Finite Group Databasebeta

← #11794546

Subgroups — #11794546

Order 1152.

625 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4972C211yesmaximal, characteristic, complemented
2C2×C3×#809C211yesmaximal, characteristic
3#10591318C211yesmaximal, characteristic
4C2×#63575C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7#10589395C211yesmaximal, characteristic, complemented
8#70180—31nomaximal
9#69630—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×Dic3⋊C4—21no—
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×(C2×D3)⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20C3×C3⋊#95—21no—
21C3×#809—22no—
22#63575—22no—
23Dic3⋊(C3⋊C8)—22no—
24#63562—22no—
25C2×C3×#102—31no—
26C3×#389—31no—
27#5221—31no—
28C2×#832—31no—
29C2×#818—31no—
30C2×Dic3⋊C8—31no—
31#4972D311yescharacteristic, complemented
32C2×#809—31no—
33C2×#809D311yescharacteristic
34C2×#807—31no—
35#4939—31no—
36C2×C4⋊(C3⋊C8)—31no—
37#4529—31no—
38#4529—31no—
39#4529—61no—
40C23×C3×D3—21no—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3D411yescharacteristic
46C22×C3×Dic3D411yescharacteristic
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12Q812yes—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D412yes—
62C3×Dic3⋊C4—42no—
63C3×C4×Dic3—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8D412yes—
68(C2×D3)⋊Dic3—42no—
69(C2×D3)⋊Dic3—42no—
70#2067—91noSylow
71C22×C3×D4—31no—
72C22×D12C2×D311yescharacteristic
73C22×C3×C8—31no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—61no—
77C2×C3×C4⋊C4C2×D311yescharacteristic
78C2×C3×C4⋊C4C2×D311yescharacteristic
79C2×C3×C42—31no—
80C2×#217—61no—
81C2×#217—61no—
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—61no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—61no—
87C2×C4⋊Dic3C2×D311yescharacteristic
88C2×Dic3⋊C4—21no—
89C2×C4×Dic3C2×D311yescharacteristic
90C22×C3⋊C8—31no—
91C22×C3⋊C8—31no—
92C22×C3⋊C8—61no—
93C22×C3⋊C8C2×D311yescharacteristic
94C3×#102—62no—
95C3×#95—61no—
96#832—62no—
97C3⋊#95—21no—
98#818—62no—
99Dic3⋊C8—62no—
100#809—22no—
101#809—62no—
102#807—62no—
103C4⋊(C3⋊C8)—62no—
104C23×C32C2×D411yescharacteristic
105C22×C3×D3—22no—
106C22×C3×D3—41no—
107C22×C3×D3—41no—
108C22×C3×D3—41no—
109C22×C3×D3—41no—
110C22×C3×D3—41no—
111C22×C3×D3—41no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×Q811yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3D812yes—
133C3×D12—22no—
134C3×D12—22no—
135C3×D12—41no—
136C3×D12—41no—
137C3⋊(C3⋊C8)—41no—
138C3×C3⋊C8—22no—
139C2×#107—91no—
140C2×C4⋊C8—91no—
141C2×#102—31no—
142C2×#102—91no—
143#390—91no—
144#389—31no—
145#340—91no—
146C24×C3—61no—
147C23×D3—21no—
148C2×C3×D4—32no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—41no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—21no—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3—121no—
167C22×Dic3#6711yescharacteristic
168C22×Dic3#6711yescharacteristic
169C2×D12—21no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—21no—
174C2×D12Dic612yes—
175C2×C3×C8—32no—
176C2×C3×C8—61no—
177C2×C3×C8—61no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—32no—
184C3×C4⋊C4—41no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—122no—
187C3×C42—61no—
188C3×C42—61no—
189#217—122no—
190#217—122no—
191(C2×D3)⋊C4—122no—
192(C2×D3)⋊C4—122no—
193C4⋊Dic3—21no—
194C4⋊Dic3—62no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3—61no—
198C4⋊Dic3—61no—
199C4⋊Dic3—121no—
200C4⋊Dic3D1212yes—
201Dic3⋊C4—42no—
202C4×Dic3—21no—
203C4×Dic3—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—62no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—121no—
214C2×C3⋊C8—121no—
215C2×C3⋊C8#6712yes—
216C22×C32#12111yescharacteristic
217C22×C32#12111yescharacteristic
218C22×C32C22⋊Q811yescharacteristic
219C22×C32C2×D811yescharacteristic
220C22×C32#13511yescharacteristic
221C22×C32AGL(1,ℤ/8)11yescharacteristic
222C22×C32#13711yescharacteristic
223C2×C3×D3—42no—
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226C2×C3×D3—81no—
227C2×C3×D3—81no—
228C2×C3×D3—81no—
229C2×C3×D3—81no—
230C32×C4—81no—
231C32×C4#12111yescharacteristic
232C32×C4C22⋊Q811yescharacteristic
233C32×C4C22⋊Q811yescharacteristic
234C32×C4#12611yescharacteristic
235C3⋊Dic3—81no—
236C3×Dic3—22no—
237C3×Dic3—42no—
238C3×Dic3—41no—
239C22×D4—31no—
240C22×C8—31no—
241C22×C8—91no—
242C2×C4⋊C4—31no—
243C2×C4⋊C4—61no—
244C2×C4⋊C4—91no—
245C2×C4⋊C4D3211yescharacteristic
246C2×C22⋊C4—181no—
247C2×C22⋊C4—181no—
248C2×C42—31no—
249#107—182no—
250C4⋊C8—182no—
251#102—62no—
252#102—182no—
253#95—61no—
254C23×C3—21no—
255C23×C3—62no—
256C23×C3—121no—
257C23×C3—121no—
258C23×C3—121no—
259C23×C3—121no—
260C23×C3—121no—
261C23×C3—121no—
262C23×C3D3×D411yescharacteristic
263C23×C3C2×#6711yescharacteristic
264C22×D3—22no—
265C22×D3—41no—
266C22×D3—41no—
267C22×D3—41no—
268C22×D3—41no—
269C22×D3—41no—
270C22×D3—41no—
271C3×D4—62no—
272C3×D4—62no—
273C3×D4—121no—
274C3×D4—121no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—32no—
282C2×C3×C4—42no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—62no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—81no—
296C2×C3×C4—81no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4C2×Dic611yescharacteristic
300C2×C3×C4C2×D1211yescharacteristic
301C2×C3×C4#23511yescharacteristic
302C2×C3×C4#23511yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4#23711yescharacteristic
307C2×C3×C4#23711yescharacteristic
308C2×C3×C4D3×Q811yescharacteristic
309C2×C3×C4#23911yescharacteristic
310C2×C3×C4C2×#6711yescharacteristic
311C2×Dic3—21no—
312C2×Dic3—21no—
313C2×Dic3—22no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—122no—
320C2×Dic3—121no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—241no—
327C2×Dic3—241no—
328C2×Dic3#21312yes—
329D12—22no—
330D12—22no—
331D12—41no—
332D12—41no—
333C3×C8—62no—
334C3⋊C8—22no—
335C3⋊C8—122no—
336C3⋊C8—121no—
337C3⋊C8—121no—
338C2×C32#39611yescharacteristic
339C2×C32#45911yescharacteristic
340C2×C32#46411yescharacteristic
341C2×C32#46611yescharacteristic
342C2×C32#46811yescharacteristic
343C2×C32#47411yescharacteristic
344C2×C32#47811yescharacteristic
345C3×D3—82no—
346C24—61no—
347C2×D4—32no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C2×D4—61no—
353C22×C4—21no—
354C22×C4—31no—
355C22×C4—31no—
356C22×C4—61no—
357C22×C4—181no—
358C22×C4C2×D3211yescharacteristic
359C2×C8—32no—
360C2×C8—61no—
361C2×C8—61no—
362C2×C8—181no—
363C2×C8—181no—
364C2×C8—181no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—32no—
368C4⋊C4—61no—
369C4⋊C4—122no—
370C4⋊C4—181no—
371C4⋊C4—181no—
372C22⋊C4—362no—
373C22⋊C4—362no—
374C42—61no—
375C42—61no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—122no—
384C22×C3—122no—
385C22×C3—122no—
386C22×C3—241no—
387C22×C3—241no—
388C22×C3—241no—
389C22×C3—241no—
390C22×C3#87811yescharacteristic
391C22×C3#88411yescharacteristic
392C22×C3D3×D811yescharacteristic
393C22×C3#91211yescharacteristic
394C22×C3#91411yescharacteristic
395C22×C3#91511yescharacteristic
396C22×C3#93011yescharacteristic
397C22×C3C2×#21311yescharacteristic
398C22×C3#93811yescharacteristic
399C22×C3#93911yescharacteristic
400C22×C3#94211yescharacteristic
401C22×C3#94611yescharacteristic
402C22×C3#94911yescharacteristic
403C22×C3#95011yescharacteristic
404C2×D3—42no—
405C2×D3—42no—
406C2×D3—42no—
407C2×D3—81no—
408C2×D3—81no—
409C2×D3—81no—
410C2×D3—81no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—62no—
416C3×C4—82no—
417C3×C4—81no—
418C3×C4—81no—
419C3×C4—121no—
420C3×C4—122no—
421C3×C4#87811yescharacteristic
422C3×C4#87911yescharacteristic
423C3×C4#89511yescharacteristic
424C3×C4#89611yescharacteristic
425C3×C4#89711yescharacteristic
426C3×C4#89811yescharacteristic
427C3×C4#92411yescharacteristic
428C3×C4#93911yescharacteristic
429Dic3—22no—
430Dic3—42no—
431Dic3—41no—
432Dic3—242no—
433Dic3—241no—
434Dic3—241no—
435C32#206711yescharacteristic, complemented, Sylow
436C23—62no—
437C23—121no—
438C23—121no—
439C23—121no—
440C23—121no—
441C23—121no—
442C23—121no—
443C23D3×#6711yescharacteristic
444D4—62no—
445D4—62no—
446D4—121no—
447D4—121no—
448C2×C4—32no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—62no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—361no—
461C2×C4—361no—
462C2×C4—361no—
463C2×C4D3×Dic611yescharacteristic
464C2×C4#379611yescharacteristic
465C2×C4#379811yescharacteristic
466C2×C4D3×D1211yescharacteristic
467C2×C4#380511yescharacteristic
468C2×C4D3×#6711yescharacteristic
469C8—62no—
470C8—361no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—242no—
479C2×C3#475911yescharacteristic
480C2×C3#476611yescharacteristic
481C2×C3#476711yescharacteristic
482C2×C3#478611yescharacteristic
483C2×C3#494811yescharacteristic
484C2×C3#499411yescharacteristic
485C2×C3#501511yescharacteristic
486C2×C3#502811yescharacteristic
487C2×C3#503811yescharacteristic
488C2×C3#504911yescharacteristic
489C2×C3#506611yescharacteristic
490C2×C3#508711yescharacteristic
491C2×C3#515711yescharacteristic
492C2×C3#517411yescharacteristic
493D3—82no—
494C22—122no—
495C22—122no—
496C22—122no—
497C22—241no—
498C22—241no—
499C22—241no—
500C22—241no—
501C22#6388711yescharacteristic
502C22#6390611yescharacteristic
503C22D3×#21311yescharacteristic
504C22#6393311yescharacteristic
505C22#6393911yescharacteristic
506C22#6394611yescharacteristic
507C22#6397011yescharacteristic
508C4—62no—
509C4—81no—
510C4—122no—
511C4—121no—
512C4—721no—
513C4#6385111yescharacteristic
514C4#6386211yescharacteristic
515C4#6388611yescharacteristic
516C4#6389311yescharacteristic
517C3—21no—
518C3#6963011yescharacteristic, complemented
519C3#7018011yescharacteristic, complemented
520C2—242no—
521C2#1059046311yescharacteristic
522C2#1059046911yescharacteristic
523C2#1059053211yescharacteristic
524C2#1059054711yescharacteristic
525C2#1059130611yescharacteristic
526C2#1059149811yescharacteristic
527C2#1059158711yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2067
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#4972C2semidirect
4. C2×#63575C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
7. #10589395C2semidirect
31. #4972D3semidirect
435. C32#2067semidirect
518. C3#69630semidirect
519. C3#70180semidirect

Maximal subgroups

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

subgroupindex
C3×#49722
C2×C3×#8092
#105913182
C2×#635752
C2×Dic3⋊(C3⋊C8)2
C2×#635622
#105893952
#701803
#696303