Finite Group Databasebeta

← #11873492

Subgroups — #11873492

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593969C211yesmaximal, characteristic
2#10593874C211yesmaximal, characteristic, complemented
3#10592396C211yesmaximal, characteristic, complemented
4C3×#4697C211yesmaximal, characteristic, complemented
5C3×C4×D3×C8C211yesmaximal, characteristic, complemented
6#10590954C212yesmaximal, complemented
7#10590890C212yesmaximal, complemented
8#10590878C212yesmaximal, complemented
9#10590690C212yesmaximal, complemented
10#10590293C211yesmaximal, characteristic, complemented
11#10590274C211yesmaximal, characteristic, complemented
12#81637—31nomaximal
13#78463—31nomaximal
14C2×#3799C2211yescharacteristic
15C2×#3795C2211yescharacteristic
16#64084C2211yescharacteristic
17#64079C2211yescharacteristic
18C2×C3×D3×C8C2212yes—
19C3×#875C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C3×#870C2211yescharacteristic
22#63918C2212yes—
23#63911C2211yescharacteristic
24#63906—22no—
25#63880—22no—
26#63866C2211yescharacteristic
27#63851—22no—
28#63841C2212yes—
29#63837—22no—
30C32×C4×C8C2211yescharacteristic
31#63648C2212yes—
32#63643C2212yes—
33C3×#821C2212yes—
34C3×#816C2212yes—
35C3×C8×Dic3C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37#63567C2212yes—
38#63566C2212yes—
39#63564C2212yes—
40#63563C2212yes—
41#5688—31no—
42#5668—31no—
43#5477—31no—
44#5470—31no—
45C3×#488—31no—
46C2×C3×C4×C8—31no—
47#5113—32no—
48#5113—32no—
49#5068—31no—
50#5056—31no—
51#4804—32no—
52#4792—32no—
53#4772—32no—
54#4760—32no—
55#4697—31no—
56#4697—31no—
57#4697—31no—
58#4697—31no—
59#4697—61no—
60#4697D311yescharacteristic, complemented
61#4694—32no—
62C4×D3×C8D311yescharacteristic, complemented
63#4681—32no—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×#634C2311yescharacteristic
66C2×C3×D12C2311yescharacteristic
67C2×C3×C4×D3D412yes—
68C2×C3×C4×D3C2311yescharacteristic
69C2×C3×Dic6C2311yescharacteristic
70C2×#627—22no—
71C2×#626—21no—
72C2×#626—22no—
73C2×#625—21no—
74C2×#624—21no—
75C2×D3×Dic3—21no—
76#3799—24no—
77#3795—24no—
78C2×C32×C8C2312yes—
79C32×C42C2311yescharacteristic
80#3752—22no—
81C4⋊(C3⋊Dic3)C2312yes—
82#3750—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3C2312yes—
85C3×Dic3⋊C4—22no—
86C3×C4×Dic3D412yes—
87C3×C4×Dic3C2311yescharacteristic
88C2×C3×C3⋊C8C2312yes—
89C3×D3×C8—24no—
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93Dic32—22no—
94#3131—91noSylow
95C2×#239—31no—
96C2×#237—31no—
97C2×#235—31no—
98C2×#235—31no—
99C22×C3×C8—32no—
100C3×#125—31no—
101C3×#124—31no—
102C2×C3×C42—31no—
103#944—31no—
104#940—31no—
105#930—62no—
106#926—32no—
107#924—62no—
108C2×D3×C8C2×D312yes—
109#896—62no—
110#892—32no—
111#888—32no—
112#887—62no—
113#884—62no—
114#67⋊C4—62no—
115#875—31no—
116#875—31no—
117#875—61no—
118#875C2×D311yescharacteristic
119#874—31no—
120C4×D12—62no—
121C42×D3C2×D311yescharacteristic
122#870—31no—
123#870—31no—
124#870—61no—
125#870C2×D311yescharacteristic
126#869—32no—
127#869—31no—
128C4×Dic6—62no—
129C3×#103—32no—
130C3×#102—32no—
131C3×C4×C8—21no—
132C3×C4×C8—32no—
133C3×C4×C8—31no—
134C3×C4×C8C2×D311yescharacteristic
135C3×C4×C8C2×D311yescharacteristic
136#835—32no—
137#832—32no—
138#821—32no—
139#821—32no—
140#821—32no—
141#821—32no—
142#821—62no—
143#821C2×D312yes—
144#816—32no—
145#816—32no—
146#816—32no—
147#816—32no—
148#816—62no—
149#816C2×D312yes—
150C8×Dic3C2×D312yes—
151#810—32no—
152#809—32no—
153C4×C3⋊C8C2×D311yescharacteristic
154C22×C3⋊D3—21no—
155C22×C3×D3—21no—
156C22×C3×D3C2×D411yescharacteristic
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—21no—
161C4⋊(C3⋊D3)—22no—
162#634—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3C2×D411yescharacteristic
166C2×C3×Dic3C2×D412yes—
167C3×D12—22no—
168C3×C4×D3—24no—
169C3×C4×D3#4114yes—
170C3×Dic6—22no—
171#627—44no—
172#626—42no—
173#626—44no—
174#625—42no—
175#624—42no—
176D3×Dic3—42no—
177C32×C8—22no—
178C3×C3⋊C8—22no—
179#533—91no—
180#532—91no—
181#488—31no—
182#488—91no—
183#488—91no—
184#488—91no—
185#487—92no—
186#486—92no—
187#416—92no—
188#416—92no—
189C2×C4×C8—31no—
190C2×C3×Q8—31no—
191C2×C3×D4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—32no—
194C2×#67—61no—
195C2×#67—61no—
196C2×#67—61no—
197C2×#67—62no—
198C22×Dic3—61no—
199#239—64no—
200#237—64no—
201#235—64no—
202#235—64no—
203C2×D12—31no—
204C2×D12—31no—
205C2×D12—61no—
206C2×D12—62no—
207C2×D12—61no—
208C2×D12C22×D311yescharacteristic
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×C4×D3D1212yes—
213C2×C4×D3C22×D311yescharacteristic
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—61no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6C22×D311yescharacteristic
220C2×C3×C8—22no—
221C2×C3×C8—32no—
222C2×C3×C8—64no—
223C2×C3×C8C22×D312yes—
224C2×C3×C8C22×D312yes—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—62no—
227C3×C22⋊C4—62no—
228C3×C42—21no—
229C3×C42—32no—
230C3×C42—31no—
231C3×C42C22×D311yescharacteristic
232C3×C42C22×D311yescharacteristic
233#217—62no—
234(C2×D3)⋊C4—22no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—122no—
239C4⋊Dic3—32no—
240C4⋊Dic3—32no—
241C4⋊Dic3—62no—
242C4⋊Dic3—62no—
243C4⋊Dic3—62no—
244C4⋊Dic3C22×D312yes—
245Dic3⋊C4—22no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250Dic3⋊C4—122no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253C4×Dic3D1212yes—
254C4×Dic3C22×D311yescharacteristic
255C2×C3⋊C8C22×D312yes—
256D3×C8—24no—
257C22×C32C22×D411yescharacteristic
258C2×C3⋊D3—41no—
259C2×C3⋊D3—42no—
260C2×C3×D3—22no—
261C2×C3×D3—41no—
262C2×C3×D3—42no—
263C2×C3×D3#12412yes—
264C32×C4—22no—
265C32×C4C2×#4112yes—
266C3⋊Dic3—41no—
267C3⋊Dic3—42no—
268C3×Dic3—41no—
269C3×Dic3—42no—
270C3×Dic3#12412yes—
271C3×Dic3#13514yes—
272C2×#41—91no—
273C2×#41—91no—
274C22×C8—32no—
275C4⋊Q8—92no—
276C4⋊Q8—91no—
277#127—91no—
278#125—31no—
279#125—91no—
280#124—31no—
281#124—91no—
282C22⋊Q8—182no—
283#121—182no—
284C4×Q8—182no—
285C4×D4—182no—
286#117—92no—
287C2×C42—31no—
288#103—32no—
289#103—92no—
290#103—92no—
291#103—92no—
292#102—32no—
293#102—92no—
294#102—92no—
295#102—92no—
296C4×C8—32no—
297C4×C8—31no—
298C4×C8D3211yescharacteristic
299C23×C3—31no—
300C23×C3—61no—
301C22×D3—21no—
302C22×D3—61no—
303C22×D3—61no—
304C22×D3—121no—
305C22×D3C2×D1211yescharacteristic
306C3×Q8—62no—
307C3×D4—62no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—31no—
311C2×C3×C4—32no—
312C2×C3×C4—34no—
313C2×C3×C4—64no—
314C2×C3×C4—62no—
315C2×C3×C4—61no—
316C2×C3×C4C2×D1212yes—
317C2×C3×C4D3×D412yes—
318C2×C3×C4C23×D311yescharacteristic
319C2×C3×C4C23×D311yescharacteristic
320#67—122no—
321#67—122no—
322#67—122no—
323#67—124no—
324C2×Dic3—22no—
325C2×Dic3—21no—
326C2×Dic3—62no—
327C2×Dic3—61no—
328C2×Dic3—62no—
329C2×Dic3—61no—
330C2×Dic3—122no—
331C2×Dic3—121no—
332C2×Dic3—122no—
333C2×Dic3C2×D1211yescharacteristic
334C2×Dic3C2×D1212yes—
335D12—22no—
336D12—62no—
337D12—62no—
338D12—122no—
339D12—124no—
340D12—122no—
341C4×D3—24no—
342C4×D3—122no—
343C4×D3—122no—
344C4×D3—122no—
345C4×D3#23514yes—
346Dic6—22no—
347Dic6—62no—
348Dic6—62no—
349Dic6—122no—
350Dic6—124no—
351Dic6—124no—
352C3×C8—22no—
353C3×C8—22no—
354C3×C8—42no—
355C3×C8—62no—
356C3⋊C8—22no—
357C2×C32C2×#12411yescharacteristic
358C2×C32C2×#13512yes—
359C3⋊D3—81no—
360C3×D3—22no—
361C3×D3—81no—
362#41—184no—
363#41—184no—
364C2×Q8—31no—
365C2×Q8—91no—
366C2×Q8—182no—
367C2×D4—31no—
368C2×D4—91no—
369C2×D4—182no—
370C2×D4—181no—
371C2×D4—181no—
372C22×C4—31no—
373C22×C4—32no—
374C22×C4—181no—
375C22×C4—181no—
376C2×C8—32no—
377C2×C8—64no—
378C2×C8C2×D3212yes—
379C4⋊C4—32no—
380C4⋊C4—62no—
381C4⋊C4—92no—
382C4⋊C4—182no—
383C4⋊C4—182no—
384C4⋊C4—182no—
385C22⋊C4—62no—
386C22⋊C4—182no—
387C22⋊C4—182no—
388C42—31no—
389C42—32no—
390C42—182no—
391C42C2×D3211yescharacteristic
392C22×C3—21no—
393C22×C3—32no—
394C22×C3—62no—
395C22×C3—121no—
396C22×C3—122no—
397C22×C3C22×D1211yescharacteristic
398C22×C3C2×D3×D411yescharacteristic
399C2×D3—22no—
400C2×D3—41no—
401C2×D3—42no—
402C2×D3—121no—
403C2×D3—121no—
404C2×D3—122no—
405C2×D3—122no—
406C2×D3—241no—
407C2×D3—242no—
408C2×D3#87512yes—
409C3×C4—22no—
410C3×C4—22no—
411C3×C4—22no—
412C3×C4—32no—
413C3×C4—34no—
414C3×C4—42no—
415C3×C4—121no—
416C3×C4—122no—
417C3×C4C2×#23512yes—
418C3×C4D3×#4112yes—
419Dic3—41no—
420Dic3—42no—
421Dic3—121no—
422Dic3—121no—
423Dic3—122no—
424Dic3—122no—
425Dic3—241no—
426Dic3—242no—
427Dic3#87512yes—
428Dic3#90414yes—
429C32#313111yescharacteristic, complemented, Sylow
430C23—31no—
431C23—61no—
432C23—181no—
433Q8—62no—
434Q8—182no—
435Q8—364no—
436D4—62no—
437D4—182no—
438D4—364no—
439D4—362no—
440D4—362no—
441C2×C4—31no—
442C2×C4—32no—
443C2×C4—34no—
444C2×C4—64no—
445C2×C4—62no—
446C2×C4—61no—
447C2×C4—182no—
448C2×C4—181no—
449C2×C4—362no—
450C2×C4—362no—
451C2×C4D3×D1212yes—
452C2×C4C22×D3211yescharacteristic
453C8—22no—
454C8—62no—
455C2×C3—22no—
456C2×C3—21no—
457C2×C3—62no—
458C2×C3—241no—
459C2×C3C2×#87511yescharacteristic
460C2×C3D3×#12411yescharacteristic
461C2×C3C2×#90412yes—
462C2×C3D3×#13512yes—
463D3—22no—
464D3—81no—
465D3—241no—
466D3—241no—
467D3—481no—
468C22—32no—
469C22—62no—
470C22—122no—
471C22—121no—
472C22—362no—
473C22—361no—
474C22C2×D3×D1211yescharacteristic
475C4—22no—
476C4—34no—
477C4—32no—
478C4—122no—
479C4—121no—
480C4—362no—
481C4—361no—
482C4D3×#23512yes—
483C3—21no—
484C3#7846311yescharacteristic, complemented
485C3#8163711yescharacteristic, complemented
486C2—62no—
487C2—241no—
488C2—721no—
489C2D3×#87511yescharacteristic
490C2D3×#90412yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10593969C2
hypercenterC4×C8D32
hypocenterC32#3131
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593874C2semidirect
3. #10592396C2semidirect
4. C3×#4697C2semidirect
5. C3×C4×D3×C8C2semidirect
6. #10590954C2semidirect
7. #10590890C2semidirect
8. #10590878C2semidirect
9. #10590690C2semidirect
10. #10590293C2semidirect
11. #10590274C2semidirect
60. #4697D3semidirect
62. C4×D3×C8D3semidirect
429. C32#3131semidirect
484. C3#78463semidirect
485. C3#81637semidirect

Maximal subgroups

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

subgroupindex
#105939692
#105938742
#105923962
C3×#46972
C3×C4×D3×C82
#105909542
#105908902
#105908782
#105906902
#105902932
#105902742
#816373
#784633