Finite Group Databasebeta

← #11778528

Subgroups — #11778528

Order 1152.

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

normal subgroups only

This group has 472 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#10594973C211yesmaximal, characteristic
2C3×#4661C211yesmaximal, characteristic, complemented
3#10591124C211yesmaximal, characteristic, complemented
4#10591089C211yesmaximal, characteristic
5#10589318C211yesmaximal, characteristic, complemented
6C3×#4451C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic, complemented
8#69711—31nomaximal
9#68296—31nomaximal
10#64133C2211yescharacteristic
11C3×#930C2211yescharacteristic
12C2×C3×C4⋊Dic3—21no—
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15Dic3×#67—21no—
16#63961—21no—
17#63896—21no—
18#63884—21no—
19#63861—21no—
20#63847—21no—
21C32×#95C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×C3⋊#95—21no—
24C3×#830C2211yescharacteristic
25#63576—21no—
26#63573—21no—
27#63567—21no—
28#63562—21no—
29#5602—31no—
30#5515—31no—
31C3×#398—31no—
32#5033—31no—
33#4971—31no—
34#4967—31no—
35#4721—31no—
36#4661D311yescharacteristic, complemented
37C3×#327—31no—
38#4528—31no—
39#4469—31no—
40#4452—31no—
41#4452—31no—
42#4452—61no—
43#4451D311yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#634D411yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×D3×Dic3—21no—
53#3757—21no—
54C4⋊(C3⋊Dic3)D411yescharacteristic
55#3750—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—42no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C2×C3×C3⋊C8—21no—
65#3724—21no—
66#3724—21no—
67Dic3⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72#1609—91noSylow
73C3×#121—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—61no—
77#935—61no—
78#935—61no—
79D4×Dic3—61no—
80#930C2×D311yescharacteristic
81#929—61no—
82C4×#67—61no—
83C2×C4⋊Dic3—21no—
84C2×C4⋊Dic3C2×D311yescharacteristic
85#924—31no—
86#924—31no—
87#924—61no—
88C2×Dic3⋊C4C2×D311yescharacteristic
89#898—61no—
90#896—61no—
91#894—61no—
92#889—61no—
93#889—61no—
94#879—61no—
95#878—61no—
96C3×C22⋊C8—31no—
97C3×#95—21no—
98C3×#95—61no—
99C3×#95C2×D311yescharacteristic
100C3×#95C2×D311yescharacteristic
101#832—61no—
102C3⋊#95—21no—
103#830—31no—
104#830—31no—
105#830—61no—
106#830C2×D311yescharacteristic
107#817—61no—
108#816—61no—
109#810—61no—
110#809—61no—
111#808—61no—
112#807—61no—
113#807—61no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—21no—
116C2×C32×C4—22no—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124#634—41no—
125C3×#67—41no—
126C3×#67—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C3×D12—41no—
137D3×Dic3—81no—
138C3⋊(C3⋊C8)—41no—
139C3×C3⋊C8—41no—
140#539—91no—
141#483—91no—
142#480—91no—
143#398—31no—
144#328—91no—
145#327—31no—
146#324—91no—
147C2×C3×D4—31no—
148C2×C3×D4—61no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—41no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C2×#67—21no—
159C22×Dic3—21no—
160C22×Dic3—61no—
161C22×Dic3#6711yescharacteristic
162C22×Dic3#6711yescharacteristic
163C2×D12D1211yescharacteristic
164C2×C4×D3—61no—
165C2×Dic6—31no—
166C2×Dic6—31no—
167C2×Dic6—61no—
168C2×C3×C8—61no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—122no—
175C3×C22⋊C4—61no—
176#217—61no—
177#217—61no—
178#217—61no—
179#217—61no—
180#217—61no—
181#217—121no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—31no—
189C4⋊Dic3—31no—
190C4⋊Dic3—42no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4⋊Dic3D1211yescharacteristic
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—121no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—121no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32#12011yescharacteristic
213C22×C32#13511yescharacteristic
214C22×C32AGL(1,ℤ/8)11yescharacteristic
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—42no—
221C3⋊Dic3—41no—
222C3⋊Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—81no—
227#126—181no—
228#125—181no—
229#123—181no—
230#123—181no—
231C22⋊Q8—91no—
232C22⋊Q8—181no—
233#121—31no—
234C4×D4—181no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—31no—
237C2×C4⋊C4—61no—
238#107—181no—
239#106—181no—
240#103—181no—
241#102—181no—
242C22⋊C8—31no—
243C22⋊C8—91no—
244#95—61no—
245#95D3211yescharacteristic
246C23×C3—21no—
247C23×C3—61no—
248C23×C3D3×D411yescharacteristic
249C23×C3C2×#6711yescharacteristic
250C22×D3—21no—
251C3×D4—121no—
252C3×D4—121no—
253C3×D4—121no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—42no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—81no—
271C2×C3×C4—81no—
272C2×C3×C4—81no—
273C2×C3×C4—121no—
274C2×C3×C4—121no—
275C2×C3×C4—121no—
276C2×C3×C4—121no—
277C2×C3×C4C2×D1211yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281#67—41no—
282#67—41no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—41no—
289C2×Dic3—41no—
290C2×Dic3—41no—
291C2×Dic3—41no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—121no—
297C2×Dic3—121no—
298C2×Dic3—241no—
299D12—41no—
300C4×D3—241no—
301Dic6—121no—
302Dic6—121no—
303Dic6—241no—
304C3×C8—121no—
305C3⋊C8—41no—
306C3⋊C8—121no—
307C3⋊C8—121no—
308C3⋊C8—241no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32#44911yescharacteristic
312C2×C32#45611yescharacteristic
313C2×C32#45811yescharacteristic
314C3×D3—81no—
315C2×Q8—91no—
316C2×D4—31no—
317C2×D4—61no—
318C22×C4—21no—
319C22×C4—31no—
320C22×C4—31no—
321C22×C4—61no—
322C22×C4—181no—
323C22×C4C2×D3211yescharacteristic
324C2×C8—61no—
325C2×C8—181no—
326C4⋊C4—31no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—91no—
332C4⋊C4—122no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C4⋊C4—181no—
336C4⋊C4—181no—
337C22⋊C4—61no—
338C22⋊C4—181no—
339C22⋊C4—181no—
340C22⋊C4—181no—
341C22⋊C4—181no—
342C42—181no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—121no—
353C22×C3—121no—
354C22×C3—121no—
355C22×C3#88211yescharacteristic
356C22×C3#91111yescharacteristic
357C22×C3#91611yescharacteristic
358C22×C3#93211yescharacteristic
359C22×C3#93711yescharacteristic
360C22×C3#95011yescharacteristic
361C2×D3—41no—
362C2×D3—41no—
363C2×D3—41no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—42no—
371C3×C4—42no—
372C3×C4—82no—
373C3×C4—121no—
374C3×C4—121no—
375C3×C4—121no—
376C3×C4—241no—
377Dic3—41no—
378Dic3—41no—
379Dic3—41no—
380Dic3—81no—
381Dic3—121no—
382Dic3—121no—
383Dic3—121no—
384Dic3—121no—
385Dic3—241no—
386Dic3—241no—
387C32#160911yescharacteristic, complemented, Sylow
388C23—61no—
389C23D3×#6711yescharacteristic
390Q8—361no—
391D4—121no—
392D4—121no—
393D4—121no—
394C2×C4—22no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4—181no—
408C2×C4—181no—
409C2×C4—721no—
410C2×C4D3×D1211yescharacteristic
411C2×C4#380211yescharacteristic
412C8—121no—
413C8—361no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—41no—
422C2×C3—41no—
423C2×C3—241no—
424C2×C3#474211yescharacteristic
425C2×C3#478111yescharacteristic
426C2×C3#482611yescharacteristic
427C2×C3#503711yescharacteristic
428C2×C3#505311yescharacteristic
429C2×C3#509511yescharacteristic
430D3—81no—
431C22—21no—
432C22—21no—
433C22—121no—
434C22—121no—
435C22—121no—
436C22#6392211yescharacteristic
437C22#6393211yescharacteristic
438C22#6394711yescharacteristic
439C4—21no—
440C4—21no—
441C4—42no—
442C4—121no—
443C4—121no—
444C4—121no—
445C4—241no—
446C4—361no—
447C4—361no—
448C3—21no—
449C3#6829611yescharacteristic, complemented
450C3#6971111yescharacteristic, complemented
451C2—21no—
452C2—21no—
453C2—241no—
454C2#1059039911yescharacteristic
455C2#1059040811yescharacteristic
456C2#1059061311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenter#95D32
hypocenterC32#1609
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. C3×#4661C2semidirect
3. #10591124C2semidirect
5. #10589318C2semidirect
7. #10589147C2semidirect
36. #4661D3semidirect
387. C32#1609semidirect
449. C3#68296semidirect
450. C3#69711semidirect

Maximal subgroups

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

subgroupindex
#105949732
C3×#46612
#105911242
#105910892
#105893182
C3×#44512
#105891472
#697113
#682963