Finite Group Databasebeta

← #11793909

Subgroups — #11793909

Order 1152.

645 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63830C211yesmaximal, characteristic
2#10592665C211yesmaximal, characteristic, complemented
3C2×C3×#809C211yesmaximal, characteristic, complemented
4C2×#63577C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6#10591073C211yesmaximal, characteristic, complemented
7C3×#4530C211yesmaximal, characteristic, complemented
8#70196—31nomaximal
9#68986—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63830—22no—
18#63830—22no—
19C2×#3716—21no—
20C2×#3714—21no—
21#63637—21no—
22#63636—21no—
23C3×#809—22no—
24#63577—22no—
25#63558—22no—
26#63557—22no—
27C2×#932—31no—
28C2×#908—31no—
29C2×C3×#102—31no—
30C2×#833—31no—
31C2×#823—31no—
32#5129—31no—
33C2×#822—31no—
34#5110—31no—
35C2×#819—31no—
36#4966—31no—
37#4966—31no—
38#4966—61no—
39C2×#809D311yescharacteristic, complemented
40C3×#343—31no—
41#4530D311yescharacteristic, complemented
42C23×C3×D3—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634D411yescharacteristic
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12D412yes—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61#3748—21no—
62#3748—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×#208—21no—
65C3×#208—21no—
66C3×#208—21no—
67C3×#208D412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D412yes—
73#3716—24no—
74#3714—24no—
75#2051—91noSylow
76C22×C3×D4—31no—
77C2×#235—31no—
78C2×#235—31no—
79C2×#235—61no—
80C22×D12C2×D311yescharacteristic
81C2×C3×M16—31no—
82C2×C3×M16—31no—
83C22×C3×C8—31no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×#214—61no—
88#932—62no—
89#932—62no—
90C2×#213—61no—
91C2×#208—31no—
92C2×#208—31no—
93C2×#208—61no—
94C2×#208C2×D311yescharacteristic
95C2×#208C2×D311yescharacteristic
96C22×C3⋊C8C2×D311yescharacteristic
97#908—62no—
98#908—62no—
99C2×D24—61no—
100C2×#204—61no—
101C3×#102—62no—
102#833—62no—
103#823—62no—
104#822—62no—
105(C2×D3)⋊C8—62no—
106(C2×D3)⋊C8—62no—
107#819—62no—
108#810—61no—
109#810—61no—
110#810—62no—
111#809—22no—
112#809—61no—
113#809—61no—
114#809—62no—
115C23×C32#4111yescharacteristic
116C22×C3⋊D3—21no—
117C22×C3×D3—22no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—81no—
121C22×C3×D3—81no—
122C2×C32×C4—41no—
123C2×C32×C4—81no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130#638—41no—
131#638—41no—
132C2×C3⋊Dic3—21no—
133C4⋊(C3⋊D3)—21no—
134C4⋊(C3⋊D3)—21no—
135C4×C3⋊D3—41no—
136C4×C3⋊D3—41no—
137#634—21no—
138#634—21no—
139C3×D12—22no—
140C3×D12—22no—
141C3×D12—41no—
142C3×D12—41no—
143C3⋊(C3⋊C8)—41no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—22no—
146C3×C3⋊C8—41no—
147C2×AGL(1,ℤ/8)—91no—
148C2×#108—91no—
149#417—91no—
150C2×#102—31no—
151C2×#100—91no—
152#408—91no—
153#343—31no—
154C24×C3—61no—
155C23×D3—21no—
156C2×C3×D4—32no—
157C2×C3×D4—61no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—41no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—61no—
169C2×#67—61no—
170C2×#67—121no—
171#235—62no—
172#235—62no—
173#235—61no—
174#235—61no—
175#235—61no—
176#235—61no—
177#235—61no—
178#235—61no—
179#235—61no—
180#235—61no—
181#235—121no—
182#235—121no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12—21no—
186C2×D12—21no—
187C2×D12—21no—
188C2×D12—31no—
189C2×D12—31no—
190C2×D12—61no—
191C2×D12D1212yes—
192C2×C4×D3—61no—
193C2×C4×D3—61no—
194C2×C4×D3—121no—
195C2×Dic6—31no—
196C2×Dic6—31no—
197C2×Dic6—61no—
198C3×M16—32no—
199C3×M16—61no—
200C3×M16—61no—
201C3×M16—61no—
202C2×C3×C8—32no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—41no—
213#214—64no—
214#213—64no—
215#208—21no—
216#208—21no—
217#208—21no—
218#208—61no—
219#208—61no—
220#208—61no—
221#208—61no—
222#208—121no—
223#208—121no—
224#208D1212yes—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8#6712yes—
233D24—64no—
234#204—64no—
235C22×C32—21no—
236C22×C32—21no—
237C22×C32#12111yescharacteristic
238C22×C32#12311yescharacteristic
239C22×C32#12411yescharacteristic
240C2×C3⋊D3—41no—
241C2×C3⋊D3—41no—
242C2×C3⋊D3—41no—
243C2×C3×D3—42no—
244C2×C3×D3—82no—
245C2×C3×D3—81no—
246C2×C3×D3—81no—
247C2×C3×D3—82no—
248C32×C4—81no—
249C32×C4#12011yescharacteristic
250C32×C4#12111yescharacteristic
251C32×C4#12111yescharacteristic
252C32×C4#12311yescharacteristic
253C3⋊Dic3—41no—
254C2×#41—91no—
255C22×D4—31no—
256AGL(1,ℤ/8)—182no—
257AGL(1,ℤ/8)—182no—
258C2×SD16—181no—
259C2×D8—181no—
260C2×M16—31no—
261C2×M16—31no—
262C2×M16—91no—
263C22×C8—31no—
264C2×C4⋊C4D3211yescharacteristic
265#108—182no—
266#103—181no—
267#102—62no—
268#102—181no—
269#100—182no—
270C22⋊C8—182no—
271C23×C3—21no—
272C23×C3—62no—
273C23×C3—121no—
274C23×C3—121no—
275C23×C3—241no—
276C23×C3—241no—
277C23×C3#23511yescharacteristic
278C23×C3#23711yescharacteristic
279C22×D3—22no—
280C22×D3—41no—
281C22×D3—41no—
282C22×D3—61no—
283C22×D3—61no—
284C22×D3—81no—
285C22×D3—81no—
286C22×D3—121no—
287C3×D4—62no—
288C3×D4—62no—
289C3×D4—121no—
290C3×D4—121no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—42no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—82no—
301C2×C3×C4—81no—
302C2×C3×C4—81no—
303C2×C3×C4C2×D1211yescharacteristic
304C2×C3×C4C2×D1211yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4#23511yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4#23711yescharacteristic
313C2×C3×C4#23911yescharacteristic
314C2×C3×C4C2×#6711yescharacteristic
315#67—122no—
316#67—122no—
317#67—121no—
318#67—121no—
319#67—121no—
320#67—121no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—121no—
324D12—22no—
325D12—22no—
326D12—41no—
327D12—41no—
328D12—62no—
329D12—61no—
330D12—61no—
331D12—61no—
332D12—61no—
333D12—121no—
334C4×D3—122no—
335C4×D3—122no—
336C4×D3—121no—
337C4×D3—121no—
338C4×D3—121no—
339C4×D3—121no—
340Dic6—62no—
341Dic6—61no—
342Dic6—61no—
343Dic6—61no—
344Dic6—61no—
345Dic6—121no—
346C3×C8—62no—
347C3×C8—62no—
348C3×C8—121no—
349C3⋊C8—22no—
350C3⋊C8—22no—
351C3⋊C8—41no—
352C3⋊C8—122no—
353C3⋊C8—121no—
354C3⋊C8—121no—
355C2×C32—21no—
356C2×C32—21no—
357C2×C32#39411yescharacteristic
358C2×C32#47111yescharacteristic
359C2×C32#47211yescharacteristic
360C3⋊D3—81no—
361C3×D3—82no—
362C24—61no—
363#41—181no—
364#41—181no—
365#41—181no—
366#41—181no—
367C2×Q8—91no—
368C2×D4—32no—
369C2×D4—61no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—91no—
375C2×D4—181no—
376C22×C4—21no—
377C22×C4—181no—
378C22×C4C2×D3211yescharacteristic
379SD16—184no—
380D8—184no—
381M16—32no—
382M16—61no—
383M16—61no—
384M16—61no—
385M16—181no—
386M16—181no—
387C2×C8—32no—
388C2×C8—61no—
389C2×C8—61no—
390C2×C8—61no—
391C2×C8—61no—
392C2×C8—181no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—122no—
405C22×C3—242no—
406C22×C3—242no—
407C22×C3—241no—
408C22×C3—241no—
409C22×C3#87511yescharacteristic
410C22×C3#88411yescharacteristic
411C22×C3#88511yescharacteristic
412C22×C3#88611yescharacteristic
413C22×C3#89411yescharacteristic
414C22×C3#93811yescharacteristic
415C2×D3—42no—
416C2×D3—82no—
417C2×D3—81no—
418C2×D3—81no—
419C2×D3—82no—
420C2×D3—122no—
421C2×D3—121no—
422C2×D3—121no—
423C2×D3—121no—
424C2×D3—121no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—241no—
428C2×D3—241no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—82no—
434C3×C4—81no—
435C3×C4—81no—
436C3×C4#88211yescharacteristic
437C3×C4#88211yescharacteristic
438C3×C4#88311yescharacteristic
439C3×C4#88411yescharacteristic
440C3×C4#89411yescharacteristic
441C3×C4#89511yescharacteristic
442C3×C4#93011yescharacteristic
443C3×C4#93911yescharacteristic
444Dic3—122no—
445Dic3—121no—
446Dic3—121no—
447C32#205111yescharacteristic, complemented, Sylow
448C23—62no—
449C23—121no—
450C23—121no—
451C23—181no—
452C23—241no—
453C23—241no—
454C23#380411yescharacteristic
455Q8—181no—
456Q8—181no—
457D4—62no—
458D4—62no—
459D4—121no—
460D4—121no—
461D4—181no—
462D4—181no—
463D4—361no—
464D4—361no—
465C2×C4—41no—
466C2×C4—81no—
467C2×C4—181no—
468C2×C4—361no—
469C2×C4—361no—
470C2×C4#379611yescharacteristic
471C2×C4#379811yescharacteristic
472C2×C4D3×D1211yescharacteristic
473C2×C4D3×D1211yescharacteristic
474C2×C4D3×#6711yescharacteristic
475C2×C4#381111yescharacteristic
476C8—62no—
477C8—62no—
478C8—121no—
479C8—361no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—41no—
488C2×C3—41no—
489C2×C3—242no—
490C2×C3#467211yescharacteristic
491C2×C3#474911yescharacteristic
492C2×C3#475411yescharacteristic
493C2×C3#496111yescharacteristic
494C2×C3#516011yescharacteristic
495C2×C3#517711yescharacteristic
496D3—82no—
497D3—242no—
498D3—241no—
499D3—241no—
500C22—21no—
501C22—21no—
502C22—122no—
503C22—242no—
504C22—242no—
505C22—241no—
506C22—241no—
507C22—361no—
508C22—361no—
509C22—361no—
510C22#6385211yescharacteristic
511C22#6389011yescharacteristic
512C22#6395811yescharacteristic
513C4—81no—
514C4—361no—
515C4#6385311yescharacteristic
516C4#6388611yescharacteristic
517C4#6390611yescharacteristic
518C4#6392311yescharacteristic
519C3—21no—
520C3#6898611yescharacteristic, complemented
521C3#7019611yescharacteristic, complemented
522C2—21no—
523C2—21no—
524C2—242no—
525C2—721no—
526C2#1059131211yescharacteristic
527C2#1059140611yescharacteristic
528C2#1059154211yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC2×#63830C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2051
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592665C2semidirect
3. C2×C3×#809C2semidirect
4. C2×#63577C2semidirect
5. C2×#63558C2semidirect
6. #10591073C2semidirect
7. C3×#4530C2semidirect
39. C2×#809D3semidirect
41. #4530D3semidirect
447. C32#2051semidirect
520. C3#68986semidirect
521. C3#70196semidirect

Maximal subgroups

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

subgroupindex
C2×#638302
#105926652
C2×C3×#8092
C2×#635772
C2×#635582
#105910732
C3×#45302
#701963
#689863