Finite Group Databasebeta

← #11859352

Subgroups — #11859352

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
1#10595022C211yesmaximal, characteristic
2C2×#63815C211yesmaximal, characteristic, complemented
3C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4#10592821C211yesmaximal, characteristic, complemented
5C3×#5129C211yesmaximal, characteristic, complemented
6C3×#5126C211yesmaximal, characteristic, complemented
7#10591119C211yesmaximal, characteristic, complemented
8#10590725C214yesmaximal, complemented
9#10590718C214yesmaximal, complemented
10#78655—31nomaximal
11#78626—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15#64135C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19#63976C412yes—
20#63961C412yes—
21#63908C412yes—
22C4×#625C2214yes—
23#63856C412yes—
24C2×#3711C2212yescomplemented
25#63815—24no—
26C2×D3×C3⋊C8—24no—
27C2×D3×C3⋊C8C2212yes—
28C2×D3×C3⋊C8C2212yes—
29C2×D3×C3⋊C8C2212yescomplemented
30#63642C2212yescomplemented
31C8×C3⋊Dic3C2212yescomplemented
32C3×(C2×D3)⋊C8C2214yes—
33C3×(C2×D3)⋊C8C2214yescomplemented
34#63572C2214yescomplemented
35#5828—31no—
36C2×#948—31no—
37#5791—31no—
38C23×C3⋊C8—31no—
39C2×#907—31no—
40C22×D3×C8—31no—
41C3×#408—31no—
42C3×#407—31no—
43#5129D311yescharacteristic, complemented
44#5126D311yescharacteristic, complemented
45#5122—31no—
46#5122—31no—
47#5122—61no—
48#5119—31no—
49#5102—31no—
50#4730—34no—
51#4728—34no—
52#67⋊C8—34no—
53#67⋊C8—34no—
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—
68C32×M16—22no—
69C2×C32×C8C2312yes—
70#3757C2×C412yes—
71C4⋊(C3⋊Dic3)C2×C412yes—
72C4×C3⋊Dic3C2312yes—
73C2×C3⋊(C3⋊C8)D414yescomplemented
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76C3×#208—22no—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80#3724C2×C414yes—
81(C2×D3)⋊Dic3C2×C414yes—
82(C2×D3)⋊Dic3C2×C414yes—
83#3711—24no—
84D3×C3⋊C8—24no—
85D3×C3⋊C8—24no—
86D3×C3⋊C8—24no—
87#2929—91noSylow
88C2×C3×#41—31no—
89C23×C3×C4—31no—
90C2×#235C2×D311yescharacteristic
91C22×C4×D3C2×D311yescharacteristic
92C2×C3×M16—21no—
93C2×C3×M16—31no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C2×D311yescharacteristic
96C22×C3×C8—31no—
97#953—32no—
98#948—64no—
99#946—32no—
100#938—32no—
101#937—32no—
102#935—32no—
103#930—32no—
104#929—32no—
105C4×#67—34no—
106C4×#67—34no—
107#926—31no—
108#926—31no—
109#926—61no—
110#924—32no—
111C2×#208—32no—
112C2×#208C2×D311yescharacteristic
113C22×C3⋊C8—31no—
114C22×C3⋊C8—31no—
115C22×C3⋊C8—32no—
116C22×C3⋊C8—32no—
117C22×C3⋊C8—32no—
118C22×C3⋊C8—61no—
119C22×C3⋊C8—64no—
120C22×C3⋊C8C2×D311yescharacteristic
121#907—64no—
122C2×ΓL(1,𝔽25)—32no—
123C2×D3×C8—32no—
124C2×D3×C8—32no—
125C2×D3×C8—32no—
126C2×D3×C8—64no—
127C3×C22⋊C8—34no—
128C3×C22⋊C8—34no—
129(C2×D3)⋊C8C2×D314yes—
130(C2×D3)⋊C8C2×D314yescomplemented
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×C8—22no—
162C3⋊(C3⋊C8)C2×D412yes—
163C3⋊(C3⋊C8)C2×D412yes—
164C3×C3⋊C8—22no—
165C3×C3⋊C8—22no—
166C2×#131—91no—
167C23×C8—91no—
168#525—91no—
169#435—94no—
170C8×D4—94no—
171#424—91no—
172#408—31no—
173#407—31no—
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—24no—
205C3×M16—22no—
206C3×M16—22no—
207C3×M16—62no—
208C2×C3×C8—22no—
209C2×C3×C8—32no—
210C2×C3×C8—32no—
211C2×C3×C8—62no—
212C2×C3×C8C22×D312yes—
213C2×C3×C8C22×D312yes—
214#217—32no—
215#217—32no—
216#217—34no—
217#217—34no—
218#217—62no—
219(C2×D3)⋊C4—34no—
220(C2×D3)⋊C4—34no—
221C4⋊Dic3—32no—
222C4⋊Dic3—32no—
223C4⋊Dic3—62no—
224Dic3⋊C4—34no—
225Dic3⋊C4—34no—
226C4×Dic3—32no—
227C4×Dic3—32no—
228C4×Dic3—62no—
229#208—22no—
230#208—64no—
231C2×C3⋊C8—22no—
232C2×C3⋊C8—34no—
233C2×C3⋊C8—34no—
234C2×C3⋊C8—31no—
235C2×C3⋊C8—31no—
236C2×C3⋊C8—31no—
237C2×C3⋊C8—31no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—64no—
241C2×C3⋊C8—64no—
242C2×C3⋊C8—64no—
243C2×C3⋊C8—64no—
244C2×C3⋊C8C22×D312yes—
245C2×C3⋊C8C22×D312yes—
246ΓL(1,𝔽25)—64no—
247D3×C8—64no—
248D3×C8—64no—
249D3×C8—64no—
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—184no—
268C2×M16—31no—
269C2×M16—92no—
270C2×M16D3211yescharacteristic
271C22×C8—31no—
272C22×C8—92no—
273C22×C8—92no—
274C22×C8—92no—
275C22×C8—91no—
276C22×C8—184no—
277#123—92no—
278C22⋊Q8—92no—
279#121—92no—
280#120—92no—
281C4×D4—94no—
282#117—91no—
283C4⋊C8—94no—
284C22⋊C8—34no—
285C22⋊C8—34no—
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—21no—
304C2×C3×C4—22no—
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×C4D3×D412yes—
317C2×C3×C4D3×D412yes—
318C2×C3×C4#23712yes—
319C2×C3×C4#23712yes—
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—24no—
339C3×C8—22no—
340C3×C8—22no—
341C3×C8—62no—
342C3×C8—62no—
343C3⋊C8—22no—
344C3⋊C8—22no—
345C3⋊C8—32no—
346C3⋊C8—32no—
347C3⋊C8—32no—
348C3⋊C8—32no—
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—22no—
371M16—62no—
372M16—184no—
373C2×C8—32no—
374C2×C8—32no—
375C2×C8—62no—
376C2×C8—91no—
377C2×C8—91no—
378C2×C8—94no—
379C2×C8—184no—
380C2×C8—184no—
381C2×C8—184no—
382C2×C8C2×D3212yes—
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—62no—
399C22×C3—64no—
400C22×C3#67⋊C412yes—
401C22×C3#67⋊C412yes—
402C22×C3C22×C4×D311yescharacteristic
403C22×C3C22×C4×D311yescharacteristic
404C2×D3—28no—
405C2×D3—22no—
406C2×D3—22no—
407C2×D3—22no—
408C2×D3—24no—
409C2×D3#90714yescomplemented
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—22no—
413C3×C4—62no—
414C3×C4—62no—
415C3×C4#67⋊C412yes—
416C3×C4#67⋊C412yes—
417C3×C4C2×D3×D411yescharacteristic
418C3×C4C2×D3×D411yescharacteristic
419C3×C4C2×#23711yescharacteristic
420C3×C4C2×#23711yescharacteristic
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×C4C4×D3211yescharacteristic
446C2×C4#380212yes—
447C2×C4#380512yes—
448C2×C4C22×D3211yescharacteristic
449C8—22no—
450C8—62no—
451C8—62no—
452C8—92no—
453C8—92no—
454C2×C3—22no—
455C2×C3—22no—
456C2×C3—22no—
457C2×C3—21no—
458C2×C3—42no—
459C2×C3—64no—
460C2×C3—122no—
461C2×C3C2×#67⋊C411yescharacteristic
462C2×C3C2×#67⋊C411yescharacteristic
463C2×C3C2×#90712yes—
464C2×C3D3×#13112yes—
465D3—24no—
466D3—42no—
467C22—22no—
468C22—34no—
469C22—68no—
470C22—62no—
471C22—62no—
472C22—64no—
473C22—62no—
474C22#6390212yes—
475C22C2×C4×D3211yescharacteristic
476C4—62no—
477C4—62no—
478C4—184no—
479C4#6390212yes—
480C4C2×#380211yescharacteristic
481C4C2×#380511yescharacteristic
482C3—21no—
483C3#7862611yescharacteristic, complemented
484C3#7865511yescharacteristic, complemented
485C2—22no—
486C2—64no—
487C2—122no—
488C2D3×#90712yes—
489C2C2×#6390211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radical#10595022C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63815C2semidirect
3. C22×D3×C3⋊C8C2semidirect
4. #10592821C2semidirect
5. C3×#5129C2semidirect
6. C3×#5126C2semidirect
7. #10591119C2semidirect
8. #10590725C2semidirect
9. #10590718C2semidirect
24. C2×#3711C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. #63642C22semidirect
31. C8×C3⋊Dic3C22semidirect
33. C3×(C2×D3)⋊C8C22semidirect
34. #63572C22semidirect
43. #5129D3semidirect
44. #5126D3semidirect
73. C2×C3⋊(C3⋊C8)D4semidirect
130. (C2×D3)⋊C8C2×D3semidirect
258. C2×C3×D3#131semidirect
409. C2×D3#907semidirect
426. C32#2929semidirect
483. C3#78626semidirect
484. C3#78655semidirect

Maximal subgroups

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

subgroupindex
#105950222
C2×#638152
C22×D3×C3⋊C82
#105928212
C3×#51292
C3×#51262
#105911192
#105907252
#105907182
#786553
#786263