Finite Group Databasebeta

← #11773792

Subgroups — #11773792

Order 1152.

703 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63879C211yesmaximal, characteristic
2C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
3D3×#830C211yesmaximal, characteristic, complemented
4#10589335C211yesmaximal, characteristic, complemented
5C3×#4468C211yesmaximal, characteristic, complemented
6#10589148C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#69919—31nomaximal
9#68119—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×#625C411yescharacteristic
12C22×D3×Dic3C411yescharacteristic
13C2×#3750C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C2211yescharacteristic
15C2×C3×D3×C8—21no—
16C2×(C2×D3)⋊Dic3C411yescharacteristic
17C2×Dic32C411yescharacteristic
18#63879—21no—
19#63879—21no—
20#63879—21no—
21#63879—21no—
22C2×D3×C3⋊C8—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×(C2×D3)⋊C8—21no—
28(C2×D3)⋊(C3⋊C8)—21no—
29C2×C4×#67—31no—
30C2×#67⋊C4—31no—
31C2×C3×C22⋊C8—31no—
32C2×#830—31no—
33D3×C22⋊C8—31no—
34D3×C22⋊C8D311yescharacteristic, complemented
35C3×#323—31no—
36#4525—31no—
37#4469—31no—
38#4469—31no—
39#4469—31no—
40#4469—31no—
41#4469—61no—
42#4468—31no—
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×C3×C4×D3—42no—
52C2×C3×C4×D3D411yescharacteristic
53C2×C3×C4×D3D411yescharacteristic
54C2×C3×C4×D3D411yescharacteristic
55C2×C3×C4×D3D411yescharacteristic
56C2×#625—21no—
57C2×#625—21no—
58C2×#625—22no—
59C2×#625C814yescomplemented
60C2×D3×Dic3—21no—
61C2×D3×Dic3—21no—
62C2×D3×Dic3—42no—
63C2×C32×C8—21no—
64#3750—21no—
65#3750—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×(C2×D3)⋊C4—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C3×D3×C8—42no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74Dic32—21no—
75Dic32—21no—
76D3×C3⋊C8—42no—
77#1459—91noSylow
78C23×C3×C4—31no—
79C22×#67—31no—
80C22×#67—31no—
81C23×Dic3—31no—
82C22×C4×D3—31no—
83C22×C4×D3C2×D311yescharacteristic
84C22×C3×C8—61no—
85C2×C3×C22⋊C4—31no—
86C2×#217—31no—
87C4×#67—61no—
88C4×#67—61no—
89C4×#67—61no—
90C4×#67—61no—
91C2×(C2×D3)⋊C4—31no—
92C2×(C2×D3)⋊C4C2×D311yescharacteristic
93C2×Dic3⋊C4—31no—
94C2×Dic3⋊C4—31no—
95C2×Dic3⋊C4—61no—
96C2×C4×Dic3—31no—
97C2×C4×Dic3—31no—
98C22×C3⋊C8—61no—
99C2×D3×C8—21no—
100C2×D3×C8—61no—
101#67⋊C4—61no—
102#67⋊C4—61no—
103#67⋊C4—61no—
104#67⋊C4—61no—
105C3×C22⋊C8—21no—
106C3×C22⋊C8—31no—
107C3×C22⋊C8—31no—
108C3×C22⋊C8—61no—
109C3×C22⋊C8C2×D311yescharacteristic
110C3×C22⋊C8C2×D311yescharacteristic
111#830—31no—
112#830—31no—
113#830—61no—
114#830—61no—
115#830C2×D311yescharacteristic
116#830C2×D311yescharacteristic
117(C2×D3)⋊C8—21no—
118(C2×D3)⋊C8—61no—
119C23×C32C22×C411yescharacteristic
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3C22⋊C411yescharacteristic
127C22×C3×D3C22⋊C411yescharacteristic
128C22×C3×D3C2×C812yes—
129C22×C3×D3C2×C812yescomplemented
130C22×C3×D3M1612yes—
131C2×C32×C4—41no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3C2×C812yescomplemented
139C2×C3×Dic3—22no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3C22⋊C411yescharacteristic
143C2×C3×Dic3C22⋊C411yescharacteristic
144C3×C4×D3—22no—
145C3×C4×D3—22no—
146C3×C4×D3—41no—
147C3×C4×D3—41no—
148#625—24no—
149#625—24no—
150D3×Dic3—42no—
151D3×Dic3—42no—
152C32×C8—41no—
153C3⋊(C3⋊C8)—41no—
154C3×C3⋊C8—41no—
155C3×C3⋊C8—41no—
156C2×C4×D4—91no—
157C2×C22⋊C8—31no—
158C2×C22⋊C8—91no—
159#324—91no—
160#324—91no—
161#323—31no—
162#323—91no—
163C24×C3—31no—
164C24×C3—31no—
165C23×D3C4×D311yescharacteristic
166C23×D3C4×D311yescharacteristic
167C22×C3×C4—21no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C22×C3×C4—122no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—34no—
178C2×#67—34no—
179C2×#67—61no—
180C2×#67—61no—
181C2×#67—62no—
182C2×#67—62no—
183C2×#67—61no—
184C2×#67—61no—
185C22×Dic3—31no—
186C22×Dic3—31no—
187C22×Dic3—31no—
188C22×Dic3—31no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—122no—
194C22×Dic3C4×D311yescharacteristic
195C22×Dic3C4×D311yescharacteristic
196C2×C4×D3—42no—
197C2×C4×D3—61no—
198C2×C4×D3—61no—
199C2×C4×D3—122no—
200C2×C4×D3D1211yescharacteristic
201C2×C4×D3D1211yescharacteristic
202C2×C4×D3#6711yescharacteristic
203C2×C4×D3#6711yescharacteristic
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—41no—
207C2×C3×C8—61no—
208C2×C3×C8—61no—
209C2×C3×C8—122no—
210C3×C22⋊C4—61no—
211C3×C22⋊C4—61no—
212#217—61no—
213#217—61no—
214(C2×D3)⋊C4—21no—
215(C2×D3)⋊C4—21no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220Dic3⋊C4—61no—
221Dic3⋊C4—61no—
222Dic3⋊C4—121no—
223Dic3⋊C4—121no—
224C4×Dic3—61no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—61no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—121no—
233C2×C3⋊C8—122no—
234D3×C8—42no—
235D3×C8—122no—
236C22×C32—21no—
237C22×C32—21no—
238C22×C32C2×C22⋊C411yescharacteristic
239C22×C32C22×C811yescharacteristic
240C22×C32C2×M1611yescharacteristic
241C2×C3×D3—21no—
242C2×C3×D3—21no—
243C2×C3×D3—21no—
244C2×C3×D3—21no—
245C2×C3×D3—22no—
246C2×C3×D3—42no—
247C2×C3×D3—42no—
248C2×C3×D3—42no—
249C2×C3×D3—41no—
250C2×C3×D3—41no—
251C2×C3×D3—42no—
252C2×C3×D3C22⋊C812yes—
253C2×C3×D3C22⋊C812yes—
254C32×C4—21no—
255C32×C4—21no—
256C3⋊Dic3—22no—
257C3⋊Dic3—41no—
258C3×Dic3—21no—
259C3×Dic3—41no—
260C3×Dic3#9912yes—
261C22×D4—91no—
262C23×C4—31no—
263C23×C4—91no—
264C22×C8—61no—
265C22×C8—181no—
266C4×D4—181no—
267C4×D4—181no—
268C4×D4—181no—
269C4×D4—181no—
270C2×C4⋊C4—91no—
271C2×C22⋊C4—31no—
272C2×C22⋊C4—91no—
273C2×C42—91no—
274C22⋊C8—31no—
275C22⋊C8—31no—
276C22⋊C8—61no—
277C22⋊C8—91no—
278C22⋊C8—181no—
279C22⋊C8D3211yescharacteristic
280C23×C3—21no—
281C23×C3—31no—
282C23×C3—31no—
283C23×C3—32no—
284C23×C3—32no—
285C23×C3—32no—
286C23×C3—61no—
287C23×C3—61no—
288C23×C3—121no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3C2×C4×D311yescharacteristic
293C23×C3C2×C4×D311yescharacteristic
294C22×D3—21no—
295C22×D3—21no—
296C22×D3—41no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—41no—
300C22×D3D3×C812yes—
301C22×D3D3×C812yescomplemented
302C22×D3ΓL(1,𝔽25)12yes—
303C22×D3(C2×D3)⋊C411yescharacteristic
304C22×D3(C2×D3)⋊C411yescharacteristic
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—31no—
308C2×C3×C4—31no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—61no—
315C2×C3×C4—81no—
316C2×C3×C4—121no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4C2×D1211yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323#67—64no—
324#67—64no—
325#67—64no—
326#67—64no—
327C2×Dic3—22no—
328C2×Dic3—21no—
329C2×Dic3—32no—
330C2×Dic3—32no—
331C2×Dic3—41no—
332C2×Dic3—62no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—121no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—241no—
347C2×Dic3(C2×D3)⋊C411yescharacteristic
348C2×Dic3(C2×D3)⋊C411yescharacteristic
349C4×D3—22no—
350C4×D3—22no—
351C4×D3—41no—
352C4×D3—41no—
353C4×D3—122no—
354C4×D3—122no—
355C3×C8—41no—
356C3×C8—41no—
357C3×C8—81no—
358C3×C8—121no—
359C3×C8—121no—
360C3⋊C8—41no—
361C3⋊C8—41no—
362C3⋊C8—121no—
363C3⋊C8—121no—
364C3⋊C8—241no—
365C2×C32—21no—
366C2×C32—21no—
367C2×C32C2×C22⋊C811yescharacteristic
368C2×C32C2×#9911yescharacteristic
369C2×C32#41311yescharacteristic
370C3×D3—22no—
371C3×D3—22no—
372C3×D3—42no—
373C24—31no—
374C24—31no—
375C2×D4—94no—
376C2×D4—181no—
377C2×D4—181no—
378C2×D4—182no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—91no—
386C22×C4—91no—
387C22×C4—122no—
388C22×C4—181no—
389C22×C4—181no—
390C22×C4—362no—
391C22×C4C2×D3211yescharacteristic
392C2×C8—21no—
393C2×C8—61no—
394C2×C8—61no—
395C2×C8—122no—
396C2×C8—181no—
397C2×C8—362no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C22⋊C4—61no—
401C22⋊C4—61no—
402C22⋊C4—181no—
403C22⋊C4—181no—
404C42—181no—
405C42—181no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—32no—
414C22×C3—32no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—61no—
418C22×C3—61no—
419C22×C3—61no—
420C22×C3—61no—
421C22×C3—62no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3—121no—
427C22×C3—121no—
428C22×C3D3×C22⋊C411yescharacteristic
429C22×C3C2×D3×C811yescharacteristic
430C22×C3C2×D3×C811yescharacteristic
431C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
432C22×C3D3×M1611yescharacteristic
433C22×C3C2×(C2×D3)⋊C411yescharacteristic
434C2×D3—21no—
435C2×D3—21no—
436C2×D3—21no—
437C2×D3—21no—
438C2×D3—22no—
439C2×D3—42no—
440C2×D3—42no—
441C2×D3—42no—
442C2×D3—41no—
443C2×D3—41no—
444C2×D3—42no—
445C2×D3(C2×D3)⋊C812yes—
446C2×D3(C2×D3)⋊C812yes—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—32no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—61no—
455C3×C4—121no—
456Dic3—21no—
457Dic3—41no—
458Dic3—62no—
459Dic3—62no—
460Dic3—122no—
461Dic3—121no—
462Dic3—121no—
463Dic3—241no—
464Dic3#80612yes—
465C32#145911yescharacteristic, complemented, Sylow
466C23—31no—
467C23—31no—
468C23—32no—
469C23—32no—
470C23—32no—
471C23—61no—
472C23—61no—
473C23—121no—
474C23—121no—
475C23—121no—
476C23—121no—
477C23C4×D3211yescharacteristic
478D4—184no—
479D4—184no—
480C2×C4—31no—
481C2×C4—31no—
482C2×C4—41no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—61no—
487C2×C4—92no—
488C2×C4—121no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—362no—
495C2×C4—362no—
496C2×C4—361no—
497C2×C4D3×D1211yescharacteristic
498C2×C4D3×#6711yescharacteristic
499C8—41no—
500C8—121no—
501C8—121no—
502C8—361no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—41no—
511C2×C3—41no—
512C2×C3—62no—
513C2×C3—62no—
514C2×C3—122no—
515C2×C3D3×C22⋊C811yescharacteristic
516C2×C3D3×#9911yescharacteristic
517C2×C3#474511yescharacteristic
518C2×C3C2×#80611yescharacteristic
519C2×C3C2×(C2×D3)⋊C811yescharacteristic
520C2×C3#513211yescharacteristic
521D3—22no—
522D3—22no—
523D3—42no—
524C22—21no—
525C22—21no—
526C22—32no—
527C22—32no—
528C22—61no—
529C22—61no—
530C22—61no—
531C22—61no—
532C22—62no—
533C22—122no—
534C22—122no—
535C22—122no—
536C22—122no—
537C22—121no—
538C22—121no—
539C22D32×C811yescharacteristic
540C22D3×ΓL(1,𝔽25)11yescharacteristic
541C22D3×(C2×D3)⋊C411yescharacteristic
542C4—21no—
543C4—21no—
544C4—32no—
545C4—61no—
546C4—121no—
547C4—182no—
548C4—361no—
549C3—21no—
550C3#6811911yescharacteristic, complemented
551C3#6991911yescharacteristic, complemented
552C2—21no—
553C2—21no—
554C2—62no—
555C2—62no—
556C2—122no—
557C2D3×#80611yescharacteristic
558C2D3×(C2×D3)⋊C811yescharacteristic
559C2#1059100611yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC22×C32C22×C8
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#625C4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1459
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×D3×C22⋊C8C2semidirect
3. D3×#830C2semidirect
4. #10589335C2semidirect
5. C3×#4468C2semidirect
6. #10589148C2semidirect
7. #10589145C2semidirect
34. D3×C22⋊C8D3semidirect
43. #4468D3semidirect
59. C2×#625C8semidirect
129. C22×C3×D3C2×C8semidirect
138. C2×C3⋊Dic3C2×C8semidirect
301. C22×D3D3×C8semidirect
465. C32#1459semidirect
550. C3#68119semidirect
551. C3#69919semidirect

Maximal subgroups

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

subgroupindex
C2×#638792
C3×D3×C22⋊C82
D3×#8302
#105893352
C3×#44682
#105891482
#105891452
#699193
#681193