Finite Group Databasebeta

← #11786740

Subgroups — #11786740

Order 1152.

627 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5523C211yesmaximal, characteristic
2C3×#4995C211yesmaximal, characteristic, complemented
3#10591230C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic
5#10591087C211yesmaximal, characteristic
6#10589398C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#71665—31nomaximal
9#70681—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#892—21no—
18C3×D3×C4⋊C4—21no—
19C3×#67⋊C4—22no—
20C3×C4×D12—21no—
21C3×C4×Dic6—21no—
22C3×#808—21no—
23C3×#807—21no—
24#63579—22no—
25#63568C414yescomplemented
26#63565—21no—
27#63562—21no—
28C3×#520—31no—
29#5523D311yescharacteristic
30C3×#428—31no—
31C2×#837—31no—
32#5232—31no—
33C2×#825—31no—
34#4995D311yescharacteristic, complemented
35#4977—31no—
36#4977—31no—
37#4966—31no—
38#4554—31no—
39#4532—31no—
40#4532—31no—
41#4532—61no—
42#4530—31no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
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×C4×D3—22no—
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C4⋊C4D411yescharacteristic
58C32×C22⋊C4—21no—
59C32×C42—21no—
60C4×C3⋊Dic3—21no—
61C4×C3⋊Dic3C2×C412yescomplemented
62#3748—21no—
63#3748—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×(C2×D3)⋊C4—22no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×Dic3⋊C4—22no—
71C3×C4×Dic3—22no—
72C3×#208—21no—
73C3×#208C2×C412yescomplemented
74C2×C3×C3⋊C8—21no—
75#1860—91noSylow
76C2×C3×#41—31no—
77C2×#235C2×D311yescharacteristic
78C2×C3×M16—31no—
79C3×C4×Q8—61no—
80C3×C4×D4—61no—
81C3×C4×D4—62no—
82C3×#117—21no—
83C3×#117—61no—
84C3×#117C2×D311yescharacteristic
85C3×#117C2×D311yescharacteristic
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—61no—
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4×Dic3—31no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—61no—
94C2×#208—31no—
95C2×#208—31no—
96C2×#208—61no—
97C2×#208C2×D311yescharacteristic
98#892—21no—
99D3×C4⋊C4—21no—
100#67⋊C4—22no—
101C4×D12—21no—
102C4×Dic6—21no—
103C3×#107—61no—
104C3×#106—61no—
105#837—34no—
106#835—61no—
107#832—61no—
108C3⋊#95—62no—
109C3⋊#95—62no—
110#825—34no—
111#810—61no—
112#809—61no—
113#808—21no—
114#807—21no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×Q811yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C3×#67—22no—
129C3×#67—22no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—41no—
135C3×D12—21no—
136C3×D12C4⋊C412yes—
137C3×C4×D3—22no—
138C3×C4×D3—22no—
139C3×C4×D3—82no—
140C3×Dic6—21no—
141C3×Dic6C4⋊C412yes—
142C3⋊(C3⋊C8)—41no—
143C3×C3⋊C8—22no—
144#520—31no—
145#428—31no—
146C2×#104—91no—
147#417—91no—
148#382—91no—
149#343—91no—
150#339—91no—
151C3×#41—32no—
152C3×#41—32no—
153C3×#41—61no—
154C3×#41—61no—
155C2×C3×Q8—31no—
156C2×C3×D4—31no—
157C2×C3×D4—61no—
158C22×C3×C4—21no—
159C22×C3×C4—32no—
160C22×C3×C4—62no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—21no—
166C22×Dic3—21no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—121no—
170C22×Dic3#6712yes—
171#235—21no—
172#235—21no—
173#235Dic612yes—
174#235C4×D312yes—
175C2×D12#6711yescharacteristic
176C2×C4×D3—21no—
177C2×C4×D3—22no—
178C2×Dic6#6711yescharacteristic
179C3×M16—32no—
180C3×M16—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—62no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4#6711yescharacteristic
190C3×C4⋊C4#6711yescharacteristic
191C3×C4⋊C4#6711yescharacteristic
192C3×C4⋊C4#6711yescharacteristic
193C3×C22⋊C4—21no—
194C3×C22⋊C4—21no—
195C3×C22⋊C4—41no—
196C3×C22⋊C4—62no—
197C3×C42—21no—
198C3×C42—21no—
199C3×C42—41no—
200C3×C42—62no—
201(C2×D3)⋊C4—22no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206Dic3⋊C4—22no—
207C4×Dic3—22no—
208C4×Dic3—32no—
209C4×Dic3—32no—
210C4×Dic3—62no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—121no—
214#208—21no—
215#208—62no—
216#208—61no—
217#208—61no—
218#208—61no—
219#208—61no—
220#208—121no—
221#208C4×D312yescomplemented
222C2×C3⋊C8—21no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32C4×D411yescharacteristic
229C22×C32#12011yescharacteristic
230C22×C32C22⋊Q811yescharacteristic
231C2×C3×D3—22no—
232C2×C3×D3—41no—
233C2×C3×D3—41no—
234C32×C4—41no—
235C32×C4—41no—
236C32×C4C2×C4⋊C411yescharacteristic
237C32×C4C4×D411yescharacteristic
238C32×C4C22⋊Q811yescharacteristic
239C32×C4#12311yescharacteristic
240C3⋊Dic3—42no—
241C3×Dic3—22no—
242C3×Dic3—42no—
243C3×Dic3—81no—
244C2×#41—31no—
245C2×M16—31no—
246C2×M16—91no—
247C4×Q8—61no—
248C4×D4—61no—
249C4×D4—62no—
250#117—61no—
251#117D3211yescharacteristic
252C2×C4⋊C4—31no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—61no—
255C2×C42—91no—
256#107—61no—
257#106—61no—
258#104—94no—
259#103—181no—
260#102—181no—
261#95—182no—
262C23×C3—21no—
263C23×C3—61no—
264C23×C3D3×D411yescharacteristic
265C23×C3C2×#6711yescharacteristic
266C22×D3—21no—
267C3×Q8—32no—
268C3×Q8—61no—
269C3×D4—32no—
270C3×D4—62no—
271C3×D4—62no—
272C3×D4—61no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—61no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—122no—
290C2×C3×C4—122no—
291C2×C3×C4—121no—
292C2×C3×C4—242no—
293C2×C3×C4C2×Dic611yescharacteristic
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4#23511yescharacteristic
298C2×C3×C4#23511yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×Q811yescharacteristic
301C2×C3×C4#23911yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305#67—22no—
306#67—22no—
307C2×Dic3—21no—
308C2×Dic3—22no—
309C2×Dic3—42no—
310C2×Dic3—42no—
311C2×Dic3—41no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—122no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321D12—21no—
322D12Dic3⋊C412yes—
323C4×D3—22no—
324C4×D3—22no—
325C4×D3—82no—
326Dic6—21no—
327Dic6Dic3⋊C412yes—
328C3×C8—62no—
329C3⋊C8—22no—
330C3⋊C8—122no—
331C3⋊C8—121no—
332C3⋊C8—121no—
333C2×C32—21no—
334C2×C32—21no—
335C2×C32#38511yescharacteristic
336C2×C32#45411yescharacteristic
337C2×C32#45511yescharacteristic
338C3×D3—42no—
339#41—32no—
340#41—32no—
341#41—61no—
342#41—61no—
343C2×Q8—31no—
344C2×D4—31no—
345C2×D4—61no—
346C22×C4—32no—
347C22×C4—62no—
348C22×C4—61no—
349C22×C4—61no—
350C22×C4—181no—
351C22×C4C2×D3211yescharacteristic
352M16—32no—
353M16—61no—
354M16—181no—
355M16—181no—
356C2×C8—61no—
357C2×C8—181no—
358C4⋊C4—62no—
359C4⋊C4—61no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—61no—
363C4⋊C4#62511yescharacteristic
364C4⋊C4#62511yescharacteristic
365C22⋊C4—21no—
366C22⋊C4—62no—
367C42—21no—
368C42—62no—
369C42—92no—
370C42—181no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—62no—
381C22×C3—121no—
382C22×C3—121no—
383C22×C3#89311yescharacteristic
384C22×C3#89611yescharacteristic
385C22×C3#92411yescharacteristic
386C22×C3C4×#6711yescharacteristic
387C22×C3#93711yescharacteristic
388C22×C3#95311yescharacteristic
389C2×D3—22no—
390C2×D3—41no—
391C2×D3—41no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—41no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—41no—
400C3×C4—62no—
401C3×C4—81no—
402C3×C4—81no—
403C3×C4—122no—
404C3×C4—241no—
405C3×C4D3×C4⋊C411yescharacteristic
406C3×C4#89411yescharacteristic
407C3×C4C2×Dic3⋊C411yescharacteristic
408C3×C4#92411yescharacteristic
409C3×C4C4×#6711yescharacteristic
410C3×C4C4×#6711yescharacteristic
411C3×C4#92911yescharacteristic
412C3×C4#94611yescharacteristic
413Dic3—22no—
414Dic3—42no—
415Dic3—81no—
416Dic3—122no—
417Dic3—122no—
418Dic3—124no—
419C32#186011yescharacteristic, complemented, Sylow
420C23—61no—
421C23D3×#6711yescharacteristic
422Q8—32no—
423Q8—61no—
424D4—32no—
425D4—62no—
426D4—62no—
427D4—61no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—61no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—122no—
435C2×C4—122no—
436C2×C4—121no—
437C2×C4—182no—
438C2×C4—242no—
439C2×C4—361no—
440C2×C4—361no—
441C2×C4D3×Dic611yescharacteristic
442C2×C4#379811yescharacteristic
443C2×C4#379911yescharacteristic
444C2×C4C4×D3211yescharacteristic
445C2×C4C2×#62511yescharacteristic
446C2×C4D3×#6711yescharacteristic
447C8—62no—
448C8—361no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—41no—
457C2×C3—41no—
458C2×C3—122no—
459C2×C3#498911yescharacteristic
460C2×C3#520111yescharacteristic
461C2×C3#520211yescharacteristic
462C2×C3#521011yescharacteristic
463C2×C3#524211yescharacteristic
464C2×C3#524511yescharacteristic
465D3—42no—
466C22—21no—
467C22—21no—
468C22—62no—
469C22—121no—
470C22—121no—
471C22#6385111yescharacteristic
472C22#6390411yescharacteristic
473C22#6397611yescharacteristic
474C4—41no—
475C4—41no—
476C4—62no—
477C4—122no—
478C4—241no—
479C4—362no—
480C4#6385011yescharacteristic
481C4#6385611yescharacteristic
482C4D3×Dic3⋊C411yescharacteristic
483C4C4×#62511yescharacteristic
484C3—21no—
485C3#7068111yescharacteristic, complemented
486C3#7166511yescharacteristic, complemented
487C2—21no—
488C2—21no—
489C2—122no—
490C2#1059127711yescharacteristic
491C2#1059166411yescharacteristic
492C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1860
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#4995C2semidirect
3. #10591230C2semidirect
6. #10589398C2semidirect
7. #10589167C2semidirect
25. #63568C4semidirect
34. #4995D3semidirect
61. C4×C3⋊Dic3C2×C4semidirect
73. C3×#208C2×C4semidirect
221. #208C4×D3semidirect
419. C32#1860semidirect
485. C3#70681semidirect
486. C3#71665semidirect

Maximal subgroups

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

subgroupindex
C3×#55232
C3×#49952
#105912302
C2×#635682
#105910872
#105893982
#105891672
#716653
#706813