Finite Group Databasebeta

← #11778782

Subgroups — #11778782

Order 1152.

549 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 549 conjugacy classes of subgroups — too many to draw. Only its 82 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#10594911C211yesmaximal, characteristic
2#10592667C211yesmaximal, characteristic, complemented
3C3×#4985C211yesmaximal, characteristic, complemented
4C3×#4968C211yesmaximal, characteristic, complemented
5#10589151C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#71171—31nomaximal
9#69718—31nomaximal
10C2×#3804—21no—
11C2×C32×C4⋊C4C2211yescharacteristic
12#64139C2211yescharacteristic
13C3×#930C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15#63978—21no—
16#63910—21no—
17#63895—21no—
18#63893—21no—
19#63886—21no—
20#63657C2211yescharacteristic
21#63636—21no—
22#63635—21no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#809—21no—
28C3×#808—21no—
29#5597—31no—
30#5510—31no—
31C3×#481—31no—
32C3×#400—31no—
33#4985D311yescharacteristic, complemented
34#4968—31no—
35#4968—31no—
36#4968—61no—
37#4968D311yescharacteristic, complemented
38#4537—31no—
39#4528—31no—
40#4470—31no—
41#4469—31no—
42#4451—31no—
43#4451—31no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C3×D12D411yescharacteristic
53C2×#627—21no—
54C2×#626—21no—
55C2×#626—21no—
56C2×#624—21no—
57#3804—42no—
58#3804—42no—
59C2×D3×Dic3—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4—21no—
62#3752—21no—
63C4⋊(C3⋊Dic3)D411yescharacteristic
64C2×C3⋊(C3⋊C8)—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C2×C3×C3⋊C8—21no—
70Dic3⋊Dic3—21no—
71#3722—21no—
72(C2×D3)⋊Dic3—21no—
73#1616—91noSylow
74C2×#237—61no—
75C2×#235—61no—
76C3×#121—31no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—31no—
79C2×C3×C4⋊C4C2×D311yescharacteristic
80C2×C3×C4⋊C4C2×D311yescharacteristic
81#939—61no—
82#939—61no—
83#930—31no—
84#930—31no—
85#930—61no—
86#930—61no—
87#930C2×D311yescharacteristic
88C2×Dic3⋊C4C2×D311yescharacteristic
89#897—61no—
90#897—61no—
91#896—61no—
92#895—61no—
93#895—61no—
94#884—61no—
95#878—61no—
96C3×#106—61no—
97C3×#102—61no—
98C3×C22⋊C8—31no—
99C3×#95—31no—
100C3×#95—61no—
101C3×#95—61no—
102C3⋊#95—21no—
103C3⋊#95—21no—
104C3⋊#95C2×D311yescharacteristic
105#830—31no—
106#830—31no—
107#830—61no—
108#830C2×D311yescharacteristic
109#809—21no—
110#809—61no—
111#809—61no—
112#809—62no—
113#808—21no—
114#808—61no—
115#808—61no—
116#808—62no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—21no—
119C22×C3×D3—21no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4—42no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125#638—41no—
126#638—41no—
127C2×C3⋊Dic3—21no—
128C4⋊(C3⋊D3)—41no—
129C3×#67—41no—
130C3×#67—41no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3SD1612yes—
140C3×D12—41no—
141#627—42no—
142#626—42no—
143#626—81no—
144#624—42no—
145D3×Dic3—42no—
146C3⋊(C3⋊C8)—41no—
147C3×C3⋊C8—41no—
148#537—91no—
149#481—31no—
150#481—91no—
151#400—31no—
152#327—91no—
153#327—91no—
154#324—91no—
155C2×C3×D4—31no—
156C2×C3×D4—61no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—31no—
161C22×C3×C4—31no—
162C22×C3×C4—41no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C2×#67—21no—
167C2×#67—61no—
168C2×#67—61no—
169C2×#67—61no—
170C2×#67—61no—
171C2×#67—121no—
172C22×Dic3—21no—
173C22×Dic3—61no—
174C22×Dic3#6711yescharacteristic
175C22×Dic3#6711yescharacteristic
176#237—122no—
177#237—122no—
178#235—122no—
179#235—122no—
180C2×D12—31no—
181C2×D12—31no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12#6711yescharacteristic
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×Dic6—61no—
190C2×Dic6—61no—
191C2×C3×C8—61no—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—31no—
198C3×C4⋊C4—41no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C22⋊C4—61no—
202#217—61no—
203(C2×D3)⋊C4—21no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—121no—
210C4⋊Dic3—31no—
211C4⋊Dic3—31no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3#6711yescharacteristic
215Dic3⋊C4—21no—
216Dic3⋊C4—21no—
217Dic3⋊C4—61no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—62no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—61no—
222C22×C32—21no—
223C22×C32—21no—
224C22×C32#12011yescharacteristic
225C22×C32C2×SD1611yescharacteristic
226C22×C32AGL(1,ℤ/8)11yescharacteristic
227C2×C3⋊D3—41no—
228C2×C3⋊D3—41no—
229C2×C3⋊D3—41no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C32×C4—21no—
234C32×C4—21no—
235C32×C4—81no—
236C3⋊Dic3—41no—
237C3×Dic3—22no—
238C3×Dic3—41no—
239C3×Dic3—41no—
240C3×Dic3—81no—
241C2×#41—181no—
242C22⋊Q8—181no—
243C22⋊Q8—181no—
244#121—31no—
245#121—91no—
246#121—181no—
247#121—181no—
248#121—181no—
249C2×C4⋊C4—31no—
250C2×C4⋊C4D3211yescharacteristic
251#106—61no—
252#106—181no—
253#102—61no—
254#102—181no—
255C22⋊C8—31no—
256C22⋊C8—91no—
257#95—31no—
258#95—61no—
259#95—61no—
260C23×C3—21no—
261C23×C3—61no—
262C23×C3D3×D411yescharacteristic
263C23×C3C2×#6711yescharacteristic
264C22×D3—21no—
265C22×D3—61no—
266C22×D3—61no—
267C22×D3—121no—
268C3×D4—121no—
269C3×D4—121no—
270C3×D4—121no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—32no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—42no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—82no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295#67—41no—
296#67—41no—
297#67—122no—
298#67—121no—
299#67—121no—
300#67—121no—
301#67—121no—
302#67—241no—
303#67—241no—
304#67—241no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—121no—
316C2×Dic3—122no—
317C2×Dic3#21512yes—
318D12—41no—
319D12—121no—
320D12—121no—
321D12—122no—
322D12—122no—
323D12—241no—
324C4×D3—122no—
325C4×D3—122no—
326C4×D3—122no—
327Dic6—122no—
328Dic6—122no—
329C3×C8—121no—
330C3⋊C8—41no—
331C3⋊C8—122no—
332C3⋊C8—121no—
333C3⋊C8—121no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32#45011yescharacteristic
337C2×C32#45411yescharacteristic
338C2×C32#45811yescharacteristic
339C3⋊D3—81no—
340C3×D3—81no—
341#41—362no—
342#41—362no—
343C2×Q8—181no—
344C2×D4—31no—
345C2×D4—61no—
346C2×D4—91no—
347C2×D4—181no—
348C2×D4—181no—
349C2×D4—181no—
350C22×C4—21no—
351C22×C4—31no—
352C22×C4—31no—
353C22×C4—61no—
354C22×C4—181no—
355C22×C4—181no—
356C22×C4C2×D3211yescharacteristic
357C2×C8—61no—
358C2×C8—181no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—31no—
362C4⋊C4—61no—
363C4⋊C4—61no—
364C4⋊C4—91no—
365C4⋊C4—181no—
366C22⋊C4—61no—
367C22⋊C4—181no—
368C22⋊C4—181no—
369C22⋊C4—181no—
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—121no—
380C22×C3—121no—
381C22×C3—121no—
382C22×C3D3×SD1611yescharacteristic
383C22×C3#91411yescharacteristic
384C22×C3#93711yescharacteristic
385C22×C3#93711yescharacteristic
386C22×C3C2×#21511yescharacteristic
387C22×C3#94911yescharacteristic
388C2×D3—41no—
389C2×D3—41no—
390C2×D3—41no—
391C2×D3—121no—
392C2×D3—121no—
393C2×D3—121no—
394C2×D3—121no—
395C2×D3—121no—
396C2×D3—121no—
397C2×D3—241no—
398C2×D3—241no—
399C2×D3—241no—
400C3×C4—22no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—41no—
406C3×C4—62no—
407C3×C4—82no—
408C3×C4—81no—
409C3×C4—81no—
410C3×C4—121no—
411C3×C4—121no—
412C3×C4—241no—
413Dic3—22no—
414Dic3—41no—
415Dic3—41no—
416Dic3—81no—
417Dic3—121no—
418Dic3—121no—
419Dic3—241no—
420C32#161611yescharacteristic, complemented, Sylow
421C23—61no—
422C23—181no—
423C23D3×#6711yescharacteristic
424Q8—362no—
425D4—121no—
426D4—121no—
427D4—121no—
428D4—361no—
429D4—362no—
430D4—361no—
431D4—361no—
432D4—721no—
433C2×C4—32no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—121no—
442C2×C4—121no—
443C2×C4—121no—
444C2×C4—121no—
445C2×C4—181no—
446C2×C4—362no—
447C2×C4—362no—
448C2×C4D3×#6711yescharacteristic
449C2×C4#381111yescharacteristic
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—241no—
462C2×C3#504611yescharacteristic
463C2×C3#505311yescharacteristic
464C2×C3#505311yescharacteristic
465C2×C3#506211yescharacteristic
466C2×C3#516911yescharacteristic
467C2×C3#520111yescharacteristic
468D3—81no—
469D3—241no—
470D3—241no—
471D3—481no—
472C22—21no—
473C22—21no—
474C22—121no—
475C22—121no—
476C22—121no—
477C22—361no—
478C22—361no—
479C22—361no—
480C22D3×#21511yescharacteristic
481C22#6393911yescharacteristic
482C22#6398311yescharacteristic
483C4—21no—
484C4—21no—
485C4—62no—
486C4—81no—
487C4—121no—
488C4—121no—
489C4—241no—
490C4—361no—
491C3—21no—
492C3#6971811yescharacteristic, complemented
493C3#7117111yescharacteristic, complemented
494C2—21no—
495C2—21no—
496C2—241no—
497C2—721no—
498C2#1059139811yescharacteristic
499C2#1059152511yescharacteristic
500C2#1059165111yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radical#10594911C2
hypercenterC2×C4⋊C4D32
hypocenterC32#1616
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592667C2semidirect
3. C3×#4985C2semidirect
4. C3×#4968C2semidirect
5. #10589151C2semidirect
6. #10589149C2semidirect
7. #10589147C2semidirect
33. #4985D3semidirect
37. #4968D3semidirect
420. C32#1616semidirect
492. C3#69718semidirect
493. C3#71171semidirect

Maximal subgroups

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

subgroupindex
#105949112
#105926672
C3×#49852
C3×#49682
#105891512
#105891492
#105891472
#711713
#697183