Finite Group Databasebeta

← #11787034

Subgroups — #11787034

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×#64116C211yesmaximal, characteristic
2C2×C3×#822C211yesmaximal, characteristic, complemented
3#10591117C211yesmaximal, characteristic, complemented
4C2×#63570C211yesmaximal, characteristic
5#10591105C211yesmaximal, characteristic
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70722—31nomaximal
9#68774—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13#64116—22no—
14#64116—22no—
15C2×#3743—21no—
16C2×C8×C3⋊D3—21no—
17C3×#926C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#822—22no—
22Dic3⋊(C3⋊C8)—21no—
23Dic3⋊(C3⋊C8)—21no—
24#63570—22no—
25#63567C411yescharacteristic, complemented
26#63567C411yescharacteristic, complemented
27#63564C411yescharacteristic, complemented
28#63564C411yescharacteristic, complemented
29C2×#907—31no—
30C2×#907—31no—
31C2×#907—61no—
32C2×C3×#108—31no—
33C2×#825—31no—
34C2×#822D311yescharacteristic, complemented
35#5119—31no—
36#5113—31no—
37#5002—31no—
38#4999—31no—
39C2×#805—31no—
40C3×#339—31no—
41#4555D311yescharacteristic, complemented
42#4550—31no—
43#4524—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46#3828—21no—
47#3828—21no—
48#3828D412yes—
49#3828Q812yes—
50C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634C2×C411yescharacteristic
53C22×C3×Dic3—21no—
54C32×M16—21no—
55C32×M16D412yes—
56C2×C32×C8—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)D411yescharacteristic
60C2×C3⋊(C3⋊C8)D411yescharacteristic
61#3743—24no—
62C8×C3⋊D3—24no—
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×#235—31no—
78C2×#235—31no—
79C2×#235—61no—
80C2×C3×M16—21no—
81C2×C3×M16—31no—
82C2×C3×M16C2×D311yescharacteristic
83C2×C3×M16C2×D311yescharacteristic
84C22×C3×C8—31no—
85C3×#117—31no—
86C2×C3×C42—31no—
87#926C2×D311yescharacteristic
88C2×C4×Dic3C2×D311yescharacteristic
89C2×#208C2×D311yescharacteristic
90C22×C3⋊C8—31no—
91C22×C3⋊C8—31no—
92C22×C3⋊C8—61no—
93C22×C3⋊C8C2×D311yescharacteristic
94#907—62no—
95#907—62no—
96#907—64no—
97#907—64no—
98#907—62no—
99#907—62no—
100C2×ΓL(1,𝔽25)—61no—
101C2×ΓL(1,𝔽25)—61no—
102C2×ΓL(1,𝔽25)—62no—
103C2×D3×C8—61no—
104C2×D3×C8—61no—
105C2×D3×C8—62no—
106C3×#108—62no—
107#825—62no—
108#822—22no—
109#821—31no—
110#821—31no—
111#816—31no—
112#816—31no—
113Dic3⋊C8—61no—
114Dic3⋊C8—61no—
115#810—31no—
116#810—31no—
117#809—31no—
118#809—31no—
119#805—62no—
120C4⋊(C3⋊C8)—61no—
121C4⋊(C3⋊C8)—61no—
122C23×C32#4111yescharacteristic
123C22×C3⋊D3—21no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×Q811yescharacteristic
129C2×C32×C4#4111yescharacteristic
130#638—22no—
131#638—22no—
132C2×C3⋊Dic3—21no—
133C4⋊(C3⋊D3)—21no—
134C4⋊(C3⋊D3)C4⋊C412yes—
135C4×C3⋊D3—22no—
136C4×C3⋊D3—22no—
137#634—21no—
138#634C4⋊C412yes—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C32×C8—22no—
145C3⋊(C3⋊C8)—21no—
146C3⋊(C3⋊C8)—21no—
147C3×C3⋊C8—21no—
148C3×C3⋊C8—21no—
149C3×C3⋊C8—41no—
150C2×#131—91no—
151C2×#108—31no—
152#424—91no—
153C2×#104—91no—
154#416—91no—
155#339—31no—
156#336—91no—
157C22×C3×C4—21no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—62no—
162C2×#67—61no—
163C2×#67—61no—
164C22×Dic3—21no—
165#235—32no—
166#235—32no—
167#235—32no—
168#235—32no—
169#235—62no—
170#235—62no—
171#235—62no—
172#235—62no—
173#235—61no—
174#235—61no—
175#235—61no—
176#235—61no—
177C2×D12—31no—
178C2×D12—31no—
179C2×D12—61no—
180C2×C4×D3—62no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×Dic6—31no—
184C2×Dic6—31no—
185C2×Dic6—61no—
186C3×M16—22no—
187C3×M16—21no—
188C3×M16—21no—
189C3×M16—22no—
190C3×M16—61no—
191C3×M16—61no—
192C3×M16D1212yes—
193C3×M16#6712yes—
194C2×C3×C8—22no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—31no—
198C2×C3×C8—31no—
199C2×C3×C8—61no—
200C2×C3×C8—61no—
201C2×C3×C8—61no—
202C3×C4⋊C4—31no—
203C3×C4⋊C4—31no—
204C3×C22⋊C4—61no—
205C3×C42—61no—
206C3×C42—61no—
207C3×C42—61no—
208#217—21no—
209C4⋊Dic3C4×D311yescharacteristic
210C4⋊Dic3C4×D311yescharacteristic
211C4×Dic3—21no—
212C4×Dic3—21no—
213C4×Dic3—21no—
214#208—21no—
215#208—21no—
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—62no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8C4×D311yescharacteristic
232C2×C3⋊C8C4×D311yescharacteristic
233ΓL(1,𝔽25)—68no—
234ΓL(1,𝔽25)—64no—
235ΓL(1,𝔽25)—64no—
236D3×C8—68no—
237D3×C8—64no—
238D3×C8—64no—
239C22×C32—21no—
240C22×C32—21no—
241C22×C32C4×D411yescharacteristic
242C22×C32C22⋊Q811yescharacteristic
243C22×C32#12311yescharacteristic
244C2×C3⋊D3—22no—
245C2×C3⋊D3—41no—
246C2×C3⋊D3—41no—
247C32×C4C2×C4⋊C411yescharacteristic
248C32×C4C4×D411yescharacteristic
249C32×C4#12011yescharacteristic
250C32×C4C22⋊Q811yescharacteristic
251C3⋊Dic3—22no—
252C3×Dic3—42no—
253C3×Dic3—41no—
254C3×Dic3—41no—
255C2×#41—91no—
256#131—182no—
257#131—182no—
258C2×M16—31no—
259C2×M16—181no—
260C2×M16D3211yescharacteristic
261C22×C8—31no—
262C22×C8—91no—
263C22×C8—181no—
264#117—31no—
265C2×C42—31no—
266#108—62no—
267C4⋊C8—181no—
268C4⋊C8—181no—
269#104—182no—
270#103—91no—
271#103—91no—
272#102—91no—
273#102—91no—
274C23×C3—21no—
275C23×C3#23711yescharacteristic
276C23×C3#23911yescharacteristic
277C22×D3—62no—
278C22×D3—61no—
279C22×D3—61no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—62no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4C2×D1211yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×Q811yescharacteristic
301C2×C3×C4D3×Q811yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303#67—64no—
304#67—64no—
305#67—62no—
306#67—62no—
307#67—62no—
308#67—62no—
309C2×Dic3—22no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—62no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317D12—32no—
318D12—32no—
319D12—62no—
320D12—62no—
321D12—61no—
322D12—61no—
323C4×D3—64no—
324C4×D3—64no—
325C4×D3—62no—
326C4×D3—62no—
327C4×D3—62no—
328C4×D3—62no—
329Dic6—32no—
330Dic6—32no—
331Dic6—62no—
332Dic6—62no—
333Dic6—61no—
334Dic6—61no—
335C3×C8—24no—
336C3×C8—22no—
337C3×C8—22no—
338C3×C8—61no—
339C3×C8—61no—
340C3×C8—121no—
341C3⋊C8—21no—
342C3⋊C8—21no—
343C3⋊C8—41no—
344C3⋊C8—62no—
345C3⋊C8—62no—
346C3⋊C8—61no—
347C3⋊C8—61no—
348C3⋊C8—61no—
349C3⋊C8—61no—
350C2×C32—21no—
351C2×C32—21no—
352C2×C32#38511yescharacteristic
353C2×C32#44311yescharacteristic
354C2×C32#44411yescharacteristic
355C3⋊D3—42no—
356#41—92no—
357#41—92no—
358#41—181no—
359#41—181no—
360C2×Q8—91no—
361C2×D4—91no—
362C2×D4—181no—
363C22×C4—61no—
364C22×C4—181no—
365C22×C4C2×D3211yescharacteristic
366M16—21no—
367M16—61no—
368M16—61no—
369M16—184no—
370M16#62612yes—
371C2×C8—21no—
372C2×C8—31no—
373C2×C8—31no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8—61no—
377C2×C8—91no—
378C2×C8—91no—
379C2×C8—184no—
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—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3#67⋊C411yescharacteristic
398C22×C3#88311yescharacteristic
399C22×C3#89311yescharacteristic
400C22×C3#89411yescharacteristic
401C22×C3#89711yescharacteristic
402C22×C3#94611yescharacteristic
403C2×D3—64no—
404C2×D3—62no—
405C2×D3—62no—
406C2×D3—122no—
407C2×D3—122no—
408C2×D3—121no—
409C2×D3—121no—
410C2×D3—121no—
411C2×D3—121no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—122no—
417C3×C4—121no—
418C3×C4—121no—
419C3×C4C4×D1211yescharacteristic
420C3×C4#88211yescharacteristic
421C3×C4D3×C4⋊C411yescharacteristic
422C3×C4D3×C4⋊C411yescharacteristic
423C3×C4#89611yescharacteristic
424C3×C4#89611yescharacteristic
425C3×C4C4×#6711yescharacteristic
426C3×C4#93711yescharacteristic
427Dic3—42no—
428Dic3—41no—
429Dic3—41no—
430Dic3—64no—
431Dic3—62no—
432Dic3—62no—
433C32#186611yescharacteristic, complemented, Sylow
434C23—181no—
435C23#379611yescharacteristic
436Q8—92no—
437Q8—181no—
438D4—92no—
439D4—182no—
440D4—182no—
441D4—181no—
442C2×C4—62no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—121no—
446C2×C4—121no—
447C2×C4—181no—
448C2×C4—182no—
449C2×C4—182no—
450C2×C4#379711yescharacteristic
451C2×C4#379811yescharacteristic
452C2×C4C4×D3211yescharacteristic
453C2×C4C2×#62611yescharacteristic
454C2×C4#381111yescharacteristic
455C2×C4#381111yescharacteristic
456C8—22no—
457C8—61no—
458C8—61no—
459C8—121no—
460C8—181no—
461C8—181no—
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#466811yescharacteristic
472C2×C3#482311yescharacteristic
473C2×C3#482411yescharacteristic
474C2×C3#489411yescharacteristic
475C2×C3#489511yescharacteristic
476C2×C3#498911yescharacteristic
477D3—124no—
478D3—122no—
479D3—122no—
480C22—21no—
481C22—21no—
482C22—182no—
483C22—361no—
484C22—361no—
485C22#6385311yescharacteristic
486C22#6387111yescharacteristic
487C22#6388111yescharacteristic
488C4—122no—
489C4—121no—
490C4—121no—
491C4—182no—
492C4#6386511yescharacteristic
493C4#6388311yescharacteristic
494C4C4×#62611yescharacteristic
495C4#6398111yescharacteristic
496C3—21no—
497C3#6877411yescharacteristic, complemented
498C3#7072211yescharacteristic, complemented
499C2—21no—
500C2—21no—
501C2—362no—
502C2#1059097711yescharacteristic
503C2#1059097811yescharacteristic
504C2#1059129011yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×#3828C22
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. #10591117C2semidirect
6. C3×#4555C2semidirect
7. #10589155C2semidirect
25. #63567C4semidirect
26. #63567C4semidirect
27. #63564C4semidirect
28. #63564C4semidirect
34. C2×#822D3semidirect
41. #4555D3semidirect
433. C32#1866semidirect
497. C3#68774semidirect
498. C3#70722semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
C2×C3×#8222
#105911172
C2×#635702
#105911052
C3×#45552
#105891552
#707223
#687743