Finite Group Databasebeta

← #11788353

Subgroups — #11788353

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 581 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#897C211yesmaximal, characteristic
2C2×D3×#208C211yesmaximal, characteristic
3C2×#63560C211yesmaximal, characteristic, complemented
4C2×#63560C211yesmaximal, characteristic, complemented
5#10591069C211yesmaximal, characteristic
6#10589396C211yesmaximal, characteristic, complemented
7C3×#4530C211yesmaximal, characteristic, complemented
8#71698—31nomaximal
9#68993—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4C412yes—
16C2×C3×C4⋊Dic3C412yes—
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#897—21no—
20C3×#897—21no—
21C3×#897—21no—
22C3×#897—21no—
23C2×#3711—21no—
24D3×#208—22no—
25D3×#208—22no—
26C2×D3×C3⋊C8—21no—
27#63560—22no—
28#63560—22no—
29(C2×D3)⋊(C3⋊C8)—21no—
30(C2×D3)⋊(C3⋊C8)—21no—
31C2×C3×C22⋊Q8—31no—
32C22×#208—31no—
33C2×D3×M16—31no—
34C2×#897D311yescharacteristic
35C2×#836—31no—
36C2×#836—31no—
37#5207—31no—
38C2×#824—31no—
39C2×#824—31no—
40#5126—31no—
41C3×#343—31no—
42#4530—31no—
43#4530—31no—
44#4530—61no—
45#4530D311yescharacteristic, complemented
46C23×C3×D3C2×C411yescharacteristic
47C22×C32×C4C2×C412yes—
48C22×C32×C4C2311yescharacteristic
49C22×C3×Dic3C2×C412yes—
50C22×C3×Dic3C2×C411yescharacteristic
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3—21no—
55C2×C3×C4×D3D411yescharacteristic
56C2×C3×C4×D3D411yescharacteristic
57C2×C3×C4×D3D411yescharacteristic
58C2×C3×C4×D3D411yescharacteristic
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67#3748—21no—
68#3748—21no—
69#3748—21no—
70#3748D412yes—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)—21no—
73C3×(C2×D3)⋊C4—22no—
74C3×(C2×D3)⋊C4—22no—
75C3×C4⋊Dic3—22no—
76C3×C4⋊Dic3—22no—
77C3×#208—21no—
78C3×#208—21no—
79C3×#208—21no—
80C3×#208D412yes—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83#3711—24no—
84D3×C3⋊C8—24no—
85#1901—91noSylow
86C22×C3×Q8—31no—
87C23×C3×C4—31no—
88C22×C4×D3C2×D311yescharacteristic
89C22×Dic6C2×D311yescharacteristic
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C3×C22⋊Q8—61no—
93C3×C22⋊Q8—61no—
94C3×C22⋊Q8—61no—
95C3×C22⋊Q8—61no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—32no—
98C2×C3×C4⋊C4C2×D311yescharacteristic
99C2×C3×C4⋊C4C2×D311yescharacteristic
100C2×C3×C22⋊C4—32no—
101C2×(C2×D3)⋊C4Dic312yes—
102C2×C4⋊Dic3Dic312yes—
103C2×#208—31no—
104C2×#208—31no—
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—61no—
108C2×#208—61no—
109C2×#208—61no—
110C2×#208—62no—
111C2×#208—62no—
112C2×#208C2×D311yescharacteristic
113C2×#208C2×D311yescharacteristic
114C22×C3⋊C8—61no—
115D3×M16—62no—
116D3×M16—62no—
117C2×ΓL(1,𝔽25)—61no—
118C2×D3×C8—61no—
119#897—21no—
120#897—21no—
121#897—21no—
122#897—21no—
123#836—62no—
124#836—62no—
125#830—61no—
126#830—61no—
127#824—62no—
128#824—62no—
129(C2×D3)⋊C8—61no—
130(C2×D3)⋊C8—61no—
131C23×C32C22×C411yescharacteristic
132C22×C3×D3—21no—
133C22×C3×D3—21no—
134C22×C3×D3—22no—
135C22×C3×D3—41no—
136C22×C3×D3C22⋊C411yescharacteristic
137C22×C3×D3C22⋊C411yescharacteristic
138C2×C32×C4—22no—
139C2×C32×C4—42no—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3C22⋊C411yescharacteristic
152C2×C3×Dic3C22⋊C411yescharacteristic
153C3×C4×D3—21no—
154C3×C4×D3—21no—
155C3×C4×D3—21no—
156C3×C4×D3—21no—
157C3×C4×D3—21no—
158C3×C4×D3—21no—
159C3×C4×D3—21no—
160C3×C4×D3—21no—
161C3×Dic6—41no—
162C3×Dic6—41no—
163C3×Dic6—41no—
164C3×Dic6—41no—
165C3⋊(C3⋊C8)—22no—
166C3⋊(C3⋊C8)—41no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—41no—
169C22×M16—91no—
170C2×C22⋊Q8—31no—
171C2×#101—91no—
172C2×#101—91no—
173#407—91no—
174#343—31no—
175#343—91no—
176C24×C3—31no—
177C23×D3C2×Dic311yescharacteristic
178C2×C3×Q8—61no—
179C2×C3×Q8—61no—
180C2×C3×Q8—61no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—31no—
187C22×C3×C4—31no—
188C22×C3×C4—31no—
189C22×C3×C4—31no—
190C22×C3×C4—31no—
191C22×C3×C4—32no—
192C22×C3×C4—61no—
193C22×C3×C4—61no—
194C22×C3×C4—61no—
195C22×C3×C4—61no—
196C22×C3×C4C4×D312yes—
197C22×C3×C4C2×Dic312yes—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×Dic3C2×Dic312yes—
201C22×Dic3C2×Dic311yescharacteristic
202C2×C4×D3—21no—
203C2×C4×D3—21no—
204C2×C4×D3—21no—
205C2×C4×D3—21no—
206C2×C4×D3#6711yescharacteristic
207C2×C4×D3#6711yescharacteristic
208C2×C4×D3#6711yescharacteristic
209C2×C4×D3#6711yescharacteristic
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6—21no—
216C3×M16—32no—
217C3×M16—61no—
218C3×M16—61no—
219C3×M16—61no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—41no—
227C3×C4⋊C4—41no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—62no—
230C3×C22⋊C4—62no—
231C3×C22⋊C4—62no—
232(C2×D3)⋊C4—22no—
233(C2×D3)⋊C4—22no—
234C4⋊Dic3—22no—
235C4⋊Dic3—22no—
236#208—21no—
237#208—21no—
238#208—21no—
239#208—32no—
240#208—32no—
241#208—62no—
242#208—64no—
243#208—61no—
244#208—61no—
245#208—62no—
246#208—61no—
247#208—61no—
248#208—61no—
249#208—61no—
250#208—121no—
251#208—121no—
252#208D1212yes—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—64no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—121no—
261C2×C3⋊C8—121no—
262ΓL(1,𝔽25)—64no—
263D3×C8—64no—
264C22×C32—21no—
265C22×C32—21no—
266C22×C32C2×C22⋊C411yescharacteristic
267C22×C32C4×D411yescharacteristic
268C22×C32C4×D411yescharacteristic
269C2×C3×D3—21no—
270C2×C3×D3—21no—
271C2×C3×D3—21no—
272C2×C3×D3—21no—
273C2×C3×D3—21no—
274C2×C3×D3—42no—
275C2×C3×D3—42no—
276C2×C3×D3#10112yescomplemented
277C32×C4—42no—
278C32×C4#12011yescharacteristic
279C32×C4#12111yescharacteristic
280C32×C4#12111yescharacteristic
281C32×C4#12311yescharacteristic
282C3×Dic3—21no—
283C3×Dic3—21no—
284C3×Dic3—42no—
285C22×Q8—31no—
286C23×C4—31no—
287C2×M16—31no—
288C2×M16—31no—
289C2×M16—91no—
290C2×M16—91no—
291C2×M16—181no—
292C2×M16—182no—
293C2×M16—182no—
294C22×C8—181no—
295C22⋊Q8—61no—
296C22⋊Q8—61no—
297C22⋊Q8—61no—
298C22⋊Q8—61no—
299C2×C4⋊C4—32no—
300C2×C4⋊C4D3211yescharacteristic
301C2×C22⋊C4—32no—
302#101—182no—
303#101—182no—
304C22⋊C8—181no—
305C22⋊C8—181no—
306C23×C3—21no—
307C23×C3—31no—
308C23×C3—31no—
309C23×C3—62no—
310C23×C3—61no—
311C23×C3—61no—
312C23×C3—121no—
313C23×C3C2×C4×D311yescharacteristic
314C23×C3C22×Dic311yescharacteristic
315C22×D3—21no—
316C22×D3—21no—
317C22×D3—22no—
318C22×D3—41no—
319C22×D3#21711yescharacteristic
320C22×D3#21711yescharacteristic
321C3×Q8—121no—
322C3×Q8—121no—
323C3×Q8—121no—
324C3×Q8—121no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—31no—
334C2×C3×C4—31no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—61no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—82no—
352C2×C3×C4C2×D1211yescharacteristic
353C2×C3×C4#23511yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4#23711yescharacteristic
360C2×C3×C4#23711yescharacteristic
361C2×C3×C4#23911yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3#21711yescharacteristic
370C2×Dic3#21711yescharacteristic
371C4×D3—21no—
372C4×D3—21no—
373C4×D3—21no—
374C4×D3—21no—
375C4×D3—21no—
376C4×D3—21no—
377C4×D3—21no—
378C4×D3—21no—
379Dic6—41no—
380Dic6—41no—
381Dic6—41no—
382Dic6—41no—
383C3×C8—62no—
384C3×C8—121no—
385C3⋊C8—22no—
386C3⋊C8—41no—
387C3⋊C8—62no—
388C3⋊C8—62no—
389C3⋊C8—122no—
390C3⋊C8—122no—
391C3⋊C8—121no—
392C3⋊C8—121no—
393C2×C32—21no—
394C2×C32—21no—
395C2×C32#38611yescharacteristic
396C2×C32C2×#10111yescharacteristic
397C2×C32#41311yescharacteristic
398C3×D3—22no—
399C3×D3—41no—
400C24—31no—
401C2×Q8—61no—
402C2×Q8—61no—
403C2×Q8—61no—
404C2×Q8—61no—
405C2×Q8—61no—
406C2×Q8—61no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—31no—
412C22×C4—32no—
413C22×C4—61no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4D3×Dic312yes—
418C22×C4C2×D3211yescharacteristic
419M16—32no—
420M16—61no—
421M16—61no—
422M16—61no—
423M16—92no—
424M16—184no—
425M16—181no—
426M16—181no—
427M16—181no—
428C2×C8—61no—
429C2×C8—61no—
430C2×C8—184no—
431C2×C8—181no—
432C2×C8—181no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—62no—
436C4⋊C4—62no—
437C22⋊C4—62no—
438C22⋊C4—62no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—32no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—61no—
450C22×C3—61no—
451C22×C3—61no—
452C22×C3—61no—
453C22×C3—61no—
454C22×C3—122no—
455C22×C3—122no—
456C22×C3C4×D1211yescharacteristic
457C22×C3D3×C22⋊C411yescharacteristic
458C22×C3#89311yescharacteristic
459C22×C3D4×Dic311yescharacteristic
460C22×C3D4×Dic311yescharacteristic
461C22×C3C2×#21711yescharacteristic
462C2×D3—21no—
463C2×D3—21no—
464C2×D3—21no—
465C2×D3—21no—
466C2×D3—21no—
467C2×D3—42no—
468C2×D3—42no—
469C2×D3#83612yescomplemented
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—42no—
475C3×C4—42no—
476C3×C4—61no—
477C3×C4—61no—
478C3×C4—82no—
479C3×C4—122no—
480C3×C4#88211yescharacteristic
481C3×C4#88411yescharacteristic
482C3×C4#89411yescharacteristic
483C3×C4#89511yescharacteristic
484C3×C4#93511yescharacteristic
485C3×C4#93711yescharacteristic
486C3×C4#93911yescharacteristic
487C3×C4#93911yescharacteristic
488Dic3—21no—
489Dic3—21no—
490Dic3—42no—
491C32#190111yescharacteristic, complemented, Sylow
492C23—31no—
493C23—31no—
494C23—62no—
495C23—61no—
496C23—61no—
497C23—121no—
498C23C2×D3×Dic311yescharacteristic
499Q8—121no—
500Q8—121no—
501Q8—121no—
502Q8—121no—
503C2×C4—22no—
504C2×C4—31no—
505C2×C4—31no—
506C2×C4—42no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4#379511yescharacteristic
521C2×C4#379611yescharacteristic
522C2×C4D3×D1211yescharacteristic
523C2×C4#380211yescharacteristic
524C2×C4D3×#6711yescharacteristic
525C2×C4D3×#6711yescharacteristic
526C8—62no—
527C8—121no—
528C8—182no—
529C8—361no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—41no—
538C2×C3—41no—
539C2×C3—62no—
540C2×C3—121no—
541C2×C3#466511yescharacteristic
542C2×C3#474511yescharacteristic
543C2×C3D3×#10111yescharacteristic
544C2×C3#522011yescharacteristic
545C2×C3C2×#83611yescharacteristic
546C2×C3#523711yescharacteristic
547D3—22no—
548D3—41no—
549C22—21no—
550C22—21no—
551C22—32no—
552C22—61no—
553C22—61no—
554C22—61no—
555C22—61no—
556C22—61no—
557C22—122no—
558C22—122no—
559C22Dic3×D1211yescharacteristic
560C22#6389811yescharacteristic
561C22D3×#21711yescharacteristic
562C4—42no—
563C4—61no—
564C4—61no—
565C4—122no—
566C4#6388411yescharacteristic
567C4#6388511yescharacteristic
568C4#6388611yescharacteristic
569C4#6392211yescharacteristic
570C3—21no—
571C3#6899311yescharacteristic, complemented
572C3#7169811yescharacteristic, complemented
573C2—21no—
574C2—21no—
575C2—62no—
576C2—121no—
577C2#1059137611yescharacteristic
578C2#1059150111yescharacteristic
579C2D3×#83611yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1901
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63560C2semidirect
4. C2×#63560C2semidirect
6. #10589396C2semidirect
7. C3×#4530C2semidirect
45. #4530D3semidirect
276. C2×C3×D3#101semidirect
469. C2×D3#836semidirect
491. C32#1901semidirect
571. C3#68993semidirect
572. C3#71698semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8972
C2×D3×#2082
C2×#635602
#105910692
#105893962
C3×#45302
#716983
#689933