Finite Group Databasebeta

← #11773237

Subgroups — #11773237

Order 1152.

1433 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C22×Dic32C211yesmaximal, characteristic
3C2×C3×C3⋊#95C212yesmaximal
4C2×#63579C211yesmaximal, characteristic
5C2×#63579C212yesmaximal
6#69406—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3×Dic3C2212yes—
11C23×C3×Dic3C2212yes—
12C2×#3750—22no—
13C2×#3750—22no—
14C2×#3750C414yescomplemented
15C2×Dic32—22no—
16C2×Dic32—24no—
17C3×C3⋊#95—24no—
18#63579—22no—
19#63579C418yescomplemented
20C22×Dic3⋊C4—32no—
21C22×Dic3⋊C4—61no—
22C22×C4×Dic3—32no—
23C2×C3×#95—32no—
24C2×C3⋊#95—32no—
25C2×C3⋊#95—32no—
26C2×C3⋊#95—32no—
27C2×C3⋊#95D312yes—
28C24×C32C2311yescharacteristic
29C22×C32×C4—21no—
30C22×C32×C4—21no—
31C22×C32×C4—22no—
32C22×C32×C4—22no—
33C22×C32×C4C2×C412yes—
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—22no—
37C22×C3⋊Dic3—22no—
38C22×C3⋊Dic3—22no—
39C22×C3⋊Dic3C2×C414yes—
40C22×C3⋊Dic3C2×C412yes—
41C22×C3⋊Dic3C2×C412yes—
42C22×C3⋊Dic3D412yes—
43C22×C3⋊Dic3D412yes—
44C22×C3×Dic3—22no—
45C22×C3×Dic3—22no—
46C22×C3×Dic3—22no—
47C22×C3×Dic3—22no—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3C2×C414yes—
55C22×C3×Dic3C2×C414yes—
56C22×C3×Dic3D414yes—
57C22×C3×Dic3Q814yes—
58#3750—28no—
59Dic32—28no—
60#1436—91noSylow
61C23×C3×C4—21no—
62C23×C3×C4—32no—
63C23×C3×C4—32no—
64C23×C3×C4C2×D312yes—
65C23×Dic3—32no—
66C23×Dic3—32no—
67C23×Dic3—61no—
68C23×Dic3—61no—
69C23×Dic3C2×D312yes—
70C23×Dic3C2×D312yes—
71C2×Dic3⋊C4—38no—
72C2×Dic3⋊C4—64no—
73C2×Dic3⋊C4—64no—
74C2×Dic3⋊C4—64no—
75C2×Dic3⋊C4—64no—
76C2×Dic3⋊C4—64no—
77C2×C4×Dic3—64no—
78C2×C4×Dic3—64no—
79C2×C4×Dic3—64no—
80C3×#95—64no—
81C3⋊#95—24no—
82C3⋊#95—38no—
83C3⋊#95—38no—
84C3⋊#95—64no—
85C23×C32C22×C411yescharacteristic
86C23×C32C22×C412yes—
87C23×C32C2×D411yescharacteristic
88C23×C32C2×D411yescharacteristic
89C23×C32C2×D412yes—
90C23×C32C2×Q812yes—
91C23×C32#4112yes—
92C23×C32#4112yes—
93C23×C32#4112yes—
94C2×C32×C4—22no—
95C2×C32×C4—24no—
96C2×C32×C4—41no—
97C2×C32×C4—42no—
98C2×C32×C4—41no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—24no—
102C2×C3⋊Dic3—24no—
103C2×C3⋊Dic3—24no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—24no—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3C4214yescomplemented
108C2×C3⋊Dic3C22⋊C414yes—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—42no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3C4⋊C418yescomplemented
123C22×C4⋊C4—91no—
124C22×C42—91no—
125C2×#95—32no—
126C2×#95—92no—
127C2×#95—91no—
128C24×C3—21no—
129C24×C3C22×D312yes—
130C22×C3×C4—22no—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—34no—
140C22×C3×C4—34no—
141C22×C3×C4—34no—
142C22×C3×C4—34no—
143C22×C3×C4—42no—
144C22×C3×C4—42no—
145C22×C3×C4—62no—
146C22×C3×C4—62no—
147C22×C3×C4—62no—
148C22×C3×C4—62no—
149C22×C3×C4—62no—
150C22×C3×C4—62no—
151C22×C3×C4—62no—
152C22×C3×C4—62no—
153C22×C3×C4—62no—
154C22×C3×C4—62no—
155C22×C3×C4C4×D314yes—
156C22×Dic3—22no—
157C22×Dic3—22no—
158C22×Dic3—22no—
159C22×Dic3—22no—
160C22×Dic3—22no—
161C22×Dic3—22no—
162C22×Dic3—22no—
163C22×Dic3—22no—
164C22×Dic3—22no—
165C22×Dic3—22no—
166C22×Dic3—34no—
167C22×Dic3—34no—
168C22×Dic3—34no—
169C22×Dic3—34no—
170C22×Dic3—34no—
171C22×Dic3—34no—
172C22×Dic3—62no—
173C22×Dic3—64no—
174C22×Dic3—62no—
175C22×Dic3—62no—
176C22×Dic3—62no—
177C22×Dic3—62no—
178C22×Dic3—62no—
179C22×Dic3—64no—
180C22×Dic3—62no—
181C22×Dic3—62no—
182C22×Dic3—62no—
183C22×Dic3—62no—
184C22×Dic3—62no—
185C22×Dic3—62no—
186C22×Dic3—62no—
187C22×Dic3—62no—
188C22×Dic3—122no—
189C22×Dic3—122no—
190C22×Dic3Dic614yes—
191C22×Dic3C4×D314yes—
192C22×Dic3C4×D314yes—
193C22×Dic3#6714yes—
194Dic3⋊C4—616no—
195Dic3⋊C4—616no—
196C4×Dic3—616no—
197C22×C32C2×C4211yescharacteristic
198C22×C32C2×C22⋊C411yescharacteristic
199C22×C32C2×C4⋊C412yes—
200C22×C32#11712yes—
201C22×C32#11711yescharacteristic
202C22×C32C4×D412yes—
203C22×C32C4×D412yes—
204C22×C32C4×D412yes—
205C22×C32C4×D412yes—
206C22×C32C4×Q812yes—
207C22×C32C4×Q812yes—
208C22×C32#12011yescharacteristic
209C22×C32#12112yes—
210C22×C32C22⋊Q812yes—
211C22×C32C22⋊Q812yes—
212C22×C32#12311yescharacteristic
213C22×C32#12312yes—
214C22×C32#12411yescharacteristic
215C22×C32#12512yes—
216C22×C32#12612yes—
217C22×C32C4⋊Q811yescharacteristic
218C32×C4—42no—
219C3⋊Dic3—24no—
220C3⋊Dic3—24no—
221C3×Dic3—28no—
222C3×Dic3—44no—
223C23×C4—32no—
224C23×C4—32no—
225C23×C4—91no—
226C23×C4—91no—
227C23×C4D3211yescharacteristic
228C2×C4⋊C4—94no—
229C2×C4⋊C4—182no—
230C2×C4⋊C4—182no—
231C2×C42—184no—
232C2×C42—182no—
233#95—64no—
234#95—98no—
235#95—182no—
236C23×C3—22no—
237C23×C3—22no—
238C23×C3—22no—
239C23×C3—22no—
240C23×C3—22no—
241C23×C3—21no—
242C23×C3—22no—
243C23×C3—21no—
244C23×C3—21no—
245C23×C3C2×Dic612yes—
246C23×C3C2×C4×D312yes—
247C23×C3C2×C4×D312yes—
248C23×C3C2×C4×D312yes—
249C23×C3#23512yes—
250C23×C3#23512yes—
251C23×C3D3×D412yes—
252C23×C3D3×D412yes—
253C23×C3D3×D412yes—
254C23×C3#23712yes—
255C23×C3#23712yes—
256C23×C3#23712yes—
257C23×C3D3×Q812yes—
258C23×C3#23912yes—
259C23×C3C2×#6712yes—
260C2×C3×C4—24no—
261C2×C3×C4—24no—
262C2×C3×C4—24no—
263C2×C3×C4—24no—
264C2×C3×C4—38no—
265C2×C3×C4—44no—
266C2×C3×C4—44no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4—42no—
273C2×C3×C4—64no—
274C2×C3×C4—64no—
275C2×C3×C4—64no—
276C2×C3×C4—64no—
277C2×C3×C4—64no—
278C2×C3×C4—64no—
279C2×C3×C4—64no—
280C2×C3×C4—64no—
281C2×C3×C4—64no—
282C2×C3×C4—122no—
283C2×C3×C4—122no—
284C2×C3×C4—122no—
285C2×C3×C4—122no—
286C2×Dic3—24no—
287C2×Dic3—24no—
288C2×Dic3—24no—
289C2×Dic3—24no—
290C2×Dic3—24no—
291C2×Dic3—24no—
292C2×Dic3—24no—
293C2×Dic3—24no—
294C2×Dic3—24no—
295C2×Dic3—38no—
296C2×Dic3—38no—
297C2×Dic3—42no—
298C2×Dic3—42no—
299C2×Dic3—42no—
300C2×Dic3—42no—
301C2×Dic3—64no—
302C2×Dic3—64no—
303C2×Dic3—64no—
304C2×Dic3—64no—
305C2×Dic3—68no—
306C2×Dic3—68no—
307C2×Dic3—64no—
308C2×Dic3—64no—
309C2×Dic3—64no—
310C2×Dic3—64no—
311C2×Dic3—64no—
312C2×Dic3—64no—
313C2×Dic3—64no—
314C2×Dic3—64no—
315C2×Dic3—64no—
316C2×Dic3—64no—
317C2×Dic3—64no—
318C2×Dic3—64no—
319C2×Dic3—124no—
320C2×Dic3—124no—
321C2×Dic3—122no—
322C2×Dic3—122no—
323C2×Dic3Dic3⋊C418yescomplemented
324C2×C32C4×C22⋊C411yescharacteristic
325C2×C32C4×C4⋊C412yes—
326C2×C32#38512yes—
327C2×C32#38611yescharacteristic
328C2×C32#38712yes—
329C2×C32#38712yes—
330C2×C32#38812yes—
331C2×C32#38912yes—
332C2×C32#39111yescharacteristic
333C24C2×D3211yescharacteristic
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—34no—
339C22×C4—34no—
340C22×C4—34no—
341C22×C4—34no—
342C22×C4—62no—
343C22×C4—62no—
344C22×C4—62no—
345C22×C4—62no—
346C22×C4—62no—
347C22×C4—62no—
348C22×C4—62no—
349C22×C4—62no—
350C22×C4—62no—
351C22×C4—62no—
352C22×C4—94no—
353C22×C4—92no—
354C22×C4—92no—
355C22×C4—92no—
356C22×C4—92no—
357C22×C4—182no—
358C22×C4—182no—
359C22×C4—182no—
360C22×C4—181no—
361C22×C4—181no—
362C22×C4#62412yes—
363C4⋊C4—188no—
364C42—188no—
365C22×C3—22no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—21no—
370C22×C3—22no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—21no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—22no—
380C22×C3—21no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3C4×Dic612yes—
387C22×C3C4×Dic612yes—
388C22×C3C42×D312yes—
389C22×C3#87212yes—
390C22×C3#87712yes—
391C22×C3#87812yes—
392C22×C3#87812yes—
393C22×C3#87912yes—
394C22×C3D3×C22⋊C412yes—
395C22×C3#67⋊C412yes—
396C22×C3#67⋊C412yes—
397C22×C3#67⋊C412yes—
398C22×C3#67⋊C412yes—
399C22×C3#88312yes—
400C22×C3#88412yes—
401C22×C3#88512yes—
402C22×C3#88712yes—
403C22×C3#88712yes—
404C22×C3#88812yes—
405C22×C3#88912yes—
406C22×C3#89012yes—
407C22×C3D3×C4⋊C412yes—
408C22×C3#89212yes—
409C22×C3#89312yes—
410C22×C3#89312yes—
411C22×C3#89412yes—
412C22×C3#89612yes—
413C22×C3#89812yes—
414C22×C3C2×Dic3⋊C412yes—
415C22×C3C4×#6712yes—
416C22×C3C4×#6712yes—
417C22×C3#93512yes—
418C22×C3#93712yes—
419C22×C3#93812yes—
420C22×C3#94612yes—
421C3×C4—44no—
422C3×C4—44no—
423C3×C4—68no—
424C3×C4—124no—
425Dic3—28no—
426Dic3—44no—
427Dic3—68no—
428Dic3—68no—
429Dic3—68no—
430Dic3—124no—
431C32#143611yescharacteristic, complemented, Sylow
432C23D3×Dic612yes—
433C23#379512yes—
434C23#379612yes—
435C23C4×D3212yes—
436C23#380412yes—
437C23C2×#62411yescharacteristic
438C23D3×#6712yes—
439C23#381111yescharacteristic
440C23#381111yescharacteristic
441C2×C4—24no—
442C2×C4—22no—
443C2×C4—38no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—64no—
448C2×C4—64no—
449C2×C4—64no—
450C2×C4—64no—
451C2×C4—64no—
452C2×C4—64no—
453C2×C4—64no—
454C2×C4—64no—
455C2×C4—64no—
456C2×C4—94no—
457C2×C4—94no—
458C2×C4—122no—
459C2×C4—122no—
460C2×C4—122no—
461C2×C4—122no—
462C2×C4—182no—
463C2×C4—184no—
464C2×C4—184no—
465C2×C4—184no—
466C2×C4—184no—
467C2×C4—182no—
468C2×C4—182no—
469C2×C4—182no—
470C2×C3—22no—
471C2×C3—22no—
472C2×C3—22no—
473C2×C3—21no—
474C2×C3—22no—
475C2×C3—21no—
476C2×C3—22no—
477C2×C3—22no—
478C2×C3—21no—
479C2×C3#464612yes—
480C2×C3#464712yes—
481C2×C3#464912yes—
482C2×C3#465212yes—
483C2×C3#465412yes—
484C2×C3#465512yes—
485C2×C3#466612yes—
486C2×C3#466912yes—
487C2×C3C4×Dic3⋊C412yes—
488C2×C3#494412yes—
489C2×C3#494612yes—
490C2×C3#495612yes—
491C2×C3#497212yes—
492C2×C3#497812yes—
493C2×C3#498912yes—
494C22#6383712yes—
495C22#6384011yescharacteristic
496C22#6384412yes—
497C22#6384612yes—
498C22#6384911yescharacteristic
499C22#6385812yes—
500C22D3×Dic3⋊C412yes—
501C22#6387712yes—
502C22#6387912yes—
503C22#6388112yes—
504C22#6388112yes—
505C22C4×#62411yescharacteristic
506C22#6388412yes—
507C22#6388712yes—
508C22#6389612yes—
509C22#6391311yescharacteristic
510C22#6395212yes—
511C22#6395812yes—
512C22#6397411yescharacteristic
513C22#6397511yescharacteristic
514C22#6398311yescharacteristic
515C4—42no—
516C4—68no—
517C4—124no—
518C4—184no—
519C4—184no—
520C3—21no—
521C3#6940612yescomplemented
522C2#1059123412yes—
523C2#1059124312yes—
524C2#1059125112yes—
525C2#1059126011yescharacteristic
526C2#1059126312yes—
527C2#1059127311yescharacteristic
528C2#1059128112yes—
529C2#1059137212yes—
530C2#1059172211yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC22×C32C2×C42
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1436
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
14. C2×#3750C4semidirect
19. #63579C4semidirect
107. C2×C3⋊Dic3C42semidirect
122. C2×C3×Dic3C4⋊C4semidirect
323. C2×Dic3Dic3⋊C4semidirect
431. C32#1436semidirect
521. C3#69406semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C22×Dic322
C2×C3×C3⋊#952
C2×#635792
#694063