Finite Group Databasebeta

← #11859492

Subgroups — #11859492

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64157C211yesmaximal, characteristic, complemented
2C3×#5832C211yesmaximal, characteristic
3C2×#63815C211yesmaximal, characteristic, complemented
4C3×#5234C211yesmaximal, characteristic, complemented
5#67⋊(C3⋊C8)C214yesmaximal, complemented
6#10591115C211yesmaximal, characteristic, complemented
7#10591070C211yesmaximal, characteristic, complemented
8#10591067C214yesmaximal, complemented
9C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
10#83275—31nomaximal
11#78657—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14#64157—24no—
15C2×#3748C2212yes—
16C2×#3748C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2212yes—
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#947C411yescharacteristic
20C3×#944C411yescharacteristic
21C3×#940C411yescharacteristic
22C3×#939C414yes—
23C3×#936C411yescharacteristic
24C3×C4×#67C2214yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3711C2212yes—
29#63815—24no—
30C2×D3×C3⋊C8C2212yes—
31C3×#830C2214yes—
32Dic3⋊(C3⋊C8)C2214yes—
33(C2×D3)⋊(C3⋊C8)C2214yes—
34Dic3×C3⋊C8C2212yes—
35Dic3×C3⋊C8C2212yes—
36C3×#532—31no—
37#5832D311yescharacteristic
38C2×#948—31no—
39C2×#948—31no—
40C2×#948—31no—
41C2×#948—61no—
42C2×#907—31no—
43C3×#408—31no—
44#5234—31no—
45#5234D311yescharacteristic, complemented
46#5118—31no—
47#5110—31no—
48C2×C8×Dic3—31no—
49#5012—34no—
50D4×C3⋊C8—34no—
51#4924—31no—
52C2×C4×C3⋊C8—31no—
53#4729—34no—
54#67⋊C8—34no—
55C32×#41—22no—
56C32×#41—22no—
57C2×C32×Q8C2×C411yescharacteristic
58C2×C32×D4C2×C411yescharacteristic
59C2×C32×D4C2×C412yes—
60C22×C32×C4C2312yes—
61C22×C32×C4C2311yescharacteristic
62C2×C3×#67C2×C414yes—
63C2×C3×#67C2×C412yes—
64C22×C3×Dic3C2×C412yes—
65C3×#235—22no—
66C3×#235—22no—
67C2×C3×D12C2×C411yescharacteristic
68C2×C3×C4×D3C2312yes—
69C2×C3×Dic6C2×C411yescharacteristic
70#3748—22no—
71#3748—24no—
72C2×C3⋊(C3⋊C8)—24no—
73C2×C3⋊(C3⋊C8)D414yescomplemented
74C2×C3⋊(C3⋊C8)C2312yes—
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2311yescharacteristic
77C3×#217C2×C414yes—
78C3×(C2×D3)⋊C4C2×C414yes—
79C3×Dic3⋊C4C2×C414yes—
80C3×C4×Dic3C2×C411yescharacteristic
81C3×C4×Dic3C2×C411yescharacteristic
82C3×C4×Dic3C2312yes—
83C3×#208—22no—
84C2×C3×C3⋊C8—22no—
85C2×C3×C3⋊C8C2312yes—
86C2×C3×C3⋊C8C2312yes—
87#3711—24no—
88D3×C3⋊C8—24no—
89#2931—91noSylow
90C2×C3×#41—21no—
91C2×C3×#41—31no—
92C2×C3×#41C2×D311yescharacteristic
93C2×C3×#41C2×D311yescharacteristic
94C2×#235C2×D311yescharacteristic
95C2×C3×M16—31no—
96C22×C3×C8—31no—
97C3×C4⋊Q8—31no—
98C3×#127—31no—
99C3×#124—31no—
100C3×#124—31no—
101C3×#121—34no—
102C3×C4×D4—34no—
103C2×C3×C42—31no—
104#948—64no—
105#948—64no—
106#948—64no—
107#948—68no—
108#947Dic311yescharacteristic
109#944Dic311yescharacteristic
110#940Dic311yescharacteristic
111#939Dic314yes—
112#936Dic311yescharacteristic
113C4×#67C2×D314yes—
114C2×C4×Dic3C2×D311yescharacteristic
115C2×#208—31no—
116C2×#208—32no—
117C2×#208—32no—
118C2×#208—31no—
119C2×#208—32no—
120C2×#208—61no—
121C2×#208—62no—
122C2×#208C2×D311yescharacteristic
123C22×C3⋊C8—31no—
124C22×C3⋊C8—31no—
125C22×C3⋊C8—32no—
126C22×C3⋊C8—32no—
127C22×C3⋊C8—32no—
128C22×C3⋊C8—61no—
129C22×C3⋊C8—62no—
130C22×C3⋊C8C2×D311yescharacteristic
131#907—64no—
132C2×ΓL(1,𝔽25)—32no—
133C2×D3×C8—32no—
134C3×C22⋊C8—34no—
135#830—34no—
136#830C2×D314yes—
137(C2×D3)⋊C8—34no—
138Dic3⋊C8—34no—
139C8×Dic3—32no—
140C8×Dic3—32no—
141C4⋊(C3⋊C8)—34no—
142C4×C3⋊C8—32no—
143C4×C3⋊C8—32no—
144C23×C32C22×C412yes—
145C23×C32C22×C411yescharacteristic
146C22×C3×D3C22×C412yes—
147C32×Q8—22no—
148C32×D4—24no—
149C32×D4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4C22×C412yes—
153C2×C32×C4C22×C411yescharacteristic
154C2×C32×C4C2×D412yes—
155C2×C32×C4#4112yes—
156C2×C32×C4C2411yescharacteristic
157C3×#67—24no—
158C3×#67—28no—
159C2×C3×Dic3—24no—
160C2×C3×Dic3C22×C412yes—
161C2×C3×Dic3C22×C412yes—
162C2×C3×Dic3C22×C412yes—
163C3×D12—22no—
164C3×C4×D3—22no—
165C3×C4×D3—22no—
166C3×Dic6—22no—
167C3⋊(C3⋊C8)—22no—
168C3⋊(C3⋊C8)C2×D412yes—
169C3⋊(C3⋊C8)C2×D412yes—
170C3×C3⋊C8—22no—
171C3×C3⋊C8—22no—
172C2×#131—91no—
173C2×#131—91no—
174#532—31no—
175#436—94no—
176C8×D4—94no—
177#423—91no—
178#408—31no—
179#408—91no—
180C2×C4×C8—91no—
181C3×#41—24no—
182C3×#41—24no—
183C3×#41—22no—
184C3×#41—22no—
185C3×#41—22no—
186C3×#41—22no—
187C3×#41—62no—
188C3×#41—62no—
189C2×C3×Q8—21no—
190C2×C3×Q8—31no—
191C2×C3×Q8C4×D311yescharacteristic
192C2×C3×Q8C2×Dic311yescharacteristic
193C2×C3×D4—22no—
194C2×C3×D4—21no—
195C2×C3×D4—34no—
196C2×C3×D4—32no—
197C2×C3×D4—31no—
198C2×C3×D4C4×D312yes—
199C2×C3×D4C4×D311yescharacteristic
200C2×C3×D4C2×Dic311yescharacteristic
201C2×C3×D4C2×Dic312yes—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4C22×D312yes—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67C2×Dic314yes—
211C2×#67C2×Dic312yes—
212C22×Dic3C2×Dic312yes—
213#235—22no—
214#235—22no—
215C2×D12C2×Dic311yescharacteristic
216C2×C4×D3C22×D312yes—
217C2×Dic6C2×Dic311yescharacteristic
218C3×M16—62no—
219C2×C3×C8—32no—
220C2×C3×C8—32no—
221C2×C3×C8—62no—
222C3×C4⋊C4—34no—
223C3×C22⋊C4—34no—
224C3×C22⋊C4—34no—
225C3×C42—31no—
226C3×C42—31no—
227C3×C42—32no—
228#217C2×Dic314yes—
229(C2×D3)⋊C4C2×Dic314yes—
230Dic3⋊C4C2×Dic314yes—
231C4×Dic3C2×Dic311yescharacteristic
232C4×Dic3C2×Dic311yescharacteristic
233C4×Dic3C22×D312yes—
234#208—22no—
235#208—64no—
236#208—64no—
237#208—64no—
238#208—68no—
239#208—64no—
240#208—62no—
241#208—62no—
242C2×C3⋊C8—22no—
243C2×C3⋊C8—34no—
244C2×C3⋊C8—34no—
245C2×C3⋊C8—31no—
246C2×C3⋊C8—31no—
247C2×C3⋊C8—31no—
248C2×C3⋊C8—31no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—64no—
255C2×C3⋊C8—64no—
256C2×C3⋊C8—64no—
257C2×C3⋊C8—64no—
258C2×C3⋊C8—68no—
259C2×C3⋊C8C22×D312yes—
260C2×C3⋊C8C22×D312yes—
261ΓL(1,𝔽25)—64no—
262D3×C8—64no—
263C22×C32—22no—
264C22×C32—22no—
265C22×C32—24no—
266C22×C32C4×D412yes—
267C22×C32C23×C411yescharacteristic
268C2×C3×D3—22no—
269C2×C3×D3—24no—
270C32×C4—22no—
271C32×C4C4×D412yes—
272C32×C4C22×D411yescharacteristic
273C32×C4C2×#4111yescharacteristic
274C3×Dic3—22no—
275C3×Dic3—22no—
276C3×Dic3#13114yescomplemented
277C2×#41—31no—
278C2×#41D3211yescharacteristic
279#131—184no—
280#131—184no—
281C2×M16—31no—
282C2×M16—92no—
283C2×M16—91no—
284C2×M16—92no—
285C22×C8—31no—
286C22×C8—92no—
287C22×C8—91no—
288C22×C8—92no—
289C4⋊Q8—31no—
290#127—31no—
291#124—31no—
292#124—31no—
293#121—34no—
294C4×D4—34no—
295C2×C42—31no—
296C4⋊C8—94no—
297C22⋊C8—34no—
298C22⋊C8—94no—
299C4×C8—92no—
300C4×C8—92no—
301C23×C3—22no—
302C23×C3—21no—
303C23×C3—32no—
304C23×C3C2×C4×D312yes—
305C23×C3C2×C4×D311yescharacteristic
306C23×C3C22×Dic312yes—
307C23×C3C22×Dic311yescharacteristic
308C22×D3C22×Dic312yes—
309C3×Q8—24no—
310C3×Q8—22no—
311C3×Q8—22no—
312C3×Q8—62no—
313C3×D4—28no—
314C3×D4—24no—
315C3×D4—24no—
316C3×D4—24no—
317C3×D4—22no—
318C3×D4—22no—
319C3×D4—68no—
320C3×D4—64no—
321C3×D4—62no—
322C2×C3×C4—24no—
323C2×C3×C4—24no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—32no—
336C2×C3×C4—64no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4C2×C4×D312yes—
340C2×C3×C4C2×C4×D311yescharacteristic
341C2×C3×C4D3×D412yes—
342C2×C3×C4D3×D412yes—
343C2×C3×C4#23712yes—
344C2×C3×C4#23712yes—
345C2×C3×C4C22×Dic312yes—
346C2×C3×C4C22×Dic311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349#67—24no—
350#67—28no—
351C2×Dic3—24no—
352C2×Dic3C22×Dic312yes—
353C2×Dic3C22×Dic312yes—
354C2×Dic3C22×Dic312yes—
355D12—22no—
356C4×D3—22no—
357C4×D3—22no—
358Dic6—22no—
359C3×C8—62no—
360C3×C8—62no—
361C3⋊C8—22no—
362C3⋊C8—22no—
363C3⋊C8—32no—
364C3⋊C8—32no—
365C3⋊C8—32no—
366C3⋊C8—32no—
367C3⋊C8—62no—
368C3⋊C8—62no—
369C3⋊C8—64no—
370C3⋊C8—62no—
371C3⋊C8—62no—
372C2×C32—22no—
373C2×C32—42no—
374C2×C32C2×C4×D411yescharacteristic
375C2×C32C2×#13112yes—
376C3×D3—42no—
377#41—22no—
378#41—22no—
379#41—62no—
380#41—62no—
381C2×Q8—31no—
382C2×Q8D3×Dic311yescharacteristic
383C2×D4—34no—
384C2×D4—32no—
385C2×D4—31no—
386C2×D4D3×Dic312yes—
387C2×D4D3×Dic311yescharacteristic
388C22×C4—32no—
389C22×C4—32no—
390C22×C4C2×D3212yes—
391C22×C4C2×D3211yescharacteristic
392M16—62no—
393M16—184no—
394M16—184no—
395M16—182no—
396C2×C8—32no—
397C2×C8—32no—
398C2×C8—62no—
399C2×C8—91no—
400C2×C8—91no—
401C2×C8—94no—
402C2×C8—92no—
403C2×C8—184no—
404C2×C8—184no—
405C4⋊C4—34no—
406C22⋊C4—34no—
407C22⋊C4—34no—
408C42—32no—
409C42—31no—
410C42—31no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—24no—
414C22×C3—22no—
415C22×C3—24no—
416C22×C3—22no—
417C22×C3—24no—
418C22×C3—21no—
419C22×C3—22no—
420C22×C3—42no—
421C22×C3—44no—
422C22×C3—62no—
423C22×C3—64no—
424C22×C3#67⋊C412yes—
425C22×C3D4×Dic312yes—
426C22×C3C22×C4×D311yescharacteristic
427C22×C3C23×Dic311yescharacteristic
428C2×D3—22no—
429C2×D3—24no—
430C3×C4—24no—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—22no—
436C3×C4—34no—
437C3×C4—62no—
438C3×C4—62no—
439C3×C4#67⋊C412yes—
440C3×C4D4×Dic312yes—
441C3×C4C2×D3×D411yescharacteristic
442C3×C4C2×D3×D411yescharacteristic
443C3×C4C2×#23711yescharacteristic
444C3×C4C2×#23711yescharacteristic
445Dic3—22no—
446Dic3—22no—
447Dic3#94814yescomplemented
448C32#293111yescharacteristic, complemented, Sylow
449C23—32no—
450C23C2×D3×Dic312yes—
451C23C2×D3×Dic311yescharacteristic
452Q8—22no—
453Q8—62no—
454D4—24no—
455D4—22no—
456D4—68no—
457D4—64no—
458D4—62no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—32no—
462C2×C4—32no—
463C2×C4—32no—
464C2×C4—64no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4C2×D3×Dic312yes—
468C2×C4C2×D3×Dic311yescharacteristic
469C2×C4#380512yes—
470C2×C4#381112yes—
471C2×C4C22×D3211yescharacteristic
472C8—62no—
473C8—62no—
474C8—92no—
475C8—92no—
476C8—182no—
477C2×C3—22no—
478C2×C3—22no—
479C2×C3—22no—
480C2×C3—21no—
481C2×C3—42no—
482C2×C3—44no—
483C2×C3—42no—
484C2×C3—42no—
485C2×C3—122no—
486C2×C3C2×#67⋊C411yescharacteristic
487C2×C3D3×#13112yes—
488C2×C3C2×D4×Dic311yescharacteristic
489C2×C3C2×#94812yes—
490D3—42no—
491C22—22no—
492C22—24no—
493C22—22no—
494C22—64no—
495C22—62no—
496C22#67⋊Dic312yes—
497C22C22×D3×Dic311yescharacteristic
498C4—22no—
499C4—34no—
500C4—62no—
501C4—62no—
502C4#67⋊Dic312yes—
503C4C2×#380511yescharacteristic
504C4C2×#381111yescharacteristic
505C3—21no—
506C3#7865711yescharacteristic, complemented
507C3#8327511yescharacteristic, complemented
508C2—22no—
509C2—42no—
510C2—122no—
511C2D3×#94812yes—
512C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×#41C22
prime radicalC3×#5832C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2931
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64157C2semidirect
3. C2×#63815C2semidirect
4. C3×#5234C2semidirect
5. #67⋊(C3⋊C8)C2semidirect
6. #10591115C2semidirect
7. #10591070C2semidirect
8. #10591067C2semidirect
9. C2×Dic3×C3⋊C8C2semidirect
45. #5234D3semidirect
73. C2×C3⋊(C3⋊C8)D4semidirect
276. C3×Dic3#131semidirect
447. Dic3#948semidirect
448. C32#2931semidirect
506. C3#78657semidirect
507. C3#83275semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C3×#58322
C2×#638152
C3×#52342
#67⋊(C3⋊C8)2
#105911152
#105910702
#105910672
C2×Dic3×C3⋊C82
#832753
#786573