Finite Group Databasebeta

← #11788128

Subgroups — #11788128

Order 1152.

1236 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3743C211yesmaximal, characteristic, complemented
2C2×#64104C211yesmaximal, characteristic
3C2×#63648C211yesmaximal, characteristic, complemented
4#10592686C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic, complemented
6C32×#340C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#68885—34nomaximal
9C22×C4⋊(C3⋊D3)—21no—
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3752—21no—
16C2×#3752—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C2×#3743—22no—
20C2×#3743—22no—
21C2×#3743—22no—
22#64104—22no—
23#64104C414yescomplemented
24#63658—21no—
25#63648—22no—
26#63636—22no—
27C22×ΓL(1,𝔽25)—34no—
28C2×#895—34no—
29C2×#821—34no—
30#4987—34no—
31C2×#809—34no—
32C3×#340D314yescomplemented
33#4529—34no—
34C23×C3⋊D3—21no—
35C23×C3⋊D3D411yescharacteristic
36C22×C32×C4—21no—
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3D411yescharacteristic
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—24no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—42no—
48C2×C4⋊(C3⋊D3)—42no—
49C2×C4⋊(C3⋊D3)C2×C412yes—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3—21no—
54C2×C4×C3⋊D3C2×C412yes—
55C2×C4×C3⋊D3D412yes—
56C2×C32×C8—21no—
57C2×C32×C8—21no—
58C2×C32×C8D412yescomplemented
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4C2×C412yes—
63#3752—24no—
64#3752—42no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)D412yescomplemented
70#3743—28no—
71#1895—91noSylow
72C22×D12—34no—
73C22×D12—64no—
74C22×C4×D3—34no—
75C22×C3×C8C2×D314yes—
76C2×C3×C4⋊C4C2×D314yes—
77C2×C3×C4⋊C4C2×D314yes—
78C2×(C2×D3)⋊C4—64no—
79C2×(C2×D3)⋊C4—64no—
80C2×C4⋊Dic3—34no—
81C22×C3⋊C8—34no—
82C2×ΓL(1,𝔽25)—68no—
83C2×ΓL(1,𝔽25)—68no—
84C2×ΓL(1,𝔽25)—68no—
85#895—316no—
86#895—68no—
87C3⋊#95—64no—
88#821—68no—
89#809—68no—
90C23×C32C2×D411yescharacteristic
91C22×C3⋊D3—21no—
92C22×C3⋊D3—21no—
93C22×C3⋊D3—21no—
94C22×C3⋊D3—21no—
95C22×C3⋊D3—21no—
96C22×C3⋊D3—21no—
97C22×C3⋊D3—22no—
98C22×C3⋊D3—41no—
99C22×C3⋊D3—41no—
100C22×C3⋊D3—41no—
101C22×C3⋊D3—41no—
102C22×C3⋊D3—41no—
103C22×C3⋊D3—41no—
104C22×C3⋊D3C22⋊C412yes—
105C2×C32×C4—22no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3C22⋊C412yes—
123C4⋊(C3⋊D3)—22no—
124C4⋊(C3⋊D3)—22no—
125C4⋊(C3⋊D3)—48no—
126C4⋊(C3⋊D3)—41no—
127C4⋊(C3⋊D3)—41no—
128C4×C3⋊D3—22no—
129C4×C3⋊D3—22no—
130C4×C3⋊D3—22no—
131C4×C3⋊D3—22no—
132C32×C8—22no—
133C3⋊(C3⋊C8)—22no—
134C22×M16—91no—
135C2×#121—91no—
136C2×#102—91no—
137C2×#102—91no—
138#380—91no—
139#340—91no—
140#340C3⋊D311yescharacteristic, complemented
141C23×D3—34no—
142C23×D3—64no—
143C22×C3×C4—24no—
144C22×C3×C4—24no—
145C22×C3×C4C22×D314yes—
146C22×Dic3—34no—
147C22×Dic3—64no—
148C2×D12—38no—
149C2×D12—64no—
150C2×D12—64no—
151C2×D12—64no—
152C2×D12—64no—
153C2×D12—616no—
154C2×D12—64no—
155C2×D12—128no—
156C2×D12—128no—
157C2×C4×D3—38no—
158C2×C4×D3—38no—
159C2×C4×D3—64no—
160C2×C4×D3—64no—
161C2×C4×D3—64no—
162C2×C4×D3—64no—
163C2×C3×C8—24no—
164C2×C3×C8—24no—
165C2×C3×C8D1218yescomplemented
166C3×C4⋊C4—24no—
167C3×C4⋊C4—24no—
168C3×C4⋊C4—24no—
169C3×C4⋊C4C4×D318yes—
170(C2×D3)⋊C4—616no—
171(C2×D3)⋊C4—128no—
172C4⋊Dic3—64no—
173C4⋊Dic3—64no—
174C2×C3⋊C8—38no—
175C2×C3⋊C8—64no—
176C2×C3⋊C8—64no—
177ΓL(1,𝔽25)—632no—
178C22×C32C2×C22⋊C411yescharacteristic
179C22×C32#12111yescharacteristic
180C22×C32#12111yescharacteristic
181C22×C32AGL(1,ℤ/8)11yescharacteristic
182C22×C32AGL(1,ℤ/8)11yescharacteristic
183C22×C32AGL(1,ℤ/8)11yescharacteristic
184C22×C32#13711yescharacteristic
185C2×C3⋊D3—22no—
186C2×C3⋊D3—22no—
187C2×C3⋊D3—22no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3—41no—
190C2×C3⋊D3—41no—
191C2×C3⋊D3—41no—
192C2×C3⋊D3—42no—
193C2×C3⋊D3—42no—
194C2×C3⋊D3—42no—
195C2×C3⋊D3—81no—
196C2×C3⋊D3—81no—
197C2×C3⋊D3—81no—
198C2×C3⋊D3—81no—
199C32×C4—42no—
200C32×C4—81no—
201C32×C4C4×D411yescharacteristic
202C32×C4C4×D411yescharacteristic
203C32×C4#12011yescharacteristic
204C32×C4#12311yescharacteristic
205C3⋊Dic3—22no—
206C3⋊Dic3—81no—
207C22×D4—91no—
208C22×D4—181no—
209C23×C4—91no—
210C2×M16—182no—
211C2×M16—182no—
212C2×M16—182no—
213C22×C8—91no—
214C22×C8C2×C3⋊D311yescharacteristic
215#121—94no—
216#121—182no—
217C2×C4⋊C4—91no—
218C2×C4⋊C4C2×C3⋊D311yescharacteristic
219C2×C4⋊C4C2×C3⋊D311yescharacteristic
220C2×C22⋊C4—181no—
221C2×C22⋊C4—181no—
222#102—182no—
223#102—182no—
224#95—181no—
225C23×C3D3×D414yes—
226C22×D3—38no—
227C22×D3—64no—
228C22×D3—64no—
229C22×D3—64no—
230C22×D3—64no—
231C22×D3—64no—
232C22×D3—64no—
233C22×D3—68no—
234C22×D3—124no—
235C22×D3—124no—
236C22×D3—124no—
237C22×D3—124no—
238C22×D3—124no—
239C22×D3—124no—
240C2×C3×C4—28no—
241C2×C3×C4—44no—
242C2×C3×C4—44no—
243C2×C3×C4—44no—
244C2×C3×C4—44no—
245C2×C3×C4—44no—
246C2×C3×C4C2×C4×D314yes—
247C2×C3×C4C2×D1214yes—
248C2×C3×C4#23514yes—
249C2×C3×C4D3×D414yes—
250C2×C3×C4D3×D414yes—
251C2×C3×C4#23914yes—
252C2×Dic3—38no—
253C2×Dic3—64no—
254C2×Dic3—64no—
255C2×Dic3—124no—
256C2×Dic3—124no—
257C2×Dic3—124no—
258D12—68no—
259D12—68no—
260D12—1232no—
261D12—124no—
262D12—124no—
263C4×D3—68no—
264C4×D3—68no—
265C4×D3—68no—
266C4×D3—68no—
267C3×C8—28no—
268C3⋊C8—68no—
269C2×C32#38611yescharacteristic
270C2×C32#41711yescharacteristic
271C2×C32#41811yescharacteristic
272C2×C32#46811yescharacteristic
273C2×C32#46811yescharacteristic
274C2×C32#46911yescharacteristic
275C2×C32#46911yescharacteristic
276C3⋊D3—42no—
277C3⋊D3—82no—
278C24—91no—
279C24—181no—
280C2×D4—92no—
281C2×D4—184no—
282C2×D4—181no—
283C2×D4—181no—
284C2×D4—181no—
285C2×D4—181no—
286C2×D4—181no—
287C2×D4—362no—
288C2×D4—362no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—91no—
292C22×C4—92no—
293C22×C4—92no—
294C22×C4—181no—
295C22×C4—181no—
296C22×C4—181no—
297C22×C4—181no—
298C22×C4—181no—
299C22×C4C22×C3⋊D311yescharacteristic
300M16—188no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—92no—
304C2×C8—181no—
305C2×C8—181no—
306C2×C8C4⋊(C3⋊D3)12yescomplemented
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—181no—
311C4⋊C4—181no—
312C4⋊C4C4×C3⋊D312yes—
313C22⋊C4—184no—
314C22⋊C4—362no—
315C22×C3D3×C22⋊C414yes—
316C22×C3#88414yes—
317C22×C3#89514yes—
318C22×C3#91114yes—
319C22×C3#91414yes—
320C22×C3#91414yes—
321C22×C3#91814yes—
322C2×D3—68no—
323C2×D3—68no—
324C2×D3—68no—
325C2×D3—124no—
326C2×D3—124no—
327C2×D3—124no—
328C2×D3—124no—
329C2×D3—128no—
330C2×D3—128no—
331C2×D3—128no—
332C2×D3—244no—
333C2×D3—244no—
334C2×D3—244no—
335C2×D3—244no—
336C3×C4—48no—
337C3×C4—84no—
338C3×C4C4×D1214yes—
339C3×C4#88214yes—
340C3×C4#89314yes—
341C3×C4#89414yes—
342Dic3—68no—
343Dic3—244no—
344C32#189511yescharacteristic, complemented, Sylow
345C23—92no—
346C23—181no—
347C23—181no—
348C23—181no—
349C23—181no—
350C23—181no—
351C23—181no—
352C23—182no—
353C23—361no—
354C23—361no—
355C23—361no—
356C23—361no—
357C23—361no—
358C23—361no—
359C23D4×C3⋊D311yescharacteristic
360D4—182no—
361D4—182no—
362D4—368no—
363D4—361no—
364D4—361no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—92no—
372C2×C4—181no—
373C2×C4—181no—
374C2×C4—182no—
375C2×C4—182no—
376C2×C4—182no—
377C2×C4—182no—
378C2×C4—361no—
379C2×C4—361no—
380C2×C4—361no—
381C2×C4C2×C4×C3⋊D311yescharacteristic
382C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
383C2×C4#382811yescharacteristic
384C2×C4D4×C3⋊D311yescharacteristic
385C2×C4D4×C3⋊D311yescharacteristic
386C2×C4#383211yescharacteristic
387C8—22no—
388C8—182no—
389C2×C3#466514yes—
390C2×C3#477014yes—
391C2×C3#478214yes—
392C2×C3#480314yes—
393C2×C3#481214yes—
394C2×C3#486514yes—
395C2×C3#488614yes—
396D3—128no—
397D3—248no—
398C22—182no—
399C22—182no—
400C22—182no—
401C22—361no—
402C22—361no—
403C22—361no—
404C22—361no—
405C22—362no—
406C22—362no—
407C22—362no—
408C22—721no—
409C22—721no—
410C22—721no—
411C22—721no—
412C22C22⋊C4×C3⋊D311yescharacteristic
413C22#6409311yescharacteristic
414C22#6410411yescharacteristic
415C22#6412011yescharacteristic
416C22#6412311yescharacteristic
417C22#6412311yescharacteristic
418C22#6412711yescharacteristic
419C4—42no—
420C4—81no—
421C4—182no—
422C4—721no—
423C4C4×C4⋊(C3⋊D3)11yescharacteristic
424C4#6409111yescharacteristic
425C4#6410211yescharacteristic
426C4#6410311yescharacteristic
427C3#6888514yescomplemented
428C2—362no—
429C2—722no—
430C2#1059236411yescharacteristic
431C2#1059246911yescharacteristic
432C2#1059248111yescharacteristic
433C2#1059250211yescharacteristic
434C2#1059251111yescharacteristic
435C2#1059256411yescharacteristic
436C2#1059258511yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC2×#64104C2
cosocleC22×C32×C4C23
hypercenter#340C3⋊D3
hypocenterC32#1895
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C22×#3743C2semidirect
3. C2×#63648C2semidirect
4. #10592686C2semidirect
5. C2×#63636C2semidirect
6. C32×#340C2semidirect
7. #10589395C2semidirect
23. #64104C4semidirect
32. C3×#340D3semidirect
58. C2×C32×C8D4semidirect
69. C2×C3⋊(C3⋊C8)D4semidirect
140. #340C3⋊D3semidirect
165. C2×C3×C8D12semidirect
306. C2×C8C4⋊(C3⋊D3)semidirect
344. C32#1895semidirect
427. C3#68885semidirect

Maximal subgroups

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

subgroupindex
C22×#37432
C2×#641042
C2×#636482
#105926862
C2×#636362
C32×#3402
#105893952
#688853