Finite Group Databasebeta

← #11778632

Subgroups — #11778632

Order 1152.

509 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 509 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5617C211yesmaximal, characteristic
2C3×#5033C211yesmaximal, characteristic, complemented
3#10591314C211yesmaximal, characteristic, complemented
4#10591101C211yesmaximal, characteristic, complemented
5#10589403C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#71882—31nomaximal
9#71165—31nomaximal
10C32×#121C2211yescharacteristic
11C3×#939—21no—
12C3×#937—21no—
13C3×D4×Dic3—21no—
14C2×C3×(C2×D3)⋊C4C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C3×#924C2211yescharacteristic
17C3×#898—21no—
18C3×#886—21no—
19C3×#885—21no—
20C2×(C2×D3)⋊Dic3—21no—
21#63658C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×#832—21no—
24C3×#830C2211yescharacteristic
25C3×#807—21no—
26#63579—21no—
27#63574—21no—
28#63565—21no—
29C3×#538—31no—
30#5617D311yescharacteristic
31C3×#480—31no—
32#5043—31no—
33#5033D311yescharacteristic, complemented
34#4992—31no—
35#4971—31no—
36#4953—31no—
37#4538—31no—
38#4537—31no—
39#4537—31no—
40#4537—61no—
41#4525—31no—
42#4468—31no—
43#4467—31no—
44C23×C3×D3D411yescharacteristic
45C2×C32×D4—21no—
46C2×C32×D4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C32×C4⋊C4D411yescharacteristic
56C32×C22⋊C4—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—21no—
59C3×#217—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3D411yescharacteristic
68C3×Dic3⋊C4—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71(C2×D3)⋊Dic3—42no—
72#1612—91noSylow
73C3×#126—61no—
74C3×#124—61no—
75C3×#123—61no—
76C3×C22⋊Q8—31no—
77C3×#121—21no—
78C3×#121—61no—
79C3×#121C2×D311yescharacteristic
80C3×#121C2×D311yescharacteristic
81C3×#120—61no—
82C3×C4×D4—61no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C22⋊C4—31no—
85C2×#217—61no—
86#939—21no—
87#937—21no—
88D4×Dic3—21no—
89C2×(C2×D3)⋊C4—61no—
90C2×(C2×D3)⋊C4C2×D311yescharacteristic
91C2×C4⋊Dic3C2×D311yescharacteristic
92#924C2×D311yescharacteristic
93#898—21no—
94#886—21no—
95#885—21no—
96C3×#107—61no—
97C3×#102—61no—
98C3×C22⋊C8—31no—
99#835—61no—
100#832—21no—
101C3⋊#95—31no—
102C3⋊#95—31no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106#830—31no—
107#830—31no—
108#830—61no—
109#830C2×D311yescharacteristic
110#810—61no—
111#808—61no—
112#808—61no—
113#807—21no—
114C23×C32—21no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C22×C3×D3—21no—
118C22×C3×D3—21no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C32×D4—41no—
122C32×D4—41no—
123C32×D4—41no—
124C2×C32×C4—21no—
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C3×#67—81no—
132C3×#67—81no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—81no—
141C3×Dic6—41no—
142C3⋊(C3⋊C8)—41no—
143C3×C3⋊C8—41no—
144#538—31no—
145#483—91no—
146#480—31no—
147#397—91no—
148#328—91no—
149#327—91no—
150#323—91no—
151C24×C3—31no—
152C23×D3#6711yescharacteristic
153C2×C3×Q8—31no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—41no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4#6711yescharacteristic
161C2×C3×D4#6711yescharacteristic
162C22×C3×C4—21no—
163C22×C3×C4—31no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—21no—
169C2×#67—21no—
170C22×Dic3—21no—
171C22×Dic3—21no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174C22×Dic3—121no—
175C22×Dic3#6711yescharacteristic
176C2×Dic6#6711yescharacteristic
177C2×C3×C8—61no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—31no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4#6711yescharacteristic
185C3×C4⋊C4#6711yescharacteristic
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—41no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C42—61no—
196#217—21no—
197#217—21no—
198#217—122no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—21no—
203(C2×D3)⋊C4—122no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3#6711yescharacteristic
208Dic3⋊C4—21no—
209C4×Dic3—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—121no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32#12011yescharacteristic
220C22×C32#13511yescharacteristic
221C22×C32AGL(1,ℤ/8)11yescharacteristic
222C2×C3×D3—42no—
223C2×C3×D3—41no—
224C2×C3×D3—41no—
225C2×C3×D3—41no—
226C2×C3×D3—81no—
227C32×C4—21no—
228C32×C4—21no—
229C32×C4—41no—
230C3⋊Dic3—81no—
231C3×Dic3—41no—
232C3×Dic3—41no—
233C3×Dic3—41no—
234C3×Dic3—81no—
235#126—61no—
236#124—61no—
237#123—61no—
238C22⋊Q8—31no—
239#121—61no—
240#121D3211yescharacteristic
241#120—61no—
242C4×D4—61no—
243C2×C4⋊C4—31no—
244C2×C22⋊C4—31no—
245C2×C22⋊C4—181no—
246#107—61no—
247#106—181no—
248#103—181no—
249#102—61no—
250C22⋊C8—31no—
251C22⋊C8—91no—
252#95—91no—
253#95—181no—
254C23×C3—21no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—41no—
258C23×C3—61no—
259C23×C3—61no—
260C23×C3—61no—
261C23×C3—121no—
262C23×C3—121no—
263C23×C3D3×D411yescharacteristic
264C23×C3C2×#6711yescharacteristic
265C22×D3—21no—
266C22×D3—21no—
267C22×D3—21no—
268C22×D3—41no—
269C22×D3—41no—
270C3×Q8—121no—
271C3×D4—41no—
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—41no—
277C3×D4—81no—
278C3×D4—81no—
279C3×D4—81no—
280C3×D4—241no—
281C3×D4—241no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—81no—
293C2×C3×C4—121no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4—241no—
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302#67—81no—
303#67—81no—
304C2×Dic3—21no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—81no—
312C2×Dic3—121no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—122no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—241no—
320C2×Dic3—241no—
321Dic6—41no—
322C3×C8—121no—
323C3⋊C8—41no—
324C3⋊C8—121no—
325C3⋊C8—121no—
326C3⋊C8—241no—
327C2×C32—21no—
328C2×C32—21no—
329C2×C32—81no—
330C2×C32#44911yescharacteristic
331C2×C32#45511yescharacteristic
332C2×C32#45811yescharacteristic
333C3×D3—81no—
334C24—31no—
335C2×Q8—31no—
336C2×D4—21no—
337C2×D4—61no—
338C2×D4—61no—
339C2×D4#62511yescharacteristic
340C22×C4—31no—
341C22×C4—61no—
342C22×C4—61no—
343C22×C4—181no—
344C22×C4C2×D3211yescharacteristic
345C2×C8—61no—
346C2×C8—181no—
347C4⋊C4—31no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—61no—
351C4⋊C4—61no—
352C4⋊C4#62511yescharacteristic
353C22⋊C4—21no—
354C22⋊C4—61no—
355C22⋊C4—61no—
356C22⋊C4—61no—
357C22⋊C4—61no—
358C22⋊C4—61no—
359C22⋊C4—61no—
360C22⋊C4—362no—
361C42—61no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—81no—
378C22×C3—81no—
379C22×C3—81no—
380C22×C3—122no—
381C22×C3—121no—
382C22×C3—121no—
383C22×C3—121no—
384C22×C3—241no—
385C22×C3#91111yescharacteristic
386C22×C3#91211yescharacteristic
387C22×C3#93711yescharacteristic
388C22×C3#94911yescharacteristic
389C22×C3#95011yescharacteristic
390C22×C3#95311yescharacteristic
391C2×D3—42no—
392C2×D3—41no—
393C2×D3—41no—
394C2×D3—41no—
395C2×D3—81no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—41no—
401C3×C4—41no—
402C3×C4—41no—
403C3×C4—41no—
404C3×C4—81no—
405C3×C4—121no—
406C3×C4—121no—
407C3×C4—121no—
408C3×C4—241no—
409Dic3—41no—
410Dic3—41no—
411Dic3—41no—
412Dic3—81no—
413Dic3—241no—
414Dic3—241no—
415Dic3—242no—
416C32#161211yescharacteristic, complemented, Sylow
417C23—21no—
418C23—61no—
419C23—61no—
420C23—61no—
421C23—121no—
422C23—121no—
423C23D3×#6711yescharacteristic
424Q8—121no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—241no—
429D4—241no—
430C2×C4—21no—
431C2×C4—41no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—121no—
436C2×C4—121no—
437C2×C4—121no—
438C2×C4—121no—
439C2×C4—241no—
440C2×C4—361no—
441C2×C4—361no—
442C2×C4—361no—
443C2×C4C2×#62511yescharacteristic
444C2×C4D3×#6711yescharacteristic
445C8—121no—
446C8—361no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—41no—
455C2×C3—41no—
456C2×C3—81no—
457C2×C3—81no—
458C2×C3—161no—
459C2×C3—241no—
460C2×C3#505311yescharacteristic
461C2×C3#515811yescharacteristic
462C2×C3#520211yescharacteristic
463C2×C3#523811yescharacteristic
464C2×C3#524211yescharacteristic
465C2×C3#524311yescharacteristic
466D3—81no—
467C22—21no—
468C22—21no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—122no—
473C22—121no—
474C22—121no—
475C22—121no—
476C22—241no—
477C22#6392511yescharacteristic
478C22#6393311yescharacteristic
479C22#6397611yescharacteristic
480C4—21no—
481C4—21no—
482C4—41no—
483C4—121no—
484C4—121no—
485C4—121no—
486C4—241no—
487C4—721no—
488C3—21no—
489C3#7116511yescharacteristic, complemented
490C3#7188211yescharacteristic, complemented
491C2—21no—
492C2—21no—
493C2—81no—
494C2—241no—
495C2#1059145011yescharacteristic
496C2#1059153311yescharacteristic
497C2#1059166411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32#120
prime radicalC3×#5617C2
hypercenter#121D32
hypocenterC32#1612
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C3×#5033C2semidirect
3. #10591314C2semidirect
4. #10591101C2semidirect
5. #10589403C2semidirect
6. #10589152C2semidirect
7. #10589145C2semidirect
33. #5033D3semidirect
416. C32#1612semidirect
489. C3#71165semidirect
490. C3#71882semidirect

Maximal subgroups

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

subgroupindex
C3×#56172
C3×#50332
#105913142
#105911012
#105894032
#105891522
#105891452
#718823
#711653