Finite Group Databasebeta

← #11859350

Subgroups — #11859350

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C211yesmaximal, characteristic, complemented
2C22×C3×D3×C8C211yesmaximal, characteristic, complemented
3#10595022C211yesmaximal, characteristic
4#10592800C211yesmaximal, characteristic, complemented
5#10591119C211yesmaximal, characteristic, complemented
6#10591070C211yesmaximal, characteristic, complemented
7#10591069C211yesmaximal, characteristic, complemented
8#10590722C214yesmaximal, complemented
9C8×#625C214yesmaximal, complemented
10#83794—31nomaximal
11#83734—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15#64135C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#901—24no—
20C2×C3×ΓL(1,𝔽25)C2212yescomplemented
21C2×C3×D3×C8—24no—
22C2×C3×D3×C8C2212yes—
23C2×C3×D3×C8C2212yes—
24C2×C3×D3×C8C2212yescomplemented
25#63976C412yes—
26#63961C412yes—
27#63908C412yes—
28C4×#625C2214yes—
29#63856C412yes—
30#63642C2212yescomplemented
31C8×C3⋊Dic3C2212yescomplemented
32#63572C2214yescomplemented
33(C2×D3)⋊(C3⋊C8)C2214yes—
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C2×C3×#131—31no—
36C23×C3×C8—31no—
37#5828—31no—
38#5791—31no—
39C2×#901D311yescharacteristic, complemented
40C22×D3×C8D311yescharacteristic, complemented
41#5234—31no—
42#5207—31no—
43#5127—34no—
44#5126—31no—
45#5119—31no—
46#5111—34no—
47#5110—31no—
48C8×#67—34no—
49C8×#67—34no—
50#5102—31no—
51#5101—31no—
52#5101—31no—
53#5101—61no—
54C23×C3×D3C2×C411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67C2×C412yes—
57C22×C3×Dic3C2×C411yescharacteristic
58C3×#235—22no—
59C3×#235—22no—
60C2×C3×D12C2×C411yescharacteristic
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3C2×C412yes—
64C2×C3×C4×D3C2312yes—
65C2×C3×C4×D3C2312yes—
66C2×C3×Dic6C2×C411yescharacteristic
67C2×#625C2×C414yes—
68C2×C32×C8D414yescomplemented
69C2×C32×C8C2311yescharacteristic
70C2×C32×C8C2311yescharacteristic
71#3757C2×C412yes—
72C4⋊(C3⋊Dic3)C2×C412yes—
73C4×C3⋊Dic3C2312yes—
74#3748—22no—
75C2×C3⋊(C3⋊C8)C2312yes—
76C3×#208—22no—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80C3×ΓL(1,𝔽25)—24no—
81C3×D3×C8—24no—
82C3×D3×C8—24no—
83C3×D3×C8—24no—
84#3724C2×C414yes—
85(C2×D3)⋊Dic3C2×C414yes—
86(C2×D3)⋊Dic3C2×C414yes—
87#2929—91noSylow
88C2×C3×#41—31no—
89C23×C3×C4—31no—
90C2×#235C2×D311yescharacteristic
91C22×C4×D3C2×D311yescharacteristic
92C3×#131—64no—
93C2×C3×M16—31no—
94C2×C3×M16—32no—
95C22×C3×C8—21no—
96C22×C3×C8—31no—
97C22×C3×C8—32no—
98C22×C3×C8—32no—
99C22×C3×C8—32no—
100C22×C3×C8—64no—
101C22×C3×C8C2×D311yescharacteristic
102C22×C3×C8C2×D311yescharacteristic
103#953—32no—
104#946—32no—
105#938—32no—
106#937—32no—
107#935—32no—
108#930—32no—
109#929—32no—
110C4×#67—34no—
111C4×#67—34no—
112#926—31no—
113#926—31no—
114#926—61no—
115#924—32no—
116C2×#208—31no—
117C2×#208—31no—
118C2×#208—61no—
119C2×#208C2×D311yescharacteristic
120C22×C3⋊C8C2×D311yescharacteristic
121#901—24no—
122C2×ΓL(1,𝔽25)C2×D312yescomplemented
123C2×D3×C8—24no—
124C2×D3×C8C2×D312yes—
125C2×D3×C8C2×D312yes—
126C2×D3×C8C2×D312yescomplemented
127#830—34no—
128#830—34no—
129(C2×D3)⋊C8—34no—
130(C2×D3)⋊C8—34no—
131#815—32no—
132#815—32no—
133#815—62no—
134Dic3⋊C8—34no—
135Dic3⋊C8—34no—
136C8×Dic3—32no—
137C8×Dic3—32no—
138C8×Dic3—62no—
139C23×C32C22×C411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—24no—
142C22×C3×D3C22×C412yes—
143C22×C3×D3C22×C412yes—
144C2×C32×C4C22×C411yescharacteristic
145C2×C32×C4C2×D412yes—
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3C22×C414yes—
149C3×#67—24no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3C22×C412yes—
152C2×C3×Dic3C22×C412yes—
153C3×D12—22no—
154C3×C4×D3—24no—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159C3×Dic6—22no—
160#625—28no—
161C32×C8C2×D412yes—
162C32×C8C2×D412yes—
163C3⋊(C3⋊C8)—22no—
164C3×C3⋊C8—22no—
165C3×C3⋊C8—22no—
166C2×#131—31no—
167C23×C8—31no—
168#525—91no—
169#435—94no—
170C8×D4—94no—
171#424—91no—
172#408—91no—
173#407—91no—
174#405—91no—
175C24×C3—31no—
176C23×D3C4×D311yescharacteristic
177C3×#41—62no—
178C3×#41—62no—
179C2×C3×Q8—31no—
180C2×C3×D4—32no—
181C2×C3×D4—31no—
182C22×C3×C4—21no—
183C22×C3×C4—31no—
184C22×C3×C4—32no—
185C22×C3×C4—32no—
186C22×C3×C4—32no—
187C22×C3×C4—62no—
188C22×C3×C4—62no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—34no—
192C2×#67—34no—
193C2×#67C4×D312yes—
194C22×Dic3C4×D311yescharacteristic
195#235—22no—
196#235—22no—
197C2×D12C4×D311yescharacteristic
198C2×C4×D3—22no—
199C2×C4×D3—22no—
200C2×C4×D3C4×D312yes—
201C2×C4×D3C22×D312yes—
202C2×C4×D3C22×D312yes—
203C2×Dic6C4×D311yescharacteristic
204C3×M16—62no—
205C3×M16—64no—
206C2×C3×C8—24no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—32no—
210C2×C3×C8—32no—
211C2×C3×C8—62no—
212C2×C3×C8—64no—
213C2×C3×C8—64no—
214C2×C3×C8—64no—
215C2×C3×C8#6714yescomplemented
216C2×C3×C8#6714yescomplemented
217C2×C3×C8C22×D311yescharacteristic
218C2×C3×C8C22×D311yescharacteristic
219C2×C3×C8C22×D311yescharacteristic
220C2×C3×C8C22×D311yescharacteristic
221#217—32no—
222#217—32no—
223#217—34no—
224#217—34no—
225#217—62no—
226(C2×D3)⋊C4—34no—
227(C2×D3)⋊C4—34no—
228C4⋊Dic3—32no—
229C4⋊Dic3—32no—
230C4⋊Dic3—62no—
231Dic3⋊C4—34no—
232Dic3⋊C4—34no—
233C4×Dic3—32no—
234C4×Dic3—32no—
235C4×Dic3—62no—
236#208—22no—
237#208—64no—
238#208—62no—
239#208—62no—
240C2×C3⋊C8—22no—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—32no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8C22×D312yes—
245C2×C3⋊C8C22×D312yes—
246ΓL(1,𝔽25)—24no—
247D3×C8—24no—
248D3×C8—24no—
249D3×C8—24no—
250C22×C32—22no—
251C22×C32C4×D412yes—
252C22×C32C23×C411yescharacteristic
253C2×C3×D3—28no—
254C2×C3×D3—22no—
255C2×C3×D3—22no—
256C2×C3×D3—22no—
257C2×C3×D3—24no—
258C2×C3×D3#13114yescomplemented
259C32×C4C4×D412yes—
260C32×C4C22×D411yescharacteristic
261C32×C4C2×#4111yescharacteristic
262C3⋊Dic3—24no—
263C3×Dic3—22no—
264C3×Dic3—22no—
265C2×#41—31no—
266C23×C4—31no—
267#131—64no—
268C2×M16—31no—
269C2×M16—32no—
270C2×M16—91no—
271C22×C8—31no—
272C22×C8—32no—
273C22×C8—32no—
274C22×C8—32no—
275C22×C8—64no—
276C22×C8D3211yescharacteristic
277#123—92no—
278C22⋊Q8—92no—
279#121—92no—
280#120—92no—
281C4×D4—94no—
282#117—91no—
283C4⋊C8—94no—
284C22⋊C8—94no—
285C22⋊C8—94no—
286#97—92no—
287C4×C8—92no—
288C23×C3—21no—
289C23×C3—32no—
290C23×C3—32no—
291C23×C3—64no—
292C23×C3—62no—
293C23×C3C2×C4×D311yescharacteristic
294C23×C3C2×C4×D311yescharacteristic
295C22×D3—22no—
296C22×D3—24no—
297C22×D3C2×C4×D312yes—
298C22×D3C2×C4×D312yes—
299C3×Q8—62no—
300C3×D4—64no—
301C3×D4—62no—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—22no—
306C2×C3×C4—32no—
307C2×C3×C4—32no—
308C2×C3×C4—62no—
309C2×C3×C4—64no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4#23512yes—
317C2×C3×C4#23512yes—
318C2×C3×C4C2×#6712yes—
319C2×C3×C4C2×#6712yes—
320C2×C3×C4C23×D311yescharacteristic
321C2×C3×C4C23×D311yescharacteristic
322#67—24no—
323#67—68no—
324#67—68no—
325C2×Dic3—22no—
326C2×Dic3—34no—
327C2×Dic3—34no—
328C2×Dic3—64no—
329C2×Dic3C2×C4×D312yes—
330C2×Dic3C2×C4×D312yes—
331D12—22no—
332C4×D3—24no—
333C4×D3—22no—
334C4×D3—22no—
335C4×D3—22no—
336C4×D3—22no—
337Dic6—22no—
338C3×C8—22no—
339C3×C8—22no—
340C3×C8—62no—
341C3×C8—62no—
342C3×C8C2×#6712yes—
343C3×C8C2×#6712yes—
344C3×C8C2×#6712yes—
345C3×C8C2×#6712yes—
346C3⋊C8—22no—
347C3⋊C8—22no—
348C3⋊C8—64no—
349C3⋊C8—62no—
350C3⋊C8—62no—
351C2×C32—22no—
352C2×C32C2×C4×D411yescharacteristic
353C2×C32C2×#13112yes—
354C3×D3—24no—
355C3×D3—42no—
356C24—31no—
357#41—62no—
358#41—62no—
359C2×Q8—31no—
360C2×D4—32no—
361C2×D4—31no—
362C2×D4—94no—
363C22×C4—31no—
364C22×C4—32no—
365C22×C4—32no—
366C22×C4—32no—
367C22×C4—62no—
368C22×C4—62no—
369C22×C4C2×D3211yescharacteristic
370M16—62no—
371M16—64no—
372M16—182no—
373C2×C8—32no—
374C2×C8—32no—
375C2×C8—62no—
376C2×C8—64no—
377C2×C8—64no—
378C2×C8—64no—
379C2×C8—92no—
380C2×C8#62514yescomplemented
381C2×C8C2×D3211yescharacteristic
382C2×C8C2×D3211yescharacteristic
383C4⋊C4—94no—
384C4⋊C4—92no—
385C22⋊C4—94no—
386C22⋊C4—94no—
387C22⋊C4—92no—
388C42—92no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—21no—
392C22×C3—22no—
393C22×C3—34no—
394C22×C3—42no—
395C22×C3—68no—
396C22×C3—62no—
397C22×C3—62no—
398C22×C3—64no—
399C22×C3—62no—
400C22×C3C4×#6712yes—
401C22×C3C4×#6712yes—
402C22×C3C22×C4×D311yescharacteristic
403C22×C3C22×C4×D311yescharacteristic
404C2×D3—28no—
405C2×D3—22no—
406C2×D3—22no—
407C2×D3—24no—
408C2×D3—22no—
409C2×D3#90114yescomplemented
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—22no—
413C3×C4—62no—
414C3×C4—62no—
415C3×C4C4×#6712yes—
416C3×C4C4×#6712yes—
417C3×C4C2×#23511yescharacteristic
418C3×C4C2×#23511yescharacteristic
419C3×C4C22×#6711yescharacteristic
420C3×C4C22×#6711yescharacteristic
421Dic3—22no—
422Dic3—22no—
423Dic3—64no—
424Dic3—64no—
425Dic3—124no—
426C32#292911yescharacteristic, complemented, Sylow
427C23—32no—
428C23—32no—
429C23—64no—
430C23—62no—
431C23C4×D3211yescharacteristic
432Q8—62no—
433D4—64no—
434D4—62no—
435D4—188no—
436C2×C4—32no—
437C2×C4—32no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—64no—
444C2×C4—94no—
445C2×C4#379812yes—
446C2×C4C4×D3211yescharacteristic
447C2×C4C2×#62512yes—
448C2×C4C22×D3211yescharacteristic
449C8—62no—
450C8—62no—
451C8—182no—
452C8C2×#62512yes—
453C8C2×#62512yes—
454C2×C3—22no—
455C2×C3—22no—
456C2×C3—22no—
457C2×C3—21no—
458C2×C3—42no—
459C2×C3—64no—
460C2×C3—122no—
461C2×C3C2×#90112yes—
462C2×C3D3×#13112yes—
463C2×C3C2×C4×#6711yescharacteristic
464C2×C3C2×C4×#6711yescharacteristic
465D3—24no—
466D3—42no—
467C22—22no—
468C22—34no—
469C22—68no—
470C22—62no—
471C22—62no—
472C22—64no—
473C22—62no—
474C22C4×#62512yes—
475C22C2×C4×D3211yescharacteristic
476C4—62no—
477C4—62no—
478C4—184no—
479C4C4×#62512yes—
480C4C2×#379811yescharacteristic
481C4C22×#62511yescharacteristic
482C3—21no—
483C3#8373411yescharacteristic, complemented
484C3#8379411yescharacteristic, complemented
485C2—22no—
486C2—64no—
487C2—122no—
488C2D3×#90112yes—
489C2C2×C4×#62511yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutator, socleC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
prime radical#10595022C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#901C2semidirect
2. C22×C3×D3×C8C2semidirect
4. #10592800C2semidirect
5. #10591119C2semidirect
6. #10591070C2semidirect
7. #10591069C2semidirect
8. #10590722C2semidirect
9. C8×#625C2semidirect
20. C2×C3×ΓL(1,𝔽25)C22semidirect
24. C2×C3×D3×C8C22semidirect
30. #63642C22semidirect
31. C8×C3⋊Dic3C22semidirect
32. #63572C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
39. C2×#901D3semidirect
40. C22×D3×C8D3semidirect
68. C2×C32×C8D4semidirect
122. C2×ΓL(1,𝔽25)C2×D3semidirect
126. C2×D3×C8C2×D3semidirect
215. C2×C3×C8#67semidirect
216. C2×C3×C8#67semidirect
258. C2×C3×D3#131semidirect
380. C2×C8#625semidirect
409. C2×D3#901semidirect
426. C32#2929semidirect
483. C3#83734semidirect
484. C3#83794semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
C22×C3×D3×C82
#105950222
#105928002
#105911192
#105910702
#105910692
#105907222
C8×#6252
#837943
#837343