Finite Group Databasebeta

← #11789914

Subgroups — #11789914

Order 1152.

653 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592627C211yesmaximal, characteristic, complemented
2C3×#4939C211yesmaximal, characteristic
3C2×C3×#803C211yesmaximal, characteristic, complemented
4C2×#63563C211yesmaximal, characteristic
5C2×#63563C211yesmaximal, characteristic
6#10589164C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#69818—31nomaximal
9#69645—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750—21no—
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20#63658—21no—
21C3×#803—22no—
22#63563—22no—
23#63563C414yescomplemented
24C2×C3×#97—31no—
25C3×#390—31no—
26C2×#832—31no—
27C2×#832—31no—
28C2×#821—31no—
29C2×#821—31no—
30#4939D311yescharacteristic
31#4928—31no—
32#4928—31no—
33#4928—61no—
34C2×#803D311yescharacteristic, complemented
35#4551—31no—
36#4551—31no—
37#4529—31no—
38#4529—31no—
39C23×C3×D3—21no—
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3—21no—
45C22×C3×Dic3—21no—
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×C42—21no—
53C32×C42—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)C2×C412yes—
58#3750—42no—
59C3×(C2×D3)⋊C4—42no—
60C3×(C2×D3)⋊C4—42no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8C2×C412yes—
68C2×C3×C3⋊C8D412yes—
69#1936—91noSylow
70C22×C3×D4—31no—
71C22×D12C2×D311yescharacteristic
72C22×C3×C8—31no—
73C22×C3×C8—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C22⋊C4—61no—
76C2×C3×C22⋊C4—61no—
77C2×C3×C42—21no—
78C2×C3×C42C2×D311yescharacteristic
79C2×C3×C42C2×D311yescharacteristic
80C2×(C2×D3)⋊C4—21no—
81C2×(C2×D3)⋊C4—21no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—61no—
87C2×C4⋊Dic3—61no—
88C2×C4⋊Dic3C2×D311yescharacteristic
89C2×Dic3⋊C4—62no—
90C2×Dic3⋊C4—61no—
91C2×Dic3⋊C4—61no—
92C22×C3⋊C8C2×D311yescharacteristic
93C22×C3⋊C8C2×D311yescharacteristic
94C3×#97—62no—
95#832—34no—
96#832—62no—
97C3⋊#95—62no—
98C3⋊#95—61no—
99C3⋊#95—61no—
100#821—34no—
101#821—62no—
102#803—22no—
103C23×C32C2×D411yescharacteristic
104C22×C3×D3—22no—
105C22×C3×D3—41no—
106C22×C3×D3—41no—
107C22×C3×D3—41no—
108C22×C3×D3—41no—
109C22×C3×D3—41no—
110C22×C3×D3—41no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C3×D12—22no—
133C3×D12—22no—
134C3×D12—41no—
135C3×D12—41no—
136C3×C3⋊C8—22no—
137C3×C3⋊C8—22no—
138C2×#102—91no—
139C2×#102—91no—
140C2×#97—31no—
141#390—31no—
142#389—91no—
143#340—91no—
144#340—91no—
145C24×C3—61no—
146C23×D3—21no—
147C2×C3×D4—32no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—61no—
157C22×C3×C4D1211yescharacteristic
158C22×C3×C4D1211yescharacteristic
159C22×C3×C4#6711yescharacteristic
160C22×C3×C4#6711yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—21no—
164C22×Dic3—62no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—62no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12C4×D312yes—
176C2×C3×C8—32no—
177C2×C3×C8—32no—
178C2×C3×C8—61no—
179C2×C3×C8—61no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C22⋊C4—122no—
185C3×C22⋊C4—122no—
186C3×C42—21no—
187C3×C42—21no—
188C3×C42—21no—
189C3×C42—21no—
190C3×C42—41no—
191C3×C42—41no—
192(C2×D3)⋊C4—42no—
193(C2×D3)⋊C4—42no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—32no—
197C4⋊Dic3—32no—
198C4⋊Dic3—62no—
199C4⋊Dic3—62no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4⋊Dic3—121no—
207C4⋊Dic3—121no—
208Dic3⋊C4—124no—
209Dic3⋊C4—122no—
210Dic3⋊C4—122no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8C4×D312yes—
216C2×C3⋊C8#6712yes—
217C22×C32C4×D411yescharacteristic
218C22×C32#12111yescharacteristic
219C22×C32#12411yescharacteristic
220C22×C32AGL(1,ℤ/8)11yescharacteristic
221C22×C32AGL(1,ℤ/8)11yescharacteristic
222C22×C32AGL(1,ℤ/8)11yescharacteristic
223C22×C32#13711yescharacteristic
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227C2×C3×D3—81no—
228C2×C3×D3—81no—
229C2×C3×D3—81no—
230C2×C3×D3—81no—
231C32×C4—41no—
232C32×C4—41no—
233C32×C4#11711yescharacteristic
234C32×C4C4×D411yescharacteristic
235C32×C4#12311yescharacteristic
236C32×C4#12611yescharacteristic
237C3⋊Dic3—42no—
238C3⋊Dic3—81no—
239C3×Dic3—81no—
240C22×D4—31no—
241C22×C8—31no—
242C22×C8—31no—
243C2×C4⋊C4—31no—
244C2×C4⋊C4—91no—
245C2×C4⋊C4—91no—
246C2×C4⋊C4—181no—
247C2×C22⋊C4—61no—
248C2×C22⋊C4—61no—
249C2×C42D3211yescharacteristic
250#102—94no—
251#102—182no—
252#97—62no—
253#95—181no—
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×C3C2×D1211yescharacteristic
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—22no—
276C2×C3×C4—22no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
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—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4C2×C4×D311yescharacteristic
303C2×C3×C4C2×C4×D311yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4#23511yescharacteristic
307C2×C3×C4#23511yescharacteristic
308C2×C3×C4#23511yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4#23711yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4#23711yescharacteristic
313C2×C3×C4C2×#6711yescharacteristic
314C2×Dic3—41no—
315C2×Dic3—41no—
316C2×Dic3—41no—
317C2×Dic3—64no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—122no—
327C2×Dic3—122no—
328C2×Dic3—122no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335D12—22no—
336D12—22no—
337D12—41no—
338D12—41no—
339C3×C8—62no—
340C3×C8—62no—
341C3⋊C8—22no—
342C3⋊C8—22no—
343C2×C32#38811yescharacteristic
344C2×C32#44011yescharacteristic
345C2×C32#44211yescharacteristic
346C2×C32#46811yescharacteristic
347C2×C32#46911yescharacteristic
348C2×C32#48911yescharacteristic
349C2×C32#49011yescharacteristic
350C3×D3—82no—
351C24—61no—
352C2×D4—32no—
353C2×D4—61no—
354C2×D4—61no—
355C2×D4—61no—
356C2×D4—61no—
357C2×D4—61no—
358C22×C4—61no—
359C22×C4—181no—
360C22×C4—181no—
361C22×C4#62611yescharacteristic
362C22×C4#62611yescharacteristic
363C22×C4C2×D3211yescharacteristic
364C2×C8—32no—
365C2×C8—32no—
366C2×C8—61no—
367C2×C8—61no—
368C2×C8—61no—
369C2×C8—61no—
370C4⋊C4—61no—
371C4⋊C4—61no—
372C4⋊C4—92no—
373C4⋊C4—181no—
374C4⋊C4—181no—
375C4⋊C4—181no—
376C4⋊C4—362no—
377C22⋊C4—122no—
378C22⋊C4—122no—
379C42—21no—
380C42—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—122no—
389C22×C3—122no—
390C22×C3—122no—
391C22×C3—241no—
392C22×C3—241no—
393C22×C3—241no—
394C22×C3—241no—
395C22×C3C4×D1211yescharacteristic
396C22×C3#87511yescharacteristic
397C22×C3#90811yescharacteristic
398C22×C3#90811yescharacteristic
399C22×C3#90811yescharacteristic
400C22×C3#90911yescharacteristic
401C22×C3C4×#6711yescharacteristic
402C22×C3#93011yescharacteristic
403C22×C3#93211yescharacteristic
404C22×C3#93211yescharacteristic
405C22×C3#93611yescharacteristic
406C22×C3#93911yescharacteristic
407C22×C3#94911yescharacteristic
408C22×C3#95111yescharacteristic
409C2×D3—42no—
410C2×D3—42no—
411C2×D3—42no—
412C2×D3—81no—
413C2×D3—81no—
414C2×D3—81no—
415C2×D3—81no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—42no—
421C3×C4—42no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—41no—
426C3×C4—241no—
427C3×C4#87211yescharacteristic
428C3×C4#87611yescharacteristic
429C3×C4#87711yescharacteristic
430C3×C4#87911yescharacteristic
431C3×C4#67⋊C411yescharacteristic
432C3×C4#88311yescharacteristic
433C3×C4C4×#6711yescharacteristic
434C3×C4#92911yescharacteristic
435Dic3—81no—
436Dic3—124no—
437Dic3—122no—
438Dic3—122no—
439Dic3—242no—
440Dic3—241no—
441Dic3—241no—
442C32#193611yescharacteristic, complemented, Sylow
443C23—62no—
444C23—121no—
445C23—121no—
446C23—121no—
447C23—121no—
448C23—121no—
449C23—121no—
450C23C2×#62611yescharacteristic
451D4—62no—
452D4—62no—
453D4—121no—
454D4—121no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—121no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—182no—
465C2×C4—361no—
466C2×C4—361no—
467C2×C4—361no—
468C2×C4—361no—
469C2×C4—361no—
470C2×C4#379511yescharacteristic
471C2×C4#379511yescharacteristic
472C2×C4#379811yescharacteristic
473C2×C4C4×D3211yescharacteristic
474C2×C4#380411yescharacteristic
475C2×C4D3×#6711yescharacteristic
476C8—62no—
477C8—62no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—242no—
486C2×C3#471011yescharacteristic
487C2×C3#471111yescharacteristic
488C2×C3#471311yescharacteristic
489C2×C3#471411yescharacteristic
490C2×C3#494011yescharacteristic
491C2×C3#494511yescharacteristic
492C2×C3#501411yescharacteristic
493C2×C3#501811yescharacteristic
494C2×C3#503911yescharacteristic
495C2×C3#504211yescharacteristic
496C2×C3#505511yescharacteristic
497C2×C3#507111yescharacteristic
498C2×C3#513411yescharacteristic
499C2×C3#513511yescharacteristic
500D3—82no—
501C22—122no—
502C22—122no—
503C22—122no—
504C22—241no—
505C22—241no—
506C22—241no—
507C22—241no—
508C22#6382511yescharacteristic
509C22#6383011yescharacteristic
510C22#6383011yescharacteristic
511C22#6383111yescharacteristic
512C22#6386011yescharacteristic
513C22C4×#62611yescharacteristic
514C22#6397811yescharacteristic
515C4—41no—
516C4—41no—
517C4—241no—
518C4—362no—
519C4—721no—
520C4#6385911yescharacteristic
521C4#6387711yescharacteristic
522C4#6387911yescharacteristic
523C4#6390511yescharacteristic
524C3—21no—
525C3#6964511yescharacteristic, complemented
526C3#6981811yescharacteristic, complemented
527C2—242no—
528C2#1059027511yescharacteristic
529C2#1059027611yescharacteristic
530C2#1059034611yescharacteristic
531C2#1059036011yescharacteristic
532C2#1059116511yescharacteristic
533C2#1059117611yescharacteristic
534C2#1059128011yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1936
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10592627C2semidirect
3. C2×C3×#803C2semidirect
6. #10589164C2semidirect
7. #10589164C2semidirect
23. #63563C4semidirect
34. C2×#803D3semidirect
442. C32#1936semidirect
525. C3#69645semidirect
526. C3#69818semidirect

Maximal subgroups

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

subgroupindex
#105926272
C3×#49392
C2×C3×#8032
C2×#635632
#105891642
#698183
#696453