Finite Group Databasebeta

← #11787035

Subgroups — #11787035

Order 1152.

595 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
1C2×C3×#907C211yesmaximal, characteristic
2C2×C3×#822C211yesmaximal, characteristic, complemented
3#10591119C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic
5#10591084C211yesmaximal, characteristic
6#10589421C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#72017—31nomaximal
9#70722—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#907—22no—
18C3×#907—22no—
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21C3×#822—22no—
22#63572—21no—
23#63572—21no—
24#63568—22no—
25#63566C411yescharacteristic, complemented
26#63566C411yescharacteristic, complemented
27#63563C411yescharacteristic, complemented
28#63563C411yescharacteristic, complemented
29C2×C3×#131—31no—
30C2×#907D311yescharacteristic
31C2×C3×#108—31no—
32C2×#837—31no—
33#5233—31no—
34C2×#825—31no—
35C2×#822D311yescharacteristic, complemented
36#5119—31no—
37#5113—31no—
38#5102—31no—
39#4555—31no—
40#4555—31no—
41#4555—61no—
42#4550—31no—
43#4550—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×C3×#67—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235D412yes—
50C3×#235Q812yes—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6C2×C411yescharacteristic
54C32×M16—21no—
55C32×M16D412yes—
56C2×C32×C8—21no—
57#3757—21no—
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic
59C4⋊(C3⋊Dic3)C2×C411yescharacteristic
60C4×C3⋊Dic3—21no—
61C4×C3⋊Dic3—21no—
62C4×C3⋊Dic3—21no—
63C3×#208—21no—
64C3×#208—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8C2×C411yescharacteristic
71C2×C3×C3⋊C8C2×C411yescharacteristic
72C2×C3×C3⋊C8D411yescharacteristic
73C2×C3×C3⋊C8D411yescharacteristic
74C3×ΓL(1,𝔽25)—24no—
75C3×D3×C8—24no—
76#1866—91noSylow
77C2×C3×#41—31no—
78C2×#235C2×D311yescharacteristic
79C3×#131—62no—
80C3×#131—62no—
81C2×C3×M16—21no—
82C2×C3×M16—31no—
83C2×C3×M16—61no—
84C2×C3×M16C2×D311yescharacteristic
85C2×C3×M16C2×D311yescharacteristic
86C22×C3×C8—31no—
87C22×C3×C8—31no—
88C22×C3×C8—61no—
89#926—31no—
90#926—31no—
91#926—61no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—61no—
95C2×#208C2×D311yescharacteristic
96C22×C3⋊C8C2×D311yescharacteristic
97C22×C3⋊C8C2×D311yescharacteristic
98#907—22no—
99#907—22no—
100C2×ΓL(1,𝔽25)—21no—
101C2×D3×C8—21no—
102C3×#108—62no—
103#837—62no—
104#835—31no—
105#835—31no—
106#832—31no—
107#832—31no—
108#825—62no—
109#822—22no—
110#821—31no—
111#821—31no—
112#816—31no—
113#816—31no—
114Dic3⋊C8—61no—
115Dic3⋊C8—61no—
116Dic3⋊C8—61no—
117Dic3⋊C8—61no—
118C23×C32#4111yescharacteristic
119C22×C3×D3—21no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×Q811yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C3×#67—22no—
132C3×#67—22no—
133C2×C3×Dic3—21no—
134C3×D12—21no—
135C3×D12C4⋊C412yes—
136C3×C4×D3—22no—
137C3×C4×D3—22no—
138C3×Dic6—21no—
139C3×Dic6C4⋊C412yes—
140C32×C8—22no—
141C3×C3⋊C8—21no—
142C3×C3⋊C8—21no—
143C3×C3⋊C8—21no—
144C3×C3⋊C8—21no—
145C3×C3⋊C8—41no—
146C2×#131—31no—
147C2×#108—31no—
148#424—91no—
149C2×#104—91no—
150#416—91no—
151#339—91no—
152#336—91no—
153C3×#41—32no—
154C3×#41—32no—
155C3×#41—61no—
156C3×#41—61no—
157C2×C3×Q8—31no—
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C2×#67—21no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—121no—
168#235—21no—
169#235—21no—
170#235Dic612yes—
171#235#6712yes—
172C2×D12C4×D311yescharacteristic
173C2×C4×D3—21no—
174C2×Dic6C4×D311yescharacteristic
175C3×M16—21no—
176C3×M16—21no—
177C3×M16—22no—
178C3×M16—41no—
179C3×M16—64no—
180C3×M16—61no—
181C3×M16—61no—
182C3×M16#6712yes—
183C3×M16#6712yes—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C2×C3×C8—31no—
187C2×C3×C8—31no—
188C2×C3×C8—31no—
189C2×C3×C8—31no—
190C2×C3×C8—41no—
191C2×C3×C8—64no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C2×C3×C8—61no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197#217—61no—
198#217—61no—
199#217—121no—
200C4⋊Dic3—31no—
201C4⋊Dic3—31no—
202C4⋊Dic3—31no—
203C4⋊Dic3—31no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3—62no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—121no—
214C4×Dic3—121no—
215#208—21no—
216#208—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8C4×D311yescharacteristic
223C2×C3⋊C8C4×D311yescharacteristic
224C2×C3⋊C8#6711yescharacteristic
225C2×C3⋊C8#6711yescharacteristic
226ΓL(1,𝔽25)—24no—
227D3×C8—24no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32C4×D411yescharacteristic
231C22×C32C22⋊Q811yescharacteristic
232C22×C32#12311yescharacteristic
233C2×C3×D3—22no—
234C2×C3×D3—41no—
235C2×C3×D3—41no—
236C32×C4C2×C4⋊C411yescharacteristic
237C32×C4C4×D411yescharacteristic
238C32×C4#12011yescharacteristic
239C32×C4C22⋊Q811yescharacteristic
240C3⋊Dic3—42no—
241C3⋊Dic3—41no—
242C3⋊Dic3—41no—
243C3×Dic3—22no—
244C2×#41—31no—
245#131—62no—
246#131—62no—
247C2×M16—31no—
248C2×M16—61no—
249C2×M16D3211yescharacteristic
250C22×C8—31no—
251C22×C8—31no—
252C22×C8—61no—
253#117—91no—
254C2×C42—91no—
255#108—62no—
256C4⋊C8—181no—
257C4⋊C8—181no—
258#104—182no—
259#103—91no—
260#103—91no—
261#102—91no—
262#102—91no—
263C23×C3—21no—
264C23×C3—61no—
265C23×C3#23511yescharacteristic
266C23×C3#23911yescharacteristic
267C22×D3—21no—
268C3×Q8—32no—
269C3×Q8—61no—
270C3×D4—32no—
271C3×D4—62no—
272C3×D4—62no—
273C3×D4—61no—
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—61no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4C2×Dic611yescharacteristic
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4C2×C4×D311yescharacteristic
286C2×C3×C4#23511yescharacteristic
287C2×C3×C4#23511yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×Q811yescharacteristic
291C2×C3×C4C2×#6711yescharacteristic
292C2×C3×C4C2×#6711yescharacteristic
293C2×C3×C4C2×#6711yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295#67—22no—
296#67—22no—
297C2×Dic3—21no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—61no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304C2×Dic3—122no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—122no—
308C2×Dic3—121no—
309C2×Dic3—121no—
310C2×Dic3—122no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313D12—21no—
314D12Dic3⋊C412yes—
315C4×D3—22no—
316C4×D3—22no—
317Dic6—21no—
318Dic6Dic3⋊C412yes—
319C3×C8—22no—
320C3×C8—22no—
321C3×C8—42no—
322C3×C8—61no—
323C3×C8—61no—
324C3×C8—61no—
325C3×C8—61no—
326C3×C8—121no—
327C3⋊C8—21no—
328C3⋊C8—21no—
329C3⋊C8—21no—
330C3⋊C8—21no—
331C3⋊C8—41no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32#38511yescharacteristic
335C2×C32#44311yescharacteristic
336C2×C32#44411yescharacteristic
337C3×D3—42no—
338#41—32no—
339#41—32no—
340#41—61no—
341#41—61no—
342C2×Q8—31no—
343C2×D4—31no—
344C2×D4—61no—
345C22×C4—61no—
346C22×C4—181no—
347C22×C4C2×D3211yescharacteristic
348M16—21no—
349M16—64no—
350M16—61no—
351M16—61no—
352M16#62512yes—
353C2×C8—21no—
354C2×C8—31no—
355C2×C8—31no—
356C2×C8—31no—
357C2×C8—31no—
358C2×C8—64no—
359C2×C8—61no—
360C2×C8—61no—
361C2×C8—61no—
362C2×C8—61no—
363C2×C8—61no—
364C4⋊C4—91no—
365C4⋊C4—91no—
366C22⋊C4—181no—
367C42—181no—
368C42—181no—
369C42—181no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—62no—
380C22×C3—121no—
381C22×C3—121no—
382C22×C3#89311yescharacteristic
383C22×C3#89411yescharacteristic
384C22×C3#92411yescharacteristic
385C22×C3C4×#6711yescharacteristic
386C22×C3#92911yescharacteristic
387C22×C3#94611yescharacteristic
388C2×D3—22no—
389C2×D3—41no—
390C2×D3—41no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—62no—
396C3×C4D3×C4⋊C411yescharacteristic
397C3×C4#89611yescharacteristic
398C3×C4C2×Dic3⋊C411yescharacteristic
399C3×C4#92411yescharacteristic
400C3×C4C4×#6711yescharacteristic
401C3×C4C4×#6711yescharacteristic
402C3×C4#93711yescharacteristic
403C3×C4#95311yescharacteristic
404Dic3—22no—
405Dic3—122no—
406Dic3—122no—
407Dic3—124no—
408Dic3—121no—
409Dic3—121no—
410Dic3—121no—
411Dic3—121no—
412Dic3—241no—
413Dic3—241no—
414C32#186611yescharacteristic, complemented, Sylow
415C23—61no—
416C23#379911yescharacteristic
417Q8—32no—
418Q8—61no—
419D4—32no—
420D4—62no—
421D4—62no—
422D4—61no—
423C2×C4—61no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—182no—
427C2×C4—181no—
428C2×C4—181no—
429C2×C4—361no—
430C2×C4—361no—
431C2×C4D3×Dic611yescharacteristic
432C2×C4#379811yescharacteristic
433C2×C4C4×D3211yescharacteristic
434C2×C4C2×#62511yescharacteristic
435C2×C4D3×#6711yescharacteristic
436C2×C4D3×#6711yescharacteristic
437C8—22no—
438C8—61no—
439C8—61no—
440C8—61no—
441C8—61no—
442C8—121no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—41no—
451C2×C3—41no—
452C2×C3—122no—
453C2×C3#489411yescharacteristic
454C2×C3#489511yescharacteristic
455C2×C3#498911yescharacteristic
456C2×C3#514411yescharacteristic
457C2×C3#514511yescharacteristic
458C2×C3#521011yescharacteristic
459D3—42no—
460C22—21no—
461C22—21no—
462C22—62no—
463C22—121no—
464C22—121no—
465C22#6385011yescharacteristic
466C22#6385611yescharacteristic
467C22#6390411yescharacteristic
468C4—62no—
469C4—362no—
470C4—361no—
471C4—361no—
472C4#6385111yescharacteristic
473C4D3×Dic3⋊C411yescharacteristic
474C4C4×#62511yescharacteristic
475C4#6397611yescharacteristic
476C3—21no—
477C3#7072211yescharacteristic, complemented
478C3#7201711yescharacteristic, complemented
479C2—21no—
480C2—21no—
481C2—122no—
482C2#1059099411yescharacteristic
483C2#1059099511yescharacteristic
484C2#1059127711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1866
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C3×#822C2semidirect
3. #10591119C2semidirect
6. #10589421C2semidirect
7. #10589156C2semidirect
25. #63566C4semidirect
26. #63566C4semidirect
27. #63563C4semidirect
28. #63563C4semidirect
35. C2×#822D3semidirect
414. C32#1866semidirect
477. C3#70722semidirect
478. C3#72017semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
C2×C3×#8222
#105911192
C2×#635682
#105910842
#105894212
#105891562
#720173
#707223