Finite Group Databasebeta

← #11803155

Subgroups — #11803155

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63902C211yesmaximal, characteristic
2C4×#3750C211yesmaximal, characteristic, complemented
3C3×#4940C212yesmaximal, complemented
4#10591386C212yesmaximal
5#10591366C212yesmaximal, complemented
6#10591362C212yesmaximal, complemented
7#10591286C212yesmaximal, complemented
8#10591256C212yesmaximal, complemented
9#10591252C211yesmaximal, characteristic, complemented
10#75458—32nomaximal
11C22×#625C2211yescharacteristic
12C22×D3×Dic3C2212yes—
13C2×C32×C42C2211yescharacteristic
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4C2212yes—
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×#3724C2211yescharacteristic
22C2×Dic3⋊Dic3C2212yes—
23C2×(C2×D3)⋊Dic3C2212yes—
24C2×(C2×D3)⋊Dic3C2212yes—
25C2×Dic32C2212yes—
26#63902C418yescomplemented
27#63658C2212yes—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30#63579C2211yescharacteristic
31#63579C2211yescharacteristic
32#63579C2212yes—
33C2×#67⋊C4—32no—
34C3×#388—32no—
35#4987—32no—
36#4976—32no—
37#4957—32no—
38#4957—32no—
39#4951—32no—
40#4943—32no—
41#4942—32no—
42#4940D312yescomplemented
43C4×Dic3⋊C4—32no—
44C4×Dic3⋊C4—61no—
45#4669—32no—
46#4664—32no—
47#4648—32no—
48#4647—32no—
49C23×C3×D3C2312yes—
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2311yescharacteristic
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C2×#625—24no—
59C2×#625C2×C414yes—
60C2×D3×Dic3—42no—
61C2×D3×Dic3—42no—
62C2×D3×Dic3C2×C418yes—
63C32×C42—41no—
64#3750—24no—
65C4×C3⋊Dic3—41no—
66C4×C3⋊Dic3C2×C414yes—
67C3×(C2×D3)⋊C4—42no—
68C3×(C2×D3)⋊C4—42no—
69C3×(C2×D3)⋊C4C2×C418yes—
70C3×Dic3⋊C4—42no—
71#3724C2×C414yes—
72Dic3⋊Dic3—42no—
73(C2×D3)⋊Dic3—42no—
74(C2×D3)⋊Dic3—42no—
75Dic32—24no—
76#2319—91noSylow
77C22×#67—32no—
78C23×Dic3—32no—
79C22×C4×D3—32no—
80C2×C3×C4⋊C4—32no—
81C2×C3×C22⋊C4—32no—
82C2×C3×C22⋊C4—32no—
83C2×C3×C22⋊C4—32no—
84C2×C3×C42—21no—
85C2×C3×C42C2×D312yes—
86C2×#217—32no—
87C2×#217—32no—
88C2×(C2×D3)⋊C4—32no—
89C2×(C2×D3)⋊C4—32no—
90C2×(C2×D3)⋊C4C2×D312yes—
91C2×(C2×D3)⋊C4C2×D312yes—
92C2×(C2×D3)⋊C4C2×D312yes—
93C2×C4⋊Dic3—32no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—32no—
96C2×Dic3⋊C4—32no—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4—62no—
99C2×Dic3⋊C4C2×D312yes—
100C2×C4×Dic3—32no—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—32no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3—61no—
106#67⋊C4—316no—
107C3×#95—32no—
108C3×#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—62no—
116C3⋊#95C2×D312yes—
117C3⋊#95C2×D312yes—
118C23×C32C2411yescharacteristic
119C22×C3×D3—22no—
120C22×C3×D3—22no—
121C22×C3×D3—22no—
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3C22×C414yes—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4C22×C412yes—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3C22×C412yes—
137C2×C3⋊Dic3C22×C412yes—
138C2×C3⋊Dic3#4114yes—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3C22×C414yes—
148#625—28no—
149D3×Dic3—48no—
150C2×C4×D4—91no—
151#390—92no—
152#389—92no—
153#388—32no—
154#388—92no—
155#381—92no—
156#380—92no—
157C4×C4⋊C4—91no—
158#376—91no—
159C24×C3—32no—
160C23×D3C22×D312yes—
161C22×C3×C4—21no—
162C22×C3×C4—22no—
163C22×C3×C4—32no—
164C22×C3×C4—32no—
165C22×C3×C4—32no—
166C22×C3×C4C22×D312yes—
167C22×C3×C4C22×D312yes—
168C22×C3×C4C22×D312yes—
169C2×#67—38no—
170C2×#67—64no—
171C2×#67—64no—
172C22×Dic3—32no—
173C22×Dic3—32no—
174C22×Dic3—38no—
175C22×Dic3—32no—
176C22×Dic3—32no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—62no—
180C22×Dic3—122no—
181C22×Dic3—122no—
182C22×Dic3C22×D312yes—
183C22×Dic3C22×D312yes—
184C22×Dic3C22×D312yes—
185C2×C4×D3—38no—
186C2×C4×D3—122no—
187C2×C4×D3—122no—
188C3×C4⋊C4—122no—
189C3×C22⋊C4—38no—
190C3×C22⋊C4—122no—
191C3×C22⋊C4—122no—
192C3×C42—42no—
193C3×C42—42no—
194#217—122no—
195#217—122no—
196(C2×D3)⋊C4—42no—
197(C2×D3)⋊C4—42no—
198(C2×D3)⋊C4—122no—
199(C2×D3)⋊C4—122no—
200(C2×D3)⋊C4C4×D318yes—
201C4⋊Dic3—122no—
202Dic3⋊C4—38no—
203Dic3⋊C4—42no—
204Dic3⋊C4—64no—
205Dic3⋊C4—64no—
206Dic3⋊C4—68no—
207Dic3⋊C4—122no—
208C4×Dic3—38no—
209C4×Dic3—64no—
210C4×Dic3—64no—
211C4×Dic3—64no—
212C4×Dic3—122no—
213C4×Dic3—122no—
214C22×C32C23×C411yescharacteristic
215C22×C32C2×#4112yes—
216C22×C32H(5,𝔽2)11yescharacteristic
217C22×C32H(5,𝔽2)12yes—
218C22×C322−1+411yescharacteristic
219C2×C3×D3—24no—
220C2×C3×D3—24no—
221C2×C3×D3—24no—
222C2×C3×D3—42no—
223C2×C3×D3—42no—
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226C32×C4—22no—
227C32×C4—42no—
228C3⋊Dic3—22no—
229C3⋊Dic3—42no—
230C3⋊Dic3#11714yes—
231C3×Dic3—24no—
232C3×Dic3—42no—
233C3×Dic3—42no—
234C22×D4—91no—
235C23×C4—92no—
236C4×D4—98no—
237C2×C4⋊C4—32no—
238C2×C4⋊C4—91no—
239C2×C4⋊C4—92no—
240C2×C4⋊C4—92no—
241C2×C22⋊C4—32no—
242C2×C22⋊C4—32no—
243C2×C22⋊C4—32no—
244C2×C22⋊C4—92no—
245C2×C22⋊C4—92no—
246C2×C42—91no—
247C2×C42—92no—
248C2×C42—91no—
249C2×C42D3211yescharacteristic
250#95—32no—
251#95—32no—
252#95—91no—
253#95—91no—
254#95—92no—
255#95—92no—
256C23×C3—21no—
257C23×C3—34no—
258C23×C3—62no—
259C23×C3—62no—
260C23×C3—62no—
261C23×C3—62no—
262C23×C3—62no—
263C23×C3—62no—
264C23×C3C23×D312yes—
265C22×D3—22no—
266C22×D3—22no—
267C22×D3—22no—
268C22×D3—22no—
269C22×D3—22no—
270C22×D3—22no—
271C22×D3C2×C4×D314yes—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—24no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—34no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4C2×C4×D314yes—
296#67—616no—
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—34no—
306C2×Dic3—34no—
307C2×Dic3—34no—
308C2×Dic3—34no—
309C2×Dic3—62no—
310C2×Dic3—64no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—64no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—122no—
322C2×Dic3—122no—
323C2×Dic3—122no—
324C2×Dic3—128no—
325C2×Dic3C2×C4×D314yes—
326C4×D3—128no—
327C2×C32C2×#11711yescharacteristic
328C2×C32#51811yescharacteristic
329C2×C32#52011yescharacteristic
330C2×C32#54012yes—
331C2×C32#54212yes—
332C3×D3—44no—
333C24—32no—
334C2×D4—94no—
335C2×D4—184no—
336C22×C4—32no—
337C22×C4—32no—
338C22×C4—32no—
339C22×C4—98no—
340C22×C4—91no—
341C22×C4—91no—
342C22×C4—92no—
343C22×C4—362no—
344C22×C4—362no—
345C22×C4C2×D3212yes—
346C22×C4C2×D3211yescharacteristic
347C4⋊C4—94no—
348C4⋊C4—122no—
349C4⋊C4—184no—
350C4⋊C4—362no—
351C22⋊C4—38no—
352C22⋊C4—122no—
353C22⋊C4—122no—
354C22⋊C4—362no—
355C22⋊C4—362no—
356C42—41no—
357C42—94no—
358C42—184no—
359C42—361no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—64no—
366C22×C3—64no—
367C22×C3—64no—
368C22×C3—122no—
369C22×C3—122no—
370C22×C3—122no—
371C22×C3—122no—
372C22×C3C22×C4×D312yes—
373C22×C3#100412yes—
374C22×C3#100412yes—
375C22×C3D3×#4112yes—
376C22×C3D3×#4112yes—
377C22×C3#100912yes—
378C22×C3#101012yes—
379C2×D3—24no—
380C2×D3—24no—
381C2×D3—24no—
382C2×D3—42no—
383C2×D3—42no—
384C2×D3—42no—
385C2×D3—42no—
386C3×C4—24no—
387C3×C4—24no—
388C3×C4—44no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—64no—
392C3×C4—122no—
393C3×C4—122no—
394Dic3—24no—
395Dic3—38no—
396Dic3—42no—
397Dic3—42no—
398Dic3—64no—
399Dic3—64no—
400Dic3—122no—
401Dic3—124no—
402Dic3—122no—
403Dic3—122no—
404C32#231911yescharacteristic, complemented, Sylow
405C23—34no—
406C23—62no—
407C23—62no—
408C23—62no—
409C23—62no—
410C23—62no—
411C23—62no—
412C23C22×D3211yescharacteristic
413D4—188no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—34no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—92no—
429C2×C4—94no—
430C2×C4—92no—
431C2×C4—182no—
432C2×C4—182no—
433C2×C4—182no—
434C2×C4—182no—
435C2×C4—368no—
436C2×C4C4×D3212yes—
437C2×C3—21no—
438C2×C3—22no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—22no—
442C2×C3—124no—
443C2×C3D3×#11712yes—
444C2×C3#554512yes—
445C2×C3#554612yes—
446C2×C3#561512yes—
447C2×C3#566312yes—
448C2×C3#566912yes—
449C2×C3#571012yes—
450D3—44no—
451C22—64no—
452C22—64no—
453C22—64no—
454C22—122no—
455C22—122no—
456C22—122no—
457C22—122no—
458C22#6429811yescharacteristic
459C22C2×C4×D3211yescharacteristic
460C22#6430612yes—
461C22#6430712yes—
462C22#6433011yescharacteristic
463C4—22no—
464C4—42no—
465C4—64no—
466C4—94no—
467C4—122no—
468C4—122no—
469C4—182no—
470C4—362no—
471C3—21no—
472C3#7545812yescomplemented
473C2—124no—
474C2#1059394412yes—
475C2#1059399211yescharacteristic
476C2#1059399611yescharacteristic
477C2#1059487611yescharacteristic
478C2#1059503112yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenterC2×C42D32
hypocenterC32#2319
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×#3750C2semidirect
3. C3×#4940C2semidirect
5. #10591366C2semidirect
6. #10591362C2semidirect
7. #10591286C2semidirect
8. #10591256C2semidirect
9. #10591252C2semidirect
26. #63902C4semidirect
42. #4940D3semidirect
404. C32#2319semidirect
472. C3#75458semidirect

Maximal subgroups

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

subgroupindex
C2×#639022
C4×#37502
C3×#49402
#105913862
#105913662
#105913622
#105912862
#105912562
#105912522
#754583