Finite Group Databasebeta

← #11778742

Subgroups — #11778742

Order 1152.

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

normal subgroups only

This group has 468 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
2#10592669C211yesmaximal, characteristic, complemented
3C3×#4985C211yesmaximal, characteristic, complemented
4C3×#4968C211yesmaximal, characteristic
5#10589154C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic, complemented
8#71170—31nomaximal
9#69717—31nomaximal
10C2×C32×C4⋊C4C2211yescharacteristic
11#64133C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14Dic3×#67—21no—
15#63961—21no—
16#63896—21no—
17#63884—21no—
18#63861—21no—
19#63847—21no—
20#63657C2211yescharacteristic
21#63637—21no—
22#63634—21no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#809—21no—
28C3×#808—21no—
29#5602—31no—
30#5515—31no—
31C3×#481—31no—
32C3×#400—31no—
33#4985D311yescharacteristic, complemented
34#4970—31no—
35#4970—31no—
36#4970—61no—
37#4968D311yescharacteristic
38#4537—31no—
39#4528—31no—
40#4469—31no—
41#4467—31no—
42#4452—31no—
43#4451—31no—
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—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55#3757—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65#3724—21no—
66Dic3⋊Dic3—21no—
67(C2×D3)⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70Dic32—21no—
71#1615—91noSylow
72C3×#121—31no—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4C2×D311yescharacteristic
76C2×C3×C4⋊C4C2×D311yescharacteristic
77#935—61no—
78#935—61no—
79D4×Dic3—61no—
80#930C2×D311yescharacteristic
81#929—61no—
82C4×#67—61no—
83#924—31no—
84#924—31no—
85#924—61no—
86C2×Dic3⋊C4C2×D311yescharacteristic
87#898—61no—
88#896—61no—
89#894—61no—
90#889—61no—
91#889—61no—
92#879—61no—
93#878—61no—
94C3×#106—61no—
95C3×#102—61no—
96C3×C22⋊C8—31no—
97C3×#95—31no—
98C3×#95—61no—
99C3×#95—61no—
100C3⋊#95—21no—
101C3⋊#95—21no—
102C3⋊#95C2×D311yescharacteristic
103#830—31no—
104#830—31no—
105#830—61no—
106#830C2×D311yescharacteristic
107#810—61no—
108#810—61no—
109#810—62no—
110#809—21no—
111#808—21no—
112#807—61no—
113#807—61no—
114#807—62no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4—42no—
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#484—91no—
142#481—31no—
143#400—31no—
144#328—91no—
145#327—91no—
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×D12#6711yescharacteristic
164C2×C4×D3—61no—
165C2×Dic6—31no—
166C2×Dic6—31no—
167C2×Dic6—61no—
168C2×C3×C8—61no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—41no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C22⋊C4—61no—
179#217—61no—
180#217—61no—
181#217—61no—
182#217—61no—
183#217—61no—
184#217—121no—
185(C2×D3)⋊C4—21no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189C4⋊Dic3—31no—
190C4⋊Dic3—31no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4⋊Dic3#6711yescharacteristic
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—62no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32#12011yescharacteristic
213C22×C32#13511yescharacteristic
214C22×C32#13711yescharacteristic
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—81no—
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⋊C4D3211yescharacteristic
237#107—181no—
238#106—61no—
239#103—181no—
240#102—61no—
241C22⋊C8—31no—
242C22⋊C8—91no—
243#95—31no—
244#95—61no—
245#95—61no—
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—21no—
255C2×C3×C4—21no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—42no—
259C2×C3×C4—42no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—82no—
270C2×C3×C4—121no—
271C2×C3×C4—121no—
272C2×C3×C4—121no—
273C2×C3×C4—121no—
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278#67—41no—
279#67—41no—
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—41no—
286C2×Dic3—41no—
287C2×Dic3—41no—
288C2×Dic3—41no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—121no—
294C2×Dic3—121no—
295C2×Dic3—241no—
296D12—41no—
297C4×D3—241no—
298Dic6—121no—
299Dic6—121no—
300Dic6—122no—
301C3×C8—121no—
302C3⋊C8—41no—
303C3⋊C8—122no—
304C3⋊C8—121no—
305C3⋊C8—121no—
306C2×C32—21no—
307C2×C32—21no—
308C2×C32#45211yescharacteristic
309C2×C32#45411yescharacteristic
310C2×C32#45811yescharacteristic
311C3×D3—81no—
312C2×Q8—91no—
313C2×D4—31no—
314C2×D4—61no—
315C22×C4—21no—
316C22×C4—31no—
317C22×C4—31no—
318C22×C4—61no—
319C22×C4—181no—
320C22×C4C2×D3211yescharacteristic
321C2×C8—61no—
322C2×C8—181no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—31no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—91no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C22⋊C4—61no—
334C22⋊C4—181no—
335C22⋊C4—181no—
336C22⋊C4—181no—
337C22⋊C4—181no—
338C42—181no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—121no—
349C22×C3—121no—
350C22×C3—121no—
351C22×C3#91511yescharacteristic
352C22×C3#91611yescharacteristic
353C22×C3#93711yescharacteristic
354C22×C3#93711yescharacteristic
355C22×C3#94211yescharacteristic
356C22×C3#95011yescharacteristic
357C2×D3—41no—
358C2×D3—41no—
359C2×D3—41no—
360C3×C4—22no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—41no—
366C3×C4—82no—
367C3×C4—81no—
368C3×C4—81no—
369C3×C4—121no—
370C3×C4—121no—
371C3×C4—121no—
372C3×C4—241no—
373Dic3—41no—
374Dic3—41no—
375Dic3—41no—
376Dic3—81no—
377Dic3—121no—
378Dic3—121no—
379Dic3—121no—
380Dic3—121no—
381Dic3—241no—
382Dic3—241no—
383C32#161511yescharacteristic, complemented, Sylow
384C23—61no—
385C23D3×#6711yescharacteristic
386Q8—361no—
387D4—121no—
388D4—121no—
389D4—121no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—121no—
399C2×C4—121no—
400C2×C4—121no—
401C2×C4—121no—
402C2×C4—181no—
403C2×C4—181no—
404C2×C4—721no—
405C2×C4D3×#6711yescharacteristic
406C2×C4#381111yescharacteristic
407C8—121no—
408C8—361no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—41no—
417C2×C3—41no—
418C2×C3—241no—
419C2×C3#504711yescharacteristic
420C2×C3#505311yescharacteristic
421C2×C3#505311yescharacteristic
422C2×C3#506211yescharacteristic
423C2×C3#517311yescharacteristic
424C2×C3#520111yescharacteristic
425D3—81no—
426C22—21no—
427C22—21no—
428C22—121no—
429C22—121no—
430C22—121no—
431C22#6394611yescharacteristic
432C22#6394711yescharacteristic
433C22#6398311yescharacteristic
434C4—21no—
435C4—21no—
436C4—81no—
437C4—121no—
438C4—121no—
439C4—121no—
440C4—241no—
441C4—361no—
442C4—361no—
443C3—21no—
444C3#6971711yescharacteristic, complemented
445C3#7117011yescharacteristic, complemented
446C2—21no—
447C2—21no—
448C2—241no—
449C2#1059139811yescharacteristic
450C2#1059152511yescharacteristic
451C2#1059165511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC2×C4⋊C4D32
hypocenterC32#1615
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. #10592669C2semidirect
3. C3×#4985C2semidirect
5. #10589154C2semidirect
7. #10589147C2semidirect
33. #4985D3semidirect
383. C32#1615semidirect
444. C3#69717semidirect
445. C3#71170semidirect

Maximal subgroups

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

subgroupindex
#105949732
#105926692
C3×#49852
C3×#49682
#105891542
#105891492
#105891472
#711703
#697173