Finite Group Databasebeta

← #11788677

Subgroups — #11788677

Order 1152.

757 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64116C211yesmaximal, characteristic
2C2×#63833C211yesmaximal, characteristic
3C2×C3×#824C211yesmaximal, characteristic, complemented
4#10591106C211yesmaximal, characteristic
5C2×#63565C211yesmaximal, characteristic, complemented
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#70123—31nomaximal
9#69007—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14#64116—22no—
15#64116—22no—
16C2×#3743—21no—
17C2×C8×C3⋊D3—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×#3719—21no—
22#63833—22no—
23#63833C414yescomplemented
24C2×#3717—21no—
25C3×#824—22no—
26#63567—21no—
27#63565—21no—
28#63565—21no—
29#63564—21no—
30C2×#942—31no—
31C2×#909—31no—
32C2×#907—31no—
33C2×#907—31no—
34C2×#907—61no—
35C2×C3×#101—31no—
36C2×#835—31no—
37C2×#824D311yescharacteristic, complemented
38#5133—31no—
39C2×#810—31no—
40#4966—31no—
41C3×#343—31no—
42#4558—31no—
43#4558—31no—
44#4554D311yescharacteristic, complemented
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47#3828—21no—
48#3828—21no—
49#3828C2×C412yes—
50#3828D412yes—
51C2×C4⋊(C3⋊D3)D411yescharacteristic
52C2×C4×C3⋊D3—21no—
53C2×#634D411yescharacteristic
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yes—
62C32×M16—21no—
63C32×M16D412yes—
64C2×C32×C8—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)D411yescharacteristic
68C2×C3⋊(C3⋊C8)D411yescharacteristic
69#3743—24no—
70C8×C3⋊D3—24no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×#208—21no—
74C3×#208—21no—
75C3×#208—21no—
76C3×#208C2×C412yes—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79#3719—24no—
80#3717—24no—
81#1908—91noSylow
82C22×C3×Q8—31no—
83C2×#235—31no—
84C2×#235—31no—
85C2×#235—61no—
86C22×Dic6C2×D311yescharacteristic
87C2×C3×M16—21no—
88C2×C3×M16—31no—
89C2×C3×M16—31no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C2×D311yescharacteristic
92C2×C3×C4⋊C4—31no—
93C2×#216—61no—
94#942—34no—
95#942—62no—
96C2×#215—61no—
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×#208C2×D311yescharacteristic
99C2×#208C2×D311yescharacteristic
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—61no—
103#909—34no—
104#909—62no—
105#907—62no—
106#907—62no—
107#907—64no—
108#907—64no—
109#907—62no—
110#907—62no—
111C2×Dic12—61no—
112C2×#204—61no—
113C2×ΓL(1,𝔽25)—61no—
114C2×ΓL(1,𝔽25)—61no—
115C2×ΓL(1,𝔽25)—62no—
116C2×D3×C8—61no—
117C2×D3×C8—61no—
118C2×D3×C8—62no—
119C3×#101—62no—
120#835—61no—
121#835—61no—
122#824—22no—
123#821—61no—
124#816—61no—
125#810—61no—
126#810—61no—
127#810—61no—
128#809—61no—
129C23×C32#4111yescharacteristic
130C22×C3⋊D3—21no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137#638—22no—
138#638—22no—
139C2×C3⋊Dic3—21no—
140C4⋊(C3⋊D3)—21no—
141C4⋊(C3⋊D3)C22⋊C412yes—
142C4×C3⋊D3—22no—
143C4×C3⋊D3—22no—
144#634—21no—
145#634C22⋊C412yes—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—81no—
151C3×Dic6—22no—
152C3×Dic6—22no—
153C3×Dic6—41no—
154C3×Dic6—41no—
155C32×C8—22no—
156C3⋊(C3⋊C8)—21no—
157C3⋊(C3⋊C8)—21no—
158C3×C3⋊C8—22no—
159C3×C3⋊C8—41no—
160C2×#137—91no—
161C2×#131—91no—
162#417—91no—
163C2×#103—91no—
164C2×#101—31no—
165#343—31no—
166#341—91no—
167C2×C3×Q8—32no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C22×C3×C4—21no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C2×#67—62no—
179C2×#67—61no—
180C2×#67—61no—
181C22×Dic3—21no—
182C22×Dic3—21no—
183#235—32no—
184#235—32no—
185#235—32no—
186#235—32no—
187#235—62no—
188#235—62no—
189#235—62no—
190#235—62no—
191#235—61no—
192#235—61no—
193#235—61no—
194#235—61no—
195C2×D12—31no—
196C2×D12—31no—
197C2×D12—61no—
198C2×C4×D3—62no—
199C2×C4×D3—61no—
200C2×C4×D3—61no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6—21no—
205C2×Dic6—21no—
206C2×Dic6—31no—
207C2×Dic6—31no—
208C2×Dic6—61no—
209C2×Dic6C4×D312yes—
210C3×M16—22no—
211C3×M16—21no—
212C3×M16—21no—
213C3×M16—22no—
214C3×M16—32no—
215C3×M16—61no—
216C3×M16—61no—
217C3×M16—61no—
218C3×M16D1212yes—
219C3×M16#6712yes—
220C2×C3×C8—22no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—61no—
224C2×C3×C8—61no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227#216—64no—
228#215—64no—
229C4⋊Dic3—21no—
230C4⋊Dic3—21no—
231#208—21no—
232#208—21no—
233#208—21no—
234#208C4×D312yes—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—31no—
238C2×C3⋊C8—31no—
239C2×C3⋊C8—31no—
240C2×C3⋊C8—31no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249Dic12—64no—
250#204—64no—
251ΓL(1,𝔽25)—68no—
252ΓL(1,𝔽25)—64no—
253ΓL(1,𝔽25)—64no—
254D3×C8—68no—
255D3×C8—64no—
256D3×C8—64no—
257C22×C32—21no—
258C22×C32—21no—
259C22×C32C4×D411yescharacteristic
260C22×C32#12111yescharacteristic
261C22×C32#12311yescharacteristic
262C2×C3⋊D3—22no—
263C2×C3⋊D3—41no—
264C2×C3⋊D3—41no—
265C32×C4C2×C22⋊C411yescharacteristic
266C32×C4C4×D411yescharacteristic
267C32×C4#12011yescharacteristic
268C32×C4#12111yescharacteristic
269C3⋊Dic3—22no—
270C3×Dic3—42no—
271C3×Dic3—81no—
272C2×#41—91no—
273C22×Q8—31no—
274#137—94no—
275#137—182no—
276C2×Q16—181no—
277C2×SD16—181no—
278#131—182no—
279#131—182no—
280C2×M16—31no—
281C2×M16—31no—
282C2×M16—181no—
283C2×M16D3211yescharacteristic
284C22×C8—91no—
285C22×C8—181no—
286C2×C4⋊C4—31no—
287#103—181no—
288#103—181no—
289#103—181no—
290#102—181no—
291#101—62no—
292C23×C3—21no—
293C23×C3#23511yescharacteristic
294C23×C3#23511yescharacteristic
295C22×D3—62no—
296C22×D3—61no—
297C22×D3—61no—
298C3×Q8—62no—
299C3×Q8—62no—
300C3×Q8—121no—
301C3×Q8—121no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—62no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4—241no—
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×D1211yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4#23911yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325#67—64no—
326#67—64no—
327#67—62no—
328#67—62no—
329#67—62no—
330#67—62no—
331C2×Dic3—22no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—62no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—81no—
339D12—32no—
340D12—32no—
341D12—62no—
342D12—62no—
343D12—61no—
344D12—61no—
345C4×D3—64no—
346C4×D3—64no—
347C4×D3—62no—
348C4×D3—62no—
349C4×D3—62no—
350C4×D3—62no—
351Dic6—22no—
352Dic6—22no—
353Dic6—32no—
354Dic6—32no—
355Dic6—41no—
356Dic6—41no—
357Dic6—62no—
358Dic6—62no—
359Dic6—61no—
360Dic6—61no—
361C3×C8—24no—
362C3×C8—22no—
363C3×C8—22no—
364C3×C8—62no—
365C3×C8—121no—
366C3⋊C8—22no—
367C3⋊C8—41no—
368C3⋊C8—62no—
369C3⋊C8—62no—
370C3⋊C8—61no—
371C3⋊C8—61no—
372C3⋊C8—61no—
373C3⋊C8—61no—
374C2×C32—21no—
375C2×C32—21no—
376C2×C32#38611yescharacteristic
377C2×C32#47111yescharacteristic
378C2×C32#47311yescharacteristic
379C3⋊D3—42no—
380#41—92no—
381#41—92no—
382#41—181no—
383#41—181no—
384C2×Q8—32no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×Q8—91no—
391C2×D4—91no—
392C2×D4—181no—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4—181no—
396C22×C4C2×D3211yescharacteristic
397Q16—184no—
398SD16—184no—
399M16—21no—
400M16—32no—
401M16—61no—
402M16—61no—
403M16—61no—
404M16—184no—
405M16#62612yes—
406C2×C8—21no—
407C2×C8—61no—
408C2×C8—61no—
409C2×C8—91no—
410C2×C8—91no—
411C2×C8—184no—
412C2×C8—181no—
413C2×C8—181no—
414C4⋊C4—61no—
415C4⋊C4—61no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3C4×D1211yescharacteristic
426C22×C3#88311yescharacteristic
427C22×C3#88411yescharacteristic
428C22×C3#88411yescharacteristic
429C22×C3#89411yescharacteristic
430C22×C3C4×#6711yescharacteristic
431C2×D3—64no—
432C2×D3—62no—
433C2×D3—62no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—121no—
437C2×D3—121no—
438C2×D3—121no—
439C2×D3—121no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—122no—
445C3×C4—241no—
446C3×C4D3×C22⋊C411yescharacteristic
447C3×C4D3×C22⋊C411yescharacteristic
448C3×C4#67⋊C411yescharacteristic
449C3×C4#88211yescharacteristic
450C3×C4#89311yescharacteristic
451C3×C4#89511yescharacteristic
452C3×C4#93711yescharacteristic
453C3×C4#93811yescharacteristic
454Dic3—42no—
455Dic3—64no—
456Dic3—62no—
457Dic3—62no—
458Dic3—81no—
459C32#190811yescharacteristic, complemented, Sylow
460C23—181no—
461C23#379811yescharacteristic
462Q8—62no—
463Q8—62no—
464Q8—92no—
465Q8—121no—
466Q8—121no—
467Q8—181no—
468D4—92no—
469D4—182no—
470D4—182no—
471D4—181no—
472C2×C4—62no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—181no—
477C2×C4—182no—
478C2×C4—182no—
479C2×C4—241no—
480C2×C4#379611yescharacteristic
481C2×C4C4×D3211yescharacteristic
482C2×C4#380211yescharacteristic
483C2×C4C2×#62611yescharacteristic
484C2×C4#381111yescharacteristic
485C2×C4#381111yescharacteristic
486C8—22no—
487C8—62no—
488C8—121no—
489C8—181no—
490C8—181no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—41no—
499C2×C3—41no—
500C2×C3#466511yescharacteristic
501C2×C3#474811yescharacteristic
502C2×C3#475411yescharacteristic
503C2×C3#475511yescharacteristic
504C2×C3#475511yescharacteristic
505C2×C3#495611yescharacteristic
506D3—124no—
507D3—122no—
508D3—122no—
509C22—21no—
510C22—21no—
511C22—182no—
512C22—361no—
513C22—361no—
514C22#6385311yescharacteristic
515C22C4×#62611yescharacteristic
516C22#6391211yescharacteristic
517C4—122no—
518C4—182no—
519C4—241no—
520C4#6388111yescharacteristic
521C4#6391611yescharacteristic
522C4#6392111yescharacteristic
523C4#6398111yescharacteristic
524C3—21no—
525C3#6900711yescharacteristic, complemented
526C3#7012311yescharacteristic, complemented
527C2—21no—
528C2—21no—
529C2—362no—
530C2#1059099111yescharacteristic
531C2#1059099311yescharacteristic
532C2#1059138711yescharacteristic
subgroupG/H
centerC22#63912
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1908
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
3. C2×C3×#824C2semidirect
5. C2×#63565C2semidirect
6. C3×#4554C2semidirect
7. #10589165C2semidirect
23. #63833C4semidirect
37. C2×#824D3semidirect
44. #4554D3semidirect
459. C32#1908semidirect
525. C3#69007semidirect
526. C3#70123semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
C2×#638332
C2×C3×#8242
#105911062
C2×#635652
C3×#45542
#105891652
#701233
#690073