Finite Group Databasebeta

← #11866350

Subgroups — #11866350

Order 1152.

1075 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5805C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3#10594818C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592914C211yesmaximal, characteristic, complemented
6#10591442C214yesmaximal, complemented
7#10591438C214yesmaximal, complemented
8#10591116C211yesmaximal, characteristic, complemented
9#10591084C211yesmaximal, characteristic, complemented
10#83849—31nomaximal
11#83391—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15#64135C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C3×#953—22no—
18C3×#940C2212yes—
19C3×#938—22no—
20C3×#936C2212yes—
21C2×C3×#214—24no—
22C2×C3×#214C2214yes—
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25#63955—22no—
26#63843—22no—
27Dic3×Dic6C2214yescomplemented
28C2×#3718C2212yescomplemented
29#63827—24no—
30C2×#3715C2212yescomplemented
31#63659C2214yes—
32Dic3⋊(C3⋊C8)C2214yescomplemented
33#63566C2212yescomplemented
34#63563C2212yescomplemented
35C22×C3×SD16—31no—
36C3×#535—31no—
37C2×#951—31no—
38#5812—31no—
39C2×#942—31no—
40#5805D311yescharacteristic
41C22×#214D311yescharacteristic, complemented
42#5516—31no—
43#5233—31no—
44#5215—31no—
45#5215—31no—
46#5215—61no—
47#5166—34no—
48#5163—34no—
49#5113—31no—
50#5102—31no—
51#5075—34no—
52#5054—34no—
53#4999—31no—
54C24×C32—21no—
55C2×C32×D4—22no—
56C2×C32×D4—21no—
57C2×C32×D4—22no—
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×C3×#67—21no—
61C2×C3×#67—24no—
62C22×C3×Dic3—21no—
63C3×#235—22no—
64C3×#235—22no—
65C2×C3×D12C2311yescharacteristic
66C2×C3×C4×D3—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6D414yescomplemented
70C2×C3×Dic6C2311yescharacteristic
71C2×C3×Dic6C2312yes—
72#3757—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74C4×C3⋊Dic3—21no—
75#3748—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×#217—24no—
78C3×#217D412yes—
79C3×#214—28no—
80C3×C4⋊Dic3D412yes—
81C3×C4×Dic3C2312yes—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84Dic3⋊Dic3—24no—
85Dic32—24no—
86#3718—24no—
87#3715—24no—
88#3043—91noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—31no—
91C22×C3×D4—21no—
92C22×C3×D4C2×D311yescharacteristic
93C22×C3×D4C2×D311yescharacteristic
94C2×#235C2×D311yescharacteristic
95C22×Dic6C2×D311yescharacteristic
96C2×C3×SD16—34no—
97C2×C3×SD16—64no—
98C22×C3×C8—31no—
99C3×#127—32no—
100C3×#124—32no—
101C3×#121—62no—
102C3×#120—62no—
103C3×#117—31no—
104#953—22no—
105#951—64no—
106Q8×Dic3—34no—
107Q8×Dic3—62no—
108C2×#216—32no—
109C2×#216—32no—
110#942—64no—
111C2×#215—32no—
112#940C2×D312yes—
113#938—22no—
114#936C2×D312yes—
115C2×#214—24no—
116C2×#214—32no—
117C2×#214C2×D314yes—
118#926—31no—
119#926—31no—
120#926—61no—
121#926—62no—
122#926C2×D311yescharacteristic
123C2×#208—31no—
124C2×#208—31no—
125C2×#208—61no—
126C22×C3⋊C8C2×D311yescharacteristic
127#887—62no—
128#877—62no—
129C4×Dic6—34no—
130#835—32no—
131#832—34no—
132#832—34no—
133#832—32no—
134#832—64no—
135#821—32no—
136#816—32no—
137Dic3⋊C8—34no—
138C4⋊(C3⋊C8)—34no—
139C23×C32—22no—
140C23×C32—42no—
141C23×C32—82no—
142C23×C32C2×D411yescharacteristic
143C22×C3×D3—21no—
144C32×D4—22no—
145C32×D4—22no—
146C32×D4—42no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D412yes—
149C2×C32×C4#4112yes—
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3—22no—
152C3×#67—42no—
153C3×#67—84no—
154C2×C3×Dic3—24no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3C2×D414yes—
158C3×D12—21no—
159C3×D12—21no—
160C3×C4×D3—42no—
161C3×Dic6—24no—
162C3×Dic6—22no—
163C3×Dic6—21no—
164C3×Dic6—21no—
165C3×Dic6C2×D414yes—
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—22no—
168C2×#137—91no—
169C22×SD16—31no—
170#535—31no—
171#519—91no—
172#464—94no—
173#460—94no—
174#424—91no—
175#418—91no—
176#416—91no—
177C24×C3—21no—
178C24×C3—21no—
179C24×C3—41no—
180C3×#41—62no—
181C3×#41—62no—
182C2×C3×Q8—34no—
183C2×C3×Q8—32no—
184C2×C3×Q8—31no—
185C2×C3×Q8—62no—
186C2×C3×Q8—61no—
187C2×C3×D4—24no—
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—22no—
191C2×C3×D4—22no—
192C2×C3×D4—22no—
193C2×C3×D4—21no—
194C2×C3×D4—22no—
195C2×C3×D4—31no—
196C2×C3×D4—42no—
197C2×C3×D4—41no—
198C2×C3×D4—64no—
199C2×C3×D4—61no—
200C2×C3×D4C22×D312yes—
201C2×C3×D4C22×D312yes—
202C22×C3×C4—21no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C2×#67—21no—
208C2×#67—24no—
209C22×Dic3—21no—
210#235—22no—
211#235—22no—
212C2×D12C22×D311yescharacteristic
213C2×C4×D3—21no—
214C2×Dic6—21no—
215C2×Dic6—22no—
216C2×Dic6#6714yescomplemented
217C2×Dic6C22×D311yescharacteristic
218C2×Dic6C22×D312yes—
219C3×SD16—68no—
220C2×C3×C8—32no—
221C2×C3×C8—62no—
222C3×C4⋊C4—32no—
223C3×C22⋊C4—32no—
224C3×C22⋊C4—64no—
225C3×C42—32no—
226#217—24no—
227#217—61no—
228#217—61no—
229#217—121no—
230#217#6712yes—
231#216—64no—
232#216—64no—
233#215—64no—
234#214—28no—
235#214—64no—
236C4⋊Dic3—32no—
237C4⋊Dic3—32no—
238C4⋊Dic3—62no—
239C4⋊Dic3—64no—
240C4⋊Dic3#6712yes—
241Dic3⋊C4—64no—
242C4×Dic3—64no—
243C4×Dic3—61no—
244C4×Dic3—61no—
245C4×Dic3—64no—
246C4×Dic3—121no—
247C4×Dic3C22×D312yes—
248#208—62no—
249#208—62no—
250#208—122no—
251C2×C3⋊C8—22no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—32no—
254C2×C3⋊C8—62no—
255C2×C3⋊C8C22×D312yes—
256C22×C32—22no—
257C22×C32—42no—
258C22×C32—44no—
259C22×C32—84no—
260C22×C32#12112yes—
261C22×C32C22×D411yescharacteristic
262C2×C3×D3—41no—
263C2×C3×D3—42no—
264C32×C4#12112yes—
265C32×C4C22×D411yescharacteristic
266C32×C4C2×#4111yescharacteristic
267C3⋊Dic3—42no—
268C3×Dic3—24no—
269C3×Dic3—24no—
270C3×Dic3—41no—
271C2×#41—31no—
272C22×Q8—31no—
273C22×D4D3211yescharacteristic
274#137—184no—
275C2×Q16—92no—
276C2×SD16—34no—
277C2×SD16—64no—
278C2×SD16—92no—
279C2×M16—91no—
280C22×C8—31no—
281#127—32no—
282#124—32no—
283#121—62no—
284#120—62no—
285C4×Q8—94no—
286C4×Q8—182no—
287#117—31no—
288#117—91no—
289#117—182no—
290C4⋊C8—94no—
291#103—92no—
292#102—92no—
293#102—94no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—21no—
297C23×C3—42no—
298C23×C3—44no—
299C23×C3—42no—
300C23×C3—42no—
301C23×C3—61no—
302C23×C3—82no—
303C23×C3—82no—
304C23×C3—84no—
305C23×C3D3×D411yescharacteristic
306C23×C3C2×#6711yescharacteristic
307C22×D3—21no—
308C3×Q8—34no—
309C3×Q8—64no—
310C3×Q8—62no—
311C3×Q8—61no—
312C3×Q8—61no—
313C3×D4—24no—
314C3×D4—22no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—42no—
319C3×D4—44no—
320C3×D4—42no—
321C3×D4—42no—
322C3×D4—61no—
323C3×D4—61no—
324C3×D4—122no—
325C3×D4—244no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—34no—
331C2×C3×C4—64no—
332C2×C3×C4—62no—
333C2×C3×C4—61no—
334C2×C3×C4—122no—
335C2×C3×C4D3×D412yes—
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4#23712yes—
338C2×C3×C4#23712yes—
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6712yes—
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343#67—42no—
344#67—84no—
345C2×Dic3—24no—
346C2×Dic3—22no—
347C2×Dic3—21no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—122no—
351C2×Dic3C2×#6714yes—
352D12—21no—
353D12—21no—
354C4×D3—42no—
355Dic6—24no—
356Dic6—22no—
357Dic6—21no—
358Dic6—21no—
359Dic6C2×#6714yes—
360C3×C8—62no—
361C3⋊C8—22no—
362C3⋊C8—62no—
363C3⋊C8—62no—
364C3⋊C8—122no—
365C2×C32—22no—
366C2×C32—82no—
367C2×C32C2×#12111yescharacteristic
368C2×C32#57712yes—
369C3×D3—81no—
370C24—21no—
371#41—62no—
372#41—62no—
373C2×Q8—32no—
374C2×Q8—31no—
375C2×Q8—34no—
376C2×Q8—62no—
377C2×Q8—61no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—31no—
382C2×D4—64no—
383C2×D4—61no—
384C2×D4C2×D3212yes—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4C2×D3211yescharacteristic
388Q16—184no—
389SD16—68no—
390SD16—184no—
391M16—182no—
392C2×C8—32no—
393C2×C8—62no—
394C2×C8—92no—
395C4⋊C4—32no—
396C4⋊C4—92no—
397C4⋊C4—184no—
398C22⋊C4—32no—
399C22⋊C4—64no—
400C22⋊C4—181no—
401C42—32no—
402C42—184no—
403C42—181no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—42no—
409C22×C3—44no—
410C22×C3—44no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—44no—
414C22×C3—84no—
415C22×C3—84no—
416C22×C3—84no—
417C22×C3—88no—
418C22×C3—122no—
419C22×C3—121no—
420C22×C3#93812yes—
421C22×C3#93912yes—
422C22×C3C2×D3×D411yescharacteristic
423C22×C3C22×#6711yescharacteristic
424C2×D3—41no—
425C2×D3—42no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—64no—
430C3×C4—64no—
431C3×C4—121no—
432C3×C4#93812yes—
433C3×C4#93912yes—
434C3×C4C2×D3×D411yescharacteristic
435C3×C4C2×#23711yescharacteristic
436C3×C4C2×#23711yescharacteristic
437C3×C4C22×#6711yescharacteristic
438Dic3—24no—
439Dic3—24no—
440Dic3—41no—
441Dic3—122no—
442Dic3—122no—
443Dic3—242no—
444C32#304311yescharacteristic, complemented, Sylow
445C23—22no—
446C23—42no—
447C23—61no—
448C23—82no—
449C23D3×#6711yescharacteristic
450Q8—34no—
451Q8—62no—
452Q8—64no—
453Q8—61no—
454Q8—61no—
455D4—22no—
456D4—22no—
457D4—42no—
458D4—61no—
459D4—61no—
460D4—122no—
461D4—244no—
462C2×C4—34no—
463C2×C4—62no—
464C2×C4—64no—
465C2×C4—61no—
466C2×C4—122no—
467C2×C4—182no—
468C2×C4#380512yes—
469C2×C4D3×#6712yes—
470C2×C4D3×#6711yescharacteristic
471C2×C4C22×D3211yescharacteristic
472C8—62no—
473C8—182no—
474C2×C3—22no—
475C2×C3—22no—
476C2×C3—22no—
477C2×C3—21no—
478C2×C3—42no—
479C2×C3—84no—
480C2×C3—82no—
481C2×C3—82no—
482C2×C3—241no—
483C2×C3#576212yes—
484C2×C3C2×#93811yescharacteristic
485C2×C3C2×#93911yescharacteristic
486C2×C3#583612yes—
487D3—81no—
488C22—22no—
489C22—44no—
490C22—42no—
491C22—84no—
492C22—122no—
493C22—121no—
494C22#6397012yes—
495C22C2×D3×#6711yescharacteristic
496C4—64no—
497C4—64no—
498C4—121no—
499C4—362no—
500C4#6397012yes—
501C4C2×#380511yescharacteristic
502C4C2×D3×#6711yescharacteristic
503C3—21no—
504C3#8339111yescharacteristic, complemented
505C3#8384911yescharacteristic, complemented
506C2—22no—
507C2—82no—
508C2—241no—
509C2#1059510512yes—
510C2C2×#6397011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×#5805C2
hypercenterC22×D4D32
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#214C2semidirect
3. #10594818C2semidirect
4. C2×#63827C2semidirect
5. #10592914C2semidirect
6. #10591442C2semidirect
7. #10591438C2semidirect
8. #10591116C2semidirect
9. #10591084C2semidirect
27. Dic3×Dic6C22semidirect
28. C2×#3718C22semidirect
30. C2×#3715C22semidirect
32. Dic3⋊(C3⋊C8)C22semidirect
33. #63566C22semidirect
34. #63563C22semidirect
41. C22×#214D3semidirect
69. C2×C3×Dic6D4semidirect
216. C2×Dic6#67semidirect
444. C32#3043semidirect
504. C3#83391semidirect
505. C3#83849semidirect

Maximal subgroups

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

subgroupindex
C3×#58052
C22×C3×#2142
#105948182
C2×#638272
#105929142
#105914422
#105914382
#105911162
#105910842
#838493
#833913