Finite Group Databasebeta

← #11783615

Subgroups — #11783615

Order 1152.

773 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63874C211yesmaximal, characteristic
2C2×#63647C211yesmaximal, characteristic
3C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
4C2×#63557C211yesmaximal, characteristic
5C2×#63554C211yesmaximal, characteristic, complemented
6C3×#4550C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#69753—31nomaximal
9#68601—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3724C412yes—
18C2×#3722C412yes—
19#63874—22no—
20#63874—22no—
21#63647C414yescomplemented
22C3×C8×Dic3—22no—
23#63557C414yescomplemented
24#63554—22no—
25C2×#872—31no—
26C2×#872—31no—
27C2×C3×C4×C8—31no—
28C2×(C2×D3)⋊C8—31no—
29C2×(C2×D3)⋊C8—31no—
30C2×(C2×D3)⋊C8—31no—
31C2×(C2×D3)⋊C8—31no—
32C2×(C2×D3)⋊C8—61no—
33C2×#815—31no—
34C2×C8×Dic3D311yescharacteristic, complemented
35C2×#803—31no—
36C3×#336—31no—
37#4550—31no—
38#4550D311yescharacteristic, complemented
39#4524—31no—
40C23×C3⋊D3C2×C411yescharacteristic
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3C2×C411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—21no—
46C2×C4×C3⋊D3—21no—
47C2×C4×C3⋊D3C2×C412yes—
48C2×C4×C3⋊D3C2×C412yes—
49C22×C3×Dic3C2×C412yes—
50C22×C3×Dic3C2×C412yes—
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C2×C32×C8C2×C412yes—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)C2×C412yes—
57C3×C4×Dic3—21no—
58C3×C4×Dic3—21no—
59C3×C4×Dic3D412yes—
60C3×C4×Dic3D412yes—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8C2×C412yes—
66C2×C3×C3⋊C8C2×C412yes—
67#3724—24no—
68#3722—24no—
69#1750—91noSylow
70C22×C4×D3—31no—
71C22×C4×D3—31no—
72C22×C4×D3—61no—
73C22×C3×C8—21no—
74C22×C3×C8—31no—
75C22×C3×C8—31no—
76C22×C3×C8C2×D311yescharacteristic
77C22×C3×C8C2×D311yescharacteristic
78C2×C3×C42—31no—
79C2×C3×C42—31no—
80C2×(C2×D3)⋊C4—32no—
81C2×(C2×D3)⋊C4—32no—
82C2×Dic3⋊C4—32no—
83C2×Dic3⋊C4—32no—
84C2×C4×Dic3C2×D311yescharacteristic
85C2×C4×Dic3C2×D311yescharacteristic
86C22×C3⋊C8—31no—
87C22×C3⋊C8—31no—
88C22×C3⋊C8—61no—
89C22×C3⋊C8C2×D311yescharacteristic
90C22×C3⋊C8C2×D311yescharacteristic
91#872—62no—
92#872—62no—
93#872—62no—
94#872—62no—
95C3×C4×C8—62no—
96(C2×D3)⋊C8—34no—
97(C2×D3)⋊C8—34no—
98(C2×D3)⋊C8—34no—
99(C2×D3)⋊C8—34no—
100(C2×D3)⋊C8—64no—
101#815—62no—
102C8×Dic3—22no—
103#803—62no—
104C23×C32C22×C411yescharacteristic
105C22×C3⋊D3—22no—
106C22×C3⋊D3—21no—
107C22×C3⋊D3—21no—
108C22×C3⋊D3—22no—
109C22×C3⋊D3C4212yes—
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3C4212yes—
119C4×C3⋊D3—22no—
120C4×C3⋊D3—22no—
121C4×C3⋊D3—22no—
122C4×C3⋊D3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3C22⋊C414yes—
129C32×C8—22no—
130C3⋊(C3⋊C8)—22no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—22no—
133C2×#117—91no—
134C2×C22⋊C8—91no—
135C2×C22⋊C8—91no—
136C2×#97—91no—
137C2×C4×C8—31no—
138#336—31no—
139#336—91no—
140C23×D3—31no—
141C23×D3—31no—
142C23×D3—61no—
143C22×C3×C4—21no—
144C22×C3×C4—32no—
145C22×C3×C4—32no—
146C22×C3×C4C22×D311yescharacteristic
147C22×C3×C4C22×D311yescharacteristic
148C22×Dic3—31no—
149C22×Dic3—31no—
150C22×Dic3—61no—
151C22×Dic3C4×D312yes—
152C22×Dic3C4×D312yes—
153C2×C4×D3—32no—
154C2×C4×D3—32no—
155C2×C4×D3—32no—
156C2×C4×D3—32no—
157C2×C4×D3—62no—
158C2×C4×D3—62no—
159C2×C4×D3—61no—
160C2×C4×D3—61no—
161C2×C4×D3—61no—
162C2×C4×D3—61no—
163C2×C4×D3—61no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
166C2×C4×D3—61no—
167C2×C4×D3—121no—
168C2×C4×D3—121no—
169C2×C4×D3—121no—
170C2×C4×D3—121no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—22no—
176C2×C3×C8—32no—
177C2×C3×C8—32no—
178C2×C3×C8—41no—
179C2×C3×C8—41no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C2×C3×C8C4×D312yes—
185C2×C3×C8C4×D312yes—
186C3×C42—32no—
187C3×C42—32no—
188C3×C42—61no—
189C3×C42—61no—
190(C2×D3)⋊C4—64no—
191(C2×D3)⋊C4—64no—
192Dic3⋊C4—64no—
193Dic3⋊C4—64no—
194C4×Dic3—21no—
195C4×Dic3—21no—
196C4×Dic3D1212yes—
197C4×Dic3#6712yes—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—32no—
203C2×C3⋊C8—32no—
204C2×C3⋊C8—62no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—121no—
210C2×C3⋊C8—121no—
211C2×C3⋊C8C4×D312yes—
212C2×C3⋊C8C4×D312yes—
213C22×C32C2×C4211yescharacteristic
214C22×C32C2×C22⋊C411yescharacteristic
215C22×C32#11711yescharacteristic
216C22×C32#13112yes—
217C22×C32#13112yes—
218C2×C3⋊D3—22no—
219C2×C3⋊D3—22no—
220C2×C3⋊D3—22no—
221C2×C3⋊D3—42no—
222C2×C3⋊D3—42no—
223C32×C4C4×D411yescharacteristic
224C32×C4C4×D411yescharacteristic
225C32×C4C4×D411yescharacteristic
226C32×C4C4×D411yescharacteristic
227C3⋊Dic3—22no—
228C3×Dic3—24no—
229C3×Dic3—42no—
230C23×C4—91no—
231C22×C8—31no—
232C22×C8—31no—
233C22×C8—91no—
234C22×C8D3211yescharacteristic
235#117—182no—
236#117—182no—
237C2×C4⋊C4—92no—
238C2×C22⋊C4—92no—
239C2×C42—31no—
240C2×C42—31no—
241C22⋊C8—94no—
242C22⋊C8—94no—
243#97—182no—
244C4×C8—62no—
245C23×C3—21no—
246C23×C3C2×C4×D311yescharacteristic
247C23×C3C2×C4×D311yescharacteristic
248C22×D3—32no—
249C22×D3—32no—
250C22×D3—62no—
251C22×D3—64no—
252C22×D3—61no—
253C22×D3—61no—
254C22×D3—61no—
255C22×D3—62no—
256C22×D3—62no—
257C22×D3—62no—
258C22×D3—62no—
259C22×D3—61no—
260C22×D3—121no—
261C22×D3—121no—
262C22×D3—122no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—34no—
270C2×C3×C4—62no—
271C2×C3×C4—62no—
272C2×C3×C4—62no—
273C2×C3×C4—62no—
274C2×C3×C4—62no—
275C2×C3×C4C2×C4×D311yescharacteristic
276C2×C3×C4C2×C4×D311yescharacteristic
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4C2×C4×D311yescharacteristic
279C2×C3×C4C2×D1211yescharacteristic
280C2×C3×C4#23511yescharacteristic
281C2×C3×C4#23511yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4#23711yescharacteristic
285C2×C3×C4#23911yescharacteristic
286C2×C3×C4C2×#6711yescharacteristic
287C2×Dic3—22no—
288C2×Dic3—22no—
289C2×Dic3—22no—
290C2×Dic3—22no—
291C2×Dic3—22no—
292C2×Dic3—32no—
293C2×Dic3—32no—
294C2×Dic3—62no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3(C2×D3)⋊C414yes—
302C4×D3—62no—
303C4×D3—62no—
304C4×D3—62no—
305C4×D3—62no—
306C4×D3—62no—
307C4×D3—62no—
308C4×D3—62no—
309C4×D3—62no—
310C4×D3—122no—
311C4×D3—122no—
312C4×D3—122no—
313C4×D3—122no—
314C3×C8—22no—
315C3×C8—22no—
316C3×C8—42no—
317C3×C8—62no—
318C3×C8—62no—
319C3⋊C8—22no—
320C3⋊C8—22no—
321C3⋊C8—62no—
322C3⋊C8—62no—
323C3⋊C8—122no—
324C2×C32C4×C22⋊C411yescharacteristic
325C2×C32#40511yescharacteristic
326C2×C32#40511yescharacteristic
327C2×C32#40812yes—
328C2×C32#43312yes—
329C3⋊D3—42no—
330C24—91no—
331C22×C4—32no—
332C22×C4—32no—
333C22×C4—91no—
334C22×C4—92no—
335C22×C4—92no—
336C22×C4—181no—
337C22×C4—181no—
338C22×C4—181no—
339C22×C4—181no—
340C22×C4C2×D3211yescharacteristic
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—32no—
344C2×C8—32no—
345C2×C8—61no—
346C2×C8—61no—
347C2×C8—61no—
348C2×C8—61no—
349C2×C8—92no—
350C2×C8—181no—
351C2×C8—181no—
352C2×C8#62412yes—
353C4⋊C4—184no—
354C22⋊C4—184no—
355C42—32no—
356C42—32no—
357C42—61no—
358C42—61no—
359C22×C3—22no—
360C22×C3—22no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3C42×D311yescharacteristic
365C22×C3C42×D311yescharacteristic
366C22×C3#87211yescharacteristic
367C22×C3D3×C22⋊C411yescharacteristic
368C22×C3#89211yescharacteristic
369C22×C3#90112yes—
370C22×C3#90112yes—
371C22×C3#90112yes—
372C22×C3#90712yes—
373C22×C3C2×(C2×D3)⋊C411yescharacteristic
374C2×D3—64no—
375C2×D3—62no—
376C2×D3—62no—
377C2×D3—62no—
378C2×D3—62no—
379C2×D3—62no—
380C2×D3—62no—
381C2×D3—122no—
382C2×D3—122no—
383C2×D3—124no—
384C2×D3—124no—
385C2×D3—122no—
386C2×D3—122no—
387C2×D3—122no—
388C2×D3—122no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—64no—
394C3×C4—122no—
395C3×C4C4×D1211yescharacteristic
396C3×C4C4×D1211yescharacteristic
397C3×C4#67⋊C411yescharacteristic
398C3×C4#67⋊C411yescharacteristic
399C3×C4#89311yescharacteristic
400C3×C4#89311yescharacteristic
401C3×C4C4×#6711yescharacteristic
402C3×C4C4×#6711yescharacteristic
403Dic3—24no—
404Dic3—42no—
405Dic3—62no—
406Dic3—62no—
407Dic3—122no—
408C32#175011yescharacteristic, complemented, Sylow
409C23—92no—
410C23—182no—
411C23—182no—
412C23—181no—
413C23—181no—
414C23C4×D3211yescharacteristic
415C2×C4—34no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—92no—
422C2×C4—181no—
423C2×C4—181no—
424C2×C4—182no—
425C2×C4—182no—
426C2×C4—182no—
427C2×C4—182no—
428C2×C4#379911yescharacteristic
429C2×C4C4×D3211yescharacteristic
430C2×C4D3×D1211yescharacteristic
431C2×C4#380411yescharacteristic
432C2×C4C2×#62411yescharacteristic
433C2×C4D3×#6711yescharacteristic
434C8—22no—
435C8—62no—
436C8—62no—
437C8—182no—
438C2×C3—21no—
439C2×C3—22no—
440C2×C3—21no—
441C2×C3—22no—
442C2×C3—21no—
443C2×C3#466611yescharacteristic
444C2×C3#468911yescharacteristic
445C2×C3#468911yescharacteristic
446C2×C3#468911yescharacteristic
447C2×C3#469012yes—
448C2×C3#470811yescharacteristic
449C2×C3#472712yes—
450C2×C3#484012yes—
451C2×C3C4×(C2×D3)⋊C411yescharacteristic
452C2×C3#511012yes—
453D3—124no—
454D3—122no—
455D3—122no—
456C22—182no—
457C22—182no—
458C22—182no—
459C22—362no—
460C22—362no—
461C22#6380312yes—
462C22#6380412yes—
463C22#6383611yescharacteristic
464C22C4×#62411yescharacteristic
465C22D3×(C2×D3)⋊C411yescharacteristic
466C4—64no—
467C4—122no—
468C4—182no—
469C4#6388011yescharacteristic
470C4#6389411yescharacteristic
471C4#6390411yescharacteristic
472C4#6395211yescharacteristic
473C3—21no—
474C3#6860111yescharacteristic, complemented
475C3#6975311yescharacteristic, complemented
476C2—362no—
477C2#1059064812yes—
478C2#1059070011yescharacteristic
479C2#1059091011yescharacteristic
480C2#1059095312yes—
481C2#1059123311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C2×C42
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1750
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×C3×C8×Dic3C2semidirect
5. C2×#63554C2semidirect
6. C3×#4550C2semidirect
7. #10589155C2semidirect
21. #63647C4semidirect
23. #63557C4semidirect
34. C2×C8×Dic3D3semidirect
38. #4550D3semidirect
408. C32#1750semidirect
474. C3#68601semidirect
475. C3#69753semidirect

Maximal subgroups

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

subgroupindex
C2×#638742
C2×#636472
C2×C3×C8×Dic32
C2×#635572
C2×#635542
C3×#45502
#105891552
#697533
#686013