Finite Group Databasebeta

← #11773900

Subgroups — #11773900

Order 1152.

553 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63836C211yesmaximal, characteristic
2C3×#4719C211yesmaximal, characteristic, complemented
3#10591063C211yesmaximal, characteristic, complemented
4#10589334C211yesmaximal, characteristic
5C3×#4469C211yesmaximal, characteristic, complemented
6#10589147C211yesmaximal, characteristic, complemented
7#10589146C211yesmaximal, characteristic
8#70826—31nomaximal
9#68126—31nomaximal
10C22×#624C411yescharacteristic
11C2×#3752C2211yescharacteristic
12C2×C3×Dic3⋊C4C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×Dic3⋊Dic3C411yescharacteristic
15C2×#3722C411yescharacteristic
16C2×Dic32C411yescharacteristic
17#63836—21no—
18#63836—21no—
19#63836—21no—
20#63836—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#815—21no—
26C3×Dic3⋊C8—21no—
27Dic3⋊(C3⋊C8)—21no—
28#63554—21no—
29C2×#892—31no—
30C2×#872—31no—
31C3×#432—31no—
32#4926—31no—
33#4719—31no—
34#4719D311yescharacteristic, complemented
35C3×#324—31no—
36#4528—31no—
37#4469—31no—
38#4469D311yescharacteristic, complemented
39#4468—31no—
40#4468—31no—
41#4468—31no—
42#4468—31no—
43#4468—61no—
44C23×C3⋊D3C2×C411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3C2×C411yescharacteristic
47C22×C3×Dic3C2×C411yescharacteristic
48C22×C3×Dic3C2×C411yescharacteristic
49C22×C3×Dic3C2×C411yescharacteristic
50C22×C3×Dic3C2×C411yescharacteristic
51C2×#624—22no—
52C2×#624—21no—
53C2×#624—21no—
54C2×#624—22no—
55C2×C32×C8—21no—
56#3752—21no—
57#3752—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×Dic3⋊C4—21no—
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D411yescharacteristic
63C3×C4×Dic3D411yescharacteristic
64C3×C4×Dic3D411yescharacteristic
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69#3722—21no—
70#3722—21no—
71Dic32—21no—
72Dic32—21no—
73#1464—91noSylow
74C22×C4×D3—31no—
75C22×C4×D3—31no—
76C2×C3×C4⋊C4—31no—
77C2×C3×C42—31no—
78C2×(C2×D3)⋊C4—31no—
79C2×(C2×D3)⋊C4—31no—
80C2×(C2×D3)⋊C4—31no—
81C2×(C2×D3)⋊C4—31no—
82C2×(C2×D3)⋊C4—61no—
83C2×C4⋊Dic3—31no—
84C2×Dic3⋊C4—31no—
85C2×Dic3⋊C4C2×D311yescharacteristic
86C2×C4×Dic3—31no—
87C2×C4×Dic3—31no—
88C2×C4×Dic3C2×D311yescharacteristic
89#892—61no—
90#892—61no—
91#892—61no—
92#892—61no—
93#872—61no—
94#872—61no—
95#872—61no—
96#872—61no—
97C3×C4⋊C8—61no—
98C3×C22⋊C8—21no—
99C3×C22⋊C8—31no—
100C3×C22⋊C8—31no—
101C3×C22⋊C8C2×D311yescharacteristic
102C3×C22⋊C8C2×D311yescharacteristic
103C3×#97—61no—
104#830—31no—
105#830—31no—
106#830—61no—
107#830C2×D311yescharacteristic
108#830C2×D311yescharacteristic
109#815—21no—
110#815—61no—
111Dic3⋊C8—21no—
112Dic3⋊C8—61no—
113C4⋊(C3⋊C8)—61no—
114#803—61no—
115C23×C32C22×C411yescharacteristic
116C22×C3⋊D3—21no—
117C22×C3⋊D3—21no—
118C22×C3⋊D3—41no—
119C22×C3⋊D3—41no—
120C22×C3⋊D3M1612yes—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3C22⋊C411yescharacteristic
134C2×C3×Dic3C22⋊C411yescharacteristic
135C2×C3×Dic3C22⋊C411yescharacteristic
136C2×C3×Dic3C22⋊C411yescharacteristic
137C2×C3×Dic3M1612yes—
138#624—24no—
139#624—24no—
140C32×C8—41no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8—41no—
144C2×#117—91no—
145#432—31no—
146#432—91no—
147#324—31no—
148#324—91no—
149#323—91no—
150#323—91no—
151C23×D3—31no—
152C23×D3—31no—
153C23×D3—61no—
154C22×C3×C4—21no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×Dic3—31no—
162C22×Dic3—31no—
163C22×Dic3—61no—
164C22×Dic3C4×D311yescharacteristic
165C22×Dic3C4×D311yescharacteristic
166C22×Dic3C4×D311yescharacteristic
167C22×Dic3C4×D311yescharacteristic
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×C4×D3—62no—
171C2×C4×D3—62no—
172C2×C4×D3—62no—
173C2×C4×D3—62no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—41no—
179C2×C3×C8—61no—
180C2×C3×C8—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C42—31no—
184C3×C42—31no—
185C3×C42—31no—
186C3×C42—31no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—61no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—121no—
196(C2×D3)⋊C4—121no—
197C4⋊Dic3—61no—
198C4⋊Dic3—61no—
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3D1211yescharacteristic
208C4×Dic3D1211yescharacteristic
209C4×Dic3#6711yescharacteristic
210C4×Dic3#6711yescharacteristic
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—121no—
216C22×C32—21no—
217C22×C32—21no—
218C22×C32C2×C22⋊C411yescharacteristic
219C22×C32C2×M1611yescharacteristic
220C22×C32C2×M1611yescharacteristic
221C2×C3⋊D3—22no—
222C2×C3⋊D3—42no—
223C2×C3⋊D3—41no—
224C2×C3⋊D3—41no—
225C2×C3⋊D3—42no—
226C32×C4—21no—
227C32×C4—21no—
228C3⋊Dic3—41no—
229C3×Dic3—21no—
230C3×Dic3—21no—
231C3×Dic3—22no—
232C3×Dic3—21no—
233C3×Dic3—21no—
234C3×Dic3—41no—
235C23×C4—91no—
236#117—181no—
237#117—181no—
238#117—181no—
239#117—181no—
240C2×C4⋊C4—31no—
241C2×C4⋊C4—91no—
242C2×C22⋊C4—91no—
243C2×C22⋊C4—91no—
244C2×C42—31no—
245C2×C42—91no—
246C4⋊C8—61no—
247C4⋊C8—181no—
248C22⋊C8—31no—
249C22⋊C8—31no—
250C22⋊C8—91no—
251C22⋊C8D3211yescharacteristic
252#97—61no—
253#97—181no—
254C23×C3—21no—
255C23×C3C2×C4×D311yescharacteristic
256C23×C3C2×C4×D311yescharacteristic
257C22×D3—32no—
258C22×D3—32no—
259C22×D3—62no—
260C22×D3—61no—
261C22×D3—61no—
262C22×D3—61no—
263C22×D3—61no—
264C22×D3—121no—
265C22×D3—121no—
266C22×D3—121no—
267C22×D3—121no—
268C22×D3—121no—
269C22×D3—121no—
270C22×D3—241no—
271C22×D3—241no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—31no—
275C2×C3×C4—31no—
276C2×C3×C4—31no—
277C2×C3×C4—31no—
278C2×C3×C4—32no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—81no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4C2×D1211yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4C2×#6711yescharacteristic
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—61no—
301C2×Dic3—61no—
302C2×Dic3—121no—
303C2×Dic3—121no—
304C2×Dic3—121no—
305C2×Dic3—241no—
306C2×Dic3ΓL(1,𝔽25)12yes—
307C2×Dic3(C2×D3)⋊C411yescharacteristic
308C2×Dic3(C2×D3)⋊C411yescharacteristic
309C2×Dic3(C2×D3)⋊C411yescharacteristic
310C2×Dic3(C2×D3)⋊C411yescharacteristic
311C4×D3—64no—
312C4×D3—64no—
313C4×D3—64no—
314C4×D3—64no—
315C3×C8—41no—
316C3×C8—41no—
317C3×C8—81no—
318C3×C8—121no—
319C3×C8—121no—
320C3⋊C8—41no—
321C3⋊C8—41no—
322C3⋊C8—121no—
323C3⋊C8—121no—
324C3⋊C8—241no—
325C2×C32—21no—
326C2×C32—21no—
327C2×C32#40711yescharacteristic
328C2×C32#41011yescharacteristic
329C2×C32#41311yescharacteristic
330C3⋊D3—42no—
331C24—91no—
332C22×C4—31no—
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—31no—
336C22×C4—91no—
337C22×C4—181no—
338C22×C4—181no—
339C22×C4—182no—
340C22×C4—182no—
341C22×C4C2×D3211yescharacteristic
342C2×C8—21no—
343C2×C8—61no—
344C2×C8—61no—
345C2×C8—181no—
346C4⋊C4—61no—
347C4⋊C4—61no—
348C4⋊C4—181no—
349C4⋊C4—181no—
350C22⋊C4—181no—
351C22⋊C4—181no—
352C22⋊C4—181no—
353C22⋊C4—181no—
354C42—31no—
355C42—31no—
356C42—31no—
357C42—31no—
358C42—181no—
359C42—181no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3D3×C22⋊C411yescharacteristic
370C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
371C22×C3D3×M1611yescharacteristic
372C22×C3D3×M1611yescharacteristic
373C22×C3D3×M1611yescharacteristic
374C22×C3C2×(C2×D3)⋊C411yescharacteristic
375C2×D3—62no—
376C2×D3—62no—
377C2×D3—122no—
378C2×D3—122no—
379C2×D3—122no—
380C2×D3—121no—
381C2×D3—121no—
382C2×D3—121no—
383C2×D3—121no—
384C2×D3—122no—
385C2×D3—122no—
386C2×D3—241no—
387C2×D3—241no—
388C2×D3—242no—
389C2×D3—242no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—41no—
395C3×C4—41no—
396C3×C4—62no—
397C3×C4—61no—
398C3×C4—61no—
399C3×C4—61no—
400C3×C4—61no—
401C3×C4—121no—
402Dic3—21no—
403Dic3—21no—
404Dic3—21no—
405Dic3—21no—
406Dic3—22no—
407Dic3—41no—
408Dic3—121no—
409Dic3—121no—
410Dic3—241no—
411C32#146411yescharacteristic, complemented, Sylow
412C23—92no—
413C23—181no—
414C23—181no—
415C23—361no—
416C23—361no—
417C23C4×D3211yescharacteristic
418C2×C4—32no—
419C2×C4—31no—
420C2×C4—31no—
421C2×C4—31no—
422C2×C4—31no—
423C2×C4—41no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—121no—
430C2×C4—121no—
431C2×C4—184no—
432C2×C4—184no—
433C2×C4—181no—
434C2×C4—361no—
435C2×C4D3×D1211yescharacteristic
436C2×C4D3×#6711yescharacteristic
437C8—41no—
438C8—121no—
439C8—121no—
440C8—361no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—41no—
449C2×C3—41no—
450C2×C3#472611yescharacteristic
451C2×C3#474011yescharacteristic
452C2×C3#475111yescharacteristic
453C2×C3#500611yescharacteristic
454C2×C3#512611yescharacteristic
455C2×C3#513211yescharacteristic
456D3—122no—
457D3—122no—
458D3—242no—
459C22—21no—
460C22—21no—
461C22—182no—
462C22—362no—
463C22—362no—
464C22—361no—
465C22—361no—
466C22D3×ΓL(1,𝔽25)11yescharacteristic
467C22#6379111yescharacteristic
468C22D3×(C2×D3)⋊C411yescharacteristic
469C4—21no—
470C4—21no—
471C4—61no—
472C4—61no—
473C4—62no—
474C4—61no—
475C4—61no—
476C4—121no—
477C4—361no—
478C3—21no—
479C3#6812611yescharacteristic, complemented
480C3#7082611yescharacteristic, complemented
481C2—21no—
482C2—21no—
483C2—362no—
484C2#1059040511yescharacteristic
485C2#1059093611yescharacteristic
486C2#1059100711yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1464
LCSG ▷ C23×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×#4719C2semidirect
3. #10591063C2semidirect
5. C3×#4469C2semidirect
6. #10589147C2semidirect
34. #4719D3semidirect
38. #4469D3semidirect
411. C32#1464semidirect
479. C3#68126semidirect
480. C3#70826semidirect

Maximal subgroups

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

subgroupindex
C2×#638362
C3×#47192
#105910632
#105893342
C3×#44692
#105891472
#105891462
#708263
#681263