Finite Group Databasebeta

← #11789900

Subgroups — #11789900

Order 1152.

625 conjugacy classes of subgroups.

The subgroup lattice has 525 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×#63562C211yesmaximal, characteristic
5C2×#63554C211yesmaximal, characteristic, complemented
6#10589395C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70188—31nomaximal
9#69617—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#63562C414yescomplemented
23#63554—22no—
24C2×C3×#102—31no—
25C3×#389—31no—
26#5221—31no—
27C2×#832—31no—
28C2×#815—31no—
29#4972D311yescharacteristic, complemented
30C2×#809—31no—
31C2×#809D311yescharacteristic
32#4939—31no—
33C2×#803—31no—
34#4551—31no—
35#4529—31no—
36#4529—31no—
37#4529—31no—
38#4529—61no—
39C23×C3×D3—21no—
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3—21no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3D411yescharacteristic
45C22×C3×Dic3D411yescharacteristic
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12C2×C412yes—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)C2×C412yes—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3C2×C412yes—
61C3×Dic3⋊C4—42no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8D412yes—
67(C2×D3)⋊Dic3—42no—
68(C2×D3)⋊Dic3—42no—
69#1936—91noSylow
70C22×C3×D4—31no—
71C22×D12C2×D311yescharacteristic
72C22×C3×C8—31no—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4—61no—
76C2×C3×C4⋊C4C2×D311yescharacteristic
77C2×C3×C4⋊C4C2×D311yescharacteristic
78C2×C3×C42—31no—
79C2×#217—61no—
80C2×#217—61no—
81C2×(C2×D3)⋊C4—61no—
82C2×(C2×D3)⋊C4—61no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—61no—
86C2×C4⋊Dic3C2×D311yescharacteristic
87C2×Dic3⋊C4—21no—
88C2×C4×Dic3C2×D311yescharacteristic
89C22×C3⋊C8—31no—
90C22×C3⋊C8—31no—
91C22×C3⋊C8—61no—
92C22×C3⋊C8C2×D311yescharacteristic
93C3×#102—62no—
94C3×#95—61no—
95#832—34no—
96C3⋊#95—21no—
97#815—62no—
98#809—22no—
99#809—34no—
100#803—62no—
101C23×C32C2×D411yescharacteristic
102C22×C3×D3—22no—
103C22×C3×D3—41no—
104C22×C3×D3—41no—
105C22×C3×D3—41no—
106C22×C3×D3—41no—
107C22×C3×D3—41no—
108C22×C3×D3—41no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C3⋊Dic3—41no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3—41no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C3×D12—22no—
131C3×D12—22no—
132C3×D12—41no—
133C3×D12—41no—
134C3⋊(C3⋊C8)—22no—
135C3×C3⋊C8—22no—
136C2×#102—31no—
137C2×#102—91no—
138C2×#97—91no—
139#390—91no—
140#389—31no—
141#340—91no—
142#340—91no—
143C24×C3—61no—
144C23×D3—21no—
145C2×C3×D4—32no—
146C2×C3×D4—61no—
147C2×C3×D4—61no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—41no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×Dic3—21no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—121no—
164C22×Dic3#6711yescharacteristic
165C22×Dic3#6711yescharacteristic
166C2×D12—21no—
167C2×D12—21no—
168C2×D12—21no—
169C2×D12—21no—
170C2×D12—21no—
171C2×D12C4×D312yes—
172C2×C3×C8—32no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—32no—
181C3×C4⋊C4—41no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—122no—
184C3×C42—61no—
185C3×C42—61no—
186#217—122no—
187#217—122no—
188(C2×D3)⋊C4—122no—
189(C2×D3)⋊C4—122no—
190C4⋊Dic3—21no—
191C4⋊Dic3—62no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—121no—
197C4⋊Dic3C4×D312yes—
198Dic3⋊C4—42no—
199C4×Dic3—21no—
200C4×Dic3—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—32no—
204C2×C3⋊C8—32no—
205C2×C3⋊C8—62no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—121no—
211C2×C3⋊C8—121no—
212C2×C3⋊C8#6712yes—
213C22×C32C4×D411yescharacteristic
214C22×C32#12111yescharacteristic
215C22×C32#12411yescharacteristic
216C22×C32AGL(1,ℤ/8)11yescharacteristic
217C22×C32AGL(1,ℤ/8)11yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C22×C32#13711yescharacteristic
220C2×C3×D3—42no—
221C2×C3×D3—42no—
222C2×C3×D3—42no—
223C2×C3×D3—81no—
224C2×C3×D3—81no—
225C2×C3×D3—81no—
226C2×C3×D3—81no—
227C32×C4—81no—
228C32×C4#11711yescharacteristic
229C32×C4C4×D411yescharacteristic
230C32×C4#12311yescharacteristic
231C32×C4#12611yescharacteristic
232C3⋊Dic3—81no—
233C3×Dic3—42no—
234C3×Dic3—41no—
235C3×Dic3—41no—
236C22×D4—31no—
237C22×C8—31no—
238C22×C8—91no—
239C2×C4⋊C4—31no—
240C2×C4⋊C4—61no—
241C2×C4⋊C4—91no—
242C2×C4⋊C4D3211yescharacteristic
243C2×C22⋊C4—181no—
244C2×C22⋊C4—181no—
245C2×C42—31no—
246#102—62no—
247#102—94no—
248#97—182no—
249#95—61no—
250C23×C3—21no—
251C23×C3—62no—
252C23×C3—121no—
253C23×C3—121no—
254C23×C3—121no—
255C23×C3—121no—
256C23×C3—121no—
257C23×C3—121no—
258C23×C3D3×D411yescharacteristic
259C23×C3C2×#6711yescharacteristic
260C22×D3—22no—
261C22×D3—41no—
262C22×D3—41no—
263C22×D3—41no—
264C22×D3—41no—
265C22×D3—41no—
266C22×D3—41no—
267C3×D4—62no—
268C3×D4—62no—
269C3×D4—121no—
270C3×D4—121no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—42no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—62no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—81no—
292C2×C3×C4—81no—
293C2×C3×C4—121no—
294C2×C3×C4—121no—
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4#23511yescharacteristic
298C2×C3×C4#23511yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4#23711yescharacteristic
302C2×C3×C4#23711yescharacteristic
303C2×C3×C4#23711yescharacteristic
304C2×C3×C4#23911yescharacteristic
305C2×C3×C4#23911yescharacteristic
306C2×C3×C4C2×#6711yescharacteristic
307C2×Dic3—22no—
308C2×Dic3—21no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—41no—
315C2×Dic3—41no—
316C2×Dic3—122no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—241no—
324C2×Dic3—241no—
325D12—22no—
326D12—22no—
327D12—41no—
328D12—41no—
329C3×C8—62no—
330C3⋊C8—22no—
331C3⋊C8—62no—
332C3⋊C8—62no—
333C3⋊C8—122no—
334C2×C32#38811yescharacteristic
335C2×C32#44011yescharacteristic
336C2×C32#44211yescharacteristic
337C2×C32#46811yescharacteristic
338C2×C32#46911yescharacteristic
339C2×C32#48911yescharacteristic
340C2×C32#49011yescharacteristic
341C3×D3—82no—
342C24—61no—
343C2×D4—32no—
344C2×D4—61no—
345C2×D4—61no—
346C2×D4—61no—
347C2×D4—61no—
348C2×D4—61no—
349C22×C4—21no—
350C22×C4—31no—
351C22×C4—31no—
352C22×C4—61no—
353C22×C4—181no—
354C22×C4C2×D3211yescharacteristic
355C2×C8—32no—
356C2×C8—61no—
357C2×C8—61no—
358C2×C8—92no—
359C2×C8—181no—
360C2×C8—181no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—32no—
364C4⋊C4—61no—
365C4⋊C4—122no—
366C4⋊C4—181no—
367C4⋊C4—181no—
368C22⋊C4—362no—
369C22⋊C4—362no—
370C42—61no—
371C42—61no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—122no—
380C22×C3—122no—
381C22×C3—122no—
382C22×C3—241no—
383C22×C3—241no—
384C22×C3—241no—
385C22×C3—241no—
386C22×C3#67⋊C411yescharacteristic
387C22×C3#88511yescharacteristic
388C22×C3#91111yescharacteristic
389C22×C3#91111yescharacteristic
390C22×C3#91411yescharacteristic
391C22×C3#91511yescharacteristic
392C22×C3C4×#6711yescharacteristic
393C22×C3#93211yescharacteristic
394C22×C3#93811yescharacteristic
395C22×C3#93911yescharacteristic
396C22×C3#94211yescharacteristic
397C22×C3#94711yescharacteristic
398C22×C3#94911yescharacteristic
399C22×C3#94911yescharacteristic
400C2×D3—42no—
401C2×D3—42no—
402C2×D3—42no—
403C2×D3—81no—
404C2×D3—81no—
405C2×D3—81no—
406C2×D3—81no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—82no—
412C3×C4—81no—
413C3×C4—81no—
414C3×C4—121no—
415C3×C4—121no—
416C3×C4—122no—
417C3×C4#87711yescharacteristic
418C3×C4#87911yescharacteristic
419C3×C4#89211yescharacteristic
420C3×C4#89311yescharacteristic
421C3×C4#89411yescharacteristic
422C3×C4#89811yescharacteristic
423C3×C4C4×#6711yescharacteristic
424C3×C4#93511yescharacteristic
425Dic3—42no—
426Dic3—41no—
427Dic3—41no—
428Dic3—242no—
429Dic3—241no—
430Dic3—241no—
431C32#193611yescharacteristic, complemented, Sylow
432C23—62no—
433C23—121no—
434C23—121no—
435C23—121no—
436C23—121no—
437C23—121no—
438C23—121no—
439C23D3×#6711yescharacteristic
440D4—62no—
441D4—62no—
442D4—121no—
443D4—121no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—62no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—361no—
457C2×C4—361no—
458C2×C4—361no—
459C2×C4#379511yescharacteristic
460C2×C4#379611yescharacteristic
461C2×C4#379911yescharacteristic
462C2×C4C4×D3211yescharacteristic
463C2×C4#380511yescharacteristic
464C2×C4D3×#6711yescharacteristic
465C8—62no—
466C8—182no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—242no—
475C2×C3#475711yescharacteristic
476C2×C3#476411yescharacteristic
477C2×C3#476511yescharacteristic
478C2×C3#478511yescharacteristic
479C2×C3#494411yescharacteristic
480C2×C3#499011yescharacteristic
481C2×C3#501411yescharacteristic
482C2×C3#502611yescharacteristic
483C2×C3#503911yescharacteristic
484C2×C3#504911yescharacteristic
485C2×C3#506711yescharacteristic
486C2×C3#508911yescharacteristic
487C2×C3#515911yescharacteristic
488C2×C3#517411yescharacteristic
489D3—82no—
490C22—122no—
491C22—122no—
492C22—122no—
493C22—241no—
494C22—241no—
495C22—241no—
496C22—241no—
497C22#6387911yescharacteristic
498C22#6390711yescharacteristic
499C22#6392511yescharacteristic
500C22#6393211yescharacteristic
501C22#6393911yescharacteristic
502C22#6394611yescharacteristic
503C22#6397011yescharacteristic
504C4—81no—
505C4—121no—
506C4—121no—
507C4—122no—
508C4—721no—
509C4#6386111yescharacteristic
510C4#6387811yescharacteristic
511C4#6388411yescharacteristic
512C4#6390411yescharacteristic
513C3—21no—
514C3#6961711yescharacteristic, complemented
515C3#7018811yescharacteristic, complemented
516C2—242no—
517C2#1059045411yescharacteristic
518C2#1059045511yescharacteristic
519C2#1059053111yescharacteristic
520C2#1059055011yescharacteristic
521C2#1059128511yescharacteristic
522C2#1059145111yescharacteristic
523C2#1059158711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1936
LCSG ▷ C2×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
5. C2×#63554C2semidirect
6. #10589395C2semidirect
7. #10589164C2semidirect
22. #63562C4semidirect
29. #4972D3semidirect
431. C32#1936semidirect
514. C3#69617semidirect
515. C3#70188semidirect

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×#635622
C2×#635542
#105893952
#105891642
#701883
#696173