Finite Group Databasebeta

← #11868044

Subgroups — #11868044

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64157C211yesmaximal, characteristic, complemented
2C3×#5822C212yesmaximal, complemented
3C2×#63822C211yesmaximal, characteristic, complemented
4#10591683C212yesmaximal, complemented
5#10591681C214yesmaximal, complemented
6#10591678C212yesmaximal, complemented
7C2×#63578C211yesmaximal, characteristic, complemented
8#10591076C212yesmaximal, complemented
9#84001—32nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2212yes—
12#64157—21no—
13#64157—21no—
14#64157C2212yes—
15#64157C2212yes—
16C2×#3748—21no—
17C2×#3748C2211yescharacteristic
18C22×C3⋊(C3⋊C8)—21no—
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C3×#951C2214yes—
21C3×#950—24no—
22C3×#949C2214yes—
23C3×#942—22no—
24C3×#932—22no—
25C2×C3×#208C2212yes—
26C2×#3718C2211yescharacteristic, complemented
27C2×#3715C2212yescomplemented
28#63822—21no—
29#63822—21no—
30#63822—21no—
31#63822—21no—
32C2×#3713C2211yescharacteristic, complemented
33#63578C2212yescomplemented
34#63578C2212yescomplemented
35#63560C2214yescomplemented
36#63558C2214yescomplemented
37C3×#575—32no—
38#5822D312yescomplemented
39C2×#950—32no—
40C2×#948—32no—
41C2×#948—61no—
42#5237—32no—
43#5204—34no—
44#5203—34no—
45#5200—34no—
46#5199—34no—
47#5132—32no—
48C2×#822—32no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41D412yes—
52C32×#41C2312yes—
53C2×C32×Q8D411yescharacteristic
54C2×C32×D4—21no—
55C2×C32×D4D411yescharacteristic
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C2×C3×#67—22no—
59C3×#235—22no—
60C3×#235—22no—
61C3×#235—22no—
62C3×#235—22no—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—22no—
65C2×C3×Dic6C2312yes—
66#3748—21no—
67#3748—22no—
68#3748—22no—
69#3748C2312yes—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—22no—
72C2×C3⋊(C3⋊C8)—22no—
73C2×C3⋊(C3⋊C8)D411yescharacteristic
74C2×C3⋊(C3⋊C8)D411yescharacteristic
75C2×C3⋊(C3⋊C8)D411yescharacteristic
76C2×C3⋊(C3⋊C8)D411yescharacteristic
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C3×#216—24no—
80C3×#215—24no—
81C3×#214—24no—
82C3×#213—24no—
83C3×#208—22no—
84C3×#208C2314yes—
85C2×C3×C3⋊C8—22no—
86#3718—21no—
87#3718—21no—
88#3715—22no—
89#3715—22no—
90#3713—21no—
91#3713—21no—
92#3067—91noSylow
93C2×C3×#41—21no—
94C2×C3×#41—32no—
95C2×C3×#41C2×D312yes—
96C2×#235C2×D312yes—
97C3×#137—34no—
98C3×#137—62no—
99C3×AGL(1,ℤ/8)—34no—
100C3×AGL(1,ℤ/8)—62no—
101C3×#135—64no—
102C2×C3×M16—32no—
103#951C2×D314yes—
104#950—24no—
105#950—62no—
106#950—62no—
107#950—62no—
108#950—62no—
109#949C2×D314yes—
110#948—34no—
111#948—34no—
112#948—62no—
113#948—62no—
114#948—62no—
115#948—62no—
116#948—62no—
117#948—62no—
118C2×#216—32no—
119#942—22no—
120C2×#215—32no—
121C2×#214—32no—
122#932—22no—
123C2×#213—32no—
124C2×#208—32no—
125C2×#208—61no—
126C2×#208—62no—
127C2×#208—62no—
128C2×#208C2×D312yes—
129C22×C3⋊C8—32no—
130C22×C3⋊C8—61no—
131C22×C3⋊C8—62no—
132C22×C3⋊C8—62no—
133#836—34no—
134#833—34no—
135#824—34no—
136#823—34no—
137#822—34no—
138#822—34no—
139C23×C32—21no—
140C23×C32#4111yescharacteristic
141C22×C3×D3—22no—
142C32×Q8—21no—
143C32×Q8C2×D412yes—
144C32×D4—22no—
145C32×D4—22no—
146C32×D4—21no—
147C32×D4C2×D412yes—
148C2×C32×C4—21no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4#4111yescharacteristic
156C2×C32×C4C2411yescharacteristic
157C3×#67—42no—
158C3×#67—42no—
159C2×C3×Dic3—22no—
160C3×D12—22no—
161C3×D12—22no—
162C3×C4×D3—42no—
163C3×C4×D3—42no—
164C3×Dic6—22no—
165C3×Dic6—22no—
166C3⋊(C3⋊C8)—22no—
167C3⋊(C3⋊C8)C2×D411yescharacteristic
168C3⋊(C3⋊C8)C2×D411yescharacteristic
169C3⋊(C3⋊C8)C2×D411yescharacteristic
170C3⋊(C3⋊C8)C2×D411yescharacteristic
171C3×C3⋊C8—24no—
172#575—32no—
173C2×#135—91no—
174C2×#131—91no—
175#473—92no—
176#472—92no—
177#471—94no—
178C2×#108—91no—
179#413—92no—
180C3×#41—22no—
181C3×#41—22no—
182C3×#41—22no—
183C3×#41—22no—
184C3×#41—22no—
185C3×#41—22no—
186C3×#41—62no—
187C3×#41—62no—
188C3×#41—62no—
189C3×#41—62no—
190C3×#41#6714yes—
191C3×#41C22×D314yes—
192C2×C3×Q8—21no—
193C2×C3×Q8—32no—
194C2×C3×Q8#6712yes—
195C2×C3×D4—22no—
196C2×C3×D4—22no—
197C2×C3×D4—21no—
198C2×C3×D4—32no—
199C2×C3×D4—62no—
200C2×C3×D4#6712yes—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—62no—
205C22×C3×C4C22×D312yes—
206C2×#67—22no—
207#235—22no—
208#235—22no—
209#235—22no—
210#235—22no—
211C2×D12C22×D312yes—
212C2×C4×D3—22no—
213C2×Dic6C22×D312yes—
214C3×Q16—64no—
215C3×SD16—64no—
216C3×SD16—64no—
217C3×D8—64no—
218C3×M16—34no—
219C3×M16—62no—
220C2×C3×C8—62no—
221#216—24no—
222#216—62no—
223#216—62no—
224#215—24no—
225#215—62no—
226#215—62no—
227#214—24no—
228#214—62no—
229#214—62no—
230#213—24no—
231#213—62no—
232#213—62no—
233#208—22no—
234#208—34no—
235#208—62no—
236#208—64no—
237#208—64no—
238#208—64no—
239#208—64no—
240#208—62no—
241#208—62no—
242#208C22×D314yes—
243C2×C3⋊C8—22no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—32no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—64no—
257C2×C3⋊C8—64no—
258C2×C3⋊C8—62no—
259C2×C3⋊C8—64no—
260C2×C3⋊C8—64no—
261C2×C3⋊C8—62no—
262C22×C32—22no—
263C22×C32—41no—
264C22×C32—42no—
265C22×C32#12111yescharacteristic
266C22×C32#12111yescharacteristic
267C22×C32C2×#4111yescharacteristic
268C2×C3×D3—42no—
269C2×C3×D3—82no—
270C32×C4—22no—
271C32×C4#12111yescharacteristic
272C32×C4#12111yescharacteristic
273C32×C4C22×D411yescharacteristic
274C32×C4C22×D411yescharacteristic
275C3×Dic3—42no—
276C2×#41—32no—
277C2×#41D3211yescharacteristic
278#137—34no—
279#137—62no—
280AGL(1,ℤ/8)—34no—
281AGL(1,ℤ/8)—62no—
282#135—64no—
283#135—181no—
284#135—181no—
285#135—181no—
286#135—181no—
287C2×Q16—91no—
288C2×SD16—92no—
289C2×D8—91no—
290#131—92no—
291#131—92no—
292#131—181no—
293#131—181no—
294C2×M16—32no—
295C2×M16—91no—
296C2×M16—181no—
297C22×C8—91no—
298C22×C8—181no—
299#108—92no—
300#108—92no—
301#101—94no—
302#100—94no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—21no—
306C23×C3—62no—
307C23×C3#23712yes—
308C22×D3—22no—
309C3×Q8—22no—
310C3×Q8—22no—
311C3×Q8—22no—
312C3×Q8—62no—
313C3×Q8—62no—
314C3×Q8C2×#6714yes—
315C3×D4—24no—
316C3×D4—24no—
317C3×D4—22no—
318C3×D4—24no—
319C3×D4—24no—
320C3×D4—22no—
321C3×D4—22no—
322C3×D4—62no—
323C3×D4—62no—
324C3×D4—122no—
325C3×D4—122no—
326C3×D4C2×#6714yes—
327C2×C3×C4—24no—
328C2×C3×C4—22no—
329C2×C3×C4—24no—
330C2×C3×C4—22no—
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—62no—
340C2×C3×C4—122no—
341C2×C3×C4—122no—
342C2×C3×C4D3×D412yes—
343C2×C3×C4D3×D412yes—
344C2×C3×C4#23712yes—
345C2×C3×C4C2×#6712yes—
346C2×C3×C4C2×#6712yes—
347C2×C3×C4C23×D312yes—
348#67—42no—
349#67—42no—
350C2×Dic3—22no—
351D12—22no—
352D12—22no—
353C4×D3—42no—
354C4×D3—42no—
355Dic6—22no—
356Dic6—22no—
357C3×C8—64no—
358C3⋊C8—24no—
359C3⋊C8—32no—
360C3⋊C8—32no—
361C3⋊C8—32no—
362C3⋊C8—32no—
363C3⋊C8—61no—
364C3⋊C8—61no—
365C3⋊C8—61no—
366C3⋊C8—61no—
367C3⋊C8—64no—
368C3⋊C8—64no—
369C2×C32—21no—
370C2×C32—21no—
371C2×C32—21no—
372C2×C32—42no—
373C2×C32C2×#12111yescharacteristic
374C3×D3—82no—
375#41—21no—
376#41—21no—
377#41—62no—
378#41—62no—
379#41—62no—
380#41—62no—
381#41#62512yes—
382#41C2×D3212yes—
383C2×Q8—32no—
384C2×Q8#62511yescharacteristic
385C2×D4—21no—
386C2×D4—32no—
387C2×D4—62no—
388C2×D4#62511yescharacteristic
389C22×C4—21no—
390C22×C4—62no—
391C22×C4C2×D3211yescharacteristic
392Q16—64no—
393Q16—181no—
394Q16—181no—
395SD16—64no—
396SD16—64no—
397SD16—182no—
398SD16—182no—
399D8—64no—
400D8—181no—
401D8—181no—
402M16—34no—
403M16—62no—
404M16—92no—
405M16—182no—
406M16—182no—
407M16—181no—
408C2×C8—62no—
409C2×C8—91no—
410C2×C8—91no—
411C2×C8—91no—
412C2×C8—91no—
413C2×C8—91no—
414C2×C8—91no—
415C2×C8—182no—
416C2×C8—182no—
417C2×C8—181no—
418C22×C3—24no—
419C22×C3—24no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—44no—
426C22×C3—44no—
427C22×C3—122no—
428C22×C3—242no—
429C22×C3#93912yes—
430C22×C3#93912yes—
431C22×C3C2×#23712yes—
432C2×D3—42no—
433C2×D3—82no—
434C3×C4—24no—
435C3×C4—24no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—122no—
441C3×C4#93912yes—
442C3×C4#93912yes—
443C3×C4C2×D3×D412yes—
444C3×C4C22×#6712yes—
445Dic3—42no—
446C32#306711yescharacteristic, complemented, Sylow
447C23—21no—
448C23—62no—
449C23#380511yescharacteristic
450Q8—21no—
451Q8—62no—
452Q8—62no—
453Q8C2×#62512yes—
454D4—22no—
455D4—22no—
456D4—21no—
457D4—62no—
458D4—62no—
459D4—122no—
460D4—122no—
461D4C2×#62512yes—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—62no—
466C2×C4—122no—
467C2×C4—122no—
468C2×C4#380511yescharacteristic
469C2×C4C2×#62511yescharacteristic
470C2×C4C2×#62511yescharacteristic
471C2×C4#381111yescharacteristic
472C2×C4#381111yescharacteristic
473C2×C4C22×D3211yescharacteristic
474C8—64no—
475C8—91no—
476C8—91no—
477C8—91no—
478C8—91no—
479C8—182no—
480C2×C3—22no—
481C2×C3—22no—
482C2×C3—22no—
483C2×C3—22no—
484C2×C3—21no—
485C2×C3—41no—
486C2×C3—41no—
487C2×C3—44no—
488C2×C3—44no—
489C2×C3—242no—
490C2×C3C2×#93912yes—
491D3—82no—
492C22—22no—
493C22—41no—
494C22—42no—
495C22—122no—
496C22—242no—
497C22#6398011yescharacteristic
498C22#6398011yescharacteristic
499C22C2×#380511yescharacteristic
500C4—22no—
501C4—122no—
502C4#6398011yescharacteristic
503C4#6398011yescharacteristic
504C4C22×#62511yescharacteristic
505C4C2×#381111yescharacteristic
506C3—21no—
507C3#8400112yescomplemented
508C2—21no—
509C2—21no—
510C2—21no—
511C2—42no—
512C2—242no—
513C2C2×#6398011yescharacteristic
subgroupG/H
centerC4#63980
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#121
hypercenterC2×#41D32
hypocenterC32#3067
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64157C2semidirect
2. C3×#5822C2semidirect
3. C2×#63822C2semidirect
4. #10591683C2semidirect
5. #10591681C2semidirect
6. #10591678C2semidirect
7. C2×#63578C2semidirect
8. #10591076C2semidirect
26. C2×#3718C22semidirect
27. C2×#3715C22semidirect
32. C2×#3713C22semidirect
33. #63578C22semidirect
34. #63578C22semidirect
35. #63560C22semidirect
36. #63558C22semidirect
38. #5822D3semidirect
446. C32#3067semidirect
507. C3#84001semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C3×#58222
C2×#638222
#105916832
#105916812
#105916782
C2×#635782
#105910762
#840013