Finite Group Databasebeta

← #11808666

Subgroups — #11808666

Order 1152.

1584 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×#64096C211yesmaximal, characteristic, complemented
3C32×#398C211yesmaximal, characteristic, complemented
4#10592693C211yesmaximal, characteristic
5#10592693C211yesmaximal, characteristic
6#10592692C211yesmaximal, characteristic
7#10592681C211yesmaximal, characteristic, complemented
8C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
9C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
10#10592372C211yesmaximal, characteristic
11#10592365C211yesmaximal, characteristic
12#10592365C211yesmaximal, characteristic
13#10592359C211yesmaximal, characteristic, complemented
14#10592355C211yesmaximal, characteristic, complemented
15#10592348C211yesmaximal, characteristic, complemented
16#77739—34nomaximal
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×#634C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36C2×C4×C3⋊Dic3C2211yescharacteristic
37C2×C4×C3⋊Dic3C2211yescharacteristic
38C2×C4×C3⋊Dic3C2211yescharacteristic
39C2×C4×C3⋊Dic3C2211yescharacteristic
40C2×C4×C3⋊Dic3C2211yescharacteristic
41C2×C4×C3⋊Dic3C2211yescharacteristic
42#64101—24no—
43#64096—24no—
44C32×#95C2211yescharacteristic
45C32×#95C2211yescharacteristic
46C32×#95C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54C2×#892—34no—
55C2×#887—34no—
56C3×#398D314yescomplemented
57#4994—34no—
58#4994—34no—
59#4993—34no—
60#4982—34no—
61Dic3×C4⋊C4—34no—
62Dic3×C4⋊C4—34no—
63#4673—34no—
64#4666—34no—
65#4666—34no—
66#4660—34no—
67#4656—34no—
68#4649—34no—
69C23×C3⋊D3C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C2×C4×C3⋊D3—22no—
85C2×C4×C3⋊D3—22no—
86C2×C4×C3⋊D3Q814yescomplemented
87C2×#634—22no—
88C2×#634—22no—
89C2×#634—22no—
90C32×C4⋊C4—22no—
91C32×C4⋊C4—22no—
92C32×C4⋊C4—22no—
93C32×C4⋊C4—22no—
94#3752—22no—
95#3752—22no—
96#3752—22no—
97#3752—22no—
98#3752—22no—
99#3752—22no—
100C4⋊(C3⋊Dic3)—22no—
101C4⋊(C3⋊Dic3)—22no—
102C4⋊(C3⋊Dic3)—22no—
103#3750—22no—
104#3750—22no—
105#3750—22no—
106#3750—22no—
107C4×C3⋊Dic3—22no—
108C4×C3⋊Dic3—22no—
109C4×C3⋊Dic3—22no—
110C4×C3⋊Dic3—22no—
111C4×C3⋊Dic3—22no—
112C4×C3⋊Dic3D414yes—
113#2396—91noSylow
114C22×C4×D3—34no—
115C22×Dic6—34no—
116C2×C3×C4⋊C4C2×D314yes—
117C2×C3×C4⋊C4C2×D314yes—
118C2×C3×C4⋊C4C2×D314yes—
119C2×C3×C4⋊C4C2×D314yes—
120C2×(C2×D3)⋊C4—34no—
121C2×(C2×D3)⋊C4—34no—
122C2×(C2×D3)⋊C4—34no—
123C2×(C2×D3)⋊C4—34no—
124C2×(C2×D3)⋊C4—34no—
125C2×(C2×D3)⋊C4—34no—
126C2×C4⋊Dic3—34no—
127C2×C4⋊Dic3—34no—
128C2×C4⋊Dic3—34no—
129C2×Dic3⋊C4—34no—
130C2×Dic3⋊C4—34no—
131C2×Dic3⋊C4—34no—
132C2×Dic3⋊C4—34no—
133C2×C4×Dic3—34no—
134C2×C4×Dic3—34no—
135C2×C4×Dic3—34no—
136C2×C4×Dic3—34no—
137C2×C4×Dic3—34no—
138C2×C4×Dic3—34no—
139#892—616no—
140#887—616no—
141C3×#95C2×D314yes—
142C3×#95C2×D314yes—
143C3×#95C2×D314yes—
144C3⋊#95—34no—
145C3⋊#95—34no—
146C3⋊#95—34no—
147C3⋊#95—34no—
148C3⋊#95—34no—
149C3⋊#95—34no—
150C3⋊#95—34no—
151C23×C32C2411yescharacteristic
152C22×C3⋊D3—21no—
153C22×C3⋊D3—21no—
154C22×C3⋊D3—21no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3C2×Q812yes—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2×Q812yes—
178C2×C32×C4#4112yes—
179C2×C32×C4#4112yes—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3C2×D412yes—
196C2×C3⋊Dic3C2×D412yes—
197C2×C3⋊Dic3C2×Q812yes—
198C2×C3⋊Dic3#4112yes—
199C2×C3⋊Dic3#4112yes—
200C2×C3⋊Dic3#4112yes—
201C4×C3⋊D3—28no—
202#634—28no—
203C2×C4×Q8—91no—
204C2×#117—91no—
205#400—91no—
206#399—91no—
207#398—91no—
208#398C3⋊D311yescharacteristic, complemented
209#396—91no—
210#396—91no—
211#395—91no—
212#393—91no—
213C4×C4⋊C4—91no—
214C4×C4⋊C4—91no—
215C4×C4⋊C4—91no—
216C4×C22⋊C4—91no—
217C4×C22⋊C4—91no—
218C23×D3—34no—
219C22×C3×C4C22×D314yes—
220C22×C3×C4C22×D314yes—
221C22×C3×C4C22×D314yes—
222C22×C3×C4C22×D314yes—
223C22×C3×C4C22×D314yes—
224C22×C3×C4C22×D314yes—
225C22×C3×C4C22×D314yes—
226C22×Dic3—34no—
227C22×Dic3—34no—
228C22×Dic3—34no—
229C22×Dic3—34no—
230C22×Dic3—34no—
231C22×Dic3—34no—
232C22×Dic3—34no—
233C2×C4×D3—316no—
234C2×C4×D3—68no—
235C2×C4×D3—68no—
236C2×Dic6—68no—
237C2×Dic6—68no—
238C2×Dic6—68no—
239C3×C4⋊C4—28no—
240C3×C4⋊C4—28no—
241C3×C4⋊C4—28no—
242C3×C4⋊C4—28no—
243(C2×D3)⋊C4—68no—
244(C2×D3)⋊C4—68no—
245(C2×D3)⋊C4—68no—
246(C2×D3)⋊C4—68no—
247(C2×D3)⋊C4—68no—
248(C2×D3)⋊C4—68no—
249C4⋊Dic3—68no—
250C4⋊Dic3—68no—
251C4⋊Dic3—68no—
252Dic3⋊C4—68no—
253Dic3⋊C4—68no—
254Dic3⋊C4—68no—
255Dic3⋊C4—68no—
256C4×Dic3—316no—
257C4×Dic3—68no—
258C4×Dic3—68no—
259C4×Dic3—68no—
260C4×Dic3—68no—
261C4×Dic3—68no—
262C22×C32C22×D411yescharacteristic
263C22×C32C22×Q811yescharacteristic
264C22×C32C2×#4111yescharacteristic
265C22×C32C2×#4111yescharacteristic
266C22×C32C2×#4111yescharacteristic
267C22×C32C2×#4111yescharacteristic
268C22×C32C2×#4111yescharacteristic
269C2×C3⋊D3—22no—
270C2×C3⋊D3—22no—
271C2×C3⋊D3—22no—
272C2×C3⋊D3—41no—
273C2×C3⋊D3—41no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C32×C4—22no—
277C32×C4—22no—
278C32×C4—22no—
279C32×C4—22no—
280C32×C4—41no—
281C32×C4—41no—
282C32×C4—41no—
283C3⋊Dic3—22no—
284C3⋊Dic3—22no—
285C3⋊Dic3—22no—
286C3⋊Dic3—41no—
287C3⋊Dic3—41no—
288C3⋊Dic3—41no—
289C3⋊Dic3C22⋊Q814yes—
290C22×Q8—91no—
291C23×C4—91no—
292C4×Q8—184no—
293#117—184no—
294C2×C4⋊C4—91no—
295C2×C4⋊C4—91no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—91no—
301C2×C4⋊C4C2×C3⋊D311yescharacteristic
302C2×C4⋊C4C2×C3⋊D311yescharacteristic
303C2×C4⋊C4C2×C3⋊D311yescharacteristic
304C2×C4⋊C4C2×C3⋊D311yescharacteristic
305C2×C22⋊C4—91no—
306C2×C22⋊C4—91no—
307C2×C22⋊C4—91no—
308C2×C22⋊C4—91no—
309C2×C22⋊C4—91no—
310C2×C22⋊C4—91no—
311C2×C42—91no—
312C2×C42—91no—
313C2×C42—91no—
314C2×C42—91no—
315C2×C42—91no—
316C2×C42—91no—
317#95—91no—
318#95—91no—
319#95—91no—
320#95—91no—
321#95—91no—
322#95—91no—
323#95—91no—
324#95C2×C3⋊D311yescharacteristic
325#95C2×C3⋊D311yescharacteristic
326#95C2×C3⋊D311yescharacteristic
327C23×C3C23×D314yes—
328C22×D3—38no—
329C22×D3—64no—
330C22×D3—64no—
331C22×D3—64no—
332C22×D3—64no—
333C22×D3—64no—
334C22×D3—64no—
335C2×C3×C4—24no—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—24no—
339C2×C3×C4—24no—
340C2×C3×C4—24no—
341C2×C3×C4—24no—
342C2×C3×C4—24no—
343C2×C3×C4—24no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4D3×D418yes—
353C2×C3×C4#23718yes—
354C2×C3×C4D3×Q818yes—
355C2×C3×C4#23918yes—
356C2×Dic3—38no—
357C2×Dic3—38no—
358C2×Dic3—38no—
359C2×Dic3—38no—
360C2×Dic3—38no—
361C2×Dic3—38no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—64no—
366C2×Dic3—64no—
367C2×Dic3—64no—
368C2×Dic3—64no—
369C2×Dic3—64no—
370C2×Dic3—64no—
371C2×Dic3—64no—
372C2×Dic3—64no—
373C2×Dic3—64no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376C2×Dic3—64no—
377C4×D3—632no—
378Dic6—632no—
379C2×C32C2×C22⋊Q811yescharacteristic
380C2×C32#52511yescharacteristic
381C2×C32#52911yescharacteristic
382C2×C32#52911yescharacteristic
383C2×C32#53211yescharacteristic
384C2×C32#53311yescharacteristic
385C2×C32#53311yescharacteristic
386C3⋊D3—42no—
387C24—91no—
388C2×Q8—182no—
389C2×Q8—182no—
390C2×Q8—182no—
391C22×C4—91no—
392C22×C4—91no—
393C22×C4—91no—
394C22×C4—91no—
395C22×C4—94no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—182no—
400C22×C4—182no—
401C22×C4C22×C3⋊D311yescharacteristic
402C22×C4C22×C3⋊D311yescharacteristic
403C22×C4C22×C3⋊D311yescharacteristic
404C22×C4C22×C3⋊D311yescharacteristic
405C22×C4C22×C3⋊D311yescharacteristic
406C22×C4C22×C3⋊D311yescharacteristic
407C22×C4C22×C3⋊D311yescharacteristic
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—182no—
413C4⋊C4—182no—
414C4⋊C4—182no—
415C4⋊C4—182no—
416C4⋊C4—182no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C22⋊C4—182no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C22⋊C4—182no—
425C42—94no—
426C42—182no—
427C42—182no—
428C42—182no—
429C42—182no—
430C42—182no—
431C22×C3C2×D3×D414yes—
432C22×C3C2×#23714yes—
433C22×C3C2×D3×Q814yes—
434C22×C3C2×#23914yes—
435C22×C3D3×#4114yes—
436C22×C3D3×#4114yes—
437C22×C3D3×#4114yes—
438C2×D3—68no—
439C2×D3—68no—
440C2×D3—68no—
441C2×D3—124no—
442C2×D3—124no—
443C2×D3—124no—
444C2×D3—124no—
445C3×C4—28no—
446C3×C4—28no—
447C3×C4—28no—
448C3×C4—28no—
449C3×C4—44no—
450C3×C4—44no—
451C3×C4—44no—
452Dic3—316no—
453Dic3—68no—
454Dic3—68no—
455Dic3—68no—
456Dic3—124no—
457Dic3—124no—
458Dic3—124no—
459C32#239611yescharacteristic, complemented, Sylow
460C23—92no—
461C23—181no—
462C23—181no—
463C23—181no—
464C23—181no—
465C23—181no—
466C23—181no—
467C23C23×C3⋊D311yescharacteristic
468Q8—188no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—92no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—92no—
491C2×C4—92no—
492C2×C4—188no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4D4×C3⋊D312yes—
509C2×C4#383012yes—
510C2×C4Q8×C3⋊D312yes—
511C2×C4#383212yes—
512C2×C3#559614yes—
513C2×C3D3×C22⋊Q814yes—
514C2×C3#562714yes—
515C2×C3#564914yes—
516C2×C3#568814yes—
517C2×C3#569114yes—
518C2×C3#572814yes—
519D3—128no—
520C22—182no—
521C22—182no—
522C22—182no—
523C22—361no—
524C22—361no—
525C22—361no—
526C22—361no—
527C22C2×D4×C3⋊D311yescharacteristic
528C22C2×#383011yescharacteristic
529C22C2×Q8×C3⋊D311yescharacteristic
530C22C2×#383211yescharacteristic
531C22#41×C3⋊D311yescharacteristic
532C22#41×C3⋊D311yescharacteristic
533C22#41×C3⋊D311yescharacteristic
534C4—22no—
535C4—22no—
536C4—22no—
537C4—22no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—94no—
542C4—182no—
543C4—182no—
544C4—182no—
545C4—361no—
546C4—361no—
547C4—361no—
548C3#7773914yescomplemented
549C2—362no—
550C2#1059606711yescharacteristic
551C2C3⋊D3×C22⋊Q811yescharacteristic
552C2#1059609811yescharacteristic
553C2#1059612011yescharacteristic
554C2#1059615911yescharacteristic
555C2#1059616211yescharacteristic
556C2#1059619911yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#398C2
prime radicalC23×C3⋊D3C23
hypercenter#398C3⋊D3
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#64096C2semidirect
3. C32×#398C2semidirect
7. #10592681C2semidirect
8. C4⋊C4×C3⋊Dic3C2semidirect
9. C4⋊C4×C3⋊Dic3C2semidirect
13. #10592359C2semidirect
14. #10592355C2semidirect
15. #10592348C2semidirect
56. C3×#398D3semidirect
86. C2×C4×C3⋊D3Q8semidirect
208. #398C3⋊D3semidirect
459. C32#2396semidirect
548. C3#77739semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#640962
C32×#3982
#105926932
#105926922
#105926812
C4⋊C4×C3⋊Dic32
#105923722
#105923652
#105923592
#105923552
#105923482
#777393