Finite Group Databasebeta

← #11869391

Subgroups — #11869391

Order 1152.

985 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594631C211yesmaximal, characteristic
2D32×C4⋊C4C211yesmaximal, characteristic
3C3⋊D3×#106C211yesmaximal, characteristic, complemented
4C3×#4862C212yesmaximal, complemented
5#10590935C211yesmaximal, characteristic
6#10590675C212yesmaximal, complemented
7#10590672C211yesmaximal, characteristic, complemented
8#10590601C211yesmaximal, characteristic, complemented
9#10590575C211yesmaximal, characteristic, complemented
10#10590516C212yesmaximal, complemented
11#10590439C212yesmaximal, complemented
12D3×#483—32nomaximal
13C2×C4×D32—21no—
14C2×C4×D32C2211yescharacteristic
15C2×#3797C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2211yescharacteristic
18C4⋊C4×C3⋊D3C2211yescharacteristic
19C3×#897C2212yes—
20C3×D3×C4⋊C4C2212yes—
21#63921—21no—
22#63900—21no—
23#63900C2211yescharacteristic
24#63899—22no—
25D3×C4⋊Dic3C2212yes—
26#63883—21no—
27D3×Dic3⋊C4—22no—
28#63856C2212yes—
29C2×#3710C2211yescharacteristic
30C32×#106C2211yescharacteristic, complemented
31#63644C2211yescharacteristic, complemented
32#63635C2211yescharacteristic, complemented
33#63635C2211yescharacteristic, complemented
34C3×(C2×D3)⋊C8C2212yes—
35C3×#816C2212yescomplemented
36C3×#810C2212yescomplemented
37C3×#808C2212yescomplemented
38#63573C2212yescomplemented
39#63566C2212yescomplemented
40#63565C2212yescomplemented
41(C2×D3)⋊(C3⋊C8)C2212yes—
42D3×C22⋊Q8—32no—
43C2×D3×C4⋊C4—32no—
44C3×#483—32no—
45#5043—32no—
46#4971—32no—
47#4862—32no—
48#4862D312yescomplemented
49D3×#106—32no—
50D3×#106—32no—
51D3×#106—61no—
52#4805—32no—
53#4805—32no—
54D3×#103—32no—
55D3×#103—32no—
56D3×C22⋊C8—32no—
57#4721—32no—
58C22×D32D411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3C2312yes—
64C2×C3×Dic6C2312yes—
65C2×#627—21no—
66C2×#624—21no—
67C2×#624—21no—
68C2×#624D411yescharacteristic
69C2×D3×Dic3—22no—
70C2×D3×Dic3D412yes—
71C4×D32—22no—
72C4×D32—22no—
73C4×D32—44no—
74#3797—22no—
75#3797—22no—
76C2×C32×C8C2311yescharacteristic
77C32×C4⋊C4C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82#3750—21no—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C8×C3⋊D3—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3C2312yes—
88C3×Dic3⋊C4—22no—
89C2×C3×C3⋊C8C2312yes—
90#3724—21no—
91#3724—22no—
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94#3710—22no—
95C2×#483—91noSylow
96C2×D3×Q8—32no—
97C22×C4×D3—32no—
98C22×C4×D3—62no—
99C3×C22⋊Q8—32no—
100C2×C3×C4⋊C4—32no—
101#946—32no—
102C2×C4⋊Dic3—32no—
103#924—32no—
104C2×Dic3⋊C4—62no—
105C2×D3×C8—32no—
106C2×D3×C8—32no—
107C2×D3×C8—61no—
108#897C2×D312yes—
109#896—62no—
110D3×C4⋊C4—32no—
111D3×C4⋊C4—32no—
112D3×C4⋊C4—32no—
113D3×C4⋊C4—32no—
114D3×C4⋊C4—61no—
115D3×C4⋊C4—61no—
116D3×C4⋊C4—62no—
117D3×C4⋊C4—62no—
118D3×C4⋊C4—62no—
119D3×C4⋊C4C2×D312yes—
120D3×C22⋊C4—62no—
121#878—62no—
122C3×#106—21no—
123C3×#106—32no—
124C3×#106C2×D312yescomplemented
125C3×#103—32no—
126C3×#103—32no—
127C3×C22⋊C8—32no—
128#835—32no—
129#835—32no—
130#830—32no—
131(C2×D3)⋊C8—32no—
132(C2×D3)⋊C8C2×D312yes—
133#817—32no—
134#817—32no—
135#817—61no—
136#816—32no—
137#816C2×D312yescomplemented
138#810—32no—
139#810C2×D312yescomplemented
140#808—32no—
141#808—32no—
142#808—32no—
143#808—61no—
144#808—61no—
145#808C2×D312yescomplemented
146C22×C3⋊D3C2×D411yescharacteristic
147C22×C3×D3C2×D412yes—
148C2×D32—22no—
149C2×D32—22no—
150C2×D32SD1614yes—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3C2×D411yescharacteristic
157C4×C3⋊D3—42no—
158C4×C3⋊D3—42no—
159C4×C3⋊D3#4112yes—
160C4×C3⋊D3#4112yes—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3C2×D412yes—
164C3×C4×D3—22no—
165C3×C4×D3—22no—
166C3×C4×D3—44no—
167C3×Dic6—22no—
168C3×Dic6—22no—
169#627—42no—
170#624—22no—
171#624—42no—
172#624—42no—
173D3×Dic3—24no—
174D3×Dic3—44no—
175C32×C8—21no—
176C3⋊(C3⋊C8)—21no—
177C3×C3⋊C8—22no—
178C2×C22⋊Q8—91no—
179C22×C4⋊C4—91no—
180#483—32no—
181#483—92no—
182#483—92no—
183#483—92no—
184C2×#106—91no—
185C2×#106—91no—
186C2×#103—91no—
187C2×#103—91no—
188C2×C22⋊C8—91no—
189C23×D3—32no—
190C2×C3×Q8—32no—
191C22×C3×C4—32no—
192C22×C3×C4—62no—
193C22×Dic3—32no—
194C22×Dic3—62no—
195D3×Q8—64no—
196D3×Q8—64no—
197C2×C4×D3—22no—
198C2×C4×D3—32no—
199C2×C4×D3—32no—
200C2×C4×D3—32no—
201C2×C4×D3—61no—
202C2×C4×D3—64no—
203C2×C4×D3—64no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×C4×D3—62no—
209C2×C4×D3—121no—
210C2×C4×D3—121no—
211C2×C4×D3—128no—
212C2×C4×D3C22×D312yes—
213C2×Dic6—62no—
214C2×Dic6C22×D312yes—
215C2×C3×C8—21no—
216C2×C3×C8—32no—
217C2×C3×C8C22×D312yes—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—32no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4—62no—
223C3×C4⋊C4C22×D312yes—
224C3×C4⋊C4C22×D312yes—
225C3×C22⋊C4—62no—
226#217—62no—
227(C2×D3)⋊C4—22no—
228(C2×D3)⋊C4—62no—
229C4⋊Dic3—22no—
230C4⋊Dic3—32no—
231C4⋊Dic3—32no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234C4⋊Dic3—62no—
235C4⋊Dic3C22×D312yes—
236Dic3⋊C4—22no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243Dic3⋊C4—121no—
244Dic3⋊C4—121no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8C22×D312yes—
248D3×C8—64no—
249D3×C8—64no—
250D3×C8—64no—
251C22×C32C22×D411yescharacteristic
252C2×C3⋊D3#12312yes—
253C2×C3⋊D3C2×SD1612yes—
254C2×C3⋊D3#13712yes—
255C2×C3×D3—22no—
256C2×C3×D3—22no—
257C2×C3×D3C2×SD1614yes—
258D32—28no—
259C32×C4—41no—
260C32×C4—41no—
261C32×C4C2×#4111yescharacteristic
262C32×C4C2×#4111yescharacteristic
263C3⋊Dic3—41no—
264C3⋊Dic3—41no—
265C3⋊Dic3#12312yes—
266C3×Dic3—22no—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C22×Q8—91no—
270C23×C4—91no—
271C23×C4—181no—
272C22×C8—91no—
273C22×C8—91no—
274C22⋊Q8—32no—
275C22⋊Q8—92no—
276C22⋊Q8—182no—
277C2×C4⋊C4—32no—
278C2×C4⋊C4—91no—
279C2×C4⋊C4—92no—
280C2×C4⋊C4—91no—
281C2×C4⋊C4—91no—
282C2×C4⋊C4—181no—
283C2×C4⋊C4—181no—
284C2×C4⋊C4—182no—
285C2×C22⋊C4—181no—
286#106—32no—
287#106—92no—
288#106—91no—
289#106—91no—
290#106—91no—
291#106D3211yescharacteristic, complemented
292#103—32no—
293#103—32no—
294#103—92no—
295#103—92no—
296C22⋊C8—32no—
297C22⋊C8—92no—
298C23×C3—32no—
299C22×D3—32no—
300C22×D3—38no—
301C22×D3—61no—
302C22×D3—64no—
303C22×D3—64no—
304C22×D3D3×D412yes—
305C3×Q8—62no—
306C3×Q8—62no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—32no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—124no—
318C2×C3×C4C23×D312yes—
319C2×Dic3—22no—
320C2×Dic3—22no—
321C2×Dic3—32no—
322C2×Dic3—61no—
323C2×Dic3—64no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—124no—
329C2×Dic3D3×D412yes—
330C4×D3—22no—
331C4×D3—22no—
332C4×D3—34no—
333C4×D3—34no—
334C4×D3—44no—
335C4×D3—62no—
336C4×D3—62no—
337C4×D3—64no—
338C4×D3—64no—
339C4×D3—124no—
340C4×D3—124no—
341C4×D3—124no—
342C4×D3—124no—
343C4×D3—124no—
344C4×D3—242no—
345C4×D3—242no—
346Dic6—22no—
347Dic6—22no—
348Dic6—124no—
349C3×C8—22no—
350C3×C8—22no—
351C3×C8—62no—
352C3⋊C8—22no—
353C3⋊C8—62no—
354C3⋊C8—62no—
355C2×C32C2×#12311yescharacteristic
356C2×C32C22×SD1611yescharacteristic
357C2×C32C2×#13711yescharacteristic
358C3⋊D3#48314yescomplemented
359C3×D3—24no—
360C24—91no—
361C2×Q8—32no—
362C2×Q8—181no—
363C2×Q8—182no—
364C2×Q8—182no—
365C22×C4—32no—
366C22×C4—62no—
367C22×C4—91no—
368C22×C4—92no—
369C22×C4—91no—
370C22×C4—181no—
371C22×C4—181no—
372C22×C4—182no—
373C22×C4—182no—
374C22×C4—181no—
375C22×C4—181no—
376C22×C4—182no—
377C22×C4—364no—
378C2×C8—32no—
379C2×C8—91no—
380C2×C8—182no—
381C2×C8—182no—
382C2×C8C2×D3211yescharacteristic
383C4⋊C4—32no—
384C4⋊C4—62no—
385C4⋊C4—62no—
386C4⋊C4—91no—
387C4⋊C4—91no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—182no—
391C4⋊C4—182no—
392C4⋊C4—181no—
393C4⋊C4C2×D3211yescharacteristic
394C4⋊C4C2×D3211yescharacteristic
395C22⋊C4—62no—
396C22⋊C4—182no—
397C22×C3—21no—
398C22×C3—34no—
399C22×C3—62no—
400C22×C3—62no—
401C22×C3C2×D3×D412yes—
402C2×D3—22no—
403C2×D3—22no—
404C2×D3—34no—
405C2×D3—34no—
406C2×D3—34no—
407C2×D3—62no—
408C2×D3—62no—
409C2×D3—62no—
410C2×D3—616no—
411C2×D3D3×SD1614yes—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—42no—
415C3×C4—42no—
416C3×C4—62no—
417C3×C4—81no—
418C3×C4—81no—
419C3×C4—122no—
420C3×C4—122no—
421C3×C4D3×#4112yes—
422C3×C4D3×#4112yes—
423Dic3—22no—
424Dic3—34no—
425Dic3—42no—
426Dic3—42no—
427Dic3—62no—
428Dic3—122no—
429Dic3—122no—
430Dic3—241no—
431Dic3—241no—
432C32C2×#48311yescharacteristic, complemented, Sylow
433C23—32no—
434C23—94no—
435C23—91no—
436C23—182no—
437C23—182no—
438Q8—62no—
439Q8—62no—
440Q8—362no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—32no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—91no—
449C2×C4—92no—
450C2×C4—92no—
451C2×C4—124no—
452C2×C4—182no—
453C2×C4—184no—
454C2×C4—181no—
455C2×C4—181no—
456C2×C4—362no—
457C2×C4—362no—
458C2×C4—362no—
459C2×C4—362no—
460C2×C4—364no—
461C2×C4C22×D3211yescharacteristic
462C8—21no—
463C8—62no—
464C8—181no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—64no—
469C2×C3D3×#12312yes—
470C2×C3C2×D3×SD1612yes—
471C2×C3D3×#13712yes—
472D3—24no—
473D3—38no—
474D3—64no—
475C22—34no—
476C22—62no—
477C22—62no—
478C22—92no—
479C22—92no—
480C22—92no—
481C22—188no—
482C22D32×D411yescharacteristic
483C4—41no—
484C4—41no—
485C4—62no—
486C4—92no—
487C4—122no—
488C4—122no—
489C4—361no—
490C4—361no—
491C4#6430611yescharacteristic
492C4#6431911yescharacteristic
493C3—21no—
494C3D3×#48312yescomplemented
495C2—64no—
496C2—94no—
497C2#1059460811yescharacteristic
498C2D32×SD1611yescharacteristic
499C2#1059474211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#106D32
hypocenterC32C2×#483
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. C3⋊D3×#106C2semidirect
4. C3×#4862C2semidirect
6. #10590675C2semidirect
7. #10590672C2semidirect
8. #10590601C2semidirect
9. #10590575C2semidirect
10. #10590516C2semidirect
11. #10590439C2semidirect
30. C32×#106C22semidirect
31. #63644C22semidirect
32. #63635C22semidirect
33. #63635C22semidirect
35. C3×#816C22semidirect
36. C3×#810C22semidirect
37. C3×#808C22semidirect
38. #63573C22semidirect
39. #63566C22semidirect
40. #63565C22semidirect
48. #4862D3semidirect
124. C3×#106C2×D3semidirect
137. #816C2×D3semidirect
139. #810C2×D3semidirect
145. #808C2×D3semidirect
291. #106D32semidirect
358. C3⋊D3#483semidirect
432. C32C2×#483semidirect
494. C3D3×#483semidirect

Maximal subgroups

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

subgroupindex
#105946312
D32×C4⋊C42
C3⋊D3×#1062
C3×#48622
#105909352
#105906752
#105906722
#105906012
#105905752
#105905162
#105904392
D3×#4833