Finite Group Databasebeta

← #11778630

Subgroups — #11778630

Order 1152.

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

normal subgroups only

This group has 521 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
2#10592732C211yesmaximal, characteristic, complemented
3#10591315C211yesmaximal, characteristic, complemented
4#10591126C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#71882—31nomaximal
9#68289—31nomaximal
10C32×#121C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C3×#939—21no—
13C3×#937—21no—
14C3×D4×Dic3—21no—
15C2×C3×(C2×D3)⋊C4C2211yescharacteristic
16C3×#924C2211yescharacteristic
17C3×#898—21no—
18C3×#886—21no—
19C3×#885—21no—
20C2×(C2×D3)⋊Dic3—21no—
21#63659—21no—
22#63657C2211yescharacteristic
23#63634—21no—
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26#63579—21no—
27#63573—21no—
28#63566—21no—
29C3×#538—31no—
30#5617D311yescharacteristic
31#5043—31no—
32#5033—31no—
33#5033—31no—
34#5033—61no—
35#4953—31no—
36#4721—31no—
37#4674—31no—
38C3×#327—31no—
39#4538—31no—
40#4537D311yescharacteristic, complemented
41#4525—31no—
42#4468—31no—
43#4452—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—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—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×C22⋊C4—31no—
84C2×#217—61no—
85#939—21no—
86#937—21no—
87D4×Dic3—21no—
88C2×(C2×D3)⋊C4—61no—
89C2×(C2×D3)⋊C4C2×D311yescharacteristic
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—61no—
93#924C2×D311yescharacteristic
94#898—21no—
95#886—21no—
96#885—21no—
97C3×C22⋊C8—31no—
98C3×#95—31no—
99#835—61no—
100#832—62no—
101#832—61no—
102#832—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95C2×D311yescharacteristic
106#830—31no—
107#830—31no—
108#830—61no—
109#830C2×D311yescharacteristic
110#817—61no—
111#816—61no—
112#808—61no—
113#807—62no—
114#807—61no—
115#807—61no—
116C23×C32—21no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C32×D4—41no—
124C32×D4—41no—
125C32×D4—41no—
126C2×C32×C4—21no—
127C2×C32×C4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C3×#67—81no—
134C3×#67—81no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—81no—
143C3×Dic6—41no—
144C3⋊(C3⋊C8)—41no—
145C3×C3⋊C8—41no—
146#538—31no—
147#483—91no—
148#480—91no—
149#397—91no—
150#328—91no—
151#327—31no—
152#323—91no—
153C24×C3—31no—
154C23×D3#6711yescharacteristic
155C2×C3×Q8—31no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—41no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4D1211yescharacteristic
163C2×C3×D4#6711yescharacteristic
164C22×C3×C4—21no—
165C22×C3×C4—31no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C2×#67—21no—
171C2×#67—21no—
172C22×Dic3—21no—
173C22×Dic3—21no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—121no—
177C22×Dic3#6711yescharacteristic
178C2×Dic6#6711yescharacteristic
179C2×C3×C8—61no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4D1211yescharacteristic
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—62no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—121no—
211C4⋊Dic3#6711yescharacteristic
212Dic3⋊C4—21no—
213C4×Dic3—21no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—62no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—61no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32—41no—
221C22×C32—41no—
222C22×C32—41no—
223C22×C32#12011yescharacteristic
224C22×C32#13511yescharacteristic
225C22×C32AGL(1,ℤ/8)11yescharacteristic
226C2×C3×D3—42no—
227C2×C3×D3—41no—
228C2×C3×D3—41no—
229C2×C3×D3—41no—
230C2×C3×D3—81no—
231C32×C4—21no—
232C32×C4—21no—
233C32×C4—41no—
234C3⋊Dic3—81no—
235C3×Dic3—41no—
236C3×Dic3—41no—
237C3×Dic3—41no—
238C3×Dic3—81no—
239#126—61no—
240#124—61no—
241#123—61no—
242C22⋊Q8—31no—
243#121—61no—
244#121D3211yescharacteristic
245#120—61no—
246C4×D4—61no—
247C2×C4⋊C4—91no—
248C2×C22⋊C4—31no—
249C2×C22⋊C4—181no—
250#107—181no—
251#106—181no—
252#103—181no—
253#102—181no—
254C22⋊C8—31no—
255C22⋊C8—91no—
256#95—31no—
257#95—181no—
258C23×C3—21no—
259C23×C3—21no—
260C23×C3—21no—
261C23×C3—41no—
262C23×C3—61no—
263C23×C3—61no—
264C23×C3—61no—
265C23×C3—121no—
266C23×C3—121no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C22×D3—21no—
270C22×D3—21no—
271C22×D3—21no—
272C22×D3—41no—
273C22×D3—41no—
274C3×Q8—121no—
275C3×D4—41no—
276C3×D4—41no—
277C3×D4—42no—
278C3×D4—41no—
279C3×D4—41no—
280C3×D4—41no—
281C3×D4—41no—
282C3×D4—81no—
283C3×D4—81no—
284C3×D4—241no—
285C3×D4—241no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—42no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—241no—
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306#67—81no—
307#67—81no—
308C2×Dic3—21no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—81no—
316C2×Dic3—122no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—241no—
324C2×Dic3—241no—
325Dic6—41no—
326C3×C8—121no—
327C3⋊C8—41no—
328C3⋊C8—122no—
329C3⋊C8—121no—
330C3⋊C8—121no—
331C2×C32—21no—
332C2×C32—21no—
333C2×C32—81no—
334C2×C32#44911yescharacteristic
335C2×C32#45511yescharacteristic
336C2×C32#45811yescharacteristic
337C3×D3—81no—
338C24—31no—
339C2×Q8—31no—
340C2×D4—21no—
341C2×D4—61no—
342C2×D4—61no—
343C2×D4#62611yescharacteristic
344C22×C4—31no—
345C22×C4—61no—
346C22×C4—61no—
347C22×C4—181no—
348C22×C4C2×D3211yescharacteristic
349C2×C8—61no—
350C2×C8—181no—
351C4⋊C4—31no—
352C4⋊C4—61no—
353C4⋊C4—61no—
354C4⋊C4—181no—
355C4⋊C4—181no—
356C4⋊C4#62611yescharacteristic
357C22⋊C4—21no—
358C22⋊C4—61no—
359C22⋊C4—61no—
360C22⋊C4—61no—
361C22⋊C4—61no—
362C22⋊C4—61no—
363C22⋊C4—61no—
364C22⋊C4—362no—
365C42—61no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—81no—
382C22×C3—81no—
383C22×C3—81no—
384C22×C3—122no—
385C22×C3—121no—
386C22×C3—121no—
387C22×C3—121no—
388C22×C3—241no—
389C22×C3#88211yescharacteristic
390C22×C3#91111yescharacteristic
391C22×C3#91611yescharacteristic
392C22×C3#94911yescharacteristic
393C22×C3#95011yescharacteristic
394C22×C3#95311yescharacteristic
395C2×D3—42no—
396C2×D3—41no—
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—81no—
400C3×C4—22no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—41no—
406C3×C4—41no—
407C3×C4—41no—
408C3×C4—81no—
409C3×C4—121no—
410C3×C4—121no—
411C3×C4—121no—
412C3×C4—241no—
413Dic3—41no—
414Dic3—41no—
415Dic3—41no—
416Dic3—81no—
417Dic3—242no—
418Dic3—241no—
419Dic3—241no—
420C32#161211yescharacteristic, complemented, Sylow
421C23—21no—
422C23—61no—
423C23—61no—
424C23—61no—
425C23—121no—
426C23—121no—
427C23D3×#6711yescharacteristic
428Q8—121no—
429D4—41no—
430D4—41no—
431D4—41no—
432D4—241no—
433D4—241no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—121no—
440C2×C4—121no—
441C2×C4—121no—
442C2×C4—121no—
443C2×C4—241no—
444C2×C4—361no—
445C2×C4—361no—
446C2×C4—361no—
447C2×C4C2×#62611yescharacteristic
448C2×C4D3×#6711yescharacteristic
449C8—121no—
450C8—361no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—41no—
459C2×C3—41no—
460C2×C3—81no—
461C2×C3—81no—
462C2×C3—161no—
463C2×C3—241no—
464C2×C3#474211yescharacteristic
465C2×C3#478111yescharacteristic
466C2×C3#482511yescharacteristic
467C2×C3#523811yescharacteristic
468C2×C3#524211yescharacteristic
469C2×C3#524311yescharacteristic
470D3—81no—
471C22—21no—
472C22—21no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—122no—
477C22—121no—
478C22—121no—
479C22—121no—
480C22—241no—
481C22#6392511yescharacteristic
482C22#6393511yescharacteristic
483C22#6397711yescharacteristic
484C4—21no—
485C4—21no—
486C4—41no—
487C4—121no—
488C4—121no—
489C4—121no—
490C4—241no—
491C4—721no—
492C3—21no—
493C3#6828911yescharacteristic, complemented
494C3#7188211yescharacteristic, complemented
495C2—21no—
496C2—21no—
497C2—81no—
498C2—241no—
499C2#1059145211yescharacteristic
500C2#1059153411yescharacteristic
501C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
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. #10592732C2semidirect
3. #10591315C2semidirect
4. #10591126C2semidirect
5. C3×#4537C2semidirect
6. #10589153C2semidirect
7. #10589145C2semidirect
40. #4537D3semidirect
420. C32#1612semidirect
493. C3#68289semidirect
494. C3#71882semidirect

Maximal subgroups

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

subgroupindex
C3×#56172
#105927322
#105913152
#105911262
C3×#45372
#105891532
#105891452
#718823
#682893