Finite Group Databasebeta

← #11786704

Subgroups — #11786704

Order 1152.

659 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594986C211yesmaximal, characteristic
2C3×#4935C211yesmaximal, characteristic, complemented
3C2×C3×#805C211yesmaximal, characteristic
4#10591130C211yesmaximal, characteristic, complemented
5#10591087C211yesmaximal, characteristic
6#10589389C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70363—31nomaximal
9#69592—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3—22no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18Dic3×#67—22no—
19#63898—21no—
20D3×C4⋊Dic3—21no—
21#63843—21no—
22#63841—21no—
23C3×#805C414yescomplemented
24#63575—21no—
25#63573—21no—
26#63565—21no—
27#63562—21no—
28#5827—31no—
29#5504—31no—
30C2×C3×#104—31no—
31C3×#384—31no—
32#5232—31no—
33#5121—31no—
34#4966—31no—
35#4964—31no—
36#4935D311yescharacteristic, complemented
37C2×#805D311yescharacteristic
38#4554—31no—
39#4530—31no—
40#4523—31no—
41#4523—31no—
42#4523—61no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3D412yes—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235C2×C412yes—
51C3×#235Q812yes—
52C2×C3×D12D411yescharacteristic
53C2×C3×C4×D3—21no—
54C2×C3×Dic6D411yescharacteristic
55C2×D3×Dic3—22no—
56C32×C42—21no—
57C32×C42C2×C412yescomplemented
58#3757—21no—
59C4⋊(C3⋊Dic3)D411yescharacteristic
60C4⋊(C3⋊Dic3)D411yescharacteristic
61C4×C3⋊Dic3—21no—
62#3748—21no—
63#3748—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—44no—
70C3×#208—21no—
71C3×#208C2×C412yescomplemented
72C2×C3×C3⋊C8—21no—
73Dic3⋊Dic3—22no—
74(C2×D3)⋊Dic3—22no—
75Dic32—22no—
76#1859—91noSylow
77C2×C3×#41—31no—
78C2×#235C2×D311yescharacteristic
79C2×C3×M16—31no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—62no—
83C2×C3×C42—21no—
84C2×C3×C42C2×D311yescharacteristic
85C2×C3×C42C2×D311yescharacteristic
86Q8×Dic3—61no—
87D4×Dic3—61no—
88D4×Dic3—62no—
89C4×#67—62no—
90#926—31no—
91#926—31no—
92#926—61no—
93#926—61no—
94C2×C4⋊Dic3—22no—
95C2×C4⋊Dic3—61no—
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×#208—31no—
99C2×#208—31no—
100C2×#208—61no—
101C2×#208C2×D311yescharacteristic
102#893—61no—
103#892—61no—
104D3×C4⋊C4—61no—
105#887—61no—
106C3×#104—34no—
107#835—61no—
108#832—61no—
109#818—61no—
110#817—61no—
111#810—61no—
112#809—61no—
113#808—61no—
114#807—61no—
115#805Dic314yescomplemented
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×Q811yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C3×#67—22no—
130C3×#67—22no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—41no—
136C3×D12—21no—
137C3×D12C4⋊C412yescomplemented
138C3×C4×D3—22no—
139C3×C4×D3—22no—
140C3×Dic6—21no—
141C3×Dic6C4⋊C412yescomplemented
142D3×Dic3—82no—
143C3⋊(C3⋊C8)—41no—
144C3×C3⋊C8—22no—
145#520—91no—
146#428—91no—
147C2×#104—31no—
148#417—91no—
149#384—31no—
150#343—91no—
151#339—91no—
152C3×#41—32no—
153C3×#41—32no—
154C3×#41—61no—
155C3×#41—61no—
156C2×C3×Q8—31no—
157C2×C3×D4—31no—
158C2×C3×D4—61no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—32no—
163C22×C3×C4—41no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—21no—
169C22×Dic3—21no—
170C22×Dic3—62no—
171C22×Dic3#6712yes—
172#235—21no—
173#235—21no—
174#235Dic612yes—
175#235C2×Dic312yes—
176C2×D12D1211yescharacteristic
177C2×C4×D3—21no—
178C2×C4×D3—62no—
179C2×Dic6D1211yescharacteristic
180C3×M16—32no—
181C3×M16—61no—
182C2×C3×C8—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—124no—
188C3×C42—21no—
189C3×C42—21no—
190C3×C42—22no—
191C3×C42—41no—
192C3×C42C4×D312yescomplemented
193C3×C42C2×Dic312yescomplemented
194#217—62no—
195#217—61no—
196#217—61no—
197#217—121no—
198(C2×D3)⋊C4—62no—
199C4⋊Dic3—21no—
200C4⋊Dic3—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3—21no—
203C4⋊Dic3—31no—
204C4⋊Dic3—31no—
205C4⋊Dic3—31no—
206C4⋊Dic3—31no—
207C4⋊Dic3—44no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—62no—
211Dic3⋊C4—62no—
212C4×Dic3—62no—
213C4×Dic3—62no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—121no—
217#208—21no—
218#208—62no—
219#208—61no—
220#208—61no—
221#208—61no—
222#208—61no—
223#208—121no—
224#208C2×Dic312yescomplemented
225C2×C3⋊C8—21no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—121no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32C4×D411yescharacteristic
232C22×C32#12011yescharacteristic
233C22×C32C22⋊Q811yescharacteristic
234C2×C3×D3—22no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C32×C4—24no—
238C32×C4C2×C4⋊C411yescharacteristic
239C32×C4C4×D411yescharacteristic
240C32×C4C22⋊Q811yescharacteristic
241C32×C4#12311yescharacteristic
242C3⋊Dic3—41no—
243C3⋊Dic3—41no—
244C3×Dic3—22no—
245C3×Dic3—42no—
246C3×Dic3—81no—
247C2×#41—31no—
248C2×M16—31no—
249C2×M16—91no—
250C4×Q8—181no—
251C4×D4—181no—
252C4×D4—182no—
253#117—91no—
254#117—181no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—31no—
257C2×C4⋊C4—62no—
258C2×C4⋊C4—181no—
259C2×C42D3211yescharacteristic
260#107—181no—
261#106—181no—
262#104—34no—
263#103—181no—
264#102—181no—
265C23×C3—21no—
266C23×C3—61no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C22×D3—21no—
270C3×Q8—32no—
271C3×Q8—61no—
272C3×D4—32no—
273C3×D4—62no—
274C3×D4—62no—
275C3×D4—61no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
291C2×C3×C4—61no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—122no—
296C2×C3×C4—122no—
297C2×C3×C4—121no—
298C2×C3×C4C2×Dic611yescharacteristic
299C2×C3×C4C2×C4×D311yescharacteristic
300C2×C3×C4C2×D1211yescharacteristic
301C2×C3×C4#23511yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4#23711yescharacteristic
307C2×C3×C4D3×Q811yescharacteristic
308C2×C3×C4#23911yescharacteristic
309C2×C3×C4C22×Dic311yescharacteristic
310#67—22no—
311#67—22no—
312C2×Dic3—21no—
313C2×Dic3—22no—
314C2×Dic3—42no—
315C2×Dic3—42no—
316C2×Dic3—41no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—242no—
324D12—21no—
325D12C4⋊Dic312yescomplemented
326C4×D3—22no—
327C4×D3—22no—
328C4×D3—242no—
329Dic6—21no—
330Dic6C4⋊Dic312yescomplemented
331C3×C8—62no—
332C3⋊C8—22no—
333C3⋊C8—122no—
334C3⋊C8—121no—
335C3⋊C8—121no—
336C2×C32—21no—
337C2×C32—21no—
338C2×C32#38511yescharacteristic
339C2×C32#45311yescharacteristic
340C2×C32#45611yescharacteristic
341C3×D3—42no—
342#41—32no—
343#41—32no—
344#41—61no—
345#41—61no—
346C2×Q8—31no—
347C2×D4—31no—
348C2×D4—61no—
349C22×C4—21no—
350C22×C4—32no—
351C22×C4—61no—
352C22×C4—61no—
353C22×C4—182no—
354C22×C4C2×D3211yescharacteristic
355M16—32no—
356M16—61no—
357M16—181no—
358M16—181no—
359C2×C8—61no—
360C2×C8—181no—
361C4⋊C4—61no—
362C4⋊C4—61no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—91no—
366C4⋊C4—91no—
367C4⋊C4—124no—
368C4⋊C4—182no—
369C22⋊C4—182no—
370C22⋊C4—181no—
371C42—21no—
372C42—182no—
373C42—181no—
374C42D3×Dic312yescomplemented
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—62no—
385C22×C3—121no—
386C22×C3—121no—
387C22×C3#87811yescharacteristic
388C22×C3#88211yescharacteristic
389C22×C3C4×#6711yescharacteristic
390C22×C3D4×Dic311yescharacteristic
391C22×C3#93711yescharacteristic
392C22×C3#94611yescharacteristic
393C2×D3—22no—
394C2×D3—41no—
395C2×D3—41no—
396C3×C4—24no—
397C3×C4—24no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—44no—
403C3×C4—62no—
404C3×C4—122no—
405C3×C4—241no—
406C3×C4#87811yescharacteristic
407C3×C4#88611yescharacteristic
408C3×C4D3×C4⋊C411yescharacteristic
409C3×C4#89311yescharacteristic
410C3×C4#89411yescharacteristic
411C3×C4#89611yescharacteristic
412C3×C4C2×C4⋊Dic311yescharacteristic
413C3×C4D4×Dic311yescharacteristic
414Dic3—22no—
415Dic3—42no—
416Dic3—81no—
417Dic3—121no—
418Dic3—121no—
419Dic3—121no—
420Dic3—121no—
421Dic3—241no—
422Dic3—241no—
423C32#185911yescharacteristic, complemented, Sylow
424C23—61no—
425C23D3×#6711yescharacteristic
426Q8—32no—
427Q8—61no—
428D4—32no—
429D4—62no—
430D4—62no—
431D4—61no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—61no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—122no—
440C2×C4—122no—
441C2×C4—121no—
442C2×C4—181no—
443C2×C4—181no—
444C2×C4—722no—
445C2×C4D3×Dic611yescharacteristic
446C2×C4#379611yescharacteristic
447C2×C4D3×D1211yescharacteristic
448C2×C4#380211yescharacteristic
449C2×C4C2×D3×Dic311yescharacteristic
450C2×C4#380411yescharacteristic
451C8—62no—
452C8—361no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—41no—
461C2×C3—41no—
462C2×C3—122no—
463C2×C3#482211yescharacteristic
464C2×C3#482611yescharacteristic
465C2×C3#495011yescharacteristic
466C2×C3#498911yescharacteristic
467C2×C3#507711yescharacteristic
468C2×C3#509511yescharacteristic
469D3—42no—
470C22—21no—
471C22—21no—
472C22—62no—
473C22—121no—
474C22—121no—
475C22#6388711yescharacteristic
476C22#6392211yescharacteristic
477C22Dic3×#6711yescharacteristic
478C4—24no—
479C4—62no—
480C4—122no—
481C4—241no—
482C4—361no—
483C4—361no—
484C4D3×C4⋊Dic311yescharacteristic
485C4#6389011yescharacteristic
486C4#6389811yescharacteristic
487C4#6389911yescharacteristic
488C3—21no—
489C3#6959211yescharacteristic, complemented
490C3#7036311yescharacteristic, complemented
491C2—21no—
492C2—21no—
493C2—122no—
494C2#1059039511yescharacteristic
495C2#1059039911yescharacteristic
496C2#1059137711yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1859
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4935C2semidirect
4. #10591130C2semidirect
6. #10589389C2semidirect
7. #10589167C2semidirect
23. C3×#805C4semidirect
36. #4935D3semidirect
57. C32×C42C2×C4semidirect
71. C3×#208C2×C4semidirect
115. #805Dic3semidirect
137. C3×D12C4⋊C4semidirect
141. C3×Dic6C4⋊C4semidirect
192. C3×C42C4×D3semidirect
193. C3×C42C2×Dic3semidirect
224. #208C2×Dic3semidirect
325. D12C4⋊Dic3semidirect
330. Dic6C4⋊Dic3semidirect
374. C42D3×Dic3semidirect
423. C32#1859semidirect
489. C3#69592semidirect
490. C3#70363semidirect

Maximal subgroups

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

subgroupindex
#105949862
C3×#49352
C2×C3×#8052
#105911302
#105910872
#105893892
#105891672
#703633
#695923