Finite Group Databasebeta

← #11788641

Subgroups — #11788641

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×C3×#901C211yesmaximal, characteristic, complemented
2C2×#63825C211yesmaximal, characteristic
3C2×#63648C211yesmaximal, characteristic, complemented
4#10591088C211yesmaximal, characteristic, complemented
5C2×#63559C211yesmaximal, characteristic, complemented
6C3×#4552C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#72018—31nomaximal
9#68948—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#901—22no—
18C3×#901—22no—
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21C2×#3717—21no—
22#63825—22no—
23#63825C414yescomplemented
24C2×#3714—21no—
25#63648—21no—
26#63648—21no—
27#63566—21no—
28#63563—21no—
29#63559—22no—
30C2×C3×#131—31no—
31C2×#949—31no—
32C2×#908—31no—
33C2×#901D311yescharacteristic, complemented
34#5232—31no—
35#5133—31no—
36C2×#823—31no—
37C2×#823—31no—
38C2×#821—31no—
39C2×#821—31no—
40C2×#821—61no—
41C3×#341—31no—
42#4554—31no—
43#4554—31no—
44#4552D311yescharacteristic, complemented
45C23×C3⋊D3—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
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
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8D411yescharacteristic
65C2×C32×C8D411yescharacteristic
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—21no—
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—
77C3×ΓL(1,𝔽25)—24no—
78C3×D3×C8—24no—
79#3717—24no—
80#3714—24no—
81#1907—91noSylow
82C2×C3×#41—31no—
83C2×#235C2×D311yescharacteristic
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C3×#131—62no—
88C3×#131—62no—
89C2×C3×M16—31no—
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C2×C3×M16—61no—
93C22×C3×C8—21no—
94C22×C3×C8—61no—
95C22×C3×C8C2×D311yescharacteristic
96C22×C3×C8C2×D311yescharacteristic
97#949—34no—
98#949—62no—
99C2×#215—61no—
100C2×#213—61no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—61no—
104C2×#208C2×D311yescharacteristic
105C2×#208C2×D311yescharacteristic
106C2×#208C2×D311yescharacteristic
107#908—34no—
108#908—62no—
109C2×D24—61no—
110C2×#204—61no—
111#901—22no—
112#901—22no—
113C2×ΓL(1,𝔽25)—21no—
114C2×D3×C8—21no—
115#835—61no—
116#832—61no—
117#823—62no—
118#823—62no—
119#821—62no—
120#821—62no—
121#821—61no—
122#821—61no—
123#821—61no—
124#821—61no—
125#821—61no—
126#816—61no—
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×C4C22×C411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—81no—
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—
155C32×C8—21no—
156C32×C8—21no—
157C3×C3⋊C8—22no—
158C3×C3⋊C8—22no—
159C3×C3⋊C8—41no—
160C2×AGL(1,ℤ/8)—91no—
161C2×#131—31no—
162#417—91no—
163C2×#102—91no—
164C2×#100—91no—
165#343—91no—
166#341—31no—
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—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—21no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—121no—
185#235—21no—
186#235—21no—
187#235C4×D312yes—
188#235#6712yes—
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×D12D1211yescharacteristic
208C2×C4×D3—21no—
209C2×Dic6D1211yescharacteristic
210C3×M16—32no—
211C3×M16—32no—
212C3×M16—64no—
213C3×M16—61no—
214C3×M16—61no—
215C3×M16—61no—
216C3×M16—61no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—41no—
224C2×C3×C8—41no—
225C2×C3×C8—64no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C2×C3×C8D1211yescharacteristic
230C2×C3×C8D1211yescharacteristic
231C2×C3×C8#6711yescharacteristic
232C2×C3×C8#6711yescharacteristic
233#215—64no—
234#213—64no—
235C4⋊Dic3—62no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—121no—
241#208—21no—
242#208—21no—
243#208—21no—
244#208—21no—
245#208C4×D312yes—
246#208#6712yes—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250D24—64no—
251#204—64no—
252ΓL(1,𝔽25)—24no—
253D3×C8—24no—
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×C4C2×C22⋊C411yescharacteristic
268C32×C4C4×D411yescharacteristic
269C32×C4#12011yescharacteristic
270C32×C4#12111yescharacteristic
271C3⋊Dic3—81no—
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—62no—
280#131—62no—
281C2×M16—31no—
282C2×M16—31no—
283C2×M16—31no—
284C2×M16—61no—
285C22×C8—61no—
286C22×C8D3211yescharacteristic
287C2×C4⋊C4—91no—
288#103—181no—
289#102—181no—
290#102—181no—
291#102—181no—
292#100—182no—
293C23×C3—21no—
294C23×C3—61no—
295C23×C3#23511yescharacteristic
296C23×C3#23911yescharacteristic
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—61no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4#23511yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×C3×C4C2×#6711yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340#67—22no—
341#67—22no—
342C2×Dic3—21no—
343C2×Dic3—122no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—242no—
347C2×Dic3—241no—
348C2×Dic3—241no—
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—21no—
368C3×C8—21no—
369C3×C8—21no—
370C3×C8—21no—
371C3×C8—41no—
372C3×C8—41no—
373C3×C8—62no—
374C3×C8—62no—
375C3×C8—121no—
376C3⋊C8—22no—
377C3⋊C8—22no—
378C3⋊C8—41no—
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—61no—
401C22×C4—181no—
402C22×C4C2×D3211yescharacteristic
403SD16—184no—
404D8—184no—
405M16—32no—
406M16—32no—
407M16—64no—
408M16—61no—
409M16—61no—
410M16—61no—
411M16—61no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—64no—
415C2×C8—61no—
416C2×C8—61no—
417C2×C8—61no—
418C2×C8#62611yescharacteristic
419C2×C8#62611yescharacteristic
420C4⋊C4—181no—
421C4⋊C4—181no—
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×C3#89311yescharacteristic
435C22×C3#89411yescharacteristic
436C22×C3#89511yescharacteristic
437C22×C3C4×#6711yescharacteristic
438C22×C3#92911yescharacteristic
439C22×C3#93011yescharacteristic
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×C4C4×D1211yescharacteristic
464C3×C4D3×C22⋊C411yescharacteristic
465C3×C4#88211yescharacteristic
466C3×C4#88411yescharacteristic
467C3×C4C2×(C2×D3)⋊C411yescharacteristic
468C3×C4C4×#6711yescharacteristic
469C3×C4#93011yescharacteristic
470C3×C4#95311yescharacteristic
471Dic3—22no—
472Dic3—242no—
473Dic3—241no—
474Dic3—241no—
475C32#190711yescharacteristic, complemented, Sylow
476C23—61no—
477C23—182no—
478C23—361no—
479C23—361no—
480C23—721no—
481C23—721no—
482C23#379911yescharacteristic
483Q8—32no—
484Q8—61no—
485D4—32no—
486D4—62no—
487D4—62no—
488D4—61no—
489D4—182no—
490D4—182no—
491D4—361no—
492D4—361no—
493C2×C4—61no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—361no—
497C2×C4—721no—
498C2×C4#379811yescharacteristic
499C2×C4C4×D3211yescharacteristic
500C2×C4D3×D1211yescharacteristic
501C2×C4C2×#62611yescharacteristic
502C2×C4D3×#6711yescharacteristic
503C2×C4D3×#6711yescharacteristic
504C8—21no—
505C8—21no—
506C8—62no—
507C8—62no—
508C8—121no—
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#489711yescharacteristic
521C2×C3#489811yescharacteristic
522C2×C3#514111yescharacteristic
523C2×C3#514211yescharacteristic
524C2×C3#521311yescharacteristic
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#6385011yescharacteristic
540C22#6390411yescharacteristic
541C22#6390911yescharacteristic
542C4—62no—
543C4—721no—
544C4C4×#62611yescharacteristic
545C4#6390611yescharacteristic
546C4D3×(C2×D3)⋊C411yescharacteristic
547C4#6397711yescharacteristic
548C3—21no—
549C3#6894811yescharacteristic, complemented
550C3#7201811yescharacteristic, complemented
551C2—21no—
552C2—21no—
553C2—122no—
554C2—722no—
555C2#1059092711yescharacteristic
556C2#1059093111yescharacteristic
557C2#1059138211yescharacteristic
subgroupG/H
centerC22#63909
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32#121
prime radicalC2×#63825C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1907
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#901C2semidirect
3. C2×#63648C2semidirect
4. #10591088C2semidirect
5. C2×#63559C2semidirect
6. C3×#4552C2semidirect
7. #10589168C2semidirect
23. #63825C4semidirect
33. C2×#901D3semidirect
44. #4552D3semidirect
475. C32#1907semidirect
549. C3#68948semidirect
550. C3#72018semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
C2×#638252
C2×#636482
#105910882
C2×#635592
C3×#45522
#105891682
#720183
#689483