Finite Group Databasebeta

← #11773814

Subgroups — #11773814

Order 1152.

673 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
1C2×#63880C211yesmaximal, characteristic
2C3×#4718C211yesmaximal, characteristic, complemented
3#10591053C211yesmaximal, characteristic, complemented
4#10589334C211yesmaximal, characteristic, complemented
5C3×#4468C211yesmaximal, characteristic, complemented
6#10589146C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#70783—31nomaximal
9#68101—31nomaximal
10C22×#626C411yescharacteristic
11C22×#624C411yescharacteristic
12C22×D3×Dic3C411yescharacteristic
13C2×#3752C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×Dic3⋊Dic3C411yescharacteristic
17#63880—21no—
18#63880—21no—
19#63880—21no—
20#63880—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×Dic3⋊C8—21no—
26C3×C8×Dic3—21no—
27Dic3⋊(C3⋊C8)—21no—
28Dic3×C3⋊C8—21no—
29C2×#67⋊C4—31no—
30C2×C4×D12—31no—
31C3×#431—31no—
32#4925—31no—
33#4718—31no—
34#4718D311yescharacteristic, complemented
35C3×#323—31no—
36#4525—31no—
37#4468—31no—
38#4468—31no—
39#4468—31no—
40#4468—31no—
41#4468—31no—
42#4468—61no—
43#4468D311yescharacteristic, complemented
44C23×C3⋊D3C2×C411yescharacteristic
45C23×C3×D3C2×C411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3C2×C411yescharacteristic
48C22×C3×Dic3C2×C411yescharacteristic
49C22×C3×Dic3C2×C411yescharacteristic
50C22×C3×Dic3C2×C411yescharacteristic
51C2×#626—21no—
52C2×#626—21no—
53C2×#626—22no—
54C2×#626C814yescomplemented
55C2×#624—21no—
56C2×#624—21no—
57C2×#624—42no—
58C2×D3×Dic3—21no—
59C2×D3×Dic3—21no—
60C2×D3×Dic3—42no—
61C2×C32×C8—21no—
62#3752—21no—
63#3752—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73Dic3⋊Dic3—21no—
74Dic3⋊Dic3—21no—
75#1460—91noSylow
76C22×#67—31no—
77C23×Dic3—31no—
78C22×D12—31no—
79C22×C4×D3—31no—
80C22×C4×D3—31no—
81C22×C4×D3—31no—
82C2×C3×C22⋊C4—31no—
83C2×C3×C42—31no—
84C2×(C2×D3)⋊C4—31no—
85C2×(C2×D3)⋊C4—31no—
86C2×(C2×D3)⋊C4—61no—
87C2×(C2×D3)⋊C4C2×D311yescharacteristic
88C2×C4⋊Dic3—31no—
89C2×Dic3⋊C4—31no—
90C2×C4×Dic3C2×D311yescharacteristic
91#67⋊C4—61no—
92#67⋊C4—61no—
93#67⋊C4—61no—
94#67⋊C4—61no—
95C4×D12—61no—
96C4×D12—61no—
97C4×D12—61no—
98C4×D12—61no—
99C3×C4⋊C8—61no—
100C3×C22⋊C8—21no—
101C3×C22⋊C8—31no—
102C3×C22⋊C8—31no—
103C3×C22⋊C8C2×D311yescharacteristic
104C3×C22⋊C8C2×D311yescharacteristic
105C3×C4×C8—61no—
106#830—31no—
107#830—31no—
108#830—61no—
109#830C2×D311yescharacteristic
110#830C2×D311yescharacteristic
111Dic3⋊C8—21no—
112Dic3⋊C8—61no—
113C8×Dic3—21no—
114C8×Dic3—61no—
115C4⋊(C3⋊C8)—61no—
116C4×C3⋊C8—61no—
117C23×C32C22×C411yescharacteristic
118C22×C3⋊D3—21no—
119C22×C3⋊D3—21no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3C2×C812yes—
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3C2×C812yes—
128C2×C32×C4—41no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—41no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3C22⋊C411yescharacteristic
137C2×C3×Dic3C22⋊C411yescharacteristic
138C2×C3×Dic3C22⋊C411yescharacteristic
139C2×C3×Dic3C22⋊C411yescharacteristic
140C2×C3×Dic3C2×C812yes—
141C2×C3×Dic3M1612yes—
142#626—24no—
143#626—24no—
144#624—42no—
145#624—42no—
146D3×Dic3—42no—
147D3×Dic3—42no—
148C32×C8—41no—
149C3⋊(C3⋊C8)—41no—
150C3×C3⋊C8—41no—
151C3×C3⋊C8—41no—
152C2×C4×D4—91no—
153#431—31no—
154#431—91no—
155#323—31no—
156#323—91no—
157#323—91no—
158#323—91no—
159C24×C3—31no—
160C23×D3—31no—
161C23×D3—31no—
162C23×D3—61no—
163C23×D3C4×D311yescharacteristic
164C22×C3×C4—21no—
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C2×#67—34no—
171C2×#67—62no—
172C2×#67—61no—
173C2×#67—61no—
174C22×Dic3—31no—
175C22×Dic3—31no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—122no—
180C22×Dic3C4×D311yescharacteristic
181C22×Dic3C4×D311yescharacteristic
182C22×Dic3C4×D311yescharacteristic
183C2×D12—34no—
184C2×D12—61no—
185C2×D12—61no—
186C2×D12—62no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×C4×D3—61no—
190C2×C4×D3—61no—
191C2×C4×D3—61no—
192C2×C4×D3—61no—
193C2×C4×D3—122no—
194C2×C4×D3—122no—
195C2×C4×D3—122no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—41no—
199C2×C3×C8—61no—
200C2×C3×C8—61no—
201C3×C22⋊C4—61no—
202C3×C22⋊C4—61no—
203C3×C42—31no—
204C3×C42—31no—
205C3×C42—31no—
206C3×C42—31no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—21no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—121no—
214(C2×D3)⋊C4—121no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219C4×Dic3D1211yescharacteristic
220C4×Dic3D1211yescharacteristic
221C4×Dic3#6711yescharacteristic
222C4×Dic3#6711yescharacteristic
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—121no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32C2×C22⋊C411yescharacteristic
231C22×C32C22×C811yescharacteristic
232C22×C32C2×M1611yescharacteristic
233C2×C3⋊D3—22no—
234C2×C3⋊D3—42no—
235C2×C3⋊D3—41no—
236C2×C3⋊D3—41no—
237C2×C3⋊D3—42no—
238C2×C3×D3—22no—
239C2×C3×D3—42no—
240C2×C3×D3—41no—
241C2×C3×D3—41no—
242C2×C3×D3—42no—
243C32×C4—21no—
244C32×C4—21no—
245C3⋊Dic3—41no—
246C3×Dic3—21no—
247C3×Dic3—41no—
248C3×Dic3C22⋊C812yes—
249C3×Dic3C22⋊C812yes—
250C3×Dic3#10012yes—
251C22×D4—91no—
252C23×C4—91no—
253C23×C4—91no—
254C4×D4—181no—
255C4×D4—181no—
256C4×D4—181no—
257C4×D4—181no—
258C2×C4⋊C4—91no—
259C2×C22⋊C4—31no—
260C2×C22⋊C4—91no—
261C2×C42—31no—
262C4⋊C8—61no—
263C4⋊C8—181no—
264C22⋊C8—31no—
265C22⋊C8—31no—
266C22⋊C8—91no—
267C22⋊C8D3211yescharacteristic
268C4×C8—61no—
269C4×C8—181no—
270C23×C3—21no—
271C23×C3—32no—
272C23×C3—61no—
273C23×C3—61no—
274C23×C3—121no—
275C23×C3—121no—
276C23×C3C2×C4×D311yescharacteristic
277C23×C3C2×C4×D311yescharacteristic
278C22×D3—21no—
279C22×D3—21no—
280C22×D3—32no—
281C22×D3—32no—
282C22×D3—41no—
283C22×D3—41no—
284C22×D3—62no—
285C22×D3—61no—
286C22×D3—61no—
287C22×D3—61no—
288C22×D3—61no—
289C22×D3—121no—
290C22×D3—121no—
291C22×D3—121no—
292C22×D3—121no—
293C22×D3—121no—
294C22×D3—121no—
295C22×D3—241no—
296C22×D3—241no—
297C22×D3D3×C812yes—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—31no—
301C2×C3×C4—31no—
302C2×C3×C4—31no—
303C2×C3×C4—32no—
304C2×C3×C4—32no—
305C2×C3×C4—31no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—62no—
309C2×C3×C4—61no—
310C2×C3×C4—81no—
311C2×C3×C4—121no—
312C2×C3×C4C2×D1211yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4C2×#6711yescharacteristic
316#67—64no—
317#67—64no—
318C2×Dic3—22no—
319C2×Dic3—21no—
320C2×Dic3—41no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—121no—
324C2×Dic3—122no—
325C2×Dic3—122no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—241no—
329C2×Dic3D3×C812yes—
330C2×Dic3ΓL(1,𝔽25)12yes—
331C2×Dic3(C2×D3)⋊C411yescharacteristic
332C2×Dic3(C2×D3)⋊C411yescharacteristic
333C2×Dic3(C2×D3)⋊C411yescharacteristic
334C2×Dic3(C2×D3)⋊C411yescharacteristic
335D12—64no—
336D12—64no—
337C4×D3—122no—
338C4×D3—122no—
339C4×D3—122no—
340C4×D3—122no—
341C4×D3—122no—
342C4×D3—122no—
343C3×C8—41no—
344C3×C8—41no—
345C3×C8—81no—
346C3×C8—121no—
347C3×C8—121no—
348C3⋊C8—41no—
349C3⋊C8—41no—
350C3⋊C8—121no—
351C3⋊C8—121no—
352C3⋊C8—241no—
353C2×C32—21no—
354C2×C32—21no—
355C2×C32C2×C22⋊C811yescharacteristic
356C2×C32#41011yescharacteristic
357C2×C32C2×#10011yescharacteristic
358C3⋊D3—42no—
359C3×D3—42no—
360C24—31no—
361C24—91no—
362C2×D4—94no—
363C2×D4—181no—
364C2×D4—181no—
365C2×D4—182no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—31no—
369C22×C4—91no—
370C22×C4—181no—
371C22×C4—181no—
372C22×C4—181no—
373C22×C4—181no—
374C22×C4—362no—
375C22×C4—362no—
376C22×C4C2×D3211yescharacteristic
377C2×C8—21no—
378C2×C8—61no—
379C2×C8—61no—
380C2×C8—181no—
381C4⋊C4—181no—
382C4⋊C4—181no—
383C22⋊C4—61no—
384C22⋊C4—61no—
385C22⋊C4—181no—
386C22⋊C4—181no—
387C42—31no—
388C42—31no—
389C42—31no—
390C42—31no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—62no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3—121no—
404C22×C3—121no—
405C22×C3D3×C22⋊C411yescharacteristic
406C22×C3C2×D3×C811yescharacteristic
407C22×C3C2×D3×C811yescharacteristic
408C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
409C22×C3D3×M1611yescharacteristic
410C22×C3C2×(C2×D3)⋊C411yescharacteristic
411C2×D3—22no—
412C2×D3—42no—
413C2×D3—41no—
414C2×D3—41no—
415C2×D3—42no—
416C2×D3—62no—
417C2×D3—62no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—121no—
422C2×D3—121no—
423C2×D3—121no—
424C2×D3—121no—
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—241no—
428C2×D3—241no—
429C2×D3—242no—
430C2×D3—242no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—32no—
436C3×C4—32no—
437C3×C4—32no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—61no—
441C3×C4—121no—
442Dic3—21no—
443Dic3—41no—
444Dic3—121no—
445Dic3—121no—
446Dic3—241no—
447Dic3(C2×D3)⋊C812yes—
448Dic3(C2×D3)⋊C812yes—
449Dic3#82312yes—
450C32#146011yescharacteristic, complemented, Sylow
451C23—32no—
452C23—61no—
453C23—61no—
454C23—92no—
455C23—121no—
456C23—121no—
457C23—181no—
458C23—181no—
459C23—361no—
460C23—361no—
461C23C4×D3211yescharacteristic
462D4—184no—
463D4—184no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—31no—
467C2×C4—31no—
468C2×C4—31no—
469C2×C4—31no—
470C2×C4—41no—
471C2×C4—62no—
472C2×C4—61no—
473C2×C4—121no—
474C2×C4—181no—
475C2×C4—362no—
476C2×C4—362no—
477C2×C4—362no—
478C2×C4—362no—
479C2×C4—361no—
480C2×C4D3×D1211yescharacteristic
481C2×C4D3×#6711yescharacteristic
482C8—41no—
483C8—121no—
484C8—121no—
485C8—361no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—41no—
494C2×C3—41no—
495C2×C3—122no—
496C2×C3D3×C22⋊C811yescharacteristic
497C2×C3#474011yescharacteristic
498C2×C3D3×#10011yescharacteristic
499C2×C3#500611yescharacteristic
500C2×C3C2×(C2×D3)⋊C811yescharacteristic
501C2×C3C2×#82311yescharacteristic
502D3—42no—
503D3—122no—
504D3—122no—
505D3—242no—
506C22—21no—
507C22—21no—
508C22—62no—
509C22—122no—
510C22—122no—
511C22—121no—
512C22—121no—
513C22—182no—
514C22—362no—
515C22—362no—
516C22—361no—
517C22—361no—
518C22D32×C811yescharacteristic
519C22D3×ΓL(1,𝔽25)11yescharacteristic
520C22D3×(C2×D3)⋊C411yescharacteristic
521C4—21no—
522C4—21no—
523C4—32no—
524C4—32no—
525C4—32no—
526C4—61no—
527C4—121no—
528C4—361no—
529C3—21no—
530C3#6810111yescharacteristic, complemented
531C3#7078311yescharacteristic, complemented
532C2—21no—
533C2—21no—
534C2—122no—
535C2—362no—
536C2#1059040511yescharacteristic
537C2D3×(C2×D3)⋊C811yescharacteristic
538C2D3×#82311yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC22×C32C22×C8
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#626C4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1460
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4718C2semidirect
3. #10591053C2semidirect
4. #10589334C2semidirect
5. C3×#4468C2semidirect
6. #10589146C2semidirect
7. #10589145C2semidirect
34. #4718D3semidirect
43. #4468D3semidirect
54. C2×#626C8semidirect
450. C32#1460semidirect
530. C3#68101semidirect
531. C3#70783semidirect

Maximal subgroups

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

subgroupindex
C2×#638802
C3×#47182
#105910532
#105893342
C3×#44682
#105891462
#105891452
#707833
#681013