Finite Group Databasebeta

← #11778786

Subgroups — #11778786

Order 1152.

537 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 537 conjugacy classes of subgroups — too many to draw. Only its 88 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×#5597C211yesmaximal, characteristic
2C3×#5034C211yesmaximal, characteristic, complemented
3#10591225C211yesmaximal, characteristic, complemented
4#10591091C211yesmaximal, characteristic, complemented
5#10589403C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#71875—31nomaximal
9#71171—31nomaximal
10C2×C3×#237—21no—
11C32×#121C2211yescharacteristic
12C3×#939—21no—
13C3×#939—21no—
14C3×#930C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×Dic3⋊C4C2211yescharacteristic
17C3×#896—21no—
18C3×#884—21no—
19C3×#878—21no—
20#63658C2211yescharacteristic
21#63657C2211yescharacteristic
22C3×#832—21no—
23C3×#830C2211yescharacteristic
24C3×#808—21no—
25#63579—21no—
26#63579—21no—
27#63574—21no—
28#63562—21no—
29C3×#537—31no—
30#5597D311yescharacteristic
31C3×#481—31no—
32#5034—31no—
33#5034D311yescharacteristic, complemented
34#4986—31no—
35#4985—31no—
36#4968—31no—
37#4537—31no—
38#4537—31no—
39#4537—31no—
40#4537—61no—
41#4528—31no—
42#4470—31no—
43#4469—31no—
44C2×C32×D4—21no—
45C2×C32×D4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C3×#237—42no—
56C3×#237—42no—
57C2×C3×D12D411yescharacteristic
58C2×C3×C4×D3—21no—
59C2×C3×Dic6—21no—
60C32×C4⋊C4D411yescharacteristic
61C32×C22⋊C4—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C3×#217—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D411yescharacteristic
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—21no—
72C2×C3×C3⋊C8—21no—
73#1616—91noSylow
74C2×C3×#41—61no—
75C2×#237—21no—
76C3×C22⋊Q8—61no—
77C3×C22⋊Q8—61no—
78C3×#121—21no—
79C3×#121—31no—
80C3×#121—61no—
81C3×#121—61no—
82C3×#121—61no—
83C3×#121C2×D311yescharacteristic
84C3×#121C2×D311yescharacteristic
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—31no—
87#939—21no—
88#939—21no—
89#930C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×Dic3⋊C4C2×D311yescharacteristic
92#896—21no—
93#884—21no—
94#878—21no—
95C3×#106—61no—
96C3×#102—61no—
97C3×C22⋊C8—31no—
98#832—21no—
99#832—61no—
100C3⋊#95—31no—
101C3⋊#95—31no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107#830—31no—
108#830—31no—
109#830—61no—
110#830C2×D311yescharacteristic
111#809—61no—
112#808—21no—
113#808—61no—
114#808—61no—
115C23×C32—21no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C32×D4—41no—
119C32×D4—41no—
120C32×D4—41no—
121C2×C32×C4—21no—
122C2×C32×C4—41no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C3×#67—42no—
129C3×#67—41no—
130C3×#67—41no—
131C3×#67—81no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—42no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—42no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3SD1612yes—
141C3×D12—41no—
142C3×C4×D3—42no—
143C3×Dic6—42no—
144C3⋊(C3⋊C8)—41no—
145C3×C3⋊C8—41no—
146#537—31no—
147#481—31no—
148#481—91no—
149#400—91no—
150#327—91no—
151#327—91no—
152#324—91no—
153C3×#41—122no—
154C3×#41—122no—
155C2×C3×Q8—61no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—31no—
160C2×C3×D4—41no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4#6711yescharacteristic
165C2×C3×D4#6711yescharacteristic
166C22×C3×C4—21no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C2×#67—21no—
175C2×#67—21no—
176C2×#67—21no—
177C22×Dic3—21no—
178C22×Dic3—21no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C22×Dic3—121no—
182C22×Dic3#6711yescharacteristic
183C22×Dic3#6711yescharacteristic
184#237—42no—
185#237—42no—
186C2×D12#6711yescharacteristic
187C2×C4×D3—21no—
188C2×Dic6—21no—
189C2×C3×C8—61no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—31no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4#6711yescharacteristic
198C3×C4⋊C4#6711yescharacteristic
199C3×C22⋊C4—21no—
200C3×C22⋊C4—21no—
201C3×C22⋊C4—41no—
202C3×C22⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—61no—
205#217—21no—
206(C2×D3)⋊C4—21no—
207(C2×D3)⋊C4—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3—21no—
210C4⋊Dic3#6711yescharacteristic
211Dic3⋊C4—21no—
212Dic3⋊C4—21no—
213Dic3⋊C4—21no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—121no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32—41no—
221C22×C32—41no—
222C22×C32—41no—
223C22×C32#12011yescharacteristic
224C22×C32C2×SD1611yescharacteristic
225C22×C32AGL(1,ℤ/8)11yescharacteristic
226C2×C3×D3—41no—
227C2×C3×D3—41no—
228C2×C3×D3—41no—
229C32×C4—21no—
230C32×C4—21no—
231C32×C4—41no—
232C3⋊Dic3—81no—
233C3×Dic3—22no—
234C3×Dic3—41no—
235C3×Dic3—41no—
236C3×Dic3—81no—
237C2×#41—61no—
238C22⋊Q8—61no—
239C22⋊Q8—61no—
240#121—31no—
241#121—61no—
242#121—61no—
243#121—61no—
244#121D3211yescharacteristic
245C2×C4⋊C4—31no—
246C2×C4⋊C4—31no—
247#106—61no—
248#106—181no—
249#102—61no—
250#102—181no—
251C22⋊C8—31no—
252C22⋊C8—91no—
253#95—91no—
254#95—181no—
255#95—181no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—21no—
259C23×C3—41no—
260C23×C3—61no—
261C23×C3D3×D411yescharacteristic
262C23×C3C2×#6711yescharacteristic
263C22×D3—21no—
264C3×Q8—122no—
265C3×D4—41no—
266C3×D4—41no—
267C3×D4—41no—
268C3×D4—41no—
269C3×D4—41no—
270C3×D4—41no—
271C3×D4—81no—
272C3×D4—81no—
273C3×D4—81no—
274C3×D4—121no—
275C3×D4—122no—
276C3×D4—121no—
277C3×D4—121no—
278C3×D4—241no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—32no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—81no—
292C2×C3×C4—122no—
293C2×C3×C4—122no—
294C2×C3×C4—121no—
295C2×C3×C4—122no—
296C2×C3×C4—121no—
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301#67—42no—
302#67—41no—
303#67—41no—
304#67—81no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—42no—
310C2×Dic3—41no—
311C2×Dic3—42no—
312C2×Dic3—41no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—122no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—241no—
321C2×Dic3—241no—
322C2×Dic3#21412yes—
323D12—41no—
324C4×D3—42no—
325Dic6—42no—
326C3×C8—121no—
327C3⋊C8—41no—
328C3⋊C8—121no—
329C3⋊C8—121no—
330C3⋊C8—241no—
331C2×C32—21no—
332C2×C32—21no—
333C2×C32—81no—
334C2×C32#45011yescharacteristic
335C2×C32#45411yescharacteristic
336C2×C32#45811yescharacteristic
337C3×D3—81no—
338#41—122no—
339#41—122no—
340C2×Q8—61no—
341C2×D4—21no—
342C2×D4—31no—
343C2×D4—61no—
344C2×D4—61no—
345C2×D4—61no—
346C2×D4#62511yescharacteristic
347C22×C4—31no—
348C22×C4—31no—
349C22×C4—61no—
350C22×C4—61no—
351C22×C4—61no—
352C22×C4—181no—
353C22×C4C2×D3211yescharacteristic
354C2×C8—61no—
355C2×C8—181no—
356C4⋊C4—31no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4#62511yescharacteristic
363C22⋊C4—21no—
364C22⋊C4—61no—
365C22⋊C4—61no—
366C22⋊C4—61no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—81no—
383C22×C3—81no—
384C22×C3—81no—
385C22×C3—121no—
386C22×C3—121no—
387C22×C3—121no—
388C22×C3D3×SD1611yescharacteristic
389C22×C3#91411yescharacteristic
390C22×C3#93211yescharacteristic
391C22×C3C2×#21411yescharacteristic
392C22×C3#93711yescharacteristic
393C22×C3#95311yescharacteristic
394C2×D3—41no—
395C2×D3—41no—
396C2×D3—41no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—41no—
402C3×C4—41no—
403C3×C4—41no—
404C3×C4—41no—
405C3×C4—62no—
406C3×C4—81no—
407C3×C4—121no—
408C3×C4—121no—
409C3×C4—241no—
410Dic3—22no—
411Dic3—41no—
412Dic3—41no—
413Dic3—81no—
414Dic3—241no—
415Dic3—241no—
416Dic3—242no—
417C32#161611yescharacteristic, complemented, Sylow
418C23—21no—
419C23—61no—
420C23D3×#6711yescharacteristic
421Q8—122no—
422D4—41no—
423D4—41no—
424D4—41no—
425D4—121no—
426D4—122no—
427D4—121no—
428D4—121no—
429D4—241no—
430C2×C4—21no—
431C2×C4—32no—
432C2×C4—41no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—122no—
438C2×C4—122no—
439C2×C4—121no—
440C2×C4—122no—
441C2×C4—121no—
442C2×C4—361no—
443C2×C4—361no—
444C2×C4—361no—
445C2×C4C2×#62511yescharacteristic
446C2×C4D3×#6711yescharacteristic
447C8—121no—
448C8—361no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—41no—
457C2×C3—41no—
458C2×C3—81no—
459C2×C3—81no—
460C2×C3—161no—
461C2×C3—241no—
462C2×C3#505311yescharacteristic
463C2×C3#516911yescharacteristic
464C2×C3#520111yescharacteristic
465C2×C3#521811yescharacteristic
466C2×C3#524311yescharacteristic
467C2×C3#524511yescharacteristic
468D3—81no—
469C22—21no—
470C22—21no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—121no—
475C22—121no—
476C22—121no—
477C22D3×#21411yescharacteristic
478C22#6393411yescharacteristic
479C22#6397611yescharacteristic
480C4—21no—
481C4—21no—
482C4—41no—
483C4—62no—
484C4—121no—
485C4—121no—
486C4—241no—
487C4—721no—
488C3—21no—
489C3#7117111yescharacteristic, complemented
490C3#7187511yescharacteristic, complemented
491C2—21no—
492C2—21no—
493C2—81no—
494C2—241no—
495C2#1059145811yescharacteristic
496C2#1059153311yescharacteristic
497C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32#120
prime radicalC3×#5597C2
hypercenter#121D32
hypocenterC32#1616
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×#5034C2semidirect
3. #10591225C2semidirect
4. #10591091C2semidirect
5. #10589403C2semidirect
6. #10589150C2semidirect
7. #10589147C2semidirect
33. #5034D3semidirect
417. C32#1616semidirect
489. C3#71171semidirect
490. C3#71875semidirect

Maximal subgroups

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

subgroupindex
C3×#55972
C3×#50342
#105912252
#105910912
#105894032
#105891502
#105891472
#718753
#711713