Finite Group Databasebeta

← #11805102

Subgroups — #11805102

Order 1152.

1229 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic
2C3×Dic3×C22⋊C4C212yesmaximal
3#10591697C211yesmaximal, characteristic
4C2×#63579C211yesmaximal, characteristic
5#10591693C212yesmaximal
6#10591360C211yesmaximal, characteristic, complemented
7C4×#3724C211yesmaximal, characteristic, complemented
8#10591229C211yesmaximal, characteristic, complemented
9#10591222C211yesmaximal, characteristic, complemented
10#10591197C212yesmaximal, complemented
11#10591197C212yesmaximal, complemented
12#73455—32nomaximal
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2212yes—
15C2×C32×C22⋊C4C2211yescharacteristic
16C2×#3757C2211yescharacteristic
17C2×#3750C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21#64086C418yescomplemented
22C2×C3×#217C2212yes—
23C2×C3×C4×Dic3C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×#3724C2212yes—
26C2×#3724C2212yes—
27C3×C3⋊#95C2212yes—
28C3×C3⋊#95C2212yes—
29#63579C2211yescharacteristic
30#63579C2211yescharacteristic
31#63579C2211yescharacteristic
32#63579C2212yes—
33#63579C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2211yescharacteristic
37C2×#877—32no—
38C2×#877—61no—
39C3×C4×C22⋊C4—32no—
40#5210—32no—
41C2×C3⋊#95—32no—
42#4946—32no—
43#4943—32no—
44Dic3×C22⋊C4D312yes—
45#4933—32no—
46#4933—32no—
47#4932—32no—
48C4×Dic3⋊C4—32no—
49#4652—32no—
50#4652—32no—
51#4651—32no—
52#4650—32no—
53C24×C32C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—24no—
57C22×C3⋊Dic3C2×C414yes—
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3×Dic3—24no—
63C22×C3×Dic3—24no—
64C22×C3×Dic3—42no—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C32×C22⋊C4C2×C414yes—
70#3757C2×C414yes—
71#3750C2×C414yescomplemented
72#3750C2×C414yescomplemented
73C4×C3⋊Dic3C2×C414yescomplemented
74C4×C3⋊Dic3C2×C414yescomplemented
75C3×#217—24no—
76C3×C4×Dic3—24no—
77C3×C4×Dic3—42no—
78#3724—24no—
79#3724—42no—
80#2343—91noSylow
81C23×C3×C4—32no—
82C23×Dic3—32no—
83C23×Dic3—61no—
84C23×Dic3C2×D312yes—
85C2×C3×C22⋊C4—21no—
86C2×C3×C22⋊C4—32no—
87C2×C3×C22⋊C4C2×D312yes—
88C2×C3×C42—32no—
89C2×C3×C42—32no—
90C2×#217—32no—
91C2×#217—61no—
92C2×#217C2×D312yes—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—32no—
96C2×Dic3⋊C4—32no—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4—32no—
99C2×Dic3⋊C4—61no—
100C2×Dic3⋊C4—61no—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—61no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3C2×D312yes—
106C2×C4×Dic3C2×D312yes—
107#877—316no—
108#877—68no—
109C3×#95—32no—
110C3×#95—32no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95C2×D312yes—
124C3⋊#95C2×D312yes—
125C23×C32—22no—
126C23×C32—21no—
127C23×C32—21no—
128C23×C32C22×C412yes—
129C23×C32#4114yes—
130C23×C32C2411yescharacteristic
131C2×C32×C4—22no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4C22×C412yes—
135C2×C32×C4C22×C412yes—
136C2×C3⋊Dic3—28no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3C22×C412yes—
143C2×C3⋊Dic3C22×C412yes—
144C2×C3⋊Dic3C22×C412yes—
145C2×C3⋊Dic3C22×C412yes—
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—48no—
158C2×C3×Dic3#4114yes—
159C2×#117—91no—
160#387—92no—
161#387—92no—
162#385—92no—
163#383—91no—
164#382—91no—
165#381—91no—
166C4×C4⋊C4—91no—
167C4×C22⋊C4—32no—
168#376—91no—
169C2×#95—91no—
170C24×C3—21no—
171C24×C3C22×D312yes—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—32no—
175C22×C3×C4—32no—
176C22×C3×C4—32no—
177C22×C3×C4—32no—
178C22×C3×C4—64no—
179C22×C3×C4—64no—
180C22×C3×C4—122no—
181C22×C3×C4C22×D312yes—
182C22×C3×C4C22×D312yes—
183C22×Dic3—24no—
184C22×Dic3—24no—
185C22×Dic3—38no—
186C22×Dic3—32no—
187C22×Dic3—32no—
188C22×Dic3—32no—
189C22×Dic3—32no—
190C22×Dic3—42no—
191C22×Dic3—64no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3—68no—
197C22×Dic3—64no—
198C22×Dic3—64no—
199C22×Dic3C22×D312yes—
200C22×Dic3C22×D312yes—
201C22×Dic3C22×D312yes—
202C22×Dic3C22×D312yes—
203C3×C22⋊C4—24no—
204C3×C22⋊C4—64no—
205C3×C22⋊C4C4×D318yes—
206C3×C42—64no—
207C3×C42—122no—
208#217—24no—
209#217—38no—
210#217—64no—
211Dic3⋊C4—38no—
212Dic3⋊C4—38no—
213Dic3⋊C4—64no—
214Dic3⋊C4—64no—
215Dic3⋊C4—64no—
216Dic3⋊C4—64no—
217Dic3⋊C4—122no—
218Dic3⋊C4—122no—
219C4×Dic3—24no—
220C4×Dic3—38no—
221C4×Dic3—38no—
222C4×Dic3—42no—
223C4×Dic3—64no—
224C4×Dic3—64no—
225C22×C32—22no—
226C22×C32—22no—
227C22×C32—24no—
228C22×C32—24no—
229C22×C32#11714yes—
230C22×C32C23×C411yescharacteristic
231C22×C32C2×#4112yes—
232C22×C32C2×#4112yes—
233C22×C32H(5,𝔽2)11yescharacteristic
234C22×C322−1+411yescharacteristic
235C32×C4—22no—
236C32×C4—22no—
237C3⋊Dic3—22no—
238C3⋊Dic3—22no—
239C3⋊Dic3—22no—
240C3⋊Dic3—22no—
241C3×Dic3—24no—
242C3×Dic3—42no—
243C3×Dic3—42no—
244C3×Dic3—42no—
245C23×C4—32no—
246C23×C4—91no—
247#117—98no—
248C2×C4⋊C4—91no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—92no—
251C2×C4⋊C4—92no—
252C2×C22⋊C4—32no—
253C2×C22⋊C4—91no—
254C2×C22⋊C4D3211yescharacteristic
255C2×C42—32no—
256C2×C42—32no—
257C2×C42—91no—
258C2×C42—91no—
259#95—32no—
260#95—32no—
261#95—91no—
262#95—91no—
263#95—92no—
264#95—91no—
265#95—92no—
266#95—91no—
267#95—92no—
268#95—92no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—21no—
274C23×C3—24no—
275C23×C3—22no—
276C23×C3—41no—
277C23×C3—42no—
278C23×C3—41no—
279C23×C3C2×C4×D314yes—
280C23×C3#23514yes—
281C23×C3#23514yes—
282C23×C3C23×D312yes—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—34no—
290C2×C3×C4—41no—
291C2×C3×C4—42no—
292C2×C3×C4—41no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
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—128no—
305C2×C3×C4C2×C4×D314yes—
306C2×C3×C4C2×C4×D314yes—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—34no—
319C2×Dic3—34no—
320C2×Dic3—34no—
321C2×Dic3—34no—
322C2×Dic3—48no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—64no—
328C2×Dic3—64no—
329C2×Dic3—616no—
330C2×Dic3—616no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—121no—
340C2×Dic3—122no—
341C2×Dic3—121no—
342C2×Dic3#23714yes—
343C2×C32—24no—
344C2×C32C2×#11711yescharacteristic
345C2×C32C4×#4111yescharacteristic
346C2×C32#52011yescharacteristic
347C2×C32#55112yes—
348C2×C32#55212yes—
349C24C2×D3211yescharacteristic
350C22×C4—32no—
351C22×C4—32no—
352C22×C4—32no—
353C22×C4—32no—
354C22×C4—64no—
355C22×C4—64no—
356C22×C4—91no—
357C22×C4—91no—
358C22×C4—91no—
359C22×C4—91no—
360C22×C4—94no—
361C22×C4—122no—
362C22×C4—184no—
363C22×C4C2×D3211yescharacteristic
364C22×C4C2×D3211yescharacteristic
365C4⋊C4—94no—
366C4⋊C4—94no—
367C4⋊C4—184no—
368C4⋊C4—362no—
369C22⋊C4—64no—
370C22⋊C4—94no—
371C22⋊C4#62414yes—
372C42—64no—
373C42—94no—
374C42—94no—
375C42—122no—
376C22×C3—24no—
377C22×C3—24no—
378C22×C3—24no—
379C22×C3—24no—
380C22×C3—24no—
381C22×C3—24no—
382C22×C3—22no—
383C22×C3—21no—
384C22×C3—22no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—24no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—44no—
391C22×C3—44no—
392C22×C3#87218yes—
393C22×C3C22×C4×D312yes—
394C22×C3C2×#23512yes—
395C22×C3C2×#23512yes—
396C22×C3C2×#23712yes—
397C22×C3#100412yes—
398C22×C3D3×#4112yes—
399C22×C3#101012yes—
400C3×C4—24no—
401C3×C4—24no—
402C3×C4—42no—
403C3×C4—42no—
404C3×C4—64no—
405C3×C4—122no—
406C3×C4—122no—
407C3×C4—122no—
408Dic3—24no—
409Dic3—42no—
410Dic3—42no—
411Dic3—42no—
412Dic3—64no—
413Dic3—64no—
414Dic3—64no—
415Dic3—64no—
416Dic3—64no—
417Dic3—64no—
418Dic3—122no—
419Dic3—122no—
420C32#234311yescharacteristic, complemented, Sylow
421C23—21no—
422C23—22no—
423C23—21no—
424C23#379814yes—
425C23C2×#62412yes—
426C23C22×D3211yescharacteristic
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—21no—
430C2×C4—34no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—92no—
443C2×C4—92no—
444C2×C4—92no—
445C2×C4—92no—
446C2×C4—128no—
447C2×C4—182no—
448C2×C4—182no—
449C2×C4—181no—
450C2×C4—182no—
451C2×C4—181no—
452C2×C4—188no—
453C2×C4C2×#62412yes—
454C2×C4C2×#62412yes—
455C2×C3—28no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—22no—
460C2×C3—22no—
461C2×C3—44no—
462C2×C3C2×#87212yes—
463C2×C3#549512yes—
464C2×C3#553112yes—
465C2×C3C4×#23712yes—
466C2×C3#554112yes—
467C2×C3#554612yes—
468C2×C3#555612yes—
469C22—22no—
470C22—22no—
471C22—24no—
472C22—24no—
473C22#6387414yes—
474C22C2×#379812yes—
475C22#6430911yescharacteristic
476C22D3×#23712yes—
477C22#6431311yescharacteristic
478C22C22×#62411yescharacteristic
479C4—22no—
480C4—22no—
481C4—64no—
482C4—122no—
483C4—122no—
484C4—122no—
485C4—182no—
486C4—182no—
487C4—182no—
488C4—182no—
489C3—21no—
490C3#7345512yescomplemented
491C2—24no—
492C2#1059403912yes—
493C2#1059420912yes—
494C2C2×#6387411yescharacteristic
495C2#1059519011yescharacteristic
496C2#1059521911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2343
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. #10591360C2semidirect
7. C4×#3724C2semidirect
8. #10591229C2semidirect
9. #10591222C2semidirect
10. #10591197C2semidirect
11. #10591197C2semidirect
21. #64086C4semidirect
71. #3750C2×C4semidirect
72. #3750C2×C4semidirect
73. C4×C3⋊Dic3C2×C4semidirect
74. C4×C3⋊Dic3C2×C4semidirect
420. C32#2343semidirect
490. C3#73455semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
C3×Dic3×C22⋊C42
#105916972
C2×#635792
#105916932
#105913602
C4×#37242
#105912292
#105912222
#105911972
#734553