Finite Group Databasebeta

← #11787036

Subgroups — #11787036

Order 1152.

625 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#948C211yesmaximal, characteristic
2C2×#63664C211yesmaximal, characteristic
3C3×#5233C211yesmaximal, characteristic
4C2×#63577C211yesmaximal, characteristic, complemented
5#10591116C211yesmaximal, characteristic, complemented
6#10589160C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#72017—31nomaximal
9#70292—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#948—22no—
14C3×#948—22no—
15C3×#926C2211yescharacteristic
16C2×C3×#208—21no—
17C2×C3×#208C2211yescharacteristic
18C22×C3×C3⋊C8—21no—
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21#63664—22no—
22C3×#835C411yescharacteristic, complemented
23C3×#835C411yescharacteristic, complemented
24C3×#832C411yescharacteristic, complemented
25C3×#832C411yescharacteristic, complemented
26#63577—22no—
27Dic3⋊(C3⋊C8)—21no—
28Dic3⋊(C3⋊C8)—21no—
29C2×C3×#131—31no—
30C2×#948D311yescharacteristic
31C3×#416—31no—
32C2×#837—31no—
33C2×#837—31no—
34C2×#837—61no—
35#5233D311yescharacteristic
36C2×#822—31no—
37C2×#819—31no—
38#5102—31no—
39#4999—31no—
40#4555—31no—
41#4550—31no—
42#4550—31no—
43#4532—31no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41D412yes—
47C32×#41Q812yes—
48C2×C32×Q8C2×C411yescharacteristic
49C2×C32×D4—21no—
50C2×C32×D4C2×C411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3—21no—
56#3748—21no—
57#3748—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×C4⋊Dic3C2×C411yescharacteristic
61C3×C4⋊Dic3C2×C411yescharacteristic
62C3×C4×Dic3—21no—
63C3×#208—24no—
64C3×#208—21no—
65C3×#208D412yes—
66C2×C3×C3⋊C8—24no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8C2×C411yescharacteristic
73C2×C3×C3⋊C8C2×C411yescharacteristic
74C2×C3×C3⋊C8D411yescharacteristic
75C2×C3×C3⋊C8D411yescharacteristic
76#1866—91noSylow
77C2×C3×#41—21no—
78C2×C3×#41C2×D311yescharacteristic
79C2×C3×#41C2×D311yescharacteristic
80C3×#131—62no—
81C3×#131—62no—
82C2×C3×M16—31no—
83C2×C3×M16—61no—
84C22×C3×C8—31no—
85C22×C3×C8—31no—
86C22×C3×C8—61no—
87C3×#117—31no—
88#948—22no—
89#948—22no—
90#926C2×D311yescharacteristic
91C2×C4×Dic3—31no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—61no—
94C2×#208—21no—
95C2×#208—31no—
96C2×#208—31no—
97C2×#208—61no—
98C2×#208C2×D311yescharacteristic
99C22×C3⋊C8—21no—
100C22×C3⋊C8C2×D311yescharacteristic
101C22×C3⋊C8C2×D311yescharacteristic
102C3×#103—31no—
103C3×#103—31no—
104C3×#102—31no—
105C3×#102—31no—
106#837—64no—
107#837—62no—
108#837—62no—
109#835Dic311yescharacteristic, complemented
110#835Dic311yescharacteristic, complemented
111#832Dic311yescharacteristic, complemented
112#832Dic311yescharacteristic, complemented
113#822—62no—
114#819—62no—
115Dic3⋊C8—61no—
116Dic3⋊C8—61no—
117C4⋊(C3⋊C8)—61no—
118C4⋊(C3⋊C8)—61no—
119C23×C32—21no—
120C23×C32#4111yescharacteristic
121C32×Q8—21no—
122C32×Q8C4⋊C412yes—
123C32×D4—22no—
124C32×D4—22no—
125C32×D4—21no—
126C32×D4C4⋊C412yes—
127C2×C32×C4—21no—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×Q811yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—21no—
143C3×C3⋊C8—21no—
144C3×C3⋊C8—21no—
145C3×C3⋊C8—22no—
146C3×C3⋊C8—21no—
147C2×#131—31no—
148C2×#108—91no—
149#424—91no—
150C2×#104—91no—
151#416—31no—
152#339—91no—
153#336—91no—
154C3×#41—21no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41—21no—
158C3×#41—22no—
159C3×#41—22no—
160C3×#41—41no—
161C3×#41—41no—
162C3×#41Dic612yes—
163C3×#41Dic612yes—
164C3×#41D1212yes—
165C3×#41#6712yes—
166C2×C3×Q8—21no—
167C2×C3×Q8C4×D311yescharacteristic
168C2×C3×Q8C2×Dic311yescharacteristic
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×C3×D4—41no—
173C2×C3×D4C4×D311yescharacteristic
174C2×C3×D4C2×Dic311yescharacteristic
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—41no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—121no—
184C3×M16—32no—
185C3×M16—64no—
186C3×M16—61no—
187C2×C3×C8—31no—
188C2×C3×C8—31no—
189C2×C3×C8—31no—
190C2×C3×C8—31no—
191C2×C3×C8—64no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C2×C3×C8—61no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C3×C4⋊C4—31no—
198C3×C4⋊C4—31no—
199C3×C22⋊C4—61no—
200C3×C42—61no—
201#217—21no—
202C4⋊Dic3C2×Dic311yescharacteristic
203C4⋊Dic3C2×Dic311yescharacteristic
204C4×Dic3—21no—
205C4×Dic3—62no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—121no—
211#208—24no—
212#208—21no—
213#208—62no—
214#208—61no—
215#208—61no—
216#208—61no—
217#208—61no—
218#208—121no—
219#208#6712yes—
220C2×C3⋊C8—24no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—121no—
229C2×C3⋊C8C2×Dic311yescharacteristic
230C2×C3⋊C8C2×Dic311yescharacteristic
231C2×C3⋊C8#6711yescharacteristic
232C2×C3⋊C8#6711yescharacteristic
233C22×C32—21no—
234C22×C32—21no—
235C22×C32—22no—
236C22×C32—41no—
237C22×C32—41no—
238C22×C32C4×D411yescharacteristic
239C22×C32C22⋊Q811yescharacteristic
240C22×C32#12311yescharacteristic
241C32×C4—22no—
242C32×C4C2×C4⋊C411yescharacteristic
243C32×C4C4×D411yescharacteristic
244C32×C4#12011yescharacteristic
245C32×C4C22⋊Q811yescharacteristic
246C3⋊Dic3—42no—
247C3×Dic3—41no—
248C3×Dic3—41no—
249C2×#41D3211yescharacteristic
250#131—62no—
251#131—62no—
252C2×M16—31no—
253C2×M16—61no—
254C2×M16—91no—
255C22×C8—31no—
256C22×C8—31no—
257C22×C8—61no—
258#117—31no—
259C2×C42—91no—
260#108—182no—
261C4⋊C8—181no—
262C4⋊C8—181no—
263#104—182no—
264#103—31no—
265#103—31no—
266#102—31no—
267#102—31no—
268C23×C3—21no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—41no—
272C23×C3#23511yescharacteristic
273C23×C3#23711yescharacteristic
274C3×Q8—21no—
275C3×Q8—21no—
276C3×Q8—22no—
277C3×Q8—41no—
278C3×Q8Dic3⋊C412yes—
279C3×Q8C4⋊Dic312yes—
280C3×D4—22no—
281C3×D4—22no—
282C3×D4—22no—
283C3×D4—22no—
284C3×D4—21no—
285C3×D4—21no—
286C3×D4—22no—
287C3×D4—41no—
288C3×D4—42no—
289C3×D4—42no—
290C3×D4Dic3⋊C412yes—
291C3×D4C4⋊Dic312yes—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—42no—
305C2×C3×C4—42no—
306C2×C3×C4—41no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4C2×Dic611yescharacteristic
310C2×C3×C4C2×Dic611yescharacteristic
311C2×C3×C4C2×C4×D311yescharacteristic
312C2×C3×C4C2×D1211yescharacteristic
313C2×C3×C4#23511yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4#23711yescharacteristic
317C2×C3×C4C22×Dic311yescharacteristic
318C2×C3×C4C2×#6711yescharacteristic
319C2×C3×C4C2×#6711yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—122no—
326C2×Dic3—122no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3—122no—
330C2×Dic3—121no—
331C2×Dic3—121no—
332C3×C8—61no—
333C3×C8—61no—
334C3×C8—62no—
335C3×C8—61no—
336C3×C8—61no—
337C3⋊C8—21no—
338C3⋊C8—21no—
339C3⋊C8—21no—
340C3⋊C8—22no—
341C3⋊C8—21no—
342C3⋊C8—122no—
343C3⋊C8—121no—
344C3⋊C8—121no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32—42no—
348C2×C32#38511yescharacteristic
349C2×C32#44311yescharacteristic
350C2×C32#44411yescharacteristic
351#41—21no—
352#41—21no—
353#41#62612yes—
354#41#62712yes—
355C2×Q8D3×Dic311yescharacteristic
356C2×D4—21no—
357C2×D4D3×Dic311yescharacteristic
358C22×C4—21no—
359C22×C4—181no—
360C22×C4C2×D3211yescharacteristic
361M16—32no—
362M16—64no—
363M16—61no—
364M16—181no—
365M16—181no—
366C2×C8—31no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—31no—
370C2×C8—64no—
371C2×C8—61no—
372C2×C8—61no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8—181no—
377C4⋊C4—31no—
378C4⋊C4—31no—
379C22⋊C4—61no—
380C42—61no—
381C42—181no—
382C42—181no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—22no—
388C22×C3—22no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—42no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—81no—
400C22×C3—81no—
401C22×C3#87811yescharacteristic
402C22×C3#88611yescharacteristic
403C22×C3#92411yescharacteristic
404C22×C3C4×#6711yescharacteristic
405C22×C3#92911yescharacteristic
406C22×C3D4×Dic311yescharacteristic
407C3×C4—22no—
408C3×C4—22no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—42no—
414C3×C4—121no—
415C3×C4—121no—
416C3×C4#87811yescharacteristic
417C3×C4#88211yescharacteristic
418C3×C4C2×Dic3⋊C411yescharacteristic
419C3×C4#92411yescharacteristic
420C3×C4C2×C4⋊Dic311yescharacteristic
421C3×C4C4×#6711yescharacteristic
422C3×C4D4×Dic311yescharacteristic
423C3×C4#95311yescharacteristic
424Dic3—41no—
425Dic3—41no—
426Dic3—122no—
427Dic3—122no—
428Dic3—124no—
429C32#186611yescharacteristic, complemented, Sylow
430C23—21no—
431C23#380411yescharacteristic
432Q8—21no—
433Q8Dic3⋊Dic312yes—
434D4—22no—
435D4—22no—
436D4—21no—
437D4Dic3⋊Dic312yes—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—61no—
442C2×C4—61no—
443C2×C4—182no—
444C2×C4—361no—
445C2×C4—361no—
446C2×C4C2×D3×Dic311yescharacteristic
447C2×C4#380411yescharacteristic
448C2×C4C2×#62611yescharacteristic
449C2×C4C2×#62711yescharacteristic
450C2×C4D3×#6711yescharacteristic
451C2×C4D3×#6711yescharacteristic
452C8—61no—
453C8—61no—
454C8—61no—
455C8—61no—
456C8—62no—
457C8—361no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—41no—
466C2×C3—41no—
467C2×C3—42no—
468C2×C3—42no—
469C2×C3—82no—
470C2×C3#495011yescharacteristic
471C2×C3#514411yescharacteristic
472C2×C3#514511yescharacteristic
473C2×C3#519611yescharacteristic
474C2×C3#519711yescharacteristic
475C2×C3#521011yescharacteristic
476C22—21no—
477C22—21no—
478C22—22no—
479C22—41no—
480C22—41no—
481C22#6396411yescharacteristic
482C22#6396611yescharacteristic
483C22Dic3×#6711yescharacteristic
484C4—22no—
485C4—121no—
486C4—121no—
487C4—362no—
488C4#6396411yescharacteristic
489C4C2×Dic3⋊Dic311yescharacteristic
490C4Dic3×#6711yescharacteristic
491C4#6397711yescharacteristic
492C3—21no—
493C3#7029211yescharacteristic, complemented
494C3#7201711yescharacteristic, complemented
495C2—21no—
496C2—21no—
497C2—42no—
498C2#1059167311yescharacteristic
499C2#1059167411yescharacteristic
500C2#1059171811yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C4×D4
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1866
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#63577C2semidirect
5. #10591116C2semidirect
6. #10589160C2semidirect
7. #10589156C2semidirect
22. C3×#835C4semidirect
23. C3×#835C4semidirect
24. C3×#832C4semidirect
25. C3×#832C4semidirect
109. #835Dic3semidirect
110. #835Dic3semidirect
111. #832Dic3semidirect
112. #832Dic3semidirect
429. C32#1866semidirect
493. C3#70292semidirect
494. C3#72017semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9482
C2×#636642
C3×#52332
C2×#635772
#105911162
#105891602
#105891562
#720173
#702923