Finite Group Databasebeta

← #11774311

Subgroups — #11774311

Order 1152.

665 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D3×D12C211yesmaximal, characteristic
2C3×#4833C211yesmaximal, characteristic, complemented
3#10590261C211yesmaximal, characteristic, complemented
4#10589349C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6#10589082C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#70756—31nomaximal
9#68167—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—
21C32×C4⋊C8C2211yescharacteristic, complemented
22C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×(C2×D3)⋊C8—21no—
24C3×C8×Dic3—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×C4×C3⋊C8C2211yescharacteristic, complemented
27Dic3⋊(C3⋊C8)—21no—
28(C2×D3)⋊(C3⋊C8)—21no—
29C4×D3×D4—31no—
30C2×C4×D12—31no—
31C3×#431—31no—
32#4925—31no—
33#4833D311yescharacteristic, complemented
34#4685—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×D12C814yescomplemented
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#1478—91noSylow
76C2×D3×D4—31no—
77C22×D12—31no—
78C22×C4×D3—61no—
79C22×C4×D3—61no—
80C3×C4×D4—31no—
81C2×C3×C42—31no—
82D4×Dic3—31no—
83C4×#67—61no—
84C2×(C2×D3)⋊C4—61no—
85C2×C4⋊Dic3—31no—
86#893—31no—
87D3×C4⋊C4—31no—
88#67⋊C4—61no—
89D3×C22⋊C4—61no—
90C4×D12—31no—
91C4×D12—31no—
92C4×D12—31no—
93C4×D12—31no—
94C4×D12—61no—
95C4×D12—61no—
96C4×D12—61no—
97C4×D12C2×D311yescharacteristic
98C42×D3C2×D311yescharacteristic
99C3×C4⋊C8—21no—
100C3×C4⋊C8—31no—
101C3×C4⋊C8C2×D311yescharacteristic, complemented
102C3×C4⋊C8C2×D311yescharacteristic, complemented
103C3×C22⋊C8—61no—
104C3×C4×C8—31no—
105C3×C4×C8—61no—
106#830—61no—
107(C2×D3)⋊C8—21no—
108(C2×D3)⋊C8—61no—
109Dic3⋊C8—61no—
110C8×Dic3—21no—
111C4⋊(C3⋊C8)—61no—
112C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
113C4×C3⋊C8—31no—
114C4×C3⋊C8—31no—
115C4×C3⋊C8—61no—
116C4×C3⋊C8C2×D311yescharacteristic, complemented
117C22×C3⋊D3—21no—
118C22×C3×D3—21no—
119C22×C3×D3C22⋊C411yescharacteristic
120C2×D32—24no—
121C2×D32—42no—
122C2×D32—42no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3—21no—
127C4⋊(C3⋊D3)—21no—
128C4⋊(C3⋊D3)C2×C812yes—
129C4×C3⋊D3—41no—
130C4×C3⋊D3—41no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3C22⋊C411yescharacteristic
133C2×C3×Dic3C22⋊C411yescharacteristic
134C2×C3×Dic3C22⋊C411yescharacteristic
135C3×D12—21no—
136C3×D12C2×C812yes—
137C3×C4×D3—21no—
138C3×C4×D3—21no—
139C3×C4×D3—41no—
140C3×C4×D3—41no—
141C3×C4×D3—41no—
142C3×C4×D3C2×C812yes—
143C3×C4×D3M1612yes—
144#626—24no—
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—
155D4⋊C8—31no—
156D4⋊C8—91no—
157D4⋊C8—91no—
158D4⋊C8—91no—
159C23×D3—61no—
160C23×D3—61no—
161C2×C3×D4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—61no—
166C2×#67—61no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169D3×D4—34no—
170D3×D4—62no—
171C2×D12—31no—
172C2×D12—31no—
173C2×D12—34no—
174C2×D12—61no—
175C2×D12—62no—
176C2×D12—61no—
177C2×D12C4×D311yescharacteristic
178C2×C4×D3—21no—
179C2×C4×D3—61no—
180C2×C4×D3—61no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×C4×D3—121no—
186C2×C4×D3—122no—
187C2×C4×D3—122no—
188C2×C4×D3—122no—
189C2×C4×D3—122no—
190C2×C4×D3C4×D311yescharacteristic
191C2×C4×D3D1211yescharacteristic
192C2×C4×D3#6711yescharacteristic
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—41no—
196C2×C3×C8—61no—
197C2×C3×C8—61no—
198C3×C4⋊C4—31no—
199C3×C22⋊C4—61no—
200C3×C42—21no—
201C3×C42—31no—
202C3×C42—31no—
203C3×C42—31no—
204C3×C42C22×D311yescharacteristic
205C3×C42C22×D311yescharacteristic
206#217—61no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—61no—
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—
214C4⋊Dic3—31no—
215C4⋊Dic3—31no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3C4×D311yescharacteristic
219Dic3⋊C4—61no—
220C4×Dic3C4×D311yescharacteristic
221C4×Dic3D1211yescharacteristic
222C4×Dic3#6711yescharacteristic
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—121no—
228C22×C32C2×C22⋊C411yescharacteristic
229C2×C3⋊D3—22no—
230C2×C3⋊D3—41no—
231C2×C3⋊D3—41no—
232C2×C3×D3—21no—
233C2×C3×D3—21no—
234C2×C3×D3—22no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C2×C3×D3C22⋊C812yes—
238D32—48no—
239C32×C4—21no—
240C32×C4C22×C811yescharacteristic
241C32×C4C2×M1611yescharacteristic
242C32×C4AGL(1,ℤ/8)11yescharacteristic
243C32×C4AGL(1,ℤ/8)11yescharacteristic
244C3⋊Dic3—41no—
245C3×Dic3—21no—
246C3×Dic3—21no—
247C3×Dic3—41no—
248C3×Dic3C22⋊C812yes—
249C22×D4—91no—
250C23×C4—181no—
251C4×D4—31no—
252C4×D4—91no—
253C4×D4—91no—
254C4×D4—91no—
255C4×D4—181no—
256C4×D4—181no—
257C2×C4⋊C4—91no—
258C2×C22⋊C4—181no—
259C2×C42—31no—
260C4⋊C8—31no—
261C4⋊C8—181no—
262C4⋊C8D3211yescharacteristic, complemented
263C22⋊C8—61no—
264C22⋊C8—181no—
265C4×C8—31no—
266C4×C8—61no—
267C4×C8—91no—
268C23×C3—31no—
269C23×C3—61no—
270C22×D3—21no—
271C22×D3—64no—
272C22×D3—61no—
273C22×D3—61no—
274C22×D3—64no—
275C22×D3—121no—
276C22×D3—122no—
277C22×D3—122no—
278C22×D3—122no—
279C22×D3—122no—
280C22×D3(C2×D3)⋊C411yescharacteristic
281C3×D4—32no—
282C3×D4—61no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—31no—
287C2×C3×C4—32no—
288C2×C3×C4—32no—
289C2×C3×C4—31no—
290C2×C3×C4—31no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4C2×C4×D311yescharacteristic
299C2×C3×C4C2×D1211yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303#67—64no—
304C2×Dic3—21no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—121no—
308C2×Dic3—122no—
309C2×Dic3—122no—
310C2×Dic3(C2×D3)⋊C411yescharacteristic
311C2×Dic3(C2×D3)⋊C411yescharacteristic
312C2×Dic3(C2×D3)⋊C411yescharacteristic
313D12—21no—
314D12—32no—
315D12—32no—
316D12—62no—
317D12—64no—
318D12—61no—
319D12—61no—
320D12—121no—
321D12D3×C812yes—
322C4×D3—21no—
323C4×D3—21no—
324C4×D3—41no—
325C4×D3—41no—
326C4×D3—41no—
327C4×D3—122no—
328C4×D3—122no—
329C4×D3—122no—
330C4×D3—122no—
331C4×D3—121no—
332C4×D3—121no—
333C4×D3—121no—
334C4×D3—121no—
335C4×D3—241no—
336C4×D3—241no—
337C4×D3D3×C812yes—
338C4×D3ΓL(1,𝔽25)12yes—
339C3×C8—41no—
340C3×C8—41no—
341C3×C8—81no—
342C3×C8—121no—
343C3×C8—121no—
344C3⋊C8—41no—
345C3⋊C8—41no—
346C3⋊C8—121no—
347C3⋊C8—121no—
348C3⋊C8—122no—
349C2×C32C2×C22⋊C811yescharacteristic
350C2×C32#41811yescharacteristic
351C2×C32#42111yescharacteristic
352C3⋊D3—42no—
353C3×D3—22no—
354C3×D3—42no—
355C24—181no—
356C2×D4—31no—
357C2×D4—94no—
358C2×D4—91no—
359C2×D4—182no—
360C2×D4—181no—
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—61no—
365C22×C4—181no—
366C22×C4—181no—
367C22×C4—181no—
368C22×C4—181no—
369C22×C4—362no—
370C22×C4—362no—
371C2×C8—21no—
372C2×C8—61no—
373C2×C8—61no—
374C2×C8—181no—
375C4⋊C4—31no—
376C4⋊C4—91no—
377C4⋊C4—181no—
378C22⋊C4—61no—
379C22⋊C4—181no—
380C22⋊C4—181no—
381C22⋊C4—181no—
382C42—31no—
383C42—31no—
384C42—31no—
385C42C2×D3211yescharacteristic
386C22×C3—21no—
387C22×C3—32no—
388C22×C3—61no—
389C22×C3—61no—
390C22×C3—62no—
391C22×C3—121no—
392C22×C3—121no—
393C22×C3D3×C22⋊C411yescharacteristic
394C22×C3C2×(C2×D3)⋊C411yescharacteristic
395C2×D3—21no—
396C2×D3—21no—
397C2×D3—22no—
398C2×D3—41no—
399C2×D3—41no—
400C2×D3—62no—
401C2×D3—62no—
402C2×D3—122no—
403C2×D3—128no—
404C2×D3—128no—
405C2×D3—121no—
406C2×D3—121no—
407C2×D3—121no—
408C2×D3—121no—
409C2×D3—241no—
410C2×D3—241no—
411C2×D3(C2×D3)⋊C812yes—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—32no—
419C3×C4—41no—
420C3×C4—61no—
421C3×C4—61no—
422C3×C4—121no—
423C3×C4C2×D3×C811yescharacteristic
424C3×C4C2×D3×C811yescharacteristic
425C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
426C3×C4D3×M1611yescharacteristic
427C3×C4#91111yescharacteristic
428C3×C4#91411yescharacteristic
429C3×C4#94911yescharacteristic
430C3×C4#94911yescharacteristic
431Dic3—21no—
432Dic3—21no—
433Dic3—41no—
434Dic3—121no—
435Dic3—121no—
436Dic3—241no—
437Dic3(C2×D3)⋊C812yes—
438C32#147811yescharacteristic, complemented, Sylow
439C23—31no—
440C23—61no—
441C23—184no—
442C23—181no—
443C23—362no—
444C23—362no—
445D4—32no—
446D4—61no—
447D4—92no—
448D4—184no—
449D4—181no—
450C2×C4—31no—
451C2×C4—32no—
452C2×C4—32no—
453C2×C4—31no—
454C2×C4—31no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—181no—
462C2×C4—362no—
463C2×C4—362no—
464C2×C4—362no—
465C2×C4—361no—
466C2×C4—361no—
467C2×C4C4×D3211yescharacteristic
468C2×C4D3×D1211yescharacteristic
469C2×C4D3×#6711yescharacteristic
470C8—41no—
471C8—121no—
472C8—121no—
473C8—361no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—62no—
478C2×C3—122no—
479C2×C3D3×C22⋊C811yescharacteristic
480C2×C3#477011yescharacteristic
481C2×C3#482111yescharacteristic
482C2×C3#500111yescharacteristic
483C2×C3C2×(C2×D3)⋊C811yescharacteristic
484C2×C3#513911yescharacteristic
485D3—22no—
486D3—42no—
487D3—122no—
488D3—122no—
489D3—242no—
490C22—32no—
491C22—61no—
492C22—61no—
493C22—62no—
494C22—121no—
495C22—121no—
496C22—182no—
497C22—368no—
498C22—361no—
499C22—361no—
500C22D3×(C2×D3)⋊C411yescharacteristic
501C4—21no—
502C4—32no—
503C4—61no—
504C4—61no—
505C4—121no—
506C4—361no—
507C4D32×C811yescharacteristic
508C4D3×ΓL(1,𝔽25)11yescharacteristic
509C4#6392511yescharacteristic
510C4#6393911yescharacteristic
511C3—21no—
512C3#6816711yescharacteristic, complemented
513C3#7075611yescharacteristic, complemented
514C2—62no—
515C2—122no—
516C2—362no—
517C2#1059059211yescharacteristic
518C2D3×(C2×D3)⋊C811yescharacteristic
519C2#1059100511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×D3×D12C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1478
LCSG ▷ 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×#4833C2semidirect
3. #10590261C2semidirect
4. #10589349C2semidirect
5. C3×#4483C2semidirect
6. #10589082C2semidirect
7. #10589080C2semidirect
21. C32×C4⋊C8C22semidirect
22. C4×C3⋊(C3⋊C8)C22semidirect
25. C3×C4⋊(C3⋊C8)C22semidirect
26. C3×C4×C3⋊C8C22semidirect
33. #4833D3semidirect
42. #4483D3semidirect
57. D3×D12C8semidirect
101. C3×C4⋊C8C2×D3semidirect
102. C3×C4⋊C8C2×D3semidirect
112. C4⋊(C3⋊C8)C2×D3semidirect
116. C4×C3⋊C8C2×D3semidirect
262. C4⋊C8D32semidirect
438. C32#1478semidirect
512. C3#68167semidirect
513. C3#70756semidirect

Maximal subgroups

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

subgroupindex
C4×D3×D122
C3×#48332
#105902612
#105893492
C3×#44832
#105890822
#105890802
#707563
#681673