Finite Group Databasebeta

← #10594064

Subgroups — #10594064

Order 576.

631 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3804C211yesmaximal, characteristic, complemented
2C2×#3799C211yesmaximal, characteristic, complemented
3#64093C211yesmaximal, characteristic, complemented
4C3×#883C211yesmaximal, characteristic, complemented
5C3×#878C211yesmaximal, characteristic, complemented
6#63975C211yesmaximal, characteristic, complemented
7#63971C211yesmaximal, characteristic, complemented
8#63952C211yesmaximal, characteristic, complemented
9#63900C211yesmaximal, characteristic, complemented
10#63897C211yesmaximal, characteristic, complemented
11#63895C211yesmaximal, characteristic, complemented
12#63890C211yesmaximal, characteristic, complemented
13#63881C211yesmaximal, characteristic, complemented
14D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#63839C211yesmaximal, characteristic, complemented
16#5655—31nomaximal
17#5631—31nomaximal
18C2×#638C2211yescharacteristic
19C2×#638C2211yescharacteristic
20C2×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C4×C3⋊D3C2211yescharacteristic
22C2×C3×#67C2211yescharacteristic
23C22×C3×Dic3C2211yescharacteristic
24C2×C3×C4×D3C2211yescharacteristic
25C2×C3×Dic6C2211yescharacteristic
26C2×#627C2211yescharacteristic
27C2×#626C2211yescharacteristic
28C2×#626C2211yescharacteristic
29C2×#624C2211yescharacteristic
30C2×#624C2211yescharacteristic
31C2×#624C2211yescharacteristic
32#3804—24no—
33C2×D3×Dic3C2211yescharacteristic
34C2×D3×Dic3C2211yescharacteristic
35#3799—24no—
36C32×C22⋊C4C2211yescharacteristic
37#3752C2211yescharacteristic
38#3750C2211yescharacteristic
39C3×#217C2211yescharacteristic
40C3×#217C2211yescharacteristic
41C3×(C2×D3)⋊C4C2211yescharacteristic
42C3×C4⋊Dic3C2211yescharacteristic
43C3×C4⋊Dic3C2211yescharacteristic
44C3×Dic3⋊C4C2211yescharacteristic
45C3×Dic3⋊C4C2211yescharacteristic
46C3×Dic3⋊C4C2211yescharacteristic
47#3724C2211yescharacteristic
48#3724C2211yescharacteristic
49Dic3⋊Dic3C2211yescharacteristic
50Dic3⋊Dic3C2211yescharacteristic
51#3722C2211yescharacteristic
52#3722C2211yescharacteristic
53#3722C2211yescharacteristic
54Dic32C2211yescharacteristic
55C2×#239—31no—
56C2×#237—31no—
57C2×#235—31no—
58C2×#235—31no—
59C3×#123—31no—
60C3×C22⋊Q8—31no—
61#944—31no—
62#939—31no—
63C4×#67—31no—
64C2×Dic3⋊C4—31no—
65#897—31no—
66#896—31no—
67#894—31no—
68#894—31no—
69#894—31no—
70#893—31no—
71D3×C4⋊C4—31no—
72D3×C4⋊C4—31no—
73D3×C4⋊C4—31no—
74#888—31no—
75#886—31no—
76#884—31no—
77#884—31no—
78#884—31no—
79#884—61no—
80#883—31no—
81#883—31no—
82#883D311yescharacteristic, complemented
83#67⋊C4—31no—
84#67⋊C4—31no—
85#878D311yescharacteristic, complemented
86C23×C32C2311yescharacteristic
87C22×C3⋊D3C2311yescharacteristic
88C22×C3⋊D3C2311yescharacteristic
89C22×C3×D3C2311yescharacteristic
90C2×C32×C4C2311yescharacteristic
91C2×C32×C4C2311yescharacteristic
92#638—22no—
93#638—22no—
94C2×C3⋊Dic3C2311yescharacteristic
95C2×C3⋊Dic3C2311yescharacteristic
96C4⋊(C3⋊D3)—22no—
97C4×C3⋊D3—22no—
98C3×#67—22no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3C2311yescharacteristic
101C2×C3×Dic3C2311yescharacteristic
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C2×C3×Dic3C2311yescharacteristic
107C3×C4×D3—22no—
108C3×Dic6—22no—
109#627—22no—
110#626—22no—
111#626D414yescomplemented
112#624—22no—
113#624—22no—
114#624—22no—
115D3×Dic3—22no—
116D3×Dic3—22no—
117#547—91noSylow
118C2×C3×Q8—31no—
119C2×C3×D4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—31no—
122C2×#67—31no—
123C2×#67—31no—
124C2×#67—31no—
125C2×#67—31no—
126C2×#67—31no—
127C2×#67—31no—
128C2×#67—61no—
129C2×#67—61no—
130C2×#67C2×D311yescharacteristic
131C22×Dic3—31no—
132C22×Dic3—31no—
133C22×Dic3C2×D311yescharacteristic
134#239—64no—
135#237—64no—
136#235—64no—
137#235—64no—
138C2×D12—31no—
139C2×D12—31no—
140C2×D12—31no—
141C2×D12—31no—
142C2×D12—61no—
143C2×C4×D3—31no—
144C2×C4×D3—31no—
145C2×C4×D3—31no—
146C2×C4×D3—31no—
147C2×C4×D3—31no—
148C2×C4×D3—31no—
149C2×C4×D3—31no—
150C2×C4×D3—31no—
151C2×C4×D3—31no—
152C2×C4×D3—31no—
153C2×C4×D3—61no—
154C2×C4×D3C2×D311yescharacteristic
155C2×Dic6—31no—
156C2×Dic6—31no—
157C2×Dic6C2×D311yescharacteristic
158C3×C4⋊C4—31no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—31no—
162C3×C4⋊C4—31no—
163C3×C22⋊C4—21no—
164C3×C22⋊C4—31no—
165C3×C22⋊C4—31no—
166C3×C22⋊C4—31no—
167C3×C22⋊C4C2×D311yescharacteristic
168C3×C22⋊C4C2×D311yescharacteristic
169#217C2×D311yescharacteristic
170#217C2×D311yescharacteristic
171(C2×D3)⋊C4—31no—
172(C2×D3)⋊C4—31no—
173(C2×D3)⋊C4—31no—
174(C2×D3)⋊C4—31no—
175(C2×D3)⋊C4—31no—
176(C2×D3)⋊C4—31no—
177(C2×D3)⋊C4—31no—
178(C2×D3)⋊C4—31no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4C2×D311yescharacteristic
181C4⋊Dic3—31no—
182C4⋊Dic3—31no—
183C4⋊Dic3C2×D311yescharacteristic
184C4⋊Dic3C2×D311yescharacteristic
185Dic3⋊C4—31no—
186Dic3⋊C4—31no—
187Dic3⋊C4—31no—
188Dic3⋊C4—31no—
189Dic3⋊C4—31no—
190Dic3⋊C4—31no—
191Dic3⋊C4—31no—
192Dic3⋊C4—31no—
193Dic3⋊C4—61no—
194Dic3⋊C4C2×D311yescharacteristic
195Dic3⋊C4C2×D311yescharacteristic
196Dic3⋊C4C2×D311yescharacteristic
197C4×Dic3—31no—
198C4×Dic3—31no—
199C22×C32—21no—
200C22×C32—21no—
201C22×C32—21no—
202C22×C32C2411yescharacteristic
203C2×C3⋊D3—21no—
204C2×C3⋊D3—21no—
205C2×C3⋊D3—21no—
206C2×C3⋊D3—21no—
207C2×C3⋊D3—21no—
208C2×C3⋊D3C2×D412yes—
209C2×C3×D3—21no—
210C2×C3×D3—21no—
211C2×C3×D3C2×D412yes—
212C32×C4—21no—
213C32×C4—21no—
214C3⋊Dic3—21no—
215C3⋊Dic3#4112yescomplemented
216C3×Dic3—21no—
217C3×Dic3—21no—
218C3×Dic3—21no—
219C3×Dic3—21no—
220C3×Dic3—21no—
221C3×Dic3—21no—
222C3×Dic3C2×D412yes—
223C2×#41—91no—
224C2×#41—91no—
225C4⋊Q8—91no—
226#123—31no—
227#123—91no—
228#123—91no—
229#123—91no—
230C22⋊Q8—31no—
231C22⋊Q8—91no—
232#121—91no—
233#121—91no—
234C4×D4—91no—
235C4×D4—91no—
236C2×C4⋊C4—91no—
237C2×C4⋊C4—91no—
238C23×C3—21no—
239C23×C3—31no—
240C23×C3C22×D311yescharacteristic
241C23×C3C22×D311yescharacteristic
242C22×D3—31no—
243C22×D3—31no—
244C22×D3—31no—
245C22×D3—31no—
246C22×D3—61no—
247C22×D3—61no—
248C22×D3C22×D311yescharacteristic
249C3×Q8—62no—
250C3×D4—62no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—31no—
254C2×C3×C4—31no—
255C2×C3×C4—31no—
256C2×C3×C4—31no—
257C2×C3×C4—31no—
258C2×C3×C4—31no—
259C2×C3×C4—31no—
260C2×C3×C4—62no—
261C2×C3×C4—62no—
262C2×C3×C4C22×D311yescharacteristic
263C2×C3×C4C22×D311yescharacteristic
264C2×C3×C4C22×D311yescharacteristic
265C2×C3×C4C22×D311yescharacteristic
266#67—22no—
267#67—34no—
268#67—62no—
269#67—62no—
270#67—62no—
271#67—62no—
272#67—62no—
273#67—122no—
274#67—122no—
275C2×Dic3—22no—
276C2×Dic3—31no—
277C2×Dic3—31no—
278C2×Dic3—31no—
279C2×Dic3—31no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3C22×D311yescharacteristic
285C2×Dic3C22×D311yescharacteristic
286C2×Dic3C22×D311yescharacteristic
287C2×Dic3C22×D311yescharacteristic
288C2×Dic3C22×D311yescharacteristic
289C2×Dic3C22×D311yescharacteristic
290C2×Dic3C22×D311yescharacteristic
291D12—34no—
292D12—62no—
293D12—62no—
294D12—62no—
295D12—122no—
296C4×D3—22no—
297C4×D3—62no—
298C4×D3—62no—
299C4×D3—62no—
300C4×D3—62no—
301C4×D3—62no—
302C4×D3—62no—
303C4×D3—62no—
304C4×D3—62no—
305C4×D3—62no—
306C4×D3—62no—
307C4×D3—122no—
308Dic6—22no—
309Dic6—62no—
310Dic6—62no—
311C2×C32—41no—
312C2×C32C22×D411yescharacteristic
313C2×C32C2×#4111yescharacteristic
314C2×C322−1+411yescharacteristic
315C3⋊D3—22no—
316C3⋊D3—41no—
317C3×D3—22no—
318#41—184no—
319#41—184no—
320C2×Q8—31no—
321C2×Q8—91no—
322C2×D4—31no—
323C2×D4—91no—
324C2×D4—91no—
325C2×D4—91no—
326C2×D4—91no—
327C2×D4—91no—
328C22×C4—31no—
329C22×C4—31no—
330C22×C4—91no—
331C22×C4—91no—
332C22×C4—91no—
333C22×C4—91no—
334C22×C4—91no—
335C22×C4—91no—
336C4⋊C4—31no—
337C4⋊C4—31no—
338C4⋊C4—31no—
339C4⋊C4—31no—
340C4⋊C4—31no—
341C4⋊C4—91no—
342C4⋊C4—91no—
343C4⋊C4—91no—
344C4⋊C4—91no—
345C4⋊C4—91no—
346C22⋊C4—31no—
347C22⋊C4—31no—
348C22⋊C4—31no—
349C22⋊C4—91no—
350C22⋊C4—91no—
351C22⋊C4—91no—
352C22⋊C4—91no—
353C22⋊C4D3211yescharacteristic
354C42—91no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—32no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—61no—
367C22×C3—61no—
368C22×C3C23×D311yescharacteristic
369C22×C3C23×D311yescharacteristic
370C2×D3—21no—
371C2×D3—21no—
372C2×D3—32no—
373C2×D3—32no—
374C2×D3—62no—
375C2×D3—61no—
376C2×D3—61no—
377C2×D3—61no—
378C2×D3—61no—
379C2×D3—61no—
380C2×D3—61no—
381C2×D3—61no—
382C2×D3—61no—
383C2×D3—61no—
384C2×D3—61no—
385C2×D3—121no—
386C2×D3—121no—
387C2×D3—121no—
388C2×D3—121no—
389C2×D3—121no—
390C2×D3D3×D412yes—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—32no—
396C3×C4—41no—
397C3×C4—41no—
398C3×C4—61no—
399C3×C4—61no—
400C3×C4—61no—
401C3×C4—61no—
402C3×C4—61no—
403C3×C4—61no—
404Dic3—21no—
405Dic3—21no—
406Dic3—21no—
407Dic3—21no—
408Dic3—21no—
409Dic3—21no—
410Dic3—32no—
411Dic3—32no—
412Dic3—62no—
413Dic3—61no—
414Dic3—61no—
415Dic3—121no—
416Dic3D3×D412yes—
417C32#54711yescharacteristic, complemented, Sylow
418C23—31no—
419C23—91no—
420C23—91no—
421C23C2×D3211yescharacteristic
422Q8—62no—
423Q8—182no—
424D4—62no—
425D4—94no—
426D4—182no—
427D4—182no—
428D4—182no—
429D4—182no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—31no—
433C2×C4—31no—
434C2×C4—31no—
435C2×C4—31no—
436C2×C4—31no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—91no—
440C2×C4—91no—
441C2×C4—182no—
442C2×C4—182no—
443C2×C4—182no—
444C2×C4—182no—
445C2×C4—182no—
446C2×C4—182no—
447C2×C4C2×D3211yescharacteristic
448C2×C4C2×D3211yescharacteristic
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—41no—
453C2×C3—41no—
454C2×C3—62no—
455C2×C3—81no—
456C2×C3C2×D3×D411yescharacteristic
457C2×C3C2×D3×D411yescharacteristic
458C2×C3#100711yescharacteristic
459C2×C3D3×#4111yescharacteristic
460C2×C3D3×#4111yescharacteristic
461C2×C3#101011yescharacteristic
462D3—22no—
463D3—62no—
464D3—62no—
465D3—122no—
466D3—121no—
467D3—121no—
468D3—241no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—32no—
473C22—61no—
474C22—61no—
475C22—92no—
476C22—181no—
477C22—181no—
478C22—181no—
479C22—181no—
480C22—181no—
481C22C22×D3211yescharacteristic
482C4—21no—
483C4—21no—
484C4—32no—
485C4—61no—
486C4—61no—
487C4—61no—
488C4—61no—
489C4—61no—
490C4—61no—
491C4—92no—
492C4—181no—
493C3—21no—
494C3#563111yescharacteristic, complemented
495C3#565511yescharacteristic, complemented
496C2—41no—
497C2—62no—
498C2—182no—
499C2—361no—
500C2#6429711yescharacteristic
501C2D32×D411yescharacteristic
502C2#6431211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
hypercenterC22⋊C4D32
hypocenterC32#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#3804C2semidirect
2. C2×#3799C2semidirect
3. #64093C2semidirect
4. C3×#883C2semidirect
5. C3×#878C2semidirect
6. #63975C2semidirect
7. #63971C2semidirect
8. #63952C2semidirect
9. #63900C2semidirect
10. #63897C2semidirect
11. #63895C2semidirect
12. #63890C2semidirect
13. #63881C2semidirect
14. D3×Dic3⋊C4C2semidirect
15. #63839C2semidirect
82. #883D3semidirect
85. #878D3semidirect
111. #626D4semidirect
215. C3⋊Dic3#41semidirect
417. C32#547semidirect
494. C3#5631semidirect
495. C3#5655semidirect

Maximal subgroups

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

subgroupindex
C2×#38042
C2×#37992
#640932
C3×#8832
C3×#8782
#639752
#639712
#639522
#639002
#638972
#638952
#638902
#638812
D3×Dic3⋊C42
#638392
#56553
#56313