Finite Group Databasebeta

← #11876997

Subgroups — #11876997

Order 1152.

958 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593968C212yesmaximal, complemented
2#10592410C211yesmaximal, characteristic, complemented
3C3×#4711C211yesmaximal, characteristic, complemented
4C3×#4707C211yesmaximal, characteristic, complemented
5#10590889C211yesmaximal, characteristic, complemented
6#10590880C211yesmaximal, characteristic, complemented
7#10590878C212yesmaximal, complemented
8#10590836C211yesmaximal, characteristic, complemented
9#10590835C211yesmaximal, characteristic, complemented
10#10590827C212yesmaximal, complemented
11#10590346C212yesmaximal, complemented
12#79877—31nomaximal
13#78535—31nomaximal
14C2×#3798—22no—
15C2×#3745C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2212yes—
17C2×C3×D24C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
19C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
20C3×C4×D12C2212yes—
21C3×C42×D3C2211yescharacteristic
22#63918C2212yes—
23#63911C2212yes—
24#63909C2212yes—
25#63908C2212yes—
26#63906—22no—
27C4×#626—22no—
28#63852—22no—
29C2×#3714C2212yes—
30C32×#97C2211yescharacteristic
31#63648C2212yes—
32#63644C2211yescharacteristic
33C3×#821C2212yes—
34C3×#817C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36C3×C8×Dic3C2211yescharacteristic
37C3×#803C2211yescharacteristic
38#63573C2212yes—
39#63564C2212yes—
40#63563C2212yes—
41#5548—32no—
42#5477—32no—
43C3×#442—31no—
44C3×C4×M16—31no—
45#5159—31no—
46#5151—31no—
47#5135—31no—
48#5135—32no—
49#5135—31no—
50#5014—32no—
51#4865—31no—
52#4855—31no—
53#4782—32no—
54#4760—32no—
55#4711—32no—
56#4711—31no—
57#4711—31no—
58#4711—61no—
59#4711D311yescharacteristic, complemented
60#4707D311yescharacteristic, complemented
61#4695—31no—
62#4694—32no—
63#4680—31no—
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C4×C3⋊D3—22no—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3D412yes—
69C2×C3×C4×D3C2311yescharacteristic
70C2×#627—22no—
71C2×#626—22no—
72C2×#626—22no—
73C2×#626—22no—
74C2×#625—22no—
75#3798—48no—
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C42C2311yescharacteristic
79#3752—22no—
80C4⋊(C3⋊Dic3)C2312yes—
81#3745—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3D412yes—
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×D24—22no—
89C3×ΓL(1,𝔽25)—22no—
90C3×ΓL(1,𝔽25)—22no—
91Dic3⋊Dic3—22no—
92#3722—22no—
93(C2×D3)⋊Dic3—22no—
94#3714—24no—
95#3184—91noSylow
96C2×#235—62no—
97C2×#235—62no—
98C2×C3×D8—31no—
99C2×C3×M16—31no—
100C2×C3×M16—31no—
101C3×C4×D4—32no—
102C2×C3×C42—31no—
103#940—32no—
104#938—32no—
105C2×#213—32no—
106#930—32no—
107#930—32no—
108#930—62no—
109C4×#67—62no—
110C2×D24—32no—
111C2×D24—31no—
112C2×D24—31no—
113C2×D24—61no—
114C2×D24C2×D311yescharacteristic
115C2×ΓL(1,𝔽25)C2×D311yescharacteristic
116C2×ΓL(1,𝔽25)C2×D311yescharacteristic
117#895—32no—
118#888—32no—
119#885—62no—
120#884—62no—
121#875—62no—
122#874—32no—
123C4×D12—32no—
124C4×D12—32no—
125C4×D12—62no—
126C4×D12—62no—
127C4×D12C2×D312yes—
128C42×D3C2×D311yescharacteristic
129#869—32no—
130C3×#106—31no—
131C3×#102—32no—
132C3×#97—21no—
133C3×#97—31no—
134C3×#97C2×D311yescharacteristic
135C3×#97C2×D311yescharacteristic
136C3×C4×C8—31no—
137C3×C4×C8—31no—
138#832—32no—
139#821—32no—
140#821—32no—
141#821—32no—
142#821—32no—
143#821—62no—
144#821C2×D312yes—
145#817—31no—
146#817—31no—
147#817—32no—
148#817—61no—
149#817C2×D311yescharacteristic
150C8×Dic3C2×D311yescharacteristic
151C8×Dic3C2×D311yescharacteristic
152#809—32no—
153#808—32no—
154#803C2×D311yescharacteristic
155C22×C3⋊D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3C2×D411yescharacteristic
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3—22no—
161C4⋊(C3⋊D3)—22no—
162C4⋊(C3⋊D3)—22no—
163C4×C3⋊D3—44no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C2×D411yescharacteristic
166C2×C3×Dic3C2×D412yes—
167C3×D12—22no—
168C3×D12—22no—
169C3×C4×D3—21no—
170C3×C4×D3—21no—
171C3×C4×D3—24no—
172C3×C4×D3—44no—
173#627—44no—
174#626—44no—
175#626—44no—
176#626—44no—
177#625—44no—
178C32×C8—21no—
179C32×C8#4112yescomplemented
180C3×C3⋊C8—21no—
181C3×C3⋊C8#4112yescomplemented
182#532—92no—
183#498—91no—
184#493—91no—
185#486—92no—
186#469—92no—
187#469—91no—
188#469—91no—
189#442—31no—
190#442—92no—
191#442—91no—
192C4×M16—31no—
193C2×C3×D4—32no—
194C22×C3×C4—32no—
195C22×C3×C4—31no—
196C22×C3×C4—62no—
197C2×#67—62no—
198C2×#67—62no—
199C2×#67—62no—
200C2×#67—62no—
201C2×#67—62no—
202#235—128no—
203#235—128no—
204C2×D12—32no—
205C2×D12—32no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12C22×D312yes—
211C2×C4×D3—22no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—122no—
215C2×C4×D3D1212yes—
216C2×C4×D3C22×D311yescharacteristic
217C2×Dic6—62no—
218C2×Dic6—62no—
219C3×D8—62no—
220C3×M16—62no—
221C3×M16—62no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—31no—
225C2×C3×C8—31no—
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C3×C4⋊C4—32no—
231C3×C22⋊C4—62no—
232C3×C42—21no—
233C3×C42—32no—
234C3×C42—31no—
235C3×C42C22×D311yescharacteristic
236C3×C42C22×D311yescharacteristic
237#217—62no—
238#213—64no—
239(C2×D3)⋊C4—22no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—122no—
246C4⋊Dic3—32no—
247C4⋊Dic3—32no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3C22×D312yes—
251Dic3⋊C4—62no—
252C4×Dic3D1212yes—
253C4×Dic3C22×D311yescharacteristic
254C2×C3⋊C8C22×D311yescharacteristic
255C2×C3⋊C8C22×D311yescharacteristic
256D24—22no—
257D24—64no—
258D24—64no—
259D24—62no—
260D24—62no—
261ΓL(1,𝔽25)—22no—
262ΓL(1,𝔽25)—22no—
263C22×C32C22×D411yescharacteristic
264C2×C3⋊D3—42no—
265C2×C3⋊D3—42no—
266C2×C3⋊D3—42no—
267C2×C3×D3—21no—
268C2×C3×D3—22no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C32×C4—22no—
273C32×C4C2×#4111yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—42no—
276C3×Dic3—21no—
277C3×Dic3—42no—
278C3×Dic3AGL(1,ℤ/8)14yes—
279C2×#41—182no—
280C2×D8—31no—
281C2×D8—92no—
282C2×D8—91no—
283C2×M16—31no—
284C2×M16—31no—
285C4⋊Q8—92no—
286#127—92no—
287#124—182no—
288#121—92no—
289#121—92no—
290#121—182no—
291C4×D4—32no—
292C4×D4—92no—
293C4×D4—182no—
294C2×C42—31no—
295#106—31no—
296#106—92no—
297#106—91no—
298#102—32no—
299#102—92no—
300#102—92no—
301#102—92no—
302#97—31no—
303#97D3211yescharacteristic
304C4×C8—31no—
305C4×C8—31no—
306C23×C3—31no—
307C23×C3—62no—
308C22×D3—22no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—122no—
312C22×D3C2×D1211yescharacteristic
313C3×D4—62no—
314C3×D4—62no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—32no—
318C2×C3×C4—31no—
319C2×C3×C4—64no—
320C2×C3×C4—61no—
321C2×C3×C4—61no—
322C2×C3×C4—62no—
323C2×C3×C4—124no—
324C2×C3×C4C2×D1212yes—
325C2×C3×C4D3×D412yes—
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328#67—124no—
329#67—124no—
330#67—124no—
331#67—124no—
332#67—124no—
333C2×Dic3—22no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—122no—
337C2×Dic3C2×D1211yescharacteristic
338C2×Dic3C2×D1212yes—
339D12—22no—
340D12—22no—
341D12—64no—
342D12—62no—
343D12—62no—
344D12—62no—
345D12—62no—
346D12—122no—
347D12—124no—
348D12—124no—
349D12—124no—
350C4×D3—21no—
351C4×D3—21no—
352C4×D3—24no—
353C4×D3—44no—
354C4×D3—124no—
355C4×D3—124no—
356C4×D3—244no—
357Dic6—124no—
358Dic6—124no—
359C3×C8—21no—
360C3×C8—21no—
361C3×C8—22no—
362C3×C8—32no—
363C3×C8—41no—
364C3×C8—61no—
365C3×C8#23512yescomplemented
366C3×C8#23512yescomplemented
367C3⋊C8—21no—
368C3⋊C8#23512yescomplemented
369C2×C32#53211yescharacteristic
370C2×C32C2×AGL(1,ℤ/8)12yes—
371C3⋊D3—82no—
372C3×D3—41no—
373C3×D3—82no—
374#41—368no—
375C2×Q8—182no—
376C2×D4—32no—
377C2×D4—92no—
378C2×D4—182no—
379C2×D4—182no—
380C2×D4—182no—
381C2×D4—182no—
382C22×C4—31no—
383C22×C4—32no—
384C22×C4—62no—
385C22×C4—182no—
386D8—62no—
387D8—184no—
388D8—182no—
389M16—62no—
390M16—62no—
391C2×C8—31no—
392C2×C8—31no—
393C2×C8C2×D3211yescharacteristic
394C2×C8C2×D3211yescharacteristic
395C4⋊C4—32no—
396C4⋊C4—92no—
397C4⋊C4—182no—
398C22⋊C4—62no—
399C22⋊C4—182no—
400C22⋊C4—182no—
401C22⋊C4—182no—
402C42—31no—
403C42—32no—
404C42C2×D3211yescharacteristic
405C22×C3—21no—
406C22×C3—62no—
407C22×C3—61no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3C22×D1211yescharacteristic
412C22×C3C2×D3×D411yescharacteristic
413C2×D3—21no—
414C2×D3—22no—
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—42no—
418C2×D3—124no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—122no—
425C2×D3—242no—
426C2×D3—242no—
427C3×C4—22no—
428C3×C4—22no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—34no—
432C3×C4—42no—
433C3×C4—61no—
434C3×C4—122no—
435C3×C4C2×#23511yescharacteristic
436C3×C4C2×#23511yescharacteristic
437C3×C4C2×#23511yescharacteristic
438C3×C4D3×#4111yescharacteristic
439Dic3—21no—
440Dic3—42no—
441Dic3—122no—
442Dic3—122no—
443Dic3—242no—
444Dic3#90814yes—
445C32#318411yescharacteristic, complemented, Sylow
446C23—31no—
447C23—62no—
448C23—182no—
449Q8—364no—
450D4—62no—
451D4—62no—
452D4—182no—
453D4—182no—
454D4—364no—
455D4—364no—
456D4—364no—
457D4—364no—
458C2×C4—32no—
459C2×C4—31no—
460C2×C4—64no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—62no—
464C2×C4—124no—
465C2×C4—182no—
466C2×C4—364no—
467C2×C4D3×D1212yes—
468C2×C4C22×D3211yescharacteristic
469C8—21no—
470C8—32no—
471C8—61no—
472C8#379812yescomplemented
473C2×C3—22no—
474C2×C3—21no—
475C2×C3—121no—
476C2×C3—242no—
477C2×C3#547711yescharacteristic
478C2×C3#554811yescharacteristic
479C2×C3C2×#90812yes—
480C2×C3D3×AGL(1,ℤ/8)12yes—
481D3—41no—
482D3—82no—
483D3—244no—
484D3—242no—
485D3—242no—
486C22—62no—
487C22—61no—
488C22—122no—
489C22—122no—
490C22—122no—
491C22—362no—
492C22—362no—
493C22—362no—
494C22C2×D3×D1211yescharacteristic
495C4—22no—
496C4—34no—
497C4—61no—
498C4—122no—
499C4—362no—
500C4C2×#379811yescharacteristic
501C4D3×#23511yescharacteristic
502C3—21no—
503C3#7853511yescharacteristic, complemented
504C3#7987711yescharacteristic, complemented
505C2—121no—
506C2—242no—
507C2—722no—
508C2#1059396811yescharacteristic
509C2D3×#90812yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
hypercenter#97D32
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. #10593968C2semidirect
2. #10592410C2semidirect
3. C3×#4711C2semidirect
4. C3×#4707C2semidirect
5. #10590889C2semidirect
6. #10590880C2semidirect
7. #10590878C2semidirect
8. #10590836C2semidirect
9. #10590835C2semidirect
10. #10590827C2semidirect
11. #10590346C2semidirect
59. #4711D3semidirect
60. #4707D3semidirect
179. C32×C8#41semidirect
181. C3×C3⋊C8#41semidirect
365. C3×C8#235semidirect
366. C3×C8#235semidirect
368. C3⋊C8#235semidirect
445. C32#3184semidirect
472. C8#3798semidirect
503. C3#78535semidirect
504. C3#79877semidirect

Maximal subgroups

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

subgroupindex
#105939682
#105924102
C3×#47112
C3×#47072
#105908892
#105908802
#105908782
#105908362
#105908352
#105908272
#105903462
#798773
#785353