Finite Group Databasebeta

← #11787809

Subgroups — #11787809

Order 1152.

813 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594996C211yesmaximal, characteristic
2C2×#63864C211yesmaximal, characteristic
3C2×#63650C211yesmaximal, characteristic
4C3×#5120C211yesmaximal, characteristic, complemented
5#10591099C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70343—31nomaximal
9#68759—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17#63974—22no—
18C2×#3722—22no—
19#63894—22no—
20#63894—22no—
21#63864—22no—
22#63864C414yescomplemented
23#63650—22no—
24C3×#816—22no—
25#63565—22no—
26C2×#947—31no—
27#5521—31no—
28#5521—31no—
29C2×#875—31no—
30C3×#419—31no—
31#5225—31no—
32C2×#823—31no—
33C2×#823—31no—
34C2×#823—61no—
35#5120D311yescharacteristic, complemented
36#5004—31no—
37C3×#339—31no—
38#4555D311yescharacteristic, complemented
39#4532—31no—
40#4523—31no—
41C23×C3⋊D3D412yes—
42C22×C32×C4C2311yescharacteristic
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)C2×C412yes—
48C2×C4⋊(C3⋊D3)D412yes—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C2×C3×Dic6—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6C2×C412yescomplemented
57C2×#624—24no—
58C32×M16—21no—
59C32×M16—21no—
60C2×C32×C8—21no—
61#3748—21no—
62#3748—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×#217—21no—
65C3×#217—21no—
66C3×C4⋊Dic3D412yes—
67C3×C4⋊Dic3D412yes—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3C2×C412yescomplemented
72#3722—24no—
73#3722—28no—
74#1885—91noSylow
75C22×C3×Q8—31no—
76C22×D12—31no—
77C22×D12—31no—
78C22×D12—61no—
79C22×Dic6C2×D311yescharacteristic
80C2×C3×M16—21no—
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×M16C2×D311yescharacteristic
83C3×#117—31no—
84C3×#117—31no—
85C2×C3×C42—31no—
86#947—34no—
87#947—62no—
88C2×(C2×D3)⋊C4—62no—
89C2×(C2×D3)⋊C4—62no—
90#926C2×D311yescharacteristic
91#926C2×D311yescharacteristic
92C2×C4×Dic3C2×D311yescharacteristic
93C2×#208—31no—
94C2×#208—31no—
95C2×#208—61no—
96#893—62no—
97#893—62no—
98D3×C22⋊C4—62no—
99D3×C22⋊C4—62no—
100#875—34no—
101#875—62no—
102C4×D12—62no—
103C4×D12—62no—
104C3×#103—62no—
105#835—62no—
106#823—62no—
107#823—62no—
108#823—64no—
109#816—22no—
110#810—62no—
111C23×C32C2×D411yescharacteristic
112C22×C3⋊D3—22no—
113C22×C3⋊D3—22no—
114C22×C3⋊D3—44no—
115C22×C3⋊D3C22⋊C414yes—
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C4⋊(C3⋊D3)—22no—
123C4⋊(C3⋊D3)—22no—
124C4⋊(C3⋊D3)—22no—
125C4⋊(C3⋊D3)—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C3×Dic6—22no—
134C3×Dic6—22no—
135C3×Dic6—41no—
136C3×Dic6—41no—
137#624—84no—
138C32×C8—41no—
139C3⋊(C3⋊C8)—41no—
140C2×#124—91no—
141#518—91no—
142#419—31no—
143#419—91no—
144C2×#100—91no—
145#339—31no—
146#339—91no—
147C23×D3—32no—
148C23×D3—32no—
149C23×D3—62no—
150C2×C3×Q8—32no—
151C2×C3×Q8—61no—
152C2×C3×Q8—61no—
153C2×C3×Q8—61no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C22×C3×C4—21no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×Dic3—21no—
162C22×Dic3—21no—
163C2×D12—32no—
164C2×D12—32no—
165C2×D12—32no—
166C2×D12—32no—
167C2×D12—62no—
168C2×D12—62no—
169C2×D12—61no—
170C2×D12—61no—
171C2×D12—61no—
172C2×D12—61no—
173C2×D12—61no—
174C2×D12—61no—
175C2×D12—61no—
176C2×D12—61no—
177C2×D12—121no—
178C2×D12—121no—
179C2×D12—121no—
180C2×D12—121no—
181C2×C4×D3—64no—
182C2×C4×D3—64no—
183C2×Dic6—21no—
184C2×Dic6—21no—
185C2×Dic6—21no—
186C2×Dic6—21no—
187C2×Dic6—21no—
188C2×Dic6C4×D312yescomplemented
189C3×M16—22no—
190C3×M16—21no—
191C3×M16—21no—
192C3×M16—21no—
193C3×M16—21no—
194C3×M16—41no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—41no—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—32no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4—61no—
202C3×C42—32no—
203C3×C42—61no—
204C3×C42—61no—
205C3×C42—61no—
206#217—21no—
207#217—21no—
208(C2×D3)⋊C4—68no—
209(C2×D3)⋊C4—68no—
210(C2×D3)⋊C4—64no—
211(C2×D3)⋊C4—64no—
212C4⋊Dic3D1212yes—
213C4⋊Dic3#6712yes—
214C4×Dic3—21no—
215C4×Dic3—21no—
216C4×Dic3—21no—
217C4×Dic3C4×D312yescomplemented
218#208—62no—
219#208—61no—
220#208—61no—
221#208—61no—
222#208—61no—
223#208—121no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—121no—
227C22×C32—22no—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32#12011yescharacteristic
230C22×C32#12311yescharacteristic
231C2×C3⋊D3—24no—
232C2×C3⋊D3—44no—
233C2×C3⋊D3—44no—
234C2×C3⋊D3—82no—
235C32×C4C4×D411yescharacteristic
236C32×C4C4×D411yescharacteristic
237C32×C4#12111yescharacteristic
238C32×C4#12111yescharacteristic
239C3×Dic3—42no—
240C3×Dic3—42no—
241C3×Dic3—42no—
242C3×Dic3—42no—
243C22×Q8—31no—
244C22×D4—91no—
245C2×M16—91no—
246C2×M16D3211yescharacteristic
247#124—94no—
248#124—182no—
249C4×D4—182no—
250C4×D4—182no—
251#117—31no—
252#117—31no—
253C2×C22⋊C4—182no—
254C2×C22⋊C4—182no—
255C2×C42—31no—
256#103—62no—
257#103—182no—
258#100—182no—
259C23×C3—21no—
260C23×C3D3×D411yescharacteristic
261C23×C3D3×D411yescharacteristic
262C22×D3—34no—
263C22×D3—34no—
264C22×D3—64no—
265C22×D3—62no—
266C22×D3—62no—
267C22×D3—62no—
268C22×D3—62no—
269C22×D3—122no—
270C22×D3—122no—
271C22×D3—124no—
272C22×D3—124no—
273C22×D3—244no—
274C3×Q8—62no—
275C3×Q8—62no—
276C3×Q8—121no—
277C3×Q8—121no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—122no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4C2×D1211yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4#23911yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—42no—
308C2×Dic3—41no—
309C2×Dic3—41no—
310D12—62no—
311D12—62no—
312D12—62no—
313D12—62no—
314D12—62no—
315D12—62no—
316D12—62no—
317D12—62no—
318D12—122no—
319D12—122no—
320D12—122no—
321D12—122no—
322C4×D3—244no—
323C4×D3—244no—
324Dic6—22no—
325Dic6—22no—
326Dic6—41no—
327Dic6—41no—
328C3×C8—42no—
329C3×C8—41no—
330C3×C8—41no—
331C3⋊C8—122no—
332C3⋊C8—121no—
333C3⋊C8—121no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32#38611yescharacteristic
337C2×C32#45512yes—
338C3⋊D3—44no—
339C24—92no—
340C2×Q8—32no—
341C2×Q8—61no—
342C2×Q8—61no—
343C2×Q8—61no—
344C2×Q8—61no—
345C2×Q8—61no—
346C2×D4—92no—
347C2×D4—92no—
348C2×D4—181no—
349C2×D4—181no—
350C2×D4—181no—
351C2×D4—181no—
352C22×C4—61no—
353C22×C4—61no—
354C22×C4—184no—
355C22×C4C2×D3211yescharacteristic
356M16—21no—
357M16—21no—
358M16—181no—
359M16—181no—
360C2×C8—21no—
361C2×C8—181no—
362C4⋊C4—32no—
363C4⋊C4—32no—
364C22⋊C4—61no—
365C22⋊C4—61no—
366C22⋊C4—188no—
367C22⋊C4—184no—
368C42—32no—
369C42—61no—
370C42—61no—
371C42—61no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—42no—
378C22×C3D3×C22⋊C411yescharacteristic
379C22×C3D3×C22⋊C411yescharacteristic
380C22×C3#88211yescharacteristic
381C22×C3#88311yescharacteristic
382C22×C3#89411yescharacteristic
383C22×C3#93711yescharacteristic
384C2×D3—64no—
385C2×D3—64no—
386C2×D3—124no—
387C2×D3—124no—
388C2×D3—124no—
389C2×D3—124no—
390C2×D3—124no—
391C2×D3—244no—
392C2×D3—244no—
393C2×D3—242no—
394C2×D3—242no—
395C2×D3—244no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—122no—
401C3×C4—122no—
402C3×C4—122no—
403C3×C4—122no—
404C3×C4C4×D1211yescharacteristic
405C3×C4#67⋊C411yescharacteristic
406C3×C4#88411yescharacteristic
407C3×C4#88411yescharacteristic
408C3×C4#89311yescharacteristic
409C3×C4#89511yescharacteristic
410C3×C4C4×#6711yescharacteristic
411C3×C4#93811yescharacteristic
412Dic3—42no—
413Dic3—42no—
414Dic3—42no—
415Dic3—42no—
416C32#188511yescharacteristic, complemented, Sylow
417C23—94no—
418C23—182no—
419C23—182no—
420C23—364no—
421C23#380211yescharacteristic
422Q8—62no—
423Q8—62no—
424Q8—121no—
425Q8—121no—
426D4—182no—
427D4—182no—
428D4—182no—
429D4—182no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—122no—
435C2×C4—121no—
436C2×C4—121no—
437C2×C4—724no—
438C2×C4#379911yescharacteristic
439C2×C4C4×D3211yescharacteristic
440C2×C4D3×D1211yescharacteristic
441C2×C4#380411yescharacteristic
442C2×C4D3×#6711yescharacteristic
443C2×C4#381111yescharacteristic
444C8—41no—
445C8—361no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—22no—
451C2×C3—21no—
452C2×C3—41no—
453C2×C3—41no—
454C2×C3#466511yescharacteristic
455C2×C3#482512yes—
456C2×C3#495611yescharacteristic
457C2×C3#520212yes—
458D3—124no—
459D3—124no—
460D3—244no—
461C22—22no—
462C22—184no—
463C22—364no—
464C22—364no—
465C22—722no—
466C22#6385411yescharacteristic
467C22#6392111yescharacteristic
468C22#6392211yescharacteristic
469C4—122no—
470C4—122no—
471C4—122no—
472C4—122no—
473C4#6388011yescharacteristic
474C4#6390411yescharacteristic
475C4#6391011yescharacteristic
476C4#6395811yescharacteristic
477C3—21no—
478C3#6875911yescharacteristic, complemented
479C3#7034311yescharacteristic, complemented
480C2—21no—
481C2—21no—
482C2—364no—
483C2#1059101112yes—
484C2#1059127511yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1885
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. C3×#5120C2semidirect
5. #10591099C2semidirect
6. C3×#4555C2semidirect
7. #10589161C2semidirect
22. #63864C4semidirect
35. #5120D3semidirect
38. #4555D3semidirect
56. C2×C3×Dic6C2×C4semidirect
71. C3×C4×Dic3C2×C4semidirect
188. C2×Dic6C4×D3semidirect
217. C4×Dic3C4×D3semidirect
416. C32#1885semidirect
478. C3#68759semidirect
479. C3#70343semidirect

Maximal subgroups

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

subgroupindex
#105949962
C2×#638642
C2×#636502
C3×#51202
#105910992
C3×#45552
#105891612
#703433
#687593