Finite Group Databasebeta

← #11778791

Subgroups — #11778791

Order 1152.

531 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 531 conjugacy classes of subgroups — too many to draw. Only its 80 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
1#10594930C211yesmaximal, characteristic
2C3×#4735C211yesmaximal, characteristic, complemented
3#10591227C211yesmaximal, characteristic, complemented
4#10591091C211yesmaximal, characteristic, complemented
5#10589335C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#71171—31nomaximal
9#68299—31nomaximal
10C2×#3805—21no—
11C2×#3750C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C3×#930C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15#63980—21no—
16#63899—21no—
17#63899—21no—
18#63885—21no—
19#63885—21no—
20C32×C22⋊C8C2211yescharacteristic
21#63657C2211yescharacteristic
22C3×C3⋊#95C2211yescharacteristic
23C3×#821—21no—
24C3×#817—21no—
25#63579—21no—
26#63579—21no—
27#63574—21no—
28#63562—21no—
29#5597—31no—
30#5597—31no—
31C3×#481—31no—
32#5034—31no—
33#4985—31no—
34#4968—31no—
35#4735D311yescharacteristic, complemented
36#4659—31no—
37C3×#327—31no—
38#4537—31no—
39#4470D311yescharacteristic, complemented
40#4469—31no—
41#4469—31no—
42#4469—61no—
43#4451—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C2×C3×D12D411yescharacteristic
52C2×C3×D12D411yescharacteristic
53C2×#627—21no—
54C2×#625—21no—
55C2×#625—21no—
56#3805—42no—
57#3805—42no—
58C2×D3×Dic3—21no—
59C2×D3×Dic3—21no—
60C2×C32×C8—21no—
61#3750—21no—
62#3750—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D411yescharacteristic
69C3×C4⋊Dic3D411yescharacteristic
70#3724—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73#1616—91noSylow
74C2×#237—61no—
75C2×#237—61no—
76C3×#121—31no—
77C3×#121—31no—
78C2×C3×C4⋊C4—31no—
79#939—61no—
80#939—61no—
81#939—61no—
82#939—61no—
83#930C2×D311yescharacteristic
84#930C2×D311yescharacteristic
85C2×C4⋊Dic3C2×D311yescharacteristic
86C2×Dic3⋊C4—31no—
87C2×Dic3⋊C4—31no—
88C2×Dic3⋊C4—61no—
89#896—61no—
90#896—61no—
91#884—61no—
92#884—61no—
93#878—61no—
94#878—61no—
95C3×#106—61no—
96C3×#102—61no—
97C3×C22⋊C8—21no—
98C3×C22⋊C8C2×D311yescharacteristic
99C3×C22⋊C8C2×D311yescharacteristic
100C3×#95—31no—
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#821—21no—
111#817—21no—
112#809—61no—
113#808—61no—
114#808—61no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C22×C3×D3—21no—
118C2×C32×C4—41no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3SD1612yes—
126C3×#67—41no—
127C3×#67—41no—
128C3×#67—41no—
129C3×#67—41no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C3×D12—41no—
138C3×D12—41no—
139#627—42no—
140#625—42no—
141#625—81no—
142D3×Dic3—42no—
143D3×Dic3—42no—
144C32×C8—41no—
145C3⋊(C3⋊C8)—41no—
146#537—91no—
147#481—31no—
148#481—91no—
149#400—91no—
150#327—31no—
151#327—91no—
152#324—91no—
153C2×C3×D4—31no—
154C2×C3×D4—31no—
155C2×C3×D4—61no—
156C2×C3×D4—61no—
157C22×C3×C4—21no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—21no—
163C2×#67—21no—
164C2×#67—61no—
165C2×#67—61no—
166C2×#67—61no—
167C2×#67—61no—
168C22×Dic3—21no—
169C22×Dic3—21no—
170C22×Dic3—31no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178#237—122no—
179#237—122no—
180#237—122no—
181#237—122no—
182C2×D12D1211yescharacteristic
183C2×D12#6711yescharacteristic
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×Dic6—61no—
187C2×Dic6—61no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—41no—
191C3×C4⋊C4—31no—
192C3×C4⋊C4—31no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—61no—
197#217—61no—
198#217—61no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—61no—
202(C2×D3)⋊C4—61no—
203C4⋊Dic3—21no—
204C4⋊Dic3—21no—
205C4⋊Dic3D1211yescharacteristic
206C4⋊Dic3#6711yescharacteristic
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—121no—
214Dic3⋊C4—121no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—121no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32#12011yescharacteristic
221C22×C32C2×SD1611yescharacteristic
222C22×C32AGL(1,ℤ/8)11yescharacteristic
223C2×C3×D3—41no—
224C2×C3×D3—41no—
225C2×C3×D3—41no—
226C2×C3×D3—41no—
227C2×C3×D3—41no—
228C2×C3×D3—41no—
229C32×C4—21no—
230C32×C4—21no—
231C3⋊Dic3—22no—
232C3⋊Dic3—41no—
233C3×Dic3—41no—
234C3×Dic3—41no—
235C3×Dic3—81no—
236C3×Dic3—81no—
237C2×#41—181no—
238C22⋊Q8—181no—
239C22⋊Q8—181no—
240#121—31no—
241#121—31no—
242#121—181no—
243#121—181no—
244#121—181no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—91no—
247#106—61no—
248#106—181no—
249#102—61no—
250#102—181no—
251C22⋊C8—91no—
252C22⋊C8D3211yescharacteristic
253#95—31no—
254#95—181no—
255#95—181no—
256C23×C3—21no—
257C23×C3—61no—
258C23×C3—61no—
259C23×C3D3×D411yescharacteristic
260C23×C3D3×D411yescharacteristic
261C22×D3—21no—
262C22×D3—21no—
263C3×D4—121no—
264C3×D4—121no—
265C3×D4—121no—
266C3×D4—121no—
267C3×D4—121no—
268C3×D4—121no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—81no—
276C2×C3×C4—121no—
277C2×C3×C4—121no—
278C2×C3×C4—122no—
279C2×C3×C4—121no—
280C2×C3×C4—121no—
281C2×C3×C4C2×D1211yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285#67—41no—
286#67—41no—
287#67—41no—
288#67—41no—
289#67—122no—
290#67—122no—
291#67—241no—
292#67—241no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—32no—
296C2×Dic3—32no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—42no—
300C2×Dic3—41no—
301C2×Dic3—41no—
302C2×Dic3—62no—
303C2×Dic3—61no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—121no—
310C2×Dic3—121no—
311C2×Dic3—121no—
312C2×Dic3—122no—
313C2×Dic3—122no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—241no—
317D12—41no—
318D12—41no—
319C4×D3—122no—
320C4×D3—122no—
321Dic6—122no—
322Dic6—122no—
323C3×C8—41no—
324C3×C8—41no—
325C3×C8—81no—
326C3⋊C8—121no—
327C3⋊C8—121no—
328C3⋊C8—241no—
329C2×C32—21no—
330C2×C32—21no—
331C2×C32#45011yescharacteristic
332C2×C32#45411yescharacteristic
333C2×C32#45811yescharacteristic
334C3×D3—81no—
335C3×D3—81no—
336#41—362no—
337#41—362no—
338C2×Q8—181no—
339C2×D4—31no—
340C2×D4—31no—
341C2×D4—61no—
342C2×D4—61no—
343C2×D4—181no—
344C2×D4—181no—
345C22×C4—61no—
346C22×C4—61no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—181no—
350C22×C4—181no—
351C22×C4C2×D3211yescharacteristic
352C2×C8—21no—
353C2×C8—181no—
354C4⋊C4—31no—
355C4⋊C4—31no—
356C4⋊C4—61no—
357C4⋊C4—61no—
358C4⋊C4—181no—
359C4⋊C4—181no—
360C4⋊C4—181no—
361C22⋊C4—61no—
362C22⋊C4—61no—
363C22⋊C4—181no—
364C22⋊C4—181no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—121no—
375C22×C3—121no—
376C22×C3—121no—
377C22×C3—121no—
378C22×C3—121no—
379C22×C3—121no—
380C22×C3#88211yescharacteristic
381C22×C3#91111yescharacteristic
382C22×C3D3×SD1611yescharacteristic
383C22×C3D3×SD1611yescharacteristic
384C22×C3#91411yescharacteristic
385C22×C3#93711yescharacteristic
386C2×D3—41no—
387C2×D3—41no—
388C2×D3—41no—
389C2×D3—41no—
390C2×D3—41no—
391C2×D3—41no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—41no—
397C3×C4—41no—
398C3×C4—121no—
399C3×C4—121no—
400C3×C4—241no—
401C3×C4—241no—
402Dic3—41no—
403Dic3—41no—
404Dic3—62no—
405Dic3—62no—
406Dic3—81no—
407Dic3—81no—
408Dic3—122no—
409Dic3—121no—
410Dic3—121no—
411Dic3—241no—
412C32#161611yescharacteristic, complemented, Sylow
413C23—61no—
414C23—61no—
415C23#380211yescharacteristic
416Q8—362no—
417D4—121no—
418D4—121no—
419D4—121no—
420D4—121no—
421D4—121no—
422D4—121no—
423D4—362no—
424D4—721no—
425C2×C4—41no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—92no—
429C2×C4—121no—
430C2×C4—121no—
431C2×C4—122no—
432C2×C4—121no—
433C2×C4—121no—
434C2×C4—181no—
435C2×C4—181no—
436C2×C4—181no—
437C2×C4—362no—
438C2×C4—362no—
439C2×C4—361no—
440C2×C4D3×D1211yescharacteristic
441C2×C4D3×#6711yescharacteristic
442C8—41no—
443C8—361no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—41no—
452C2×C3—41no—
453C2×C3—241no—
454C2×C3—241no—
455C2×C3#474211yescharacteristic
456C2×C3#477611yescharacteristic
457C2×C3#482711yescharacteristic
458C2×C3#505311yescharacteristic
459C2×C3#516911yescharacteristic
460C2×C3#520111yescharacteristic
461D3—81no—
462D3—81no—
463C22—21no—
464C22—21no—
465C22—121no—
466C22—121no—
467C22—121no—
468C22—121no—
469C22—121no—
470C22—121no—
471C22#6379611yescharacteristic
472C22#6379811yescharacteristic
473C22#6392211yescharacteristic
474C4—21no—
475C4—21no—
476C4—121no—
477C4—121no—
478C4—182no—
479C4—241no—
480C4—241no—
481C4—361no—
482C3—21no—
483C3#6829911yescharacteristic, complemented
484C3#7117111yescharacteristic, complemented
485C2—21no—
486C2—21no—
487C2—241no—
488C2—241no—
489C2#1059040811yescharacteristic
490C2#1059094311yescharacteristic
491C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10594930C2
hypercenterC22⋊C8D32
hypocenterC32#1616
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4735C2semidirect
3. #10591227C2semidirect
4. #10591091C2semidirect
5. #10589335C2semidirect
6. C3×#4470C2semidirect
7. #10589149C2semidirect
35. #4735D3semidirect
39. #4470D3semidirect
412. C32#1616semidirect
483. C3#68299semidirect
484. C3#71171semidirect

Maximal subgroups

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

subgroupindex
#105949302
C3×#47352
#105912272
#105910912
#105893352
C3×#44702
#105891492
#711713
#682993