Finite Group Databasebeta

← #11775582

Subgroups — #11775582

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4#10589151C214yesmaximal, complemented
5#69944—31nomaximal
6#69509—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×C4⋊Dic3—21no—
18C22×C3×C3⋊C8—21no—
19C3×C3⋊#95C2212yescomplemented
20C3×#830—21no—
21C3×#830C2212yescomplemented
22C2×#930—31no—
23C2×#930—31no—
24C2×#930—61no—
25C2×C3×C22⋊C8—31no—
26C3×#380—31no—
27#5212D311yescharacteristic, complemented
28C2×#830D311yescharacteristic, 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—42no—
43C2×#638—42no—
44C22×C3⋊Dic3—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—42no—
47C2×C4⋊(C3⋊D3)C2×C412yes—
48C22×C3×Dic3—22no—
49#3752—22no—
50#3752—22no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)C2×C412yes—
53C3×#217—42no—
54C3×C4⋊Dic3—42no—
55C2×C3×C3⋊C8—22no—
56C2×C3×C3⋊C8—42no—
57#1519—91noSylow
58C23×C3×C4—21no—
59C23×C3×C4C2×D311yescharacteristic
60C23×C3×C4C2×D311yescharacteristic
61C22×#67—62no—
62C22×#67—61no—
63C22×#67—61no—
64C22×D12—31no—
65C22×D12—31no—
66C22×D12—61no—
67C22×C3×C8—61no—
68C2×C3×C4⋊C4—61no—
69C2×C3×C22⋊C4—61no—
70C2×#217—21no—
71#930—32no—
72#930—32no—
73#930—32no—
74#930—32no—
75#930—62no—
76#930—62no—
77#930—62no—
78#930—62no—
79#930—61no—
80#930—61no—
81#930—61no—
82#930—61no—
83C2×(C2×D3)⋊C4—62no—
84C2×(C2×D3)⋊C4—61no—
85C2×(C2×D3)⋊C4—61no—
86C2×C4⋊Dic3—21no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—61no—
90C22×C3⋊C8—21no—
91C3×C22⋊C8—32no—
92C3×C22⋊C8—61no—
93C3×#95—32no—
94C3⋊#95C2×D312yescomplemented
95#830—21no—
96#830C2×D312yescomplemented
97C23×C32—41no—
98C23×C32—41no—
99C23×C32C22⋊C411yescharacteristic
100C23×C32C22⋊C411yescharacteristic
101C23×C32D812yes—
102C23×C32SD1612yes—
103C23×C32C2×D411yescharacteristic
104C22×C3⋊D3—22no—
105C22×C3⋊D3—42no—
106C22×C3⋊D3—42no—
107C22×C3⋊D3—42no—
108C2×C32×C4—22no—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4C22⋊C411yescharacteristic
115C2×C32×C4C22⋊C411yescharacteristic
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118#638—44no—
119#638—42no—
120#638—42no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—42no—
123C4⋊(C3⋊D3)—42no—
124C4⋊(C3⋊D3)—42no—
125C2×C3×Dic3—42no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—42no—
128C3×C3⋊C8—42no—
129C2×#121—91no—
130C2×C22⋊C8—31no—
131#380—31no—
132#327—94no—
133C24×C3—21no—
134C24×C3D1211yescharacteristic
135C24×C3#6711yescharacteristic
136C23×D3—62no—
137C23×D3—61no—
138C23×D3—61no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—42no—
146C22×C3×C4—42no—
147C22×C3×C4—44no—
148C22×C3×C4—62no—
149C22×C3×C4C4×D311yescharacteristic
150C22×C3×C4C4×D311yescharacteristic
151C22×C3×C4C4×D311yescharacteristic
152C22×C3×C4C4×D311yescharacteristic
153C22×C3×C4D1211yescharacteristic
154C22×C3×C4D1211yescharacteristic
155C22×C3×C4D1211yescharacteristic
156C22×C3×C4#6711yescharacteristic
157C22×C3×C4#6711yescharacteristic
158C22×C3×C4#6711yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—64no—
162C2×#67—64no—
163C2×#67—62no—
164C2×#67—62no—
165C2×#67—62no—
166C2×#67—62no—
167C2×#67—124no—
168C2×#67—124no—
169C2×#67—122no—
170C2×#67—122no—
171C2×#67—122no—
172C2×#67—122no—
173C22×Dic3—22no—
174C22×Dic3—62no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C2×D12—32no—
178C2×D12—32no—
179C2×D12—62no—
180C2×D12—62no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—124no—
184C2×D12—122no—
185C2×D12—122no—
186C2×C3×C8—62no—
187C2×C3×C8—122no—
188C3×C4⋊C4—122no—
189C3×C22⋊C4—122no—
190#217—42no—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—64no—
193(C2×D3)⋊C4—62no—
194(C2×D3)⋊C4—62no—
195(C2×D3)⋊C4—62no—
196(C2×D3)⋊C4—62no—
197C4⋊Dic3—32no—
198C4⋊Dic3—32no—
199C4⋊Dic3—42no—
200C4⋊Dic3—62no—
201C4⋊Dic3—62no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C2×C3⋊C8—22no—
205C2×C3⋊C8—42no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—42no—
213C22×C32—42no—
214C22×C32#10212yes—
215C22×C32#10212yes—
216C22×C32C2×C22⋊C411yescharacteristic
217C22×C32C2×D811yescharacteristic
218C22×C32C2×SD1611yescharacteristic
219C2×C3⋊D3—42no—
220C2×C3⋊D3—42no—
221C2×C3⋊D3—42no—
222C2×C3⋊D3—84no—
223C32×C4—21no—
224C32×C4—21no—
225C32×C4—21no—
226C32×C4#9912yes—
227C3⋊Dic3—42no—
228C3×Dic3—82no—
229C22×D4—91no—
230C22×D4—181no—
231C23×C4D3211yescharacteristic
232C22×C8—61no—
233#121—92no—
234#121—92no—
235#121—181no—
236#121—181no—
237C2×C4⋊C4—61no—
238C2×C4⋊C4—91no—
239C2×C22⋊C4—61no—
240C2×C22⋊C4—181no—
241C22⋊C8—32no—
242C22⋊C8—61no—
243#95—32no—
244C23×C3—22no—
245C23×C3—22no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—21no—
249C23×C3—41no—
250C23×C3—41no—
251C23×C3—41no—
252C23×C3—41no—
253C23×C3—42no—
254C23×C3—42no—
255C23×C3#20412yes—
256C23×C3D2412yes—
257C23×C3(C2×D3)⋊C411yescharacteristic
258C23×C3(C2×D3)⋊C411yescharacteristic
259C23×C3(C2×D3)⋊C411yescharacteristic
260C23×C3(C2×D3)⋊C411yescharacteristic
261C23×C3#21312yes—
262C23×C3#21512yes—
263C23×C3C2×D1211yescharacteristic
264C23×C3C2×#6711yescharacteristic
265C22×D3—64no—
266C22×D3—62no—
267C22×D3—62no—
268C22×D3—124no—
269C22×D3—122no—
270C22×D3—122no—
271C22×D3—124no—
272C22×D3—124no—
273C22×D3—122no—
274C22×D3—122no—
275C22×D3—122no—
276C22×D3—122no—
277C2×C3×C4—24no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4—42no—
299C2×C3×C4—122no—
300C2×C3×C4—122no—
301C2×C3×C4—122no—
302C2×C3×C4(C2×D3)⋊C411yescharacteristic
303C2×C3×C4(C2×D3)⋊C411yescharacteristic
304C2×C3×C4(C2×D3)⋊C411yescharacteristic
305C2×C3×C4(C2×D3)⋊C411yescharacteristic
306C2×C3×C4C2×C4×D311yescharacteristic
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4C2×D1211yescharacteristic
309C2×C3×C4C2×#6711yescharacteristic
310#67—128no—
311#67—124no—
312#67—124no—
313#67—124no—
314#67—124no—
315#67—122no—
316#67—122no—
317#67—122no—
318#67—122no—
319C2×Dic3—42no—
320C2×Dic3—42no—
321C2×Dic3—42no—
322C2×Dic3—64no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—124no—
326C2×Dic3—122no—
327C2×Dic3—122no—
328D12—122no—
329D12—122no—
330D12—124no—
331D12—124no—
332D12—122no—
333D12—122no—
334C3×C8—122no—
335C3⋊C8—42no—
336C2×C32—22no—
337C2×C32—21no—
338C2×C32—22no—
339C2×C32—21no—
340C2×C32C2×#9911yescharacteristic
341C2×C32C2×#10211yescharacteristic
342C2×C32#42111yescharacteristic
343C3⋊D3—82no—
344C24—181no—
345C24#62611yescharacteristic
346C2×D4—92no—
347C2×D4—182no—
348C2×D4—182no—
349C2×D4—181no—
350C2×D4—362no—
351C2×D4—362no—
352C2×D4—362no—
353C22×C4—42no—
354C22×C4—62no—
355C22×C4—181no—
356C22×C4#62411yescharacteristic
357C22×C4#62411yescharacteristic
358C22×C4#62611yescharacteristic
359C22×C4#62611yescharacteristic
360C22×C4#62611yescharacteristic
361C22×C4C2×D3211yescharacteristic
362C2×C8—62no—
363C2×C8—122no—
364C4⋊C4—92no—
365C4⋊C4—122no—
366C4⋊C4—181no—
367C22⋊C4—122no—
368C22⋊C4—182no—
369C22⋊C4—182no—
370C22×C3—22no—
371C22×C3—22no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—42no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—44no—
398C22×C3—44no—
399C22×C3#80912yes—
400C22×C3#80912yes—
401C22×C3#82112yes—
402C22×C3#82112yes—
403C22×C3C2×#20411yescharacteristic
404C22×C3C2×D2411yescharacteristic
405C22×C3C2×(C2×D3)⋊C411yescharacteristic
406C22×C3C2×(C2×D3)⋊C411yescharacteristic
407C22×C3C2×#21311yescharacteristic
408C22×C3C2×#21511yescharacteristic
409C2×D3—124no—
410C2×D3—124no—
411C2×D3—124no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—122no—
415C2×D3—122no—
416C2×D3—122no—
417C2×D3—122no—
418C2×D3—248no—
419C2×D3—244no—
420C2×D3—244no—
421C3×C4—22no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—41no—
430C3×C4—41no—
431C3×C4—242no—
432C3×C4#80612yes—
433C3×C4#80612yes—
434Dic3—82no—
435Dic3—124no—
436Dic3—122no—
437Dic3—122no—
438C32#151911yescharacteristic, complemented, Sylow
439C23—41no—
440C23—41no—
441C23—182no—
442C23—362no—
443C23—362no—
444C23—362no—
445C23#371412yes—
446C23#371712yes—
447C23#372211yescharacteristic
448C23#372211yescharacteristic
449C23C2×#62611yescharacteristic
450D4—362no—
451D4—364no—
452D4—362no—
453D4—362no—
454D4—362no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—122no—
462C2×C4—122no—
463C2×C4—122no—
464C2×C4—182no—
465C2×C4—362no—
466C2×C4#372211yescharacteristic
467C2×C4#372211yescharacteristic
468C2×C4C2×#62411yescharacteristic
469C2×C4C2×#62611yescharacteristic
470C8—122no—
471C2×C3—24no—
472C2×C3—21no—
473C2×C3—22no—
474C2×C3—22no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—22no—
478C2×C3—22no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—41no—
484C2×C3—42no—
485C2×C3—41no—
486C2×C3C2×#80611yescharacteristic
487C2×C3C2×#80611yescharacteristic
488C2×C3C2×#80911yescharacteristic
489C2×C3#500511yescharacteristic
490C2×C3C2×#82111yescharacteristic
491C2×C3#513911yescharacteristic
492D3—244no—
493D3—242no—
494D3—242no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—42no—
502C22—42no—
503C22—362no—
504C22—362no—
505C22—362no—
506C22—724no—
507C22#6356412yes—
508C22#6356412yes—
509C22C2×#371411yescharacteristic
510C22C2×#371711yescharacteristic
511C22C2×#372211yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—242no—
516C4—362no—
517C4#6358112yes—
518C3—21no—
519C3#6950911yescharacteristic, complemented
520C3#6994411yescharacteristic, complemented
521C2—21no—
522C2—22no—
523C2—22no—
524C2—21no—
525C2—722no—
526C2C2×#6356411yescharacteristic
527C2#1059111311yescharacteristic
528C2C2×#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#1519
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×#5212C2semidirect
3. C2×C3×#830C2semidirect
4. #10589151C2semidirect
9. C22×C4⋊(C3⋊D3)C4semidirect
12. #64139C4semidirect
15. C2×C4⋊(C3⋊Dic3)C4semidirect
19. C3×C3⋊#95C22semidirect
21. C3×#830C22semidirect
27. #5212D3semidirect
28. C2×#830D3semidirect
94. C3⋊#95C2×D3semidirect
96. #830C2×D3semidirect
438. C32#1519semidirect
519. C3#69509semidirect
520. C3#69944semidirect

Maximal subgroups

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

subgroupindex
C2×#641392
C3×#52122
C2×C3×#8302
#105891512
#699443
#695093