Finite Group Databasebeta

← #11787037

Subgroups — #11787037

Order 1152.

673 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64157C211yesmaximal, characteristic
2C2×C3×#837C211yesmaximal, characteristic
3C3×#5233C211yesmaximal, characteristic
4C2×#63577C211yesmaximal, characteristic, complemented
5#10591117C211yesmaximal, characteristic, complemented
6#10589161C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70376—31nomaximal
9#70292—31nomaximal
10C2×C32×#41C2211yescharacteristic
11#64157—22no—
12#64157—22no—
13C2×#3748—21no—
14C2×#3748C2211yescharacteristic
15C22×C3⋊(C3⋊C8)—21no—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#837—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×#948—31no—
30C2×#948—31no—
31C2×#948—61no—
32C2×C3×#104—31no—
33C3×#416—31no—
34C2×#837D311yescharacteristic
35#5233D311yescharacteristic
36C2×#822—31no—
37#5119—31no—
38C2×#819—31no—
39#4999—31no—
40#4550—31no—
41#4532—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#3748—24no—
55#3748—21no—
56#3748D412yes—
57C2×C3⋊(C3⋊C8)—24no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)D411yescharacteristic
62C2×C3⋊(C3⋊C8)D411yescharacteristic
63C3×#217—21no—
64C3×C4⋊Dic3C2×C411yescharacteristic
65C3×C4⋊Dic3C2×C411yescharacteristic
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8C2×C411yescharacteristic
75C2×C3×C3⋊C8C2×C411yescharacteristic
76#1866—91noSylow
77C2×C3×#41—21no—
78C2×C3×#41C2×D311yescharacteristic
79C2×C3×#41C2×D311yescharacteristic
80C2×C3×M16—31no—
81C22×C3×C8—31no—
82C3×#117—31no—
83C2×C3×C42—31no—
84#948—62no—
85#948—62no—
86#948—64no—
87#948—64no—
88#948—62no—
89#948—62no—
90#926C2×D311yescharacteristic
91C2×C4×Dic3C2×D311yescharacteristic
92C2×#208—31no—
93C2×#208—31no—
94C2×#208—61no—
95C2×#208—61no—
96C2×#208—61no—
97C2×#208—62no—
98C2×#208C2×D311yescharacteristic
99C22×C3⋊C8—31no—
100C22×C3⋊C8—31no—
101C22×C3⋊C8—61no—
102C22×C3⋊C8—61no—
103C22×C3⋊C8—61no—
104C22×C3⋊C8—62no—
105C22×C3⋊C8C2×D311yescharacteristic
106C3×#104—62no—
107C3×#103—31no—
108C3×#103—31no—
109C3×#102—31no—
110C3×#102—31no—
111#837—22no—
112#835Dic311yescharacteristic, complemented
113#835Dic311yescharacteristic, complemented
114#832Dic311yescharacteristic, complemented
115#832Dic311yescharacteristic, complemented
116#822—62no—
117#819—62no—
118Dic3⋊C8—61no—
119Dic3⋊C8—61no—
120C4⋊(C3⋊C8)—61no—
121C4⋊(C3⋊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—22no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C3⋊(C3⋊C8)—21no—
145C3⋊(C3⋊C8)—22no—
146C3⋊(C3⋊C8)—21no—
147C3×C3⋊C8—21no—
148C3×C3⋊C8—21no—
149C3×C3⋊C8—41no—
150C2×#131—91no—
151C2×#108—91no—
152#424—91no—
153C2×#104—31no—
154#416—31no—
155#339—91no—
156#336—91no—
157C3×#41—22no—
158C3×#41—22no—
159C3×#41—21no—
160C3×#41—21no—
161C3×#41—21no—
162C3×#41—21no—
163C3×#41—22no—
164C3×#41—22no—
165C3×#41Dic612yes—
166C3×#41Dic612yes—
167C3×#41D1212yes—
168C3×#41#6712yes—
169C2×C3×Q8—21no—
170C2×C3×Q8C4×D311yescharacteristic
171C2×C3×Q8C2×Dic311yescharacteristic
172C2×C3×D4—22no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4C4×D311yescharacteristic
177C2×C3×D4C2×Dic311yescharacteristic
178C22×C3×C4—22no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—21no—
186C3×M16—61no—
187C3×M16—61no—
188C2×C3×C8—31no—
189C2×C3×C8—31no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C2×C3×C8—61no—
193C3×C4⋊C4—31no—
194C3×C4⋊C4—31no—
195C3×C22⋊C4—61no—
196C3×C42—61no—
197C3×C42—61no—
198C3×C42—61no—
199#217—21no—
200C4⋊Dic3C2×Dic311yescharacteristic
201C4⋊Dic3C2×Dic311yescharacteristic
202C4×Dic3—21no—
203C4×Dic3—21no—
204C4×Dic3—21no—
205#208—21no—
206#208—21no—
207#208—32no—
208#208—32no—
209#208—62no—
210#208—68no—
211#208—64no—
212#208—64no—
213#208—62no—
214#208—61no—
215#208—61no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—31no—
220C2×C3⋊C8—31no—
221C2×C3⋊C8—31no—
222C2×C3⋊C8—31no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—68no—
227C2×C3⋊C8—64no—
228C2×C3⋊C8—64no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8C2×Dic311yescharacteristic
238C2×C3⋊C8C2×Dic311yescharacteristic
239C22×C32—22no—
240C22×C32—21no—
241C22×C32—21no—
242C22×C32—41no—
243C22×C32—41no—
244C22×C32C4×D411yescharacteristic
245C22×C32C22⋊Q811yescharacteristic
246C22×C32#12311yescharacteristic
247C32×C4—22no—
248C32×C4C2×C4⋊C411yescharacteristic
249C32×C4C4×D411yescharacteristic
250C32×C4#12011yescharacteristic
251C32×C4C22⋊Q811yescharacteristic
252C3×Dic3—42no—
253C3×Dic3—41no—
254C3×Dic3—41no—
255C2×#41D3211yescharacteristic
256#131—182no—
257#131—182no—
258C2×M16—31no—
259C2×M16—91no—
260C2×M16—181no—
261C22×C8—31no—
262C22×C8—91no—
263C22×C8—181no—
264#117—31no—
265C2×C42—31no—
266#108—182no—
267C4⋊C8—181no—
268C4⋊C8—181no—
269#104—62no—
270#103—31no—
271#103—31no—
272#102—31no—
273#102—31no—
274C23×C3—22no—
275C23×C3—21no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3#23711yescharacteristic
279C23×C3#23711yescharacteristic
280C3×Q8—22no—
281C3×Q8—21no—
282C3×Q8—21no—
283C3×Q8—22no—
284C3×Q8Dic3⋊C412yes—
285C3×Q8C4⋊Dic312yes—
286C3×D4—24no—
287C3×D4—24no—
288C3×D4—22no—
289C3×D4—22no—
290C3×D4—22no—
291C3×D4—22no—
292C3×D4—22no—
293C3×D4—21no—
294C3×D4—21no—
295C3×D4—22no—
296C3×D4Dic3⋊C412yes—
297C3×D4C4⋊Dic312yes—
298C2×C3×C4—24no—
299C2×C3×C4—22no—
300C2×C3×C4—24no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—62no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—121no—
317C2×C3×C4—121no—
318C2×C3×C4C2×Dic611yescharacteristic
319C2×C3×C4C2×Dic611yescharacteristic
320C2×C3×C4C2×C4×D311yescharacteristic
321C2×C3×C4C2×D1211yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4#23711yescharacteristic
327C2×C3×C4#23711yescharacteristic
328C2×C3×C4C22×Dic311yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330C2×Dic3—22no—
331C2×Dic3—21no—
332C2×Dic3—21no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C3×C8—61no—
336C3×C8—61no—
337C3×C8—121no—
338C3⋊C8—21no—
339C3⋊C8—21no—
340C3⋊C8—41no—
341C3⋊C8—62no—
342C3⋊C8—62no—
343C3⋊C8—64no—
344C3⋊C8—61no—
345C3⋊C8—61no—
346C3⋊C8—62no—
347C3⋊C8—61no—
348C3⋊C8—61no—
349C3⋊C8—62no—
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#62612yes—
359#41#62712yes—
360C2×Q8D3×Dic311yescharacteristic
361C2×D4—21no—
362C2×D4D3×Dic311yescharacteristic
363C22×C4—21no—
364C22×C4—61no—
365C22×C4C2×D3211yescharacteristic
366M16—61no—
367M16—61no—
368M16—92no—
369M16—184no—
370M16—181no—
371C2×C8—31no—
372C2×C8—31no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8—91no—
377C2×C8—91no—
378C2×C8—184no—
379C2×C8—181no—
380C2×C8—181no—
381C2×C8—181no—
382C4⋊C4—31no—
383C4⋊C4—31no—
384C22⋊C4—61no—
385C42—61no—
386C42—61no—
387C42—61no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—24no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3#87811yescharacteristic
407C22×C3#87811yescharacteristic
408C22×C3#67⋊C411yescharacteristic
409C22×C3#88611yescharacteristic
410C22×C3D4×Dic311yescharacteristic
411C22×C3#93511yescharacteristic
412C3×C4—24no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—122no—
420C3×C4—121no—
421C3×C4—121no—
422C3×C4#87811yescharacteristic
423C3×C4#87811yescharacteristic
424C3×C4#67⋊C411yescharacteristic
425C3×C4#88211yescharacteristic
426C3×C4C2×Dic3⋊C411yescharacteristic
427C3×C4C2×C4⋊Dic311yescharacteristic
428C3×C4D4×Dic311yescharacteristic
429C3×C4#93711yescharacteristic
430Dic3—42no—
431Dic3—41no—
432Dic3—41no—
433C32#186611yescharacteristic, complemented, Sylow
434C23—21no—
435C23#380511yescharacteristic
436Q8—21no—
437Q8Dic3⋊Dic312yes—
438D4—22no—
439D4—22no—
440D4—21no—
441D4Dic3⋊Dic312yes—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—62no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—121no—
449C2×C4—121no—
450C2×C4C2×D3×Dic311yescharacteristic
451C2×C4#380511yescharacteristic
452C2×C4C2×#62611yescharacteristic
453C2×C4C2×#62711yescharacteristic
454C2×C4#381111yescharacteristic
455C2×C4#381111yescharacteristic
456C8—61no—
457C8—61no—
458C8—121no—
459C8—181no—
460C8—181no—
461C8—182no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—41no—
470C2×C3—41no—
471C2×C3—44no—
472C2×C3—42no—
473C2×C3—42no—
474C2×C3#482311yescharacteristic
475C2×C3#482411yescharacteristic
476C2×C3#494611yescharacteristic
477C2×C3#495011yescharacteristic
478C2×C3#519611yescharacteristic
479C2×C3#519711yescharacteristic
480C22—21no—
481C22—21no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22#6396211yescharacteristic
486C22#67⋊Dic311yescharacteristic
487C22#6398211yescharacteristic
488C4—22no—
489C4—122no—
490C4—121no—
491C4—121no—
492C4C2×Dic3⋊Dic311yescharacteristic
493C4#67⋊Dic311yescharacteristic
494C4#6398111yescharacteristic
495C4#6398211yescharacteristic
496C3—21no—
497C3#7029211yescharacteristic, complemented
498C3#7037611yescharacteristic, complemented
499C2—21no—
500C2—21no—
501C2—42no—
502C2#1059167511yescharacteristic
503C2#1059167611yescharacteristic
504C2#1059171911yescharacteristic
subgroupG/H
centerC2×C4#3811
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. #10591117C2semidirect
6. #10589161C2semidirect
7. #10589155C2semidirect
22. C3×#835C4semidirect
23. C3×#835C4semidirect
24. C3×#832C4semidirect
25. C3×#832C4semidirect
112. #835Dic3semidirect
113. #835Dic3semidirect
114. #832Dic3semidirect
115. #832Dic3semidirect
433. C32#1866semidirect
497. C3#70292semidirect
498. C3#70376semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C2×C3×#8372
C3×#52332
C2×#635772
#105911172
#105891612
#105891552
#703763
#702923