Finite Group Databasebeta

← #11788628

Subgroups — #11788628

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64116C211yesmaximal, characteristic, complemented
2C2×#63830C211yesmaximal, characteristic
3C2×C3×#823C211yesmaximal, characteristic, complemented
4#10591106C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic, complemented
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#70088—31nomaximal
9#69006—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
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
21#63830—22no—
22#63830C414yescomplemented
23C2×#3716—21no—
24C2×#3714—21no—
25C3×#823—22no—
26#63567—21no—
27#63564—21no—
28#63562—21no—
29#63562—21no—
30C2×#932—31no—
31C2×#908—31no—
32C2×#907—31no—
33C2×#907—31no—
34C2×#907—61no—
35C2×C3×#100—31no—
36C2×#832—31no—
37#5133—31no—
38C2×#823D311yescharacteristic, complemented
39#4966—31no—
40C2×#809—31no—
41C3×#343—31no—
42#4558—31no—
43#4558—31no—
44#4554D311yescharacteristic, complemented
45C23×C3×D3—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48#3828—21no—
49#3828—21no—
50#3828C2×C412yes—
51#3828D412yes—
52C2×C4⋊(C3⋊D3)D411yescharacteristic
53C2×C4×C3⋊D3—21no—
54C2×#634D411yescharacteristic
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×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#3716—24no—
80#3714—24no—
81#1907—91noSylow
82C22×C3×D4—31no—
83C2×#235—31no—
84C2×#235—31no—
85C2×#235—61no—
86C22×D12C2×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×#214—61no—
94#932—34no—
95#932—62no—
96C2×#213—61no—
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×#208C2×D311yescharacteristic
99C2×#208C2×D311yescharacteristic
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—61no—
103#908—34no—
104#908—62no—
105#907—62no—
106#907—62no—
107#907—64no—
108#907—64no—
109#907—62no—
110#907—62no—
111C2×D24—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×#100—62no—
120#832—61no—
121#832—61no—
122#823—22no—
123#821—61no—
124#816—61no—
125#810—61no—
126#809—61no—
127#809—61no—
128#809—61no—
129C23×C32#4111yescharacteristic
130C22×C3⋊D3—21no—
131C22×C3×D3—22no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3—81no—
135C22×C3×D3—81no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142#638—22no—
143#638—22no—
144C2×C3⋊Dic3—21no—
145C4⋊(C3⋊D3)—21no—
146C4⋊(C3⋊D3)C22⋊C412yes—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149#634—21no—
150#634C22⋊C412yes—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—81no—
153C3×D12—22no—
154C3×D12—22no—
155C3×D12—41no—
156C3×D12—41no—
157C32×C8—22no—
158C3⋊(C3⋊C8)—21no—
159C3⋊(C3⋊C8)—21no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8—41no—
162C2×AGL(1,ℤ/8)—91no—
163C2×#131—91no—
164#417—91no—
165C2×#102—91no—
166C2×#100—31no—
167#343—31no—
168#341—91no—
169C24×C3—61no—
170C23×D3—21no—
171C2×C3×D4—32no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C22×C3×C4—21no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—62no—
182C2×#67—61no—
183C2×#67—61no—
184C22×Dic3—21no—
185#235—32no—
186#235—32no—
187#235—32no—
188#235—32no—
189#235—62no—
190#235—62no—
191#235—62no—
192#235—62no—
193#235—61no—
194#235—61no—
195#235—61no—
196#235—61no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—31no—
203C2×D12—31no—
204C2×D12—61no—
205C2×D12C4×D312yes—
206C2×C4×D3—62no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×Dic6—31no—
210C2×Dic6—31no—
211C2×Dic6—61no—
212C3×M16—22no—
213C3×M16—21no—
214C3×M16—21no—
215C3×M16—22no—
216C3×M16—32no—
217C3×M16—61no—
218C3×M16—61no—
219C3×M16—61no—
220C3×M16D1212yes—
221C3×M16#6712yes—
222C2×C3×C8—22no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229#214—64no—
230#213—64no—
231C4⋊Dic3—21no—
232C4⋊Dic3—21no—
233#208—21no—
234#208—21no—
235#208—21no—
236#208C4×D312yes—
237C2×C3⋊C8—21no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—31no—
240C2×C3⋊C8—31no—
241C2×C3⋊C8—31no—
242C2×C3⋊C8—31no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—61no—
251D24—64no—
252#204—64no—
253ΓL(1,𝔽25)—68no—
254ΓL(1,𝔽25)—64no—
255ΓL(1,𝔽25)—64no—
256D3×C8—68no—
257D3×C8—64no—
258D3×C8—64no—
259C22×C32—21no—
260C22×C32—21no—
261C22×C32C4×D411yescharacteristic
262C22×C32#12111yescharacteristic
263C22×C32#12311yescharacteristic
264C2×C3⋊D3—22no—
265C2×C3⋊D3—41no—
266C2×C3⋊D3—41no—
267C2×C3×D3—42no—
268C2×C3×D3—82no—
269C2×C3×D3—81no—
270C2×C3×D3—81no—
271C2×C3×D3—82no—
272C32×C4C2×C22⋊C411yescharacteristic
273C32×C4C4×D411yescharacteristic
274C32×C4#12011yescharacteristic
275C32×C4#12111yescharacteristic
276C3⋊Dic3—22no—
277C3×Dic3—81no—
278C2×#41—91no—
279C22×D4—31no—
280AGL(1,ℤ/8)—94no—
281AGL(1,ℤ/8)—182no—
282C2×SD16—181no—
283C2×D8—181no—
284#131—182no—
285#131—182no—
286C2×M16—31no—
287C2×M16—31no—
288C2×M16—181no—
289C2×M16D3211yescharacteristic
290C22×C8—91no—
291C22×C8—181no—
292C2×C4⋊C4—31no—
293#103—181no—
294#102—181no—
295#102—181no—
296#102—181no—
297#100—62no—
298C23×C3—21no—
299C23×C3—62no—
300C23×C3—121no—
301C23×C3—121no—
302C23×C3—241no—
303C23×C3—241no—
304C23×C3#23511yescharacteristic
305C23×C3#23511yescharacteristic
306C22×D3—22no—
307C22×D3—41no—
308C22×D3—41no—
309C22×D3—62no—
310C22×D3—61no—
311C22×D3—61no—
312C22×D3—81no—
313C22×D3—81no—
314C3×D4—62no—
315C3×D4—62no—
316C3×D4—121no—
317C3×D4—121no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—121no—
325C2×C3×C4—241no—
326C2×C3×C4C2×C4×D311yescharacteristic
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4#23711yescharacteristic
336C2×C3×C4#23911yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338#67—64no—
339#67—64no—
340#67—62no—
341#67—62no—
342#67—62no—
343#67—62no—
344C2×Dic3—41no—
345C2×Dic3—62no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—81no—
349D12—22no—
350D12—22no—
351D12—32no—
352D12—32no—
353D12—41no—
354D12—41no—
355D12—62no—
356D12—62no—
357D12—61no—
358D12—61no—
359C4×D3—64no—
360C4×D3—64no—
361C4×D3—62no—
362C4×D3—62no—
363C4×D3—62no—
364C4×D3—62no—
365Dic6—32no—
366Dic6—32no—
367Dic6—62no—
368Dic6—62no—
369Dic6—61no—
370Dic6—61no—
371C3×C8—24no—
372C3×C8—22no—
373C3×C8—22no—
374C3×C8—62no—
375C3×C8—121no—
376C3⋊C8—22no—
377C3⋊C8—41no—
378C3⋊C8—62no—
379C3⋊C8—62no—
380C3⋊C8—61no—
381C3⋊C8—61no—
382C3⋊C8—61no—
383C3⋊C8—61no—
384C2×C32—21no—
385C2×C32—21no—
386C2×C32#38611yescharacteristic
387C2×C32#47111yescharacteristic
388C2×C32#47211yescharacteristic
389C3⋊D3—42no—
390C3×D3—82no—
391C24—61no—
392#41—92no—
393#41—92no—
394#41—181no—
395#41—181no—
396C2×Q8—91no—
397C2×D4—32no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—61no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—91no—
404C2×D4—181no—
405C22×C4—61no—
406C22×C4—181no—
407C22×C4C2×D3211yescharacteristic
408SD16—184no—
409D8—184no—
410M16—21no—
411M16—32no—
412M16—61no—
413M16—61no—
414M16—61no—
415M16—184no—
416M16#62612yes—
417C2×C8—21no—
418C2×C8—61no—
419C2×C8—61no—
420C2×C8—91no—
421C2×C8—91no—
422C2×C8—184no—
423C2×C8—181no—
424C2×C8—181no—
425C4⋊C4—61no—
426C4⋊C4—61no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—122no—
437C22×C3—242no—
438C22×C3—242no—
439C22×C3—241no—
440C22×C3—241no—
441C22×C3C4×D1211yescharacteristic
442C22×C3#88311yescharacteristic
443C22×C3#88411yescharacteristic
444C22×C3#88411yescharacteristic
445C22×C3#89411yescharacteristic
446C22×C3C4×#6711yescharacteristic
447C2×D3—42no—
448C2×D3—64no—
449C2×D3—62no—
450C2×D3—62no—
451C2×D3—82no—
452C2×D3—81no—
453C2×D3—81no—
454C2×D3—82no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—241no—
466C3×C4D3×C22⋊C411yescharacteristic
467C3×C4D3×C22⋊C411yescharacteristic
468C3×C4#67⋊C411yescharacteristic
469C3×C4#88211yescharacteristic
470C3×C4#89311yescharacteristic
471C3×C4#89511yescharacteristic
472C3×C4#93711yescharacteristic
473C3×C4#93811yescharacteristic
474Dic3—64no—
475Dic3—62no—
476Dic3—62no—
477Dic3—81no—
478C32#190711yescharacteristic, complemented, Sylow
479C23—62no—
480C23—121no—
481C23—121no—
482C23—181no—
483C23—241no—
484C23—241no—
485C23#379811yescharacteristic
486Q8—92no—
487Q8—181no—
488D4—62no—
489D4—62no—
490D4—92no—
491D4—121no—
492D4—121no—
493D4—182no—
494D4—182no—
495D4—181no—
496C2×C4—121no—
497C2×C4—181no—
498C2×C4—182no—
499C2×C4—182no—
500C2×C4—241no—
501C2×C4#379611yescharacteristic
502C2×C4C4×D3211yescharacteristic
503C2×C4#380211yescharacteristic
504C2×C4C2×#62611yescharacteristic
505C2×C4#381111yescharacteristic
506C2×C4#381111yescharacteristic
507C8—22no—
508C8—62no—
509C8—121no—
510C8—181no—
511C8—181no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—41no—
520C2×C3—41no—
521C2×C3—242no—
522C2×C3#466511yescharacteristic
523C2×C3#474811yescharacteristic
524C2×C3#474911yescharacteristic
525C2×C3#474911yescharacteristic
526C2×C3#475411yescharacteristic
527C2×C3#495611yescharacteristic
528D3—82no—
529D3—124no—
530D3—122no—
531D3—122no—
532C22—21no—
533C22—21no—
534C22—122no—
535C22—182no—
536C22—242no—
537C22—242no—
538C22—241no—
539C22—241no—
540C22—361no—
541C22—361no—
542C22#6385311yescharacteristic
543C22C4×#62611yescharacteristic
544C22#6391211yescharacteristic
545C4—182no—
546C4—241no—
547C4#6388111yescharacteristic
548C4#6391611yescharacteristic
549C4#6392111yescharacteristic
550C4#6398111yescharacteristic
551C3—21no—
552C3#6900611yescharacteristic, complemented
553C3#7008811yescharacteristic, complemented
554C2—21no—
555C2—21no—
556C2—242no—
557C2—362no—
558C2#1059098811yescharacteristic
559C2#1059099111yescharacteristic
560C2#1059138711yescharacteristic
subgroupG/H
centerC22#63912
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#63830C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1907
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
1. C2×#64116C2semidirect
3. C2×C3×#823C2semidirect
4. #10591106C2semidirect
5. C2×#63562C2semidirect
6. C3×#4554C2semidirect
7. #10589165C2semidirect
22. #63830C4semidirect
38. C2×#823D3semidirect
44. #4554D3semidirect
478. C32#1907semidirect
552. C3#69006semidirect
553. C3#70088semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
C2×#638302
C2×C3×#8232
#105911062
C2×#635622
C3×#45542
#105891652
#700883
#690063