Finite Group Databasebeta

← #11785591

Subgroups — #11785591

Order 1152.

609 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#948C211yesmaximal, characteristic
2#10592931C211yesmaximal, characteristic
3C3×#5232C211yesmaximal, characteristic
4C2×#63577C211yesmaximal, characteristic, complemented
5C2×#63573C211yesmaximal, characteristic, complemented
6#10589168C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#72015—31nomaximal
9#70299—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#948—22no—
14C3×#948C414yescomplemented
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208—21no—
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C22×C3×C3⋊C8—21no—
20C22×C3×C3⋊C8C2211yescharacteristic
21#63662—21no—
22#63659—21no—
23C3×#835—21no—
24C3×#832—21no—
25#63577—22no—
26#63573—21no—
27#63573—21no—
28C2×C3×#131—31no—
29C2×#948D311yescharacteristic
30C3×#417—31no—
31#5232—31no—
32#5232—31no—
33#5232—61no—
34#5232D311yescharacteristic
35C2×#822—31no—
36C2×#819—31no—
37C2×#817—31no—
38C2×#808—31no—
39#4554—31no—
40#4554—31no—
41#4554—31no—
42#4530—31no—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41C2×C412yes—
46C32×#41Q812yes—
47C2×C32×Q8D411yescharacteristic
48C2×C32×D4—21no—
49C2×C32×D4D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3×Dic3—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56#3748—21no—
57#3748—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×#208—21no—
62C3×#208—24no—
63C3×#208—21no—
64C3×#208—21no—
65C3×#208C2×C412yes—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—24no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8C2×C412yes—
70C2×C3×C3⋊C8D411yescharacteristic
71C2×C3×C3⋊C8D411yescharacteristic
72C2×C3×C3⋊C8D412yes—
73#1815—91noSylow
74C2×C3×#41—21no—
75C2×C3×#41C2×D311yescharacteristic
76C2×C3×#41C2×D311yescharacteristic
77C3×#131—34no—
78C3×#131—62no—
79C2×C3×M16—31no—
80C2×C3×M16—31no—
81C2×C3×M16—61no—
82C22×C3×C8—31no—
83C22×C3×C8—61no—
84C2×C3×C4⋊C4—31no—
85#948—22no—
86#948Dic314yescomplemented
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—61no—
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×#208—21no—
92C2×#208—31no—
93C2×#208—31no—
94C2×#208—61no—
95C2×#208C2×D311yescharacteristic
96C2×#208C2×D311yescharacteristic
97C22×C3⋊C8—21no—
98C22×C3⋊C8C2×D311yescharacteristic
99C3×#103—61no—
100C3×#102—61no—
101#835—21no—
102#835—62no—
103#835—61no—
104#835—61no—
105#832—21no—
106#832—62no—
107#832—61no—
108#832—61no—
109#822—62no—
110#819—62no—
111#817—61no—
112#817—61no—
113#808—61no—
114#808—61no—
115C23×C32—21no—
116C23×C32#4111yescharacteristic
117C32×Q8—21no—
118C32×Q8C4⋊C412yes—
119C32×D4—22no—
120C32×D4—22no—
121C32×D4—21no—
122C32×D4C4⋊C412yes—
123C2×C32×C4—21no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×Q811yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—81no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—81no—
136C3⋊(C3⋊C8)—41no—
137C3×C3⋊C8—22no—
138C3×C3⋊C8—41no—
139C3×C3⋊C8C22⋊C412yes—
140C3×C3⋊C8C22⋊C412yes—
141C2×#131—31no—
142C2×#108—91no—
143C2×#106—91no—
144#417—31no—
145#417—91no—
146#343—91no—
147#343—91no—
148C3×#41—21no—
149C3×#41—21no—
150C3×#41—21no—
151C3×#41—21no—
152C3×#41—22no—
153C3×#41—22no—
154C3×#41—41no—
155C3×#41—41no—
156C3×#41Dic612yes—
157C3×#41Dic612yes—
158C3×#41C4×D312yes—
159C3×#41C2×Dic312yes—
160C2×C3×Q8—21no—
161C2×C3×Q8D1211yescharacteristic
162C2×C3×Q8#6711yescharacteristic
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—41no—
167C2×C3×D4D1211yescharacteristic
168C2×C3×D4#6711yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—41no—
173C22×C3×C4—61no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×Dic3—21no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—121no—
180C3×M16—32no—
181C3×M16—64no—
182C3×M16—61no—
183C3×M16—61no—
184C3×M16—61no—
185C2×C3×C8—32no—
186C2×C3×C8—31no—
187C2×C3×C8—31no—
188C2×C3×C8—32no—
189C2×C3×C8—64no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—62no—
197C4⋊Dic3—61no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—121no—
202#208—21no—
203#208—24no—
204#208—21no—
205#208—21no—
206#208—61no—
207#208—61no—
208#208—61no—
209#208—61no—
210#208—121no—
211#208—121no—
212#208C2×Dic312yes—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—24no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8C2×Dic312yes—
220C2×C3⋊C8#6711yescharacteristic
221C2×C3⋊C8#6711yescharacteristic
222C2×C3⋊C8#6712yes—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32—22no—
226C22×C32—41no—
227C22×C32—41no—
228C22×C32#11711yescharacteristic
229C22×C32#12111yescharacteristic
230C22×C32C22⋊Q811yescharacteristic
231C32×C4—22no—
232C32×C4C2×C22⋊C411yescharacteristic
233C32×C4C2×C4⋊C411yescharacteristic
234C32×C4#12111yescharacteristic
235C32×C4C22⋊Q811yescharacteristic
236C3⋊Dic3—81no—
237C3×Dic3—81no—
238C2×#41D3211yescharacteristic
239#131—34no—
240#131—62no—
241C2×M16—31no—
242C2×M16—31no—
243C2×M16—61no—
244C2×M16—91no—
245C22×C8—31no—
246C22×C8—61no—
247C2×C4⋊C4—31no—
248C2×C4⋊C4—91no—
249#108—182no—
250#106—181no—
251#106—181no—
252#103—61no—
253#103—181no—
254#102—61no—
255#102—181no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—21no—
259C23×C3—41no—
260C23×C3#23511yescharacteristic
261C23×C3#23711yescharacteristic
262C3×Q8—21no—
263C3×Q8—21no—
264C3×Q8—22no—
265C3×Q8—41no—
266C3×Q8Dic3⋊C412yes—
267C3×Q8C4⋊Dic312yes—
268C3×D4—22no—
269C3×D4—22no—
270C3×D4—22no—
271C3×D4—22no—
272C3×D4—21no—
273C3×D4—21no—
274C3×D4—22no—
275C3×D4—41no—
276C3×D4—42no—
277C3×D4—42no—
278C3×D4Dic3⋊C412yes—
279C3×D4C4⋊Dic312yes—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—41no—
295C2×C3×C4—121no—
296C2×C3×C4—241no—
297C2×C3×C4C2×Dic611yescharacteristic
298C2×C3×C4C2×Dic611yescharacteristic
299C2×C3×C4C2×C4×D311yescharacteristic
300C2×C3×C4C2×D1211yescharacteristic
301C2×C3×C4#23511yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4#23711yescharacteristic
305C2×C3×C4C22×Dic311yescharacteristic
306C2×C3×C4C2×#6711yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308C2×C3×C4C2×#6711yescharacteristic
309C2×Dic3—41no—
310C2×Dic3—81no—
311C2×Dic3—122no—
312C2×Dic3—121no—
313C2×Dic3—121no—
314C2×Dic3—242no—
315C2×Dic3—241no—
316C2×Dic3—241no—
317C3×C8—32no—
318C3×C8—32no—
319C3×C8—62no—
320C3×C8—121no—
321C3⋊C8—22no—
322C3⋊C8—41no—
323C3⋊C8—122no—
324C3⋊C8—121no—
325C3⋊C8—121no—
326C3⋊C8#21712yes—
327C3⋊C8#21712yes—
328C2×C32—21no—
329C2×C32—21no—
330C2×C32—42no—
331C2×C32#38011yescharacteristic
332C2×C32#47111yescharacteristic
333C2×C32#47111yescharacteristic
334#41—21no—
335#41—21no—
336#41D3×Dic312yes—
337#41#62712yes—
338C2×Q8#62611yescharacteristic
339C2×D4—21no—
340C2×D4#62611yescharacteristic
341C22×C4—21no—
342C22×C4—61no—
343C22×C4—181no—
344C22×C4C2×D3211yescharacteristic
345M16—32no—
346M16—64no—
347M16—61no—
348M16—61no—
349M16—61no—
350M16—181no—
351M16—181no—
352C2×C8—32no—
353C2×C8—31no—
354C2×C8—31no—
355C2×C8—32no—
356C2×C8—64no—
357C2×C8—61no—
358C2×C8—61no—
359C2×C8—181no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—181no—
363C4⋊C4—181no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3—42no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—81no—
381C22×C3—81no—
382C22×C3#87711yescharacteristic
383C22×C3#87811yescharacteristic
384C22×C3#92411yescharacteristic
385C22×C3#92611yescharacteristic
386C22×C3#93011yescharacteristic
387C22×C3#93911yescharacteristic
388C3×C4—22no—
389C3×C4—22no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—42no—
395C3×C4—241no—
396C3×C4#87811yescharacteristic
397C3×C4D3×C22⋊C411yescharacteristic
398C3×C4C2×Dic3⋊C411yescharacteristic
399C3×C4#92411yescharacteristic
400C3×C4C2×C4⋊Dic311yescharacteristic
401C3×C4#93011yescharacteristic
402C3×C4#93911yescharacteristic
403C3×C4C2×#21711yescharacteristic
404Dic3—81no—
405Dic3—242no—
406Dic3—241no—
407Dic3—241no—
408C32#181511yescharacteristic, complemented, Sylow
409C23—21no—
410C23#380411yescharacteristic
411Q8—21no—
412Q8Dic3⋊Dic312yes—
413D4—22no—
414D4—22no—
415D4—21no—
416D4Dic3⋊Dic312yes—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—121no—
421C2×C4—241no—
422C2×C4—361no—
423C2×C4—721no—
424C2×C4C2×D3×Dic311yescharacteristic
425C2×C4#380411yescharacteristic
426C2×C4C2×#62611yescharacteristic
427C2×C4C2×#62711yescharacteristic
428C2×C4D3×#6711yescharacteristic
429C2×C4D3×#6711yescharacteristic
430C8—32no—
431C8—32no—
432C8—62no—
433C8—121no—
434C8—361no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—41no—
443C2×C3—41no—
444C2×C3—42no—
445C2×C3—42no—
446C2×C3—82no—
447C2×C3#494211yescharacteristic
448C2×C3#514111yescharacteristic
449C2×C3#514111yescharacteristic
450C2×C3#520011yescharacteristic
451C2×C3#520311yescharacteristic
452C2×C3#521211yescharacteristic
453C22—21no—
454C22—21no—
455C22—22no—
456C22—41no—
457C22—41no—
458C22#6395511yescharacteristic
459C22#6396411yescharacteristic
460C22#6397811yescharacteristic
461C4—22no—
462C4—241no—
463C4—721no—
464C4#6396411yescharacteristic
465C4C2×Dic3⋊Dic311yescharacteristic
466C4D3×#21711yescharacteristic
467C4#6397811yescharacteristic
468C3—21no—
469C3#7029911yescharacteristic, complemented
470C3#7201511yescharacteristic, complemented
471C2—21no—
472C2—21no—
473C2—42no—
474C2#1059167911yescharacteristic
475C2#1059168011yescharacteristic
476C2#1059171611yescharacteristic
subgroupG/H
centerC22#63978
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#121
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1815
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#63577C2semidirect
5. C2×#63573C2semidirect
6. #10589168C2semidirect
7. #10589167C2semidirect
14. C3×#948C4semidirect
86. #948Dic3semidirect
408. C32#1815semidirect
469. C3#70299semidirect
470. C3#72015semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9482
#105929312
C3×#52322
C2×#635772
C2×#635732
#105891682
#105891672
#720153
#702993