Finite Group Databasebeta

← #11859489

Subgroups — #11859489

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×#64116C211yesmaximal, characteristic, complemented
2#10595029C211yesmaximal, characteristic
3C2×#63815C211yesmaximal, characteristic, complemented
4C3×#5129C211yesmaximal, characteristic, complemented
5C3×#5118C211yesmaximal, characteristic, complemented
6#10591073C211yesmaximal, characteristic, complemented
7C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#10590906C214yesmaximal, complemented
9#10590732C214yesmaximal, complemented
10#79041—31nomaximal
11#78657—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16#64116—24no—
17C2×#3743C2212yes—
18C2×C8×C3⋊D3C2212yes—
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63978C414yes—
23#63911C411yescharacteristic
24C4×#626C2214yes—
25#63866C411yescharacteristic
26#63864C411yescharacteristic
27#63860C411yescharacteristic
28C2×#3711C2212yes—
29#63815—24no—
30C2×D3×C3⋊C8C2212yes—
31C3×(C2×D3)⋊C8C2214yes—
32C3×Dic3⋊C8C2214yes—
33#63557C2214yes—
34Dic3×C3⋊C8C2212yes—
35Dic3×C3⋊C8C2212yes—
36#5832—31no—
37C2×#948—31no—
38C2×#907—31no—
39C2×#907—31no—
40C2×#907—31no—
41C2×#907—61no—
42#5477—31no—
43C3×#423—31no—
44C3×#408—31no—
45#5129—31no—
46#5129D311yescharacteristic, complemented
47#5118D311yescharacteristic, complemented
48#5110—31no—
49C2×C8×Dic3—31no—
50C2×C4×C3⋊C8—31no—
51#4838—34no—
52#4834—34no—
53#4729—34no—
54#67⋊C8—34no—
55C22×C32×C4C2311yescharacteristic
56C2×#638C2×C412yes—
57#3828—22no—
58#3828—22no—
59C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
60C2×C4×C3⋊D3C2312yes—
61C2×#634C2×C411yescharacteristic
62C2×C3×#67C2×C412yes—
63C22×C3×Dic3C2×C412yes—
64C3×#235—22no—
65C3×#235—22no—
66C2×C3×D12C2×C411yescharacteristic
67C2×C3×C4×D3C2312yes—
68C2×C3×Dic6C2×C411yescharacteristic
69C2×#626C2×C414yes—
70C32×M16—22no—
71C2×C32×C8C2312yes—
72C2×C3⋊(C3⋊C8)D414yescomplemented
73C2×C3⋊(C3⋊C8)C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75#3743—24no—
76C8×C3⋊D3—24no—
77C3×C4×Dic3C2×C411yescharacteristic
78C3×C4×Dic3C2×C411yescharacteristic
79C3×C4×Dic3C2312yes—
80C3×#208—22no—
81C2×C3×C3⋊C8—22no—
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2312yes—
84Dic3⋊Dic3C2×C414yes—
85#3722C2×C414yes—
86(C2×D3)⋊Dic3C2×C414yes—
87#3711—24no—
88D3×C3⋊C8—24no—
89#2931—91noSylow
90C2×C3×#41—31no—
91C2×#235—31no—
92C2×#235—31no—
93C2×#235—61no—
94C2×#235C2×D311yescharacteristic
95C2×C3×M16—21no—
96C2×C3×M16—31no—
97C2×C3×M16C2×D311yescharacteristic
98C2×C3×M16C2×D311yescharacteristic
99C22×C3×C8—31no—
100C2×C3×C42—31no—
101#948—64no—
102#947—31no—
103#944—31no—
104#940—31no—
105#939—34no—
106#936—31no—
107#930—34no—
108C4×#67—34no—
109C2×C4×Dic3C2×D311yescharacteristic
110C2×#208—32no—
111C2×#208C2×D311yescharacteristic
112C22×C3⋊C8—31no—
113C22×C3⋊C8—31no—
114C22×C3⋊C8—32no—
115C22×C3⋊C8—61no—
116C22×C3⋊C8C2×D311yescharacteristic
117#907—64no—
118#907—64no—
119#907—64no—
120#907—68no—
121C2×ΓL(1,𝔽25)—32no—
122C2×ΓL(1,𝔽25)—32no—
123C2×ΓL(1,𝔽25)—32no—
124C2×ΓL(1,𝔽25)—62no—
125C2×D3×C8—32no—
126C2×D3×C8—32no—
127C2×D3×C8—32no—
128C2×D3×C8—62no—
129#875—31no—
130#875—31no—
131#874—31no—
132C4×D12—34no—
133#869—31no—
134C3×C4⋊C8—34no—
135C3×C22⋊C8—34no—
136(C2×D3)⋊C8—34no—
137(C2×D3)⋊C8—34no—
138(C2×D3)⋊C8C2×D314yes—
139Dic3⋊C8C2×D314yes—
140C8×Dic3—32no—
141C8×Dic3—32no—
142C4×C3⋊C8—32no—
143C4×C3⋊C8—32no—
144C23×C32C22×C411yescharacteristic
145C22×C3⋊D3C22×C412yes—
146C22×C3×D3C22×C412yes—
147C2×C32×C4C22×C411yescharacteristic
148C2×C32×C4C2×D412yes—
149C2×C32×C4#4112yes—
150C2×C32×C4C2411yescharacteristic
151#638—24no—
152C2×C3⋊Dic3C22×C412yes—
153C4⋊(C3⋊D3)—22no—
154C4×C3⋊D3—22no—
155C4×C3⋊D3—22no—
156#634—22no—
157C3×#67—24no—
158C2×C3×Dic3—24no—
159C2×C3×Dic3C22×C412yes—
160C2×C3×Dic3C22×C412yes—
161C2×C3×Dic3C22×C412yes—
162C3×D12—22no—
163C3×C4×D3—22no—
164C3×C4×D3—22no—
165C3×Dic6—22no—
166#626—28no—
167C32×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—91no—
175#436—94no—
176C8×D4—94no—
177#423—31no—
178#408—31no—
179#408—91no—
180C2×C4×C8—91no—
181C3×#41—62no—
182C3×#41—62no—
183C2×C3×Q8—31no—
184C2×C3×D4—32no—
185C2×C3×D4—31no—
186C22×C3×C4—21no—
187C22×C3×C4—32no—
188C22×C3×C4—32no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—32no—
192C2×#67—32no—
193C2×#67—34no—
194C2×#67—62no—
195C2×#67C4×D312yes—
196C22×Dic3C4×D312yes—
197#235—22no—
198#235—22no—
199#235—64no—
200#235—64no—
201#235—62no—
202#235—62no—
203#235—62no—
204#235—62no—
205C2×D12—34no—
206C2×D12—31no—
207C2×D12—31no—
208C2×D12—61no—
209C2×D12C4×D311yescharacteristic
210C2×C4×D3—32no—
211C2×C4×D3—32no—
212C2×C4×D3—62no—
213C2×C4×D3C22×D312yes—
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—61no—
217C2×Dic6C4×D311yescharacteristic
218C3×M16—24no—
219C3×M16—22no—
220C3×M16—22no—
221C3×M16—62no—
222C2×C3×C8—22no—
223C2×C3×C8—32no—
224C2×C3×C8—32no—
225C2×C3×C8—62no—
226C2×C3×C8C22×D312yes—
227C2×C3×C8C22×D312yes—
228C3×C42—31no—
229C3×C42—31no—
230C3×C42—32no—
231#217—34no—
232(C2×D3)⋊C4—34no—
233(C2×D3)⋊C4—34no—
234(C2×D3)⋊C4—34no—
235C4⋊Dic3—34no—
236Dic3⋊C4—34no—
237C4×Dic3C4×D311yescharacteristic
238C4×Dic3C4×D311yescharacteristic
239C4×Dic3C22×D312yes—
240#208—22no—
241#208—64no—
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—61no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—64no—
252C2×C3⋊C8—64no—
253C2×C3⋊C8C22×D312yes—
254C2×C3⋊C8C22×D312yes—
255ΓL(1,𝔽25)—64no—
256ΓL(1,𝔽25)—64no—
257ΓL(1,𝔽25)—64no—
258ΓL(1,𝔽25)—68no—
259D3×C8—64no—
260D3×C8—64no—
261D3×C8—64no—
262D3×C8—68no—
263C22×C32—22no—
264C22×C32C4×D412yes—
265C22×C32C23×C411yescharacteristic
266C2×C3⋊D3—22no—
267C2×C3⋊D3—24no—
268C2×C3×D3—22no—
269C2×C3×D3—24no—
270C32×C4C4×D412yes—
271C32×C4C22×D411yescharacteristic
272C32×C4C2×#4111yescharacteristic
273C3⋊Dic3—22no—
274C3×Dic3—22no—
275C3×Dic3—22no—
276C3×Dic3#13114yescomplemented
277C2×#41—31no—
278C2×#41—91no—
279#131—184no—
280#131—184no—
281C2×M16—31no—
282C2×M16—92no—
283C2×M16—92no—
284C2×M16D3211yescharacteristic
285C22×C8—31no—
286C22×C8—92no—
287C22×C8—91no—
288C22×C8—92no—
289C4⋊Q8—91no—
290#127—91no—
291#124—91no—
292#124—91no—
293#121—94no—
294C4×D4—94no—
295C2×C42—31no—
296C4⋊C8—34no—
297C22⋊C8—34no—
298C22⋊C8—94no—
299C4×C8—92no—
300C4×C8—92no—
301C23×C3—21no—
302C23×C3—32no—
303C23×C3C2×C4×D311yescharacteristic
304C23×C3C2×C4×D311yescharacteristic
305C22×D3—32no—
306C22×D3—32no—
307C22×D3—62no—
308C22×D3C2×C4×D312yes—
309C3×Q8—62no—
310C3×D4—64no—
311C3×D4—62no—
312C2×C3×C4—21no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—22no—
316C2×C3×C4—32no—
317C2×C3×C4—32no—
318C2×C3×C4—32no—
319C2×C3×C4—64no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4C2×C4×D311yescharacteristic
323C2×C3×C4C2×C4×D311yescharacteristic
324C2×C3×C4D3×D412yes—
325C2×C3×C4D3×D412yes—
326C2×C3×C4#23712yes—
327C2×C3×C4#23912yes—
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330#67—24no—
331#67—68no—
332#67—64no—
333#67—64no—
334#67—68no—
335C2×Dic3—24no—
336C2×Dic3—32no—
337C2×Dic3—32no—
338C2×Dic3—62no—
339C2×Dic3C2×C4×D312yes—
340C2×Dic3C2×C4×D312yes—
341C2×Dic3C2×C4×D312yes—
342D12—22no—
343D12—64no—
344D12—68no—
345D12—62no—
346D12—62no—
347C4×D3—22no—
348C4×D3—22no—
349C4×D3—64no—
350C4×D3—64no—
351C4×D3—62no—
352C4×D3—62no—
353C4×D3—62no—
354C4×D3—62no—
355Dic6—22no—
356Dic6—64no—
357Dic6—62no—
358Dic6—62no—
359C3×C8—24no—
360C3×C8—22no—
361C3×C8—22no—
362C3×C8—62no—
363C3×C8—62no—
364C3⋊C8—22no—
365C3⋊C8—22no—
366C3⋊C8—32no—
367C3⋊C8—32no—
368C3⋊C8—32no—
369C3⋊C8—32no—
370C3⋊C8—62no—
371C3⋊C8—62no—
372C2×C32—22no—
373C2×C32C2×C4×D411yescharacteristic
374C2×C32C2×#13112yes—
375C3⋊D3—42no—
376C3×D3—42no—
377#41—62no—
378#41—62no—
379#41—182no—
380#41—182no—
381C2×Q8—31no—
382C2×Q8—91no—
383C2×D4—32no—
384C2×D4—31no—
385C2×D4—94no—
386C2×D4—92no—
387C2×D4—91no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—92no—
391C22×C4C2×D3211yescharacteristic
392M16—22no—
393M16—62no—
394M16—184no—
395M16—184no—
396C2×C8—32no—
397C2×C8—32no—
398C2×C8—62no—
399C2×C8—91no—
400C2×C8—91no—
401C2×C8—94no—
402C2×C8—184no—
403C2×C8—184no—
404C2×C8C2×D3212yes—
405C4⋊C4—94no—
406C22⋊C4—94no—
407C22⋊C4—94no—
408C42—32no—
409C42—31no—
410C42—31no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—21no—
414C22×C3—22no—
415C22×C3—42no—
416C22×C3—64no—
417C22×C3—62no—
418C22×C3#67⋊C412yes—
419C22×C3#89312yes—
420C22×C3C22×C4×D311yescharacteristic
421C22×C3C22×C4×D311yescharacteristic
422C2×D3—22no—
423C2×D3—24no—
424C2×D3—64no—
425C2×D3—62no—
426C2×D3—64no—
427C2×D3—64no—
428C2×D3—62no—
429C2×D3—124no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—22no—
433C3×C4—34no—
434C3×C4—62no—
435C3×C4—62no—
436C3×C4#67⋊C412yes—
437C3×C4#89312yes—
438C3×C4C2×D3×D411yescharacteristic
439C3×C4C2×D3×D411yescharacteristic
440C3×C4C2×#23711yescharacteristic
441C3×C4C2×#23911yescharacteristic
442Dic3—22no—
443Dic3—22no—
444Dic3—64no—
445Dic3—62no—
446Dic3—62no—
447Dic3#90714yescomplemented
448C32#293111yescharacteristic, complemented, Sylow
449C23—32no—
450C23—92no—
451C23C4×D3211yescharacteristic
452Q8—62no—
453Q8—182no—
454D4—64no—
455D4—62no—
456D4—188no—
457D4—184no—
458D4—182no—
459C2×C4—32no—
460C2×C4—32no—
461C2×C4—32no—
462C2×C4—64no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—92no—
466C2×C4—182no—
467C2×C4—182no—
468C2×C4#379612yes—
469C2×C4C4×D3211yescharacteristic
470C2×C4#381112yes—
471C2×C4C22×D3211yescharacteristic
472C8—22no—
473C8—62no—
474C8—62no—
475C8—92no—
476C8—92no—
477C2×C3—22no—
478C2×C3—22no—
479C2×C3—21no—
480C2×C3—22no—
481C2×C3—42no—
482C2×C3—122no—
483C2×C3C2×#67⋊C411yescharacteristic
484C2×C3C2×#89311yescharacteristic
485C2×C3C2×#90712yes—
486C2×C3D3×#13112yes—
487D3—42no—
488D3—124no—
489D3—122no—
490D3—122no—
491C22—22no—
492C22—62no—
493C22—64no—
494C22—182no—
495C22—184no—
496C22#6388112yes—
497C22C2×C4×D3211yescharacteristic
498C4—34no—
499C4—62no—
500C4—62no—
501C4—182no—
502C4#6388112yes—
503C4C2×#379611yescharacteristic
504C4C2×#381111yescharacteristic
505C3—21no—
506C3#7865711yescharacteristic, complemented
507C3#7904111yescharacteristic, complemented
508C2—22no—
509C2—122no—
510C2—362no—
511C2D3×#90712yes—
512C2C2×#6388111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radical#10595029C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2931
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#64116C2semidirect
3. C2×#63815C2semidirect
4. C3×#5129C2semidirect
5. C3×#5118C2semidirect
6. #10591073C2semidirect
7. C2×Dic3×C3⋊C8C2semidirect
8. #10590906C2semidirect
9. #10590732C2semidirect
46. #5129D3semidirect
47. #5118D3semidirect
72. C2×C3⋊(C3⋊C8)D4semidirect
276. C3×Dic3#131semidirect
447. Dic3#907semidirect
448. C32#2931semidirect
506. C3#78657semidirect
507. C3#79041semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
#105950292
C2×#638152
C3×#51292
C3×#51182
#105910732
C2×Dic3×C3⋊C82
#105909062
#105907322
#790413
#786573