Finite Group Databasebeta

← #11878578

Subgroups — #11878578

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595004C212yesmaximal, complemented
2#10592836C211yesmaximal, characteristic, complemented
3C3×#5135C211yesmaximal, characteristic, complemented
4C3×#5129C211yesmaximal, characteristic, complemented
5#10591175C212yesmaximal, complemented
6#10590969C212yesmaximal, complemented
7#10590962C212yesmaximal, complemented
8#10590676C212yesmaximal, complemented
9#10590674C212yesmaximal, complemented
10#80873—31nomaximal
11#78677—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C2×#3795C2212yes—
14C2×C32×M16C2211yescharacteristic
15#64133C2212yes—
16C2×#3746C2211yescharacteristic
17C3×#930C2212yes—
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×D24C2211yescharacteristic
20#63970—22no—
21#63970—22no—
22#63908C2212yes—
23D3×C4⋊Dic3C2212yes—
24#63887—22no—
25#63885—22no—
26#63857C2212yes—
27C2×#3716C2212yes—
28#63644C2211yescharacteristic
29#63643C2212yes—
30C3×#821C2212yes—
31C3×(C2×D3)⋊C8C2212yes—
32C3×(C2×D3)⋊C8C2212yes—
33C3×#817C2211yescharacteristic
34#63573C2212yes—
35#63567C2212yes—
36#63563C2212yes—
37#5833—32no—
38#5608—32no—
39C3×#469—31no—
40C3×#408—31no—
41#5158—32no—
42#5137—31no—
43#5137—31no—
44#5137—61no—
45#5135D311yescharacteristic, complemented
46#5129D311yescharacteristic, complemented
47#5114—32no—
48#5041—32no—
49#4862—32no—
50#4783—32no—
51#4777—32no—
52#4735—32no—
53#4734—32no—
54#4733—32no—
55#4721—32no—
56C22×C32×C4C2311yescharacteristic
57C2×#634C2312yes—
58C2×C3×#67—22no—
59C2×C3×#67D412yes—
60C3×#235—41no—
61C3×#235—41no—
62C2×C3×D12D411yescharacteristic
63C2×C3×D12C2312yes—
64C2×C3×C4×D3C2312yes—
65C2×C3×Dic6D411yescharacteristic
66C2×#625—22no—
67C2×#625—22no—
68C2×D3×Dic3—22no—
69C2×D3×Dic3—22no—
70#3795—42no—
71#3795—42no—
72C32×M16—41no—
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75#3757—22no—
76C4⋊(C3⋊Dic3)C2312yes—
77#3750—22no—
78#3746—41no—
79C3×(C2×D3)⋊C4—22no—
80C3×C4⋊Dic3C2312yes—
81C2×C3×C3⋊C8—41no—
82C2×C3×C3⋊C8C2312yes—
83C3×D24—41no—
84Dic3⋊Dic3—22no—
85Dic3⋊Dic3—22no—
86(C2×D3)⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88#3716—42no—
89#3204—91noSylow
90C2×C3×#41—31no—
91C2×#237—32no—
92C2×#235—32no—
93C2×#235C2×D311yescharacteristic
94C2×C3×D8—31no—
95C2×C3×M16—21no—
96C2×C3×M16C2×D311yescharacteristic
97C2×C3×M16C2×D311yescharacteristic
98C22×C3×C8—31no—
99C3×#121—32no—
100#946—62no—
101#939—62no—
102#939—62no—
103#939—62no—
104#938—32no—
105#938—62no—
106#938—62no—
107C2×#214—32no—
108#930—32no—
109#930C2×D312yes—
110C2×C4⋊Dic3—32no—
111#924—32no—
112#924—32no—
113#924—32no—
114#924—62no—
115C22×C3⋊C8C2×D311yescharacteristic
116C2×Dic12—31no—
117C2×Dic12—31no—
118C2×Dic12—61no—
119C2×D24C2×D311yescharacteristic
120C2×#204—32no—
121#897—32no—
122D3×C4⋊C4—32no—
123#884—62no—
124#878—62no—
125C3×#106—31no—
126C3×#102—32no—
127C3×C22⋊C8—32no—
128C3×C22⋊C8—32no—
129#832—32no—
130#821—32no—
131#821C2×D312yes—
132(C2×D3)⋊C8C2×D312yes—
133(C2×D3)⋊C8C2×D312yes—
134#817—31no—
135#817—31no—
136#817—32no—
137#817—61no—
138#817C2×D311yescharacteristic
139#816—32no—
140#816—32no—
141#816—32no—
142#816—62no—
143#810—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
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154#634—22no—
155#634—22no—
156C3×#67—42no—
157C3×#67—82no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3C2×D412yes—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12—41no—
163C3×C4×D3—22no—
164C3×C4×D3—22no—
165C3×Dic6—41no—
166#625—44no—
167#625—82no—
168D3×Dic3—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—91no—
177#469—31no—
178#465—92no—
179#452—92no—
180#449—92no—
181#408—31no—
182C3×#41—121no—
183C3×#41—121no—
184C2×C3×Q8—31no—
185C2×C3×D4—32no—
186C2×C3×D4—31no—
187C2×C3×D4—32no—
188C2×C3×D4—62no—
189C22×C3×C4—21no—
190C22×C3×C4—32no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C2×#67—22no—
194C2×#67—62no—
195C2×#67—62no—
196C2×#67—62no—
197C2×#67—62no—
198C2×#67D1212yes—
199C22×Dic3—62no—
200C22×Dic3—62no—
201#237—122no—
202#237—122no—
203#235—41no—
204#235—41no—
205#235—122no—
206#235—122no—
207C2×D12D1211yescharacteristic
208C2×D12C22×D312yes—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3C22×D312yes—
212C2×Dic6—32no—
213C2×Dic6—32no—
214C2×Dic6—62no—
215C2×Dic6D1211yescharacteristic
216C3×D8—121no—
217C3×M16—41no—
218C3×M16—41no—
219C3×M16—42no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—32no—
223C2×C3×C8—121no—
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C3×C4⋊C4—32no—
229C3×C22⋊C4—62no—
230#217—62no—
231#217—62no—
232#217—62no—
233#217—62no—
234#217—122no—
235#214—122no—
236(C2×D3)⋊C4—22no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239C4⋊Dic3—32no—
240C4⋊Dic3—32no—
241C4⋊Dic3—62no—
242C4⋊Dic3—62no—
243C4⋊Dic3—62no—
244C4⋊Dic3C22×D312yes—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—122no—
250C2×C3⋊C8—41no—
251C2×C3⋊C8C22×D312yes—
252Dic12—121no—
253Dic12—121no—
254Dic12—122no—
255D24—41no—
256#204—122no—
257C22×C32—21no—
258C22×C32—22no—
259C22×C32C22×D411yescharacteristic
260C2×C3×D3—22no—
261C2×C3×D3—22no—
262C2×C3×D3—22no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C32×C4—21no—
267C32×C4H(5,𝔽2)11yescharacteristic
268C32×C4H(5,𝔽2)11yescharacteristic
269C3⋊Dic3—42no—
270C3⋊Dic3—42no—
271C3×Dic3—22no—
272C3×Dic3—42no—
273C2×#41—31no—
274C2×#41—92no—
275C2×Q16—91no—
276C2×SD16—92no—
277C2×D8—31no—
278C2×M16D3211yescharacteristic
279C22×C8—31no—
280C22⋊Q8—92no—
281C22⋊Q8—92no—
282C22⋊Q8—182no—
283#121—32no—
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—92no—
293#103—92no—
294#102—32no—
295#102—92no—
296C22⋊C8—32no—
297C22⋊C8—32no—
298C23×C3—21no—
299C23×C3—32no—
300C23×C3—62no—
301C23×C3C2×D1211yescharacteristic
302C23×C3D3×D411yescharacteristic
303C22×D3—22no—
304C22×D3C2×D1212yes—
305C3×Q8—121no—
306C3×D4—62no—
307C3×D4—62no—
308C3×D4—121no—
309C3×D4—122no—
310C3×D4—242no—
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×C4C2×D1211yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327#67—42no—
328#67—82no—
329#67—124no—
330#67—124no—
331#67—242no—
332#67—242no—
333C2×Dic3—22no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—122no—
339C2×Dic3—122no—
340C2×Dic3—124no—
341C2×Dic3—242no—
342C2×Dic3C2×D1212yes—
343D12—22no—
344D12—22no—
345D12—41no—
346C4×D3—22no—
347C4×D3—22no—
348C4×D3—124no—
349C4×D3—242no—
350Dic6—41no—
351Dic6—62no—
352Dic6—62no—
353Dic6—62no—
354Dic6—62no—
355Dic6—122no—
356Dic6—122no—
357C3×C8—22no—
358C3×C8—21no—
359C3×C8—21no—
360C3×C8—21no—
361C3×C8—21no—
362C3×C8—41no—
363C3×C8—62no—
364C3⋊C8—22no—
365C2×C32—41no—
366C2×C32#53411yescharacteristic
367C2×C32#57712yes—
368C3×D3—42no—
369C3×D3—82no—
370#41—121no—
371#41—121no—
372#41—362no—
373#41—362no—
374C2×Q8—31no—
375C2×Q8—92no—
376C2×D4—32no—
377C2×D4—32no—
378C2×D4—31no—
379C2×D4—62no—
380C2×D4—182no—
381C2×D4—182no—
382C22×C4—32no—
383C22×C4—182no—
384C22×C4—182no—
385C22×C4C2×D3211yescharacteristic
386Q16—361no—
387SD16—362no—
388D8—121no—
389M16—41no—
390C2×C8—32no—
391C2×C8—121no—
392C2×C8C2×D3211yescharacteristic
393C2×C8C2×D3211yescharacteristic
394C4⋊C4—32no—
395C4⋊C4—92no—
396C4⋊C4—182no—
397C4⋊C4—182no—
398C4⋊C4—182no—
399C22⋊C4—62no—
400C22⋊C4—182no—
401C22⋊C4—182no—
402C22⋊C4—182no—
403C22×C3—21no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—41no—
409C22×C3—42no—
410C22×C3—62no—
411C22×C3—62no—
412C22×C3—62no—
413C22×C3—122no—
414C22×C3—122no—
415C22×C3—122no—
416C22×C3C22×D1211yescharacteristic
417C22×C3C2×D3×D411yescharacteristic
418C2×D3—22no—
419C2×D3—22no—
420C2×D3—22no—
421C2×D3—42no—
422C2×D3—42no—
423C2×D3—42no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—41no—
429C3×C4—62no—
430C3×C4—122no—
431C3×C4#100411yescharacteristic
432C3×C4#100411yescharacteristic
433C3×C4#100411yescharacteristic
434C3×C4#100911yescharacteristic
435Dic3—22no—
436Dic3—42no—
437Dic3—122no—
438Dic3—122no—
439Dic3—122no—
440Dic3—122no—
441Dic3—242no—
442Dic3—242no—
443C32#320411yescharacteristic, complemented, Sylow
444C23—32no—
445C23—62no—
446C23D3×D1211yescharacteristic
447Q8—121no—
448Q8—182no—
449Q8—182no—
450D4—62no—
451D4—62no—
452D4—121no—
453D4—122no—
454D4—242no—
455D4—364no—
456D4—722no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—32no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—182no—
464C2×C4—182no—
465C2×C4—364no—
466C2×C4—722no—
467C2×C4D3×D1211yescharacteristic
468C2×C4C22×D3211yescharacteristic
469C8—21no—
470C8—21no—
471C8—62no—
472C2×C3—21no—
473C2×C3—22no—
474C2×C3—41no—
475C2×C3—41no—
476C2×C3—81no—
477C2×C3—122no—
478C2×C3—242no—
479C2×C3#549311yescharacteristic
480C2×C3#560511yescharacteristic
481C2×C3#575112yes—
482C2×C3#577512yes—
483D3—42no—
484D3—82no—
485C22—21no—
486C22—22no—
487C22—62no—
488C22—62no—
489C22—62no—
490C22—122no—
491C22—122no—
492C22—122no—
493C22C2×D3×D1211yescharacteristic
494C4—21no—
495C4—62no—
496C4—122no—
497C4—362no—
498C4—362no—
499C4#6430711yescharacteristic
500C4#6433011yescharacteristic
501C3—21no—
502C3#7867711yescharacteristic, complemented
503C3#8087311yescharacteristic, complemented
504C2—41no—
505C2—122no—
506C2—242no—
507C2#1059471312yes—
508C2#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. #10595004C2semidirect
2. #10592836C2semidirect
3. C3×#5135C2semidirect
4. C3×#5129C2semidirect
5. #10591175C2semidirect
6. #10590969C2semidirect
7. #10590962C2semidirect
8. #10590676C2semidirect
9. #10590674C2semidirect
45. #5135D3semidirect
46. #5129D3semidirect
443. C32#3204semidirect
502. C3#78677semidirect
503. C3#80873semidirect

Maximal subgroups

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

subgroupindex
#105950042
#105928362
C3×#51352
C3×#51292
#105911752
#105909692
#105909622
#105906762
#105906742
#808733
#786773