Finite Group Databasebeta

← #11774685

Subgroups — #11774685

Order 1152.

673 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
1C4×D3×D12C211yesmaximal, characteristic
2C3×#4835C211yesmaximal, characteristic, complemented
3C4×#3711C211yesmaximal, characteristic, complemented
4#10589349C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6#10589082C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#70799—31nomaximal
9#68175—31nomaximal
10C2×D3×D12C411yescharacteristic
11C2×C4×D32—21no—
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×C42×D3C2211yescharacteristic
15D3×(C2×D3)⋊C4—21no—
16C4×#626—21no—
17#63894C411yescharacteristic
18Dic3×D12C411yescharacteristic
19D3×C4⋊Dic3C411yescharacteristic
20#63880—21no—
21C2×#3711—21no—
22C32×C4⋊C8C2211yescharacteristic, complemented
23C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
24C3×(C2×D3)⋊C8—21no—
25C3×#815—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
27C3×C4×C3⋊C8C2211yescharacteristic, complemented
28#63554—21no—
29C4×D3×D4—31no—
30C2×C4×D12—31no—
31C3×#432—31no—
32C4×#208—31no—
33#4835D311yescharacteristic, complemented
34C4×ΓL(1,𝔽25)—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4483—31no—
38#4483—31no—
39#4483—31no—
40#4483—31no—
41#4483—61no—
42#4483D311yescharacteristic, complemented
43#4459—31no—
44C22×D32—21no—
45C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
46C2×C4×C3⋊D3—21no—
47C2×C3×D12C2×C411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3C2×C411yescharacteristic
50C2×C3×C4×D3D411yescharacteristic
51C2×C3×C4×D3D411yescharacteristic
52C2×#626—21no—
53C2×#624—21no—
54C2×D3×Dic3—21no—
55C2×D3×Dic3—21no—
56D3×D12—22no—
57D3×D12—22no—
58C4×D32—42no—
59C4×D32—42no—
60C2×C32×C8—21no—
61C32×C42C2311yescharacteristic
62#3752—21no—
63C4⋊(C3⋊Dic3)C2×C411yescharacteristic
64C2×C3⋊(C3⋊C8)—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3C2×C411yescharacteristic
67C3×C4×Dic3C2×C411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72Dic3⋊Dic3—21no—
73#3722—21no—
74(C2×D3)⋊Dic3—21no—
75#3711—24no—
76#1490—91noSylow
77C2×D3×D4—31no—
78C22×D12—31no—
79C22×C4×D3—61no—
80C22×C4×D3—61no—
81C3×C4×D4—31no—
82C2×C3×C42—31no—
83D4×Dic3—31no—
84C4×#67—61no—
85C2×(C2×D3)⋊C4—61no—
86C2×C4⋊Dic3—31no—
87C2×#208—61no—
88C2×ΓL(1,𝔽25)—61no—
89#893—31no—
90D3×C4⋊C4—31no—
91#67⋊C4—61no—
92D3×C22⋊C4—61no—
93C4×D12—31no—
94C4×D12—31no—
95C4×D12—31no—
96C4×D12—31no—
97C4×D12—61no—
98C4×D12—61no—
99C4×D12—61no—
100C4×D12C2×D311yescharacteristic
101C42×D3C2×D311yescharacteristic
102C3×C4⋊C8—21no—
103C3×C4⋊C8—31no—
104C3×C4⋊C8C2×D311yescharacteristic, complemented
105C3×C4⋊C8C2×D311yescharacteristic, complemented
106C3×C22⋊C8—61no—
107C3×#97—61no—
108C3×C4×C8—31no—
109(C2×D3)⋊C8—21no—
110#815—21no—
111#815—61no—
112C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
113#803—61no—
114C4×C3⋊C8—31no—
115C4×C3⋊C8—31no—
116C4×C3⋊C8—61no—
117C4×C3⋊C8C2×D311yescharacteristic, complemented
118C22×C3⋊D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3C22⋊C411yescharacteristic
121C2×D32—24no—
122C2×D32—42no—
123C2×D32—42no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C3⋊Dic3—21no—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)M1612yescomplemented
130C4×C3⋊D3—41no—
131C4×C3⋊D3—41no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3C22⋊C411yescharacteristic
134C2×C3×Dic3C22⋊C411yescharacteristic
135C2×C3×Dic3C22⋊C411yescharacteristic
136C3×D12—21no—
137C3×D12M1612yescomplemented
138C3×C4×D3—22no—
139C3×C4×D3—21no—
140C3×C4×D3—21no—
141C3×C4×D3—21no—
142C3×C4×D3—21no—
143C3×C4×D3—41no—
144C3×C4×D3—41no—
145#626—24no—
146#624—42no—
147D3×Dic3—42no—
148D3×Dic3—42no—
149C32×C8—41no—
150C3⋊(C3⋊C8)—22no—
151C3×C3⋊C8—22no—
152C3×C3⋊C8—41no—
153C2×C4×D4—91no—
154#432—31no—
155C4×M16—91no—
156D4⋊C8—31no—
157D4⋊C8—91no—
158D4⋊C8—91no—
159D4⋊C8—91no—
160C23×D3—61no—
161C23×D3—61no—
162C2×C3×D4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—31no—
166C22×C3×C4—61no—
167C2×#67—61no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170D3×D4—62no—
171D3×D4—62no—
172C2×D12—31no—
173C2×D12—31no—
174C2×D12—61no—
175C2×D12—62no—
176C2×D12—61no—
177C2×D12—62no—
178C2×D12C4×D311yescharacteristic
179C2×C4×D3—21no—
180C2×C4×D3—61no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×C4×D3—121no—
187C2×C4×D3—122no—
188C2×C4×D3—122no—
189C2×C4×D3—122no—
190C2×C4×D3—122no—
191C2×C4×D3C4×D311yescharacteristic
192C2×C4×D3D1211yescharacteristic
193C2×C4×D3#6711yescharacteristic
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—41no—
197C2×C3×C8—61no—
198C2×C3×C8—61no—
199C3×C4⋊C4—31no—
200C3×C22⋊C4—61no—
201C3×C42—21no—
202C3×C42—31no—
203C3×C42—31no—
204C3×C42—31no—
205C3×C42C22×D311yescharacteristic
206C3×C42C22×D311yescharacteristic
207#217—61no—
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—61no—
214(C2×D3)⋊C4—121no—
215C4⋊Dic3—31no—
216C4⋊Dic3—31no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3C4×D311yescharacteristic
220Dic3⋊C4—61no—
221C4×Dic3C4×D311yescharacteristic
222C4×Dic3D1211yescharacteristic
223C4×Dic3#6711yescharacteristic
224#208—64no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—121no—
230ΓL(1,𝔽25)—64no—
231C22×C32C2×C22⋊C411yescharacteristic
232C2×C3⋊D3—22no—
233C2×C3⋊D3—41no—
234C2×C3⋊D3—41no—
235C2×C3×D3—21no—
236C2×C3×D3—21no—
237C2×C3×D3—22no—
238C2×C3×D3—41no—
239C2×C3×D3—41no—
240C2×C3×D3#10412yes—
241D32—48no—
242C32×C4—21no—
243C32×C4C2×M1611yescharacteristic
244C32×C4C2×M1611yescharacteristic
245C32×C4AGL(1,ℤ/8)11yescharacteristic
246C32×C4AGL(1,ℤ/8)11yescharacteristic
247C3⋊Dic3—41no—
248C3×Dic3—21no—
249C3×Dic3—21no—
250C3×Dic3—21no—
251C3×Dic3—41no—
252C22×D4—91no—
253C23×C4—181no—
254C2×M16—181no—
255C4×D4—31no—
256C4×D4—91no—
257C4×D4—91no—
258C4×D4—91no—
259C4×D4—181no—
260C4×D4—181no—
261C2×C4⋊C4—91no—
262C2×C22⋊C4—181no—
263C2×C42—31no—
264C4⋊C8—31no—
265C4⋊C8D3211yescharacteristic, complemented
266C22⋊C8—61no—
267#97—61no—
268#97—181no—
269C4×C8—31no—
270C4×C8—91no—
271C23×C3—31no—
272C23×C3—61no—
273C22×D3—21no—
274C22×D3—64no—
275C22×D3—64no—
276C22×D3—61no—
277C22×D3—61no—
278C22×D3—121no—
279C22×D3—122no—
280C22×D3—122no—
281C22×D3—122no—
282C22×D3—122no—
283C22×D3(C2×D3)⋊C411yescharacteristic
284C3×D4—32no—
285C3×D4—61no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—31no—
290C2×C3×C4—31no—
291C2×C3×C4—31no—
292C2×C3×C4—62no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4C2×C4×D311yescharacteristic
301C2×C3×C4C2×C4×D311yescharacteristic
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306#67—64no—
307C2×Dic3—21no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—121no—
311C2×Dic3—122no—
312C2×Dic3—122no—
313C2×Dic3(C2×D3)⋊C411yescharacteristic
314C2×Dic3(C2×D3)⋊C411yescharacteristic
315C2×Dic3(C2×D3)⋊C411yescharacteristic
316D12—21no—
317D12—32no—
318D12—32no—
319D12—62no—
320D12—64no—
321D12—61no—
322D12—61no—
323D12—121no—
324D12ΓL(1,𝔽25)12yescomplemented
325C4×D3—22no—
326C4×D3—21no—
327C4×D3—21no—
328C4×D3—21no—
329C4×D3—21no—
330C4×D3—41no—
331C4×D3—41no—
332C4×D3—122no—
333C4×D3—122no—
334C4×D3—122no—
335C4×D3—122no—
336C4×D3—121no—
337C4×D3—121no—
338C4×D3—121no—
339C4×D3—121no—
340C4×D3—241no—
341C4×D3—241no—
342C3×C8—41no—
343C3×C8—41no—
344C3×C8—62no—
345C3×C8—81no—
346C3×C8—121no—
347C3⋊C8—22no—
348C3⋊C8—41no—
349C3⋊C8—62no—
350C3⋊C8—62no—
351C3⋊C8—122no—
352C2×C32#40711yescharacteristic
353C2×C32#41811yescharacteristic
354C2×C32C2×#10411yescharacteristic
355C3⋊D3—42no—
356C3×D3—22no—
357C3×D3—42no—
358C24—181no—
359C2×D4—31no—
360C2×D4—91no—
361C2×D4—181no—
362C2×D4—182no—
363C2×D4—182no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—61no—
368C22×C4—181no—
369C22×C4—181no—
370C22×C4—181no—
371C22×C4—181no—
372C22×C4—362no—
373C22×C4—362no—
374M16—184no—
375C2×C8—21no—
376C2×C8—61no—
377C2×C8—61no—
378C2×C8—181no—
379C4⋊C4—31no—
380C4⋊C4—91no—
381C4⋊C4—181no—
382C22⋊C4—61no—
383C22⋊C4—181no—
384C22⋊C4—181no—
385C22⋊C4—181no—
386C42—31no—
387C42—31no—
388C42—31no—
389C42C2×D3211yescharacteristic
390C22×C3—21no—
391C22×C3—32no—
392C22×C3—61no—
393C22×C3—61no—
394C22×C3—62no—
395C22×C3—121no—
396C22×C3—121no—
397C22×C3D3×C22⋊C411yescharacteristic
398C22×C3C2×(C2×D3)⋊C411yescharacteristic
399C2×D3—21no—
400C2×D3—21no—
401C2×D3—22no—
402C2×D3—41no—
403C2×D3—41no—
404C2×D3—62no—
405C2×D3—62no—
406C2×D3—122no—
407C2×D3—128no—
408C2×D3—128no—
409C2×D3—121no—
410C2×D3—121no—
411C2×D3—121no—
412C2×D3—121no—
413C2×D3—241no—
414C2×D3—241no—
415C2×D3#82512yes—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—41no—
423C3×C4—61no—
424C3×C4—61no—
425C3×C4—61no—
426C3×C4—121no—
427C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
428C3×C4D3×M1611yescharacteristic
429C3×C4D3×M1611yescharacteristic
430C3×C4D3×M1611yescharacteristic
431C3×C4#91111yescharacteristic
432C3×C4#91411yescharacteristic
433C3×C4#94911yescharacteristic
434C3×C4#94911yescharacteristic
435Dic3—21no—
436Dic3—21no—
437Dic3—21no—
438Dic3—41no—
439Dic3—121no—
440Dic3—121no—
441Dic3—241no—
442C32#149011yescharacteristic, complemented, Sylow
443C23—31no—
444C23—61no—
445C23—184no—
446C23—181no—
447C23—362no—
448C23—362no—
449D4—32no—
450D4—61no—
451D4—92no—
452D4—184no—
453D4—181no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—31no—
457C2×C4—62no—
458C2×C4—61no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—181no—
466C2×C4—362no—
467C2×C4—362no—
468C2×C4—362no—
469C2×C4—361no—
470C2×C4—361no—
471C2×C4C4×D3211yescharacteristic
472C2×C4D3×D1211yescharacteristic
473C2×C4D3×#6711yescharacteristic
474C8—41no—
475C8—62no—
476C8—121no—
477C8—182no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—62no—
482C2×C3—122no—
483C2×C3#472611yescharacteristic
484C2×C3#477011yescharacteristic
485C2×C3D3×#10411yescharacteristic
486C2×C3#500111yescharacteristic
487C2×C3#512611yescharacteristic
488C2×C3C2×#82511yescharacteristic
489D3—22no—
490D3—42no—
491D3—122no—
492D3—122no—
493D3—242no—
494C22—32no—
495C22—61no—
496C22—61no—
497C22—62no—
498C22—121no—
499C22—121no—
500C22—182no—
501C22—368no—
502C22—361no—
503C22—361no—
504C22D3×(C2×D3)⋊C411yescharacteristic
505C4—21no—
506C4—61no—
507C4—61no—
508C4—61no—
509C4—121no—
510C4—361no—
511C4D3×ΓL(1,𝔽25)11yescharacteristic
512C4#6379111yescharacteristic
513C4#6392511yescharacteristic
514C4#6393911yescharacteristic
515C3—21no—
516C3#6817511yescharacteristic, complemented
517C3#7079911yescharacteristic, complemented
518C2—62no—
519C2—122no—
520C2—362no—
521C2#1059059211yescharacteristic
522C2#1059093611yescharacteristic
523C2D3×#82511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×D3×D12C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4835C2semidirect
3. C4×#3711C2semidirect
4. #10589349C2semidirect
5. C3×#4483C2semidirect
6. #10589082C2semidirect
7. #10589080C2semidirect
22. C32×C4⋊C8C22semidirect
23. C4×C3⋊(C3⋊C8)C22semidirect
26. C3×C4⋊(C3⋊C8)C22semidirect
27. C3×C4×C3⋊C8C22semidirect
33. #4835D3semidirect
42. #4483D3semidirect
104. C3×C4⋊C8C2×D3semidirect
105. C3×C4⋊C8C2×D3semidirect
112. C4⋊(C3⋊C8)C2×D3semidirect
117. C4×C3⋊C8C2×D3semidirect
129. C4⋊(C3⋊D3)M16semidirect
137. C3×D12M16semidirect
265. C4⋊C8D32semidirect
324. D12ΓL(1,𝔽25)semidirect
442. C32#1490semidirect
516. C3#68175semidirect
517. C3#70799semidirect

Maximal subgroups

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

subgroupindex
C4×D3×D122
C3×#48352
C4×#37112
#105893492
C3×#44832
#105890822
#105890802
#707993
#681753