Finite Group Databasebeta

← #11778784

Subgroups — #11778784

Order 1152.

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

normal subgroups only

This group has 549 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
2#10592733C211yesmaximal, characteristic, complemented
3#10591226C211yesmaximal, characteristic, complemented
4#10591092C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#71875—31nomaximal
9#68299—31nomaximal
10C2×C3×#237—21no—
11C32×#121C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C3×#939—21no—
14C3×#939—21no—
15C3×#930C2211yescharacteristic
16C2×C3×Dic3⋊C4C2211yescharacteristic
17C3×#896—21no—
18C3×#884—21no—
19C3×#878—21no—
20#63659—21no—
21#63657C2211yescharacteristic
22#63635—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63579—21no—
26#63579—21no—
27#63573—21no—
28#63563—21no—
29C3×#537—31no—
30#5597D311yescharacteristic
31#5034—31no—
32#5034—31no—
33#5034—31no—
34#5034—61no—
35#4986—31no—
36#4735—31no—
37#4659—31no—
38C3×#327—31no—
39#4537—31no—
40#4537D311yescharacteristic, complemented
41#4528—31no—
42#4469—31no—
43#4451—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—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×#217—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—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—
86#939—21no—
87#939—21no—
88#930C2×D311yescharacteristic
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—61no—
92C2×Dic3⋊C4C2×D311yescharacteristic
93#896—21no—
94#884—21no—
95#878—21no—
96C3×C22⋊C8—31no—
97C3×#95—31no—
98#832—61no—
99#832—62no—
100#832—61no—
101#832—61no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106C3⋊#95C2×D311yescharacteristic
107#830—31no—
108#830—31no—
109#830—61no—
110#830C2×D311yescharacteristic
111#821—61no—
112#817—61no—
113#808—61no—
114#808—62no—
115#808—61no—
116#808—61no—
117C23×C32—21no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—21no—
120C32×D4—41no—
121C32×D4—41no—
122C32×D4—41no—
123C2×C32×C4—21no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—42no—
129C3×#67—42no—
130C3×#67—41no—
131C3×#67—41no—
132C3×#67—81no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—42no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3SD1612yes—
143C3×D12—41no—
144C3×C4×D3—42no—
145C3×Dic6—42no—
146C3⋊(C3⋊C8)—41no—
147C3×C3⋊C8—41no—
148#537—31no—
149#481—91no—
150#481—91no—
151#400—91no—
152#327—31no—
153#327—91no—
154#324—91no—
155C3×#41—122no—
156C3×#41—122no—
157C2×C3×Q8—61no—
158C2×C3×D4—21no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—31no—
162C2×C3×D4—41no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4D1211yescharacteristic
167C2×C3×D4#6711yescharacteristic
168C22×C3×C4—21no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—61no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C2×#67—21no—
177C2×#67—21no—
178C2×#67—21no—
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—121no—
184C22×Dic3#6711yescharacteristic
185C22×Dic3#6711yescharacteristic
186#237—42no—
187#237—42no—
188C2×D12#6711yescharacteristic
189C2×C4×D3—21no—
190C2×Dic6—21no—
191C2×C3×C8—61no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—31no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4D1211yescharacteristic
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—62no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—121no—
214C4⋊Dic3#6711yescharacteristic
215Dic3⋊C4—21no—
216Dic3⋊C4—21no—
217Dic3⋊C4—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—62no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—61no—
222C22×C32—21no—
223C22×C32—21no—
224C22×C32—41no—
225C22×C32—41no—
226C22×C32—41no—
227C22×C32#12011yescharacteristic
228C22×C32C2×SD1611yescharacteristic
229C22×C32AGL(1,ℤ/8)11yescharacteristic
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C32×C4—21no—
234C32×C4—21no—
235C32×C4—41no—
236C3⋊Dic3—81no—
237C3×Dic3—22no—
238C3×Dic3—41no—
239C3×Dic3—41no—
240C3×Dic3—81no—
241C2×#41—61no—
242C22⋊Q8—61no—
243C22⋊Q8—61no—
244#121—31no—
245#121—61no—
246#121—61no—
247#121—61no—
248#121D3211yescharacteristic
249C2×C4⋊C4—31no—
250C2×C4⋊C4—91no—
251#106—181no—
252#106—181no—
253#102—181no—
254#102—181no—
255C22⋊C8—31no—
256C22⋊C8—91no—
257#95—31no—
258#95—181no—
259#95—181no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—41no—
264C23×C3—61no—
265C23×C3D3×D411yescharacteristic
266C23×C3C2×#6711yescharacteristic
267C22×D3—21no—
268C3×Q8—122no—
269C3×D4—41no—
270C3×D4—41no—
271C3×D4—42no—
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—81no—
277C3×D4—81no—
278C3×D4—121no—
279C3×D4—122no—
280C3×D4—121no—
281C3×D4—121no—
282C3×D4—241no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—32no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—42no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—122no—
297C2×C3×C4—122no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306#67—42no—
307#67—41no—
308#67—41no—
309#67—81no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—42no—
315C2×Dic3—41no—
316C2×Dic3—41no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—242no—
325C2×Dic3#21412yes—
326D12—41no—
327C4×D3—42no—
328Dic6—42no—
329C3×C8—121no—
330C3⋊C8—41no—
331C3⋊C8—122no—
332C3⋊C8—121no—
333C3⋊C8—121no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32—81no—
337C2×C32#45011yescharacteristic
338C2×C32#45411yescharacteristic
339C2×C32#45811yescharacteristic
340C3×D3—81no—
341#41—122no—
342#41—122no—
343C2×Q8—61no—
344C2×D4—21no—
345C2×D4—31no—
346C2×D4—61no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4#62611yescharacteristic
350C22×C4—31no—
351C22×C4—31no—
352C22×C4—61no—
353C22×C4—61no—
354C22×C4—61no—
355C22×C4—181no—
356C22×C4C2×D3211yescharacteristic
357C2×C8—61no—
358C2×C8—181no—
359C4⋊C4—31no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—61no—
363C4⋊C4—181no—
364C4⋊C4—181no—
365C4⋊C4#62611yescharacteristic
366C22⋊C4—21no—
367C22⋊C4—61no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—41no—
385C22×C3—81no—
386C22×C3—81no—
387C22×C3—81no—
388C22×C3—121no—
389C22×C3—121no—
390C22×C3—121no—
391C22×C3#88211yescharacteristic
392C22×C3#91111yescharacteristic
393C22×C3D3×SD1611yescharacteristic
394C22×C3#93211yescharacteristic
395C22×C3C2×#21411yescharacteristic
396C22×C3#95311yescharacteristic
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—41no—
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—62no—
409C3×C4—81no—
410C3×C4—121no—
411C3×C4—121no—
412C3×C4—241no—
413Dic3—22no—
414Dic3—41no—
415Dic3—41no—
416Dic3—81no—
417Dic3—242no—
418Dic3—241no—
419Dic3—241no—
420C32#161611yescharacteristic, complemented, Sylow
421C23—21no—
422C23—61no—
423C23D3×#6711yescharacteristic
424Q8—122no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—121no—
429D4—122no—
430D4—121no—
431D4—121no—
432D4—241no—
433C2×C4—21no—
434C2×C4—32no—
435C2×C4—41no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—122no—
441C2×C4—122no—
442C2×C4—121no—
443C2×C4—121no—
444C2×C4—121no—
445C2×C4—121no—
446C2×C4—362no—
447C2×C4—361no—
448C2×C4C2×#62611yescharacteristic
449C2×C4D3×#6711yescharacteristic
450C8—121no—
451C8—361no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—41no—
460C2×C3—41no—
461C2×C3—81no—
462C2×C3—81no—
463C2×C3—161no—
464C2×C3—241no—
465C2×C3#474211yescharacteristic
466C2×C3#477611yescharacteristic
467C2×C3#482711yescharacteristic
468C2×C3#521811yescharacteristic
469C2×C3#524311yescharacteristic
470C2×C3#524511yescharacteristic
471D3—81no—
472C22—21no—
473C22—21no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—121no—
478C22—121no—
479C22—121no—
480C22D3×#21411yescharacteristic
481C22#6393211yescharacteristic
482C22#6397711yescharacteristic
483C4—21no—
484C4—21no—
485C4—41no—
486C4—62no—
487C4—121no—
488C4—121no—
489C4—241no—
490C4—721no—
491C3—21no—
492C3#6829911yescharacteristic, complemented
493C3#7187511yescharacteristic, complemented
494C2—21no—
495C2—21no—
496C2—81no—
497C2—241no—
498C2#1059145911yescharacteristic
499C2#1059153411yescharacteristic
500C2#1059168511yescharacteristic
subgroupG/H
centerC22#63977
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. #10592733C2semidirect
3. #10591226C2semidirect
4. #10591092C2semidirect
5. C3×#4537C2semidirect
6. #10589149C2semidirect
7. #10589147C2semidirect
40. #4537D3semidirect
420. C32#1616semidirect
492. C3#68299semidirect
493. C3#71875semidirect

Maximal subgroups

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

subgroupindex
C3×#55972
#105927332
#105912262
#105910922
C3×#45372
#105891492
#105891472
#718753
#682993