Finite Group Databasebeta

← #11793902

Subgroups — #11793902

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#10592832C211yesmaximal, characteristic, complemented
3C2×C3×#823C211yesmaximal, characteristic, complemented
4C2×C3×#822C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic, complemented
6#10591073C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#70714—31nomaximal
9#70092—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63830—22no—
18#63830—22no—
19C2×#3716—21no—
20C2×#3714—21no—
21#63648—21no—
22#63643—21no—
23C3×#823—22no—
24C3×#822—22no—
25#63563—22no—
26#63557—22no—
27C2×#932—31no—
28C2×#908—31no—
29C2×C3×#108—31no—
30C2×C3×#100—31no—
31C2×#832—31no—
32#5133—31no—
33#5133—31no—
34#5133—61no—
35C2×#823D311yescharacteristic, complemented
36#5129—31no—
37C2×#822D311yescharacteristic, complemented
38C2×#821—31no—
39#5110—31no—
40#4554—31no—
41#4554—31no—
42C23×C3×D3—21no—
43C22×C32×C4C2311yescharacteristic
44C2×#638—21no—
45C22×C3⋊Dic3—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×M16—21no—
60C32×M16—21no—
61C2×C32×C8—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—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—21no—
82C2×C3×M16—31no—
83C2×C3×M16—31no—
84C2×C3×M16C2×D311yescharacteristic
85C2×C3×M16C2×D311yescharacteristic
86C22×C3×C8—31no—
87C2×#214—61no—
88#932—62no—
89#932—62no—
90C2×#213—61no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—61no—
94C2×#208C2×D311yescharacteristic
95C2×#208C2×D311yescharacteristic
96C22×C3⋊C8C2×D311yescharacteristic
97#908—62no—
98#908—62no—
99C2×D24—61no—
100C2×#204—61no—
101C3×#108—62no—
102C3×#100—62no—
103#832—62no—
104#823—22no—
105#822—22no—
106#821—61no—
107#821—61no—
108#821—62no—
109#821—62no—
110(C2×D3)⋊C8—62no—
111(C2×D3)⋊C8—62no—
112#816—61no—
113#816—61no—
114#816—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×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128#638—41no—
129#638—41no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—81no—
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—
143C32×C8—41no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—22no—
146C3×C3⋊C8—41no—
147C2×AGL(1,ℤ/8)—91no—
148C2×#108—31no—
149#417—91no—
150C2×#102—91no—
151C2×#100—31no—
152#408—91no—
153#343—91no—
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×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—61no—
166C2×#67—61no—
167C2×#67—121no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—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×D12#6712yes—
192C2×C4×D3—61no—
193C2×C4×D3—61no—
194C2×C4×D3—121no—
195C2×Dic6—31no—
196C2×Dic6—31no—
197C2×Dic6—61no—
198C3×M16—21no—
199C3×M16—21no—
200C3×M16—21no—
201C3×M16—21no—
202C3×M16—32no—
203C3×M16—41no—
204C3×M16—41no—
205C3×M16—61no—
206C3×M16—61no—
207C3×M16—61no—
208C2×C3×C8—22no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—32no—
212C2×C3×C8—61no—
213C2×C3×C8—61no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216#214—64no—
217#213—64no—
218C4⋊Dic3—62no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3—121no—
224#208—21no—
225#208—21no—
226#208—21no—
227#208#6712yes—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8D1212yes—
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#12011yescharacteristic
249C32×C4#12111yescharacteristic
250C32×C4#12111yescharacteristic
251C32×C4#12311yescharacteristic
252C3⋊Dic3—41no—
253C3⋊Dic3—81no—
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×M16D3211yescharacteristic
263C22×C8—31no—
264C2×C4⋊C4—91no—
265#108—62no—
266#103—181no—
267#102—181no—
268#102—182no—
269#100—62no—
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#23911yescharacteristic
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×C4C2×D1211yescharacteristic
298C2×C3×C4#23511yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4#23911yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308C2×C3×C4C2×#6711yescharacteristic
309#67—122no—
310#67—122no—
311#67—121no—
312#67—121no—
313#67—121no—
314#67—121no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—121no—
318C2×Dic3—122no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—242no—
322C2×Dic3—241no—
323C2×Dic3—241no—
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—42no—
347C3×C8—41no—
348C3×C8—41no—
349C3×C8—62no—
350C3×C8—62no—
351C3×C8—121no—
352C3⋊C8—22no—
353C3⋊C8—22no—
354C3⋊C8—41no—
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—181no—
377C22×C4—181no—
378C22×C4C2×D3211yescharacteristic
379SD16—184no—
380D8—184no—
381M16—21no—
382M16—21no—
383M16—32no—
384M16—61no—
385M16—61no—
386M16—61no—
387C2×C8—21no—
388C2×C8—32no—
389C2×C8—61no—
390C2×C8—61no—
391C2×C8—61no—
392C2×C8—61no—
393C4⋊C4—181no—
394C4⋊C4—181no—
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#88411yescharacteristic
410C22×C3#88511yescharacteristic
411C22×C3#89411yescharacteristic
412C22×C3#89511yescharacteristic
413C22×C3#92911yescharacteristic
414C22×C3#94711yescharacteristic
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#88311yescharacteristic
434C3×C4#88411yescharacteristic
435C3×C4#89411yescharacteristic
436C3×C4#89511yescharacteristic
437C3×C4#93011yescharacteristic
438C3×C4#93711yescharacteristic
439C3×C4#93711yescharacteristic
440C3×C4#93911yescharacteristic
441Dic3—122no—
442Dic3—121no—
443Dic3—121no—
444Dic3—242no—
445Dic3—241no—
446Dic3—241no—
447C32#205111yescharacteristic, complemented, Sylow
448C23—62no—
449C23—121no—
450C23—121no—
451C23—181no—
452C23—241no—
453C23—241no—
454C23#379911yescharacteristic
455Q8—181no—
456Q8—181no—
457D4—62no—
458D4—62no—
459D4—121no—
460D4—121no—
461D4—181no—
462D4—181no—
463D4—361no—
464D4—361no—
465C2×C4—181no—
466C2×C4—361no—
467C2×C4—361no—
468C2×C4—361no—
469C2×C4—721no—
470C2×C4#379611yescharacteristic
471C2×C4#379811yescharacteristic
472C2×C4D3×D1211yescharacteristic
473C2×C4D3×#6711yescharacteristic
474C2×C4D3×#6711yescharacteristic
475C2×C4#381111yescharacteristic
476C8—41no—
477C8—62no—
478C8—62no—
479C8—121no—
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#474811yescharacteristic
491C2×C3#474911yescharacteristic
492C2×C3#489711yescharacteristic
493C2×C3#489811yescharacteristic
494C2×C3#495911yescharacteristic
495C2×C3#499111yescharacteristic
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#6385011yescharacteristic
511C22#6390711yescharacteristic
512C22#6391011yescharacteristic
513C4—361no—
514C4—721no—
515C4#6385311yescharacteristic
516C4#6388611yescharacteristic
517C4#6390611yescharacteristic
518C4#6398311yescharacteristic
519C3—21no—
520C3#7009211yescharacteristic, complemented
521C3#7071411yescharacteristic, complemented
522C2—21no—
523C2—21no—
524C2—242no—
525C2—721no—
526C2#1059098711yescharacteristic
527C2#1059098911yescharacteristic
528C2#1059129111yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#63830C2
hypercenterC2×M16D32
hypocenterC32#2051
LCSG ▷ C22×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. #10592832C2semidirect
3. C2×C3×#823C2semidirect
4. C2×C3×#822C2semidirect
5. C2×#63563C2semidirect
6. #10591073C2semidirect
7. #10589168C2semidirect
35. C2×#823D3semidirect
37. C2×#822D3semidirect
447. C32#2051semidirect
520. C3#70092semidirect
521. C3#70714semidirect

Maximal subgroups

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

subgroupindex
C2×#638302
#105928322
C2×C3×#8232
C2×C3×#8222
C2×#635632
#105910732
#105891682
#707143
#700923