Finite Group Databasebeta

← #11807842

Subgroups — #11807842

Order 1152.

1089 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
2C3×#5212C211yesmaximal, characteristic
3C3×#5211C211yesmaximal, characteristic
4#10591703C212yesmaximal
5#10591703C212yesmaximal
6#10591273C212yesmaximal, complemented
7#10591271C212yesmaximal, complemented
8#10591264C212yesmaximal, complemented
9#10591263C212yesmaximal, complemented
10#74062—31nomaximal
11#73886—31nomaximal
12C23×C32×C4C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C2×#3757C2212yes—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16#64133C418yescomplemented
17C2×#3750C2212yes—
18C2×C3×#217C2212yes—
19C2×C3×#217C2211yescharacteristic
20C2×C3×#217C2211yescharacteristic
21C2×C3×C4⋊Dic3C2212yes—
22C2×#3724C2212yes—
23C2×#3724C2212yes—
24C2×Dic32C2212yes—
25C2×Dic32C2212yes—
26C3×C3⋊#95C2211yescharacteristic
27C3×C3⋊#95C2211yescharacteristic
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33#63579C2212yes—
34C2×#924—31no—
35C2×#924—31no—
36C2×#924—61no—
37C3×#381—31no—
38C3×#380—31no—
39#5212D311yescharacteristic
40#5211D311yescharacteristic
41#4978—32no—
42#4976—32no—
43#4945—32no—
44#4945—32no—
45#4944—32no—
46#4944—32no—
47#4655—32no—
48#4654—32no—
49#4653—32no—
50#4647—32no—
51#4646—32no—
52#4646—32no—
53C24×C32C2311yescharacteristic
54C22×C32×C4—42no—
55C22×C32×C4C2×C414yes—
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2312yes—
60C2×#634—42no—
61C2×#634C2×C414yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66#3757C2×C418yes—
67C4⋊(C3⋊Dic3)C2×C414yes—
68#3750C2×C418yes—
69C3×#217—41no—
70C3×#217—42no—
71C3×#217—41no—
72C3×C4⋊Dic3—42no—
73#3724—42no—
74#3724—42no—
75Dic32—42no—
76Dic32—42no—
77#2378—91noSylow
78C23×C3×C4—21no—
79C23×C3×C4C2×D311yescharacteristic
80C23×C3×C4C2×D311yescharacteristic
81C22×Dic6—31no—
82C22×Dic6—31no—
83C22×Dic6—61no—
84C2×C3×C4⋊C4—32no—
85C2×C3×C22⋊C4—31no—
86C2×C3×C22⋊C4—32no—
87C2×C3×C22⋊C4—31no—
88C2×#217—32no—
89C2×#217—32no—
90C2×#217—62no—
91C2×#217C2×D311yescharacteristic
92C2×#217C2×D312yes—
93C2×#217C2×D311yescharacteristic
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—61no—
97C2×C4⋊Dic3C2×D312yes—
98#924—38no—
99#924—38no—
100#924—68no—
101C2×Dic3⋊C4—32no—
102C2×Dic3⋊C4—32no—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—32no—
107C2×Dic3⋊C4—62no—
108C2×C4×Dic3—32no—
109C2×C4×Dic3—32no—
110C2×C4×Dic3—32no—
111C2×C4×Dic3—32no—
112C3×#95—32no—
113C3×#95—32no—
114C3×#95—31no—
115C3×#95—31no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95C2×D312yes—
125C3⋊#95C2×D312yes—
126C3⋊#95C2×D311yescharacteristic
127C3⋊#95C2×D311yescharacteristic
128C23×C32—22no—
129C23×C32—21no—
130C23×C32—22no—
131C23×C32—21no—
132C23×C32C22×C412yes—
133C23×C32C2411yescharacteristic
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—44no—
137C2×C32×C4C22×C412yes—
138C2×C32×C4C22×C412yes—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3C22×C414yes—
144C2×C3⋊Dic3C22×C414yes—
145#634—44no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C22⋊Q8—91no—
159#391—92no—
160#389—92no—
161#388—92no—
162#388—92no—
163#387—92no—
164#387—92no—
165#381—31no—
166#380—31no—
167C24×C3—21no—
168C24×C3C22×D311yescharacteristic
169C24×C3C22×D311yescharacteristic
170C22×C3×C4—24no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4—32no—
176C22×C3×C4—32no—
177C22×C3×C4—42no—
178C22×C3×C4—42no—
179C22×C3×C4—44no—
180C22×C3×C4C4×D314yes—
181C22×C3×C4C4×D314yes—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×Dic3—32no—
187C22×Dic3—32no—
188C22×Dic3—32no—
189C22×Dic3—32no—
190C22×Dic3—62no—
191C22×Dic3—62no—
192C22×Dic3C22×D312yes—
193C22×Dic3C22×D312yes—
194C22×Dic3C22×D312yes—
195C22×Dic3C22×D312yes—
196C2×Dic6—34no—
197C2×Dic6—34no—
198C2×Dic6—64no—
199C2×Dic6—122no—
200C2×Dic6—122no—
201C2×Dic6—124no—
202C3×C4⋊C4—122no—
203C3×C22⋊C4—122no—
204C3×C22⋊C4—121no—
205C3×C22⋊C4—121no—
206#217—38no—
207#217—38no—
208#217—41no—
209#217—42no—
210#217—41no—
211#217—68no—
212C4⋊Dic3—34no—
213C4⋊Dic3—34no—
214C4⋊Dic3—42no—
215C4⋊Dic3—64no—
216Dic3⋊C4—38no—
217Dic3⋊C4—38no—
218Dic3⋊C4—68no—
219Dic3⋊C4—122no—
220Dic3⋊C4—122no—
221Dic3⋊C4—122no—
222Dic3⋊C4—122no—
223C4×Dic3—122no—
224C4×Dic3—122no—
225C4×Dic3—122no—
226C4×Dic3—122no—
227C22×C32—22no—
228C22×C32—22no—
229C22×C32—22no—
230C22×C32—42no—
231C22×C32—42no—
232C22×C32C23×C411yescharacteristic
233C22×C32H(5,𝔽2)12yes—
234C22×C32H(5,𝔽2)11yescharacteristic
235C22×C322−1+411yescharacteristic
236C22×C322−1+412yes—
237C32×C4—22no—
238C32×C4—22no—
239C3⋊Dic3—24no—
240C3⋊Dic3—24no—
241C3×Dic3—42no—
242C3×Dic3—42no—
243C3×Dic3—42no—
244C3×Dic3—42no—
245C22×Q8—91no—
246C23×C4D3211yescharacteristic
247C22⋊Q8—98no—
248C2×C4⋊C4—32no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—92no—
251C2×C4⋊C4—92no—
252C2×C4⋊C4—92no—
253C2×C22⋊C4—31no—
254C2×C22⋊C4—31no—
255C2×C22⋊C4—32no—
256C2×C22⋊C4—92no—
257C2×C42—92no—
258C2×C42—92no—
259#95—32no—
260#95—31no—
261#95—32no—
262#95—31no—
263#95—92no—
264#95—92no—
265#95—92no—
266#95—92no—
267C23×C3—24no—
268C23×C3—21no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—21no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3—21no—
277C23×C3—22no—
278C23×C3—42no—
279C23×C3—41no—
280C23×C3—41no—
281C23×C3C2×C4×D312yes—
282C23×C3C2×C4×D312yes—
283C23×C3C23×D311yescharacteristic
284C23×C3C23×D311yescharacteristic
285C2×C3×C4—24no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—42no—
293C2×C3×C4—44no—
294C2×C3×C4—44no—
295C2×C3×C4—48no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4C2×C4×D312yes—
309C2×C3×C4C2×C4×D312yes—
310C2×C3×C4C2×C4×D312yes—
311C2×C3×C4C2×C4×D312yes—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—34no—
325C2×Dic3—34no—
326C2×Dic3—34no—
327C2×Dic3—34no—
328C2×Dic3—64no—
329C2×Dic3—64no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—122no—
339C2×Dic3—122no—
340C2×Dic3—122no—
341C2×Dic3—122no—
342Dic6—124no—
343Dic6—124no—
344Dic6—128no—
345C2×C32—42no—
346C2×C32#51811yescharacteristic
347C2×C32#51911yescharacteristic
348C2×C32#52011yescharacteristic
349C2×C32#56212yes—
350C2×C32#56312yes—
351C24C2×D3211yescharacteristic
352C2×Q8—94no—
353C2×Q8—362no—
354C22×C4—32no—
355C22×C4—32no—
356C22×C4—32no—
357C22×C4—32no—
358C22×C4—42no—
359C22×C4—92no—
360C22×C4—92no—
361C22×C4#62414yes—
362C22×C4C2×D3211yescharacteristic
363C22×C4C2×D3211yescharacteristic
364C4⋊C4—98no—
365C4⋊C4—94no—
366C4⋊C4—122no—
367C4⋊C4—362no—
368C4⋊C4—362no—
369C22⋊C4—98no—
370C22⋊C4—121no—
371C22⋊C4—121no—
372C22⋊C4—122no—
373C42—362no—
374C42—362no—
375C22×C3—24no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—21no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—22no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—44no—
390C22×C3—44no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—42no—
394C22×C3—42no—
395C22×C3C22×C4×D311yescharacteristic
396C22×C3C22×C4×D311yescharacteristic
397C22×C3#100411yescharacteristic
398C22×C3#100412yes—
399C22×C3#100412yes—
400C22×C3#100711yescharacteristic
401C22×C3#100911yescharacteristic
402C22×C3#101011yescharacteristic
403C22×C3#101012yes—
404C22×C3#101012yes—
405C3×C4—24no—
406C3×C4—22no—
407C3×C4—22no—
408C3×C4—22no—
409C3×C4—22no—
410C3×C4—42no—
411C3×C4—122no—
412C3×C4—122no—
413C3×C4—122no—
414C3×C4—122no—
415Dic3—42no—
416Dic3—42no—
417Dic3—42no—
418Dic3—42no—
419Dic3—64no—
420Dic3—64no—
421Dic3—64no—
422Dic3—64no—
423Dic3—124no—
424Dic3—124no—
425C32#237811yescharacteristic, complemented, Sylow
426C23—21no—
427C23—22no—
428C23—21no—
429C23—22no—
430C23C2×#62412yes—
431C23C22×D3211yescharacteristic
432Q8—364no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—44no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—94no—
449C2×C4—94no—
450C2×C4—182no—
451C2×C4—182no—
452C2×C4—182no—
453C2×C4—182no—
454C2×C4C2×#62412yes—
455C2×C4C2×#62412yes—
456C2×C3—21no—
457C2×C3—22no—
458C2×C3—22no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—44no—
462C2×C3—42no—
463C2×C3—42no—
464C2×C3#548611yescharacteristic
465C2×C3#548611yescharacteristic
466C2×C3#550411yescharacteristic
467C2×C3#551611yescharacteristic
468C2×C3#551611yescharacteristic
469C2×C3#552311yescharacteristic
470C2×C3#562112yes—
471C2×C3#564612yes—
472C2×C3#565112yes—
473C2×C3#566712yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—42no—
478C22—42no—
479C22#6429711yescharacteristic
480C22#6429812yes—
481C22#6430711yescharacteristic
482C22C22×#62411yescharacteristic
483C22#6433012yes—
484C4—22no—
485C4—22no—
486C4—122no—
487C4—122no—
488C4—122no—
489C4—122no—
490C4—184no—
491C4—184no—
492C3—21no—
493C3#7388611yescharacteristic, complemented
494C3#7406211yescharacteristic, complemented
495C2—42no—
496C2#1059482811yescharacteristic
497C2#1059497212yes—
498C2#1059497512yes—
499C2#1059499011yescharacteristic
500C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2378
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591273C2semidirect
7. #10591271C2semidirect
8. #10591264C2semidirect
9. #10591263C2semidirect
16. #64133C4semidirect
425. C32#2378semidirect
493. C3#73886semidirect
494. C3#74062semidirect

Maximal subgroups

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

subgroupindex
C2×#641332
C3×#52122
C3×#52112
#105917032
#105912732
#105912712
#105912642
#105912632
#740623
#738863