Finite Group Databasebeta

← #11794544

Subgroups — #11794544

Order 1152.

653 conjugacy classes of subgroups.

The subgroup lattice has 540 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×#63575C211yesmaximal, characteristic, complemented
5C2×#63572C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7C3×#4529C211yesmaximal, characteristic, complemented
8#70180—31nomaximal
9#68901—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#63575—22no—
23#63572—22no—
24#63563—22no—
25C2×C3×#102—31no—
26#5221—31no—
27C2×#832—31no—
28C2×#821—31no—
29C2×#818—31no—
30C2×Dic3⋊C8—31no—
31C2×Dic3⋊C8—31no—
32#4988—31no—
33#4972—31no—
34#4972—31no—
35#4972—61no—
36C2×#809D311yescharacteristic
37C2×#807—31no—
38C3×#340—31no—
39#4529D311yescharacteristic, complemented
40C23×C3×D3—21no—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3D411yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3×Dic3—21no—
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)D412yes—
57#3750—42no—
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—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—
74C22×C3×C8—31no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4—31no—
77C2×C3×C4⋊C4C2×D311yescharacteristic
78C2×C3×C4⋊C4C2×D311yescharacteristic
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—61no—
88C2×Dic3⋊C4—61no—
89C2×Dic3⋊C4—62no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—31no—
92C2×C4×Dic3—61no—
93C22×C3⋊C8C2×D311yescharacteristic
94C22×C3⋊C8C2×D311yescharacteristic
95C3×#102—62no—
96#832—62no—
97C3⋊#95—61no—
98C3⋊#95—61no—
99C3⋊#95—62no—
100#821—62no—
101#818—62no—
102Dic3⋊C8—62no—
103Dic3⋊C8—62no—
104#809—22no—
105#807—62no—
106C23×C32C2×D411yescharacteristic
107C22×C3×D3—22no—
108C22×C3×D3—41no—
109C22×C3×D3—41no—
110C22×C3×D3—41no—
111C22×C3×D3—41no—
112C22×C3×D3—41no—
113C22×C3×D3—41no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×Q811yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3D812yes—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C3×D12—22no—
136C3×D12—22no—
137C3×D12—41no—
138C3×D12—41no—
139C3×C3⋊C8—22no—
140C3×C3⋊C8—41no—
141C2×#107—91no—
142C2×C4⋊C8—91no—
143C2×#102—31no—
144C2×#102—91no—
145#390—91no—
146#389—91no—
147#340—31no—
148C24×C3—61no—
149C23×D3—21no—
150C2×C3×D4—32no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C2×C3×D4—61no—
155C2×C3×D4—61no—
156C22×C3×C4—22no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—21no—
164C22×Dic3—31no—
165C22×Dic3—31no—
166C22×Dic3—31no—
167C22×Dic3—31no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—62no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12—21no—
176C2×D12—21no—
177C2×D12—21no—
178C2×D12Dic612yes—
179C2×C3×C8—32no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C2×C3×C8—61no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—41no—
190C3×C4⋊C4—41no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—61no—
193#217—122no—
194#217—122no—
195(C2×D3)⋊C4—122no—
196(C2×D3)⋊C4—122no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—32no—
200C4⋊Dic3—32no—
201C4⋊Dic3—62no—
202C4⋊Dic3—62no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205Dic3⋊C4—122no—
206Dic3⋊C4—122no—
207Dic3⋊C4—124no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—121no—
213C4×Dic3—121no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8#6712yes—
220C22×C32#12111yescharacteristic
221C22×C32#12111yescharacteristic
222C22×C32C22⋊Q811yescharacteristic
223C22×C32C2×D811yescharacteristic
224C22×C32#13511yescharacteristic
225C22×C32AGL(1,ℤ/8)11yescharacteristic
226C22×C32#13711yescharacteristic
227C2×C3×D3—42no—
228C2×C3×D3—42no—
229C2×C3×D3—42no—
230C2×C3×D3—81no—
231C2×C3×D3—81no—
232C2×C3×D3—81no—
233C2×C3×D3—81no—
234C32×C4—81no—
235C32×C4#12111yescharacteristic
236C32×C4C22⋊Q811yescharacteristic
237C32×C4C22⋊Q811yescharacteristic
238C32×C4#12611yescharacteristic
239C3⋊Dic3—22no—
240C3⋊Dic3—42no—
241C3⋊Dic3—41no—
242C3×Dic3—81no—
243C22×D4—31no—
244C22×C8—31no—
245C22×C8—31no—
246C2×C4⋊C4—31no—
247C2×C4⋊C4—91no—
248C2×C4⋊C4—181no—
249C2×C4⋊C4D3211yescharacteristic
250C2×C22⋊C4—181no—
251C2×C22⋊C4—181no—
252C2×C42—91no—
253#107—182no—
254C4⋊C8—182no—
255#102—62no—
256#102—182no—
257#95—181no—
258C23×C3—21no—
259C23×C3—62no—
260C23×C3—121no—
261C23×C3—121no—
262C23×C3—121no—
263C23×C3—121no—
264C23×C3—121no—
265C23×C3—121no—
266C23×C3D3×D411yescharacteristic
267C23×C3D3×D411yescharacteristic
268C22×D3—22no—
269C22×D3—41no—
270C22×D3—41no—
271C22×D3—41no—
272C22×D3—41no—
273C22×D3—41no—
274C22×D3—41no—
275C3×D4—62no—
276C3×D4—62no—
277C3×D4—121no—
278C3×D4—121no—
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—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4C2×Dic611yescharacteristic
298C2×C3×C4#23511yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4#23511yescharacteristic
301C2×C3×C4#23511yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4#23711yescharacteristic
307C2×C3×C4D3×Q811yescharacteristic
308C2×C3×C4C2×#6711yescharacteristic
309C2×Dic3—32no—
310C2×Dic3—32no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—62no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—64no—
320C2×Dic3—62no—
321C2×Dic3—61no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—61no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—122no—
334C2×Dic3—122no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339D12—22no—
340D12—22no—
341D12—41no—
342D12—41no—
343C3×C8—62no—
344C3×C8—121no—
345C3⋊C8—22no—
346C3⋊C8—41no—
347C2×C32#39611yescharacteristic
348C2×C32#45911yescharacteristic
349C2×C32#46411yescharacteristic
350C2×C32#46611yescharacteristic
351C2×C32#46811yescharacteristic
352C2×C32#47411yescharacteristic
353C2×C32#47811yescharacteristic
354C3×D3—82no—
355C24—61no—
356C2×D4—32no—
357C2×D4—61no—
358C2×D4—61no—
359C2×D4—61no—
360C2×D4—61no—
361C2×D4—61no—
362C22×C4—21no—
363C22×C4—61no—
364C22×C4—91no—
365C22×C4—91no—
366C22×C4—181no—
367C22×C4C2×D3211yescharacteristic
368C2×C8—32no—
369C2×C8—61no—
370C2×C8—61no—
371C2×C8—61no—
372C2×C8—61no—
373C2×C8—61no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4—92no—
379C4⋊C4—181no—
380C4⋊C4—362no—
381C22⋊C4—362no—
382C22⋊C4—362no—
383C42—181no—
384C42—181no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—122no—
393C22×C3—122no—
394C22×C3—122no—
395C22×C3—241no—
396C22×C3—241no—
397C22×C3—241no—
398C22×C3—241no—
399C22×C3#87811yescharacteristic
400C22×C3#88411yescharacteristic
401C22×C3#88411yescharacteristic
402C22×C3#88411yescharacteristic
403C22×C3#89611yescharacteristic
404C22×C3D3×D811yescharacteristic
405C22×C3D3×D811yescharacteristic
406C22×C3#91211yescharacteristic
407C22×C3#91411yescharacteristic
408C22×C3#91411yescharacteristic
409C22×C3#91511yescharacteristic
410C22×C3#91611yescharacteristic
411C22×C3#91811yescharacteristic
412C22×C3#93811yescharacteristic
413C2×D3—42no—
414C2×D3—42no—
415C2×D3—42no—
416C2×D3—81no—
417C2×D3—81no—
418C2×D3—81no—
419C2×D3—81no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—82no—
425C3×C4—81no—
426C3×C4—81no—
427C3×C4—241no—
428C3×C4#87611yescharacteristic
429C3×C4#87811yescharacteristic
430C3×C4#87911yescharacteristic
431C3×C4#88411yescharacteristic
432C3×C4#89611yescharacteristic
433C3×C4#89611yescharacteristic
434C3×C4#92411yescharacteristic
435C3×C4#93911yescharacteristic
436Dic3—62no—
437Dic3—62no—
438Dic3—81no—
439Dic3—122no—
440Dic3—124no—
441Dic3—122no—
442Dic3—121no—
443Dic3—122no—
444Dic3—122no—
445Dic3—121no—
446C32#206711yescharacteristic, complemented, Sylow
447C23—62no—
448C23—121no—
449C23—121no—
450C23—121no—
451C23—121no—
452C23—121no—
453C23—121no—
454C23#381111yescharacteristic
455D4—62no—
456D4—62no—
457D4—121no—
458D4—121no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—92no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—121no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—182no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—361no—
473C2×C4—361no—
474C2×C4D3×Dic611yescharacteristic
475C2×C4#379511yescharacteristic
476C2×C4#379811yescharacteristic
477C2×C4#380211yescharacteristic
478C2×C4#380411yescharacteristic
479C2×C4D3×#6711yescharacteristic
480C8—62no—
481C8—121no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—242no—
490C2×C3#467611yescharacteristic
491C2×C3#475911yescharacteristic
492C2×C3#476611yescharacteristic
493C2×C3#476711yescharacteristic
494C2×C3#477511yescharacteristic
495C2×C3#478611yescharacteristic
496C2×C3#478611yescharacteristic
497C2×C3#479811yescharacteristic
498C2×C3#481211yescharacteristic
499C2×C3#487111yescharacteristic
500C2×C3#489011yescharacteristic
501C2×C3#494811yescharacteristic
502C2×C3#515711yescharacteristic
503C2×C3#517411yescharacteristic
504D3—82no—
505C22—122no—
506C22—122no—
507C22—122no—
508C22—241no—
509C22—241no—
510C22—241no—
511C22—241no—
512C22#6389611yescharacteristic
513C22#6391211yescharacteristic
514C22#6392611yescharacteristic
515C22#6393611yescharacteristic
516C22#6394111yescharacteristic
517C22#6395111yescharacteristic
518C22#6395811yescharacteristic
519C4—81no—
520C4—182no—
521C4—241no—
522C4—362no—
523C4—361no—
524C4#6385111yescharacteristic
525C4#6385911yescharacteristic
526C4#6388511yescharacteristic
527C4#6389911yescharacteristic
528C3—21no—
529C3#6890111yescharacteristic, complemented
530C3#7018011yescharacteristic, complemented
531C2—242no—
532C2#1059047111yescharacteristic
533C2#1059047411yescharacteristic
534C2#1059053811yescharacteristic
535C2#1059055111yescharacteristic
536C2#1059130911yescharacteristic
537C2#1059145511yescharacteristic
538C2#1059159011yescharacteristic
subgroupG/H
centerC23#3811
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. #10592671C2semidirect
4. C2×#63575C2semidirect
5. C2×#63572C2semidirect
7. C3×#4529C2semidirect
39. #4529D3semidirect
446. C32#2067semidirect
529. C3#68901semidirect
530. C3#70180semidirect

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×#635752
C2×#635722
C2×#635632
C3×#45292
#701803
#689013