Finite Group Databasebeta

← #11783911

Subgroups — #11783911

Order 1152.

729 conjugacy classes of subgroups.

The subgroup lattice has 475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594958C211yesmaximal, characteristic
2#10592631C211yesmaximal, characteristic, complemented
3C2×C3×#805C211yesmaximal, characteristic
4C2×#63568C211yesmaximal, characteristic
5#10591060C211yesmaximal, characteristic, complemented
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70354—31nomaximal
9#68729—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#67⋊Dic3—22no—
18#63898C412yescomplemented
19C4×D3×Dic3—21no—
20#63855—21no—
21#63843C412yescomplemented
22#63658—22no—
23C3×#805C414yescomplemented
24#63568C414yescomplemented
25#63555—21no—
26#63553—21no—
27Dic3×#41—31no—
28#5522—31no—
29C2×C3×#104—31no—
30C2×#837—31no—
31C2×#825—31no—
32Dic3×M16—31no—
33Dic3×M16—31no—
34#4932—31no—
35#4932—31no—
36#4932—61no—
37C2×#805D311yescharacteristic
38C3×#339—31no—
39#4555—31no—
40#4532—31no—
41#4523D311yescharacteristic, complemented
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3D412yes—
46C2×C3×#67—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235C2×C412yes—
50C3×#235C2×C412yes—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6C2×C411yescharacteristic
54C2×D3×Dic3—22no—
55C32×C42—21no—
56C32×C42C2×C412yescomplemented
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3C2×C412yes—
59C4×C3⋊Dic3C2×C412yescomplemented
60C4×C3⋊Dic3D411yescharacteristic
61C4×C3⋊Dic3D411yescharacteristic
62C3×#217—21no—
63C3×C4⋊Dic3C2×C412yes—
64C3×C4×Dic3—21no—
65C3×#208—21no—
66C3×#208—21no—
67C3×#208C2×C412yescomplemented
68C3×#208C2×C412yescomplemented
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—22no—
72(C2×D3)⋊Dic3—22no—
73Dic32—22no—
74#1759—91noSylow
75C2×C3×#41—31no—
76C2×#235C2×D311yescharacteristic
77C2×C3×M16—31no—
78C2×C3×M16—31no—
79C3×#117—31no—
80C2×C3×C42—21no—
81C2×C3×C42C2×D311yescharacteristic
82C2×C3×C42C2×D311yescharacteristic
83Q8×Dic3—32no—
84D4×Dic3—32no—
85D4×Dic3—62no—
86#926—61no—
87#926C2×D311yescharacteristic
88C2×C4×Dic3—31no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—31no—
92C2×C4×Dic3—61no—
93C2×C4×Dic3—61no—
94C2×C4×Dic3—61no—
95C2×#208C2×D311yescharacteristic
96C2×#208C2×D311yescharacteristic
97#893—32no—
98#887—32no—
99#67⋊C4—62no—
100#872—61no—
101C42×D3—61no—
102C3×#104—34no—
103#837—34no—
104C3⋊#95—62no—
105C3⋊#95—62no—
106C3⋊#95—64no—
107#825—34no—
108#815—61no—
109#815—61no—
110C8×Dic3—61no—
111C8×Dic3—61no—
112#805Dic314yescomplemented
113C23×C32C2×D411yescharacteristic
114C22×C3×D3—21no—
115C2×C32×C4—22no—
116C2×C32×C4—42no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—42no—
125C2×C3⋊Dic3—42no—
126C2×C3⋊Dic3C22⋊C412yes—
127C2×C3⋊Dic3C22⋊C412yes—
128C3×#67—22no—
129C3×#67—22no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—22no—
132C3×D12—21no—
133C3×D12C4212yes—
134C3×C4×D3—22no—
135C3×C4×D3—22no—
136C3×Dic6—21no—
137C3×Dic6C4212yes—
138D3×Dic3—44no—
139C3×C3⋊C8—22no—
140C3×C3⋊C8—22no—
141C4×#41—91no—
142C2×#104—31no—
143C2×#104—91no—
144C4×M16—91no—
145#376—91no—
146#339—31no—
147#339—91no—
148C3×#41—32no—
149C3×#41—32no—
150C3×#41—61no—
151C3×#41—61no—
152C2×C3×Q8—31no—
153C2×C3×D4—31no—
154C2×C3×D4—61no—
155C22×C3×C4—22no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—21no—
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—62no—
166C22×Dic3—62no—
167C22×Dic3—62no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170#235—21no—
171#235—21no—
172#235C4×D312yes—
173#235C2×Dic312yes—
174C2×D12C4×D311yescharacteristic
175C2×C4×D3—21no—
176C2×C4×D3—62no—
177C2×Dic6C4×D311yescharacteristic
178C3×M16—32no—
179C3×M16—32no—
180C3×M16—61no—
181C3×M16—61no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C3×C4⋊C4—32no—
185C3×C22⋊C4—61no—
186C3×C42—22no—
187C3×C42—21no—
188C3×C42—21no—
189C3×C42—22no—
190C3×C42—61no—
191C3×C42C4×D312yescomplemented
192C3×C42C2×Dic312yescomplemented
193#217—21no—
194#217—62no—
195(C2×D3)⋊C4—62no—
196C4⋊Dic3—62no—
197C4⋊Dic3C4×D312yes—
198Dic3⋊C4—62no—
199C4×Dic3—21no—
200C4×Dic3—32no—
201C4×Dic3—32no—
202C4×Dic3—31no—
203C4×Dic3—31no—
204C4×Dic3—31no—
205C4×Dic3—31no—
206C4×Dic3—32no—
207C4×Dic3—32no—
208C4×Dic3—62no—
209C4×Dic3—62no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—62no—
213C4×Dic3—62no—
214C4×Dic3—62no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217#208—21no—
218#208—21no—
219#208C4×D312yescomplemented
220#208C2×Dic312yescomplemented
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C22×C32—22no—
224C22×C32C2×C22⋊C411yescharacteristic
225C22×C32C4×D411yescharacteristic
226C22×C32C4×D411yescharacteristic
227C2×C3×D3—22no—
228C2×C3×D3—42no—
229C32×C4—42no—
230C32×C4C2×C4211yescharacteristic
231C32×C4#11711yescharacteristic
232C32×C4C4×D411yescharacteristic
233C32×C4C4×D411yescharacteristic
234C3⋊Dic3—22no—
235C3⋊Dic3—22no—
236C3⋊Dic3—42no—
237C3×Dic3—22no—
238C3×Dic3—42no—
239C2×#41—31no—
240C2×M16—31no—
241C2×M16—31no—
242C4×Q8—92no—
243C4×D4—92no—
244C4×D4—182no—
245#117—31no—
246#117—181no—
247C2×C42—91no—
248C2×C42—91no—
249C2×C42—181no—
250C2×C42D3211yescharacteristic
251#104—34no—
252#104—94no—
253#97—181no—
254C4×C8—181no—
255#95—182no—
256C23×C3—21no—
257C23×C3—61no—
258C23×C3D3×D411yescharacteristic
259C23×C3D3×D411yescharacteristic
260C22×D3—21no—
261C3×Q8—32no—
262C3×Q8—61no—
263C3×D4—32no—
264C3×D4—62no—
265C3×D4—62no—
266C3×D4—61no—
267C2×C3×C4—24no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—44no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—61no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4C2×C4×D311yescharacteristic
286C2×C3×C4C2×C4×D311yescharacteristic
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4#23711yescharacteristic
291C2×C3×C4#23711yescharacteristic
292C2×C3×C4#23711yescharacteristic
293C2×C3×C4#23911yescharacteristic
294C2×C3×C4C22×Dic311yescharacteristic
295#67—22no—
296#67—22no—
297C2×Dic3—21no—
298C2×Dic3—22no—
299C2×Dic3—32no—
300C2×Dic3—32no—
301C2×Dic3—32no—
302C2×Dic3—32no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—64no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—124no—
309C2×Dic3—122no—
310C2×Dic3—122no—
311C2×Dic3—124no—
312C2×Dic3—124no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315D12—21no—
316D12C4×Dic312yes—
317C4×D3—22no—
318C4×D3—22no—
319C4×D3—124no—
320Dic6—21no—
321Dic6C4×Dic312yes—
322C3×C8—62no—
323C3×C8—62no—
324C3⋊C8—22no—
325C3⋊C8—22no—
326C2×C32—21no—
327C2×C32—21no—
328C2×C32C4×C22⋊C411yescharacteristic
329C2×C32#42112yes—
330C3×D3—42no—
331#41—32no—
332#41—32no—
333#41—61no—
334#41—61no—
335C2×Q8—31no—
336C2×D4—31no—
337C2×D4—61no—
338C22×C4—21no—
339C22×C4—61no—
340C22×C4—92no—
341C22×C4—182no—
342C22×C4—181no—
343C22×C4C2×D3211yescharacteristic
344M16—32no—
345M16—32no—
346M16—61no—
347M16—61no—
348C2×C8—61no—
349C2×C8—61no—
350C4⋊C4—32no—
351C4⋊C4—182no—
352C22⋊C4—61no—
353C22⋊C4—182no—
354C42—21no—
355C42—61no—
356C42—92no—
357C42—91no—
358C42—91no—
359C42—92no—
360C42—182no—
361C42—181no—
362C42D3×Dic312yescomplemented
363C22×C3—24no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—62no—
370C22×C3—122no—
371C22×C3D3×C22⋊C411yescharacteristic
372C22×C3D3×C22⋊C411yescharacteristic
373C22×C3#67⋊C411yescharacteristic
374C22×C3#67⋊C411yescharacteristic
375C22×C3#89311yescharacteristic
376C22×C3D4×Dic311yescharacteristic
377C2×D3—22no—
378C2×D3—42no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—44no—
384C3×C4—42no—
385C3×C4—42no—
386C3×C4—62no—
387C3×C4—122no—
388C3×C4C42×D311yescharacteristic
389C3×C4#87711yescharacteristic
390C3×C4#67⋊C411yescharacteristic
391C3×C4#67⋊C411yescharacteristic
392C3×C4#89211yescharacteristic
393C3×C4#89311yescharacteristic
394C3×C4C2×C4×Dic311yescharacteristic
395C3×C4D4×Dic311yescharacteristic
396Dic3—22no—
397Dic3—42no—
398Dic3—62no—
399Dic3—62no—
400Dic3—62no—
401Dic3—62no—
402Dic3—122no—
403Dic3—122no—
404Dic3—124no—
405Dic3—122no—
406Dic3—122no—
407C32#175911yescharacteristic, complemented, Sylow
408C23—61no—
409C23#381111yescharacteristic
410Q8—32no—
411Q8—61no—
412D4—32no—
413D4—62no—
414D4—62no—
415D4—61no—
416C2×C4—22no—
417C2×C4—42no—
418C2×C4—61no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—92no—
423C2×C4—92no—
424C2×C4—182no—
425C2×C4—364no—
426C2×C4—362no—
427C2×C4—362no—
428C2×C4#379611yescharacteristic
429C2×C4C4×D3211yescharacteristic
430C2×C4C4×D3211yescharacteristic
431C2×C4#380211yescharacteristic
432C2×C4C2×D3×Dic311yescharacteristic
433C2×C4#380511yescharacteristic
434C8—62no—
435C8—62no—
436C2×C3—22no—
437C2×C3—22no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—22no—
444C2×C3—122no—
445C2×C3#466611yescharacteristic
446C2×C3#482112yes—
447C2×C3#482112yes—
448C2×C3Dic3×C22⋊C411yescharacteristic
449D3—42no—
450C22—22no—
451C22—62no—
452C22—122no—
453C22#6388111yescharacteristic
454C22#6392111yescharacteristic
455C22#67⋊Dic311yescharacteristic
456C4—42no—
457C4—62no—
458C4—122no—
459C4—182no—
460C4—182no—
461C4—362no—
462C4C4×D3×Dic311yescharacteristic
463C4#6387811yescharacteristic
464C4#6389811yescharacteristic
465C4#6390211yescharacteristic
466C3—21no—
467C3#6872911yescharacteristic, complemented
468C3#7035411yescharacteristic, complemented
469C2—21no—
470C2—21no—
471C2—122no—
472C2#1059039412yes—
473C2#1059136811yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1759
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592631C2semidirect
5. #10591060C2semidirect
6. C3×#4523C2semidirect
7. #10589160C2semidirect
18. #63898C4semidirect
21. #63843C4semidirect
23. C3×#805C4semidirect
24. #63568C4semidirect
41. #4523D3semidirect
56. C32×C42C2×C4semidirect
59. C4×C3⋊Dic3C2×C4semidirect
67. C3×#208C2×C4semidirect
68. C3×#208C2×C4semidirect
112. #805Dic3semidirect
191. C3×C42C4×D3semidirect
192. C3×C42C2×Dic3semidirect
219. #208C4×D3semidirect
220. #208C2×Dic3semidirect
362. C42D3×Dic3semidirect
407. C32#1759semidirect
467. C3#68729semidirect
468. C3#70354semidirect

Maximal subgroups

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

subgroupindex
#105949582
#105926312
C2×C3×#8052
C2×#635682
#105910602
C3×#45232
#105891602
#703543
#687293