Finite Group Databasebeta

← #11792741

Subgroups — #11792741

Order 1152.

769 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic
2C2×#63827C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic, complemented
4C2×C3×#824C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6#10591071C211yesmaximal, characteristic, complemented
7#10589424C211yesmaximal, characteristic, complemented
8#72097—31nomaximal
9#70117—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#908—22no—
18C3×#908—22no—
19C2×C3×D24—21no—
20C2×C3×#204—21no—
21C2×#3718—21no—
22#63827—22no—
23#63827—22no—
24C2×#3715—22no—
25C2×#3715—21no—
26C2×#3715—22no—
27C2×#3715—22no—
28C3×#824—22no—
29#63558—22no—
30(C2×D3)⋊(C3⋊C8)—22no—
31C2×C3×AGL(1,ℤ/8)—31no—
32C2×#951—31no—
33C2×#942—31no—
34C22×#215—31no—
35C22×#214—31no—
36C2×#908D311yescharacteristic
37C2×C3×#101—31no—
38#5234—31no—
39C2×#833—31no—
40C2×#824D311yescharacteristic, complemented
41C2×#823—31no—
42#5129—31no—
43#4558—31no—
44#4558—31no—
45#4558—61no—
46C23×C3×D3—21no—
47C22×C32×C4C2311yescharacteristic
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12D411yescharacteristic
60C2×C3×D12D412yes—
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
69C32×M16—21no—
70C32×M16D412yes—
71C2×C32×C8—21no—
72#3748—21no—
73#3748D412yes—
74C2×C3⋊(C3⋊C8)—21no—
75C2×C3⋊(C3⋊C8)—21no—
76C2×C3⋊(C3⋊C8)—21no—
77C2×C3⋊(C3⋊C8)D412yes—
78C3×#208—21no—
79C3×#208—21no—
80C2×C3×C3⋊C8—21no—
81C3×D24—24no—
82C3×#204—24no—
83#3718—24no—
84#3715—28no—
85#3715—24no—
86#2019—91noSylow
87C2×C3×#41—31no—
88C22×C3×Q8—31no—
89C22×C3×D4—31no—
90C2×#235C2×D311yescharacteristic
91C22×D12C2×D311yescharacteristic
92C22×Dic6C2×D311yescharacteristic
93C3×AGL(1,ℤ/8)—62no—
94C3×AGL(1,ℤ/8)—62no—
95C2×C3×SD16—61no—
96C2×C3×D8—61no—
97C2×C3×M16—21no—
98C2×C3×M16—31no—
99C2×C3×M16C2×D311yescharacteristic
100C2×C3×M16C2×D311yescharacteristic
101#951—62no—
102#951—62no—
103C2×#216—61no—
104C2×#216—61no—
105#942—62no—
106#942—62no—
107C2×#215—62no—
108C2×#215—62no—
109C2×#215—62no—
110C2×#215—61no—
111C2×#214—62no—
112C2×#214—62no—
113C2×#214—61no—
114C2×#214—62no—
115C2×#208—31no—
116C2×#208—31no—
117C2×#208—61no—
118C2×#208C2×D311yescharacteristic
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—61no—
122#908—22no—
123#908—22no—
124C2×D24—21no—
125C2×#204—21no—
126C3×#101—62no—
127#833—62no—
128#830—62no—
129#824—22no—
130#823—62no—
131(C2×D3)⋊C8—62no—
132C23×C32#4111yescharacteristic
133C22×C3×D3—21no—
134C22×C3×D3—22no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C22×C3×D3—82no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C3×#67—41no—
145C3×#67—41no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C3×D12—22no—
151C3×D12—21no—
152C3×D12—22no—
153C3×D12—21no—
154C3×D12—41no—
155C3×D12—41no—
156C3×C4×D3—41no—
157C3×C4×D3—41no—
158C3×Dic6—22no—
159C3×Dic6—22no—
160C3×Dic6—21no—
161C3×Dic6—21no—
162C3×Dic6—41no—
163C3×Dic6—41no—
164C32×C8—22no—
165C3⋊(C3⋊C8)—22no—
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—41no—
168C2×#137—91no—
169C2×AGL(1,ℤ/8)—31no—
170C22×SD16—91no—
171C2×#101—31no—
172C2×#100—91no—
173#408—91no—
174#341—91no—
175C24×C3—61no—
176C23×D3—21no—
177C3×#41—61no—
178C3×#41—61no—
179C3×#41—61no—
180C3×#41—61no—
181C2×C3×Q8—32no—
182C2×C3×Q8—31no—
183C2×C3×Q8—61no—
184C2×C3×Q8—61no—
185C2×C3×Q8—61no—
186C2×C3×Q8—61no—
187C2×C3×Q8—61no—
188C2×C3×D4—31no—
189C2×C3×D4—32no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C2×C3×D4—61no—
196C22×C3×C4—21no—
197C22×C3×C4—61no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C2×#67—21no—
202C22×Dic3—21no—
203#235—21no—
204#235—21no—
205#235—21no—
206#235—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12#6711yescharacteristic
213C2×D12#6712yes—
214C2×C4×D3—21no—
215C2×Dic6—21no—
216C2×Dic6—21no—
217C2×Dic6—21no—
218C2×Dic6—21no—
219C2×Dic6—21no—
220C2×Dic6D1212yes—
221C2×Dic6#6711yescharacteristic
222C3×SD16—64no—
223C3×D8—64no—
224C3×M16—21no—
225C3×M16—21no—
226C3×M16—22no—
227C3×M16—41no—
228C3×M16—61no—
229C3×M16—61no—
230C3×M16#6712yes—
231C3×M16#6712yes—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—41no—
235C2×C3×C8—61no—
236#216—64no—
237#216—64no—
238#215—68no—
239#215—64no—
240#214—68no—
241#214—64no—
242#208—21no—
243#208—21no—
244#208—32no—
245#208—32no—
246#208—62no—
247#208—61no—
248#208—61no—
249#208—121no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—121no—
261C2×C3⋊C8—121no—
262C2×C3⋊C8—121no—
263D24—24no—
264#204—24no—
265C22×C32—22no—
266C22×C32#12111yescharacteristic
267C22×C32#12111yescharacteristic
268C22×C32#12111yescharacteristic
269C2×C3×D3—41no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—82no—
273C2×C3×D3—82no—
274C2×C3×D3—82no—
275C32×C4#12011yescharacteristic
276C32×C4#12011yescharacteristic
277C32×C4#12011yescharacteristic
278C32×C4#12711yescharacteristic
279C3×Dic3—42no—
280C3×Dic3—41no—
281C2×#41—31no—
282C22×Q8—31no—
283C22×D4—31no—
284#137—182no—
285#137—182no—
286AGL(1,ℤ/8)—62no—
287AGL(1,ℤ/8)—62no—
288C2×Q16—181no—
289C2×SD16—61no—
290C2×SD16—182no—
291C2×SD16—182no—
292C2×SD16—181no—
293C2×SD16—182no—
294C2×D8—61no—
295C2×M16—31no—
296C2×M16—91no—
297C2×M16D3211yescharacteristic
298C22×C8—91no—
299#101—62no—
300#100—182no—
301C22⋊C8—182no—
302C23×C3—21no—
303C23×C3—61no—
304C23×C3—62no—
305C23×C3—121no—
306C23×C3—121no—
307C23×C3—242no—
308C23×C3#23511yescharacteristic
309C23×C3#23711yescharacteristic
310C22×D3—21no—
311C22×D3—22no—
312C22×D3—41no—
313C22×D3—41no—
314C22×D3—82no—
315C3×Q8—61no—
316C3×Q8—62no—
317C3×Q8—62no—
318C3×Q8—61no—
319C3×Q8—121no—
320C3×Q8—121no—
321C3×D4—62no—
322C3×D4—61no—
323C3×D4—61no—
324C3×D4—62no—
325C3×D4—121no—
326C3×D4—121no—
327C3×D4—121no—
328C3×D4—121no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—61no—
336C2×C3×C4—62no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4—121no—
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×C4D3×D411yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353#67—41no—
354#67—41no—
355C2×Dic3—22no—
356C2×Dic3—21no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359D12—22no—
360D12—21no—
361D12—22no—
362D12—21no—
363D12—41no—
364D12—41no—
365C4×D3—41no—
366C4×D3—41no—
367Dic6—22no—
368Dic6—22no—
369Dic6—21no—
370Dic6—21no—
371Dic6—41no—
372Dic6—41no—
373C3×C8—22no—
374C3×C8—22no—
375C3×C8—42no—
376C3×C8—121no—
377C3⋊C8—41no—
378C3⋊C8—62no—
379C3⋊C8—62no—
380C3⋊C8—62no—
381C3⋊C8—62no—
382C3⋊C8—122no—
383C3⋊C8—122no—
384C2×C32—21no—
385C2×C32—21no—
386C2×C32#39211yescharacteristic
387C2×C32#47112yes—
388C3×D3—81no—
389C3×D3—82no—
390C24—61no—
391#41—61no—
392#41—61no—
393#41—61no—
394#41—61no—
395C2×Q8—32no—
396C2×Q8—31no—
397C2×Q8—61no—
398C2×Q8—61no—
399C2×Q8—61no—
400C2×Q8—61no—
401C2×Q8—61no—
402C2×D4—31no—
403C2×D4—32no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—61no—
409C2×D4—61no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4C2×D3211yescharacteristic
413Q16—184no—
414SD16—64no—
415SD16—188no—
416SD16—184no—
417D8—64no—
418M16—21no—
419M16—61no—
420M16—61no—
421M16—92no—
422M16—181no—
423M16#62512yes—
424C2×C8—21no—
425C2×C8—61no—
426C2×C8—92no—
427C2×C8—181no—
428C2×C8—181no—
429C2×C8—181no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—42no—
436C22×C3—121no—
437C22×C3—122no—
438C22×C3—122no—
439C22×C3—242no—
440C22×C3—242no—
441C22×C3—242no—
442C22×C3#88411yescharacteristic
443C22×C3#88411yescharacteristic
444C22×C3#93011yescharacteristic
445C22×C3#93811yescharacteristic
446C22×C3#93911yescharacteristic
447C22×C3#93911yescharacteristic
448C2×D3—42no—
449C2×D3—41no—
450C2×D3—42no—
451C2×D3—82no—
452C2×D3—82no—
453C2×D3—82no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—121no—
459C3×C4—122no—
460C3×C4#88211yescharacteristic
461C3×C4#88211yescharacteristic
462C3×C4#93711yescharacteristic
463C3×C4#93711yescharacteristic
464C3×C4#93711yescharacteristic
465C3×C4#94011yescharacteristic
466C3×C4#94011yescharacteristic
467C3×C4#95311yescharacteristic
468Dic3—42no—
469Dic3—41no—
470C32#201911yescharacteristic, complemented, Sylow
471C23—61no—
472C23—62no—
473C23—121no—
474C23—121no—
475C23—242no—
476C23#379511yescharacteristic
477Q8—62no—
478Q8—62no—
479Q8—61no—
480Q8—61no—
481Q8—121no—
482Q8—121no—
483D4—62no—
484D4—61no—
485D4—61no—
486D4—62no—
487D4—121no—
488D4—121no—
489D4—121no—
490D4—121no—
491C2×C4—61no—
492C2×C4—62no—
493C2×C4—121no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4—121no—
497C2×C4D3×D1211yescharacteristic
498C2×C4#380211yescharacteristic
499C2×C4#380211yescharacteristic
500C2×C4C2×#62511yescharacteristic
501C2×C4D3×#6711yescharacteristic
502C2×C4D3×#6711yescharacteristic
503C8—22no—
504C8—121no—
505C8—182no—
506C8—182no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—41no—
514C2×C3—41no—
515C2×C3—241no—
516C2×C3—242no—
517C2×C3#475412yes—
518C2×C3#496011yescharacteristic
519C2×C3#520012yes—
520C2×C3#522311yescharacteristic
521D3—81no—
522D3—82no—
523C22—22no—
524C22—122no—
525C22—121no—
526C22—122no—
527C22—242no—
528C22—242no—
529C22—242no—
530C22#6388511yescharacteristic
531C22#6388511yescharacteristic
532C22#6390811yescharacteristic
533C4—121no—
534C4—122no—
535C4#6391411yescharacteristic
536C4#6392211yescharacteristic
537C4#6392211yescharacteristic
538C4#6397611yescharacteristic
539C3—21no—
540C3#7011711yescharacteristic, complemented
541C3#7209711yescharacteristic, complemented
542C2—21no—
543C2—21no—
544C2—241no—
545C2—242no—
546C2#1059098012yes—
547C2#1059138911yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×C3×#908C2
hypercenterC2×M16D32
hypocenterC32#2019
LCSG ▷ C22×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
2. C2×#63827C2semidirect
3. C22×#3715C2semidirect
4. C2×C3×#824C2semidirect
5. C2×#63558C2semidirect
6. #10591071C2semidirect
7. #10589424C2semidirect
40. C2×#824D3semidirect
470. C32#2019semidirect
540. C3#70117semidirect
541. C3#72097semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
C2×#638272
C22×#37152
C2×C3×#8242
C2×#635582
#105910712
#105894242
#720973
#701173