Finite Group Databasebeta

← #11788350

Subgroups — #11788350

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic
2C22×C3×#208C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4C2×#63561C212yesmaximal, complemented
5#10589168C212yesmaximal, complemented
6#72003—31nomaximal
7#69986—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×#634C2211yescharacteristic
10C2×#3757C412yes—
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12#64133—21no—
13#64133—21no—
14#64133—21no—
15#64133—21no—
16C2×#3750C412yes—
17C2×C3×#208—21no—
18C2×C3×#208—24no—
19C2×C3×#208C2212yes—
20C2×C3×#208C2212yes—
21C22×C3×C3⋊C8—21no—
22C3×#830—21no—
23C3×#830—21no—
24#63561—24no—
25C22×C3×M16—31no—
26C2×#924—31no—
27C2×#924—31no—
28C2×#924—61no—
29C22×#208D311yescharacteristic
30C3×#407—31no—
31#5207D311yescharacteristic
32C2×#824—32no—
33C2×#824—32no—
34#4554—32no—
35#4554—32no—
36C24×C32C2×C411yescharacteristic
37C22×C32×C4—22no—
38C22×C32×C4—22no—
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3C2×C412yes—
46C22×C3⋊Dic3C2×C412yes—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—22no—
50C2×#634—22no—
51#3757—22no—
52#3757—22no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55#3750—22no—
56#3750—22no—
57C3×#208—24no—
58C3×#208—22no—
59C3×#208—22no—
60C3×#208—22no—
61C3×#208D414yes—
62C2×C3×C3⋊C8—24no—
63C2×C3×C3⋊C8—22no—
64C2×C3×C3⋊C8—22no—
65#1901—91noSylow
66C23×C3×C4—21no—
67C23×C3×C4C2×D311yescharacteristic
68C23×C3×C4C2×D311yescharacteristic
69C22×Dic6—31no—
70C22×Dic6—31no—
71C22×Dic6—61no—
72C2×C3×M16—32no—
73C2×C3×M16—32no—
74C2×C3×M16—64no—
75C2×C3×M16—61no—
76C22×C3×C8—61no—
77C2×#217—32no—
78C2×#217—32no—
79C2×#217—62no—
80C2×C4⋊Dic3—31no—
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—61no—
83#924—62no—
84#924—62no—
85#924—62no—
86#924—62no—
87#924—61no—
88#924—61no—
89#924—61no—
90#924—61no—
91#924—61no—
92#924—61no—
93#924—61no—
94#924—61no—
95C2×Dic3⋊C4—32no—
96C2×Dic3⋊C4—32no—
97C2×Dic3⋊C4—62no—
98C2×#208—21no—
99C2×#208—24no—
100C2×#208C2×D312yes—
101C2×#208C2×D312yes—
102C22×C3⋊C8—21no—
103C3×C22⋊C8—61no—
104C3×C22⋊C8—61no—
105#830—21no—
106#830—21no—
107#824—64no—
108#824—64no—
109C23×C32—22no—
110C23×C32—22no—
111C23×C32—41no—
112C23×C32C22⋊C411yescharacteristic
113C23×C32C22⋊C411yescharacteristic
114C23×C32C22×C411yescharacteristic
115C2×C32×C4—22no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4C22⋊C411yescharacteristic
123C2×C32×C4C22⋊C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D412yes—
127C2×C32×C4#4112yes—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—24no—
131C2×C3⋊Dic3—42no—
132#634—41no—
133#634—42no—
134#634—41no—
135C3×C3⋊C8—24no—
136C3×C3⋊C8—42no—
137C22×M16—31no—
138C2×C22⋊Q8—91no—
139C2×#101—92no—
140#407—31no—
141#343—92no—
142C24×C3—21no—
143C24×C3C4×D311yescharacteristic
144C24×C3C4×D311yescharacteristic
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—42no—
156C22×C3×C4—42no—
157C22×C3×C4C4×D311yescharacteristic
158C22×C3×C4C4×D311yescharacteristic
159C22×C3×C4D1211yescharacteristic
160C22×C3×C4D1211yescharacteristic
161C22×C3×C4D1211yescharacteristic
162C22×C3×C4D1211yescharacteristic
163C22×C3×C4#6711yescharacteristic
164C22×C3×C4#6711yescharacteristic
165C22×C3×C4#6711yescharacteristic
166C22×C3×C4#6711yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×Dic3—32no—
170C22×Dic3—32no—
171C22×Dic3—32no—
172C22×Dic3—32no—
173C22×Dic3—62no—
174C22×Dic3—62no—
175C2×Dic6—62no—
176C2×Dic6—62no—
177C2×Dic6—61no—
178C2×Dic6—61no—
179C2×Dic6—62no—
180C2×Dic6—62no—
181C2×Dic6—62no—
182C2×Dic6—62no—
183C2×Dic6—61no—
184C2×Dic6—61no—
185C2×Dic6—122no—
186C2×Dic6—122no—
187C3×M16—34no—
188C3×M16—64no—
189C3×M16—62no—
190C3×M16—62no—
191C3×M16—62no—
192C2×C3×C8—64no—
193C2×C3×C8—62no—
194C2×C3×C8—62no—
195#217—64no—
196#217—64no—
197#217—62no—
198#217—62no—
199#217—62no—
200#217—62no—
201C4⋊Dic3—62no—
202C4⋊Dic3—62no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207Dic3⋊C4—64no—
208Dic3⋊C4—64no—
209Dic3⋊C4—62no—
210Dic3⋊C4—62no—
211Dic3⋊C4—62no—
212Dic3⋊C4—62no—
213#208—24no—
214#208—22no—
215#208—22no—
216#208—22no—
217#208#6714yes—
218C2×C3⋊C8—24no—
219C2×C3⋊C8—22no—
220C2×C3⋊C8—22no—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32—21no—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32—44no—
229C22×C32#10112yescomplemented
230C22×C32C2×C22⋊C411yescharacteristic
231C22×C32C4×D412yes—
232C32×C4—21no—
233C32×C4—21no—
234C32×C4#12011yescharacteristic
235C32×C4#12112yes—
236C32×C4#12311yescharacteristic
237C3⋊Dic3—42no—
238C3⋊Dic3—42no—
239C22×Q8—91no—
240C23×C4D3211yescharacteristic
241C2×M16—32no—
242C2×M16—32no—
243C2×M16—64no—
244C2×M16—61no—
245C22×C8—61no—
246C22⋊Q8—181no—
247C22⋊Q8—181no—
248C22⋊Q8—181no—
249C22⋊Q8—181no—
250C2×C4⋊C4—92no—
251C2×C4⋊C4—91no—
252C2×C22⋊C4—92no—
253#101—184no—
254C22⋊C8—61no—
255C22⋊C8—61no—
256C23×C3—24no—
257C23×C3—22no—
258C23×C3—22no—
259C23×C3—22no—
260C23×C3—22no—
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—21no—
264C23×C3—42no—
265C23×C3—41no—
266C23×C3—41no—
267C23×C3—42no—
268C23×C3(C2×D3)⋊C411yescharacteristic
269C23×C3(C2×D3)⋊C411yescharacteristic
270C23×C3(C2×D3)⋊C411yescharacteristic
271C23×C3(C2×D3)⋊C411yescharacteristic
272C23×C3C2×C4×D311yescharacteristic
273C23×C3C2×C4×D311yescharacteristic
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—22no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4(C2×D3)⋊C411yescharacteristic
302C2×C3×C4(C2×D3)⋊C411yescharacteristic
303C2×C3×C4(C2×D3)⋊C411yescharacteristic
304C2×C3×C4(C2×D3)⋊C411yescharacteristic
305C2×C3×C4C2×D1211yescharacteristic
306C2×C3×C4C2×D1211yescharacteristic
307C2×C3×C4#23512yes—
308C2×C3×C4D3×D412yes—
309C2×C3×C4#23712yes—
310C2×C3×C4C2×#6711yescharacteristic
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C2×#6712yes—
313C2×Dic3—64no—
314C2×Dic3—64no—
315C2×Dic3—64no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—64no—
321C2×Dic3—124no—
322C2×Dic3—124no—
323C2×Dic3—122no—
324C2×Dic3—122no—
325Dic6—122no—
326Dic6—122no—
327Dic6—124no—
328Dic6—121no—
329Dic6—121no—
330Dic6—121no—
331Dic6—122no—
332Dic6—122no—
333Dic6—121no—
334C3×C8—64no—
335C3×C8—122no—
336C3⋊C8—24no—
337C3⋊C8—42no—
338C2×C32—22no—
339C2×C32—22no—
340C2×C32—41no—
341C2×C32#38611yescharacteristic
342C2×C32C2×#10111yescharacteristic
343C2×C32#41311yescharacteristic
344C24#62411yescharacteristic
345C2×Q8—182no—
346C2×Q8—181no—
347C2×Q8—181no—
348C2×Q8—182no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—92no—
352C22×C4—92no—
353C22×C4#62411yescharacteristic
354C22×C4#62611yescharacteristic
355C22×C4#62611yescharacteristic
356C22×C4#62611yescharacteristic
357C22×C4#62611yescharacteristic
358C22×C4C2×D3211yescharacteristic
359M16—34no—
360M16—64no—
361M16—62no—
362M16—62no—
363M16—62no—
364C2×C8—64no—
365C2×C8—62no—
366C2×C8—62no—
367C4⋊C4—182no—
368C4⋊C4—182no—
369C4⋊C4—181no—
370C4⋊C4—181no—
371C22⋊C4—182no—
372C22⋊C4—182no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—21no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—44no—
398C22×C3—44no—
399C22×C3—48no—
400C22×C3#82412yescomplemented
401C22×C3#82412yescomplemented
402C22×C3#67⋊C412yes—
403C22×C3C2×(C2×D3)⋊C411yescharacteristic
404C22×C3C2×(C2×D3)⋊C411yescharacteristic
405C22×C3C4×#6712yes—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—22no—
413C3×C4—41no—
414C3×C4—41no—
415C3×C4#88211yescharacteristic
416C3×C4#88611yescharacteristic
417C3×C4#92911yescharacteristic
418C3×C4#93012yes—
419C3×C4#93912yes—
420C3×C4#95311yescharacteristic
421Dic3—124no—
422Dic3—124no—
423Dic3—122no—
424Dic3—122no—
425Dic3—122no—
426Dic3—122no—
427C32#190111yescharacteristic, complemented, Sylow
428C23—22no—
429C23—22no—
430C23—41no—
431C23#372211yescharacteristic
432C23#372211yescharacteristic
433C23C2×#62411yescharacteristic
434Q8—361no—
435Q8—361no—
436Q8—362no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—184no—
445C2×C4—182no—
446C2×C4—182no—
447C2×C4—362no—
448C2×C4#372211yescharacteristic
449C2×C4#372211yescharacteristic
450C2×C4#380412yes—
451C2×C4C2×#62611yescharacteristic
452C2×C4C2×#62611yescharacteristic
453C2×C4D3×#6712yes—
454C8—64no—
455C8—122no—
456C2×C3—24no—
457C2×C3—22no—
458C2×C3—22no—
459C2×C3—22no—
460C2×C3—22no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—42no—
465C2×C3—42no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3#495811yescharacteristic
469C2×C3#513211yescharacteristic
470C2×C3#513211yescharacteristic
471C2×C3C2×#82411yescharacteristic
472C2×C3C2×#82411yescharacteristic
473C2×C3#521311yescharacteristic
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—44no—
482C22#6356112yescomplemented
483C22#6395212yes—
484C22C2×#372211yescharacteristic
485C4—21no—
486C4—21no—
487C4—362no—
488C4—362no—
489C4#6396611yescharacteristic
490C4#6397711yescharacteristic
491C4#6397812yes—
492C3—21no—
493C3#6998611yescharacteristic, complemented
494C3#7200311yescharacteristic, complemented
495C2—22no—
496C2—22no—
497C2—41no—
498C2#1059107811yescharacteristic
499C2C2×#6356111yescharacteristic
500C2#1059171111yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1901
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63561C2semidirect
5. #10589168C2semidirect
229. C22×C32#101semidirect
400. C22×C3#824semidirect
401. C22×C3#824semidirect
427. C32#1901semidirect
482. C22#63561semidirect
493. C3#69986semidirect
494. C3#72003semidirect

Maximal subgroups

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

subgroupindex
C2×#641332
C22×C3×#2082
C3×#52072
C2×#635612
#105891682
#720033
#699863