Finite Group Databasebeta

← #11775304

Subgroups — #11775304

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic
2C3×#5211C211yesmaximal, characteristic, complemented
3C3×#5207C211yesmaximal, characteristic, complemented
4#10589151C214yesmaximal, complemented
5#69978—31nomaximal
6#69531—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×#638—21no—
9C22×C4⋊(C3⋊D3)C411yescharacteristic, complemented
10#64139—21no—
11#64139—21no—
12#64139C412yescomplemented
13#64139C2212yes—
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
16C2×C3×#217—21no—
17C2×C3×#208—21no—
18C3×C3⋊#95—21no—
19C3×C3⋊#95C2212yescomplemented
20C3×#830—21no—
21C3×#830C2212yescomplemented
22C2×#930—31no—
23C2×#930—31no—
24C2×#930—61no—
25C3×#407—31no—
26C3×#381—31no—
27#5211D311yescharacteristic, complemented
28#5207D311yescharacteristic, complemented
29#4470—34no—
30#4451—34no—
31C24×C32D411yescharacteristic
32C23×C3⋊D3—21no—
33C22×C32×C4—42no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C2×#638—22no—
41C2×#638—22no—
42C2×#638—44no—
43C22×C3⋊Dic3—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—42no—
46C2×C4⋊(C3⋊D3)C2×C412yes—
47C22×C3×Dic3—22no—
48#3752—22no—
49#3752—22no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)C2×C412yes—
52C3×#217—42no—
53C3×#208—42no—
54C2×C3×C3⋊C8—22no—
55#1510—91noSylow
56C23×C3×C4—21no—
57C23×C3×C4C2×D311yescharacteristic
58C23×C3×C4C2×D311yescharacteristic
59C22×#67—62no—
60C22×#67—61no—
61C22×#67—61no—
62C22×D12—31no—
63C22×D12—31no—
64C22×D12—61no—
65C2×C3×M16—61no—
66C2×C3×C22⋊C4—61no—
67C2×#217—21no—
68#930—32no—
69#930—32no—
70#930—32no—
71#930—32no—
72#930—62no—
73#930—62no—
74#930—62no—
75#930—62no—
76#930—61no—
77#930—61no—
78#930—61no—
79#930—61no—
80C2×(C2×D3)⋊C4—62no—
81C2×(C2×D3)⋊C4—61no—
82C2×(C2×D3)⋊C4—61no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—61no—
86C2×#208—21no—
87C3×C22⋊C8—32no—
88C3×C22⋊C8—61no—
89C3×#95—32no—
90C3×#95—61no—
91C3⋊#95—21no—
92C3⋊#95C2×D312yescomplemented
93#830—21no—
94#830C2×D312yescomplemented
95C23×C32—22no—
96C23×C32—22no—
97C23×C32—41no—
98C23×C32C22⋊C411yescharacteristic
99C23×C32C22⋊C411yescharacteristic
100C23×C32C2×D411yescharacteristic
101C22×C3⋊D3—22no—
102C22×C3⋊D3—42no—
103C22×C3⋊D3—42no—
104C22×C3⋊D3—42no—
105C2×C32×C4—22no—
106C2×C32×C4—22no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4C22⋊C411yescharacteristic
112C2×C32×C4C22⋊C411yescharacteristic
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115#638—44no—
116#638—44no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—42no—
119C4⋊(C3⋊D3)—42no—
120C4⋊(C3⋊D3)—42no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3—42no—
123C2×C3×Dic3—42no—
124C3×C3⋊C8—42no—
125C2×#121—91no—
126#407—31no—
127#381—31no—
128#327—94no—
129C24×C3—21no—
130C24×C3D1211yescharacteristic
131C24×C3#6711yescharacteristic
132C23×D3—62no—
133C23×D3—61no—
134C23×D3—61no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—42no—
142C22×C3×C4—42no—
143C22×C3×C4—44no—
144C22×C3×C4—62no—
145C22×C3×C4C4×D311yescharacteristic
146C22×C3×C4C4×D311yescharacteristic
147C22×C3×C4C4×D311yescharacteristic
148C22×C3×C4C4×D311yescharacteristic
149C22×C3×C4D1211yescharacteristic
150C22×C3×C4D1211yescharacteristic
151C22×C3×C4D1211yescharacteristic
152C22×C3×C4#6711yescharacteristic
153C22×C3×C4#6711yescharacteristic
154C22×C3×C4#6711yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C2×#67—64no—
158C2×#67—64no—
159C2×#67—62no—
160C2×#67—62no—
161C2×#67—62no—
162C2×#67—62no—
163C2×#67—128no—
164C2×#67—124no—
165C2×#67—124no—
166C22×Dic3—22no—
167C22×Dic3—62no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C2×D12—32no—
171C2×D12—32no—
172C2×D12—62no—
173C2×D12—62no—
174C2×D12—61no—
175C2×D12—61no—
176C2×D12—122no—
177C2×D12—122no—
178C2×D12—124no—
179C3×M16—122no—
180C2×C3×C8—62no—
181C3×C22⋊C4—122no—
182#217—42no—
183(C2×D3)⋊C4—64no—
184(C2×D3)⋊C4—64no—
185(C2×D3)⋊C4—62no—
186(C2×D3)⋊C4—62no—
187(C2×D3)⋊C4—62no—
188(C2×D3)⋊C4—62no—
189C4⋊Dic3—32no—
190C4⋊Dic3—32no—
191C4⋊Dic3—62no—
192C4⋊Dic3—62no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195#208—42no—
196C2×C3⋊C8—22no—
197C22×C32—21no—
198C22×C32—21no—
199C22×C32—21no—
200C22×C32—21no—
201C22×C32—21no—
202C22×C32—21no—
203C22×C32—21no—
204C22×C32—44no—
205C22×C32#9912yes—
206C22×C32C2×C22⋊C411yescharacteristic
207C22×C32AGL(1,ℤ/8)12yes—
208C2×C3⋊D3—42no—
209C2×C3⋊D3—42no—
210C2×C3⋊D3—42no—
211C2×C3⋊D3—84no—
212C32×C4—21no—
213C32×C4—21no—
214C32×C4—21no—
215C32×C4—21no—
216C3⋊Dic3—42no—
217C3×Dic3—82no—
218C22×D4—91no—
219C22×D4—181no—
220C23×C4D3211yescharacteristic
221C2×M16—61no—
222#121—92no—
223#121—92no—
224#121—181no—
225#121—181no—
226C2×C4⋊C4—91no—
227C2×C22⋊C4—61no—
228C2×C22⋊C4—181no—
229C22⋊C8—32no—
230C22⋊C8—61no—
231#95—32no—
232#95—61no—
233C23×C3—24no—
234C23×C3—22no—
235C23×C3—22no—
236C23×C3—22no—
237C23×C3—22no—
238C23×C3—21no—
239C23×C3—21no—
240C23×C3—21no—
241C23×C3—42no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3—42no—
245C23×C3(C2×D3)⋊C411yescharacteristic
246C23×C3(C2×D3)⋊C411yescharacteristic
247C23×C3(C2×D3)⋊C411yescharacteristic
248C23×C3(C2×D3)⋊C411yescharacteristic
249C23×C3C2×D1211yescharacteristic
250C23×C3C2×#6711yescharacteristic
251C22×D3—64no—
252C22×D3—62no—
253C22×D3—62no—
254C22×D3—124no—
255C22×D3—124no—
256C22×D3—122no—
257C22×D3—122no—
258C22×D3—124no—
259C22×D3—122no—
260C22×D3—122no—
261C22×D3—122no—
262C22×D3—122no—
263C2×C3×C4—24no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—42no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—122no—
286C2×C3×C4—122no—
287C2×C3×C4—122no—
288C2×C3×C4(C2×D3)⋊C411yescharacteristic
289C2×C3×C4(C2×D3)⋊C411yescharacteristic
290C2×C3×C4(C2×D3)⋊C411yescharacteristic
291C2×C3×C4(C2×D3)⋊C411yescharacteristic
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4C2×C4×D311yescharacteristic
294C2×C3×C4C2×D1211yescharacteristic
295C2×C3×C4C2×#6711yescharacteristic
296#67—128no—
297#67—124no—
298#67—124no—
299#67—128no—
300#67—124no—
301#67—124no—
302C2×Dic3—42no—
303C2×Dic3—42no—
304C2×Dic3—42no—
305C2×Dic3—64no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—124no—
309C2×Dic3—122no—
310C2×Dic3—122no—
311D12—122no—
312D12—122no—
313D12—124no—
314D12—124no—
315D12—122no—
316D12—122no—
317C3×C8—122no—
318C3⋊C8—42no—
319C2×C32—22no—
320C2×C32—22no—
321C2×C32—41no—
322C2×C32C2×#9911yescharacteristic
323C2×C32#41811yescharacteristic
324C2×C32#42111yescharacteristic
325C3⋊D3—82no—
326C24—181no—
327C24#62611yescharacteristic
328C2×D4—92no—
329C2×D4—182no—
330C2×D4—182no—
331C2×D4—181no—
332C2×D4—362no—
333C2×D4—364no—
334C22×C4—42no—
335C22×C4—62no—
336C22×C4—181no—
337C22×C4#62411yescharacteristic
338C22×C4#62411yescharacteristic
339C22×C4#62611yescharacteristic
340C22×C4#62611yescharacteristic
341C22×C4#62611yescharacteristic
342C22×C4C2×D3211yescharacteristic
343M16—122no—
344C2×C8—62no—
345C4⋊C4—92no—
346C4⋊C4—181no—
347C22⋊C4—122no—
348C22⋊C4—182no—
349C22⋊C4—182no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—22no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—21no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—44no—
375C22×C3—44no—
376C22×C3—48no—
377C22×C3#80612yes—
378C22×C3#80612yes—
379C22×C3#90812yes—
380C22×C3C2×(C2×D3)⋊C411yescharacteristic
381C22×C3C2×(C2×D3)⋊C411yescharacteristic
382C22×C3#94912yes—
383C2×D3—124no—
384C2×D3—124no—
385C2×D3—124no—
386C2×D3—122no—
387C2×D3—122no—
388C2×D3—122no—
389C2×D3—122no—
390C2×D3—122no—
391C2×D3—122no—
392C2×D3—248no—
393C2×D3—244no—
394C2×D3—244no—
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—41no—
406C3×C4—41no—
407C3×C4—242no—
408Dic3—82no—
409Dic3—124no—
410Dic3—122no—
411Dic3—122no—
412C32#151011yescharacteristic, complemented, Sylow
413C23—22no—
414C23—22no—
415C23—41no—
416C23—182no—
417C23—362no—
418C23—362no—
419C23—362no—
420C23#372211yescharacteristic
421C23#372211yescharacteristic
422C23C2×#62611yescharacteristic
423D4—362no—
424D4—362no—
425D4—364no—
426D4—364no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—122no—
434C2×C4—122no—
435C2×C4—122no—
436C2×C4—182no—
437C2×C4—362no—
438C2×C4#372211yescharacteristic
439C2×C4#372211yescharacteristic
440C2×C4C2×#62411yescharacteristic
441C2×C4C2×#62611yescharacteristic
442C8—122no—
443C2×C3—24no—
444C2×C3—22no—
445C2×C3—22no—
446C2×C3—22no—
447C2×C3—22no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—42no—
452C2×C3—42no—
453C2×C3—41no—
454C2×C3—41no—
455C2×C3C2×#80611yescharacteristic
456C2×C3C2×#80611yescharacteristic
457C2×C3#500111yescharacteristic
458C2×C3#500511yescharacteristic
459C2×C3#513111yescharacteristic
460C2×C3#513911yescharacteristic
461D3—244no—
462D3—242no—
463D3—242no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—44no—
472C22—362no—
473C22—362no—
474C22—362no—
475C22—724no—
476C22#6358112yes—
477C22#6382512yes—
478C22C2×#372211yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—242no—
484C4—362no—
485C3—21no—
486C3#6953111yescharacteristic, complemented
487C3#6997811yescharacteristic, complemented
488C2—22no—
489C2—22no—
490C2—41no—
491C2—722no—
492C2#1059109611yescharacteristic
493C2#1059111311yescharacteristic
494C2C2×#6358111yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#64139C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1510
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C3×#5211C2semidirect
3. C3×#5207C2semidirect
4. #10589151C2semidirect
9. C22×C4⋊(C3⋊D3)C4semidirect
12. #64139C4semidirect
15. C2×C4⋊(C3⋊Dic3)C4semidirect
19. C3×C3⋊#95C22semidirect
21. C3×#830C22semidirect
27. #5211D3semidirect
28. #5207D3semidirect
92. C3⋊#95C2×D3semidirect
94. #830C2×D3semidirect
412. C32#1510semidirect
486. C3#69531semidirect
487. C3#69978semidirect

Maximal subgroups

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

subgroupindex
C2×#641392
C3×#52112
C3×#52072
#105891512
#699783
#695313