Finite Group Databasebeta

← #11775608

Subgroups — #11775608

Order 1152.

616 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C22⋊Q8C211yesmaximal, characteristic
2#10591295C211yesmaximal, characteristic
3D3×#830C211yesmaximal, characteristic
4#10589404C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589152C211yesmaximal, characteristic, complemented
8#71690—31nomaximal
9#68339—31nomaximal
10C2×C3×D3×Q8C411yescharacteristic, complemented
11C22×C3×C4×D3C2211yescharacteristic
12C32×C22⋊Q8C2211yescharacteristic
13C3×#946C411yescharacteristic, complemented
14C3×#924C2211yescharacteristic
15C3×#897C411yescharacteristic, complemented
16C3×#896—21no—
17C3×D3×C4⋊C4—21no—
18C3×D3×C4⋊C4C411yescharacteristic, complemented
19C3×D3×C22⋊C4—21no—
20C3×#878—21no—
21C2×Dic3⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×D3×C3⋊C8—21no—
24#63658C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28(C2×D3)⋊(C3⋊C8)—21no—
29C2×C3×C22⋊Q8—31no—
30D3×C22⋊Q8D311yescharacteristic
31#5212—31no—
32C2×#830—31no—
33D3×C22⋊C8—31no—
34#4667—31no—
35C3×#328—31no—
36#4538—31no—
37#4538—31no—
38#4538—31no—
39#4538—31no—
40#4538—61no—
41#4538D311yescharacteristic, complemented
42#4467—31no—
43#4452—31no—
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8C2×C411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C3×D3×Q8—42no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3—42no—
54C2×C3×C4×D3C2×C411yescharacteristic
55C2×C3×C4×D3C2×C411yescharacteristic
56C2×C3×C4×D3D411yescharacteristic
57C2×C3×C4×D3D411yescharacteristic
58C2×C3×Dic6—21no—
59C2×C3×Dic6C2×C411yescharacteristic
60C32×C4⋊C4—21no—
61C32×C4⋊C4C2×C411yescharacteristic
62C32×C22⋊C4—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×#217—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3C2×C411yescharacteristic
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—21no—
72C2×C3×C3⋊C8—21no—
73Dic3⋊Dic3—42no—
74(C2×D3)⋊Dic3—42no—
75D3×C3⋊C8—42no—
76#1520—91noSylow
77C22×C3×Q8—31no—
78C23×C3×C4—31no—
79C2×D3×Q8Dic311yescharacteristic, complemented
80C22×C4×D3C2×D311yescharacteristic
81C3×C22⋊Q8—21no—
82C3×C22⋊Q8—31no—
83C3×C22⋊Q8—31no—
84C3×C22⋊Q8—31no—
85C3×C22⋊Q8—61no—
86C3×C22⋊Q8—61no—
87C3×C22⋊Q8C2×D311yescharacteristic
88C3×C22⋊Q8C2×D311yescharacteristic
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—61no—
91C2×C3×C22⋊C4—61no—
92C2×#217—61no—
93#946Dic311yescharacteristic, complemented
94C2×(C2×D3)⋊C4—61no—
95C2×C4⋊Dic3—61no—
96#924C2×D311yescharacteristic
97C2×Dic3⋊C4—61no—
98C22×C3⋊C8—61no—
99C2×D3×C8—61no—
100#897Dic311yescharacteristic, complemented
101#896—21no—
102D3×C4⋊C4—21no—
103D3×C4⋊C4Dic311yescharacteristic, complemented
104D3×C22⋊C4—21no—
105#878—21no—
106C3×C22⋊C8—31no—
107C3×#95—31no—
108C3⋊#95—31no—
109C3⋊#95—31no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic
112#830—31no—
113#830—31no—
114#830—61no—
115#830—61no—
116#830C2×D311yescharacteristic
117(C2×D3)⋊C8—61no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3C22⋊C411yescharacteristic
122C22×C3×D3C22⋊C411yescharacteristic
123C22×C3×D3SD1612yes—
124C22×C3×D3Q1612yes—
125C32×Q8—41no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—41no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3C22⋊C411yescharacteristic
141C2×C3×Dic3C22⋊C411yescharacteristic
142C3×C4×D3—22no—
143C3×C4×D3—22no—
144C3×C4×D3—41no—
145C3×C4×D3—41no—
146C3×C4×D3—42no—
147C3×C4×D3—42no—
148C3×Dic6—42no—
149C3×Dic6—41no—
150C3⋊(C3⋊C8)—41no—
151C3×C3⋊C8—41no—
152C2×C22⋊Q8—31no—
153C2×C22⋊C8—91no—
154#380—91no—
155#328—31no—
156#328—91no—
157#328—91no—
158#328—91no—
159C24×C3—31no—
160C23×D3#6711yescharacteristic
161C2×C3×Q8—21no—
162C2×C3×Q8—31no—
163C2×C3×Q8—61no—
164C2×C3×Q8—122no—
165C2×C3×Q8C4×D311yescharacteristic
166C2×C3×Q8C2×Dic311yescharacteristic
167C22×C3×C4—21no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—61no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4—122no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×Dic3—21no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—121no—
183C22×Dic3#6711yescharacteristic
184D3×Q8—42no—
185C2×C4×D3—21no—
186C2×C4×D3—21no—
187C2×C4×D3—42no—
188C2×C4×D3C2×Dic311yescharacteristic
189C2×C4×D3C2×Dic311yescharacteristic
190C2×C4×D3#6711yescharacteristic
191C2×C4×D3#6711yescharacteristic
192C2×Dic6—21no—
193C2×Dic6C2×Dic311yescharacteristic
194C2×C3×C8—61no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—31no—
199C3×C4⋊C4—41no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4C4×D311yescharacteristic
205C3×C4⋊C4C2×Dic311yescharacteristic
206C3×C22⋊C4—21no—
207C3×C22⋊C4—21no—
208C3×C22⋊C4—41no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4—61no—
211C3×C22⋊C4—61no—
212#217—21no—
213#217—122no—
214(C2×D3)⋊C4—21no—
215(C2×D3)⋊C4—21no—
216(C2×D3)⋊C4—122no—
217C4⋊Dic3—21no—
218C4⋊Dic3—122no—
219C4⋊Dic3C2×Dic311yescharacteristic
220Dic3⋊C4—21no—
221Dic3⋊C4—21no—
222Dic3⋊C4—21no—
223Dic3⋊C4—122no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—121no—
228C2×C3⋊C8—122no—
229D3×C8—122no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32C2×C22⋊C411yescharacteristic
233C22×C32C2×SD1611yescharacteristic
234C22×C32C2×Q1611yescharacteristic
235C2×C3×D3—21no—
236C2×C3×D3—21no—
237C2×C3×D3—21no—
238C2×C3×D3—21no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3#10312yes—
242C2×C3×D3#10312yes—
243C32×C4—21no—
244C32×C4—21no—
245C32×C4—41no—
246C32×C4—41no—
247C3⋊Dic3—81no—
248C3×Dic3—21no—
249C3×Dic3—41no—
250C3×Dic3—41no—
251C3×Dic3—81no—
252C3×Dic3#9912yes—
253C22×Q8—31no—
254C23×C4—31no—
255C22×C8—181no—
256C22⋊Q8—31no—
257C22⋊Q8—31no—
258C22⋊Q8—31no—
259C22⋊Q8—61no—
260C22⋊Q8—61no—
261C22⋊Q8D3211yescharacteristic
262C2×C4⋊C4—31no—
263C2×C4⋊C4—61no—
264C2×C4⋊C4—181no—
265C2×C22⋊C4—61no—
266C2×C22⋊C4—181no—
267C22⋊C8—31no—
268C22⋊C8—91no—
269C22⋊C8—181no—
270#95—31no—
271#95—91no—
272C23×C3—21no—
273C23×C3—31no—
274C23×C3—31no—
275C23×C3—32no—
276C23×C3—32no—
277C23×C3—121no—
278C23×C3—121no—
279C23×C3D3×D411yescharacteristic
280C23×C3C2×#6711yescharacteristic
281C22×D3—41no—
282C22×D3—41no—
283C22×D3#21512yes—
284C22×D3#21612yes—
285C22×D3#21711yescharacteristic
286C22×D3#21711yescharacteristic
287C3×Q8—41no—
288C3×Q8—41no—
289C3×Q8—81no—
290C3×Q8—121no—
291C3×Q8—122no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—31no—
299C2×C3×C4—31no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—81no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4—122no—
313C2×C3×C4—122no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4C22×Dic311yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321C2×Dic3—22no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—122no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—241no—
335C2×Dic3—241no—
336C2×Dic3#21711yescharacteristic
337C2×Dic3#21711yescharacteristic
338C4×D3—22no—
339C4×D3—22no—
340C4×D3—41no—
341C4×D3—41no—
342C4×D3—42no—
343C4×D3—42no—
344Dic6—42no—
345Dic6—41no—
346C3×C8—121no—
347C3⋊C8—41no—
348C3⋊C8—121no—
349C3⋊C8—121no—
350C3⋊C8—241no—
351C2×C32—21no—
352C2×C32—21no—
353C2×C32C2×#9911yescharacteristic
354C2×C32C2×#10311yescharacteristic
355C2×C32#42111yescharacteristic
356C3×D3—22no—
357C3×D3—22no—
358C24—31no—
359C2×Q8—31no—
360C2×Q8—61no—
361C2×Q8—122no—
362C2×Q8D3×Dic311yescharacteristic
363C22×C4—31no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—122no—
372C22×C4—181no—
373C22×C4C2×D3211yescharacteristic
374C2×C8—61no—
375C2×C8—181no—
376C2×C8—362no—
377C4⋊C4—21no—
378C4⋊C4—31no—
379C4⋊C4—61no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C4⋊C4—61no—
383C4⋊C4—362no—
384C4⋊C4D3×Dic311yescharacteristic
385C22⋊C4—21no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—61no—
389C22⋊C4—362no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—32no—
398C22×C3—32no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—61no—
402C22×C3—61no—
403C22×C3—61no—
404C22×C3—61no—
405C22×C3—122no—
406C22×C3—122no—
407C22×C3D3×C22⋊C411yescharacteristic
408C22×C3D3×SD1611yescharacteristic
409C22×C3D3×Q1611yescharacteristic
410C22×C3C2×#21511yescharacteristic
411C22×C3C2×#21611yescharacteristic
412C22×C3C2×#21711yescharacteristic
413C2×D3—21no—
414C2×D3—21no—
415C2×D3—21no—
416C2×D3—21no—
417C2×D3—42no—
418C2×D3—42no—
419C2×D3#83512yes—
420C2×D3#83512yes—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—32no—
426C3×C4—41no—
427C3×C4—41no—
428C3×C4—41no—
429C3×C4—41no—
430C3×C4—41no—
431C3×C4—41no—
432C3×C4—61no—
433C3×C4—81no—
434C3×C4—81no—
435C3×C4—121no—
436C3×C4—121no—
437C3×C4—241no—
438Dic3—21no—
439Dic3—41no—
440Dic3—41no—
441Dic3—81no—
442Dic3—241no—
443Dic3—241no—
444Dic3—242no—
445Dic3#83412yes—
446C32#152011yescharacteristic, complemented, Sylow
447C23—31no—
448C23—31no—
449C23—32no—
450C23—32no—
451C23—121no—
452C23—121no—
453C23D3×#6711yescharacteristic
454Q8—41no—
455Q8—121no—
456Q8—122no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—31no—
460C2×C4—31no—
461C2×C4—41no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—121no—
468C2×C4—121no—
469C2×C4—122no—
470C2×C4—122no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—361no—
475C2×C4—361no—
476C2×C4—361no—
477C2×C4C2×D3×Dic311yescharacteristic
478C2×C4D3×#6711yescharacteristic
479C8—121no—
480C8—361no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—41no—
489C2×C3—41no—
490C2×C3—62no—
491C2×C3—62no—
492C2×C3D3×#9911yescharacteristic
493C2×C3D3×#10311yescharacteristic
494C2×C3#482111yescharacteristic
495C2×C3C2×#83411yescharacteristic
496C2×C3C2×#83511yescharacteristic
497C2×C3#523611yescharacteristic
498D3—22no—
499D3—22no—
500C22—21no—
501C22—21no—
502C22—32no—
503C22—32no—
504C22—61no—
505C22—61no—
506C22—61no—
507C22—61no—
508C22—122no—
509C22—122no—
510C22D3×#21511yescharacteristic
511C22D3×#21611yescharacteristic
512C22D3×#21711yescharacteristic
513C4—21no—
514C4—21no—
515C4—32no—
516C4—41no—
517C4—41no—
518C4—61no—
519C4—121no—
520C4—121no—
521C4—241no—
522C4—721no—
523C3—21no—
524C3#6833911yescharacteristic, complemented
525C3#7169011yescharacteristic, complemented
526C2—21no—
527C2—21no—
528C2—62no—
529C2—62no—
530C2D3×#83411yescharacteristic
531C2D3×#83511yescharacteristic
532C2#1059167011yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC22⋊Q8D32
hypocenterC32#1520
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. #10589404C2semidirect
5. C3×#4538C2semidirect
6. #10589153C2semidirect
7. #10589152C2semidirect
10. C2×C3×D3×Q8C4semidirect
13. C3×#946C4semidirect
15. C3×#897C4semidirect
18. C3×D3×C4⋊C4C4semidirect
41. #4538D3semidirect
79. C2×D3×Q8Dic3semidirect
93. #946Dic3semidirect
100. #897Dic3semidirect
103. D3×C4⋊C4Dic3semidirect
446. C32#1520semidirect
524. C3#68339semidirect
525. C3#71690semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C22⋊Q82
#105912952
D3×#8302
#105894042
C3×#45382
#105891532
#105891522
#716903
#683393