Finite Group Databasebeta

← #11787905

Subgroups — #11787905

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63860C211yesmaximal, characteristic
2#10594828C211yesmaximal, characteristic, complemented
3C2×#63651C211yesmaximal, characteristic, complemented
4C3×#5131C211yesmaximal, characteristic
5#10591085C211yesmaximal, characteristic
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70325—31nomaximal
9#68766—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×(C2×D3)⋊Dic3—22no—
18#63957—22no—
19#63860—22no—
20#63860C414yescomplemented
21#63844—22no—
22#63844—22no—
23#63651—22no—
24C3×#821—22no—
25#63562—22no—
26C2×#936—31no—
27#5516—31no—
28#5516—31no—
29C2×#875—31no—
30C3×#418—31no—
31#5215—31no—
32C2×#824—31no—
33C2×#824—31no—
34C2×#824—61no—
35#5131D311yescharacteristic
36#5001—31no—
37C3×#339—31no—
38#4555D311yescharacteristic, complemented
39#4532—31no—
40#4523—31no—
41C23×C3×D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3D412yes—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634C2×C412yes—
49C2×#634D412yes—
50C22×C3×Dic3—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12C2×C412yes—
57C32×M16—21no—
58C32×M16—21no—
59C2×C32×C8—21no—
60#3748—21no—
61#3748—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C3×#217—21no—
64C3×#217—21no—
65C3×C4⋊Dic3D412yes—
66C3×C4⋊Dic3D412yes—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C3×C4×Dic3C2×C412yes—
71#3724—24no—
72(C2×D3)⋊Dic3—28no—
73Dic32—24no—
74#1888—91noSylow
75C22×C3×D4—31no—
76C22×D12C2×D311yescharacteristic
77C22×Dic6—31no—
78C22×Dic6—31no—
79C22×Dic6—61no—
80C2×C3×M16—21no—
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×M16C2×D311yescharacteristic
83C3×#117—31no—
84C3×#117—31no—
85C2×C3×C42—31no—
86C2×#217—62no—
87#936—34no—
88#936—62no—
89C2×(C2×D3)⋊C4—62no—
90#926C2×D311yescharacteristic
91#926C2×D311yescharacteristic
92C2×C4×Dic3C2×D311yescharacteristic
93C2×#208—31no—
94C2×#208—31no—
95C2×#208—61no—
96#887—62no—
97#887—62no—
98#877—62no—
99#877—62no—
100#875—34no—
101#875—62no—
102C4×Dic6—62no—
103C4×Dic6—62no—
104C3×#102—62no—
105#832—62no—
106#824—62no—
107#824—62no—
108#824—64no—
109#821—22no—
110#809—62no—
111C23×C32C2×D411yescharacteristic
112C22×C3×D3—22no—
113C22×C3×D3—44no—
114C22×C3×D3—41no—
115C22×C3×D3—41no—
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3C22⋊C414yes—
125#634—22no—
126#634—22no—
127#634—22no—
128#634—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—42no—
133C3×D12—22no—
134C3×D12—22no—
135C3×D12—41no—
136C3×D12—41no—
137C32×C8—41no—
138C3⋊(C3⋊C8)—41no—
139C2×#124—91no—
140#519—91no—
141#418—31no—
142#418—91no—
143C2×#101—91no—
144#339—31no—
145#339—91no—
146C24×C3—61no—
147C23×D3—21no—
148C2×C3×D4—32no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C22×C3×C4—21no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×Dic3—21no—
159C22×Dic3—32no—
160C22×Dic3—32no—
161C22×Dic3—62no—
162C2×D12—21no—
163C2×D12—21no—
164C2×D12—21no—
165C2×D12—21no—
166C2×D12—21no—
167C2×D12C4×D312yes—
168C2×Dic6—32no—
169C2×Dic6—32no—
170C2×Dic6—32no—
171C2×Dic6—32no—
172C2×Dic6—62no—
173C2×Dic6—62no—
174C2×Dic6—61no—
175C2×Dic6—61no—
176C2×Dic6—61no—
177C2×Dic6—61no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C2×Dic6—121no—
183C2×Dic6—121no—
184C2×Dic6—121no—
185C2×Dic6—121no—
186C3×M16—22no—
187C3×M16—21no—
188C3×M16—21no—
189C3×M16—21no—
190C3×M16—21no—
191C3×M16—41no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—41no—
195C3×C4⋊C4—32no—
196C3×C4⋊C4—32no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C42—32no—
200C3×C42—61no—
201C3×C42—61no—
202C3×C42—61no—
203#217—21no—
204#217—21no—
205#217—68no—
206(C2×D3)⋊C4—68no—
207C4⋊Dic3D1212yes—
208C4⋊Dic3#6712yes—
209Dic3⋊C4—64no—
210Dic3⋊C4—64no—
211C4×Dic3—21no—
212C4×Dic3—21no—
213C4×Dic3—21no—
214C4×Dic3—64no—
215C4×Dic3—64no—
216C4×Dic3C4×D312yes—
217#208—62no—
218#208—61no—
219#208—61no—
220#208—61no—
221#208—61no—
222#208—121no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226C22×C32—22no—
227C22×C32C2×C22⋊C411yescharacteristic
228C22×C32#12011yescharacteristic
229C22×C32#12311yescharacteristic
230C2×C3×D3—44no—
231C2×C3×D3—42no—
232C2×C3×D3—82no—
233C2×C3×D3—82no—
234C32×C4C4×D411yescharacteristic
235C32×C4C4×D411yescharacteristic
236C32×C4#12111yescharacteristic
237C32×C4#12111yescharacteristic
238C3⋊Dic3—24no—
239C3×Dic3—42no—
240C3×Dic3—42no—
241C3×Dic3—42no—
242C22×Q8—91no—
243C22×D4—31no—
244C2×M16—91no—
245C2×M16D3211yescharacteristic
246#124—94no—
247#124—182no—
248C4×Q8—182no—
249C4×Q8—182no—
250#117—31no—
251#117—31no—
252#117—182no—
253C2×C22⋊C4—182no—
254C2×C42—31no—
255#102—62no—
256#102—182no—
257#101—182no—
258C23×C3—21no—
259C23×C3—62no—
260C23×C3—124no—
261C23×C3—121no—
262C23×C3—121no—
263C23×C3D3×D411yescharacteristic
264C23×C3D3×D411yescharacteristic
265C22×D3—22no—
266C22×D3—44no—
267C22×D3—41no—
268C22×D3—41no—
269C3×D4—62no—
270C3×D4—62no—
271C3×D4—121no—
272C3×D4—121no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4—122no—
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4C2×D1211yescharacteristic
286C2×C3×C4#23511yescharacteristic
287C2×C3×C4#23511yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4#23711yescharacteristic
293C2×C3×C4#23911yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—34no—
299C2×Dic3—34no—
300C2×Dic3—42no—
301C2×Dic3—64no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—122no—
307C2×Dic3—122no—
308D12—22no—
309D12—22no—
310D12—41no—
311D12—41no—
312Dic6—62no—
313Dic6—62no—
314Dic6—62no—
315Dic6—62no—
316Dic6—62no—
317Dic6—62no—
318Dic6—62no—
319Dic6—62no—
320Dic6—122no—
321Dic6—122no—
322Dic6—122no—
323Dic6—122no—
324C3×C8—42no—
325C3×C8—41no—
326C3×C8—41no—
327C3⋊C8—122no—
328C3⋊C8—121no—
329C3⋊C8—121no—
330C2×C32—21no—
331C2×C32—21no—
332C2×C32#38611yescharacteristic
333C2×C32#45412yes—
334C3×D3—82no—
335C24—61no—
336C2×Q8—92no—
337C2×Q8—92no—
338C2×Q8—181no—
339C2×Q8—181no—
340C2×Q8—181no—
341C2×Q8—181no—
342C2×D4—32no—
343C2×D4—61no—
344C2×D4—61no—
345C2×D4—61no—
346C2×D4—61no—
347C2×D4—61no—
348C22×C4—61no—
349C22×C4—92no—
350C22×C4C2×D3211yescharacteristic
351M16—21no—
352M16—21no—
353M16—181no—
354M16—181no—
355C2×C8—21no—
356C2×C8—181no—
357C4⋊C4—32no—
358C4⋊C4—32no—
359C4⋊C4—184no—
360C22⋊C4—61no—
361C22⋊C4—61no—
362C22⋊C4—188no—
363C42—32no—
364C42—61no—
365C42—61no—
366C42—61no—
367C42—184no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—42no—
374C22×C3—124no—
375C22×C3—122no—
376C22×C3—242no—
377C22×C3—242no—
378C22×C3D3×C22⋊C411yescharacteristic
379C22×C3D3×C22⋊C411yescharacteristic
380C22×C3#88211yescharacteristic
381C22×C3#88311yescharacteristic
382C22×C3#89411yescharacteristic
383C22×C3#93711yescharacteristic
384C2×D3—44no—
385C2×D3—42no—
386C2×D3—82no—
387C2×D3—82no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—122no—
393C3×C4—122no—
394C3×C4—122no—
395C3×C4C4×D1211yescharacteristic
396C3×C4#67⋊C411yescharacteristic
397C3×C4#88411yescharacteristic
398C3×C4#88411yescharacteristic
399C3×C4#89311yescharacteristic
400C3×C4#89511yescharacteristic
401C3×C4C4×#6711yescharacteristic
402C3×C4#93811yescharacteristic
403Dic3—42no—
404Dic3—42no—
405Dic3—42no—
406Dic3—64no—
407Dic3—64no—
408Dic3—124no—
409C32#188811yescharacteristic, complemented, Sylow
410C23—62no—
411C23—124no—
412C23—121no—
413C23—121no—
414C23#380211yescharacteristic
415Q8—182no—
416Q8—182no—
417Q8—182no—
418Q8—182no—
419D4—62no—
420D4—62no—
421D4—121no—
422D4—121no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—94no—
427C2×C4—122no—
428C2×C4—182no—
429C2×C4—182no—
430C2×C4#379911yescharacteristic
431C2×C4C4×D3211yescharacteristic
432C2×C4D3×D1211yescharacteristic
433C2×C4#380411yescharacteristic
434C2×C4D3×#6711yescharacteristic
435C2×C4#381111yescharacteristic
436C8—41no—
437C8—361no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—22no—
443C2×C3—21no—
444C2×C3—41no—
445C2×C3—41no—
446C2×C3—242no—
447C2×C3#466511yescharacteristic
448C2×C3#482712yes—
449C2×C3#495611yescharacteristic
450C2×C3#520112yes—
451D3—82no—
452C22—22no—
453C22—124no—
454C22—122no—
455C22—242no—
456C22—242no—
457C22#6385411yescharacteristic
458C22#6392111yescharacteristic
459C22#6392211yescharacteristic
460C4—122no—
461C4—122no—
462C4—122no—
463C4—184no—
464C4#6388011yescharacteristic
465C4#6390411yescharacteristic
466C4#6391011yescharacteristic
467C4#6395811yescharacteristic
468C3—21no—
469C3#6876611yescharacteristic, complemented
470C3#7032511yescharacteristic, complemented
471C2—21no—
472C2—21no—
473C2—242no—
474C2#1059101912yes—
475C2#1059127511yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1888
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
2. #10594828C2semidirect
3. C2×#63651C2semidirect
6. C3×#4555C2semidirect
7. #10589161C2semidirect
20. #63860C4semidirect
38. #4555D3semidirect
409. C32#1888semidirect
469. C3#68766semidirect
470. C3#70325semidirect

Maximal subgroups

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

subgroupindex
C2×#638602
#105948282
C2×#636512
C3×#51312
#105910852
C3×#45552
#105891612
#703253
#687663