Finite Group Databasebeta

← #11858751

Subgroups — #11858751

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×C3⋊D3C211yesmaximal, characteristic
2C3×#4926C212yesmaximal, complemented
3#10591152C212yesmaximal
4#10591066C212yesmaximal, complemented
5#10590331C212yesmaximal, complemented
6#10590322C212yesmaximal, complemented
7#10590299C212yesmaximal, complemented
8#10590260C212yesmaximal, complemented
9D3×#432—32nomaximal
10C22×C4×C3⋊D3C411yescharacteristic
11C22×C4×C3⋊D3C411yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C4×C3⋊Dic3C411yescharacteristic
15C2×C4×C3⋊Dic3C411yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C42×C3⋊D3C411yescharacteristic
18C42×C3⋊D3C411yescharacteristic
19C42×C3⋊D3C411yescharacteristic
20C42×C3⋊D3C411yescharacteristic
21C42×C3⋊D3C2211yescharacteristic
22C42×C3⋊D3C2211yescharacteristic
23C42×C3⋊D3C2211yescharacteristic
24C42×C3⋊D3C2211yescharacteristic
25C2×#3710C2214yes—
26C3×#830C2214yes—
27C3×C4⋊(C3⋊C8)C2214yescomplemented
28C3×#803C2214yescomplemented
29#63572C2214yescomplemented
30#63557C2214yes—
31#63555C2214yescomplemented
32C2×C42×D3—32no—
33C2×C42×D3—61no—
34C3×#432—32no—
35#4926D312yescomplemented
36#4835—34no—
37D3×C4⋊C8—34no—
38D3×C22⋊C8—34no—
39#4719—34no—
40#4705—34no—
41D3×#97—34no—
42C23×C3⋊D3C2×C411yescharacteristic
43C22×C32×C4C2×C411yescharacteristic
44C22×C32×C4C2×C411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3C2×C411yescharacteristic
47C22×C3⋊Dic3C2×C411yescharacteristic
48C22×C3⋊Dic3C2×C411yescharacteristic
49C2×C4×C3⋊D3—24no—
50C2×C4×C3⋊D3—24no—
51C2×C4×C3⋊D3—24no—
52C2×C4×C3⋊D3C2×C411yescharacteristic
53C2×C4×C3⋊D3C2×C411yescharacteristic
54C2×C4×C3⋊D3C2×C411yescharacteristic
55C2×C4×C3⋊D3C2×C411yescharacteristic
56C2×C4×C3⋊D3C2×C411yescharacteristic
57C2×C4×C3⋊D3C2×C411yescharacteristic
58C2×C4×C3⋊D3C2×C411yescharacteristic
59C2×C4×C3⋊D3C2×C411yescharacteristic
60C2×C4×C3⋊D3C2×C411yescharacteristic
61C2×C4×C3⋊D3C2×C411yescharacteristic
62C2×C4×C3⋊D3C2311yescharacteristic
63C2×C4×C3⋊D3C2311yescharacteristic
64C32×C42C2×C411yescharacteristic
65C32×C42C2×C411yescharacteristic
66C32×C42C2311yescharacteristic
67C32×C42C2311yescharacteristic
68C4×C3⋊Dic3C2×C411yescharacteristic
69C4×C3⋊Dic3C2×C411yescharacteristic
70C4×C3⋊Dic3C2×C411yescharacteristic
71C4×C3⋊Dic3C2×C411yescharacteristic
72C4×C3⋊Dic3C2×C411yescharacteristic
73C4×C3⋊Dic3C2×C411yescharacteristic
74C4×C3⋊Dic3C2×C411yescharacteristic
75C4×C3⋊Dic3C2×C411yescharacteristic
76C4×C3⋊Dic3C2×C411yescharacteristic
77C4×C3⋊Dic3C2×C411yescharacteristic
78C4×C3⋊Dic3C2311yescharacteristic
79C4×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊C8C2318yes—
81#3710—28no—
82C2×#432—91noSylow
83C22×C4×D3—32no—
84C22×C4×D3—32no—
85C22×C4×D3—32no—
86C22×C4×D3—61no—
87C22×C4×D3—61no—
88C22×C4×D3—61no—
89C2×C3×C42—21no—
90C2×C3×C42C2×D312yes—
91C2×C4×Dic3—32no—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—32no—
94C2×C4×Dic3—61no—
95C2×C4×Dic3—61no—
96C2×C4×Dic3—61no—
97C2×D3×C8—38no—
98C42×D3—32no—
99C42×D3—32no—
100C42×D3—32no—
101C42×D3—32no—
102C42×D3—32no—
103C42×D3—32no—
104C42×D3—32no—
105C42×D3—32no—
106C42×D3—61no—
107C42×D3—61no—
108C42×D3—61no—
109C42×D3—61no—
110C42×D3—61no—
111C42×D3—61no—
112C42×D3—61no—
113C42×D3—61no—
114C3×C4⋊C8—34no—
115C3×C22⋊C8—34no—
116C3×#97—34no—
117#830C2×D314yes—
118(C2×D3)⋊C8—38no—
119#815—38no—
120Dic3⋊C8—38no—
121C4⋊(C3⋊C8)C2×D314yescomplemented
122#803C2×D314yescomplemented
123C23×C32C22×C411yescharacteristic
124C22×C3⋊D3—22no—
125C22×C3⋊D3—22no—
126C22×C3⋊D3M1614yes—
127C22×C3⋊D3C22×C411yescharacteristic
128C22×C3⋊D3C22×C411yescharacteristic
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C22×C411yescharacteristic
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2411yescharacteristic
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3C22×C411yescharacteristic
142C2×C3⋊Dic3C22×C411yescharacteristic
143C2×C3⋊Dic3C22×C411yescharacteristic
144C2×C3⋊Dic3C22×C411yescharacteristic
145C2×C3⋊Dic3C22×C411yescharacteristic
146C2×C3⋊Dic3C22×C411yescharacteristic
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149C4×C3⋊D3—22no—
150C4×C3⋊D3—22no—
151C4×C3⋊D3—22no—
152C4×C3⋊D3—22no—
153C4×C3⋊D3—22no—
154C4×C3⋊D3—22no—
155C4×C3⋊D3—22no—
156C4×C3⋊D3—22no—
157C4×C3⋊D3M1614yes—
158C4×C3⋊D3#4114yes—
159C3×C3⋊C8—28no—
160C22×C42—91no—
161#432—32no—
162#432—92no—
163#432—92no—
164#432—92no—
165C2×C4⋊C8—92no—
166C2×C22⋊C8—92no—
167C2×#97—92no—
168C23×D3—32no—
169C23×D3—61no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4C4×D312yes—
174C22×C3×C4C4×D312yes—
175C22×C3×C4C22×D312yes—
176C22×Dic3—32no—
177C22×Dic3—32no—
178C22×Dic3—32no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C2×C4×D3—32no—
183C2×C4×D3—32no—
184C2×C4×D3—32no—
185C2×C4×D3—32no—
186C2×C4×D3—32no—
187C2×C4×D3—32no—
188C2×C4×D3—32no—
189C2×C4×D3—32no—
190C2×C4×D3—32no—
191C2×C4×D3—32no—
192C2×C4×D3—32no—
193C2×C4×D3—32no—
194C2×C4×D3—61no—
195C2×C4×D3—61no—
196C2×C4×D3—61no—
197C2×C4×D3—61no—
198C2×C4×D3—61no—
199C2×C4×D3—61no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×C4×D3—61no—
203C2×C4×D3—61no—
204C2×C4×D3—61no—
205C2×C4×D3—61no—
206C2×C4×D3—68no—
207C2×C4×D3—68no—
208C2×C4×D3—68no—
209C2×C4×D3—68no—
210C2×C4×D3—68no—
211C2×C4×D3—68no—
212C2×C3×C8—38no—
213C3×C42—21no—
214C3×C42—21no—
215C3×C42—21no—
216C3×C42—21no—
217C3×C42C4×D312yes—
218C3×C42C4×D312yes—
219C3×C42C22×D312yes—
220C3×C42C22×D312yes—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—32no—
226C4×Dic3—32no—
227C4×Dic3—32no—
228C4×Dic3—32no—
229C4×Dic3—32no—
230C4×Dic3—32no—
231C4×Dic3—32no—
232C4×Dic3—32no—
233C4×Dic3—61no—
234C4×Dic3—61no—
235C4×Dic3—61no—
236C4×Dic3—61no—
237C4×Dic3—61no—
238C4×Dic3—61no—
239C4×Dic3—61no—
240C4×Dic3—61no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C4×Dic3—61no—
244C4×Dic3—61no—
245C2×C3⋊C8C22×D318yes—
246D3×C8—616no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32C2×M1612yes—
250C22×C32C23×C411yescharacteristic
251C2×C3⋊D3—21no—
252C2×C3⋊D3—21no—
253C2×C3⋊D3—28no—
254C2×C3⋊D3#11712yes—
255C2×C3⋊D3C2×M1612yes—
256C2×C3⋊D3C2×M1612yes—
257C2×C3⋊D3C2×M1612yes—
258C32×C4—21no—
259C32×C4—21no—
260C32×C4—21no—
261C32×C4—21no—
262C32×C4C2×M1612yes—
263C32×C4C2×#4112yes—
264C3⋊Dic3—21no—
265C3⋊Dic3—21no—
266C3⋊Dic3—21no—
267C3⋊Dic3—21no—
268C3⋊Dic3#11712yes—
269C3⋊Dic3C2×M1612yes—
270C23×C4—91no—
271C23×C4—91no—
272C23×C4—91no—
273C22×C8—94no—
274C2×C42—91no—
275C2×C42—91no—
276C2×C42—91no—
277C2×C42—91no—
278C2×C42—91no—
279C2×C42—91no—
280C2×C42—91no—
281C2×C42—91no—
282C2×C42—91no—
283C2×C42—91no—
284C2×C42—91no—
285C2×C42D3211yescharacteristic
286C4⋊C8—34no—
287C4⋊C8—94no—
288C22⋊C8—34no—
289C22⋊C8—94no—
290#97—34no—
291#97—94no—
292C23×C3—21no—
293C23×C3C2×C4×D312yes—
294C22×D3—32no—
295C22×D3—38no—
296C22×D3—32no—
297C22×D3—64no—
298C22×D3—61no—
299C22×D3—61no—
300C22×D3—64no—
301C22×D3—64no—
302C22×D3—64no—
303C22×D3—64no—
304C2×C3×C4—24no—
305C2×C3×C4—24no—
306C2×C3×C4—24no—
307C2×C3×C4—24no—
308C2×C3×C4—24no—
309C2×C3×C4—24no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4C2×C4×D312yes—
317C2×C3×C4C2×C4×D312yes—
318C2×C3×C4C2×C4×D312yes—
319C2×C3×C4C2×C4×D312yes—
320C2×C3×C4C2×C4×D312yes—
321C2×C3×C4C23×D312yes—
322C2×Dic3—32no—
323C2×Dic3—32no—
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—32no—
327C2×Dic3—32no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—64no—
335C2×Dic3—64no—
336C2×Dic3—64no—
337C2×Dic3—64no—
338C2×Dic3—64no—
339C2×Dic3—64no—
340C4×D3—38no—
341C4×D3—38no—
342C4×D3—64no—
343C4×D3—64no—
344C4×D3—64no—
345C4×D3—64no—
346C4×D3—64no—
347C4×D3—64no—
348C4×D3—64no—
349C4×D3—64no—
350C4×D3—64no—
351C4×D3—64no—
352C4×D3—64no—
353C4×D3—64no—
354C4×D3—64no—
355C4×D3—64no—
356C4×D3—64no—
357C4×D3—64no—
358C4×D3—64no—
359C4×D3—64no—
360C4×D3—64no—
361C4×D3—64no—
362C4×D3—64no—
363C4×D3—64no—
364C3×C8—68no—
365C3⋊C8—28no—
366C2×C32—22no—
367C2×C32C2×#11711yescharacteristic
368C2×C32C22×M1611yescharacteristic
369C2×C32C22×M1611yescharacteristic
370C3⋊D3—22no—
371C3⋊D3#43214yescomplemented
372C24—91no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4—91no—
386C22×C4—91no—
387C22×C4—91no—
388C22×C4—184no—
389C22×C4—184no—
390C22×C4—184no—
391C22×C4#62411yescharacteristic
392C22×C4#62411yescharacteristic
393C22×C4C2×D3211yescharacteristic
394C2×C8—38no—
395C2×C8—188no—
396C42—91no—
397C42—91no—
398C42—91no—
399C42—91no—
400C42—91no—
401C42—91no—
402C42—91no—
403C42—91no—
404C42—91no—
405C42—91no—
406C42—91no—
407C42—91no—
408C42#62411yescharacteristic
409C42#62411yescharacteristic
410C42C2×D3211yescharacteristic
411C42C2×D3211yescharacteristic
412C22×C3—22no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—21no—
417C22×C3—22no—
418C22×C3D3×M1614yes—
419C22×C3C22×C4×D312yes—
420C2×D3—34no—
421C2×D3—34no—
422C2×D3—34no—
423C2×D3—34no—
424C2×D3—62no—
425C2×D3—62no—
426C2×D3—62no—
427C2×D3—62no—
428C2×D3—616no—
429C2×D3—62no—
430C2×D3—62no—
431C2×D3—616no—
432C2×D3—62no—
433C2×D3—62no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—22no—
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—22no—
444C3×C4D3×M1614yes—
445C3×C4D3×#4114yes—
446Dic3—34no—
447Dic3—34no—
448Dic3—62no—
449Dic3—62no—
450Dic3—62no—
451Dic3—62no—
452Dic3—62no—
453Dic3—62no—
454Dic3—62no—
455Dic3—62no—
456Dic3—62no—
457Dic3—62no—
458C32C2×#43211yescharacteristic, complemented, Sylow
459C23—91no—
460C23—91no—
461C23—94no—
462C23—182no—
463C23—182no—
464C23C2×#62411yescharacteristic
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—91no—
469C2×C4—91no—
470C2×C4—94no—
471C2×C4—94no—
472C2×C4—91no—
473C2×C4—91no—
474C2×C4—91no—
475C2×C4—91no—
476C2×C4—182no—
477C2×C4—182no—
478C2×C4—182no—
479C2×C4—182no—
480C2×C4—182no—
481C2×C4—182no—
482C2×C4—182no—
483C2×C4—182no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4—182no—
487C2×C4—182no—
488C2×C4—182no—
489C2×C4C2×#62411yescharacteristic
490C2×C4C2×#62411yescharacteristic
491C2×C4C2×#62411yescharacteristic
492C2×C4C2×#62411yescharacteristic
493C2×C4C2×#62411yescharacteristic
494C2×C4C22×D3211yescharacteristic
495C8—68no—
496C2×C3—24no—
497C2×C3—24no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3D3×#11712yes—
502C2×C3C2×D3×M1612yes—
503C2×C3C2×D3×M1612yes—
504D3—38no—
505D3—64no—
506D3—64no—
507D3—64no—
508C22—21no—
509C22—21no—
510C22—92no—
511C22—92no—
512C22—92no—
513C22—92no—
514C22—188no—
515C22—181no—
516C22—181no—
517C22#6381812yes—
518C22C22×#62411yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—92no—
524C4—92no—
525C4—181no—
526C4—181no—
527C4—181no—
528C4—181no—
529C4#6381812yes—
530C4#6430612yes—
531C3—21no—
532C3D3×#43212yescomplemented
533C2—22no—
534C2—94no—
535C2—182no—
536C2C2×#6381811yescharacteristic
537C2C2×#6381811yescharacteristic
538C2#1059496911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×C42C22
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#432
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4926C2semidirect
4. #10591066C2semidirect
5. #10590331C2semidirect
6. #10590322C2semidirect
7. #10590299C2semidirect
8. #10590260C2semidirect
27. C3×C4⋊(C3⋊C8)C22semidirect
28. C3×#803C22semidirect
29. #63572C22semidirect
31. #63555C22semidirect
35. #4926D3semidirect
121. C4⋊(C3⋊C8)C2×D3semidirect
122. #803C2×D3semidirect
371. C3⋊D3#432semidirect
458. C32C2×#432semidirect
532. C3D3×#432semidirect

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
C3×#49262
#105911522
#105910662
#105903312
#105903222
#105902992
#105902602
D3×#4323