Finite Group Databasebeta

← #11787038

Subgroups — #11787038

Order 1152.

619 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#948C211yesmaximal, characteristic
2#10592932C211yesmaximal, characteristic
3C2×C3×#837C211yesmaximal, characteristic
4C2×#63578C211yesmaximal, characteristic, complemented
5#10591119C211yesmaximal, characteristic, complemented
6#10589162C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#72017—31nomaximal
9#70376—31nomaximal
10C2×C32×#41C2211yescharacteristic
11#64135C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#948—22no—
14C3×#948—22no—
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208—21no—
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C22×C3×C3⋊C8—21no—
20C22×C3×C3⋊C8C2211yescharacteristic
21#63662C411yescharacteristic, complemented
22#63662C411yescharacteristic, complemented
23#63659C411yescharacteristic, complemented
24#63659C411yescharacteristic, complemented
25C3×#837—22no—
26#63578—22no—
27#63572—21no—
28#63572—21no—
29C2×C3×#131—31no—
30C2×#948D311yescharacteristic
31C2×C3×#104—31no—
32C2×#837D311yescharacteristic
33#5233—31no—
34#5233—31no—
35#5233—61no—
36C2×#822—31no—
37C2×#822—31no—
38#5119—31no—
39#5102—31no—
40#4555—31no—
41#4550—31no—
42#4524—31no—
43#4523—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—
54#3757—21no—
55C4⋊(C3⋊Dic3)C2×C411yescharacteristic
56C4⋊(C3⋊Dic3)C2×C411yescharacteristic
57C4×C3⋊Dic3—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
61C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
62C3×C4×Dic3—21no—
63C3×C4×Dic3—21no—
64C3×#208—24no—
65C3×#208—21no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208D412yes—
69C2×C3×C3⋊C8—24no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
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—31no—
84C2×C3×M16—61no—
85C22×C3×C8—31no—
86C22×C3×C8—61no—
87C2×C3×C42—31no—
88#948—22no—
89#948—22no—
90#926—31no—
91#926—31no—
92#926—61no—
93C2×C4×Dic3C2×D311yescharacteristic
94C2×#208—21no—
95C2×#208C2×D311yescharacteristic
96C2×#208C2×D311yescharacteristic
97C22×C3⋊C8—21no—
98C22×C3⋊C8—31no—
99C22×C3⋊C8—31no—
100C22×C3⋊C8—61no—
101C22×C3⋊C8C2×D311yescharacteristic
102C3×#104—62no—
103#837—22no—
104#835—31no—
105#835—31no—
106#835—31no—
107#835—31no—
108#835—61no—
109#835—61no—
110#832—31no—
111#832—31no—
112#832—31no—
113#832—31no—
114#832—61no—
115#832—61no—
116#822—62no—
117#822—62no—
118Dic3⋊C8—61no—
119Dic3⋊C8—61no—
120Dic3⋊C8—61no—
121Dic3⋊C8—61no—
122C23×C32—21no—
123C23×C32#4111yescharacteristic
124C32×Q8—21no—
125C32×Q8C4⋊C412yes—
126C32×D4—22no—
127C32×D4—22no—
128C32×D4—21no—
129C32×D4C4⋊C412yes—
130C2×C32×C4—21no—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×Q811yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C3⋊(C3⋊C8)—21no—
145C3⋊(C3⋊C8)—21no—
146C3×C3⋊C8—21no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—21no—
149C3×C3⋊C8—41no—
150C2×#131—31no—
151C2×#108—91no—
152#424—91no—
153C2×#104—31no—
154#416—91no—
155#339—91no—
156#336—91no—
157C3×#41—21no—
158C3×#41—21no—
159C3×#41—21no—
160C3×#41—21no—
161C3×#41—22no—
162C3×#41—22no—
163C3×#41—41no—
164C3×#41—41no—
165C3×#41Dic612yes—
166C3×#41Dic612yes—
167C3×#41#6712yes—
168C3×#41#6712yes—
169C2×C3×Q8—21no—
170C2×C3×Q8C4×D311yescharacteristic
171C2×C3×Q8C4×D311yescharacteristic
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—41no—
176C2×C3×D4C4×D311yescharacteristic
177C2×C3×D4C4×D311yescharacteristic
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—41no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—21no—
186C3×M16—32no—
187C3×M16—64no—
188C3×M16—61no—
189C3×M16—61no—
190C3×M16—61no—
191C2×C3×C8—31no—
192C2×C3×C8—31no—
193C2×C3×C8—64no—
194C2×C3×C8—61no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C2×C3×C8—61no—
198C3×C42—61no—
199C3×C42—61no—
200#217—61no—
201#217—61no—
202#217—121no—
203C4⋊Dic3—31no—
204C4⋊Dic3—31no—
205C4⋊Dic3—31no—
206C4⋊Dic3—31no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4×Dic3—21no—
210C4×Dic3—21no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—121no—
214#208—24no—
215#208—21no—
216#208—21no—
217#208—21no—
218#208#6712yes—
219C2×C3⋊C8—24no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—31no—
225C2×C3⋊C8—31no—
226C2×C3⋊C8—31no—
227C2×C3⋊C8—31no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—121no—
235C2×C3⋊C8—121no—
236C2×C3⋊C8#6711yescharacteristic
237C2×C3⋊C8#6711yescharacteristic
238C22×C32—21no—
239C22×C32—21no—
240C22×C32—22no—
241C22×C32—41no—
242C22×C32—41no—
243C22×C32C4×D411yescharacteristic
244C22×C32C22⋊Q811yescharacteristic
245C22×C32#12311yescharacteristic
246C32×C4—22no—
247C32×C4C2×C4⋊C411yescharacteristic
248C32×C4C4×D411yescharacteristic
249C32×C4#12011yescharacteristic
250C32×C4C22⋊Q811yescharacteristic
251C3⋊Dic3—41no—
252C3⋊Dic3—41no—
253C3×Dic3—42no—
254C2×#41D3211yescharacteristic
255#131—62no—
256#131—62no—
257C2×M16—31no—
258C2×M16—31no—
259C2×M16—61no—
260C22×C8—31no—
261C22×C8—61no—
262C22×C8—91no—
263#117—91no—
264C2×C42—31no—
265#108—182no—
266C4⋊C8—181no—
267C4⋊C8—181no—
268#104—62no—
269#103—91no—
270#103—91no—
271#102—91no—
272#102—91no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—41no—
277C23×C3#23511yescharacteristic
278C23×C3#23711yescharacteristic
279C3×Q8—21no—
280C3×Q8—21no—
281C3×Q8—22no—
282C3×Q8—41no—
283C3×Q8Dic3⋊C412yes—
284C3×Q8Dic3⋊C412yes—
285C3×D4—22no—
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—22no—
289C3×D4—21no—
290C3×D4—21no—
291C3×D4—22no—
292C3×D4—41no—
293C3×D4—42no—
294C3×D4—42no—
295C3×D4Dic3⋊C412yes—
296C3×D4Dic3⋊C412yes—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—41no—
312C2×C3×C4—62no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4C2×Dic611yescharacteristic
316C2×C3×C4C2×Dic611yescharacteristic
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4C2×C4×D311yescharacteristic
319C2×C3×C4#23511yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325C2×C3×C4C2×#6711yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327C2×Dic3—22no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C3×C8—61no—
337C3×C8—61no—
338C3×C8—62no—
339C3×C8—121no—
340C3⋊C8—21no—
341C3⋊C8—22no—
342C3⋊C8—21no—
343C3⋊C8—41no—
344C3⋊C8—61no—
345C3⋊C8—61no—
346C3⋊C8—61no—
347C3⋊C8—61no—
348C3⋊C8—121no—
349C3⋊C8—121no—
350C2×C32—21no—
351C2×C32—21no—
352C2×C32—42no—
353C2×C32#38511yescharacteristic
354C2×C32#44311yescharacteristic
355C2×C32#44411yescharacteristic
356#41—21no—
357#41—21no—
358#41#62512yes—
359#41#62712yes—
360C2×Q8#62411yescharacteristic
361C2×D4—21no—
362C2×D4#62411yescharacteristic
363C22×C4—21no—
364C22×C4—61no—
365C22×C4C2×D3211yescharacteristic
366M16—32no—
367M16—64no—
368M16—61no—
369M16—61no—
370M16—61no—
371C2×C8—31no—
372C2×C8—31no—
373C2×C8—64no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8—61no—
377C2×C8—61no—
378C2×C8—91no—
379C2×C8—91no—
380C2×C8—181no—
381C2×C8—181no—
382C4⋊C4—91no—
383C4⋊C4—91no—
384C22⋊C4—181no—
385C42—61no—
386C42—61no—
387C42—181no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—42no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—81no—
405C22×C3—81no—
406C22×C3#87811yescharacteristic
407C22×C3#67⋊C411yescharacteristic
408C22×C3#92411yescharacteristic
409C22×C3C4×#6711yescharacteristic
410C22×C3#92911yescharacteristic
411C22×C3#93511yescharacteristic
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—42no—
419C3×C4—122no—
420C3×C4#87811yescharacteristic
421C3×C4#67⋊C411yescharacteristic
422C3×C4C2×Dic3⋊C411yescharacteristic
423C3×C4C2×Dic3⋊C411yescharacteristic
424C3×C4#92411yescharacteristic
425C3×C4C4×#6711yescharacteristic
426C3×C4#93711yescharacteristic
427C3×C4#95311yescharacteristic
428Dic3—42no—
429Dic3—121no—
430Dic3—121no—
431Dic3—121no—
432Dic3—121no—
433Dic3—241no—
434Dic3—241no—
435C32#186611yescharacteristic, complemented, Sylow
436C23—21no—
437C23#380411yescharacteristic
438Q8—21no—
439Q8#372412yes—
440D4—22no—
441D4—22no—
442D4—21no—
443D4#372412yes—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—62no—
448C2×C4—121no—
449C2×C4—121no—
450C2×C4—181no—
451C2×C4—181no—
452C2×C4#380411yescharacteristic
453C2×C4C2×#62411yescharacteristic
454C2×C4C2×#62511yescharacteristic
455C2×C4C2×#62711yescharacteristic
456C2×C4D3×#6711yescharacteristic
457C2×C4D3×#6711yescharacteristic
458C8—61no—
459C8—61no—
460C8—62no—
461C8—121no—
462C8—181no—
463C8—181no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—41no—
472C2×C3—41no—
473C2×C3—42no—
474C2×C3—42no—
475C2×C3—82no—
476C2×C3#482311yescharacteristic
477C2×C3#482411yescharacteristic
478C2×C3#494611yescharacteristic
479C2×C3#514411yescharacteristic
480C2×C3#514511yescharacteristic
481C2×C3#521011yescharacteristic
482C22—21no—
483C22—21no—
484C22—22no—
485C22—41no—
486C22—41no—
487C22#6395211yescharacteristic
488C22#6396111yescharacteristic
489C22#6396411yescharacteristic
490C4—22no—
491C4—122no—
492C4—361no—
493C4—361no—
494C4#6395211yescharacteristic
495C4#6396411yescharacteristic
496C4C2×#372411yescharacteristic
497C4#6397611yescharacteristic
498C3—21no—
499C3#7037611yescharacteristic, complemented
500C3#7201711yescharacteristic, complemented
501C2—21no—
502C2—21no—
503C2—42no—
504C2#1059166211yescharacteristic
505C2#1059166311yescharacteristic
506C2#1059169311yescharacteristic
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×#63578C2semidirect
5. #10591119C2semidirect
6. #10589162C2semidirect
7. #10589155C2semidirect
21. #63662C4semidirect
22. #63662C4semidirect
23. #63659C4semidirect
24. #63659C4semidirect
435. C32#1866semidirect
499. C3#70376semidirect
500. 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
#105929322
C2×C3×#8372
C2×#635782
#105911192
#105891622
#105891552
#720173
#703763