Finite Group Databasebeta

← D3×#4567 #11796768

Subgroups — D3×#4567 #11796768

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
1C3×D3×#135C211yesmaximal, characteristic
2D3×#819C211yesmaximal, characteristic, complemented
3C2×D3×C3⋊C16C211yesmaximal, characteristic, complemented
4#10589433C211yesmaximal, characteristic, complemented
5C3×#4567C211yesmaximal, characteristic, complemented
6#10589121C211yesmaximal, characteristic, complemented
7#10589120C211yesmaximal, characteristic, complemented
8C2×#4567—31nomaximal
9D3×#359—31nomaximal
10C3×D3×#41—21no—
11C32×#135C2211yescharacteristic
12C3×#950—21no—
13C3×#919C411yescharacteristic
14C3×D3×Q16C411yescharacteristic
15C3×#916—21no—
16C3×D3×SD16—21no—
17C3×#912C411yescharacteristic
18C3×D3×D8C411yescharacteristic
19C3×#904C2211yescharacteristic
20C2×C3×D3×C8C2211yescharacteristic
21D3×#208—21no—
22#63646C2211yescharacteristic, complemented
23C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
24C3×#819C2211yescharacteristic, complemented
25C2×C3×C3⋊C16C2211yescharacteristic, complemented
26#63577—21no—
27D3×C3⋊C16—21no—
28D3×C3⋊C16—21no—
29C2×C3×#135—31no—
30D3×#135D311yescharacteristic
31C2×#819—31no—
32C22×C3⋊C16—31no—
33C2×D3×C16—31no—
34D3×#108—31no—
35C3×#359—31no—
36#4567—31no—
37#4567—31no—
38#4567—31no—
39#4567—31no—
40#4567—61no—
41#4567D311yescharacteristic, direct product factor
42#4510—31no—
43#4497—31no—
44C32×#41—21no—
45C3×#239—21no—
46C3×D3×Q8—21no—
47C3×#237—21no—
48C3×#237—41no—
49C3×D3×D4—21no—
50C3×D3×D4—41no—
51C3×#235—21no—
52C3×#235—41no—
53C2×C3×C4×D3—41no—
54C2×C3×C4×D3D411yescharacteristic
55C32×Q16C2×C411yescharacteristic
56C32×SD16—21no—
57C32×D8C2×C411yescharacteristic
58C2×C32×C8C2311yescharacteristic
59#3748—21no—
60C3×#216—21no—
61C3×#215—21no—
62C3×#214—21no—
63C3×#213—21no—
64C3×#208—21no—
65C2×C3×C3⋊C8D411yescharacteristic
66C3×Dic12C2×C411yescharacteristic
67C3×D24C2×C411yescharacteristic
68C3×#204—21no—
69C3×D3×C8C2×C411yescharacteristic
70C3×D3×C8C2×C411yescharacteristic
71C3×D3×C8D411yescharacteristic
72C3×D3×C8D411yescharacteristic
73#3711—41no—
74D3×C3⋊C8—41no—
75C3⋊(C3⋊C16)—21no—
76C3×C3⋊C16—21no—
77C2×#359—91noSylow
78C2×C3×#41—61no—
79D3×#41—21no—
80C3×#135—21no—
81C3×#135—31no—
82C3×#135—31no—
83C3×#135—31no—
84C3×#135—61no—
85C3×#135—61no—
86C3×#135C2×D311yescharacteristic
87C3×#135C2×D311yescharacteristic
88C2×C3×Q16—31no—
89C2×C3×SD16—61no—
90C2×C3×D8—31no—
91C22×C3×C8—31no—
92#950—21no—
93C2×#208—61no—
94#919Dic311yescharacteristic
95D3×Q16Dic311yescharacteristic
96#916—21no—
97D3×SD16—21no—
98#912Dic311yescharacteristic
99D3×D8Dic311yescharacteristic
100D3×M16—61no—
101#904C2×D311yescharacteristic
102C2×D3×C8C2×D311yescharacteristic
103C2×C3×C16—31no—
104C3×#108—31no—
105#822—61no—
106#819—31no—
107#819—31no—
108#819—61no—
109#819—61no—
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×D3—41no—
120C22×C3×D3SD1611yescharacteristic
121C32×Q8—21no—
122C32×D4—21no—
123C32×D4—41no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C3×#67—41no—
127C3×#67—41no—
128C3×#67—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3SD1611yescharacteristic
131C3×D12—21no—
132C3×D12—41no—
133C3×C4×D3—41no—
134C3×C4×D3—41no—
135C3×C4×D3—41no—
136C3×C4×D3C22⋊C411yescharacteristic
137C3×C4×D3C22⋊C411yescharacteristic
138C3×C4×D3D811yescharacteristic
139C3×C4×D3D811yescharacteristic
140C3×Dic6—21no—
141C3×Dic6—41no—
142C32×C8C22×C411yescharacteristic
143C32×C8C2×D411yescharacteristic
144C3⋊(C3⋊C8)—41no—
145C3×C3⋊C8—41no—
146C3×C3⋊C8C22⋊C411yescharacteristic
147C3×C3⋊C8C22⋊C411yescharacteristic
148C2×#135—31no—
149C22×C16—91no—
150C2×#108—91no—
151#359—31no—
152#359—91no—
153#359—91no—
154#359—91no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41—41no—
158C3×#41—61no—
159C3×#41—61no—
160C3×#41—61no—
161C3×#41—121no—
162C3×#41—121no—
163C2×C3×Q8—61no—
164C2×C3×D4—61no—
165C2×C3×D4—121no—
166C22×C3×C4—31no—
167C22×C3×C4—121no—
168#239—21no—
169D3×Q8—21no—
170#237—21no—
171#237—41no—
172D3×D4—21no—
173D3×D4—41no—
174#235—21no—
175#235—41no—
176C2×C4×D3—41no—
177C2×C4×D3#6711yescharacteristic
178C3×Q16—21no—
179C3×Q16—31no—
180C3×Q16—61no—
181C3×Q16C4×D311yescharacteristic
182C3×Q16C2×Dic311yescharacteristic
183C3×SD16—21no—
184C3×SD16—21no—
185C3×SD16—41no—
186C3×SD16—61no—
187C3×SD16—61no—
188C3×SD16—61no—
189C3×D8—21no—
190C3×D8—31no—
191C3×D8—61no—
192C3×D8C4×D311yescharacteristic
193C3×D8C2×Dic311yescharacteristic
194C3×M16—61no—
195C2×C3×C8—21no—
196C2×C3×C8—31no—
197C2×C3×C8—31no—
198C2×C3×C8—31no—
199C2×C3×C8—31no—
200C2×C3×C8—31no—
201C2×C3×C8C22×D311yescharacteristic
202C2×C3×C8C22×D311yescharacteristic
203#216—21no—
204#215—21no—
205#214—21no—
206#213—21no—
207#208—21no—
208#208—61no—
209#208—61no—
210#208—121no—
211#208—121no—
212C2×C3⋊C8—121no—
213C2×C3⋊C8#6711yescharacteristic
214Dic12C2×Dic311yescharacteristic
215D24C2×Dic311yescharacteristic
216#204—21no—
217ΓL(1,𝔽25)—121no—
218D3×C8—121no—
219D3×C8C2×Dic311yescharacteristic
220D3×C8C2×Dic311yescharacteristic
221D3×C8#6711yescharacteristic
222D3×C8#6711yescharacteristic
223C3×C16—61no—
224C3⋊C16—21no—
225C3⋊C16—61no—
226C3⋊C16—61no—
227C3⋊C16—121no—
228C22×C32—41no—
229C22×C32C2×SD1611yescharacteristic
230C2×C3×D3—22no—
231C2×C3×D3—41no—
232C2×C3×D3—82no—
233C2×C3×D3#10211yescharacteristic
234C2×C3×D3#10211yescharacteristic
235C32×C4—41no—
236C32×C4C2×C22⋊C411yescharacteristic
237C32×C4C2×D811yescharacteristic
238C3×Dic3—41no—
239C3×Dic3#10211yescharacteristic
240C3×Dic3#10211yescharacteristic
241C2×#41—61no—
242#135—31no—
243#135—31no—
244#135—31no—
245#135—61no—
246#135—61no—
247#135D3211yescharacteristic
248C2×Q16—31no—
249C2×SD16—61no—
250C2×D8—31no—
251C2×M16—181no—
252C22×C8—31no—
253C2×C16—31no—
254C2×C16—91no—
255C2×C16—181no—
256C2×C16—181no—
257#108—31no—
258#108—91no—
259#108—181no—
260C23×C3—31no—
261C23×C3—121no—
262C22×D3—41no—
263C22×D3#21411yescharacteristic
264C3×Q8—21no—
265C3×Q8—21no—
266C3×Q8—41no—
267C3×Q8—61no—
268C3×Q8—121no—
269C3×D4—21no—
270C3×D4—21no—
271C3×D4—41no—
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—61no—
275C3×D4—81no—
276C3×D4—121no—
277C3×D4—121no—
278C3×D4—121no—
279C3×D4—121no—
280C2×C3×C4—21no—
281C2×C3×C4—31no—
282C2×C3×C4—31no—
283C2×C3×C4—31no—
284C2×C3×C4—31no—
285C2×C3×C4—31no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—81no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4—121no—
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295#67—41no—
296#67—41no—
297#67—41no—
298C2×Dic3—41no—
299C2×Dic3#21411yescharacteristic
300D12—21no—
301D12—41no—
302C4×D3—41no—
303C4×D3—41no—
304C4×D3—41no—
305C4×D3#21311yescharacteristic
306C4×D3#21311yescharacteristic
307C4×D3#21711yescharacteristic
308C4×D3#21711yescharacteristic
309Dic6—21no—
310Dic6—41no—
311C3×C8—21no—
312C3×C8—21no—
313C3×C8—31no—
314C3×C8—31no—
315C3×C8—121no—
316C3×C8C2×C4×D311yescharacteristic
317C3×C8D3×D411yescharacteristic
318C3×C8C22×Dic311yescharacteristic
319C3×C8C2×#6711yescharacteristic
320C3⋊C8—41no—
321C3⋊C8—121no—
322C3⋊C8—121no—
323C3⋊C8—241no—
324C3⋊C8#21711yescharacteristic
325C3⋊C8#21711yescharacteristic
326C2×C32—21no—
327C2×C32—81no—
328C2×C32C2×#10211yescharacteristic
329C3×D3—21no—
330C3×D3—81no—
331C3×D3#35912yescomplemented
332#41—21no—
333#41—61no—
334#41—61no—
335#41—61no—
336#41—121no—
337#41—121no—
338C2×Q8—61no—
339C2×D4—61no—
340C2×D4—121no—
341C22×C4—31no—
342C22×C4—121no—
343Q16—31no—
344Q16—61no—
345Q16D3×Dic311yescharacteristic
346SD16—21no—
347SD16—61no—
348SD16—61no—
349SD16—61no—
350D8—31no—
351D8—61no—
352D8D3×Dic311yescharacteristic
353M16—61no—
354M16—181no—
355M16—361no—
356C2×C8—31no—
357C2×C8—31no—
358C2×C8—31no—
359C2×C8—31no—
360C2×C8—31no—
361C2×C8—361no—
362C2×C8C2×D3211yescharacteristic
363C16—61no—
364C16—181no—
365C22×C3—21no—
366C22×C3—31no—
367C22×C3—31no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—62no—
371C22×C3—81no—
372C22×C3—121no—
373C22×C3—242no—
374C22×C3D3×SD1611yescharacteristic
375C22×C3C2×#21411yescharacteristic
376C2×D3—22no—
377C2×D3—41no—
378C2×D3—82no—
379C2×D3#83211yescharacteristic
380C2×D3#83211yescharacteristic
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—31no—
384C3×C4—31no—
385C3×C4—41no—
386C3×C4—41no—
387C3×C4—81no—
388C3×C4—121no—
389C3×C4D3×C22⋊C411yescharacteristic
390C3×C4D3×D811yescharacteristic
391C3×C4C2×#21311yescharacteristic
392C3×C4C2×#21711yescharacteristic
393Dic3—41no—
394Dic3#83211yescharacteristic
395Dic3#83211yescharacteristic
396C32C2×#35911yescharacteristic, complemented, Sylow
397C23—31no—
398C23—121no—
399Q8—21no—
400Q8—61no—
401Q8—121no—
402D4—21no—
403D4—41no—
404D4—61no—
405D4—121no—
406D4—121no—
407D4—121no—
408D4—121no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—41no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C4—121no—
419C2×C4D3×#6711yescharacteristic
420C8—31no—
421C8—31no—
422C8—121no—
423C8—361no—
424C8C2×D3×Dic311yescharacteristic
425C8D3×#6711yescharacteristic
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—32no—
430C2×C3—41no—
431C2×C3—61no—
432C2×C3—81no—
433C2×C3—81no—
434C2×C3—161no—
435C2×C3—241no—
436C2×C3D3×#10211yescharacteristic
437C2×C3C2×#83211yescharacteristic
438D3—21no—
439D3—81no—
440D3#456712yesdirect product factor
441C22—31no—
442C22—31no—
443C22—41no—
444C22—62no—
445C22—121no—
446C22—242no—
447C22D3×#21411yescharacteristic
448C4—31no—
449C4—31no—
450C4—41no—
451C4—121no—
452C4D3×#21311yescharacteristic
453C4D3×#21711yescharacteristic
454C3—21no—
455C3D3×#35911yescharacteristic, complemented
456C3C2×#456711yescharacteristic, complemented
457C2—21no—
458C2—32no—
459C2—61no—
460C2—81no—
461C2—241no—
462C2D3×#83211yescharacteristic
subgroupG/H
centerC4D3×#213
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#135C22
socleC2×C32C2×#102
prime radicalC3×D3×#135C2
cosocleC2×C32×C8C23
hypercenter#135D32
hypocenterC32C2×#359
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
2. D3×#819C2semidirect
3. C2×D3×C3⋊C16C2semidirect
4. #10589433C2semidirect
5. C3×#4567C2semidirect
6. #10589121C2semidirect
7. #10589120C2semidirect
22. #63646C22semidirect
23. C2×C3⋊(C3⋊C16)C22semidirect
24. C3×#819C22semidirect
25. C2×C3×C3⋊C16C22semidirect
41. #4567D3direct (N × H)
110. #819C2×D3semidirect
116. C2×C3⋊C16C2×D3semidirect
331. C3×D3#359semidirect
396. C32C2×#359semidirect
440. D3#4567direct (N × H)
455. C3D3×#359semidirect
456. C3C2×#4567semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1352
D3×#8192
C2×D3×C3⋊C162
#105894332
C3×#45672
#105891212
#105891202
C2×#45673
D3×#3593