Finite Group Databasebeta

← #11788638

Subgroups — #11788638

Order 1152.

765 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63825C211yesmaximal, characteristic
2C2×#63815C211yesmaximal, characteristic, complemented
3C2×#63636C211yesmaximal, characteristic, complemented
4C3×#4966C211yesmaximal, characteristic, complemented
5C2×#63559C211yesmaximal, characteristic, complemented
6C3×#4530C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#70303—31nomaximal
9#69006—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3717—21no—
18#63825—22no—
19#63825C414yescomplemented
20C2×#3714—21no—
21C2×#3711—21no—
22#63815—22no—
23#63815—22no—
24C2×D3×C3⋊C8—21no—
25#63636—21no—
26#63636—21no—
27C3×#810—21no—
28C3×#809—21no—
29#63559—22no—
30C2×#949—31no—
31C2×#948—31no—
32C2×#908—31no—
33C2×#907—31no—
34C3×#417—31no—
35C2×#823—31no—
36C2×#823—31no—
37#4966D311yescharacteristic, complemented
38C2×#809—31no—
39C2×#809—31no—
40C2×#809—61no—
41C3×#343—31no—
42#4558—31no—
43#4558—31no—
44#4530D311yescharacteristic, complemented
45C23×C3⋊D3—21no—
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)C2×C412yes—
54C2×C3×#67—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235C2×C412yes—
58C3×#235D412yes—
59C2×C3×D12D411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×Dic6D411yescharacteristic
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)D411yescharacteristic
67C2×C3⋊(C3⋊C8)D411yescharacteristic
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208C2×C412yes—
73C3×#208D412yes—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77#3717—24no—
78#3714—24no—
79#3711—24no—
80D3×C3⋊C8—24no—
81#1907—91noSylow
82C2×C3×#41—31no—
83C2×#235C2×D311yescharacteristic
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C2×C3×M16—31no—
88C2×C3×M16—31no—
89C2×C3×M16—31no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C4⋊C4C2×D311yescharacteristic
93#949—34no—
94#949—62no—
95#948—62no—
96#948—62no—
97C2×#215—61no—
98C2×#213—61no—
99C2×#208—61no—
100C2×#208C2×D311yescharacteristic
101C2×#208C2×D311yescharacteristic
102C2×#208C2×D311yescharacteristic
103C22×C3⋊C8—31no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—61no—
106C22×C3⋊C8—61no—
107#908—34no—
108#908—62no—
109#907—62no—
110#907—62no—
111C2×D24—61no—
112C2×#204—61no—
113C2×ΓL(1,𝔽25)—61no—
114C2×D3×C8—61no—
115C3×#103—61no—
116C3×#102—61no—
117#823—62no—
118#823—62no—
119#810—21no—
120#809—21no—
121#809—61no—
122#809—61no—
123#809—61no—
124#809—61no—
125#809—62no—
126#809—62no—
127C23×C32#4111yescharacteristic
128C22×C3⋊D3—22no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—41no—
131C22×C3⋊D3—81no—
132C22×C3⋊D3—81no—
133C22×C3×D3—21no—
134C2×C32×C4—41no—
135C2×C32×C4—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
142C4⋊(C3⋊D3)—22no—
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)—41no—
145C4⋊(C3⋊D3)—41no—
146C3×#67—22no—
147C3×#67—22no—
148C2×C3×Dic3—21no—
149C3×D12—21no—
150C3×D12C22⋊C412yes—
151C3×C4×D3—22no—
152C3×C4×D3—22no—
153C3×Dic6—21no—
154C3×Dic6C22⋊C412yes—
155C3⋊(C3⋊C8)—21no—
156C3⋊(C3⋊C8)—21no—
157C3×C3⋊C8—22no—
158C3×C3⋊C8—22no—
159C3×C3⋊C8—41no—
160C2×AGL(1,ℤ/8)—91no—
161C2×#131—91no—
162#417—31no—
163C2×#102—91no—
164C2×#100—91no—
165#343—31no—
166#341—91no—
167C23×D3—61no—
168C23×D3—61no—
169C23×D3—121no—
170C3×#41—32no—
171C3×#41—32no—
172C3×#41—61no—
173C3×#41—61no—
174C2×C3×Q8—31no—
175C2×C3×D4—31no—
176C2×C3×D4—61no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—41no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—21no—
185#235—21no—
186#235—21no—
187#235C4×D312yes—
188#235D1212yes—
189C2×D12—32no—
190C2×D12—32no—
191C2×D12—62no—
192C2×D12—62no—
193C2×D12—62no—
194C2×D12—61no—
195C2×D12—61no—
196C2×D12—61no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12—61no—
204C2×D12—121no—
205C2×D12—121no—
206C2×D12—121no—
207C2×D12#6711yescharacteristic
208C2×C4×D3—21no—
209C2×Dic6#6711yescharacteristic
210C3×M16—32no—
211C3×M16—32no—
212C3×M16—61no—
213C3×M16—61no—
214C3×M16—61no—
215C3×M16—61no—
216C2×C3×C8—61no—
217C2×C3×C8—61no—
218C2×C3×C8—61no—
219C3×C4⋊C4—22no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—41no—
225#215—64no—
226#213—64no—
227#208—21no—
228#208—21no—
229#208—21no—
230#208—21no—
231#208—64no—
232#208C4×D312yes—
233#208D1212yes—
234C2×C3⋊C8—21no—
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—64no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—121no—
249C2×C3⋊C8—121no—
250D24—64no—
251#204—64no—
252ΓL(1,𝔽25)—64no—
253D3×C8—64no—
254C22×C32—21no—
255C22×C32—21no—
256C22×C32C4×D411yescharacteristic
257C22×C32#12111yescharacteristic
258C22×C32#12311yescharacteristic
259C2×C3⋊D3—42no—
260C2×C3⋊D3—82no—
261C2×C3⋊D3—81no—
262C2×C3⋊D3—81no—
263C2×C3⋊D3—82no—
264C2×C3×D3—22no—
265C2×C3×D3—41no—
266C2×C3×D3—41no—
267C32×C4—81no—
268C32×C4C2×C22⋊C411yescharacteristic
269C32×C4C4×D411yescharacteristic
270C32×C4#12011yescharacteristic
271C32×C4#12111yescharacteristic
272C3×Dic3—22no—
273C2×#41—31no—
274C22×D4—91no—
275AGL(1,ℤ/8)—94no—
276AGL(1,ℤ/8)—182no—
277C2×SD16—181no—
278C2×D8—181no—
279#131—182no—
280#131—182no—
281C2×M16—31no—
282C2×M16—31no—
283C2×M16—31no—
284C2×M16—181no—
285C22×C8—91no—
286C22×C8—181no—
287C2×C4⋊C4D3211yescharacteristic
288#103—61no—
289#102—61no—
290#102—181no—
291#102—181no—
292#100—182no—
293C23×C3—21no—
294C23×C3—61no—
295C23×C3#23511yescharacteristic
296C23×C3#23711yescharacteristic
297C22×D3—21no—
298C22×D3—62no—
299C22×D3—62no—
300C22×D3—122no—
301C22×D3—122no—
302C22×D3—122no—
303C22×D3—121no—
304C22×D3—121no—
305C22×D3—121no—
306C22×D3—121no—
307C22×D3—242no—
308C22×D3—242no—
309C22×D3—241no—
310C22×D3—241no—
311C22×D3—241no—
312C22×D3—241no—
313C3×Q8—32no—
314C3×Q8—61no—
315C3×D4—32no—
316C3×D4—62no—
317C3×D4—62no—
318C3×D4—61no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—42no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—61no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—82no—
332C2×C3×C4—81no—
333C2×C3×C4—81no—
334C2×C3×C4C2×C4×D311yescharacteristic
335C2×C3×C4C2×C4×D311yescharacteristic
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4#23711yescharacteristic
344C2×C3×C4#23911yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346#67—22no—
347#67—22no—
348C2×Dic3—21no—
349D12—21no—
350D12—64no—
351D12—62no—
352D12—62no—
353D12—62no—
354D12—62no—
355D12—122no—
356D12—122no—
357D12—122no—
358D12—121no—
359D12—121no—
360D12—121no—
361D12—121no—
362D12(C2×D3)⋊C412yes—
363C4×D3—22no—
364C4×D3—22no—
365Dic6—21no—
366Dic6(C2×D3)⋊C412yes—
367C3×C8—62no—
368C3×C8—62no—
369C3×C8—121no—
370C3⋊C8—22no—
371C3⋊C8—22no—
372C3⋊C8—41no—
373C3⋊C8—61no—
374C3⋊C8—61no—
375C3⋊C8—61no—
376C3⋊C8—61no—
377C3⋊C8—121no—
378C3⋊C8—121no—
379C2×C32—21no—
380C2×C32—21no—
381C2×C32#38611yescharacteristic
382C2×C32#47111yescharacteristic
383C2×C32#47211yescharacteristic
384C3⋊D3—82no—
385C3×D3—42no—
386C24—181no—
387#41—32no—
388#41—32no—
389#41—61no—
390#41—61no—
391C2×Q8—31no—
392C2×D4—31no—
393C2×D4—61no—
394C2×D4—92no—
395C2×D4—181no—
396C2×D4—181no—
397C2×D4—181no—
398C2×D4—181no—
399C2×D4—181no—
400C22×C4—21no—
401C22×C4—61no—
402C22×C4C2×D3211yescharacteristic
403SD16—184no—
404D8—184no—
405M16—32no—
406M16—32no—
407M16—61no—
408M16—61no—
409M16—61no—
410M16—61no—
411M16—184no—
412C2×C8—61no—
413C2×C8—61no—
414C2×C8—61no—
415C2×C8—91no—
416C2×C8—91no—
417C2×C8—184no—
418C2×C8—181no—
419C2×C8—181no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C22×C3—22no—
423C22×C3—22no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—62no—
432C22×C3—121no—
433C22×C3—121no—
434C22×C3C4×D1211yescharacteristic
435C22×C3#67⋊C411yescharacteristic
436C22×C3#88411yescharacteristic
437C22×C3#88611yescharacteristic
438C22×C3#89411yescharacteristic
439C22×C3#93911yescharacteristic
440C2×D3—22no—
441C2×D3—41no—
442C2×D3—41no—
443C2×D3—124no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—244no—
447C2×D3—244no—
448C2×D3—242no—
449C2×D3—242no—
450C2×D3—242no—
451C2×D3—242no—
452C2×D3—241no—
453C2×D3—241no—
454C2×D3—241no—
455C2×D3—241no—
456C2×D3—242no—
457C2×D3—242no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—62no—
463C3×C4—82no—
464C3×C4—81no—
465C3×C4—81no—
466C3×C4D3×C22⋊C411yescharacteristic
467C3×C4#67⋊C411yescharacteristic
468C3×C4#88211yescharacteristic
469C3×C4#88211yescharacteristic
470C3×C4#89311yescharacteristic
471C3×C4#89511yescharacteristic
472C3×C4C2×(C2×D3)⋊C411yescharacteristic
473C3×C4#93911yescharacteristic
474Dic3—22no—
475C32#190711yescharacteristic, complemented, Sylow
476C23—61no—
477C23—182no—
478C23—361no—
479C23—361no—
480C23—721no—
481C23—721no—
482C23#380411yescharacteristic
483Q8—32no—
484Q8—61no—
485D4—32no—
486D4—62no—
487D4—62no—
488D4—61no—
489D4—182no—
490D4—182no—
491D4—361no—
492D4—361no—
493C2×C4—41no—
494C2×C4—61no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—81no—
498C2×C4#379611yescharacteristic
499C2×C4C4×D3211yescharacteristic
500C2×C4D3×D1211yescharacteristic
501C2×C4D3×D1211yescharacteristic
502C2×C4D3×#6711yescharacteristic
503C2×C4#381111yescharacteristic
504C8—62no—
505C8—62no—
506C8—121no—
507C8—181no—
508C8—181no—
509C2×C3—22no—
510C2×C3—22no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—122no—
519C2×C3#466511yescharacteristic
520C2×C3#474911yescharacteristic
521C2×C3#475411yescharacteristic
522C2×C3#495811yescharacteristic
523C2×C3#519911yescharacteristic
524C2×C3#520311yescharacteristic
525D3—42no—
526D3—244no—
527D3—242no—
528D3—242no—
529C22—21no—
530C22—21no—
531C22—62no—
532C22—121no—
533C22—121no—
534C22—362no—
535C22—722no—
536C22—722no—
537C22—721no—
538C22—721no—
539C22#6388011yescharacteristic
540C22#6389011yescharacteristic
541C22#6397111yescharacteristic
542C4—62no—
543C4—81no—
544C4#6388111yescharacteristic
545C4#6388611yescharacteristic
546C4D3×(C2×D3)⋊C411yescharacteristic
547C4#6392311yescharacteristic
548C3—21no—
549C3#6900611yescharacteristic, complemented
550C3#7030311yescharacteristic, complemented
551C2—21no—
552C2—21no—
553C2—122no—
554C2—722no—
555C2#1059136411yescharacteristic
556C2#1059150811yescharacteristic
557C2#1059164311yescharacteristic
subgroupG/H
centerC22#63971
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC2×#63825C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1907
LCSG ▷ C2×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. C2×#63815C2semidirect
3. C2×#63636C2semidirect
4. C3×#4966C2semidirect
5. C2×#63559C2semidirect
6. C3×#4530C2semidirect
7. #10589165C2semidirect
19. #63825C4semidirect
37. #4966D3semidirect
44. #4530D3semidirect
475. C32#1907semidirect
549. C3#69006semidirect
550. C3#70303semidirect

Maximal subgroups

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

subgroupindex
C2×#638252
C2×#638152
C2×#636362
C3×#49662
C2×#635592
C3×#45302
#105891652
#703033
#690063