Finite Group Databasebeta

← #11773468

Subgroups — #11773468

Order 1152.

1249 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C2×C3×C3⋊#95C212yesmaximal
3C2×#63579C211yesmaximal, characteristic
4C2×#63579C211yesmaximal, characteristic
5C2×#63579C212yesmaximal
6#69421—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3×Dic3C2212yes—
11C23×C3×Dic3C2212yes—
12C2×#3750—22no—
13C2×#3750—22no—
14C2×#3750C414yescomplemented
15C3×C3⋊#95—24no—
16#63579—22no—
17#63579—22no—
18#63579—24no—
19C22×Dic3⋊C4—32no—
20C22×Dic3⋊C4—61no—
21C2×C3×#95—32no—
22C2×C3⋊#95—32no—
23C2×C3⋊#95—32no—
24C2×C3⋊#95—32no—
25C2×C3⋊#95—32no—
26C2×C3⋊#95D312yes—
27C24×C32C2311yescharacteristic
28C22×C32×C4—21no—
29C22×C32×C4—21no—
30C22×C32×C4—22no—
31C22×C32×C4—22no—
32C22×C32×C4C2×C412yes—
33C22×C3⋊Dic3—22no—
34C22×C3⋊Dic3—22no—
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—22no—
38C22×C3⋊Dic3—22no—
39C22×C3⋊Dic3C2×C412yes—
40C22×C3⋊Dic3C2×C412yes—
41C22×C3⋊Dic3D412yes—
42C22×C3⋊Dic3D412yes—
43C22×C3×Dic3—22no—
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×Dic3—22no—
55C22×C3×Dic3D414yes—
56C22×C3×Dic3Q814yes—
57#3750—28no—
58#1445—91noSylow
59C23×C3×C4—21no—
60C23×C3×C4—32no—
61C23×C3×C4—32no—
62C23×C3×C4C2×D312yes—
63C23×Dic3—32no—
64C23×Dic3—32no—
65C23×Dic3—61no—
66C23×Dic3—61no—
67C23×Dic3C2×D312yes—
68C23×Dic3C2×D312yes—
69C2×Dic3⋊C4—38no—
70C2×Dic3⋊C4—64no—
71C2×Dic3⋊C4—64no—
72C2×Dic3⋊C4—64no—
73C2×Dic3⋊C4—64no—
74C2×Dic3⋊C4—64no—
75C3×#95—64no—
76C3⋊#95—24no—
77C3⋊#95—64no—
78C3⋊#95—64no—
79C3⋊#95—64no—
80C3⋊#95—64no—
81C23×C32C22×C411yescharacteristic
82C23×C32C2×D411yescharacteristic
83C23×C32C2×D411yescharacteristic
84C23×C32C2×D412yes—
85C23×C32C2×Q812yes—
86C23×C32#4112yes—
87C23×C32#4112yes—
88C23×C32#4112yes—
89C23×C32#4112yes—
90C2×C32×C4—22no—
91C2×C32×C4—24no—
92C2×C32×C4—42no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—24no—
98C2×C3⋊Dic3—24no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—24no—
101C2×C3⋊Dic3—42no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3C22⋊C414yes—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—42no—
112C2×C3×Dic3—42no—
113C2×C3×Dic3—42no—
114C2×C3×Dic3—42no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3—42no—
118C2×C3×Dic3—42no—
119C22×C4⋊C4—91no—
120C2×#95—32no—
121C2×#95—92no—
122C2×#95—91no—
123C2×#95—91no—
124C24×C3—21no—
125C24×C3C22×D312yes—
126C22×C3×C4—22no—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—22no—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—34no—
136C22×C3×C4—34no—
137C22×C3×C4—42no—
138C22×C3×C4—42no—
139C22×C3×C4—62no—
140C22×C3×C4—62no—
141C22×C3×C4—62no—
142C22×C3×C4—62no—
143C22×C3×C4—62no—
144C22×C3×C4—62no—
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×C4C4×D314yes—
152C22×Dic3—22no—
153C22×Dic3—22no—
154C22×Dic3—22no—
155C22×Dic3—22no—
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—34no—
165C22×Dic3—34no—
166C22×Dic3—34no—
167C22×Dic3—34no—
168C22×Dic3—62no—
169C22×Dic3—62no—
170C22×Dic3—62no—
171C22×Dic3—62no—
172C22×Dic3—64no—
173C22×Dic3—64no—
174C22×Dic3—62no—
175C22×Dic3—62no—
176C22×Dic3—62no—
177C22×Dic3—62no—
178C22×Dic3—62no—
179C22×Dic3—62no—
180C22×Dic3—62no—
181C22×Dic3—62no—
182C22×Dic3—62no—
183C22×Dic3—62no—
184C22×Dic3—62no—
185C22×Dic3—62no—
186C22×Dic3—122no—
187C22×Dic3—122no—
188C22×Dic3Dic614yes—
189C22×Dic3#6714yes—
190Dic3⋊C4—616no—
191Dic3⋊C4—616no—
192C22×C32C2×C22⋊C411yescharacteristic
193C22×C32#11711yescharacteristic
194C22×C32#11711yescharacteristic
195C22×C32C4×D412yes—
196C22×C32C4×Q812yes—
197C22×C32#12112yes—
198C22×C32C22⋊Q812yes—
199C22×C32C22⋊Q812yes—
200C22×C32C22⋊Q812yes—
201C22×C32#12312yes—
202C22×C32#12312yes—
203C22×C32#12312yes—
204C22×C32#12312yes—
205C22×C32#12411yescharacteristic
206C22×C32#12411yescharacteristic
207C22×C32#12512yes—
208C22×C32#12512yes—
209C22×C32#12612yes—
210C22×C32#12612yes—
211C22×C32#12711yescharacteristic
212C22×C32C4⋊Q811yescharacteristic
213C32×C4—42no—
214C3⋊Dic3—24no—
215C3⋊Dic3—42no—
216C3×Dic3—44no—
217C3×Dic3—44no—
218C23×C4—32no—
219C23×C4—32no—
220C23×C4—91no—
221C23×C4—91no—
222C23×C4D3211yescharacteristic
223C2×C4⋊C4—94no—
224C2×C4⋊C4—182no—
225C2×C4⋊C4—182no—
226#95—64no—
227#95—184no—
228#95—182no—
229#95—182no—
230C23×C3—22no—
231C23×C3—22no—
232C23×C3—22no—
233C23×C3—22no—
234C23×C3—22no—
235C23×C3—21no—
236C23×C3—22no—
237C23×C3—21no—
238C23×C3—21no—
239C23×C3C2×Dic612yes—
240C23×C3C2×C4×D312yes—
241C23×C3#23512yes—
242C23×C3#23512yes—
243C23×C3#23512yes—
244C23×C3#23512yes—
245C23×C3D3×D412yes—
246C23×C3D3×D412yes—
247C23×C3D3×D412yes—
248C23×C3#23712yes—
249C23×C3#23712yes—
250C23×C3#23712yes—
251C23×C3D3×Q812yes—
252C23×C3#23912yes—
253C23×C3C2×#6712yes—
254C2×C3×C4—24no—
255C2×C3×C4—24no—
256C2×C3×C4—24no—
257C2×C3×C4—24no—
258C2×C3×C4—44no—
259C2×C3×C4—42no—
260C2×C3×C4—44no—
261C2×C3×C4—42no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—42no—
265C2×C3×C4—42no—
266C2×C3×C4—64no—
267C2×C3×C4—64no—
268C2×C3×C4—64no—
269C2×C3×C4—64no—
270C2×C3×C4—64no—
271C2×C3×C4—64no—
272C2×C3×C4—122no—
273C2×C3×C4—122no—
274C2×C3×C4—122no—
275C2×C3×C4—122no—
276C2×C3×C4—122no—
277C2×C3×C4—122no—
278C2×C3×C4—122no—
279C2×C3×C4—122no—
280C2×Dic3—24no—
281C2×Dic3—24no—
282C2×Dic3—24no—
283C2×Dic3—24no—
284C2×Dic3—24no—
285C2×Dic3—24no—
286C2×Dic3—38no—
287C2×Dic3—42no—
288C2×Dic3—42no—
289C2×Dic3—42no—
290C2×Dic3—42no—
291C2×Dic3—42no—
292C2×Dic3—42no—
293C2×Dic3—42no—
294C2×Dic3—42no—
295C2×Dic3—64no—
296C2×Dic3—64no—
297C2×Dic3—68no—
298C2×Dic3—68no—
299C2×Dic3—64no—
300C2×Dic3—64no—
301C2×Dic3—64no—
302C2×Dic3—64no—
303C2×Dic3—64no—
304C2×Dic3—64no—
305C2×Dic3—64no—
306C2×Dic3—64no—
307C2×Dic3—64no—
308C2×Dic3—64no—
309C2×Dic3—64no—
310C2×Dic3—124no—
311C2×Dic3—122no—
312C2×Dic3—124no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315C2×Dic3—122no—
316C2×Dic3—122no—
317C2×Dic3—122no—
318C2×C32#38111yescharacteristic
319C2×C32#38712yes—
320C2×C32#38712yes—
321C2×C32#39011yescharacteristic
322C2×C32#39111yescharacteristic
323C2×C32#39712yes—
324C2×C32#39812yes—
325C2×C32#39912yes—
326C2×C32#40012yes—
327C24C2×D3211yescharacteristic
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—34no—
333C22×C4—34no—
334C22×C4—62no—
335C22×C4—62no—
336C22×C4—62no—
337C22×C4—62no—
338C22×C4—62no—
339C22×C4—62no—
340C22×C4—62no—
341C22×C4—62no—
342C22×C4—62no—
343C22×C4—62no—
344C22×C4—62no—
345C22×C4—62no—
346C22×C4—92no—
347C22×C4—92no—
348C22×C4—92no—
349C22×C4—92no—
350C22×C4—182no—
351C22×C4—182no—
352C22×C4—182no—
353C22×C4—182no—
354C22×C4—181no—
355C22×C4—181no—
356C22×C4#62412yes—
357C4⋊C4—188no—
358C22×C3—21no—
359C22×C3—22no—
360C22×C3—22no—
361C22×C3—21no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—22no—
370C22×C3—22no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3C4×Dic612yes—
380C22×C3#87012yes—
381C22×C3#87212yes—
382C22×C3#87612yes—
383C22×C3#87812yes—
384C22×C3#87812yes—
385C22×C3#87912yes—
386C22×C3#87912yes—
387C22×C3D3×C22⋊C412yes—
388C22×C3#67⋊C412yes—
389C22×C3#88312yes—
390C22×C3#88312yes—
391C22×C3#88312yes—
392C22×C3#88412yes—
393C22×C3#88512yes—
394C22×C3#88512yes—
395C22×C3#88712yes—
396C22×C3#88812yes—
397C22×C3#88912yes—
398C22×C3#88912yes—
399C22×C3#89012yes—
400C22×C3#89212yes—
401C22×C3#89412yes—
402C22×C3#89412yes—
403C22×C3#89412yes—
404C22×C3#89612yes—
405C22×C3#89612yes—
406C22×C3#89812yes—
407C22×C3#92412yes—
408C22×C3C4×#6712yes—
409C22×C3#92912yes—
410C22×C3#93512yes—
411C22×C3#93912yes—
412C22×C3#94012yes—
413C22×C3#94612yes—
414C3×C4—44no—
415C3×C4—44no—
416C3×C4—124no—
417C3×C4—124no—
418Dic3—44no—
419Dic3—44no—
420Dic3—68no—
421Dic3—68no—
422Dic3—124no—
423Dic3—124no—
424C32#144511yescharacteristic, complemented, Sylow
425C23D3×Dic612yes—
426C23#379512yes—
427C23#379612yes—
428C23#379812yes—
429C23#380412yes—
430C23C2×#62411yescharacteristic
431C23D3×#6712yes—
432C23#381111yescharacteristic
433C23#381111yescharacteristic
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—64no—
440C2×C4—64no—
441C2×C4—64no—
442C2×C4—64no—
443C2×C4—64no—
444C2×C4—64no—
445C2×C4—94no—
446C2×C4—122no—
447C2×C4—122no—
448C2×C4—122no—
449C2×C4—122no—
450C2×C4—122no—
451C2×C4—122no—
452C2×C4—122no—
453C2×C4—122no—
454C2×C4—182no—
455C2×C4—184no—
456C2×C4—184no—
457C2×C4—182no—
458C2×C4—184no—
459C2×C4—182no—
460C2×C4—361no—
461C2×C4—362no—
462C2×C4—361no—
463C2×C3—22no—
464C2×C3—21no—
465C2×C3—22no—
466C2×C3—22no—
467C2×C3—22no—
468C2×C3—21no—
469C2×C3—22no—
470C2×C3—22no—
471C2×C3—21no—
472C2×C3#464612yes—
473C2×C3#465212yes—
474C2×C3#465512yes—
475C2×C3#465712yes—
476C2×C3#465812yes—
477C2×C3#466012yes—
478C2×C3#466412yes—
479C2×C3#467512yes—
480C2×C3#493312yes—
481C2×C3#494912yes—
482C2×C3#495212yes—
483C2×C3#495712yes—
484C2×C3#497812yes—
485C2×C3#498212yes—
486C2×C3#499312yes—
487C22#6384011yescharacteristic
488C22#6384412yes—
489C22#6384612yes—
490C22#6384911yescharacteristic
491C22#6385112yes—
492C22#6385312yes—
493C22#6385312yes—
494C22#6385812yes—
495C22#6385912yes—
496C22#6386712yes—
497C22#6387411yescharacteristic
498C22#6388412yes—
499C22#6388712yes—
500C22#6389612yes—
501C22#6390512yes—
502C22#6391311yescharacteristic
503C22#6395212yes—
504C22#6395311yescharacteristic
505C22#6397112yes—
506C22#6397411yescharacteristic
507C22#6397911yescharacteristic
508C4—42no—
509C4—124no—
510C4—124no—
511C4—184no—
512C4—362no—
513C3—21no—
514C3#6942112yescomplemented
515C2#1059119712yes—
516C2#1059121012yes—
517C2#1059121911yescharacteristic
518C2#1059126312yes—
519C2#1059127311yescharacteristic
520C2#1059129812yes—
521C2#1059130312yes—
522C2#1059134012yes—
523C2#1059170411yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1445
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
14. C2×#3750C4semidirect
424. C32#1445semidirect
514. C3#69421semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C2×C3×C3⋊#952
C2×#635792
#694213