Finite Group Databasebeta

← #11778640

Subgroups — #11778640

Order 1152.

549 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 549 conjugacy classes of subgroups — too many to draw. Only its 78 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#10594979C211yesmaximal, characteristic
2#10592373C211yesmaximal, characteristic, complemented
3#10591126C211yesmaximal, characteristic, complemented
4#10591094C211yesmaximal, characteristic, complemented
5C3×#4452C211yesmaximal, characteristic, complemented
6C3×#4451C211yesmaximal, characteristic, complemented
7#10589146C211yesmaximal, characteristic, complemented
8#68321—31nomaximal
9#68289—31nomaximal
10C2×#3752—21no—
11C2×#3752C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C3×#930C2211yescharacteristic
14C3×#924C2211yescharacteristic
15#63981—21no—
16#67⋊Dic3—21no—
17#63907—21no—
18#63890—21no—
19#63886—21no—
20#63848—21no—
21C32×#95C2211yescharacteristic
22#63658—21no—
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63566—21no—
28#63563—21no—
29#5644—31no—
30#5617—31no—
31#5043—31no—
32#5033—31no—
33#4736—31no—
34#4721—31no—
35#4674—31no—
36#4674—31no—
37#4674—61no—
38C3×#328—31no—
39C3×#327—31no—
40#4468—31no—
41#4468—31no—
42#4452D311yescharacteristic, complemented
43#4451D311yescharacteristic, complemented
44C23×C3⋊D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C2×C3×#67—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×Dic6D411yescharacteristic
52C2×#626—21no—
53C2×#626—21no—
54C2×D3×Dic3—21no—
55#3752—21no—
56#3752—21no—
57#3752—42no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)—21no—
60C3×#217—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67Dic3⋊Dic3—21no—
68#3722—21no—
69#3722—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72#1612—91noSylow
73C3×C22⋊Q8—31no—
74C3×#121—31no—
75#947—61no—
76#939—61no—
77#937—61no—
78D4×Dic3—61no—
79#930C2×D311yescharacteristic
80C2×(C2×D3)⋊C4—31no—
81C2×(C2×D3)⋊C4—31no—
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—61no—
84C2×(C2×D3)⋊C4—61no—
85C2×(C2×D3)⋊C4—62no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—61no—
89#924C2×D311yescharacteristic
90#898—61no—
91#898—61no—
92#895—61no—
93#894—61no—
94#886—61no—
95#885—61no—
96#882—61no—
97#67⋊C4—61no—
98C3×C22⋊C8—31no—
99C3×C22⋊C8—31no—
100C3×#95—21no—
101C3×#95C2×D311yescharacteristic
102C3×#95C2×D311yescharacteristic
103#835—61no—
104#832—61no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107C3⋊#95—62no—
108#830C2×D311yescharacteristic
109#830C2×D311yescharacteristic
110#821—61no—
111#818—61no—
112#817—61no—
113#816—61no—
114#808—61no—
115#807—61no—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3⋊D3—21no—
119C22×C3⋊D3—21no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—41no—
122C22×C3×D3—21no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C3×#67—41no—
135C3×#67—41no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C3×D12—41no—
140C3×Dic6—41no—
141#626—81no—
142#626—81no—
143D3×Dic3—81no—
144C3×C3⋊C8—41no—
145C3×C3⋊C8—41no—
146#538—91no—
147#483—91no—
148#480—91no—
149#397—91no—
150#328—31no—
151#327—31no—
152#323—91no—
153C23×D3—31no—
154C23×D3—31no—
155C23×D3—61no—
156C2×C3×Q8—31no—
157C2×C3×D4—31no—
158C2×C3×D4—61no—
159C22×C3×C4—22no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—21no—
166C2×#67—61no—
167C2×#67—61no—
168C22×Dic3—31no—
169C22×Dic3—31no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—62no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C2×D12—61no—
176C2×D12—61no—
177C2×D12D1211yescharacteristic
178C2×C4×D3—61no—
179C2×Dic6D1211yescharacteristic
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—31no—
184C3×C4⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187#217—21no—
188#217—61no—
189(C2×D3)⋊C4—21no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—61no—
199(C2×D3)⋊C4—121no—
200(C2×D3)⋊C4—121no—
201(C2×D3)⋊C4—124no—
202(C2×D3)⋊C4—122no—
203(C2×D3)⋊C4—122no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—121no—
210C4⋊Dic3—121no—
211C4⋊Dic3D1211yescharacteristic
212C4⋊Dic3D1211yescharacteristic
213Dic3⋊C4—21no—
214Dic3⋊C4—61no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C22×C32—21no—
220C22×C32—21no—
221C22×C32#12011yescharacteristic
222C22×C32#13511yescharacteristic
223C22×C32AGL(1,ℤ/8)11yescharacteristic
224C2×C3⋊D3—42no—
225C2×C3⋊D3—41no—
226C2×C3⋊D3—41no—
227C2×C3⋊D3—41no—
228C2×C3⋊D3—81no—
229C2×C3×D3—41no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C32×C4—21no—
233C32×C4—21no—
234C32×C4—81no—
235C3⋊Dic3—41no—
236C3⋊Dic3—81no—
237C3×Dic3—41no—
238C3×Dic3—41no—
239C3×Dic3—41no—
240#126—181no—
241#124—181no—
242#123—181no—
243C22⋊Q8—31no—
244#121—31no—
245#121—181no—
246#120—181no—
247C4×D4—181no—
248C2×C4⋊C4—91no—
249C2×C22⋊C4—91no—
250C2×C22⋊C4—181no—
251#107—181no—
252#106—181no—
253#103—181no—
254#102—181no—
255C22⋊C8—31no—
256C22⋊C8—31no—
257#95—181no—
258#95D3211yescharacteristic
259C23×C3—21no—
260C23×C3—61no—
261C23×C3D3×D411yescharacteristic
262C23×C3D3×D411yescharacteristic
263C22×D3—21no—
264C22×D3—62no—
265C22×D3—61no—
266C22×D3—61no—
267C22×D3—61no—
268C22×D3—61no—
269C22×D3—61no—
270C22×D3—61no—
271C22×D3—121no—
272C22×D3—121no—
273C22×D3—121no—
274C22×D3—121no—
275C22×D3—121no—
276C22×D3—121no—
277C22×D3—122no—
278C22×D3—122no—
279C3×Q8—121no—
280C3×D4—121no—
281C3×D4—121no—
282C3×D4—121no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—61no—
300C2×C3×C4C2×D1211yescharacteristic
301C2×C3×C4C2×D1211yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304#67—41no—
305#67—41no—
306#67—241no—
307#67—241no—
308C2×Dic3—21no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—122no—
317C2×Dic3—122no—
318C2×Dic3—122no—
319C2×Dic3—122no—
320C2×Dic3—121no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—241no—
327D12—41no—
328D12—241no—
329D12—241no—
330C4×D3—241no—
331Dic6—41no—
332C3×C8—121no—
333C3×C8—121no—
334C3⋊C8—41no—
335C3⋊C8—41no—
336C2×C32—21no—
337C2×C32—21no—
338C2×C32#44911yescharacteristic
339C2×C32#45511yescharacteristic
340C2×C32#45811yescharacteristic
341C3⋊D3—81no—
342C3×D3—81no—
343C24—91no—
344C2×Q8—31no—
345C2×D4—31no—
346C2×D4—61no—
347C2×D4—181no—
348C2×D4—181no—
349C22×C4—21no—
350C22×C4—91no—
351C22×C4—181no—
352C22×C4—181no—
353C22×C4C2×D3211yescharacteristic
354C2×C8—61no—
355C2×C8—61no—
356C4⋊C4—31no—
357C4⋊C4—31no—
358C4⋊C4—61no—
359C4⋊C4—181no—
360C4⋊C4—181no—
361C4⋊C4—181no—
362C22⋊C4—61no—
363C22⋊C4—61no—
364C22⋊C4—181no—
365C22⋊C4—181no—
366C22⋊C4—181no—
367C22⋊C4—181no—
368C22⋊C4—181no—
369C22⋊C4—362no—
370C42—181no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—121no—
381C22×C3—121no—
382C22×C3—121no—
383C22×C3#88211yescharacteristic
384C22×C3#88211yescharacteristic
385C22×C3#91111yescharacteristic
386C22×C3#91411yescharacteristic
387C22×C3#91611yescharacteristic
388C22×C3#91911yescharacteristic
389C2×D3—41no—
390C2×D3—41no—
391C2×D3—41no—
392C2×D3—124no—
393C2×D3—122no—
394C2×D3—122no—
395C2×D3—122no—
396C2×D3—121no—
397C2×D3—121no—
398C2×D3—121no—
399C2×D3—121no—
400C2×D3—121no—
401C2×D3—121no—
402C2×D3—241no—
403C2×D3—241no—
404C2×D3—242no—
405C2×D3—241no—
406C2×D3—241no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—82no—
414C3×C4—81no—
415C3×C4—81no—
416C3×C4—121no—
417C3×C4—121no—
418C3×C4—121no—
419Dic3—41no—
420Dic3—41no—
421Dic3—41no—
422Dic3—121no—
423Dic3—121no—
424Dic3—241no—
425Dic3—242no—
426Dic3—241no—
427Dic3—241no—
428C32#161211yescharacteristic, complemented, Sylow
429C23—61no—
430C23—181no—
431C23—181no—
432C23—181no—
433C23—361no—
434C23—361no—
435C23#381111yescharacteristic
436Q8—121no—
437D4—121no—
438D4—121no—
439D4—121no—
440D4—721no—
441D4—721no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—181no—
450C2×C4—361no—
451C2×C4—361no—
452C2×C4—361no—
453C2×C4—361no—
454C2×C4—721no—
455C2×C4D3×D1211yescharacteristic
456C2×C4D3×D1211yescharacteristic
457C8—121no—
458C8—121no—
459C2×C3—22no—
460C2×C3—22no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—241no—
469C2×C3#474211yescharacteristic
470C2×C3#474211yescharacteristic
471C2×C3#478111yescharacteristic
472C2×C3#481011yescharacteristic
473C2×C3#482511yescharacteristic
474C2×C3#482511yescharacteristic
475D3—81no—
476D3—242no—
477D3—241no—
478D3—241no—
479C22—21no—
480C22—21no—
481C22—121no—
482C22—121no—
483C22—121no—
484C22—362no—
485C22—361no—
486C22—361no—
487C22—361no—
488C22—721no—
489C22#6392311yescharacteristic
490C22#6393711yescharacteristic
491C22#6395011yescharacteristic
492C4—21no—
493C4—21no—
494C4—81no—
495C4—121no—
496C4—121no—
497C4—121no—
498C4—361no—
499C4—721no—
500C3—21no—
501C3#6828911yescharacteristic, complemented
502C3#6832111yescharacteristic, complemented
503C2—21no—
504C2—21no—
505C2—241no—
506C2—721no—
507C2#1059039811yescharacteristic
508C2#1059040911yescharacteristic
509C2#1059061711yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radical#10594979C2
hypercenter#95D32
hypocenterC32#1612
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592373C2semidirect
3. #10591126C2semidirect
4. #10591094C2semidirect
5. C3×#4452C2semidirect
6. C3×#4451C2semidirect
7. #10589146C2semidirect
42. #4452D3semidirect
43. #4451D3semidirect
428. C32#1612semidirect
501. C3#68289semidirect
502. C3#68321semidirect

Maximal subgroups

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

subgroupindex
#105949792
#105923732
#105911262
#105910942
C3×#44522
C3×#44512
#105891462
#683213
#682893