Finite Group Databasebeta

← #11787299

Subgroups — #11787299

Order 1152.

1368 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64147C211yesmaximal, characteristic
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C32×#102C211yesmaximal, characteristic, complemented
4C2×#63659C211yesmaximal, characteristic, complemented
5C2×#63647C211yesmaximal, characteristic, complemented
6#10589417C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#70200—34nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×#638—21no—
11C22×C4×C3⋊D3—21no—
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3757—21no—
16#64147—22no—
17#64147C414yescomplemented
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×#3750—21no—
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C4⋊C4×C3⋊D3—22no—
23C4⋊C4×C3⋊D3—22no—
24C32×#102—22no—
25#63659—22no—
26#63647—22no—
27C2×#938—34no—
28C2×D3×C4⋊C4—34no—
29C2×C3×#102D314yescomplemented
30C2×#832—34no—
31C2×(C2×D3)⋊C8—34no—
32#4551—34no—
33#4529—34no—
34C24×C32—21no—
35C23×C3⋊D3D411yescharacteristic
36C2×C32×D4—21no—
37C2×C32×D4—21no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4C2×C412yescomplemented
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C2×#638—24no—
45C2×#638—42no—
46C2×#638—42no—
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3D411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3—21no—
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3—42no—
56C2×C4×C3⋊D3—42no—
57C2×C4×C3⋊D3C2×C412yes—
58C2×C4×C3⋊D3D412yes—
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8—21no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4D412yescomplemented
64#3757—24no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2×C412yescomplemented
68C4⋊(C3⋊Dic3)D412yescomplemented
69#3750—24no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)—21no—
73#1874—91noSylow
74C22×C3×D4C2×D314yes—
75C22×#67—64no—
76C22×C4×D3—34no—
77C22×C4×D3—64no—
78C22×C3×C8C2×D314yes—
79C2×C3×C4⋊C4C2×D314yes—
80C2×#217—64no—
81#938—316no—
82#938—68no—
83C2×C4⋊Dic3—34no—
84C2×C4⋊Dic3—34no—
85C2×Dic3⋊C4—64no—
86C22×C3⋊C8—34no—
87D3×C4⋊C4—68no—
88D3×C4⋊C4—68no—
89C3×#102—28no—
90#832—68no—
91(C2×D3)⋊C8—68no—
92C23×C32—22no—
93C23×C32—41no—
94C23×C32—41no—
95C23×C32—41no—
96C23×C32—41no—
97C23×C32—41no—
98C23×C32—41no—
99C23×C32C2×D411yescharacteristic
100C22×C3⋊D3—21no—
101C22×C3⋊D3—21no—
102C22×C3⋊D3—21no—
103C22×C3⋊D3—21no—
104C22×C3⋊D3C22⋊C412yes—
105C22×C3⋊D3D812yes—
106C22×C3⋊D3SD1612yes—
107C32×D4—22no—
108C32×D4—22no—
109C32×D4—41no—
110C32×D4—41no—
111C2×C32×C4—22no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120#638—48no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3C22⋊C412yes—
130C4×C3⋊D3—22no—
131C4×C3⋊D3—22no—
132C4×C3⋊D3—22no—
133C4×C3⋊D3—22no—
134C4×C3⋊D3—48no—
135C32×C8—41no—
136C3⋊(C3⋊C8)—41no—
137C2×#121—91no—
138C22×C4⋊C4—91no—
139C2×#102—91no—
140C2×#102C3⋊D311yescharacteristic, complemented
141C2×C22⋊C8—91no—
142#340—91no—
143#340—91no—
144C24×C3—24no—
145C23×D3—34no—
146C2×C3×D4—24no—
147C2×C3×D4—24no—
148C2×C3×D4—24no—
149C2×C3×D4—24no—
150C2×C3×D4—24no—
151C2×C3×D4C4×D318yescomplemented
152C22×C3×C4—24no—
153C22×C3×C4C22×D314yes—
154C2×#67—616no—
155C2×#67—128no—
156C2×#67—128no—
157C22×Dic3—34no—
158C22×Dic3—64no—
159C22×Dic3—64no—
160C2×C4×D3—38no—
161C2×C4×D3—38no—
162C2×C4×D3—64no—
163C2×C4×D3—64no—
164C2×C4×D3—64no—
165C2×C4×D3—64no—
166C2×C4×D3—616no—
167C2×C4×D3—128no—
168C2×C4×D3—128no—
169C2×C3×C8—24no—
170C2×C3×C8—24no—
171C2×C3×C8—24no—
172C3×C4⋊C4—24no—
173C3×C4⋊C4#6718yescomplemented
174#217—616no—
175C4⋊Dic3—38no—
176C4⋊Dic3—38no—
177C4⋊Dic3—64no—
178C4⋊Dic3—64no—
179Dic3⋊C4—616no—
180C2×C3⋊C8—64no—
181C2×C3⋊C8—64no—
182C2×C3⋊C8—64no—
183C22×C32—42no—
184C22×C32—42no—
185C22×C32—42no—
186C22×C32—81no—
187C22×C32—81no—
188C22×C32—81no—
189C22×C32—81no—
190C22×C32C2×C22⋊C411yescharacteristic
191C22×C32#12011yescharacteristic
192C22×C32#12311yescharacteristic
193C22×C32C2×D811yescharacteristic
194C22×C32C2×SD1611yescharacteristic
195C22×C32AGL(1,ℤ/8)11yescharacteristic
196C22×C32#13711yescharacteristic
197C2×C3⋊D3—22no—
198C2×C3⋊D3—22no—
199C2×C3⋊D3—22no—
200C2×C3⋊D3—22no—
201C2×C3⋊D3—22no—
202C2×C3⋊D3—22no—
203C2×C3⋊D3#10214yescomplemented
204C32×C4—42no—
205C32×C4C4×D411yescharacteristic
206C32×C4C4×D411yescharacteristic
207C32×C4#12111yescharacteristic
208C32×C4#12111yescharacteristic
209C3⋊Dic3—22no—
210C3⋊Dic3—42no—
211C3⋊Dic3—42no—
212C22×D4—181no—
213C22×D4C2×C3⋊D311yescharacteristic
214C23×C4—91no—
215C23×C4—181no—
216C22×C8—91no—
217C22×C8C2×C3⋊D311yescharacteristic
218#121—94no—
219#121—182no—
220C2×C4⋊C4—91no—
221C2×C4⋊C4—91no—
222C2×C4⋊C4—182no—
223C2×C4⋊C4—181no—
224C2×C4⋊C4—182no—
225C2×C4⋊C4C2×C3⋊D311yescharacteristic
226C2×C22⋊C4—181no—
227#102—22no—
228#102—182no—
229C22⋊C8—182no—
230C23×C3—28no—
231C23×C3—44no—
232C23×C3—44no—
233C23×C3—44no—
234C23×C3—44no—
235C23×C3—44no—
236C23×C3—44no—
237C23×C3D3×D414yes—
238C22×D3—38no—
239C22×D3—38no—
240C22×D3—38no—
241C22×D3—64no—
242C22×D3—64no—
243C22×D3—64no—
244C22×D3—64no—
245C3×D4—28no—
246C3×D4—28no—
247C3×D4—44no—
248C3×D4—44no—
249C2×C3×C4—28no—
250C2×C3×C4—44no—
251C2×C3×C4—44no—
252C2×C3×C4C2×C4×D314yes—
253C2×C3×C4#23514yes—
254C2×C3×C4D3×D414yes—
255C2×C3×C4D3×D414yes—
256C2×C3×C4#23714yes—
257C2×C3×C4C2×#6714yes—
258#67—1232no—
259C2×Dic3—38no—
260C2×Dic3—64no—
261C2×Dic3—64no—
262C2×Dic3—68no—
263C2×Dic3—68no—
264C2×Dic3—124no—
265C2×Dic3—124no—
266C2×Dic3—124no—
267C2×Dic3—124no—
268C4×D3—68no—
269C4×D3—68no—
270C4×D3—68no—
271C4×D3—68no—
272C4×D3—1232no—
273C3×C8—44no—
274C3⋊C8—124no—
275C2×C32—82no—
276C2×C32#38611yescharacteristic
277C2×C32C2×#10211yescharacteristic
278C2×C32#41711yescharacteristic
279C2×C32#44711yescharacteristic
280C2×C32#44811yescharacteristic
281C2×C32#48011yescharacteristic
282C2×C32#48111yescharacteristic
283C3⋊D3—24no—
284C24—21no—
285C24—91no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—184no—
292C2×D4—362no—
293C2×D4—362no—
294C2×D4C4×C3⋊D312yescomplemented
295C22×C4—21no—
296C22×C4—91no—
297C22×C4—92no—
298C22×C4—92no—
299C22×C4—184no—
300C22×C4—181no—
301C22×C4—181no—
302C22×C4—181no—
303C22×C4—181no—
304C22×C4—181no—
305C22×C4—181no—
306C22×C4—362no—
307C22×C4—362no—
308C22×C4C22×C3⋊D311yescharacteristic
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—181no—
313C2×C8—181no—
314C2×C8—181no—
315C4⋊C4—21no—
316C4⋊C4—92no—
317C4⋊C4—92no—
318C4⋊C4—184no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4#63812yescomplemented
322C22⋊C4—184no—
323C22×C3—48no—
324C22×C3—48no—
325C22×C3—48no—
326C22×C3—84no—
327C22×C3—84no—
328C22×C3—84no—
329C22×C3—84no—
330C22×C3D3×C22⋊C414yes—
331C22×C3#88314yes—
332C22×C3D3×D814yes—
333C22×C3#91114yes—
334C22×C3D3×SD1614yes—
335C22×C3#91514yes—
336C22×C3#93714yes—
337C2×D3—316no—
338C2×D3—68no—
339C2×D3—68no—
340C2×D3—68no—
341C2×D3—68no—
342C2×D3—68no—
343C2×D3—68no—
344C3×C4—48no—
345C3×C4#67⋊C414yes—
346C3×C4#88414yes—
347C3×C4C4×#6714yes—
348C3×C4#93814yes—
349Dic3—68no—
350Dic3—128no—
351Dic3—128no—
352C32#187411yescharacteristic, complemented, Sylow
353C23—22no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—92no—
361C23—92no—
362C23—92no—
363C23—181no—
364C23—181no—
365C23—181no—
366C23—181no—
367C23D4×C3⋊D311yescharacteristic
368D4—22no—
369D4—22no—
370D4—41no—
371D4—41no—
372D4—368no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—92no—
377C2×C4—181no—
378C2×C4—181no—
379C2×C4—182no—
380C2×C4—182no—
381C2×C4—182no—
382C2×C4—182no—
383C2×C4—182no—
384C2×C4—182no—
385C2×C4—368no—
386C2×C4—361no—
387C2×C4—361no—
388C2×C4—361no—
389C2×C4—361no—
390C2×C4C2×C4×C3⋊D311yescharacteristic
391C2×C4#382811yescharacteristic
392C2×C4D4×C3⋊D311yescharacteristic
393C2×C4D4×C3⋊D311yescharacteristic
394C2×C4#383011yescharacteristic
395C2×C4C2×#63811yescharacteristic
396C8—41no—
397C8—361no—
398C2×C3—88no—
399C2×C3D3×#10214yes—
400C2×C3#477114yes—
401C2×C3#477414yes—
402C2×C3#477714yes—
403C2×C3#495614yes—
404C2×C3#515614yes—
405C2×C3#517014yes—
406D3—616no—
407C22—42no—
408C22—42no—
409C22—42no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—94no—
415C22—182no—
416C22—182no—
417C22—182no—
418C22—182no—
419C22—182no—
420C22—182no—
421C22C22⋊C4×C3⋊D311yescharacteristic
422C22#6409211yescharacteristic
423C22D8×C3⋊D311yescharacteristic
424C22#6412011yescharacteristic
425C22SD16×C3⋊D311yescharacteristic
426C22#6412411yescharacteristic
427C22#6414611yescharacteristic
428C4—42no—
429C4—182no—
430C4—362no—
431C4—362no—
432C4#6409011yescharacteristic
433C4#6409311yescharacteristic
434C4C4×#63811yescharacteristic
435C4#6414711yescharacteristic
436C3#7020014yescomplemented
437C2—82no—
438C2—184no—
439C2C3⋊D3×#10211yescharacteristic
440C2#1059247011yescharacteristic
441C2#1059247311yescharacteristic
442C2#1059247611yescharacteristic
443C2#1059265511yescharacteristic
444C2#1059285511yescharacteristic
445C2#1059286911yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC2×#64147C2
cosocleC22×C32×C4C23
hypercenterC2×#102C3⋊D3
hypocenterC32#1874
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×C3⋊D3C2semidirect
3. C2×C32×#102C2semidirect
4. C2×#63659C2semidirect
5. C2×#63647C2semidirect
6. #10589417C2semidirect
7. #10589395C2semidirect
17. #64147C4semidirect
29. C2×C3×#102D3semidirect
41. C2×C32×D4C2×C4semidirect
63. C32×C4⋊C4D4semidirect
67. C4⋊(C3⋊Dic3)C2×C4semidirect
68. C4⋊(C3⋊Dic3)D4semidirect
140. C2×#102C3⋊D3semidirect
151. C2×C3×D4C4×D3semidirect
173. C3×C4⋊C4#67semidirect
203. C2×C3⋊D3#102semidirect
294. C2×D4C4×C3⋊D3semidirect
321. C4⋊C4#638semidirect
352. C32#1874semidirect
436. C3#70200semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
C2×C4⋊C4×C3⋊D32
C2×C32×#1022
C2×#636592
C2×#636472
#105894172
#105893952
#702003