Finite Group Databasebeta

← #11789901

Subgroups — #11789901

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#10592671C211yesmaximal, characteristic, complemented
2C2×C3×#809C211yesmaximal, characteristic
3#10591323C211yesmaximal, characteristic
4C2×#63563C211yesmaximal, characteristic
5C2×#63555C211yesmaximal, characteristic, complemented
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70188—31nomaximal
9#68856—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3750—21no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×(C2×D3)⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20#63658—21no—
21C3×#809—22no—
22#63563C414yescomplemented
23#63555—22no—
24C2×C3×#102—31no—
25#5221—31no—
26C2×#832—31no—
27C2×#821—31no—
28C2×#815—31no—
29C2×#815—31no—
30#4988—31no—
31#4972—31no—
32#4972—31no—
33#4972—61no—
34C2×#809D311yescharacteristic
35C3×#340—31no—
36#4551—31no—
37#4529—31no—
38#4529D311yescharacteristic, complemented
39C23×C3×D3—21no—
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3D411yescharacteristic
44C22×C3⋊Dic3D411yescharacteristic
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×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)C2×C412yes—
56#3750—42no—
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8C2×C412yes—
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—
73C22×C3×C8—31no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4C2×D311yescharacteristic
77C2×C3×C4⋊C4C2×D311yescharacteristic
78C2×#217—61no—
79C2×#217—61no—
80C2×(C2×D3)⋊C4—61no—
81C2×(C2×D3)⋊C4—61no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—61no—
85C2×C4⋊Dic3C2×D311yescharacteristic
86C2×Dic3⋊C4—61no—
87C2×Dic3⋊C4—61no—
88C2×Dic3⋊C4—62no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—61no—
92C22×C3⋊C8C2×D311yescharacteristic
93C22×C3⋊C8C2×D311yescharacteristic
94C3×#102—62no—
95#832—34no—
96C3⋊#95—61no—
97C3⋊#95—61no—
98C3⋊#95—62no—
99#821—34no—
100#815—62no—
101#815—62no—
102#809—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—41no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
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—31no—
139C2×#102—91no—
140C2×#97—91no—
141#390—91no—
142#389—91no—
143#340—31no—
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—22no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×Dic3—21no—
161C22×Dic3—31no—
162C22×Dic3—31no—
163C22×Dic3—31no—
164C22×Dic3—31no—
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—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—41no—
187C3×C4⋊C4—41no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190#217—122no—
191#217—122no—
192(C2×D3)⋊C4—122no—
193(C2×D3)⋊C4—122no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—32no—
197C4⋊Dic3—32no—
198C4⋊Dic3—62no—
199C4⋊Dic3—62no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202Dic3⋊C4—124no—
203Dic3⋊C4—122no—
204Dic3⋊C4—122no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C4×Dic3—121no—
210C4×Dic3—121no—
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—81no—
232C32×C4#11711yescharacteristic
233C32×C4C4×D411yescharacteristic
234C32×C4#12311yescharacteristic
235C32×C4#12611yescharacteristic
236C3⋊Dic3—42no—
237C3⋊Dic3—41no—
238C3⋊Dic3—41no—
239C3×Dic3—81no—
240C22×D4—31no—
241C22×C8—31no—
242C22×C8—31no—
243C2×C4⋊C4—31no—
244C2×C4⋊C4—91no—
245C2×C4⋊C4—181no—
246C2×C4⋊C4D3211yescharacteristic
247C2×C22⋊C4—181no—
248C2×C22⋊C4—181no—
249C2×C42—91no—
250#102—62no—
251#102—94no—
252#97—182no—
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×C3D3×D411yescharacteristic
263C23×C3D3×D411yescharacteristic
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—42no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4—121no—
293C2×C3×C4C2×C4×D311yescharacteristic
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4#23511yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23711yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4#23711yescharacteristic
302C2×C3×C4#23711yescharacteristic
303C2×C3×C4#23911yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—62no—
309C2×Dic3—64no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—61no—
313C2×Dic3—61no—
314C2×Dic3—62no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3—122no—
330C2×Dic3—122no—
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—21no—
359C22×C4—61no—
360C22×C4—91no—
361C22×C4—91no—
362C22×C4—181no—
363C22×C4C2×D3211yescharacteristic
364C2×C8—32no—
365C2×C8—32no—
366C2×C8—61no—
367C2×C8—61no—
368C2×C8—61no—
369C2×C8—61no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4—92no—
375C4⋊C4—181no—
376C4⋊C4—362no—
377C22⋊C4—362no—
378C22⋊C4—362no—
379C42—181no—
380C42—181no—
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×C3#67⋊C411yescharacteristic
396C22×C3#88411yescharacteristic
397C22×C3#88511yescharacteristic
398C22×C3#88511yescharacteristic
399C22×C3#89311yescharacteristic
400C22×C3#91111yescharacteristic
401C22×C3#91111yescharacteristic
402C22×C3#91111yescharacteristic
403C22×C3#91411yescharacteristic
404C22×C3#91411yescharacteristic
405C22×C3#91411yescharacteristic
406C22×C3#91511yescharacteristic
407C22×C3#91811yescharacteristic
408C22×C3#93811yescharacteristic
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—82no—
421C3×C4—81no—
422C3×C4—81no—
423C3×C4—241no—
424C3×C4#87211yescharacteristic
425C3×C4#87711yescharacteristic
426C3×C4#87911yescharacteristic
427C3×C4#67⋊C411yescharacteristic
428C3×C4#89411yescharacteristic
429C3×C4#89811yescharacteristic
430C3×C4C4×#6711yescharacteristic
431C3×C4#93511yescharacteristic
432Dic3—81no—
433Dic3—122no—
434Dic3—122no—
435Dic3—124no—
436Dic3—122no—
437Dic3—121no—
438Dic3—121no—
439Dic3—121no—
440Dic3—122no—
441Dic3—121no—
442C32#193611yescharacteristic, complemented, Sylow
443C23—62no—
444C23—121no—
445C23—121no—
446C23—121no—
447C23—121no—
448C23—121no—
449C23—121no—
450C23#381111yescharacteristic
451D4—62no—
452D4—62no—
453D4—121no—
454D4—121no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—182no—
462C2×C4—181no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—361no—
469C2×C4—361no—
470C2×C4#379511yescharacteristic
471C2×C4#379511yescharacteristic
472C2×C4#379611yescharacteristic
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#466911yescharacteristic
487C2×C3#475711yescharacteristic
488C2×C3#476411yescharacteristic
489C2×C3#476411yescharacteristic
490C2×C3#476511yescharacteristic
491C2×C3#478211yescharacteristic
492C2×C3#478511yescharacteristic
493C2×C3#479411yescharacteristic
494C2×C3#481211yescharacteristic
495C2×C3#486911yescharacteristic
496C2×C3#488911yescharacteristic
497C2×C3#494411yescharacteristic
498C2×C3#515911yescharacteristic
499C2×C3#517411yescharacteristic
500D3—82no—
501C22—122no—
502C22—122no—
503C22—122no—
504C22—241no—
505C22—241no—
506C22—241no—
507C22—241no—
508C22#6388111yescharacteristic
509C22#6391311yescharacteristic
510C22#6392711yescharacteristic
511C22#6393711yescharacteristic
512C22#6394111yescharacteristic
513C22#6395111yescharacteristic
514C22#6395811yescharacteristic
515C4—81no—
516C4—241no—
517C4—361no—
518C4—361no—
519C4—362no—
520C4#6385811yescharacteristic
521C4#6387711yescharacteristic
522C4#6387911yescharacteristic
523C4#6388411yescharacteristic
524C3—21no—
525C3#6885611yescharacteristic, complemented
526C3#7018811yescharacteristic, complemented
527C2—242no—
528C2#1059046111yescharacteristic
529C2#1059046211yescharacteristic
530C2#1059054111yescharacteristic
531C2#1059055411yescharacteristic
532C2#1059128111yescharacteristic
533C2#1059145411yescharacteristic
534C2#1059159011yescharacteristic
subgroupG/H
centerC23#3811
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. #10592671C2semidirect
5. C2×#63555C2semidirect
6. C3×#4529C2semidirect
7. #10589164C2semidirect
22. #63563C4semidirect
38. #4529D3semidirect
442. C32#1936semidirect
525. C3#68856semidirect
526. C3#70188semidirect

Maximal subgroups

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

subgroupindex
#105926712
C2×C3×#8092
#105913232
C2×#635632
C2×#635552
C3×#45292
#105891642
#701883
#688563