Finite Group Databasebeta

← #11774501

Subgroups — #11774501

Order 1152.

565 conjugacy classes of subgroups.

The subgroup lattice has 505 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5548C211yesmaximal, characteristic
2C4×#3711C211yesmaximal, characteristic, complemented
3#10590248C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589081C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71801—31nomaximal
9#68171—31nomaximal
10C2×C3×#235—21no—
11C32×C4×D4C2211yescharacteristic
12C3×#940C411yescharacteristic
13C3×#938C411yescharacteristic
14C3×C4×#67—21no—
15C3×#895C411yescharacteristic
16C3×#888C411yescharacteristic
17C3×#885—21no—
18C3×#884—21no—
19C3×C4×D12C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C2×#3711—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×C3⋊C8C2211yescharacteristic
26(C2×D3)⋊(C3⋊C8)—21no—
27#63554—21no—
28Dic3×C3⋊C8—21no—
29C3×#532—31no—
30#5548D311yescharacteristic
31#4925—31no—
32C4×#208—31no—
33#4833—31no—
34C4×ΓL(1,𝔽25)—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37D4⋊(C3⋊C8)—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)—31no—
40D4⋊(C3⋊C8)—61no—
41D4⋊(C3⋊C8)D311yescharacteristic, complemented
42#4483—31no—
43#4459—31no—
44C2×C32×D4C2×C411yescharacteristic
45C22×C32×C4—21no—
46C2×C3×#67—21no—
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C3×#235—42no—
50C3×#235—42no—
51C2×C3×D12—21no—
52C2×C3×D12C2×C411yescharacteristic
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3C2×C411yescharacteristic
55C2×C3×C4×D3D411yescharacteristic
56C2×C3×C4×D3D411yescharacteristic
57C2×C3×Dic6—21no—
58C32×C4⋊C4C2×C411yescharacteristic
59C32×C22⋊C4—21no—
60C32×C42C2311yescharacteristic
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C3×#217—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3C2×C411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#3711—24no—
74#1484—91noSylow
75C2×C3×#41—61no—
76C2×#235—21no—
77C3×C4⋊Q8—31no—
78C3×#127—31no—
79C3×#124—61no—
80C3×#121—31no—
81C3×#121—31no—
82C3×#121—61no—
83C3×C4×D4—21no—
84C3×C4×D4—31no—
85C3×C4×D4—61no—
86C3×C4×D4C2×D311yescharacteristic
87C3×C4×D4C2×D311yescharacteristic
88C2×C3×C42—31no—
89#940Dic311yescharacteristic
90#938Dic311yescharacteristic
91C4×#67—21no—
92C2×#208—61no—
93C2×ΓL(1,𝔽25)—61no—
94#895Dic311yescharacteristic
95#888Dic311yescharacteristic
96#885—21no—
97#884—21no—
98C4×D12C2×D311yescharacteristic
99C42×D3C2×D311yescharacteristic
100C3×C4⋊C8—31no—
101C3×C4×C8—31no—
102#830—61no—
103(C2×D3)⋊C8—61no—
104#815—61no—
105C8×Dic3—61no—
106C4⋊(C3⋊C8)—31no—
107C4⋊(C3⋊C8)—31no—
108C4⋊(C3⋊C8)—61no—
109C4⋊(C3⋊C8)C2×D311yescharacteristic
110#803—61no—
111C4×C3⋊C8—31no—
112C4×C3⋊C8—31no—
113C4×C3⋊C8—61no—
114C4×C3⋊C8—61no—
115C4×C3⋊C8C2×D311yescharacteristic
116C23×C32—21no—
117C22×C3×D3—21no—
118C22×C3×D3C22⋊C411yescharacteristic
119C32×D4—21no—
120C32×D4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C3×#67—42no—
128C3×#67—42no—
129C3×#67—42no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3C22⋊C411yescharacteristic
132C2×C3×Dic3C22⋊C411yescharacteristic
133C2×C3×Dic3C22⋊C411yescharacteristic
134C3×D12—21no—
135C3×D12—21no—
136C3×D12—42no—
137C3×C4×D3—21no—
138C3×C4×D3—21no—
139C3×C4×D3—21no—
140C3×C4×D3—21no—
141C3×C4×D3—22no—
142C3×C4×D3—41no—
143C3×C4×D3—41no—
144C3×Dic6—42no—
145C3⋊(C3⋊C8)—22no—
146C3⋊(C3⋊C8)—41no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—41no—
149#532—31no—
150#431—91no—
151C4×M16—91no—
152D4⋊C8—31no—
153D4⋊C8—91no—
154D4⋊C8—91no—
155D4⋊C8—91no—
156C3×#41—122no—
157C3×#41—122no—
158C2×C3×Q8—61no—
159C2×C3×D4—21no—
160C2×C3×D4—31no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4C4×D311yescharacteristic
166C2×C3×D4C2×Dic311yescharacteristic
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—41no—
173C22×C3×C4—61no—
174C2×#67—21no—
175C2×#67—21no—
176C2×#67—21no—
177#235—42no—
178#235—42no—
179C2×D12—21no—
180C2×D12C2×Dic311yescharacteristic
181C2×C4×D3—21no—
182C2×C4×D3C2×Dic311yescharacteristic
183C2×C4×D3#6711yescharacteristic
184C2×C4×D3#6711yescharacteristic
185C2×Dic6—21no—
186C2×C3×C8—61no—
187C2×C3×C8—61no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—31no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4C4×D311yescharacteristic
192C3×C4⋊C4C2×Dic311yescharacteristic
193C3×C22⋊C4—21no—
194C3×C22⋊C4—21no—
195C3×C22⋊C4—41no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C42—21no—
200C3×C42—31no—
201C3×C42—31no—
202C3×C42—31no—
203C3×C42C22×D311yescharacteristic
204C3×C42C22×D311yescharacteristic
205#217—21no—
206(C2×D3)⋊C4—21no—
207(C2×D3)⋊C4—21no—
208C4⋊Dic3C2×Dic311yescharacteristic
209Dic3⋊C4—21no—
210C4×Dic3C2×Dic311yescharacteristic
211C4×Dic3#6711yescharacteristic
212C4×Dic3#6711yescharacteristic
213#208—64no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—121no—
221C2×C3⋊C8—121no—
222ΓL(1,𝔽25)—64no—
223C22×C32—41no—
224C22×C32—41no—
225C22×C32—41no—
226C22×C32C2×C22⋊C411yescharacteristic
227C2×C3×D3—21no—
228C2×C3×D3—21no—
229C2×C3×D3—21no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C32×C4—21no—
234C32×C4—41no—
235C32×C4#13111yescharacteristic
236C32×C4#13111yescharacteristic
237C32×C4AGL(1,ℤ/8)11yescharacteristic
238C32×C4AGL(1,ℤ/8)11yescharacteristic
239C3×Dic3—21no—
240C3×Dic3—21no—
241C3×Dic3—41no—
242C3×Dic3#10412yes—
243C2×#41—61no—
244C2×M16—181no—
245C4⋊Q8—31no—
246#127—31no—
247#124—61no—
248#121—31no—
249#121—31no—
250#121—61no—
251C4×D4—31no—
252C4×D4—61no—
253C4×D4D3211yescharacteristic
254C2×C42—31no—
255C4⋊C8—31no—
256C4⋊C8—91no—
257C22⋊C8—181no—
258#97—181no—
259C4×C8—31no—
260C4×C8—91no—
261C4×C8—181no—
262C23×C3—21no—
263C23×C3—21no—
264C23×C3—31no—
265C23×C3—41no—
266C23×C3—61no—
267C22×D3—21no—
268C22×D3#21711yescharacteristic
269C3×Q8—122no—
270C3×D4—22no—
271C3×D4—21no—
272C3×D4—21no—
273C3×D4—21no—
274C3×D4—21no—
275C3×D4—41no—
276C3×D4—61no—
277C3×D4—61no—
278C3×D4—122no—
279C3×D4—122no—
280C3×D4—122no—
281C3×D4—122no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—31no—
288C2×C3×C4—31no—
289C2×C3×C4—31no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—62no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—81no—
302C2×C3×C4—81no—
303C2×C3×C4—121no—
304C2×C3×C4—121no—
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4C22×Dic311yescharacteristic
309C2×C3×C4C2×#6711yescharacteristic
310C2×C3×C4C2×#6711yescharacteristic
311#67—42no—
312#67—42no—
313#67—42no—
314C2×Dic3—21no—
315C2×Dic3#21711yescharacteristic
316C2×Dic3#21711yescharacteristic
317C2×Dic3#21711yescharacteristic
318D12—21no—
319D12—21no—
320D12—42no—
321C4×D3—21no—
322C4×D3—21no—
323C4×D3—21no—
324C4×D3—21no—
325C4×D3—22no—
326C4×D3—41no—
327C4×D3—41no—
328Dic6—42no—
329C3×C8—62no—
330C3×C8—121no—
331C3⋊C8—22no—
332C3⋊C8—41no—
333C3⋊C8—62no—
334C3⋊C8—62no—
335C3⋊C8—122no—
336C3⋊C8—121no—
337C3⋊C8—121no—
338C3⋊C8—241no—
339C2×C32—81no—
340C2×C32#40811yescharacteristic
341C2×C32#41811yescharacteristic
342C2×C32C2×#10411yescharacteristic
343C3×D3—41no—
344C3×D3—81no—
345#41—122no—
346#41—122no—
347C2×Q8—61no—
348C2×D4—31no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C2×D4—61no—
353C2×D4D3×Dic311yescharacteristic
354C22×C4—21no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—61no—
359M16—184no—
360C2×C8—61no—
361C2×C8—61no—
362C2×C8—181no—
363C2×C8—181no—
364C4⋊C4—31no—
365C4⋊C4—61no—
366C4⋊C4D3×Dic311yescharacteristic
367C22⋊C4—21no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C22⋊C4—61no—
371C42—31no—
372C42—31no—
373C42—31no—
374C42C2×D3211yescharacteristic
375C22×C3—21no—
376C22×C3—42no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—41no—
383C22×C3—61no—
384C22×C3—61no—
385C22×C3—61no—
386C22×C3—81no—
387C22×C3—81no—
388C22×C3—121no—
389C22×C3—121no—
390C22×C3—121no—
391C22×C3D3×C22⋊C411yescharacteristic
392C22×C3C2×#21711yescharacteristic
393C2×D3—21no—
394C2×D3—21no—
395C2×D3—21no—
396C2×D3—41no—
397C2×D3—41no—
398C2×D3—41no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—32no—
406C3×C4—41no—
407C3×C4—41no—
408C3×C4—41no—
409C3×C4—61no—
410C3×C4—61no—
411C3×C4—81no—
412C3×C4—121no—
413C3×C4#90111yescharacteristic
414C3×C4#90711yescharacteristic
415C3×C4#91111yescharacteristic
416C3×C4#91411yescharacteristic
417C3×C4#93211yescharacteristic
418C3×C4#93211yescharacteristic
419C3×C4#94811yescharacteristic
420C3×C4#94811yescharacteristic
421Dic3—21no—
422Dic3—21no—
423Dic3—41no—
424Dic3#83712yes—
425C32#148411yescharacteristic, complemented, Sylow
426C23—21no—
427C23—31no—
428C23—61no—
429Q8—122no—
430D4—21no—
431D4—21no—
432D4—61no—
433D4—61no—
434D4—122no—
435D4—122no—
436D4—122no—
437D4—122no—
438C2×C4—21no—
439C2×C4—31no—
440C2×C4—31no—
441C2×C4—31no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—62no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—121no—
451C2×C4—121no—
452C2×C4C2×D3×Dic311yescharacteristic
453C2×C4D3×#6711yescharacteristic
454C2×C4D3×#6711yescharacteristic
455C8—62no—
456C8—121no—
457C8—182no—
458C8—361no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—82no—
463C2×C3—81no—
464C2×C3—81no—
465C2×C3—121no—
466C2×C3—241no—
467C2×C3#472711yescharacteristic
468C2×C3#477011yescharacteristic
469C2×C3D3×#10411yescharacteristic
470C2×C3#521511yescharacteristic
471C2×C3#523411yescharacteristic
472C2×C3C2×#83711yescharacteristic
473D3—41no—
474D3—81no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—61no—
479C22—61no—
480C22—61no—
481C22—121no—
482C22—121no—
483C22—121no—
484C22D3×#21711yescharacteristic
485C4—21no—
486C4—32no—
487C4—41no—
488C4—61no—
489C4—61no—
490C4—121no—
491C4#6381411yescharacteristic
492C4#6381511yescharacteristic
493C4#6393211yescharacteristic
494C4#6393411yescharacteristic
495C3—21no—
496C3#6817111yescharacteristic, complemented
497C3#7180111yescharacteristic, complemented
498C2—81no—
499C2—121no—
500C2—241no—
501C2#1059114511yescharacteristic
502C2#1059142111yescharacteristic
503C2D3×#83711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5548C2
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1484
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×#3711C2semidirect
3. #10590248C2semidirect
4. D4⋊(C3⋊(C3⋊C8))C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589081C2semidirect
7. #10589080C2semidirect
41. D4⋊(C3⋊C8)D3semidirect
425. C32#1484semidirect
496. C3#68171semidirect
497. C3#71801semidirect

Maximal subgroups

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

subgroupindex
C3×#55482
C4×#37112
#105902482
D4⋊(C3⋊(C3⋊C8))2
C3×D4⋊(C3⋊C8)2
#105890812
#105890802
#718013
#681713