Finite Group Databasebeta

← #11792736

Subgroups — #11792736

Order 1152.

803 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic, complemented
2C2×#63833C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic
4#10592809C211yesmaximal, characteristic, complemented
5C2×#63560C211yesmaximal, characteristic, complemented
6C2×#63558C211yesmaximal, characteristic, complemented
7C3×#4552C211yesmaximal, characteristic, complemented
8#72059—31nomaximal
9#68943—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#204—22no—
18C2×C3×#204—22no—
19C2×C3×#204—22no—
20C2×#3719—21no—
21#63833—22no—
22#63833—22no—
23C2×#3717—21no—
24#63830—22no—
25#63830—22no—
26C2×#3716—21no—
27C2×#3714—21no—
28#63647—22no—
29#63560—22no—
30#63558—22no—
31C22×C3×SD16—31no—
32C2×#942—31no—
33C2×#932—31no—
34C2×#909—31no—
35C2×#908—31no—
36C22×#204D311yescharacteristic, complemented
37C2×#836—31no—
38C2×#833—31no—
39C2×#824—31no—
40C2×#823—31no—
41#5110—31no—
42#5110—31no—
43#5110—61no—
44C3×#341—31no—
45#4552D311yescharacteristic, complemented
46C23×C3×D3—21no—
47C22×C32×C4C2311yescharacteristic
48C2×#638—21no—
49#3828—21no—
50#3828—21no—
51#3828—21no—
52#3828—21no—
53C2×C4⋊(C3⋊D3)D411yescharacteristic
54C2×C4×C3⋊D3—21no—
55C2×#634D411yescharacteristic
56C22×C3×Dic3—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12D412yes—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6D412yes—
69C2×C32×C8—21no—
70C2×C32×C8—21no—
71C2×C32×C8D412yes—
72#3748—21no—
73#3748—21no—
74C2×C3⋊(C3⋊C8)—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208D412yes—
78C3×#208D412yes—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C3×#204—28no—
82#3719—24no—
83#3717—24no—
84#3716—24no—
85#3714—24no—
86#2019—91noSylow
87C22×C3×Q8—31no—
88C22×C3×D4—31no—
89C2×#235—31no—
90C2×#235—31no—
91C2×#235—61no—
92C22×D12C2×D311yescharacteristic
93C22×Dic6C2×D311yescharacteristic
94C2×C3×SD16—62no—
95C2×C3×SD16—62no—
96C2×C3×SD16—62no—
97C2×C3×M16—31no—
98C2×C3×M16—31no—
99C22×C3×C8—21no—
100C22×C3×C8C2×D311yescharacteristic
101C22×C3×C8C2×D311yescharacteristic
102C2×#216—61no—
103#942—62no—
104#942—62no—
105C2×#215—61no—
106C2×#214—61no—
107#932—62no—
108#932—62no—
109C2×#213—61no—
110C2×#208—31no—
111C2×#208—31no—
112C2×#208—61no—
113C2×#208C2×D311yescharacteristic
114C2×#208C2×D311yescharacteristic
115#909—62no—
116#909—62no—
117#908—62no—
118#908—62no—
119C2×Dic12—61no—
120C2×D24—61no—
121C2×#204—22no—
122C2×#204—22no—
123C2×#204—22no—
124C2×#204—61no—
125C2×#204—61no—
126#836—62no—
127#833—62no—
128#824—62no—
129#823—62no—
130(C2×D3)⋊C8—64no—
131(C2×D3)⋊C8—62no—
132(C2×D3)⋊C8—62no—
133C23×C32#4111yescharacteristic
134C22×C3⋊D3—21no—
135C22×C3×D3—22no—
136C22×C3×D3—41no—
137C22×C3×D3—41no—
138C22×C3×D3—82no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145#638—41no—
146#638—41no—
147C2×C3⋊Dic3—21no—
148C4⋊(C3⋊D3)—21no—
149C4⋊(C3⋊D3)—21no—
150C4×C3⋊D3—41no—
151C4×C3⋊D3—41no—
152#634—21no—
153#634—21no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—41no—
160C3×D12—41no—
161C3×Dic6—22no—
162C3×Dic6—22no—
163C3×Dic6—41no—
164C3×Dic6—41no—
165C32×C8—22no—
166C3⋊(C3⋊C8)—41no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—22no—
169C2×#137—91no—
170C2×AGL(1,ℤ/8)—91no—
171C22×SD16—31no—
172C2×#101—91no—
173C2×#100—91no—
174#408—91no—
175#341—31no—
176C24×C3—61no—
177C23×D3—21no—
178C2×C3×Q8—32no—
179C2×C3×Q8—61no—
180C2×C3×Q8—61no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×D4—32no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C22×C3×C4—21no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—62no—
195C2×#67—61no—
196C2×#67—61no—
197C22×Dic3—21no—
198#235—61no—
199#235—61no—
200#235—61no—
201#235—61no—
202#235—61no—
203#235—61no—
204#235—61no—
205#235—61no—
206#235—121no—
207#235—121no—
208#235—121no—
209#235—121no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—31no—
216C2×D12—31no—
217C2×D12—61no—
218C2×D12#6712yes—
219C2×C4×D3—62no—
220C2×C4×D3—61no—
221C2×C4×D3—61no—
222C2×Dic6—21no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C2×Dic6—31no—
228C2×Dic6—31no—
229C2×Dic6—61no—
230C2×Dic6#6712yes—
231C3×SD16—68no—
232C3×M16—32no—
233C3×M16—32no—
234C3×M16—61no—
235C3×M16—61no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—22no—
241C2×C3×C8—41no—
242C2×C3×C8—41no—
243C2×C3×C8—61no—
244C2×C3×C8—61no—
245C2×C3×C8D1212yes—
246C2×C3×C8#6712yes—
247#216—64no—
248#215—64no—
249#214—64no—
250#213—64no—
251#208—21no—
252#208—21no—
253#208—61no—
254#208—61no—
255#208—61no—
256#208—61no—
257#208—121no—
258#208—121no—
259#208D1212yes—
260#208D1212yes—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—62no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—61no—
266Dic12—64no—
267D24—64no—
268#204—28no—
269#204—64no—
270#204—64no—
271C22×C32—22no—
272C22×C32#12111yescharacteristic
273C22×C32#12111yescharacteristic
274C22×C32#12111yescharacteristic
275C2×C3⋊D3—41no—
276C2×C3⋊D3—42no—
277C2×C3×D3—42no—
278C2×C3×D3—82no—
279C2×C3×D3—82no—
280C2×C3×D3—82no—
281C32×C4#12011yescharacteristic
282C32×C4#12011yescharacteristic
283C32×C4#12011yescharacteristic
284C32×C4#12711yescharacteristic
285C3⋊Dic3—41no—
286C3×Dic3—42no—
287C2×#41—91no—
288C22×Q8—31no—
289C22×D4—31no—
290#137—182no—
291#137—182no—
292AGL(1,ℤ/8)—182no—
293AGL(1,ℤ/8)—182no—
294C2×Q16—181no—
295C2×SD16—62no—
296C2×SD16—62no—
297C2×SD16—62no—
298C2×SD16—181no—
299C2×SD16—181no—
300C2×D8—181no—
301C2×M16—31no—
302C2×M16—31no—
303C2×M16—91no—
304C22×C8D3211yescharacteristic
305#101—182no—
306#100—182no—
307C22⋊C8—182no—
308C23×C3—21no—
309C23×C3—62no—
310C23×C3—121no—
311C23×C3—121no—
312C23×C3—242no—
313C23×C3#23711yescharacteristic
314C23×C3#23911yescharacteristic
315C22×D3—22no—
316C22×D3—41no—
317C22×D3—41no—
318C22×D3—62no—
319C22×D3—61no—
320C22×D3—61no—
321C22×D3—82no—
322C3×Q8—62no—
323C3×Q8—62no—
324C3×Q8—121no—
325C3×Q8—121no—
326C3×D4—62no—
327C3×D4—62no—
328C3×D4—121no—
329C3×D4—121no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—62no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4C2×D1211yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351#67—122no—
352#67—122no—
353#67—121no—
354#67—121no—
355#67—121no—
356#67—121no—
357C2×Dic3—22no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360C2×Dic3—62no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363D12—22no—
364D12—22no—
365D12—41no—
366D12—41no—
367D12—61no—
368D12—61no—
369D12—61no—
370D12—61no—
371D12—121no—
372D12—121no—
373C4×D3—122no—
374C4×D3—122no—
375C4×D3—121no—
376C4×D3—121no—
377C4×D3—121no—
378C4×D3—121no—
379Dic6—22no—
380Dic6—22no—
381Dic6—41no—
382Dic6—41no—
383Dic6—61no—
384Dic6—61no—
385Dic6—61no—
386Dic6—61no—
387Dic6—121no—
388Dic6—121no—
389C3×C8—22no—
390C3×C8—22no—
391C3×C8—42no—
392C3×C8—62no—
393C3×C8—62no—
394C3⋊C8—22no—
395C3⋊C8—22no—
396C3⋊C8—122no—
397C3⋊C8—121no—
398C3⋊C8—121no—
399C2×C32—21no—
400C2×C32—21no—
401C2×C32#39211yescharacteristic
402C2×C32#47112yes—
403C3⋊D3—81no—
404C3×D3—82no—
405C24—61no—
406#41—181no—
407#41—181no—
408#41—181no—
409#41—181no—
410C2×Q8—32no—
411C2×Q8—61no—
412C2×Q8—61no—
413C2×Q8—61no—
414C2×Q8—61no—
415C2×Q8—61no—
416C2×Q8—91no—
417C2×D4—32no—
418C2×D4—61no—
419C2×D4—61no—
420C2×D4—61no—
421C2×D4—61no—
422C2×D4—61no—
423C2×D4—91no—
424C2×D4—181no—
425C22×C4—61no—
426C22×C4—181no—
427C22×C4C2×D3211yescharacteristic
428Q16—184no—
429SD16—68no—
430SD16—184no—
431SD16—184no—
432D8—184no—
433M16—32no—
434M16—32no—
435M16—61no—
436M16—61no—
437M16—181no—
438M16—181no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—61no—
442C2×C8—61no—
443C2×C8—181no—
444C2×C8#62612yes—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—42no—
451C22×C3—122no—
452C22×C3—242no—
453C22×C3—242no—
454C22×C3—242no—
455C22×C3#89511yescharacteristic
456C22×C3#89511yescharacteristic
457C22×C3#89511yescharacteristic
458C22×C3#93811yescharacteristic
459C22×C3#93911yescharacteristic
460C22×C3#93911yescharacteristic
461C2×D3—42no—
462C2×D3—82no—
463C2×D3—82no—
464C2×D3—82no—
465C2×D3—122no—
466C2×D3—124no—
467C2×D3—122no—
468C2×D3—122no—
469C2×D3—121no—
470C2×D3—121no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—122no—
476C3×C4#87411yescharacteristic
477C3×C4#88211yescharacteristic
478C3×C4#88211yescharacteristic
479C3×C4#88211yescharacteristic
480C3×C4#93711yescharacteristic
481C3×C4#93711yescharacteristic
482C3×C4#94011yescharacteristic
483C3×C4#95311yescharacteristic
484Dic3—42no—
485Dic3—122no—
486Dic3—121no—
487Dic3—121no—
488C32#201911yescharacteristic, complemented, Sylow
489C23—62no—
490C23—121no—
491C23—121no—
492C23—181no—
493C23—242no—
494C23#379611yescharacteristic
495Q8—62no—
496Q8—62no—
497Q8—121no—
498Q8—121no—
499Q8—181no—
500Q8—181no—
501D4—62no—
502D4—62no—
503D4—121no—
504D4—121no—
505D4—181no—
506D4—181no—
507D4—361no—
508D4—361no—
509C2×C4—62no—
510C2×C4—121no—
511C2×C4—121no—
512C2×C4—181no—
513C2×C4—361no—
514C2×C4—361no—
515C2×C4D3×D1211yescharacteristic
516C2×C4D3×D1211yescharacteristic
517C2×C4#380211yescharacteristic
518C2×C4C2×#62611yescharacteristic
519C2×C4D3×#6711yescharacteristic
520C2×C4D3×#6711yescharacteristic
521C8—22no—
522C8—62no—
523C8—62no—
524C8—361no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—22no—
531C2×C3—41no—
532C2×C3—41no—
533C2×C3—242no—
534C2×C3#467111yescharacteristic
535C2×C3#489812yes—
536C2×C3#517712yes—
537C2×C3#522311yescharacteristic
538D3—82no—
539D3—242no—
540D3—241no—
541D3—241no—
542C22—22no—
543C22—122no—
544C22—242no—
545C22—242no—
546C22—242no—
547C22—361no—
548C22—362no—
549C22#6388611yescharacteristic
550C22#6388611yescharacteristic
551C22#6391611yescharacteristic
552C4—122no—
553C4—361no—
554C4#6391111yescharacteristic
555C4#6392211yescharacteristic
556C4#6392211yescharacteristic
557C4#6397711yescharacteristic
558C3—21no—
559C3#6894311yescharacteristic, complemented
560C3#7205911yescharacteristic, complemented
561C2—21no—
562C2—21no—
563C2—242no—
564C2—721no—
565C2#1059092812yes—
566C2#1059139111yescharacteristic
subgroupG/H
centerC22#63916
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32#121
prime radicalC2×#63830C2
hypercenterC22×C8D32
hypocenterC32#2019
LCSG ▷ C22×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. C22×C3×#204C2semidirect
2. C2×#63833C2semidirect
4. #10592809C2semidirect
5. C2×#63560C2semidirect
6. C2×#63558C2semidirect
7. C3×#4552C2semidirect
36. C22×#204D3semidirect
45. #4552D3semidirect
488. C32#2019semidirect
559. C3#68943semidirect
560. C3#72059semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×#638332
C2×#638302
#105928092
C2×#635602
C2×#635582
C3×#45522
#720593
#689433