—91no—
154#359—91no—
155C3×#41—61no—
156C22×C3×C4—31no—
157C2×#67—121no—
158#239—61no—
159D3×Q8—61no—
160#237—61no—
161#237—121no—
162D3×D4—61no—
163D3×D4—121no—
164#235—21no—
165#235—61no—
166#235—61no—
167#235—61no—
168#235—61no—
169#235—121no—
170#235—121no—
171#235—121no—
172#235—121no—
173C2×D12—61no—
174C2×C4×D3—121no—
175C2×C4×D3—121no—
176C2×C4×D3#6711yescharacteristic
177C2×Dic6—61no—
178C3×Q16—31no—
179C3×SD16—61no—
180C3×D8—31no—
181C3×M16—21no—
182C3×M16—21no—
183C3×M16—41no—
184C3×M16—61no—
185C3×M16—121no—
186C2×C3×C8—21no—
187C2×C3×C8—31no—
188C2×C3×C8—31no—
189C2×C3×C8—31no—
190C2×C3×C8—31no—
191C2×C3×C8—31no—
192C2×C3×C8—121no—
193C2×C3×C8C22×D311yescharacteristic
194C2×C3×C8C22×D311yescharacteristic
195#216—61no—
196#215—61no—
197#214—61no—
198#213—61no—
199#208—21no—
200C2×C3⋊C8#6711yescharacteristic
201Dic12—31no—
202Dic12—31no—
203Dic12—61no—
204Dic12—61no—
205Dic12C4×D311yescharacteristic
206D24—31no—
207D24—31no—
208D24—61no—
209D24—61no—
210D24C4×D311yescharacteristic
211#204—21no—
212#204—61no—
213#204—61no—
214#204—61no—
215#204—61no—
216#204—121no—
217ΓL(1,𝔽25)—41no—
218D3×C8—41no—
219D3×C8C4×D311yescharacteristic
220D3×C8C4×D311yescharacteristic
221D3×C8D1211yescharacteristic
222D3×C8D1211yescharacteristic
223C3×C16—61no—
224C3⋊C16—21no—
225C3⋊C16—61no—
226C3⋊C16—61no—
227C3⋊C16—121no—
228C22×C32C2×SD1611yescharacteristic
229C2×C3⋊D3—41no—
230C2×C3×D3—22no—
231C2×C3×D3—41no—
232C2×C3×D3#10211yescharacteristic
233C2×C3×D3#10211yescharacteristic
234D32—82no—
235C32×C4C2×C22⋊C411yescharacteristic
236C32×C4C2×D811yescharacteristic
237C3⋊Dic3—41no—
238C3×Dic3—41no—
239C3×Dic3#10211yescharacteristic
240C3×Dic3#10211yescharacteristic
241C2×#41—181no—
242#135—31no—
243#135—91no—
244#135—91no—
245#135—91no—
246#135—181no—
247#135—181no—
248C2×Q16—91no—
249C2×SD16—181no—
250C2×D8—91no—
251C2×M16—61no—
252C22×C8—31no—
253C2×C16—31no—
254C2×C16—91no—
255C2×C16—181no—
256C2×C16—181no—
257#108—31no—
258#108—61no—
259#108D3211yescharacteristic, complemented
260C23×C3—31no—
261C22×D3—121no—
262C22×D3—121no—
263C22×D3#21511yescharacteristic
264C3×Q8—61no—
265C3×D4—61no—
266C3×D4—121no—
267C2×C3×C4—21no—
268C2×C3×C4—31no—
269C2×C3×C4—31no—
270C2×C3×C4—31no—
271C2×C3×C4—31no—
272C2×C3×C4—31no—
273C2×C3×C4—121no—
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276#67—41no—
277#67—121no—
278#67—121no—
279#67—121no—
280#67—121no—
281#67—121no—
282#67—121no—
283#67—241no—
284C2×Dic3—121no—
285C2×Dic3—121no—
286C2×Dic3#21511yescharacteristic
287D12—21no—
288D12—61no—
289D12—61no—
290D12—121no—
291D12—121no—
292D12—121no—
293C4×D3—41no—
294C4×D3—121no—
295C4×D3—121no—
296C4×D3—121no—
297C4×D3—121no—
298C4×D3—121no—
299C4×D3—121no—
300C4×D3—241no—
301C4×D3(C2×D3)⋊C411yescharacteristic
302C4×D3(C2×D3)⋊C411yescharacteristic
303C4×D3#21311yescharacteristic
304C4×D3#21311yescharacteristic
305Dic6—21no—
306Dic6—61no—
307Dic6—61no—
308Dic6—121no—
309Dic6—121no—
310Dic6—121no—
311C3×C8—21no—
312C3×C8—21no—
313C3×C8—31no—
314C3×C8—31no—
315C3×C8—41no—
316C3×C8—41no—
317C3×C8—81no—
318C3×C8—121no—
319C3×C8C2×C4×D311yescharacteristic
320C3×C8C2×C4×D311yescharacteristic
321C3×C8C2×D1211yescharacteristic
322C3×C8D3×D411yescharacteristic
323C3⋊C8—41no—
324C3⋊C8(C2×D3)⋊C411yescharacteristic
325C3⋊C8(C2×D3)⋊C411yescharacteristic
326C2×C32—21no—
327C2×C32C2×#10211yescharacteristic
328C3⋊D3—81no—
329C3×D3—21no—
330C3×D3—81no—
331C3×D3#35912yescomplemented
332#41—61no—
333#41—181no—
334#41—181no—
335#41—181no—
336#41—361no—
337#41—361no—
338C2×Q8—181no—
339C2×D4—181no—
340C2×D4—361no—
341C22×C4—31no—
342C22×C4—361no—
343Q16—31no—
344Q16—91no—
345Q16—181no—
346SD16—61no—
347SD16—181no—
348SD16—181no—
349SD16—181no—
350D8—31no—
351D8—91no—
352D8—181no—
353M16—21no—
354M16—61no—
355M16—121no—
356C2×C8—31no—
357C2×C8—31no—
358C2×C8—31no—
359C2×C8—31no—
360C2×C8—31no—
361C2×C8—121no—
362C2×C8C2×D3211yescharacteristic
363C16—61no—
364C16—181no—
365C22×C3—21no—
366C22×C3—31no—
367C22×C3—31no—
368C22×C3—62no—
369C22×C3—121no—
370C22×C3D3×SD1611yescharacteristic
371C22×C3C2×#21511yescharacteristic
372C2×D3—22no—
373C2×D3—41no—
374C2×D3—121no—
375C2×D3—121no—
376C2×D3—241no—
377C2×D3—242no—
378C2×D3—242no—
379C2×D3#80911yescharacteristic
380C2×D3#80911yescharacteristic
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—31no—
384C3×C4—31no—
385C3×C4—121no—
386C3×C4D3×C22⋊C411yescharacteristic
387C3×C4D3×D811yescharacteristic
388C3×C4C2×(C2×D3)⋊C411yescharacteristic
389C3×C4C2×#21311yescharacteristic
390Dic3—41no—
391Dic3—121no—
392Dic3—121no—
393Dic3—241no—
394Dic3#80911yescharacteristic
395Dic3#80911yescharacteristic
396C32C2×#35911yescharacteristic, complemented, Sylow
397C23—31no—
398C23—361no—
399Q8—61no—
400Q8—181no—
401Q8—361no—
402D4—61no—
403D4—121no—
404D4—181no—
405D4—361no—
406D4—361no—
407D4—361no—
408D4—361no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—121no—
415C2×C4—361no—
416C2×C4—361no—
417C2×C4—361no—
418C2×C4—361no—
419C2×C4D3×#6711yescharacteristic
420C8—31no—
421C8—31no—
422C8—41no—
423C8—121no—
424C8C4×D3211yescharacteristic
425C8D3×D1211yescharacteristic
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—32no—
430C2×C3—41no—
431C2×C3—61no—
432C2×C3—241no—
433C2×C3D3×#10211yescharacteristic
434C2×C3C2×#80911yescharacteristic
435D3—21no—
436D3—81no—
437D3—241no—
438D3—241no—
439D3—481no—
440D3#449712yesdirect product factor
441C22—31no—
442C22—31no—
443C22—62no—
444C22—121no—
445C22—361no—
446C22—722no—
447C22D3×#21511yescharacteristic
448C4—31no—
449C4—31no—
450C4—121no—
451C4—361no—
452C4D3×(C2×D3)⋊C411yescharacteristic
453C4D3×#21311yescharacteristic
454C3—21no—
455C3D3×#35911yescharacteristic, complemented
456C3C2×#449711yescharacteristic, complemented
457C2—21no—
458C2—32no—
459C2—61no—
460C2—241no—
461C2—721no—
462C2D3×#80911yescharacteristic
subgroupG/H
centerC4D3×#213
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#108C22
socleC2×C32C2×#102
prime radicalD3×#904C2
cosocleC2×C32×C8C23
hypercenter#108D32
hypocenterC32C2×#359
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
2. C3×D3×#108C2semidirect
3. C2×D3×C3⋊C16C2semidirect
4. #10589363C2semidirect
5. C3×#4497C2semidirect
6. #10589122C2semidirect
7. #10589120C2semidirect
22. C32×#108C22semidirect
23. C2×C3⋊(C3⋊C16)C22semidirect
25. C3×#819C22semidirect
26. C2×C3×C3⋊C16C22semidirect
34. D3×#108D3semidirect
43. #4497D3direct (N × H)
107. C3×#108C2×D3semidirect
108. C3×#108C2×D3semidirect
110. #819C2×D3semidirect
116. C2×C3⋊C16C2×D3semidirect
259. #108D32semidirect
331. C3×D3#359semidirect
396. C32C2×#359semidirect
440. D3#4497direct (N × H)
455. C3D3×#359semidirect
456. C3C2×#4497semidirect

Maximal subgroups

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

subgroupindex
D3×#9042
C3×D3×#1082
C2×D3×C3⋊C162
#105893632
C3×#44972
#105891222
#105891202
C2×#44973
D3×#3593