Finite Group Databasebeta

← #11878576

Subgroups — #11878576

Order 1152.

869 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
1#10594894C212yesmaximal, complemented
2#10592834C211yesmaximal, characteristic, complemented
3C3×#5137C211yesmaximal, characteristic, complemented
4C3×#5129C211yesmaximal, characteristic, complemented
5#10591177C212yesmaximal, complemented
6#10590967C212yesmaximal, complemented
7#10590966C212yesmaximal, complemented
8#10590677C212yesmaximal, complemented
9#10590675C212yesmaximal, complemented
10#80913—31nomaximal
11#78677—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C2×#3799C2212yes—
14C2×C32×M16C2211yescharacteristic
15#64139C2212yes—
16C2×#3745C2211yescharacteristic
17C3×#924C2212yes—
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×Dic12C2211yescharacteristic
20#63971—22no—
21#63958—22no—
22#63909C2212yes—
23D3×C4⋊Dic3C2212yes—
24#63888—22no—
25#63886—22no—
26#63856C2212yes—
27C2×#3717C2212yes—
28#63648C2212yes—
29#63644C2211yescharacteristic
30C3×(C2×D3)⋊C8C2212yes—
31C3×(C2×D3)⋊C8C2212yes—
32C3×#817C2211yescharacteristic
33C3×#816C2212yes—
34#63573C2212yes—
35#63566C2212yes—
36#63564C2212yes—
37#5833—32no—
38#5629—32no—
39C3×#470—31no—
40C3×#408—31no—
41#5187—32no—
42#5137D311yescharacteristic, complemented
43#5135—31no—
44#5135—31no—
45#5135—61no—
46#5129D311yescharacteristic, complemented
47#5114—32no—
48#5048—32no—
49#4863—32no—
50#4810—32no—
51#4805—32no—
52#4735—32no—
53#4734—32no—
54#4733—32no—
55#4721—32no—
56C22×C32×C4C2311yescharacteristic
57C2×#638—22no—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C3×#67D412yes—
60C3×#235—41no—
61C3×#235—41no—
62C2×C3×D12D411yescharacteristic
63C2×C3×C4×D3C2312yes—
64C2×C3×Dic6D411yescharacteristic
65C2×C3×Dic6C2312yes—
66C2×#626—22no—
67C2×#626—22no—
68C2×#624—22no—
69C2×D3×Dic3—22no—
70#3799—42no—
71#3799—42no—
72C32×M16—41no—
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75#3752—22no—
76C4⋊(C3⋊Dic3)C2312yes—
77#3745—41no—
78C3×#217—22no—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C2×C3×C3⋊C8—41no—
82C2×C3×C3⋊C8C2312yes—
83C3×Dic12—41no—
84#3724—22no—
85Dic3⋊Dic3—22no—
86#3722—22no—
87(C2×D3)⋊Dic3—22no—
88#3717—42no—
89#3204—91noSylow
90C2×C3×#41—31no—
91C2×#239—32no—
92C2×#235—32no—
93C2×#235C2×D311yescharacteristic
94C2×C3×Q16—31no—
95C2×C3×M16—21no—
96C2×C3×M16C2×D311yescharacteristic
97C2×C3×M16C2×D311yescharacteristic
98C22×C3×C8—31no—
99C3×C22⋊Q8—32no—
100#946—32no—
101#946—62no—
102C2×#215—32no—
103#939—62no—
104#939—62no—
105#938—62no—
106#930—32no—
107#930—32no—
108#930—32no—
109#930—62no—
110C2×C4⋊Dic3—32no—
111#924—32no—
112#924C2×D312yes—
113C22×C3⋊C8C2×D311yescharacteristic
114C2×Dic12C2×D311yescharacteristic
115C2×D24—31no—
116C2×D24—31no—
117C2×D24—61no—
118C2×#204—32no—
119#896—62no—
120#895—32no—
121#895—62no—
122D3×C4⋊C4—32no—
123#884—62no—
124#884—62no—
125C3×#106—31no—
126C3×#103—32no—
127C3×C22⋊C8—32no—
128C3×C22⋊C8—32no—
129#835—32no—
130#821—32no—
131#821—32no—
132#821—32no—
133#821—62no—
134(C2×D3)⋊C8C2×D312yes—
135(C2×D3)⋊C8C2×D312yes—
136#817—31no—
137#817—31no—
138#817—32no—
139#817—61no—
140#817C2×D311yescharacteristic
141#816—32no—
142#816C2×D312yes—
143#809—32no—
144#808—32no—
145C23×C32C2×D411yescharacteristic
146C22×C3⋊D3—22no—
147C22×C3×D3C2×D412yes—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2411yescharacteristic
152#638—82no—
153C2×C3⋊Dic3—22no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—22no—
156C3×#67—42no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3C2×D412yes—
160C3×D12—41no—
161C3×C4×D3—22no—
162C3×C4×D3—22no—
163C3×Dic6—22no—
164C3×Dic6—22no—
165C3×Dic6—41no—
166#626—44no—
167#626—82no—
168#624—44no—
169D3×Dic3—82no—
170C32×C8—21no—
171C32×C8—21no—
172C3×C3⋊C8—22no—
173#537—92no—
174#483—92no—
175#481—92no—
176#470—31no—
177#469—91no—
178#465—92no—
179#452—92no—
180#449—92no—
181#408—31no—
182C3×#41—121no—
183C3×#41—121no—
184C2×C3×Q8—31no—
185C2×C3×Q8—32no—
186C2×C3×D4—32no—
187C2×C3×D4—31no—
188C22×C3×C4—21no—
189C22×C3×C4—32no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C2×#67—62no—
193C2×#67—62no—
194C2×#67—62no—
195C2×#67—62no—
196C2×#67—122no—
197C2×#67D1212yes—
198C22×Dic3—62no—
199#239—122no—
200#239—122no—
201#235—41no—
202#235—41no—
203#235—122no—
204#235—122no—
205C2×D12—32no—
206C2×D12—32no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12D1211yescharacteristic
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3C22×D312yes—
215C2×Dic6D1211yescharacteristic
216C2×Dic6C22×D312yes—
217C3×Q16—121no—
218C3×M16—41no—
219C3×M16—41no—
220C3×M16—42no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—32no—
224C2×C3×C8—121no—
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C3×C4⋊C4—32no—
230C3×C4⋊C4—62no—
231C3×C22⋊C4—62no—
232#217—22no—
233#217—62no—
234#215—122no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—122no—
241C4⋊Dic3—32no—
242C4⋊Dic3—32no—
243C4⋊Dic3—62no—
244C4⋊Dic3—62no—
245C4⋊Dic3C22×D312yes—
246Dic3⋊C4—22no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250C2×C3⋊C8—41no—
251C2×C3⋊C8C22×D312yes—
252Dic12—41no—
253D24—121no—
254D24—121no—
255D24—122no—
256#204—122no—
257C22×C32—21no—
258C22×C32—22no—
259C22×C32C22×D411yescharacteristic
260C2×C3⋊D3—42no—
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3×D3—22no—
264C2×C3×D3—22no—
265C2×C3×D3—22no—
266C32×C4—21no—
267C32×C4H(5,𝔽2)11yescharacteristic
268C32×C4H(5,𝔽2)11yescharacteristic
269C3⋊Dic3—42no—
270C3×Dic3—22no—
271C3×Dic3—42no—
272C3×Dic3—42no—
273C2×#41—31no—
274C2×#41—92no—
275C2×Q16—31no—
276C2×SD16—92no—
277C2×D8—91no—
278C2×M16D3211yescharacteristic
279C22×C8—31no—
280C22⋊Q8—32no—
281C22⋊Q8—92no—
282C22⋊Q8—182no—
283#121—92no—
284#121—92no—
285#121—182no—
286#121—182no—
287#121—182no—
288C2×C4⋊C4—92no—
289#106—31no—
290#106—92no—
291#106—91no—
292#103—32no—
293#103—92no—
294#102—92no—
295#102—92no—
296C22⋊C8—32no—
297C22⋊C8—32no—
298C23×C3—21no—
299C23×C3—32no—
300C23×C3C2×D1211yescharacteristic
301C23×C3D3×D411yescharacteristic
302C22×D3—62no—
303C22×D3—62no—
304C22×D3—122no—
305C22×D3C2×D1212yes—
306C3×Q8—62no—
307C3×Q8—62no—
308C3×Q8—121no—
309C3×D4—121no—
310C3×D4—122no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—32no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4C2×D1211yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328#67—42no—
329#67—124no—
330#67—242no—
331#67—242no—
332#67—242no—
333#67—244no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—122no—
339C2×Dic3—242no—
340C2×Dic3C2×D1212yes—
341D12—41no—
342D12—62no—
343D12—62no—
344D12—62no—
345D12—62no—
346D12—122no—
347D12—122no—
348D12—124no—
349D12—242no—
350C4×D3—22no—
351C4×D3—22no—
352C4×D3—124no—
353C4×D3—124no—
354C4×D3—242no—
355Dic6—22no—
356Dic6—22no—
357Dic6—41no—
358C3×C8—22no—
359C3×C8—21no—
360C3×C8—21no—
361C3×C8—21no—
362C3×C8—21no—
363C3×C8—41no—
364C3×C8—62no—
365C3⋊C8—22no—
366C2×C32—41no—
367C2×C32#53411yescharacteristic
368C2×C32#57712yes—
369C3⋊D3—82no—
370C3×D3—42no—
371#41—121no—
372#41—121no—
373#41—362no—
374#41—362no—
375C2×Q8—31no—
376C2×Q8—32no—
377C2×D4—32no—
378C2×D4—31no—
379C2×D4—92no—
380C2×D4—182no—
381C2×D4—182no—
382C2×D4—182no—
383C22×C4—32no—
384C22×C4—182no—
385C22×C4—182no—
386C22×C4C2×D3211yescharacteristic
387Q16—121no—
388SD16—362no—
389D8—361no—
390M16—41no—
391C2×C8—32no—
392C2×C8—121no—
393C2×C8C2×D3211yescharacteristic
394C2×C8C2×D3211yescharacteristic
395C4⋊C4—32no—
396C4⋊C4—62no—
397C4⋊C4—92no—
398C4⋊C4—182no—
399C4⋊C4—182no—
400C22⋊C4—62no—
401C22⋊C4—182no—
402C22⋊C4—182no—
403C22⋊C4—182no—
404C22×C3—21no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—42no—
410C22×C3—41no—
411C22×C3—62no—
412C22×C3—62no—
413C22×C3—62no—
414C22×C3C22×D1211yescharacteristic
415C22×C3C2×D3×D411yescharacteristic
416C2×D3—22no—
417C2×D3—22no—
418C2×D3—22no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—122no—
425C2×D3—242no—
426C2×D3—242no—
427C2×D3—242no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—41no—
433C3×C4—62no—
434C3×C4—122no—
435C3×C4—122no—
436C3×C4#100411yescharacteristic
437C3×C4#100411yescharacteristic
438C3×C4#100411yescharacteristic
439C3×C4#100911yescharacteristic
440Dic3—22no—
441Dic3—42no—
442Dic3—42no—
443Dic3—122no—
444Dic3—122no—
445Dic3—242no—
446C32#320411yescharacteristic, complemented, Sylow
447C23—32no—
448C23—182no—
449C23D3×D1211yescharacteristic
450Q8—62no—
451Q8—62no—
452Q8—121no—
453D4—121no—
454D4—122no—
455D4—182no—
456D4—182no—
457D4—364no—
458D4—722no—
459D4—722no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—32no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—182no—
468C2×C4—364no—
469C2×C4—722no—
470C2×C4D3×D1211yescharacteristic
471C2×C4C22×D3211yescharacteristic
472C8—21no—
473C8—21no—
474C8—62no—
475C2×C3—21no—
476C2×C3—22no—
477C2×C3—41no—
478C2×C3—41no—
479C2×C3—81no—
480C2×C3—122no—
481C2×C3#549311yescharacteristic
482C2×C3#560511yescharacteristic
483C2×C3#575112yes—
484C2×C3#577812yes—
485D3—42no—
486D3—242no—
487D3—242no—
488D3—482no—
489C22—21no—
490C22—22no—
491C22—62no—
492C22—62no—
493C22—62no—
494C22—362no—
495C22—362no—
496C22—362no—
497C22C2×D3×D1211yescharacteristic
498C4—21no—
499C4—62no—
500C4—122no—
501C4—122no—
502C4—362no—
503C4#6430711yescharacteristic
504C4#6433011yescharacteristic
505C3—21no—
506C3#7867711yescharacteristic, complemented
507C3#8091311yescharacteristic, complemented
508C2—41no—
509C2—122no—
510C2—722no—
511C2#1059471512yes—
512C2#1059507211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3204
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10594894C2semidirect
2. #10592834C2semidirect
3. C3×#5137C2semidirect
4. C3×#5129C2semidirect
5. #10591177C2semidirect
6. #10590967C2semidirect
7. #10590966C2semidirect
8. #10590677C2semidirect
9. #10590675C2semidirect
42. #5137D3semidirect
46. #5129D3semidirect
446. C32#3204semidirect
506. C3#78677semidirect
507. C3#80913semidirect

Maximal subgroups

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

subgroupindex
#105948942
#105928342
C3×#51372
C3×#51292
#105911772
#105909672
#105909662
#105906772
#105906752
#809133
#786773