Finite Group Databasebeta

← #11787219

Subgroups — #11787219

Order 1152.

881 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
1C3×#5791C211yesmaximal, characteristic
2C22×C3×#208C211yesmaximal, characteristic, complemented
3C4×#3757C211yesmaximal, characteristic, complemented
4C2×#63568C212yesmaximal, complemented
5#10589160C212yesmaximal, complemented
6#71984—31nomaximal
7#71713—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×C3×#235C2211yescharacteristic
10C2×#3757—21no—
11C2×C4×C3⋊Dic3C2212yes—
12C3×#953—21no—
13C3×#930C411yescharacteristic, complemented
14C3×#930C411yescharacteristic, complemented
15C3×#929—21no—
16C3×C4×#67—21no—
17C3×C4×#67—21no—
18C3×#926C2211yescharacteristic
19C3×#924C411yescharacteristic, complemented
20C3×#924C411yescharacteristic, complemented
21C2×C3×#208—21no—
22C2×C3×#208—24no—
23C2×C3×#208C2212yes—
24C22×C3×C3⋊C8—21no—
25#63658—21no—
26#63568—24no—
27C22×C3×M16—31no—
28C3×#525—31no—
29#5791D311yescharacteristic
30C22×#208D311yescharacteristic, complemented
31C2×#837—32no—
32C4×#217—31no—
33C4×#217—31no—
34C4×#217—61no—
35C2×#825—32no—
36#4555—32no—
37#4532—32no—
38C24×C32D411yescharacteristic
39C22×C32×C4—22no—
40C22×C32×C4—22no—
41C22×C32×C4C2×C411yescharacteristic
42C22×C32×C4C2×C411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—22no—
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C3×#235—22no—
52C3×#235—22no—
53C2×C3×D12C2×C411yescharacteristic
54C2×C3×C4×D3—21no—
55C2×C3×Dic6C2×C411yescharacteristic
56#3757—24no—
57C4×C3⋊Dic3—22no—
58C4×C3⋊Dic3—22no—
59C3×#217—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3C2×C411yescharacteristic
65C3×C4⋊Dic3C2×C411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×C4×Dic3—21no—
69C3×#208—24no—
70C3×#208—22no—
71C3×#208D414yescomplemented
72C2×C3×C3⋊C8—24no—
73C2×C3×C3⋊C8—22no—
74#1871—91noSylow
75C2×C3×#41—31no—
76C23×C3×C4—21no—
77C23×C3×C4C2×D311yescharacteristic
78C23×C3×C4C2×D311yescharacteristic
79C2×#235C2×D311yescharacteristic
80C2×C3×M16—32no—
81C2×C3×M16—64no—
82C2×C3×M16—61no—
83C22×C3×C8—61no—
84C3×#123—61no—
85C3×C22⋊Q8—31no—
86C3×C22⋊Q8—31no—
87C3×#121—31no—
88C3×#121—31no—
89C3×#120—61no—
90C3×C4×D4—61no—
91C3×C4×D4—61no—
92C3×#117—31no—
93#953—21no—
94C2×#217—62no—
95C2×#217—61no—
96C2×#217—61no—
97#930Dic311yescharacteristic, complemented
98#930Dic311yescharacteristic, complemented
99#929—21no—
100C4×#67—21no—
101C4×#67—21no—
102#926C2×D311yescharacteristic
103#924Dic311yescharacteristic, complemented
104#924Dic311yescharacteristic, complemented
105C2×C4×Dic3—32no—
106C2×C4×Dic3—32no—
107C2×C4×Dic3—62no—
108C2×#208—21no—
109C2×#208—24no—
110C2×#208C2×D312yes—
111C22×C3⋊C8—21no—
112#837—64no—
113C3⋊#95—62no—
114C3⋊#95—61no—
115C3⋊#95—61no—
116#825—64no—
117C23×C32—22no—
118C23×C32—22no—
119C23×C32—41no—
120C23×C32C22⋊C411yescharacteristic
121C23×C32C22⋊C411yescharacteristic
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—21no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4C22⋊C411yescharacteristic
132C2×C32×C4C22⋊C411yescharacteristic
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D412yes—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4112yes—
137C2×C3⋊Dic3—24no—
138C2×C3⋊Dic3—42no—
139C2×C3⋊Dic3—42no—
140C3×#67—42no—
141C3×#67—42no—
142C3×#67—42no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C3×D12—22no—
147C3×C4×D3—41no—
148C3×C4×D3—41no—
149C3×Dic6—22no—
150C3×C3⋊C8—24no—
151C22×M16—31no—
152#525—31no—
153C2×#104—92no—
154C4×C22⋊C4—91no—
155#339—92no—
156C24×C3—21no—
157C24×C3D1211yescharacteristic
158C24×C3#6711yescharacteristic
159C3×#41—62no—
160C3×#41—62no—
161C2×C3×Q8—31no—
162C2×C3×D4—31no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—22no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—42no—
177C22×C3×C4—42no—
178C22×C3×C4—61no—
179C22×C3×C4C4×D311yescharacteristic
180C22×C3×C4C4×D311yescharacteristic
181C22×C3×C4D1211yescharacteristic
182C22×C3×C4C2×Dic311yescharacteristic
183C22×C3×C4C2×Dic311yescharacteristic
184C22×C3×C4#6711yescharacteristic
185C22×C3×C4#6711yescharacteristic
186C22×C3×C4#6711yescharacteristic
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4#6711yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—21no—
192C2×#67—21no—
193C2×#67—21no—
194C22×Dic3—64no—
195C22×Dic3—62no—
196C22×Dic3—62no—
197#235—22no—
198#235—22no—
199C2×D12C2×Dic311yescharacteristic
200C2×C4×D3—21no—
201C2×Dic6C2×Dic311yescharacteristic
202C3×M16—34no—
203C3×M16—64no—
204C3×M16—62no—
205C2×C3×C8—64no—
206C2×C3×C8—62no—
207C3×C4⋊C4—31no—
208C3×C4⋊C4—31no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C22⋊C4—61no—
212C3×C22⋊C4—61no—
213C3×C22⋊C4—61no—
214C3×C22⋊C4—61no—
215C3×C22⋊C4—61no—
216C3×C42—61no—
217#217—21no—
218#217—21no—
219#217—21no—
220#217—68no—
221#217—64no—
222#217—64no—
223(C2×D3)⋊C4—21no—
224(C2×D3)⋊C4—21no—
225C4⋊Dic3C2×Dic311yescharacteristic
226C4⋊Dic3C2×Dic311yescharacteristic
227Dic3⋊C4—21no—
228Dic3⋊C4—21no—
229C4×Dic3—21no—
230C4×Dic3—62no—
231C4×Dic3—62no—
232C4×Dic3—62no—
233C4×Dic3—62no—
234C4×Dic3—122no—
235C4×Dic3—122no—
236#208—24no—
237#208—22no—
238#208#6714yescomplemented
239C2×C3⋊C8—24no—
240C2×C3⋊C8—22no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32—21no—
245C22×C32—21no—
246C22×C32—21no—
247C22×C32—21no—
248C22×C32—44no—
249C22×C32#10412yescomplemented
250C22×C32C2×C22⋊C411yescharacteristic
251C22×C32#12112yes—
252C2×C3×D3—41no—
253C2×C3×D3—41no—
254C2×C3×D3—41no—
255C32×C4—21no—
256C32×C4—21no—
257C32×C4C4×D412yes—
258C32×C4#12011yescharacteristic
259C32×C4#12311yescharacteristic
260C3⋊Dic3—44no—
261C3×Dic3—41no—
262C3×Dic3—41no—
263C3×Dic3—41no—
264C2×#41—31no—
265C23×C4D3211yescharacteristic
266C2×M16—32no—
267C2×M16—64no—
268C2×M16—61no—
269C22×C8—61no—
270#123—61no—
271C22⋊Q8—31no—
272C22⋊Q8—31no—
273#121—31no—
274#121—31no—
275#120—61no—
276C4×D4—61no—
277C4×D4—61no—
278#117—31no—
279C2×C22⋊C4—181no—
280C2×C42—92no—
281#104—184no—
282#95—181no—
283C23×C3—24no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—22no—
287C23×C3—22no—
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—42no—
292C23×C3—41no—
293C23×C3—41no—
294C23×C3—42no—
295C23×C3—61no—
296C23×C3(C2×D3)⋊C411yescharacteristic
297C23×C3(C2×D3)⋊C411yescharacteristic
298C23×C3#21711yescharacteristic
299C23×C3#21711yescharacteristic
300C23×C3C2×D1211yescharacteristic
301C23×C3C2×#6711yescharacteristic
302C22×D3—21no—
303C3×Q8—62no—
304C3×D4—62no—
305C3×D4—122no—
306C3×D4—122no—
307C3×D4—122no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
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—22no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—42no—
331C2×C3×C4—42no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—42no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4(C2×D3)⋊C411yescharacteristic
341C2×C3×C4(C2×D3)⋊C411yescharacteristic
342C2×C3×C4#21711yescharacteristic
343C2×C3×C4#21711yescharacteristic
344C2×C3×C4C2×C4×D311yescharacteristic
345C2×C3×C4#23512yes—
346C2×C3×C4D3×D412yes—
347C2×C3×C4#23712yes—
348C2×C3×C4C22×Dic311yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6712yes—
352#67—42no—
353#67—42no—
354#67—42no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—68no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—124no—
362C2×Dic3—124no—
363C2×Dic3—122no—
364C2×Dic3—122no—
365C2×Dic3—122no—
366C2×Dic3—122no—
367D12—22no—
368C4×D3—41no—
369C4×D3—41no—
370Dic6—22no—
371C3×C8—64no—
372C3⋊C8—24no—
373C2×C32—22no—
374C2×C32—22no—
375C2×C32—41no—
376C2×C32#38611yescharacteristic
377C2×C32C2×#10411yescharacteristic
378C2×C32#42111yescharacteristic
379C3×D3—81no—
380C24#62611yescharacteristic
381#41—62no—
382#41—62no—
383C2×Q8—31no—
384C2×D4—31no—
385C2×D4—61no—
386C2×D4—61no—
387C2×D4—61no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—61no—
391C22×C4—182no—
392C22×C4D3×Dic311yescharacteristic
393C22×C4D3×Dic311yescharacteristic
394C22×C4#62511yescharacteristic
395C22×C4#62511yescharacteristic
396C22×C4#62611yescharacteristic
397C22×C4C2×D3211yescharacteristic
398M16—34no—
399M16—64no—
400M16—62no—
401C2×C8—64no—
402C2×C8—62no—
403C4⋊C4—31no—
404C4⋊C4—31no—
405C4⋊C4—61no—
406C4⋊C4—61no—
407C22⋊C4—61no—
408C22⋊C4—61no—
409C22⋊C4—61no—
410C22⋊C4—61no—
411C22⋊C4—61no—
412C22⋊C4—184no—
413C42—61no—
414C42—182no—
415C42—182no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—44no—
441C22×C3—44no—
442C22×C3—48no—
443C22×C3—121no—
444C22×C3—121no—
445C22×C3—121no—
446C22×C3#82512yescomplemented
447C22×C3#83712yescomplemented
448C22×C3C2×(C2×D3)⋊C411yescharacteristic
449C22×C3#93012yes—
450C22×C3#93912yes—
451C22×C3C2×#21711yescharacteristic
452C2×D3—41no—
453C2×D3—41no—
454C2×D3—41no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—21no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—121no—
465C3×C4—121no—
466C3×C4—121no—
467C3×C4C4×#6712yes—
468C3×C4#92911yescharacteristic
469C3×C4D4×Dic312yes—
470C3×C4#93511yescharacteristic
471C3×C4#93711yescharacteristic
472C3×C4#95311yescharacteristic
473Dic3—41no—
474Dic3—41no—
475Dic3—41no—
476Dic3—128no—
477Dic3—124no—
478Dic3—124no—
479C32#187111yescharacteristic, complemented, Sylow
480C23—22no—
481C23—22no—
482C23—41no—
483C23—61no—
484C23(C2×D3)⋊Dic311yescharacteristic
485C23(C2×D3)⋊Dic311yescharacteristic
486C23C2×#62611yescharacteristic
487Q8—62no—
488D4—62no—
489D4—122no—
490D4—122no—
491D4—122no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—184no—
505C2×C4—362no—
506C2×C4—362no—
507C2×C4(C2×D3)⋊Dic311yescharacteristic
508C2×C4(C2×D3)⋊Dic311yescharacteristic
509C2×C4C2×D3×Dic311yescharacteristic
510C2×C4#380412yes—
511C2×C4C2×#62511yescharacteristic
512C2×C4D3×#6712yes—
513C8—64no—
514C2×C3—24no—
515C2×C3—22no—
516C2×C3—22no—
517C2×C3—22no—
518C2×C3—22no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—42no—
523C2×C3—42no—
524C2×C3—41no—
525C2×C3—41no—
526C2×C3—241no—
527C2×C3C2×#82511yescharacteristic
528C2×C3#513911yescharacteristic
529C2×C3#521311yescharacteristic
530C2×C3#522011yescharacteristic
531C2×C3C2×#83711yescharacteristic
532C2×C3#523611yescharacteristic
533D3—81no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—44no—
542C22—121no—
543C22—121no—
544C22—121no—
545C22#6356812yescomplemented
546C22C2×(C2×D3)⋊Dic311yescharacteristic
547C22#6397812yes—
548C4—21no—
549C4—21no—
550C4—121no—
551C4—121no—
552C4—121no—
553C4—364no—
554C4#6396111yescharacteristic
555C4Dic3×#6712yes—
556C4#6397611yescharacteristic
557C3—21no—
558C3#7171311yescharacteristic, complemented
559C3#7198411yescharacteristic, complemented
560C2—22no—
561C2—22no—
562C2—41no—
563C2—241no—
564C2C2×#6356811yescharacteristic
565C2#1059111011yescharacteristic
566C2#1059171011yescharacteristic
subgroupG/H
centerC2×C4C2×#625
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5791C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1871
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#208C2semidirect
3. C4×#3757C2semidirect
4. C2×#63568C2semidirect
5. #10589160C2semidirect
13. C3×#930C4semidirect
14. C3×#930C4semidirect
19. C3×#924C4semidirect
20. C3×#924C4semidirect
30. C22×#208D3semidirect
71. C3×#208D4semidirect
97. #930Dic3semidirect
98. #930Dic3semidirect
103. #924Dic3semidirect
104. #924Dic3semidirect
238. #208#67semidirect
249. C22×C32#104semidirect
446. C22×C3#825semidirect
447. C22×C3#837semidirect
479. C32#1871semidirect
545. C22#63568semidirect
558. C3#71713semidirect
559. C3#71984semidirect

Maximal subgroups

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

subgroupindex
C3×#57912
C22×C3×#2082
C4×#37572
C2×#635682
#105891602
#719843
#717133