Finite Group Databasebeta

← #11792732

Subgroups — #11792732

Order 1152.

817 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#214C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic
3C2×#63827C211yesmaximal, characteristic, complemented
4C2×#63660C211yesmaximal, characteristic, complemented
5C2×#63560C211yesmaximal, characteristic, complemented
6#10591070C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#72097—31nomaximal
9#72059—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×#214—22no—
16C2×C3×#214—21no—
17C2×C3×#214—22no—
18C2×C3×#214—22no—
19C3×#932—22no—
20C3×#932—22no—
21C2×C3×#213—21no—
22C2×C3×#208C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×#3718—21no—
25#63827—22no—
26#63827—22no—
27C2×#3715—21no—
28#63660—22no—
29#63560—22no—
30(C2×D3)⋊(C3⋊C8)—22no—
31C2×C3×AGL(1,ℤ/8)—31no—
32C22×C3×SD16—31no—
33C2×#951—31no—
34C2×#942—31no—
35C22×#214D311yescharacteristic, complemented
36C2×#932D311yescharacteristic
37#5234—31no—
38C2×#836—31no—
39C2×#833—31no—
40C2×#833—31no—
41C2×#833—61no—
42C2×#824—31no—
43#5110—31no—
44#4558—31no—
45#4552—31no—
46C24×C32—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4—21no—
52C2×C32×D4D412yes—
53C22×C32×C4C2311yescharacteristic
54C2×C3×#67—21no—
55C22×C3×Dic3—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C2×C3×D12D411yescharacteristic
61C2×C3×C4×D3—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6D412yes—
68C2×C3×Dic6D411yescharacteristic
69#3748—21no—
70#3748—21no—
71#3748—21no—
72#3748D412yes—
73C2×C3⋊(C3⋊C8)—21no—
74C2×C3⋊(C3⋊C8)—21no—
75C3×#214—24no—
76C3×#214—28no—
77C3×#213—24no—
78C3×#208—21no—
79C3×#208D412yes—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8D412yes—
84#3718—24no—
85#3715—24no—
86#2019—91noSylow
87C2×C3×#41—31no—
88C22×C3×Q8—31no—
89C22×C3×D4—21no—
90C22×C3×D4C2×D311yescharacteristic
91C22×C3×D4C2×D311yescharacteristic
92C2×#235C2×D311yescharacteristic
93C22×Dic6C2×D311yescharacteristic
94C3×AGL(1,ℤ/8)—62no—
95C3×AGL(1,ℤ/8)—62no—
96C2×C3×SD16—62no—
97C2×C3×SD16—62no—
98C2×C3×SD16—61no—
99C2×C3×SD16—62no—
100C2×C3×D8—61no—
101C2×C3×M16—31no—
102C22×C3×C8—31no—
103#951—62no—
104#951—62no—
105C2×#216—61no—
106C2×#216—61no—
107#942—62no—
108#942—62no—
109C2×#215—61no—
110C2×#214—22no—
111C2×#214—21no—
112C2×#214—22no—
113C2×#214—22no—
114C2×#214—61no—
115#932—22no—
116#932—22no—
117C2×#213—21no—
118C2×#208—31no—
119C2×#208—31no—
120C2×#208—31no—
121C2×#208—31no—
122C2×#208—61no—
123C2×#208—61no—
124C2×#208C2×D311yescharacteristic
125C22×C3⋊C8C2×D311yescharacteristic
126#836—62no—
127#833—62no—
128#833—62no—
129#833—64no—
130#830—62no—
131#824—62no—
132(C2×D3)⋊C8—62no—
133C23×C32—22no—
134C23×C32—41no—
135C23×C32—41no—
136C23×C32—82no—
137C23×C32#4111yescharacteristic
138C22×C3×D3—21no—
139C32×D4—22no—
140C32×D4—22no—
141C32×D4—41no—
142C32×D4—41no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C3×#67—41no—
150C3×#67—41no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C3×D12—21no—
156C3×D12—21no—
157C3×C4×D3—41no—
158C3×C4×D3—41no—
159C3×Dic6—22no—
160C3×Dic6—21no—
161C3×Dic6—22no—
162C3×Dic6—21no—
163C3×Dic6—41no—
164C3×Dic6—41no—
165C3⋊(C3⋊C8)—22no—
166C3⋊(C3⋊C8)—41no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—22no—
169C2×#137—91no—
170C2×AGL(1,ℤ/8)—31no—
171C22×SD16—31no—
172C2×#101—91no—
173C2×#100—91no—
174#408—91no—
175#341—91no—
176C24×C3—22no—
177C24×C3—21no—
178C24×C3—21no—
179C3×#41—61no—
180C3×#41—61no—
181C3×#41—61no—
182C3×#41—61no—
183C2×C3×Q8—32no—
184C2×C3×Q8—31no—
185C2×C3×Q8—61no—
186C2×C3×Q8—61no—
187C2×C3×Q8—61no—
188C2×C3×Q8—61no—
189C2×C3×Q8—61no—
190C2×C3×D4—22no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—22no—
202C2×C3×D4—31no—
203C2×C3×D4—41no—
204C2×C3×D4—41no—
205C2×C3×D4—41no—
206C2×C3×D4—41no—
207C2×C3×D4—61no—
208C2×C3×D4#6712yes—
209C2×C3×D4#6712yes—
210C22×C3×C4—21no—
211C22×C3×C4—61no—
212C22×C3×C4—61no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—21no—
216C22×Dic3—21no—
217#235—21no—
218#235—21no—
219#235—21no—
220#235—21no—
221C2×D12#6711yescharacteristic
222C2×C4×D3—21no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C2×Dic6—21no—
228C2×Dic6#6711yescharacteristic
229C2×Dic6#6712yes—
230C3×SD16—68no—
231C3×SD16—64no—
232C3×D8—64no—
233C3×M16—32no—
234C3×M16—61no—
235C2×C3×C8—32no—
236C2×C3×C8—61no—
237C2×C3×C8—61no—
238C2×C3×C8—61no—
239#216—64no—
240#216—64no—
241#215—64no—
242#214—24no—
243#214—28no—
244#214—64no—
245#213—24no—
246#208—21no—
247#208—32no—
248#208—32no—
249#208—62no—
250#208—61no—
251#208—61no—
252#208—62no—
253#208—61no—
254#208—61no—
255#208—61no—
256#208—61no—
257#208—121no—
258#208—121no—
259#208#6712yes—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—121no—
268C2×C3⋊C8—121no—
269C2×C3⋊C8#6712yes—
270C22×C32—22no—
271C22×C32—42no—
272C22×C32—82no—
273C22×C32—82no—
274C22×C32—82no—
275C22×C32#12111yescharacteristic
276C22×C32#12111yescharacteristic
277C22×C32#12111yescharacteristic
278C2×C3×D3—41no—
279C2×C3×D3—42no—
280C32×C4#12011yescharacteristic
281C32×C4#12011yescharacteristic
282C32×C4#12011yescharacteristic
283C32×C4#12711yescharacteristic
284C3×Dic3—42no—
285C3×Dic3—41no—
286C2×#41—31no—
287C22×Q8—31no—
288C22×D4D3211yescharacteristic
289#137—182no—
290#137—182no—
291AGL(1,ℤ/8)—62no—
292AGL(1,ℤ/8)—62no—
293C2×Q16—181no—
294C2×SD16—62no—
295C2×SD16—62no—
296C2×SD16—61no—
297C2×SD16—62no—
298C2×SD16—181no—
299C2×D8—61no—
300C2×M16—31no—
301C2×M16—91no—
302C2×M16—91no—
303C22×C8—31no—
304#101—182no—
305#100—182no—
306C22⋊C8—182no—
307C23×C3—24no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—21no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—41no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—61no—
318C23×C3—82no—
319C23×C3—82no—
320C23×C3—84no—
321C23×C3#23711yescharacteristic
322C23×C3#23711yescharacteristic
323C22×D3—21no—
324C3×Q8—62no—
325C3×Q8—61no—
326C3×Q8—62no—
327C3×Q8—61no—
328C3×Q8—121no—
329C3×Q8—121no—
330C3×D4—22no—
331C3×D4—22no—
332C3×D4—22no—
333C3×D4—22no—
334C3×D4—42no—
335C3×D4—42no—
336C3×D4—42no—
337C3×D4—42no—
338C3×D4—41no—
339C3×D4—41no—
340C3×D4—41no—
341C3×D4—41no—
342C3×D4—61no—
343C3×D4—61no—
344C3×D4—121no—
345C3×D4—121no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4—121no—
357C2×C3×C4—121no—
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370#67—41no—
371#67—41no—
372C2×Dic3—22no—
373C2×Dic3—21no—
374C2×Dic3—41no—
375C2×Dic3—41no—
376D12—21no—
377D12—21no—
378C4×D3—41no—
379C4×D3—41no—
380Dic6—22no—
381Dic6—21no—
382Dic6—22no—
383Dic6—21no—
384Dic6—41no—
385Dic6—41no—
386C3×C8—62no—
387C3×C8—62no—
388C3⋊C8—22no—
389C3⋊C8—22no—
390C3⋊C8—62no—
391C3⋊C8—62no—
392C3⋊C8—122no—
393C3⋊C8—122no—
394C3⋊C8—121no—
395C3⋊C8—121no—
396C2×C32—21no—
397C2×C32—21no—
398C2×C32—82no—
399C2×C32#39211yescharacteristic
400C2×C32#47112yes—
401C3×D3—81no—
402C24—21no—
403#41—61no—
404#41—61no—
405#41—61no—
406#41—61no—
407C2×Q8—31no—
408C2×Q8—32no—
409C2×Q8—61no—
410C2×Q8—61no—
411C2×Q8—61no—
412C2×Q8—61no—
413C2×Q8—61no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—31no—
420C2×D4—61no—
421C2×D4#62512yes—
422C22×C4—61no—
423C22×C4—61no—
424C22×C4C2×D3211yescharacteristic
425Q16—184no—
426SD16—68no—
427SD16—64no—
428SD16—184no—
429D8—64no—
430M16—32no—
431M16—61no—
432M16—92no—
433M16—181no—
434M16—181no—
435M16—181no—
436C2×C8—32no—
437C2×C8—61no—
438C2×C8—61no—
439C2×C8—61no—
440C2×C8—181no—
441C2×C8—181no—
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—42no—
448C22×C3—44no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—82no—
452C22×C3—82no—
453C22×C3—82no—
454C22×C3—82no—
455C22×C3—84no—
456C22×C3—84no—
457C22×C3—84no—
458C22×C3—82no—
459C22×C3—82no—
460C22×C3—122no—
461C22×C3—121no—
462C22×C3#93811yescharacteristic
463C22×C3#93811yescharacteristic
464C22×C3#93911yescharacteristic
465C22×C3#93911yescharacteristic
466C22×C3#93911yescharacteristic
467C22×C3#93911yescharacteristic
468C2×D3—42no—
469C2×D3—41no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—121no—
475C3×C4—122no—
476C3×C4#93711yescharacteristic
477C3×C4#93711yescharacteristic
478C3×C4#93711yescharacteristic
479C3×C4#93711yescharacteristic
480C3×C4#94011yescharacteristic
481C3×C4#94011yescharacteristic
482C3×C4#95311yescharacteristic
483C3×C4#95311yescharacteristic
484Dic3—42no—
485Dic3—41no—
486C32#201911yescharacteristic, complemented, Sylow
487C23—22no—
488C23—41no—
489C23—41no—
490C23—61no—
491C23—82no—
492C23#380511yescharacteristic
493Q8—62no—
494Q8—61no—
495Q8—62no—
496Q8—61no—
497Q8—121no—
498Q8—121no—
499D4—22no—
500D4—22no—
501D4—41no—
502D4—41no—
503D4—61no—
504D4—61no—
505D4—121no—
506D4—121no—
507C2×C4—62no—
508C2×C4—61no—
509C2×C4—121no—
510C2×C4—121no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4C2×#62511yescharacteristic
514C2×C4D3×#6711yescharacteristic
515C2×C4D3×#6711yescharacteristic
516C2×C4D3×#6711yescharacteristic
517C2×C4D3×#6711yescharacteristic
518C2×C4#381111yescharacteristic
519C8—62no—
520C8—62no—
521C8—182no—
522C8—361no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—22no—
528C2×C3—21no—
529C2×C3—41no—
530C2×C3—41no—
531C2×C3—84no—
532C2×C3—82no—
533C2×C3—82no—
534C2×C3—241no—
535C2×C3#517712yes—
536C2×C3#520012yes—
537C2×C3#522311yescharacteristic
538C2×C3#522311yescharacteristic
539D3—81no—
540C22—22no—
541C22—42no—
542C22—82no—
543C22—82no—
544C22—82no—
545C22—122no—
546C22—121no—
547C22#6397011yescharacteristic
548C22#6397011yescharacteristic
549C22#6398011yescharacteristic
550C4—121no—
551C4—122no—
552C4#6397611yescharacteristic
553C4#6397611yescharacteristic
554C4#6397911yescharacteristic
555C4#6398311yescharacteristic
556C3—21no—
557C3#7205911yescharacteristic, complemented
558C3#7209711yescharacteristic, complemented
559C2—21no—
560C2—21no—
561C2—82no—
562C2—241no—
563C2#1059150612yes—
564C2#1059172311yescharacteristic
subgroupG/H
centerC22#63970
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#121
prime radicalC2×C3×#932C2
hypercenterC22×D4D32
hypocenterC32#2019
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#214C2semidirect
3. C2×#63827C2semidirect
4. C2×#63660C2semidirect
5. C2×#63560C2semidirect
6. #10591070C2semidirect
7. #10589166C2semidirect
35. C22×#214D3semidirect
486. C32#2019semidirect
557. C3#72059semidirect
558. C3#72097semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2142
C2×C3×#9322
C2×#638272
C2×#636602
C2×#635602
#105910702
#105891662
#720973
#720593